MULTI-OBJECTIVE OPTIMIZATION APPROACHES TO PLANT BREEDING By Robert Zachary Shrote A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Plant Breeding, Genetics and Biotechnology - Crop and Soil Sciences – Doctor of Philosophy 2024 ABSTRACT Most plant breeding programs must contend with achieving multiple breeding objectives while subject to time and resource constraints. Breeding objectives may include, but are not limited to, yield, standability, adaptation to mechanical harvesting, resistance to abiotic and biotic stressors, flavor and texture quality attributes, environmental adaptation, and genetic diversity. Many times, breeding objectives are conflicting in nature and a balance must be achieved between objectives. Both single- and multi-objective optimization techniques can be used to assist breeders in identifying trade-offs between conflicting objectives and determine a single, optimal solution which satisfies the goals of a breeding program. In this dissertation, we address and tackle several of the challenges faced when balancing multiple breeding objectives. Most of our efforts in addressing these challenges revolve around selection or mate-pairing methodologies. First, we begin by reviewing many of the selection strategies which have been proposed over the years, offer insights into the mathematical nature of several of these selection strategies, and observe attributes of successful selection strategies. Next, we introduce the software package PyBrOpS, a Python package capable of performing single- and multi-objective optimizations and single- and multi-trait simulations for breeding programs. PyBrOpS is unique among other simulation software packages in that it emphasizes multi-objective optimizations for multi-trait breeding scenarios and allows breeders to identify and visualize optimal trade-offs. Next, we introduce two new multi-objective selection strategies that seek to balance genetic gain and genetic diversity. While not the best tested selection strategies, we find that these two new selection strategies are performant, robust, and offer high long-term genetic gain while maintaining a high level of genetic diversity. Next, we introduce two new, multi-trait selection strategies which are customizable variations of marker effect upweighting-based selection strategies. One of these selection strategies dynamically adjusts its upweighting parameter based on the time to a final generation. We find that these upweighting-based selection strategies offer improvements in genetic gain and genetic diversity in ideal scenarios but fail in realistic scenarios unless a low degree of upweighting is specified. Finally, we empirically test the ability to predict the mean and variance of progenies from a diverse set of crosses. Predicting progeny mean and variance is important because it can be used to inform selections and mate-pairings. We developed genomic prediction models using information from a diversity panel, crossed several members of the diversity panel together to create progeny families, and compared predictions of progeny mean and variance using our genomic prediction models to what we observed. We were successful in predicting progeny mean, but largely unable to predict progeny variance. To my family father, mother, brother, sister, grandmother, and bothers and sisters in Christ. Without your support, I could not have accomplished this. iv ACKNOWLEDGEMENTS First, I would like to acknowledge and thank my father, Curtis K. Shrote. Throughout the development of PyBrOpS, he was a constant source of advice and wisdom regarding software engineering. I would also like to thank him for reminding me that incremental improvements are superior to monumental improvements, especially from a product development perspective. There were times during my research when I was trying to advance science in large leaps, when I should have focused on advancing it in small steps. Second, I would like to acknowledge and thank my advisor, Dr. Addie M. Thompson. She was very gracious in allowing me to pursue my own research projects. Without the freedom she gave me, my PhD research and dissertation would be, in my opinion, less exciting and less challenging. I also want to thank her for all the advice she has given me over the past several years, which helped refine and focus my research. Third, I would like to acknowledge and thank Linsey Newton, our lab technician. Thank you for your tireless efforts to manage lab field activities and experiments. Without your efforts, I would not have any field data. Fourth, I would like to thank Dr. Gustavo de los Campos, one of my committee members, for assisting me in implementing RR-BLUP from scratch. His sample code assisted me in implementing the EMMA and Gauss-Seidel methods used in PyBrOpS and probably saved me a couple of weeks of grief trying to figure out the errors in my own implementations. Fifth, I would like to thank Dr. Wolfgang Banzhaf, another one of my committee members, for his class on evolutionary algorithms advice on multi-objective optimization. Sixth, I would like to thank my other two committee members, Drs. Francisco Gomez and Eric Olson, for their valuable contributions in committee meetings. v Finally, I would like to thank Dr. Shawn Kaeppler at the University of Wisconsin- Madison for allowing me to use four of his doubled haploid families to test my progeny mean and variance hypotheses. Without those families, I probably would not have had enough results for a fifth chapter to this dissertation. vi TABLE OF CONTENTS CHAPTER 1: BREEDING SELECTION STRATEGIES & NUMERICAL OPTIMIZATION .... 1 1. Introduction ..................................................................................................................... 1 2. Terminology .................................................................................................................... 8 3. Mathematical notation .................................................................................................. 12 4. Breeding strategies ........................................................................................................ 18 5. Selection strategy insights and proposed new areas of research ................................... 66 6. Conclusion .................................................................................................................... 79 CHAPTER 2: PYBROPS: A PYTHON PACKAGE FOR BREEDING PROGRAM SIMULATION AND OPTIMIZATION FOR MULTI-OBJECTIVE BREEDING ..................... 82 1. Introduction ................................................................................................................... 82 CHAPTER 3: TOWARDS MULTI-OBJECTIVE GENOMIC SELECTION AND GENOMIC MATING ....................................................................................................................................... 83 1. Introduction ................................................................................................................... 83 2. Methods......................................................................................................................... 94 3. Results ......................................................................................................................... 108 4. Discussion ................................................................................................................... 135 5. Conclusion .................................................................................................................. 145 CHAPTER 4: TOWARDS THE DEVELOPMENT OF MULTI-OBJECTIVE, TIME- COGNIZANT SELECTION STRATEGIES .............................................................................. 147 1. Introduction ................................................................................................................. 147 2. Methods....................................................................................................................... 154 3. Results ......................................................................................................................... 166 4. Discussion ................................................................................................................... 221 5. Conclusion .................................................................................................................. 234 CHAPTER 5: PREDICTION OF PROGENY MEAN AND VARIANCE FROM PARENTAL INFORMATION ......................................................................................................................... 236 1. Introduction ................................................................................................................. 236 2. Methods....................................................................................................................... 240 3. Results ......................................................................................................................... 258 4. Discussion ................................................................................................................... 269 5. Conclusion .................................................................................................................. 272 BIBLIOGRAPHY ....................................................................................................................... 274 APPENDIX A: SUPPLEMENTAL FIGURES AND TABLES FOR CHAPTER 3: TOWARDS MULTI-OBJECTIVE GENOMIC SELECTION AND GENOMIC MATING ......................... 284 APPENDIX B: SUPPLEMENTAL FIGURES AND TABLES FOR CHAPTER 4: TOWARDS THE DEVELOPMENT OF MULTI-OBJECTIVE, TIME-COGNIZANT SELECTION STRATEGIES ............................................................................................................................. 353 vii CHAPTER 1: BREEDING SELECTION STRATEGIES & NUMERICAL OPTIMIZATION 1. Introduction 1.1. Importance of breeding optimization In plant and animal breeding, selection is the primary means by which a breeder may improve a plant or animal species (Falconer & Mackay, 1996). The selection strategy chosen by a breeder has long lasting consequences for a breeding program and largely determines the short- and long-term success of the program. Fundamentally, the task of selection is an optimization problem which is stated in this manner: given a set of individuals or mating crosses, select the best subset with which to create the next generation. Though simply stated, defining what is deemed as “best” and identifying a “best” solution is neither straightforward nor easy in many instances. Fortunately, optimization is ubiquitous across scientific disciplines and a wealth of knowledge exists regarding how to construct optimization problems and efficiently identify solutions. Much can be learned from the optimization community, and indeed, many authors of novel selection strategies have utilized this literature to help them formulate their selection techniques as mathematical optimization problems and optimize them using established techniques (Akdemir et al., 2019; Akdemir & Sánchez, 2016; Allier, Lehermeier, et al., 2019; Amini et al., 2022; Goiffon et al., 2017; Hunter & McClosky, 2016; Moeinizade et al., 2019, 2020; Zhang & Wang, 2022). Due to the importance of selection, selection methodology continues to be an area of active research. The purpose of this chapter is to review notable selection strategies from a numerical optimization lens, offer insights on selection strategies, and propose new areas of research for the breeding community. 1 1.2. Numerical optimization and its parallels in breeding selection strategies 1.2.1. Overview of numerical optimization In any numerical optimization, we must first identify an objective, a quantitative measure of the desirability of a proposed solution (Nocedal & Wright, 2006). An objective depends on a set of decision variables which represent inputs used to evaluate a proposed solution. Our goal is to identify a set of decision variable values which minimize (or maximize) our objective. Often there are constraints associated with a numerical optimization problem which limit the range of values that a solution may take. Points that satisfy all constraints are called feasible and points that do not satisfy all constraints are called infeasible (Nocedal & Wright, 2006). The process of identifying an objective, its associated decision variables, and constraints is known as modeling (Nocedal & Wright, 2006). Without loss of generality, a single-objective optimization problem can be expressed as (Coello Coello et al., 2007; Nocedal & Wright, 2006): Subject to constraints: min 𝐱 𝑓(𝐱) 𝑔𝑟(𝐱) ≤ 𝑏𝑟, 𝑟 = 1,2, … , 𝑅 ℎ𝑠(𝐱) = 𝑐𝑠, 𝑠 = 1,2, … , 𝑆 𝐱 ∈ 𝒳, where 𝐱 is a vector of decision variables, 𝑓(⋅) is a scalar objective function that we seek to minimize, 𝑔𝑟(⋅) is the 𝑟th scalar inequality constraint function with 𝑏𝑟 as its associated limit, ℎ𝑠(⋅) is the 𝑠th scalar equality constraint function with 𝑐𝑠 as its associated limit, 𝑅 is the number of inequality constraints, 𝑆 is the number of equality constraints, and 𝒳 is the search space for the decision vector. Although the above generalized single-objective optimization problem is expressed as a task in minimization, optimization problems may also be expressed as a task in 2 maximization. Indeed, by negating an objective function, a minimization problem may be converted into a maximization problem and vice versa: min 𝐱 𝑓(𝐱) ≡ max 𝐱 −𝑓(𝐱). Numerical optimization problems may be classified into different categories based on the nature of their decision variables, objective function, and constraints. Problems where all decision variables are real numbers are considered continuous optimization problems, while problems where at least one decision variable represents an integer, binary value, or permutation are considered discrete optimization problems (Nocedal & Wright, 2006). Continuous optimization problems are generally easier to solve because the smoothness of the objective function and associated constraints make it easier to infer the behavior of points surrounding an arbitrary 𝐱 value. Optimization problems may also be classified by the convexity or non- convexity of their objective and constraint functions. A function 𝑓(⋅) is called convex if for any two points 𝐱𝟏 and 𝐱𝟐 within its domain, a line segment connecting two points 𝑓(𝐱𝟏) and 𝑓(𝐱𝟐) along the graph lies entirely above the graph of the function: 𝑓(𝛼𝐱𝟏 + (1 − 𝛼)𝐱𝟐) ≤ 𝛼𝑓(𝐱𝟏) + (1 − 𝛼)𝑓(𝐱𝟐), ∀𝛼 ∈ [0,1] An optimization problem is called convex if its objective is convex, all its inequality constraints are convex, and its equality constraints are linear (Nocedal & Wright, 2006). By this definition, all discrete optimization problems are non-convex. Finally, an optimization problem may be classified by its constraints. If an optimization problem does not have any constraints, then it is an unconstrained optimization problem. If an optimization problem has constraints, then it is considered a constrained optimization problem. After defining a numerical optimization problem, an optimization algorithm can be used to identify a solution. Optimization algorithms seek to identify a locally optimal solution and ideally a globally optimal solution. A solution is considered locally optimal if it is the best 3 solution in its search space neighborhood and considered globally optimal if it is the best solution in the entire search space. The convexity of a numerical optimization problem can determine the ease with which the globally optimal solution is identified. For instance, convex optimization problems have local solutions which are also global solutions (Nocedal & Wright, 2006). Following from the No Free Lunch (NFL) theorem (Wolpert & Macready, 1997), there is no best optimization algorithm which can be applied to all problem types. To efficiently solve an optimization problem, we should examine the type of problem under consideration and apply an algorithm specialized for the problem type. 1.2.2. Numerical optimization parallels in breeding In breeding, our formulation of a selection strategy closely mirrors that of a numerical optimization problem. Our objective corresponds to our breeding goals and usually relates to biological traits such as yield, biotic stress tolerance, abiotic stress tolerance, quality attributes, or genetic diversity (Bernardo, 2020a; Fehr, 1991). We seek to maximize these biological traits for human benefit. Our decision variables may represent but are not limited to parent and cross selections (Akdemir & Sánchez, 2016; Allier, Lehermeier, et al., 2019), and parental and cross resource allocations (Hunter & McClosky, 2016; Meuwissen, 1997). Breeding constraints may involve the same aforementioned biological traits (Moeinizade et al., 2020), but commonly, they involve genetic diversity (Akdemir et al., 2019; Akdemir & Sánchez, 2016; Allier, Lehermeier, et al., 2019; Meuwissen, 1997), monetary cost (Han et al., 2021; Xu et al., 2011), resource utilization (Hunter & McClosky, 2016), and time considerations (Liu et al., 2015; Moeinizade et al., 2019, 2020; Zhang & Wang, 2022). Additionally, there may be cross restrictions that reflect sexual incompatibilities between breeding individuals. Finally, the modeling of an optimization problem corresponds to the actual selection strategy employed by a breeding program. This may 4 be a strictly analytical selection methodology, but often breeder intuition is incorporated into the process. Analytical selection methodologies have changed dramatically. In prior decades, analytical selection methodologies were restricted to computationally tractable phenotypic selection, index selection, and pedigree-based (Piepho et al., 2008) methods. In recent decades, the invention of the polymerase chain reaction (Mullis et al., 1986), high-throughput genotyping methods (Singh & Singh, 2015) and improvements in computing power (Bernardo, 2020b) have facilitated the development of numerous novel selection strategies which can incorporate observed genetic information into selection decisions. These more recent selection strategies include marker-assisted selection (MAS) (Lande & Thompson, 1990), marker-assisted introgression (Hospital & Charcosset, 1997), marker-assisted recurrent selection (Bernardo & Charcosset, 2006), genomic selection (Meuwissen et al., 2001), and genomic mating (Akdemir & Sánchez, 2016). Broadly speaking, selection methodology has been improved by using genotypic information. 1.3. Special cases of and extensions to numerical optimization 1.3.1. Linear problems with linear constraints (LPLC) One subset of general single-objective optimization problems are linear problems with linear constraints (LPLC). LPLC problems have the general form: Subject to constraints: 𝐟′𝐱 min 𝐱 ′ 𝐱 ≤ 𝑏𝑟, 𝑟 = 1,2, … , 𝑅 𝐠𝐫 ′ 𝐱 = 𝑐𝑠, 𝑠 = 1,2, … , 𝑆 𝐡𝐬 𝐱 ∈ 𝒳 5 As seen above, these problems have linear objective functions with linear inequality and equality constraints. This class of problems is particularly nice when the search space is continuous. If the search space is continuous, then the problem is a linear programming (LP) problem. LP problems are convex and can be solved using well developed, specialized algorithms such as the simplex method (Dantzig, 1963) and various interior point methods (Potra & Wright, 2000). 1.3.2. Linear problems with quadratic constraints (LPQC) Another subset of single-objective optimization problems are linear problems with quadratic constraints (LPQC). LPQC problems have the general form: Subject to constraints: 𝐟′𝐱 min 𝐱 𝐱′𝐆𝐫𝐱 + 𝐠𝐫 ′ 𝐱 ≤ 𝑏𝑟, 𝑟 = 1,2, … , 𝑅 𝐱′𝐇𝐬𝐱 + 𝐡𝐬 ′ 𝐱 = 𝑐𝑠, 𝑠 = 1,2, … , 𝑆 𝐱 ∈ 𝒳 As defined above, LPQC problems have linear objective functions with at least one quadratic inequality or equality constraint. Like LPLC problems, if the search space for an LPQC problem is continuous, then the problem is a quadratic programming (QP) problem. QP problems are also convex and can be solved using established algorithms such as various interior point methods (Potra & Wright, 2000). 1.3.3. Multi-Objective Optimization Multi-objective optimization is an extension of single-objective optimization. The mathematical formulation for a multi-objective optimization problem is like that of a single- objective optimization problem and, without loss of generality, is expressed as (Coello Coello et al., 2007; Deb, 2001): 6 Subject to constraints: min 𝐱 𝑓𝑞(𝐱) , 𝑞 = 1,2, … , 𝑄 𝑔𝑟(𝐱) ≤ 𝑏𝑟, 𝑟 = 1,2, … , 𝑅 ℎ𝑠(𝐱) = 𝑐𝑠, 𝑠 = 1,2, … , 𝑆 𝐱 ∈ 𝒳, where 𝐱 is a vector of decision variables, 𝑓𝑞(⋅) is the 𝑞th scalar objective function that we seek to minimize, 𝑔𝑟(⋅) is the 𝑟th inequality constraint function with 𝑏𝑟 as its associated limit, ℎ𝑠(⋅) is the 𝑠th equality constraint function with 𝑐𝑠 as its associated limit, 𝑄 is the number of objectives, 𝑅 is the number of inequality constraints, 𝑆 is the number of equality constraints, and 𝒳 is the search space of the decision vector. In multi-objective optimization, our objective functions are often competing in nature and there exists a set of tradeoffs along a Pareto frontier. We seek to identify a set of solutions that represent decision tradeoffs along this Pareto frontier for an arbitrary preference of objectives. This set of solutions is non-dominated, meaning that for each pair of solutions one solution is not objectively better in all objectives. 1.4. Outline of this chapter As mentioned at the beginning, the purpose of this chapter is to review notable selection strategies from a numerical optimization lens, offer insights on selection strategies, and propose new areas of research for the breeding community. This chapter consists of four parts. First, we will define several key terminologies which we have found helpful in describing selection strategies. Second, we will define several key mathematical notations useful for mathematically defining selection strategies. Third, we will review key selection strategies and discuss their relative performances. Finally, we will offer insights into the reviewed selection strategies and propose new areas of research going forward. 7 2. Terminology Below we define several key terms which will be used throughout this chapter to describe selection strategies. Some of these terms, to our knowledge, are new terminology and have not been described in breeding literature. 2.1. Mating patterns and mating configurations We define a mating pattern as a series of mating steps taken to produce offspring from a set of arbitrary ancestors. Mating patterns only represent the way in which individuals are mated and do not contain information on the specific individuals which are mated. Examples of mating patterns are self-crosses, two-way crosses, two-way crosses followed by doubled haploid production, backcrosses, etc. We define a mating configuration as a series of mating steps taken to produce offspring from a set of specific ancestors. Mating configurations are mating patterns with specific ancestral data attached. An example mating configuration is the action: perform a two-way cross between parents A and B. 2.2. Candidate and selection sets We define a candidate set as a set of individuals and/or possible mating configurations which may be considered for selection in a breeding program. A selection set is a subset of individuals and/or mating configurations chosen from a candidate set and represents selections which are made in a breeding program. 2.3. Linear selection strategy objectives and constraints We define a selection strategy objective or constraint as being linear in nature if it satisfies addition and scalar multiplication axioms. Let 𝑓(𝐱) represent the objective or constraint function for a selection strategy. 𝑓(𝐱) is linear if: 8 𝑓(𝐱𝟏 + 𝐱𝟐) = 𝑓(𝐱𝟏) + 𝑓(𝐱𝟐) ∀𝐱𝟏, 𝐱𝟐 ∈ 𝒳 𝑓(𝑐𝐱) = 𝑐𝑓(𝐱) ∀𝐱 ∈ 𝒳 As an example, suppose that our selection strategy objective function is defined as 𝑓(𝐱) = 𝐯′𝐱. We see that the addition axiom is satisfied: 𝑓(𝐱𝟏 + 𝐱𝟐) = 𝐯′(𝐱𝟏 + 𝐱𝟐) = 𝐯′𝐱𝟏 + 𝐯′𝐱𝟐 = 𝑓(𝐱𝟏) + 𝑓(𝐱𝟐) The scalar multiplication axiom is also satisfied: 𝑓(𝑐𝐱) = 𝐯′(𝑐𝐱) = 𝑐𝐯′𝐱 = 𝑐𝑓(𝐱) Since these two axioms are satisfied, the objective function is linear in nature. 2.4. Non-linear selection strategy objectives and constraints We define a selection strategy objective or constraint as being non-linear in nature if it violates at least one of the linear axioms defined above. As an example, suppose that our selection strategy objective function is defined as 𝑓(𝐱) = 𝐱′𝐕𝐱. We see that the addition axiom is violated: 𝑓(𝐱𝟏 + 𝐱𝟐) = (𝐱𝟏 + 𝐱𝟐)′𝐕(𝐱𝟏 + 𝐱𝟐) = 𝐱𝟏 ′ 𝐕𝐱𝟏 + 𝐱𝟏 ′ 𝐕𝐱𝟐 + 𝐱𝟐 ′ 𝐕𝐱𝟏 + 𝐱𝟐 ′ 𝐕𝐱𝟐 = 𝑓(𝐱𝟏) + 𝑓(𝐱𝟐) + 𝐱𝟏 ′ 𝐕𝐱𝟐 + 𝐱𝟐 ′ 𝐕𝐱𝟏 We also see that the scalar multiplication axiom is violated: ≠ 𝑓(𝐱𝟏) + 𝑓(𝐱𝟐) 𝑓(𝑐𝐱) = (𝑐𝐱)′𝐕(𝑐𝐱) 9 = 𝑐2𝐱′𝐕𝐱 = 𝑐2𝑓(𝐱) ≠ 𝑐𝑓(𝐱) Since more than one linearity axiom is violated, the objective function is non-linear in nature. 2.5. Selection units in breeding selection strategies Selection strategies have previously been classified into two major groups: truncating selection, and mate selection (Akdemir & Sánchez, 2016). The former selection strategy group selects the best individuals by order of their independent merit (Falconer & Mackay, 1996), while the latter selection strategy selects the best mating configurations by order of their independent merit (Akdemir & Sánchez, 2016). These terms are certainly helpful, but for some selection strategies, they are inadequate descriptors. Selection strategies that fall outside of these descriptors include those that select individuals or mating configurations on their collective merit. With these selection strategies, the merit of individuals or mating configurations is dependent on the merit of other selected individuals or mating configurations. We propose a new way of classifying selection strategies according to fundamental units of selection which derive from the nature of their candidate sets, objectives, and constraints. This idea takes inspiration from the concept of “units of selection” in evolutionary biology (Lewontin, 1970). Here, we define four selection units on which breeding selection strategies operate and summarize them in Table 1.1. 2.5.1. Parent selection units The first selection unit we identify is the parent selection unit. A breeding selection strategy operates on parents if the candidate set consists of extant individuals (no mating configurations are permitted) and the objective and constraint functions are all linear in nature. 10 Selection strategies that operate on parent selection units are called parental selection strategies and can be interpreted as selecting individuals based on their merits as individuals. 2.5.2. Progeny selection units The second selection unit we identify is the progeny selection unit. A breeding selection strategy operates on progenies if the candidate set contains mating configurations (mixtures of extant individuals and mating configurations are allowed) and the objective and constraint functions are all linear in nature. Selection strategies that operate on progeny selection units are called progenitive selection strategies and can be interpreted as selecting mating configurations based on the merits of their progenies. 2.5.3. Parent-population selection units The third selection unit we identify is the parent-population selection unit. A breeding selection strategy operates on the parent-population if the candidate set consists of extant individuals (no mating configurations are permitted) and if at least one objective or constraint function is non-linear in nature. Selection strategies that operate on parent-population selection units are called parental population selection strategies and can be interpreted as selecting sets of individuals based on their collective merits as a population. 2.5.4. Progeny-population selection units The fourth and final selection unit we identify is the progeny-population selection unit. A breeding selection strategy operates on the progeny-population if the candidate set consists of mating configurations (mixtures of extant individuals and mating configurations are allowed) and if at least one objective or constraint functions is non-linear in nature. Selection strategies that operate on progeny-population selection units are called progenitive population selection 11 strategies and can be interpreted as selecting sets of mating configurations based on their collective ability to produce meritorious progenies. Selection Unit Parent Progeny Parent-Population Progeny-Population Selection Candidate Set Constitution Objective(s) and Constraint(s) Extant individuals Mating configurations + optional extant individuals Extant individuals Mating configurations + optional extant individuals All linear All linear At least one non-linear At least one non-linear Table 1.1: A summary of the selection units defined and described in this chapter. 3. Mathematical notation Before describing previous approaches to breeding and mating optimization, it is necessary to establish common notations for key variables. 3.1. Number set definitions Let ℝ+ represent the set of non-negative, real numbers, [0, ∞). Let ℤ+ represent the set of all non-negative integers, {0,1, … }. Let 𝔹 represent the set of all binary numbers, {0,1}. 3.2. Population set definitions Let Ω represent the candidate set. The candidate set represents the set of existing individuals or possible mating configurations which may be considered for selection in a breeding program. The elements in this set depend on the selection strategy, as some selection strategies may only consider existing individuals, possible mating configurations, or both. The cardinality of this set |Ω| is denoted by 𝑁Ω, and elements in Ω are accessed by 𝜔, where 𝜔 ∈ Ω. Let Ξ represent a selection set. A selection set is a subset of the candidate set, Ξ ⊆ Ω and represents the set of existing individuals and/or possible mating configurations which are 12 selected in a breeding program from the pool of candidates. The cardinality of this set |Ξ| denoted by 𝑁Ξ and defined by the user according to the number of extant individuals or mating configurations to be selected. Elements in Ξ are accessed by 𝜉, where 𝜉 ∈ Ξ. Both the candidate and selection sets help define the search space for a selection strategy. They most crucially help define the dimensionality of the search space and the set of values which decision variables may take. 3.3. Search space set definitions Let ℝ+ 𝑁Ω represent a non-negative, real-valued search space with dimension equal to the cardinality of the candidate set, 𝑁Ω. Vectors within this search space are accessed by 𝐱, where 𝐱 ∈ ℝ+ 𝑁Ω. Vectors in this continuous search space typically represent the gametic contribution proportions made by members of the candidate set Ω to the next generation. Let ℤ+ 𝑁Ω represent a non-negative, integer-valued search space with dimension equal to the cardinality of the candidate set, 𝑁Ω. Vectors within this search space are accessed by 𝐱, where 𝐱 ∈ ℤ+ 𝑁Ω. Vectors in this discrete search space typically represent discrete gametic contributions made by members of the candidate set Ω to the next generation. Let 𝔹𝑁Ω represent a binary-valued search space with dimension equal to the cardinality of the candidate set, 𝑁Ω. Vectors within this search space are accessed by 𝐱, where 𝐱 ∈ 𝔹𝑁Ω. Vectors in this discrete search space typically represent whether a member in the candidate set Ω is selected (1) or not (0) to contribute to the next generation. Some binary-valued search spaces may apply an additional summation constraint on vectors within the search space to indicate that a subset of constant size 𝑁Ξ is to be selected. This constraint can be denoted as 𝟏𝐍𝛀 ′ 𝐱 = 𝑁Ξ. 13 3.4. Decision vector definitions Let 𝐱 represent a vector of length 𝑁Ω containing decision variables. Decision variables may be real-, integer-, or binary-valued, depending on the associated search space 𝒳. Elements are accessed as 𝑥𝑖 ∈ 𝐱, 𝑖 ∈ {1,2, … , 𝑁Ω} 3.5. Population genotypic data: size definitions Let Φ represent the number of homologous chromosome phases in the sporophytic stage of an organism. For diploid and allopolyploid species, Φ = 2. For autopolyploid species, Φ varies according to the species ploidy level. Specific chromosome phases are indexed by 𝜙, where 𝜙 ∈ {1, … , Φ}. Let 𝑁 represent the number of existing individuals in a breeding population. Specific individuals are indexed by 𝑛, where 𝑛 ∈ {1, … , 𝑁}. In many selection strategies, the set of individuals in a selection candidate set are the same as the set of existing individuals in a breeding population. In circumstances such as these, indices for existing individuals and selection candidates can be mapped to each other via some function 𝑓𝐼𝐷(⋅) in a one-to-one manner: {1, … , 𝑁} ∋ 𝑛 ∈ {𝑓𝐼𝐷(𝜔) ∀ 𝜔 ∈ Ω}. This of course implies that 𝑁 = 𝑁Ω = |Ω|. Let 𝑀 represent the number of genomic markers surveyed. Individual markers are indexed by 𝑚, where 𝑚 ∈ {1, … , 𝑀}. 3.6. Population genotypic data: haplotype definitions Let 𝐵 represent the number of haplotype block groupings into which the genome is divided. The number of haplotype blocks varies according to user preference. Specific haplotype blocks are indexed by 𝑏, where 𝑏 ∈ {1, … , 𝐵}. Let ℋ𝑏 represent the set of markers ℋ𝑏 ⊆ {1, … , 𝑀} belonging to haplotype block 𝑏. The set of markers assigned to each haplotype block varies according to user preference. 14 3.7. Population genotypic data: matrix and vector definitions Let 𝐙 represent a generic 𝑁 × 𝑀 genotype matrix. Genomic markers are assumed to be biallelic. For this symbol, the genotype encoding scheme is not restricted to a particular method. Genotypes may be coded as −1 for ‘aa’, 0 for ‘Aa’, and 1 for ‘AA’, 0 for ‘aa’, 1 for ‘Aa’, and 2 for ‘AA’, or any other valid scheme. Let 𝐙̃ represent an 𝑁 × 𝑀 genotype matrix encoding 0 for ‘aa’, 1 for ‘Aa’, and 2 for ‘AA’, where ‘A’ is the favorable allele (the allele with positive effect) and ‘a’ is the deleterious allele (the allele with negative effect). Let 𝐙̅ represent an 𝑁 × 𝑀 genotype matrix encoding 0 for ‘aa’, 1 for ‘Aa’, and 2 for ‘AA’, where ‘A’ is the minor allele and ‘a’ is the major allele. Let 𝓩 represent a generic Φ × 𝑁 × 𝑀 genotype tensor encoding the alleles for each chromosome phase. For this symbol, the genotype encoding scheme is not restricted to a particular method. Genotypes may be coded as 0 for ‘a’ and 1 for ‘A’, 0 for ‘A’ and 1 for ‘a’, or any other valid scheme. Let 𝓩̃ represent a Φ × 𝑁 × 𝑀 genotype tensor encoding 0 for ‘a’ and 1 for ‘A’, where ‘A’ is the favorable allele (the allele with positive effect) and ‘a’ is the deleterious allele (the allele with negative effect). Let 𝓩̅ represent a Φ × 𝑁 × 𝑀 genotype tensor encoding 0 for ‘a’ and 1 for ‘A’, where ‘A’ is the minor allele and ‘a’ is the major allele. Let 𝐮 represent a vector of length 𝑀 containing additive marker effect coefficients. Marker effect coefficients can be estimated using linear mixed models or Bayesian regression strategies. 15 Let 𝐩 represent a vector of length 𝑀 containing allele frequency probabilities for ‘A’ at biallelic marker loci. Let 𝐰 represent a vector of length 𝑀 containing marker weight coefficients. The calculation of marker weights depends on method implementation. 𝐰 may depend on 𝛃, 𝐩, or other terms. Let 𝐀 represent an 𝑁 × 𝑁 additive relationship (coancestry) matrix. This matrix can be calculated through pedigree relationships or genomic markers. Let 𝐊 represent an 𝑁 × 𝑁 kinship matrix. This matrix is equivalent to 1 2 𝐀. Let 𝐆 represent an 𝑁 × 𝑁 genomic relationship matrix. This matrix can be calculated using multiple different methods such as by the VanRaden (VanRaden, 2008) or Yang (Yang et al., 2010) methods. 3.8. Population phenotypic data: matrix and vector definitions Let 𝐲𝐓𝐁𝐕 represent a vector of length 𝑁 containing true breeding values for a single trait for all 𝑁 existing individuals in a breeding population. True breeding values reflect additive effects which can be transmitted from parent to offspring. Let 𝐲𝐓𝐆𝐕 represent a vector of length 𝑁 containing true genotypic values for a single trait for all 𝑁 existing individuals in a breeding population. True genotypic values reflect the sum of additive, dominance, and epistatic effects exhibited in an individual. Let 𝐲𝐄𝐁𝐕 represent a vector of length 𝑁 containing estimated breeding values for a single trait for all 𝑁 existing individuals in a breeding population. In this notation, the EBV subscript may refer to breeding values derived from any estimation technique. To denote a specific estimation technique, one may slightly modify the subscript. Let 𝐲𝐏𝐄𝐁𝐕, 𝐲𝐀𝐄𝐁𝐕, and 𝐲𝐆𝐄𝐁𝐕 16 refer to breeding values that have been estimated using strictly phenotypic data, pedigree relationship data, and genomic data, respectively. Let 𝐲𝐄𝐆𝐕 represent a vector of length 𝑁 containing estimated breeding values for a single trait for the existing individuals in a breeding population. Let 𝐘𝐓𝐁𝐕 represent an 𝑁 × 𝑇 matrix containing true breeding values for all 𝑁 existing individuals in a breeding population for 𝑇 traits. Let 𝐘𝐓𝐆𝐕 represent an 𝑁 × 𝑇 matrix containing true genotypic values for all 𝑁 existing individuals in a breeding population for 𝑇 traits. Let 𝐘𝐄𝐁𝐕 represent an 𝑁 × 𝑇 matrix containing estimated breeding values for all 𝑁 existing individuals in a breeding population for 𝑇 traits. Like the 𝐲𝐄𝐁𝐕 notation, the EBV subscript may refer to breeding values derived from any estimation technique and may be slightly modified to denote a specific estimation technique. Let 𝐘𝐏𝐄𝐁𝐕, 𝐘𝐀𝐄𝐁𝐕, and 𝐘𝐆𝐄𝐁𝐕 refer to breeding values that have been estimated using strictly phenotypic data, pedigree relationship data, and genomic data, respectively. Let 𝐘𝐄𝐆𝐕 represent an 𝑁 × 𝑇 matrix containing estimated genotypic values for all 𝑁 existing individuals in a breeding population for 𝑇 traits. Let 𝚺𝐆 represent a 𝑇 × 𝑇 genetic variance-covariance matrix for 𝑇 traits. Let 𝚺𝐏 represent a 𝑇 × 𝑇 phenotype variance-covariance matrix for all 𝑇 traits. 3.9. Miscellaneous definitions Let 𝑄 represent the number of objectives. Objectives are indexed by 𝑞, where 𝑞 ∈ {1, … , 𝑄} Let 𝑅 represent the number of inequality constraints. Inequality constraints are indexed by 𝑟, where 𝑟 ∈ {1, … , 𝑅}. 17 Let 𝑆 represent the number of equality constraints. Equality constraints are indexed by 𝑠, where 𝑠 ∈ {1, … , 𝑆}. Let 𝑇 represent the number of agronomic traits undergoing selection in a breeding population. Individual traits are indexed by 𝑡, where 𝑡 ∈ {1, … , 𝑇}. Let 𝒯 represent the number of selection cycles a breeding population will experience. Individual selection cycles are indexed by 𝓉, where 𝓉 ∈ {0,1, … , 𝒯}. If 𝓉 = 0, this represents initial conditions when no selection has occurred yet. 4. Breeding strategies 4.1. Optimal index selection (OIS) (1936, 1943) 4.1.1. Background Optimal index selection (OIS; also called Smith-Hazel index selection) is a multi-trait, parental selection strategy that seeks to identify a subset of individuals with maximal linear indices. Indices are calculated as a weighted sum between an economic weight vector 𝐞 and true genotypic values 𝐘𝐓𝐆𝐕 for multiple traits: 𝐲𝐈 = 𝐘𝐓𝐆𝐕𝐞. The 𝑇 trait economic weights in 𝐞 are assigned by the breeder using expert knowledge and may vary based on the target customer market or breeder preference (Hazel, 1943; Smith, 1936). In practice, true genotypic values cannot be directly observed, so Smith and Hazel derived a method by which economic weights can be adjusted using trait phenotypic and genotypic covariances to maximize the probability that individuals with the desired true genotypic value index are selected (Hazel, 1943; Smith, 1936). Instead, optimal indices may be calculated as: 𝐲𝐎𝐈 = 𝐘𝐄𝐆𝐕𝚺𝐆𝚺𝐏 −𝟏𝐞. If it can be assumed that environmental and experimental effects are independent from genotypic effects, then 𝚺𝐏 can be decomposed into 𝚺𝐆 + 𝚺𝛜𝐏 where 𝚺𝛜𝐏 is a matrix of size 𝑇 × 𝑇 containing variances and covariances of trait residuals for the corresponding experimental design used to estimate 18 genotypic values (Hazel, 1943). The product 𝚺𝐆𝚺𝐏 −𝟏 is of special importance because it is equivalent to a matrix of broad-sense heritabilities and coheritabilities: 𝚺𝐇𝟐 = 𝚺𝐆𝚺𝐏 −𝟏. In the calculation of the optimal index, trait broad-sense heritabilities and coheritabilities serve to adjust economic weights in a way such that information from one trait may be utilized to inform selections made on another trait. The adjustment is illustrated in the following thought experiment. Suppose there are two traits for which we wish to select. Suppose that the first trait has high economic value and low heritability, and the second trait has low economic value and high heritability. Now suppose that there exists a moderate co-heritability with the two traits. In this scenario, we could use information about the second trait to select for the first to achieve a higher selection accuracy. 4.1.2. Formulation as an optimization problem In OIS, the candidate set Ω is defined as the set of existing individuals in a breeding population that the breeder desires to consider. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, OIS is an LPLC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐱 𝐲𝐎𝐈 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐎𝐈 is a vector of length 𝑁Ω containing optimal indices for all individuals. Due to the linear nature of its objective function and the discrete nature of its search space, solving the OIS optimization problem can be accomplished in 𝒪(𝑁Ω log2 𝑁Ω) time on average using sorting algorithms such as quicksort (Hoare, 1961). To solve, optimal indices for 19 all individuals are calculated, sorted, and the top 𝑁Ξ individuals with the highest index values are selected. 4.2. Base index selection (BIS) (1962) 4.2.1. Background Like OIS, base index selection (BIS; also called Williams’ index selection) is a parental selection strategy that seeks to identify a subset of individuals with maximal trait values according to a linear index. BIS is based on OIS but removes economic weight adjustments for trait broad-sense heritabilities and coheritabilities (Williams, 1962). Instead, optimal indices may be calculated as a simple weighted sum between genotypic value estimates and economic weights determined using expert knowledge: 𝐲𝐁𝐈 = 𝐘𝐄𝐆𝐕𝐞. Williams notes that the variance- covariance matrices present in OIS each require 1 2 (𝑇(𝑇 − 1)) parameters to be estimated, and if the sample size is low, the accuracy of the parameter estimates may suffer. In situations where variance-covariance parameters are poorly estimated, there may not be much advantage to using adjusted economic weights over unadjusted economic weights, or worse, selection might occur in the wrong direction (Williams, 1962). Williams notes that if variance-covariance estimations are reliable, OIS will always offer greater or equal performance to BIS (Williams, 1962). 4.2.2. Formulation as an optimization problem The BIS optimization problem formulation is very similar to that of OIS. In BIS, the candidate set is defined as the set of existing individuals in a breeding population that the breeder desires to consider for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, BIS is an LPLC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐱 𝐲𝐁𝐈 20 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐁𝐈 is a vector of length 𝑁Ω containing base indices for individuals in the candidate set. Like OIS, parents are the selection units of BIS. Like OIS, BIS can be solved in 𝒪(𝑁Ω log2 𝑁Ω) time on average using sorting algorithms. 4.3. Weight-free index selection (WFIS) (1963) 4.3.1. Background Weight-free index selection (WFIS; also called multiplicative index selection) is a parental selection strategy that seeks to identify a subset of individuals with maximal measures of multiple traits when economic weights cannot be applied but minimum values for a trait can be supplied (Elston, 1963). WFIS has three important assumptions for its use. First, all traits under consideration must be transformed so that higher trait values are more desirable (Elston, 1963). Second, any individuals that do not meet a minimum performance measure must be eliminated from the set of selection candidates (Elston, 1963). Indices for these individuals are assumed to be zero (Elston, 1963). Finally, the distributions for each trait within the set of selection candidates must be similar or identical (Elston, 1963). If the distributions are not similar, they must be transformed to be similar or a remedial measure must be used (Elston, 1963). WFIS has the property that it is invariant, meaning that if trait values are transformed using a set of linear weights, the individuals selected by WFIS will remain identical (Elston, 1963). Unlike OIS and BIS which apply linear transformations to estimated genotypic values, WFIS applies a hyperbolic transformation to estimated genotypic values due to its multiplicative index function. 21 The weight-free index for the 𝑛th individual, (𝑦𝑊𝐹𝐼)𝑛, is calculated as the product of the differences between the individual’s “trait value,” (𝑌𝐸𝐺𝑉 ∗ )𝑛,𝑡, and a trait lower bound value, 𝑘𝑡 ∗, for all 𝑇 traits: 𝑇 (𝑦𝑊𝐹𝐼)𝑛 = ∏((𝑌𝐸𝐺𝑉 ∗ ∗) )𝑛,𝑡 − 𝑘𝑡 𝑡=1 The lower bound value for the 𝑡th trait is calculated using the minimum and maximum trait values for the population (𝐘𝐄𝐁𝐕 ∗ )𝐭: ∗ = 𝑘𝑡 𝑁Ω min(𝐘𝐄𝐆𝐕 ∗ )𝐭 − max(𝐘𝐄𝐆𝐕 ∗ )𝐭 𝑁Ω − 1 Above, we referred to (𝑌𝐸𝐺𝑉 ∗ )𝑛,𝑡 as an individual’s “trait value.” The meaning of “trait value” depends on the circumstance. In circumstances where estimated genotypic values meet WFIS’s distribution assumptions, trait values represent untransformed estimated genotypic values. In instances where distribution assumptions are violated, Elston suggests that trait values should represent transformed estimated genotypic values for better results. Elston suggests that a log transformation of the difference between the individual’s estimated genotypic value (𝑌𝐸𝐺𝑉)𝑛,𝑡 and a trait lower bound value 𝑘𝑡 for the trait violating assumptions should be used: ∗ (𝑌𝐸𝐺𝑉 )𝑛,𝑡 = log((𝑌𝐸𝐺𝑉)𝑛,𝑡 − 𝑘𝑡) The lower bound value for trait 𝑡 is calculated using the minimum and maximum trait values for the population (𝐘𝐄𝐆𝐕)𝐭: 𝑘𝑡 = 𝑁Ω min(𝐘𝐄𝐆𝐕)𝐭 − max(𝐘𝐄𝐆𝐕)𝐭 𝑁Ω − 1 Note that after applying a log transformation, 𝑘𝑡 ∗ values must be recursively constructed. 22 4.3.2. Formulation as an optimization problem In WFIS, the candidate set Ω is the set of existing individuals in a breeding population which meet minimum performance measures. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, WFIS is an LPLC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐲𝐖𝐅𝐈 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐖𝐅𝐈 is a vector of size 𝑁Ω containing weight-free indices calculated using the procedure described above. Despite the complicated formulation of the WFIS index, the optimization problem remains fundamentally linear, meaning that parents are the selection unit for WFIS. Like OIS and BIS, WFIS can be solved in 𝒪(𝑁Ω log2 𝑁Ω) time using sorting algorithms. 4.4. Desired gains index selection (DGIS) (1969) 4.4.1. Background Desired gains index selection (DGIS), proposed in 1969 by Pešek and Baker, is a variant of BIS that seeks to identify a subset of individuals that make maximal progress towards a set of desired genetic gains. The motivation behind this selection strategy is that instead of assigning economic weights for a set of traits as is done in BIS, breeders may specify a set of desired genetic gains which may be more intuitive than the former (Pešek & Baker, 1969). Desired gains indices are calculated as: 𝐲𝐃𝐆𝐈 = 𝐘𝐄𝐆𝐕𝚺𝐆𝐝, where 𝐝 is a vector of length 𝑇 containing desired genetic gains. 23 4.4.2. Formulation as an optimization problem As with BIS, the candidate set Ω in DGIS is defined as the set of existing individuals in a breeding population that the breeder desires to consider for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, DGIS is an LPLC- type problem and is defined as: Subject to: max 𝐱 ′ 𝐱 𝐲𝐃𝐆𝐈 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐃𝐆𝐈 is a vector of length 𝑁Ω containing the desired gains indices for individuals in the population. Like BIS, parents are the selection unit for DGIS. 4.5. Rank-sum index selection (RSIS) (1978) 4.5.1. Background Rank-sum index selection (RSIS) is a parental selection strategy that seeks to identify a subset of individuals with the best rankings for multiple traits (Mulamba & Mock, 1978). To calculate the rank-sum index, first individuals are ranked according to their performance for each trait to create an 𝑁Ω × 𝑇 ranking matrix 𝐘𝐑𝐚𝐧𝐤. A ranking value of 1 indicates the best individual, with worse individuals increasing in rank (Mulamba & Mock, 1978). Rank values for each trait are added together to get a rank-sum index for individuals: 𝐲𝐑𝐒𝐈 = 𝐘𝐑𝐚𝐧𝐤𝟏𝐓. No economic weights are considered in this selection strategy. 4.5.2. Formulation as an optimization problem In RSIS, the candidate set Ω is defined as the set of existing individuals in a breeding population that the breeder desires to consider for selection. From this candidate set, a constant 24 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, RSIS is an LPLC-type problem and is defined as: Subject to: min 𝐱 ′ 𝐱 𝐲𝐑𝐒𝐈 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐑𝐒𝐈 is a vector of length 𝑁Ω containing rank-sum indices for population individuals. 4.6. Optimal contribution selection (OCS) (1997) 4.6.1. Background Optimal contribution selection (OCS) is a parental population selection strategy proposed by Meuwissen (1997) that seeks to identify parental contribution proportions that maximize genetic gain underneath a genetic diversity constraint. Although it was developed for animal breeding, it can easily be repurposed for plant breeding. OCS utilizes the Lagrange method to identify a vector of parental contributions 𝐱 that maximize genetic gain, given mating and inbreeding constraints. 4.6.2. Formulation as an optimization problem In OCS, the candidate set Ω is defined as the set of existing individuals in a breeding population that the breeder considers for selection. From this candidate set, proportions of individuals are selected. Mathematically, OCS is an LPQC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐲𝐄𝐁𝐕 𝐱 𝐐′𝐱 = 𝟏/𝟐 25 1 2 𝐱′𝐀𝐱 = 𝐶̅𝓉+1 𝐱 ∈ ℝ+ 𝑁Ω, where 𝐐 is an 𝑁Ω × 2 incidence matrix indicating the sex of an individual (first column males, second column females), 𝟏/𝟐 is a vector of 0.5 of length 2, and 𝐶̅𝓉+1 is the desired mean population relationship coefficient in the next generation. Furthermore, 𝐶̅𝑡+1 can be written as a function of the change in the population inbreeding: 𝐶̅𝓉+1 = 1 − (1 − Δ𝐹𝑑)𝓉 (Sonesson et al., 2012). Solutions for 𝐱 can be used as weights to perform weighted, random mating between male and female individuals (Meuwissen, 1997). In a scenario where all breeding individuals can serve as both male and female parents, the constraint 𝐐′𝐱 = 𝟏/𝟐 can be simplified to 𝟏𝐍 ′ 𝐱 = 1. 4.7. Conventional genomic selection (CGS) (2001) 4.7.1. Background Conventional genomic selection is a parental selection strategy that seeks to maximize the sum of genomic estimated breeding values (GEBVs) for the selected subset (Meuwissen et al., 2001). GEBVs are linear indices whose economic weights are determined using marker effects estimated through linear mixed model or Bayesian regression techniques (Meuwissen et al., 2001). Mathematically, GEBVs are calculated as 𝐲𝐆𝐄𝐁𝐕 = 𝐙𝐮 or 𝐲𝐆𝐄𝐁𝐕 = ∑ Φ 𝜙=1 𝐙𝛟𝐮 for unphased and phased data, respectively. 4.7.2. Formulation as an optimization problem In CGS, the candidate set Ω is the set of existing individuals in a breeding population considered for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, CGS is an LPLC-type problem and is defined as: 26 Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω Solving for CGS can be accomplished in average 𝒪(𝑁Ω log2 𝑁Ω) time using sorting algorithms like other index selection techniques. 4.8. Weighted genomic selection (WGS) (2010) 4.8.1. Background Weighted genomic selection (WGS), a modification of conventional genomic selection, is a parental selection strategy that alters additive marker effect coefficients according to an optimal index proposed by Goddard (2009). Prior to developing his optimal index, Goddard made two observations. First, under the assumption that marker effects are constant and strictly additive, the proportion of genetic variance explained by a given marker decreases over many generations of selection due to allele frequency changes and the reduction of genetic diversity (Goddard, 2009). Second, the response to selection decreases over time because of the former phenomenon (Goddard, 2009). Goddard proposed that marker index weights should be adjusted in a manner proportional to 1 √𝑝(1−𝑝) and that allele frequencies should be transformed to 𝑧 = sin−1 √𝑝, where 𝑝 is the allele frequency. This set of adjustments “converts a problem with non-constant selection response but linear objective into a problem with a constant selection response but a non-linear objective” (Goddard, 2009). Building upon Goddard’s work, Jannink (2010) developed a practical long-term selection strategy to fix favorable alleles. Jannink (2010) determined, assuming sufficient time, known 27 marker effects, and fixation of the favorable allele regardless of the magnitude of its effect, that genomic marker weights should be assigned as 𝑢̂𝑚 = − sin−1(√𝑝̃𝑚) 𝜋 2 √𝑝̃𝑚(1 − 𝑝̃𝑚) sgn(𝑢𝑚), where 𝑢̂𝑚 is the weight of the 𝑚th genomic marker, 𝑝̃𝑚 is the population favorable allele frequency for the 𝑚th genomic marker, and sgn(𝑢𝑚) is the sign of the 𝑚th allele effect. In cases where 𝑝̃𝑚 = 0, the fraction is set to 1 to avoid division by zero. In this formula, the numerator term represents the difference in transformed space between complete fixation of the favorable allele and the population’s current favorable allele frequency, and the sgn(𝑢𝑚) term indicates the direction of selection for an allele based on whether it is favorable (+) or not (-). By using this marker weighting strategy, markers with low favorable allele frequencies are upweighted in a manner that is non-linear with respect to their favorable allele frequencies. Since there is uncertainty in estimating allele effects, Jannink replaced the sgn(𝑢𝑚) term with its marker effect estimate 𝑢𝑚 to reduce the importance of small-effect loci. Additionally, Jannink proposed an inverse square root approximation which he and others (De Beukelaer et al., 2017; Goiffon et al., 2017) used as a selection criterion. 𝑢̂𝑚 = − sin−1(√𝑝̃𝑚) 𝜋 2 √𝑝̃𝑚(1 − 𝑝̃𝑚) 𝑢𝑚 ≈ 1 √𝑝̃𝑚 𝑢𝑚 Using these marker weight adjustments, weighted genomic estimated breeding values (wGEBVs) can be calculated as 𝐲𝐰𝐆𝐄𝐁𝐕 = 𝐙𝐮̂ or 𝐲𝐰𝐆𝐄𝐁𝐕 = ∑ Φ 𝜙=1 𝓩𝛟𝐮̂ for unphased and phased data, respectively. It is wGEBVs which are used to assess the merit of individuals in WGS. 28 4.8.2. Formulation as an optimization problem In WGS, the candidate set Ω is the set of breeding individuals considered for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. WGS is an LPLC-type problem and is mathematically defined as: Subject to: max 𝐱 ′ 𝐲𝐰𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω Like CGS, an optimal solution to WGS can be solved in average 𝒪(𝑁Ω log2 𝑁Ω) time using sorting algorithms. 4.8.3. Performance as a selection strategy WGS has been tested by multiple research groups and is a generally robust long-term selection strategy (De Beukelaer et al., 2017; Goiffon et al., 2017; Jannink, 2010). WGS was demonstrated to improve long-term genetic gain when compared with CGS (De Beukelaer et al., 2017; Jannink, 2010). Another study found that WGS performed similarly to CGS (Goiffon et al., 2017). 4.9. Genomic optimal contribution selection (GOCS) (2012) 4.9.1. Background Genomic optimal contribution selection (GOCS) is a parental population selection strategy that is a modification to OCS proposed by Sonesson et al. (2012). GOCS is nearly identical to OCS, except that estimated breeding values are derived from genomic prediction estimates and the additive relationship matrix 𝐀 is replaced by a genomic relationship matrix 𝐆 (Sonesson et al., 2012). 29 4.9.2. Formulation as an optimization problem Like OCS, the candidate set Ω in GOCS is defined as the set of existing individuals in a breeding population considered for selection. From this candidate set, proportions of individuals are selected. Mathematically, GOCS is an LPQC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 1 2 𝐱′𝐆𝐱 = 𝐶̅𝓉+1 = 1 − (1 − Δ𝐹𝑑)𝓉 𝟏′𝐱 = 1 𝐱 ∈ ℝ+ 𝑁Ω, where 𝐲𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing genomic estimated breeding values for each candidate set member, 𝐶̅𝓉+1 is the expected mean genomic relationship in generation 𝓉, and Δ𝐹𝑑 is the change in population inbreeding. 4.9.3. Performance as a selection strategy In their paper, Sonesson et al. found that pedigree-based calculations and genomic-based calculations should not be intermixed (i.e. pedigree-based breeding value estimates mixed with genomic-based relationships) as they can act antagonistically (Sonesson et al., 2012). 4.10. Genotype building selection (GBS-KK) (2012) 4.10.1. Background Genotype building selection (GBS-KK) is a parental population selection strategy method proposed by Kemper et al. (2012). Originally developed for animal breeding, the goal of GBS- KK is to select a subset of individuals that contain the haplotype blocks necessary to develop an ideal animal genotype. Since animals do not tolerate inbreeding, the ideal genotype is defined as 30 the genotype heterozygous for the 𝐾 best haplotype blocks for each haplotype region, where 𝐾 is the ploidy of the species 𝐾 = Φ. GBS-KK is broken up into three steps: haplotype region assignment and identification of ideal haplotype blocks in a founding population, calculation of ideal haplotype block target frequencies, and selection of individuals containing ideal haplotype blocks. In the first step, the genome is partitioned into 𝐵 haplotype blocks that are assumed to segregate together and a set of ideal haplotype blocks is identified from an optimized set of founders. Haplotype regions are typically assigned to have the same length based on genetic map distances (Kemper et al., 2012). For each genomic segment designated as a haplotype block segment, the value of the best performant haplotype between the chromosome phases within each member of a founder candidate set is calculated. If we define 𝐁𝐦𝐚𝐱 to be a 𝑁 × 𝐵 matrix of haplotype 𝐵 block effects for the best haplotype blocks within each of 𝑁 individuals in the founder candidate set, then haplotype block values elements are calculated as: (𝐵𝑚𝑎𝑥)𝑛,𝑏 = max 𝜙∈{1,…,Φ} ∑ 𝒵𝜙,𝑛,𝑚𝑢𝑚 ∀𝑛 ∈ {1, … , 𝑁}, 𝑏 ∈ {1, … , 𝐵} 𝑚∈𝐻(𝑏) From the founder candidate set, 𝐽 founders are selected to maximize the sum of the 𝐾 best, unique haplotype blocks within the founders for all haplotype regions. This founder selection problem is defined by the following optimization problem: max 𝐱,𝐘 Φ 𝐾 Such that: 𝐵 𝑁 ∑ ∑ 𝑥𝑛𝑦𝑛,𝑏(𝐵𝑚𝑎𝑥)𝑛,𝑏 𝑛=1 𝑏=1 ′ 𝐱 = 𝐽 𝟏𝐍 ′ 𝐘 = 𝐾𝟏𝐁 𝟏𝐍 𝑦𝑛,𝑏 ≤ 𝑥𝑛 ∀𝑛 ∈ {1, … , 𝑁}, 𝑏 ∈ {1, … , 𝐵} 31 𝐱 ∈ 𝔹𝑁 𝐘 ∈ 𝔹𝑁×𝐵, where 𝐱 is a binary decision vector of shape 𝑁 indicating whether (1) or not (0) an individual is selected as a founder, 𝐘 is an indicator matrix for whether (𝑦𝑛,𝑏 = 1) or not (𝑦𝑛,𝑏 = 0) the 𝑛th individual contributes to the 𝑏th haplotype block among selected founders. After solving for the founders, ideal haplotype blocks are extracted from the 𝐘 matrix. In the second step, an appropriate target frequency for each ideal haplotype block is assigned either manually or using an optimal contribution method. In the manual assignment scenario, ideal haplotype block target frequencies are simply assigned as 0.5 (Kemper et al., 2012). In the optimal contribution method scenario, ideal haplotype block target frequencies for each haplotype region are calculated by solving the following optimization problem: Such that: max 𝐱 ′ 𝐱 − 𝑐𝐱′𝐱 𝐲𝐒𝐈 ′ 𝐱 = 1 𝟏𝚽𝐅 𝐱 ∈ ℝ+ Φ𝐹, where 𝐱 is a real decision vector of length Φ𝐹 containing non-negative haplotype block contribution frequencies for each of Φ chromosome phases across 𝐹 founders, 𝐲𝐒𝐈 is a vector of length Φ𝐹 containing selection index values for each haplotype block for each of Φ chromosome phases across 𝐹 founders, and 𝑐 is a segment diversity penalty factor. After solving for optimal haplotype block contribution frequencies, the contribution frequencies of the ideal haplotype blocks identified in the first step are extracted and used as target frequencies. These target ideal haplotype block frequencies are fixed for the duration of selection. 32 In the third and final step, a subset of individuals from a candidate selection set is selected to optimize a selection metric. Kemper et al. (2012) propose two metrics detailed in the section below. The first metric is an optimal squared distance metric based on Goddard (2009), denoted as GBS-KK-ARCSIN, while the second metric is a logarithmic index, denoted as GBS- KK-LOG 4.10.2. Formulation as an optimization problem In both variants of GBS-KK, the candidate set Ω is defined as the set of existing individuals in a breeding population considered for selection. From this candidate set, 𝑁Ξ individuals are selected to form a selection set Ξ. The optimization problem for the ARCSIN case is defined as: Such that: min 𝐱 𝐾𝐵 ∑ (sin−1(√𝑡𝑖) − sin−1 (√ 𝑖=1 1 Φ𝑁Ξ 2 ′𝐱)) 𝐡𝐢 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected as a parent, 𝐡𝐢 is a vector of length 𝑁Ω containing counts of the 𝑖th target chromosome segment for each parental candidate, 𝑡𝑖 is the target frequency of the 𝑖th ideal haplotype block, and 1 Φ𝐽 ′𝐱 calculates the frequency of the 𝑖th ideal haplotype block in the selected individuals. 𝐡𝐢 In the LOG case, the optimization problem is defined as: Such that: max 𝐱 𝐾𝐵 ∑ 𝑡𝑖 log ( 𝑖=1 1 2𝑁 ′𝐱) 𝐡𝐢 33 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁, where variables are the same as in the ARCSIN case. For both ARCSIN and LOG cases, if 1 2𝑁 ′𝐱 = 0 then a penalty is applied. In Kemper et al., (2012), this was defined as -100. 𝐡𝐢 4.10.3. Performance as a selection strategy Kemper et al. (2012) reported that GBS-KK-ARCSIN and GBS-KK-LOG outperformed OCS as a long-term selection strategy, however in the short-term, OCS offered better genetic gain. The same authors reported that coancestry control is more flexible in OCS than in GBS. 4.11. Dynamically weighted genomic selection (DWGS) (2015) 4.11.1. Background Dynamically weighted genomic selection (DWGS), like WGS, is a parental selection strategy that seeks to maximize weighted genomic estimated breeding values that have been calculated from additive marker effect coefficients upweighted according to favorable allele frequencies (Liu et al., 2015). DWGS differs from WGS in two regards. First, DWGS uses a beta distribution to upweight rare favorable alleles in a manner which is more extreme than WGS, and second, rare favorable allele upweighting is reduced based on the remaining number of selection generations (Liu et al., 2015). Liu et al., (2015) proposed that allele marker weights should be assigned as 𝑢̂𝑚|𝓉 = PBeta(𝑝̃𝑚|𝛼 = 𝛼𝓉, 𝛽 = 1)𝑢𝑚 = (𝛼𝓉−1) 𝑝̃𝑚 B(𝛼𝓉, 1) 𝑢𝑚 𝑝̃𝑚 = (𝛼0+( )𝓉−1) B (𝛼0 + ( ) 𝓉, 1) 1−𝛼0 𝒯 1 − 𝛼0 𝒯 𝑢𝑚, 34 where 𝑢̂𝑚|𝓉 is the weight of the 𝑚th genomic marker assigned at the 𝓉th generation, PBeta is the probability density function for the beta distribution, 𝑝̃𝑚 is the population favorable allele frequency for the 𝑚th genomic marker, and 𝛼𝓉 is the shape parameter assigned at the 𝓉th generation. The shape parameter 𝛼𝓉 is calculated as 𝛼𝓉 = 𝛼0 + ( 1−𝛼0 𝒯 ) 𝓉 where 𝛼0 is the shape parameter given at the initial generation, 𝓉 is the generation number and 𝒯 is the final generation for which selection will be conducted. Acceptable values of 𝛼0 to upweight rare favorable alleles lie in the range (0,1]. In cases where 𝑝̃𝑚 = 0, the weight can be set to 1 to avoid infinite weights. As seen in its formula, the shape parameter 𝛼𝓉 is gradually increased to 1 as 𝓉 tends to 𝒯. This has the effect of reducing the upweighting of rare favorable alleles over time and consequently the preference for long-term genetic gains. In the last generation of selection, the preference for short-term genetic gains is maximized, culminating in the selection of the best individuals without regard for the rarity of favorable alleles. Using the above marker upweighting schemes, dynamically weighted genomic estimated breeding values (dwGEBVs) for individuals can be calculated as 𝐲𝐝𝐰𝐆𝐄𝐁𝐕|𝓽 = 𝐙𝐮̂𝓽 or 𝐲𝐝𝐰𝐆𝐄𝐁𝐕|𝓽 = ∑ Φ 𝜙=1 𝓩𝛟𝐮̂𝓽 for unphased and phased data, respectively. Individuals are selected based on their dwGEBVs. 4.11.2. Formulation as an optimization problem In DWGS, the candidate set Ω is the set of breeding individuals considered for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. DWGS is an LPLC-type problem and is mathematically defined as: Subject to: max 𝐱 ′ 𝐲𝐝𝐰𝐆𝐄𝐁𝐕|𝓽 𝐱 35 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω Like WGS, an optimal solution to DWGS can be solved in average 𝒪(𝑁Ω log2 𝑁Ω) time using sorting algorithms. 4.11.3. Performance as a selection strategy In their study, Liu et al. (2015) tested DWGS for 𝛼0 values of 0.2 and 0.05 for time horizons of 15 and 40 generations. Generally, DWGS outperformed WGS and CGS in the terminal generation and for long-term selection. In the short-term, however, DWGS underperformed both WGS and CGS. 4.12. Optimal haploid value selection (OHVS) (2015) 4.12.1. Background Optimal haploid value selection (OHVS) is a progenitive selection strategy that seeks to identify a subset of mating configurations that maximize the sum of best possible doubled haploid (DH) GEBVs the mating configurations can produce (Daetwyler et al., 2015). Daetwyler et al. (2015) assumed that the candidate set consisted of two-way crosses produced through random mating, however this can be generalized to consider crosses which have not been made and/or other mating patterns. In OHVS, the genome is first partitioned into 𝐵 haplotype blocks that are assumed to segregate together. Next, haplotype allele values for all chromosome phases and mating configurations are calculated by adding estimated allele values within the haplotype block boundaries. Finally, a mating configuration is scored by adding the values of the best haplotype blocks accessible to the mating configuration for all haplotype blocks and multiplying by the resulting sum by the ploidy of the species. The resulting score is called an optimal haploid value. Mathematically, optimal haploid values are calculated as: 36 𝐵 (𝑦𝑂𝐻𝑉)𝑛 = Φ ∑ max 𝜙∈{1,…,Φ} 𝑏=1 ∑ 𝒵𝜙,𝑛,𝑚𝑢𝑚 𝑚∈𝐻(𝑏) Optimal haplotype block sizes are empirically determined through simulation and are inversely proportional to the duration of selection (Daetwyler et al., 2015). The optimal haploid value of an individual is always greater than or equal to the individual’s GEBV. OHVS differentiates itself from CGS only in the selection of heterozygous, segregating individuals (Daetwyler et al., 2015). 4.12.2. Formulation as an optimization problem In OHVS, the candidate set Ω is the set of mating configurations and/or breeding individuals considered for selection. From this candidate set, a constant 𝑁Ξ mating configurations and/or breeding individuals are selected to form a selection set Ξ. Mathematically, OHVS is defined as: Subject to: max 𝐱 ′ 𝐲𝐎𝐇𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐎𝐇𝐕 is a vector of length 𝑁Ω containing optimal haploid values for considered mating configurations. 4.12.3. Performance as a selection strategy OHV selection was shown to outperform CGS (Daetwyler et al., 2015; Goiffon et al., 2017) and WGS (Goiffon et al., 2017). 37 4.13. Resource allocated expected maximum breeding value selection (RAEMBVS) (2016) 4.13.1. Background In 2016, Hunter and McClosky introduced an integer programming formulation of the following mating design problem: given a set of potential crosses and a fixed number of progenies allowed, allocate a breeding budget to the potential crosses to maximize the expected performance of the best progeny. Herein we refer to this breeding optimization strategy as resource allocated expected maximum breeding value selection (RAEMBVS). RAEMBV assumes the infinitesimal model of genetic control and that trait values of progenies originating from a cross are normally distributed (Hunter & McClosky, 2016). If all possible crosses are considered, the number of possible resource allocations is enormous, and the mating design problem becomes extremely challenging to solve. In their work, the authors prove that not all possible crosses need to be considered. In fact, only crosses that are Pareto optimal for expected progeny mean and variance will receive any of the budget. Hunter and McClosky note that the number of crosses in the Pareto set increases approximately logarithmically. For example, the authors estimate that the size of the Pareto set rarely exceeds 25 when 20000 crosses are considered (Hunter & McClosky, 2016). 4.13.2. Formulation as an optimization problem In RAEMBVS, the candidate set Ω is the set of mating configurations considered for selection which are Pareto optimal for their expected progeny mean and variance. Across all members of the candidate set, a constant 𝑏 > 0 progenies are derived. Each mating configuration is allocated 𝑏𝑖 ≥ 0 progenies. Mathematically, RAEMBV is defined as follows: ∞ 𝑁Ω max 𝑏1,…,𝑏𝑁Ω ∫ 1 − ∏ Φ ( 0 𝑖=1 𝑏𝑖 ) 𝑦 − 𝜇𝑖 𝜎𝑖 𝑑𝑦 38 − ∫ ∏ Φ ( 𝑁Ω 0 −∞ 𝑖=1 𝑏𝑖 ) 𝑑𝑦 𝑦 − 𝜇𝑖 𝜎𝑖 Subject to: 𝑁Ω ∑ 𝑏𝑖 𝑖=1 = 𝑏 𝑏𝑖 ≥ 0 ∀𝑖 = 1, … , 𝑁Ω 𝑏𝑖 ∈ ℤ ∀𝑖 = 1, … , 𝑁Ω, where 𝜇𝑖 is the expected progeny mean for the 𝑖th mating configuration in the Pareto set, 𝜎𝑖 is the expected progeny standard deviation for the 𝑖th mating configuration in the Pareto set. The integral expression in the objective function serves to calculate the expected value of the best trait value in progenies derived from the provided breeding budget: E [ max 𝑖=1,…,𝑁Ω max 𝑗=1,…,𝑏𝑖 𝑌𝑖𝑗] where 𝑌𝑖𝑗 is the 𝑗th progeny from the 𝑖th cross. To solve this integer programming problem, the authors use a branch-and-bound algorithm (Hunter & McClosky, 2016). 4.13.3. Performance as a selection strategy Hunter and McClosky focused on solving the resource allocation problem, especially for large numbers of potential crosses, but they did not examine the impact of RAEMBV in a recurrent selection scenario. Thus, it is unknown how RAEMBV compares to previous selection methods. 4.14. Genomic mating (GM) (2016) 4.14.1. Background Genomic mating (GM) is a multi-objective, progenitive population selection strategy proposed by Akdemir and Sánchez (2016). Inspired by the quadratic optimization strategies proposed by Meuwissen (1997) and others (Goddard, 2009; Pryce et al., 2012; Schierenbeck et al., 2011), GM incorporates an inbreeding objective and a novel “risk” objective to make mate selections. GM assumes that mate selections are restricted to two-way or self-crosses. The 39 inbreeding objective controls for the genetic relatedness of selected mating configurations, and the “risk” objective attempts to maximize the genetic gain and a level of “risk” related to the beneficial allele complementarity of the mating configuration. In their original publication, Akdemir and Sánchez (2016) provide equations to describe each objective in GM. Here, we provide a mathematically equivalent and significantly simplified version of their equations. For their inbreeding objective, the genomic relationship matrix relating pairs of mating configurations to each other can be calculated as: 𝐆𝛀 = 𝐐𝔼 ′ 𝐆𝐐𝔼 + 𝐃𝛙 Where 𝐆𝛀 is a 𝑁Ω × 𝑁Ω mating configuration genomic relationship matrix, 𝐐𝔼 is a 𝑁 × 𝑁Ω transformation matrix containing expected parental contributions for each of 𝑁Ω mating configurations, 𝐆 is an 𝑁 × 𝑁 parental genomic relationship matrix calculated via the VanRaden (2008) method, and 𝐃𝛙 is a 𝑁Ω × 𝑁Ω diagonal matrix of variances caused by Mendelian sampling related to inbreeding in the parents of a mating configuration. The transformation matrix 𝐐𝔼 has two restrictions: elements representing parental contributions must be 0, 0.5, or 1 for two-way or self- crosses, 𝑞𝑖𝑗 ∈ {0, 1 2 , 1} ∀𝑖, 𝑗, and columns must sum to unity, 𝐐𝔼 ′ 𝟏𝐍 = 𝟏|𝛀|. Diagonal elements of 𝐃𝛙 are equivalent to the inbreeding in the parents: (𝑑𝜓) = 1 2 − 𝑖𝑖 1 4 (𝐹1 + 𝐹2) where 𝐹1 and 𝐹2 are the inbreeding coefficients of the parents which can be extracted from the diagonal of the 𝐆 matrix. The “risk” objective is composed of a mating configuration mean and a mating configuration beneficial allele standard deviation component. Mating configuration means are calculated as: 𝐲𝛍 = 𝐐𝔼 ′ 𝐙𝐮 40 Where 𝐲𝛍 is a vector of length 𝑁Ω containing parental means for the considered mating configuration, 𝐐𝔼 is a 𝑁 × 𝑁Ω transformation matrix containing expected parental contributions for each of 𝑁Ω mating configurations as described previously, 𝐙 is an 𝑁 × 𝑀 genotype matrix, and 𝐮 is a vector of length 𝑀 containing additive marker effect coefficients. Mating configuration beneficial allele standard deviations are calculated as: 𝐲𝛔 = 𝐒𝐮 Where 𝐲𝛔 is a vector of length 𝑁Ω containing beneficial standard deviations, 𝐒 is a 𝑁Ω × 𝑀 allele standard deviation matrix, 𝐮 is a vector of length 𝑀 containing additive marker effect coefficients. Elements of the beneficial allele standard deviation matrix 𝐒 are calculated as 𝑠𝑖𝑗 = sign(𝑢𝑗) √𝜎𝑖𝑗 2 for the 𝑖th mating configuration and 𝑗th genomic locus, where sign(𝑢𝑗) is the sign of the 𝑗th marker effect, and 𝜎𝑖𝑗 2 is the allelic variance for the 𝑖th mating configuration and 𝑗th genomic locus. The purpose of the sign(𝑢𝑗) term is so that the variance of beneficial allele is considered. Allele variances 𝜎𝑖𝑗 2 are assigned according to values in Table 1.2 below: Parent 1 Genotype AA AA AA Aa Aa Aa aa aa aa Parent 2 Genotype AA Aa aa AA Aa aa AA Aa aa Mating Configuration Allele Variance 0 0.25 0 0.25 0.5 0.25 0 0.25 0 Table 1.2: Summary of allele variances assigned for mating configuration beneficial allele standard deviations. The full “risk” of a mating configuration is defined as a weighted sum between its mean and beneficial allele standard deviation: 𝐲𝛍 + 𝜆1𝐲𝛔. The weight parameter 𝜆1 ≥ 0 controls the 41 relative “risk” that the breeder is willing to subsume. From the allele variance table above, it can be deduced that a mating configuration has zero beneficial allele standard deviation if both parents are completely inbred. For the breeding of inbred species, this means that the risk of a mating configuration is equivalent to the parental mean, regardless of the value of the weight parameter 𝜆1. 4.14.2. Formulation as an optimization problem In GM, the candidate set Ω is the set of two-way and self-cross mating configurations which can be constructed from available parental candidates. From this candidate set, a constant 𝑁Ξ mating configurations are selected to form a selection set Ξ. Mathematically, GM is defined as: Such that: 𝐱′𝐆𝛀𝐱 min 𝐱,𝜆1 max 𝐱,𝜆1 (𝐲𝛍 + 𝜆1𝐲𝛔) ′ 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω The former objective is the mating configuration inbreeding objective, and the latter objective is the “risk” objective. If 𝜆1 is assigned beforehand and either the inbreeding or “risk” objective is converted to a constraint, this optimization problem is of the same form as classical OCS. In their study, Akdemir and Sánchez convert the multi-objective optimization problem above into a single objective via the weighted sum method. They add an additional progeny coancestry hyperparameter 𝜆2 and minimize the weighted sum: 42 Such that: −(𝐲𝛍 + 𝜆1𝐲𝛔) ′ 𝐱 + 𝜆2𝐱′𝐆𝛀𝐱 min 𝐱,𝜆1,𝜆2 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω Hyperparameters 𝜆1 and 𝜆2 are assigned a priori or by mapping out the Pareto frontier and selecting a set of hyperparameters. In their study, Akdemir and Sánchez used a hybrid Tabu search (Glover, 1989, 1990) genetic algorithm to solve for 𝐱. 4.14.3. Performance as a selection strategy GM was determined to outperform phenotypic selection, CGS, and OCS (Akdemir & Sánchez, 2016). 4.15. Genotype building selection (GBS-MG) (2017) 4.15.1. Background Using Kemper et al., (2012) as inspiration, Goiffon et al., (2017) proposed their own genotype building selection strategy based on the founder identification step in Kemper et al.’s selection protocols. This variant of genotype building selection (GBS-MG) is a parental population selection strategy that, like its predecessor, seeks to maximize the sum of the values of the best 𝐾 haplotype blocks for a selection subset. Haplotype values are calculated in a manner identical to Kemper et al. (2012), but Goiffon et al., (2017) empirically determine the number of haplotype regions into which to divide the genome via simulation. Goiffon et al., (2017) do not apply any diversity preservation mechanisms or selection of individuals based on an identified set of ideal haplotype blocks like Kemper et al., (2012). 43 4.15.2. Formulation as an optimization problem In GBS-MG, the candidate set Ω is defined as the set of existing individuals in a breeding population considered for selection. From this candidate set, 𝑁Ξ individuals are selected for inclusion into the selection set Ξ. Mathematically, GBS-MG is defined as: max 𝐱,𝐘 Φ 𝐾 Such that: 𝐵 𝑁Ω ∑ ∑ 𝑥𝑛𝑦𝑛,𝑏(𝐵𝑚𝑎𝑥)𝑛,𝑏 𝑛=1 𝑏=1 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 ′ 𝐘 = 𝐾𝟏𝐁 𝟏𝐍𝛀 𝑦𝑛,𝑏 ≤ 𝑥𝑛 ∀𝑛 ∈ {1, … , 𝑁Ω}, 𝑏 ∈ {1, … , 𝐵} 𝐱 ∈ 𝔹𝑁Ω 𝐘 ∈ 𝔹𝑁Ω×𝐵, where 𝐱 is a binary decision vector of shape 𝑁Ω indicating whether (1) or not (0) an individual is selected as a parent, and 𝐘 is an indicator matrix for whether (𝑦𝑛,𝑏 = 1) or not (𝑦𝑛,𝑏 = 0) the 𝑛th individual contributes to the 𝑏th haplotype block among selected subset. 4.15.3. Performance as a selection strategy Goiffon et al. (2017) reported that GBS-MG outperforms CGS, WGS, and OHVS in long-term genetic gains, but underperforms compared to OPVS in the same metric. 4.16. Optimal population value selection (OPVS) (2017) 4.16.1. Background Optimal population value selection (OPVS), proposed by Goiffon et al. (2017), is a parental population selection strategy that takes inspiration from GBS-MG and OHVS in its scoring mechanism. Like GBS-MG and OHVS, in OPVS the genome is partitioned into 𝐵 44 haplotype blocks that are assumed to segregate together. OPVS attempts to identify a subset of individuals that contain a maximal sum of best haplotype blocks for each haplotype region. The haplotype value calculation and scoring protocol for OPVS is identical to GBS-MG, except that instead of identifying 𝐾 best, unique haplotypes only one best haplotype is identified, 𝐾 = 1. OPVS is a generalization of the upper selection limit (Goiffon et al., 2017), allowing for haplotypes of varying lengths rather than a single marker. Like OHVS, the number of haplotype blocks are empirically determined through simulation (Goiffon et al., 2017). 4.16.2. Formulation as an optimization problem In OPVS, the candidate set Ω is defined as the set of existing individuals in a breeding population considered for selection. From this candidate set, a 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, OPVS is defined as: Such that: 𝐵 max 𝐱 Φ ∑ 𝑏=1 max 𝑛∈{𝑖∈{1,…,𝑁Ω}|𝑥𝑖=1} (𝐵𝑚𝑎𝑥)𝑛,𝑏 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where (𝐵𝑚𝑎𝑥)𝑛,𝑏 is the best haplotype block effect for the 𝑛th individual at the 𝑏th haplotype block position. 4.16.3. Performance as a selection strategy OPVS outperforms CGS, WGS, OHVS, and GBS-MG selection strategies in producing long-term genetic gains (Goiffon et al., 2017). 45 4.17. Usefulness criterion selection (UCS) (2017) 4.17.1. Background Usefulness criterion selection (UCS) is a progenitive selection strategy proposed by Lehermeier et al. (2017). UCS was inspired by the usefulness criterion (Schnell & Utz, 1975). The usefulness criterion is defined as the mean performance of an upper fraction of selected progenies. For a single individual, the usefulness criterion (UC) is calculated as 𝑈𝐶 = 𝜇 + 𝑖ℎ𝜎𝑔, where 𝜇 is the expected progeny mean for a given mating configuration, 𝑖 is the selection intensity, ℎ is the selection accuracy, and 𝜎𝐺 is the expected progeny genetic standard deviation. In matrix notation, the expected progeny means for available mating configurations can be calculated as: 𝐲𝛍 = 𝐐𝔼 ′ 𝐲𝐄𝐁𝐕, where 𝐲𝛍 is a vector of length 𝑁Ω containing expected progeny means for all considered mating configurations, 𝐐𝔼 is a 𝑁 × 𝑁Ω transformation matrix relating parents and their expected parental contributions to a mating configuration, and 𝐲𝐄𝐁𝐕 is a vector of length 𝑁 containing estimated breeding values (or genomic estimated breeding values) for parental candidates. The transformation matrix 𝐐𝔼 has two restrictions: elements representing parental contributions must be between 0 and 1 and represent the expected genome contributions for each parent, 𝑞𝑖𝑗 ∈ [0,1] ∀𝑖, 𝑗, and columns must sum to unity, 𝐐𝔼 ′ 𝟏𝐍 = 𝟏|𝛀|. In vector notation, the expected progeny genetic standard deviations for available mating configurations are denoted by 𝐲𝛔, a vector of length 𝑁Ω. Elements of this vector are calculated by taking the square root of the expected genetic variance of a mating configuration: (𝑦𝜎)𝑖 = 46 √𝜎𝑖 2 ∀𝑖 ∈ {1,2, … , 𝑁Ω}. Expected genetic variances for mating configurations may be estimated via simulation (Mohammadi et al., 2015) or through deterministic calculations of additive genetic variance (Lehermeier et al., 2017). Combining the progeny mean and standard deviation components, we arrive at the following formula for the usefulness criteria for considered mating configurations (Schnell & Utz, 1975): 𝐲𝐔𝐂 = 𝐲𝛍 + 𝑖ℎ𝐲𝛔, where 𝐲𝐔𝐂 is a vector of length 𝑁Ω containing usefulness criteria and the remaining terms have been described previously. The selection intensity 𝑖 is calculated as 𝑖 = Φ−1(1−𝑝) 𝑝 where, Φ−1(⋅) denotes the inverse cumulative distribution function for the standard normal distribution and 𝑝 is the upper fraction of individuals which are to be selected for each mating configuration. The selection accuracy ℎ is normally considered to be 1 since selection is conducted using genotypic markers. 4.17.2. Formulation as an optimization problem In UCS, the candidate set Ω is the set of mating configurations considered for selection. From this candidate set, a constant 𝑁Ξ mating configurations are selected to form a selection set Ξ. Mathematically, OHVS is a LPLC-type problem and is defined as: Subject to: max 𝐱 ′ 𝐱 𝐲𝐔𝐂 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω 47 Like other LPLC problems, optimization of UCS can be solved in average 𝒪(𝑁Ω log2 𝑁Ω) time using sorting algorithms. 4.17.3. Performance as a selection strategy UCS was reported to outperform OHV in terms of genetic gain (Lehermeier et al., 2017). 4.18. Rare allele selection (RAS) (2017) 4.18.1. Background Rare allele selection (RAS) is a parental population selection strategy proposed by De Beukelaer et al (2017). RAS contains two objectives: one which seeks to maximize the mean GEBV of selected individuals and the other that seeks to directly managing rare alleles (De Beukelaer et al., 2017). Management of rare alleles is accomplished by taking the logarithm of minor allele frequencies, which was inspired by work done by Li et al. (2008). The use of the logarithm in the second objective applies an exponential penalty for the loss of minor alleles. 4.18.2. Formulation as an optimization problem In RAS, the candidate set Ω is the set of breeding individuals considered for selection. From this candidate set, a constant 𝑁Ξ individuals are selected to form a selection set Ξ. RAS is mathematically defined as: max 𝐱 1 𝑁Ξ ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 max 𝐱 1 𝑀 Such that: 𝑀 ∑ log ( 𝑚=1 1 Φ𝑁Ω 𝐙̅∗,𝐦 ⋅ 𝐱) ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, 48 where 𝐙̅∗,𝐦 is the 𝑚th matrix column vector containing minor allele genotypic values for each of 𝑁Ω individuals. In instances where the minor allele frequency of the selected subset is zero, the logarithm is truncated to log(0) ≔ −(log(𝑁Ω) + 1) 4.18.3. Performance as a selection strategy RAS was reported to outperform WGS, GOCS, and CGS in long-term genetic gain (De Beukelaer et al., 2017). 4.19. Expected maximum breeding value selection (EMBVS) (2018) 4.19.1. Background Expected maximum breeding value selection (EMBVS) is a progenitive selection strategy that seeks to identify a subset of parents and/or mating configurations that maximizes the sum of expected maximum GEBVs from a finite sample of DH progenies derived from a parent or mating configuration (Müller et al., 2018). By evaluating an individual or mating configuration based on its progenies, EMBVS can better incorporate linkage disequilibrium and the probability that a certain progeny is observed in a finite sample when compared to OHVS (Müller et al., 2018). Expected maximum breeding values (EMBVs) are calculated as follows. Let 𝑁𝐺 denote the number of DH progenies derived from a candidate parent. For each sampling of progenies from parent 𝜔 ∈ Ω, the progeny with maximum GEBV is calculated as: 𝑦𝑀𝐵𝑉(𝑁𝐺),𝜔 = max 𝐲𝐆𝐄𝐁𝐕(𝐍𝐆),𝜔, where 𝑦𝑀𝐵𝑉(𝑁𝐺),𝜔 is the maximum GEBV observed from a finite sample of 𝑁𝐺 progenies derived from the 𝜔th individual and 𝐲𝐆𝐄𝐁𝐕(𝐍𝐆),𝜔 is a vector of length 𝑁𝐺 containing GEBVs of simulated DH progenies from the 𝜔th individual. The EMBV for parent 𝜔 ∈ Ω is thus defined as: 49 𝑦𝐸𝑀𝐵𝑉(𝑁𝐺),𝜔 = E(𝑦𝑀𝐵𝑉(𝑁𝐺),𝜔), where 𝑦𝐸𝑀𝐵𝑉(𝑁𝐺),𝜔 denotes the expected maximum breeding value observed from a sample of 𝑁𝐺 progenies derived from the 𝜔th parent and 𝐸(⋅) denotes the expectation function. To estimate the expectation, Müller et al. (2018) propose to repeatedly simulate progenies and take the mean of the maximum progeny values. EMBVS better incorporates linkage disequilibrium and the probability that a certain progeny is observed in a finite sample when compared to OHVS (Müller et al., 2018). However, like OHV, EMBV does not pair mates and relies on random mating between generations. 4.19.2. Formulation as an optimization problem In EMBVS, the candidate set Ω consists of existing individuals in a breeding population considered for selection. Müller et al. (2018) assumed in their work that candidates in this set are the products of random mating, however the candidate set can also be extended to contain mating configurations between individuals. From this candidate set, 𝑁Ξ individuals are selected to form a selection set Ξ. Putting these components together, EMBV is mathematically defined as: Subject to: max 𝐱 ′ 𝐲𝐄𝐌𝐁𝐕(𝐍𝐆) 𝐱 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝐲𝐄𝐌𝐁𝐕(𝐍𝐆) is a vector of length 𝑁Ω containing expected maximum breeding values from a sample of 𝑁𝐺 progenies derived from each parent or mating configuration in the candidate set. 4.19.3. Performance as a selection strategy The performance of EMBV is somewhat mixed. Müller et al. (2018) determined that it is superior to CGS in most scenarios with respect to genetic gain and genetic variance, however in 50 many circumstances, WGS and OHV maintained equal or better genetic gain and genetic variance than that of EMBV (Müller et al., 2018). 4.20. Look-ahead selection (LAS) (2019) 4.20.1. Background Look-ahead selection (LAS) is a progenitive population selection strategy that utilizes computer simulation to identify a set of mating configurations that maximize the “expected GEBV of the best offspring in the terminal generation” (Moeinizade et al., 2019). LAS takes into consideration recombination probabilities, time remaining to a production deadline, and allocates resources to mating configurations weighted by the range of potential progenies that a mating configuration can produce (Moeinizade et al., 2019). Proposed mating configuration subsets are tested by simulating the proposed crosses and randomly intermating progenies until the established production deadline. The GEBV of the maximum performant individual observed among the simulated individuals in the terminal generation is used to approximate the performance of the mating configuration. A generalized version of LAS was also proposed to allow for a percentile to be used to score proposed mating configuration subsets (Moeinizade et al., 2020). Instead of only considering the GEBV of the best individual, the GEBV of the 100𝛾th percentile individual can be considered in this version. 4.20.2. Formulation as an optimization problem In LAS, the candidate set Ω is defined as the set of considered mating configurations. In Moeinizade et al. (2019), this was defined as the set of two-way crosses for a set of parental candidates. From this candidate set, 𝑁Ξ mating configurations are selected to form a selection set Ξ. Mathematically, LAS is defined as: max 𝐱 𝑓LAS(𝐱, 𝐫, 𝒯 − 𝓉) 51 Such that: 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝑓LAS(⋅) denotes the simulation function used to evaluate the GEBV of the maximum performant individual resulting from a proposed set of mating configuration, 𝐫 is a vector of recombination probabilities between neighboring genetic markers, and 𝒯 − 𝓉 is the number of generations until the terminal generation. The optimization problem formulation of the generalized version of LAS is similar in construction to the original: Such that: max 𝐱 𝜓 P[𝑔1(𝐱, 𝐫, 𝒯 − 𝓉) ≥ 𝜓] ≥ 1 − 𝛾 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝛾 defines the GEBV percentile of the simulated progenies used to evaluate a proposed mating configuration subset, 𝜓 is a threshold value representing the GEBV of the 100𝛾th percentile simulated individual, P[⋅] is the probability function, and 𝑔1(𝐱, 𝐫, 𝒯 − 𝓉) is a random variable representing the GEBVs of progenies derived from the proposed mating configuration subset 𝐱 for the first (and only) trait, given a set of recombination probabilities 𝐫 and remaining generations 𝒯 − 𝓉. In this formulation, 𝑔1(⋅) is evaluated in the same manner as 𝑓LAS(⋅), however it returns the full distribution of GEBVs, rather than only the best GEBV. 52 4.20.3. Performance as a selection strategy LAS was demonstrated to outperform CGS, OHV, and OPV (Moeinizade et al., 2019). LAS without resource allocation (denoted LAS-X) was also tested by Moeinizade et al. LAS-X exhibited poorer performance compared to LAS, but still outperformed CGS, OHV, and OPV (Moeinizade et al., 2019). 4.21. Multi-trait optimal contribution selection (MT-OCS) (2019) 4.21.1. Background In 2019, Akdemir et al. introduced several multi-objective optimized breeding (MOOB) approaches. One of these approaches was a multi-objective variant of OCS, herein which we refer to as multi-trait optimal contribution selection (MT-OCS). MT-OCS, like OCS, is a parental population selection strategy that seeks to identify a set of parental contribution proportions that maximize the genetic gain for several traits and that minimize inbreeding. 4.21.2. Formulation as an optimization problem Like OCS, the candidate set Ω in MT-OCS is defined as the set of existing individuals in a breeding population considered for selection. Contribution proportions to the next generation for parental candidates in the candidate set are determined. MT-OCS is an LPQC-type problem and is mathematically defined as: max 𝐗 ′ 𝐲𝐄𝐁𝐕,𝑡 𝐱 , 𝑡 = 1,2, … , 𝑇 Such that: 1 2 min 𝐱 𝐱′𝐀𝐱 𝟏′𝐱 = 1 𝐱 ∈ ℝ+ 𝑁Ω, 53 where 𝐲𝐄𝐁𝐕,𝑡 is a vector of length 𝑁Ω containing estimated breeding values for each of 𝑁 individuals for the 𝑡th trait. In their paper, Akdemir et al. (2019) also proposed a modification to the traditional formulation of inbreeding. To penalize negative trait correlations the authors proposed to adjust the coancestry matrix by the number of traits minus twice the sum of pairwise trait genetic correlations: 1 2 min 𝐱 𝑇 𝑇 𝐱′ ((𝑇 − 2 ∑ ∑ Ψ𝑖,𝑗 ) 𝐀) 𝐱, 𝑖=1 𝑗>𝑖 where Ψ𝑖𝑗 is the genetic correlation between traits 𝑖 and 𝑗. It should be noted that this only changes the scale for the inbreeding objective so minimizing the unpenalized and penalized inbreeding objectives results in the same solution. The authors used the weighted sum method to reduce the problem to a single objective problem and optimized on this weighted sum. 4.21.3. Performance as a selection strategy In breeding simulations for two traits, MOOB-OCS achieved better progeny performance for both traits compared to phenotypic selection, CGS, and NDS (Akdemir et al., 2019). 4.22. Multi-trait genomic mating (MT-GM) (2019) 4.22.1. Background Multi-trait genomic mating (MT-GM) is a progenitive population selection strategy proposed by Akdemir et al. (2019). It is one of Akdemir et al.’s MOOB strategies. MT-GM extends GM by adding multiple trait and progeny variance objectives along with an inbreeding objective. Trait objectives are calculated using the expected progeny performance for mating configurations. The expected progeny performance is calculated by taking a weighted mean of 54 genomic estimated breeding values for each of the parents involved in a cross. Mathematically, this is calculated as: 𝐲𝛍,𝑡 = 𝐐𝔼 ′ 𝐲𝐆𝐄𝐁𝐕,𝑡, where 𝐲𝛍,𝑡 is a vector of length 𝑁Ω containing parental means for the considered mating configuration for the 𝑡th trait, 𝐐𝔼 is a 𝑁 × 𝑁Ω transformation matrix containing expected parental contributions for each of 𝑁Ω mating configurations, and 𝐲𝐆𝐄𝐁𝐕,𝑡 is a vector of length 𝑁 containing genomic estimated breeding values for each of 𝑁 parental candidates for the 𝑡th trait. Progeny variance objectives are calculated using the expected progeny family performance variance for mating configurations. Progeny variances can be calculated using a variety of means (Akdemir & Sánchez, 2016; Bernardo, 2014; Lehermeier et al., 2017; Mohammadi et al., 2015) and are implementation dependent. Here, we use the symbol 𝐲𝛔,𝑡 to denote a vector of length 𝑁Ω containing expected progeny family variances for each of 𝑁Ω mating configurations for the 𝑡th trait. Finally, for their inbreeding objective, genomic relationships may be calculated using methods described in Akdemir & Sánchez (2016) or by analogous means. Here, we denote this 𝑁Ω × 𝑁Ω relationship matrix as 𝐀𝛀. 4.22.2. Formulation as an optimization problem Like GM, the candidate set Ω in MT-GM is defined as the set of mating configurations considered for selection. From this candidate set, 𝑁Ξ mating configurations are selected to form a selection set Ξ. MT-GM is an LPQC-type problem and is mathematically defined as: max 𝐗 max 𝐗 ′ 𝐱 , 𝑡 = 1,2, … , 𝑇 𝐲𝛍,𝑡 ′ 𝐱 , 𝑡 = 1,2, … , 𝑇 𝐲𝛔,𝑡 55 Such that: 1 2 min 𝐱 𝐱′𝐀𝛀𝐱 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω 4.22.3. Performance as a selection strategy In their study, Akdemir et al. (2019) did not test MT-GM, however they did map a Pareto frontier to visualize tradeoffs between its various objectives. Thus, MT-GM remains untested in its ability to select for multiple traits. 4.23. Non-dominated selection (NDS) (2019) 4.23.1. Background Non-dominated selection (NDS) is a multi-trait, parental selection strategy proposed by Akdemir et al. (2019). The premise of NDS is to assign parental contribution proportions according to a parental candidate’s dominance ranking for multiple traits. There are two steps to how this is done. First, individuals are sorted according to their non-dominance rank 𝑟𝜔, with lower rank values indicating higher dominance. There are several algorithms that can be used to assign non-dominance ranks. Popular algorithms include Deb et al.’s fast non-dominated sorting (Deb et al., 2002), Du et al.’s algorithm (Du et al., 2007), or Kung et al.’s algorithm (Kung et al., 1975). Second and finally, parental contributions are assigned according to some manner that is inversely proportional to the non-dominance rank of individuals: individuals with lower rank (higher dominance) are assigned higher weights. Akdemir et al. (2019) proposed and tested NDS weights (𝑦𝐷𝑅𝑊)𝜔 assigned according to the inverse of the dominance rank: (𝑦𝐷𝑅𝑊)𝜔 = 1 𝑟𝜔 ∀𝜔 ∈ Ω. Additionally, they proposed, but did not test, weights assigned according to the inverse of the squared dominance rank, the inverse of the non-dominance counts with respect to agronomic 56 trait objectives, and according to the mean of the former two assignment strategies (Akdemir et al., 2019). 4.23.2. Formulation as an optimization problem In NDS, the candidate set Ω is defined as the set of existing individuals in a breeding population considered for multi-trait selection. For this candidate set, contribution proportions to the next generation are determined. NDS is an LPLC-type problem and is mathematically defined as: Such that: max 𝐱 ′ 𝐲𝐃𝐑𝐖 𝐱 𝐏𝐱 = 𝟎 𝟏′𝐱 = 1 𝐱 ∈ ℝ+ 𝑁Ω, where 𝑦𝐷𝑅𝑊 is a vector of length 𝑁Ω containing dominance rank weights and 𝐏 is an orthogonal projection transformation matrix. 𝐏 calculates the orthogonal projection of 𝐱 onto the non- dominance rank weight vector and is calculated as 1 ′ 𝐲𝐃𝐑𝐖 𝐲𝐃𝐑𝐖 𝐲𝐃𝐑𝐖𝐲𝐃𝐑𝐖 ′ − 𝐈. The constraint 𝐏𝐱 = 𝟎 ensures that the decision vector is a scalar multiple of 𝐲𝐃𝐑𝐖. Assigning contribution proportions is equivalent to a vector scaling problem. Contributions can be assigned as: 𝐱 = 1 𝟏′𝐲𝐃𝐑𝐖 𝐲𝐃𝐑𝐖. 4.23.3. Performance as a selection strategy Akdemir et al. (2019) found that NDS, with respect to generating genetic gains for multiple traits, was comparable to index selection, tandem selection, and independent culling selection, but underperformed relative to MT-OCS. 57 4.24. Usefulness criterion parental contribution selection (UCPCS) (2019) 4.24.1. Background Usefulness criterion parental contribution selection (UCPCS) is a progenitive-population selection strategy that builds on principles from UCS and OCS. UCPCS seeks to maximize the usefulness criteria of selected mating configurations while accounting for inbreeding resulting from within-family selection. Allier, et al. (2019a) began by noting that within-family selection results in biased parental genome contributions (Allier, et al., 2019b). This bias is especially significant in cases where progenies are selected within a family resulting from a cross between parents with large performance differences, often referred to as elite × donor crosses. High performant progenies selected within a family may contain a higher fraction of the elite parent genome than is expected (Allier, et al., 2019a). This bias contributes to inbreeding beyond simple parental contribution as is typically accounted for in OCS. Here, we provide slightly altered mathematical expressions to the methods described in Allier et al, (2019b). The usefulness criteria for mating configuration candidates are calculated in a manner identical to that described in UCS (Schnell & Utz, 1975): 𝐲𝐔𝐂 = 𝐲𝛍 + 𝑖ℎ𝐲𝛔 = 𝐐𝔼 ′ 𝐲𝐄𝐁𝐕 + ( Φ−1(1 − 𝑝) 𝑝 ) ℎ𝐲𝛔, where all terms have been previously described for UCS. Inbreeding in UCPCS is calculated as a measure of kinship. The kinship matrix relating pairs of mating configurations to each other can be calculated as: 𝐊𝛀 = 𝐐𝐏𝐒 ′ 𝐊𝐐𝐏𝐒 Where 𝐊𝛀 is a 𝑁Ω × 𝑁Ω mating configuration kinship matrix, 𝐐𝐏𝐒 is a 𝑁 × 𝑁Ω transformation matrix containing post-selection parental contributions for each of 𝑁Ω mating configurations, and 58 𝐊 is an 𝑁 × 𝑁 parental kinship matrix calculated method. The transformation matrix 𝐐𝐏𝐒 has two restrictions. First, elements must be in the range of 0 to 1, (𝑞𝑃𝑆)𝑖,𝑗 ∈ [0,1] ∀𝑖, 𝑗. Second, columns must sum to unity, 𝐐𝐏𝐒 ′ 𝟏𝐍 = 𝟏|𝛀|. Elements of 𝐐𝐏𝐒 are assigned as 0 if the parent was not used in the mating configuration or according to the estimated post-selection genome contribution for each parent in a mating configuration. Estimated post-selection genome contributions are calculated using the formulae in Allier et al., (2019a). 4.24.2. Formulation as an optimization problem In UCPCS, the candidate set Ω is defined as the set of mating configurations the breeder considers for selection. From this candidate set, 𝑁Ξ crosses are selected to form a selection set Ξ. Mathematically, OCS is an LPQC-type problem and is defined as: Such that: max 𝐱 ′ 𝐱 𝐲𝐔𝐂 1 − 1 2 𝐱′𝐊𝛀𝐱 ≥ 𝐻𝑒(𝓉) 𝑁Ξ 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝐻𝑒(𝓉) is a function determining the mean expected heterozygosity constraint at generation 𝓉 defined by the user. 4.24.3. Performance as a selection strategy In their simulations, Allier et al. (2019a) gradually decreased the desired population diversity over time according to a defined linear diversity trajectory 𝐻𝑒(𝓉). Depending on the diversity trajectory, UCPC outperformed phenotypic selection, UCS, and OCS in long-term genetic gain (Allier, Lehermeier, et al., 2019). In short-term gain, UCS performed better than 59 phenotypic selection, OCS, and UCPC (Allier, Lehermeier, et al., 2019). In their study, Allier et al. (2019a) noted that UCPC could be improved by optimizing two additional parameters: the trajectory of 𝐻𝑒(𝓉) and the number of progenies produced by a given family. These questions were not addressed in their study and remain active areas of research. 4.25. Multi-trait look-ahead selection (MT-LAS) (2020) 4.25.1. Background Multi-trait look-ahead selection (MT-LAS) is a multi-trait generalization of LAS proposed by Moeinizade et al. (2020). Like its predecessor, it is a progenitive population selection strategy that uses computer simulation to identify a subset of mating configurations that maximize the 100𝛾th percentile GEBV for a single, primary trait while meeting GEBV constraints for one or more secondary traits. MT-LAS uses a dynamic penalty function to automatically adjust the objective function in response to boundary violations (Moeinizade et al., 2020). This reduces the optimization challenge and allows for improvements to be made in the primary trait while tolerating small violations for the secondary traits. 4.25.2. Formulation as an optimization problem The mathematical formulation of MT-LAS is like that of LAS. As before, the candidate set Ω is defined as the set of considered mating configurations. In Moeinizade et al. (2020), this was defined as the set of two-way crosses for a set of parental candidates. From this candidate set, 𝑁Ξ mating configurations are selected to form a selection set Ξ. There are two ways to mathematically formulate MT-LAS: the first formulation uses conditional probabilities, and the second formulation uses a dynamic penalty function instead of conditional probabilities. The conditional probability formulation is defined as: max 𝐱 𝜓 60 Such that: P[𝑔1(𝐱, 𝐫, 𝒯 − 𝓉) ≥ 𝜓|𝑙𝑡 ≤ 𝑔𝑡(𝐱, 𝐫, 𝒯 − 𝓉) ≤ 𝑢𝑡 ∀𝑡 ∈ {2,3, … , 𝑇}] ≥ 1 − 𝛾 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝛾 defines the GEBV percentile of the simulated progenies used to evaluate a proposed mating configuration subset, 𝜓 is a threshold value representing the GEBV of the 100𝛾th percentile simulated individual, P[⋅] is the probability function, 𝑔1(𝐱, 𝐫, 𝒯 − 𝓉) is a random variable representing the GEBVs of progenies derived from the proposed mating configuration subset 𝐱 for the primary trait, given recombination probabilities 𝐫 and remaining generations 𝒯 − 𝓉, 𝑔𝑡(𝐱, 𝐫, 𝒯 − 𝓉) ∀𝑡 ∈ {2,3, … , 𝑇} are random variables representing the GEBVs of progenies derived from the proposed mating configuration subset 𝐱 for the 𝑡 = 2,3, … , 𝑇 secondary traits, given recombination probabilities 𝐫 and remaining generations 𝒯 − 𝓉, 𝑙𝑡 is the lower bound for the 𝑡th secondary trait, and 𝑢𝑡 is the upper bound for the 𝑡th secondary trait. Without loss of generality, lower and upper bounds may be assigned as 𝑙𝑡 = −∞ or 𝑢𝑡 = ∞ to specify conditions when only upper or lower bounds should be considered, respectively. Since the above formulation is computationally challenging to optimize owing to its non- linear and non-convex constraints, Moeinizade et al. (2020) reformulated MT-LAS using a dynamic penalty function instead. The dynamic penalty version of MT-LAS is stated as follows: Such that: max 𝐱 𝜓 P[ℎ(𝐱, 𝐫, 𝒯 − 𝓉) ≥ 𝜓] ≥ 1 − 𝛾 𝟏′𝐱 = 𝐽 𝐱 ∈ 𝔹𝑁Ω, 61 where ℎ(𝐱, 𝐫, 𝒯 − 𝓉) is a random variable representing penalized GEBVs of progenies derived from the proposed mating configuration subset 𝐱, given recombination probabilities 𝐫 and remaining generations 𝒯 − 𝓉. Penalized GEBVs for progenies are calculated as: 𝑇 ℎ(𝐱, 𝐫, 𝒯 − 𝓉) = 𝜃1𝑔1(𝐱, 𝐫, 𝒯 − 𝓉) − ∑ 𝑡=1 1 − 𝜃𝑡 𝑇 − 1 Δ𝑡 where 𝜃𝑡 is the probability that a random progeny meets the constraints for the 𝑡th trait, calculated as 𝜃𝑡 = P[𝑙𝑡 ≤ 𝑔𝑡(𝐱, 𝐫, 𝒯 − 𝓉) ≤ 𝑢𝑡], 𝜃1 is the weight assigned to the primary trait, calculated as 𝜃1 = 1 𝑇−1 ∑ 𝑇 𝑡=2 𝜃𝑡 , Δ𝑡 is the penalty for violating the constraint for the 𝑡th secondary trait, calculated as Δ𝑡 = max(𝑔𝑡(𝐱, 𝐫, 𝒯 − 𝓉) − 𝑢𝑡, 𝑙𝑡 − 𝑔𝑡(𝐱, 𝐫, 𝒯 − 𝓉), 0) 4.25.3. Performance as a selection strategy MT-LAS was found to achieve higher long-term genetic gain and genetic diversity compared to index and penalized index selection strategies (Moeinizade et al., 2020). 4.26. Present value look-ahead selection (PV-LAS) (2022) 4.26.1. Background Present value look-ahead selection (PV-LAS) is a variant of LAS (Moeinizade et al., 2019) proposed by Zhang and Wang (2022). Like its predecessor, it is a progenitive population selection strategy that uses computer simulations to evaluate the merit of proposed mating configuration subsets. PV-LAS seeks to address two shortcomings of LAS. The first addressed shortcoming is the difficulty of assigning a breeding deadline (Zhang & Wang, 2022). Breeding programs usually aim to generate continuous genetic gains indefinitely and consequently do not have fixed deadlines. The second shortcoming PV-LAS seeks to address is the unacceptably low genetic gains produced by LAS in early generations (Zhang & Wang, 2022). LAS underperforms other established selection strategies in early generations, reserving major genetic gains for later 62 generations (Moeinizade et al., 2019). This feature of LAS is undesirable since short-term genetic gains that can be translated into new commercial products are often preferrable to long- term genetic gains with poor short-term performance (Zhang & Wang, 2022). To address these shortcomings, the Zhang and Wang (2022) use the financial concept of present value to improve upon LAS. Briefly, present value in finance calculates the current value of a future sum of money, provided a discount rate. Present value posits that money is worth more in the present than in the future and aims to quantify the time value of money. The present value 𝑃𝑉 of a set of cash flows 𝑓𝜏 over time periods 𝜏 ∈ {1, … , 𝑊} can be calculated as: 𝑃𝑉 = ∑ 𝑊 𝜏=1 𝑓𝜏 (1+𝜆)𝜏 where 𝜆 is the discount rate (Weitzman, 1998; Žižlavský, 2014). PV-LAS applies the present value formula over a window of progeny values derived from breeding simulations to maximize the present value of a mating configuration subset. This solves the deadline specification issue by converting it to a question of window size and discount rate – which may be easier to define – and solves the short-term genetic gain issues in LAS by emphasizing genetic gains in the near future, even if they come at a slight cost of long-term gains. 4.26.2. Formulation as an optimization problem The mathematical formulation of MT-LAS is like its LAS predecessor. As in LAS, the candidate set Ω in PV-LAS is defined as the set of mating configurations which are to be considered. In Zhang and Wang (2022), this is defined as the set of self- and two-way crosses for the set of parental candidates. From this candidate set, 𝑁Ξ mating configurations are selected to form a selection set Ξ. Mathematically, PV-LAS is defined as: Such that: max 𝐱 W ∑ 𝜏=1 𝜓𝜏 (1 + 𝜆)𝜏 63 P[𝑔1(𝐱, 𝐫, 𝜏) ≥ 𝜓𝜏] ≥ 1 − 𝛾 ∀𝜏 ∈ {1, … , 𝑊} 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, where 𝛾 defines the GEBV percentile of the simulated progenies used to evaluate a proposed mating configuration subset, 𝜏 is the number of generations into the future, 𝑊 is the window size used to calculate the present value, 𝜓𝜏 is a threshold value representing the GEBV of the 100𝛾th percentile simulated individual for 𝜏 generations into the future, P[⋅] is the probability function, and 𝑔1(𝐱, 𝐫, 𝜏) is a random variable representing the GEBVs of progenies derived from the proposed mating configuration subset 𝐱 for the first (and only) trait, given a set of recombination probabilities 𝐫 and for 𝜏 generations into the future. 4.26.3. Performance as a selection strategy Given an appropriate window size and discount rate, Zhang and Wang (2022) found that PV-LAS outperformed LAS and CGS in its ability to generate genetic gains as measured by their present values. These genetic gains, however, came at the cost of genetic diversity (Zhang & Wang, 2022). 4.27. L-shaped selection (LSS) (2022) 4.27.1. Background L-shaped selection (LSS) is a multi-trait, parental selection strategy proposed by Amini et al. (2022). LSS seeks to address two shortcomings of linear index selection techniques. Amini et al. (2022) noted that linear index selection techniques may be sensitive to the units assigned to traits in a multi-trait selection scenario. For example, changing units from bushels per acre to tonnes per hectare may radically change the linear weights needed to achieve the same index selection goal (Amini et al., 2022). Additionally, linear index selection techniques are incapable 64 of finding all Pareto optimal selection solutions due to the convexity of the linear index (Amini et al., 2022). To remedy these two problems, Amini et al. (2022) constructed a non-linear index which uses normalized genetic values as inputs. Normalized genetic values for the 𝑡th trait, 𝐲̃𝐄𝐁𝐕,𝑡 ′ , are calculated as: (𝑦̃𝐸𝐵𝑉,𝑡) = 𝑛 (𝑦𝐸𝐵𝑉,𝑡) − 𝑦𝑚𝑖𝑛,𝑡 𝑛 𝑦𝑚𝑎𝑥,𝑡 − 𝑦𝑚𝑖𝑛,𝑡 ∀𝑛 ∈ {1, … , 𝑁Ω}, where (𝑦̃𝐸𝐵𝑉,𝑡) 𝑛 is the 𝑛th normalized genetic value for the 𝑡th trait, (𝑦𝐸𝐵𝑉,𝑡) is the 𝑛th genetic 𝑛 value for the 𝑡th trait, 𝑦𝑚𝑖𝑛,𝑡 is the minimum genetic value for the 𝑡th trait calculated as 𝑦𝑚𝑖𝑛,𝑡 = min 𝑛 ((𝑦𝐸𝐵𝑉,𝑡) 𝑛 − 𝜖) ∀𝑡 ∈ {1, … , 𝑇}, and 𝑦𝑚𝑎𝑥,𝑡 is the maximum genetic value for the 𝑡th trait calculated as 𝑦𝑚𝑎𝑥,𝑡 = max 𝑛 ((𝑦𝐸𝐵𝑉,𝑡) 𝑛 + 𝜖) ∀𝑡 ∈ {1, … , 𝑇}. The minimum and maximum genetic values have a small positive value 𝜖 subtracted or added, respectively, to ensure that normalized genetic values fall within the range (0,1) and not along the boundaries (Amini et al., 2022). 4.27.2. Formulation as an optimization problem In LSS, the candidate set Ω is defined as the set of individuals in a breeding population which are to be considered for selection. From this candidate set, 𝑁Ξ individuals are selected to form a selection set Ξ. Mathematically, LSS is defined as: Such that: max 𝐱 min 𝑡 1 𝑤𝑡 ′ 𝐲̃𝐄𝐁𝐕,𝑡 𝐱 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω, 65 where 𝐲̃𝐄𝐁𝐕,𝑡 ′ is a vector of length 𝑁Ω containing normalized genetic values for the 𝑡th trait and 𝑤𝑡 is the weight applied to the 𝑡th trait. 4.27.3. Performance as a selection strategy LSS was reported to improve multi-trait selection in both its Pareto optimality and the diversity of its generated progeny compared to index selection (Amini et al., 2022). 5. Selection strategy insights and proposed new areas of research In the preceding section, we reviewed 27 different selection strategies presented in the literature and cast them as numerical optimization problems. The numerical optimization problems for these reviewed selection strategies were diverse, ranging from simple deterministic, linear problems to stochastic, non-linear problems. Table 1.3 summarizes the reviewed methods. In the following subsections, we discuss patterns of performance for selection strategies, remark on the mathematical interconnectedness of several of the reviewed selection strategies, and suggest new avenues of selection strategy research. 5.1. Remarks on formulating an ideal selection strategy Perhaps the most pertinent question for a breeder is: what selection strategy should I use for my breeding program? But more broadly: what is an ideal selection strategy? Among the reviewed selection strategies, several patterns emerge. First, progenitive and progenitive- population selection strategies typically outperform their parental and parental-population selection strategy counterparts. This makes sense logically. Suppose we select 10 parents and seek to pair them to make 5 two-way crosses. Regardless of how we pair our parents, the expected mean of the progenies remains is equivalent to the mean of the parents and remains constant. However, assuming our parents have varying degrees of relatedness, how we pair them affects the variance of the progenies. Generally, progenies resulting from a cross between two 66 highly related parents will be less variable than progenies resulting from a cross between two nominally related parents. If we can maximize the variance of our progenies, we can select individuals with more extreme phenotypes. Optimized assignment of parents to specific mating configurations, even if small in effect, adds up over time and contributes to long-term genetic gain. Therefore, an ideal selection strategy should select specific mating configurations and not simply individuals. Second, parental-population and progenitive-population selection strategies typically outperform their parental and progenitive selection strategy counterparts in the long-term. This is because they take into consideration some measure of population genetic diversity through their non-linear objectives and/or constraints. Since maintaining genetic diversity is crucial for sustaining genetic gains, parental-population and progenitive-population selection strategies produce better results long-term. Better long-term performance through improved diversity maintenance often comes at the cost of short-term genetic gain, so these tradeoffs must be considered by the breeder. Finally, selection strategies that are cognizant of time perform typically better than those that are agnostic of time. This observed pattern may be partially attributable to the finite-length simulation scenarios used to test selection strategies, but it also speaks to a deeper truth: genetic diversity is only relevant with respect to a time horizon. If a breeding time horizon is short, we should immediately and maximally exploit our genetic diversity to attain a high performance. If a breeding time horizon is long, we should be more conservative in our exploitation of genetic diversity, preserving it so that we might attain a high performance many generations into the future. 67 In summary, a time-cognizant, progenitive-population selection strategy is an ideal long- term selection strategy. These types of selection strategies take into consideration the merit of progenies produced from specific mating configurations, incorporate a measure of genetic diversity into their evaluation mechanisms, and determine selection decisions within the context of a finite time horizon. These three attributes are necessary for the long-term success of breeding programs. 5.2. Remarks on diversity preservation mechanisms Efforts to preserve genetic diversity in selection strategies fall into four approaches: allele upweighting, coancestry-constrained, haplotype-based, and simulation-based approaches. Of the four approaches, allele upweighting is perhaps the easiest and most computationally efficient. Coancestry-constrained approaches are also easy to apply, but more computationally expensive than allele upweighting methods. Haplotype-based approaches vary in their ease of application and computational challenge, ranging from being similar in complexity to allele upweighting to more challenging than coancestry-constrained approaches. Finally, simulation-based approaches are the most difficult to implement and the most computationally challenging among the four diversity preservation approaches. For large breeding programs, allele upweighting or coancestry-constrained diversity preservation strategies are perhaps the most practical and computationally tractable. Indeed, animal breeding programs have extensively used coancestry- constrained based diversity preservation techniques (Kohl et al., 2020; Nielsen et al., 2011; Pryce et al., 2012; Schierenbeck et al., 2011; Sørensen et al., 2008; Wang et al., 2017). 5.3. Remarks on search spaces and extending selection strategies to new search domains In the reviewed selection strategies above, there are broadly three search spaces used: 𝔹𝑁Ω, ℤ+ 𝑁Ω, and ℝ+ 𝑁Ω. These three search spaces have the following relationship to each other: 68 𝔹𝑁Ω ⊆ ℤ+ 𝑁Ω ⊆ ℝ+ 𝑁Ω. This suggests that some selection strategies originally designed to operate in one search space will also work in subsets of the original search space. For example, OCS and GOCS can easily be converted from their native search spaces of ℝ+ 𝑁Ω to ℤ+ 𝑁Ω or 𝔹𝑁Ω by altering the vector summation to 𝟏′𝐱 = 𝑁Ξ where 𝑁Ξ is some number of individuals to be selected. Indeed, this has been done in GM, MT-GM, and UCPCS where the optimization problem formulations are like those of OCS and GOCS but operate in binary-valued search spaces as opposed to real-valued search spaces. It should be noted that changing the search space may also change the difficulty of the problem in question. Using OCS and GOCS as examples again, OCS and GOCS are convex optimization problems that can be solved relatively easily using established algorithms (Dantzig, 1963; Potra & Wright, 2000). If the search spaces for OCS and GOCS are changed to be binary- or integer-valued, the optimization challenge substantially increases because the search space is now discrete thereby making the optimization problem non-convex. While narrowing a selection strategy’s search space to consider a subset of the original search space is relatively easy to do, expanding a selection strategy’s search space may not be logical or helpful to do. For example, many of the index-type selections strategies like OIS, BIS, etc. assume a binary-valued search space which represents the selection of discrete individuals. If we expand the search space to be real-valued, interpreting the decision vector as representing parental contributions, it is easy to see that the optimal solution would be to allocate all the contribution to the best individual. This result is unhelpful and illogical to do in the context of a breeding program. 69 5.4. Weighted 𝑳𝒑-norm distance metrics to describe selection strategies All selection strategies seek to alter allele frequencies in a breeding population to drive improvement towards a specific breeding goal or goals. We propose that for several reviewed selection strategies, weighted 𝐿𝑝-norm distance metrics can be used to describe the breeding objective or objectives. Specifically, we propose that the weighted 𝐿𝑝-norm of the difference between the selection allele frequencies and target allele frequencies describes the objectives of several of the reviewed selection strategies. This 𝐿𝑝-norm distance is mathematically defined as: 𝑀 ‖𝛑 − 𝛕‖𝑝|𝐰 = (∑ 𝑤𝑚|𝜋𝑚 − 𝜏𝑚|𝑝 𝑚=1 1/𝑝 ) , where ‖∙‖𝑝|𝐰 denotes the weighted 𝐿𝑝-norm for a set of weights, 𝛑 is a selection allele frequency vector of length 𝑀, 𝜋𝑚 ∈ [0,1] is the selection allele frequency at the 𝑚th locus, 𝛕 is a target allele frequency vector of length 𝑀, 𝜏𝑚 ∈ [0,1] is the target allele frequency at the 𝑚th locus, 𝐰 is a weight vector of length 𝑀, 𝑤𝑚 ≥ 0 is the weight assigned to the 𝑚th locus, and 𝑝 is the order of the weighted 𝐿𝑝-norm. 5.4.1. Conventional genomic selection and its variants as weighted 𝑳𝟏-norm distance minimization problems In this section, we propose and provide proof that CGS and its variants like WGS and DWGS can be expressed as weighted 𝐿1-norm minimization problems. This indicates that CGS and its variants attempt to minimize a weighted Manhattan distance between the selection allele frequency and a target allele frequency, namely fixation of the favorable allele. As reviewed above, CGS and its variants have the optimization problem form as: Such that: max 𝐱 𝑓(𝐱) = 𝐲𝐁𝐕 ′ 𝐱 70 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω Breeding values, 𝐲𝐁𝐕 are calculated according to markers and some linear index 𝐲𝐁𝐕 = 𝐙𝐮̃, where 𝐙 ∈ {0,1,2, … , Φ}𝑁Ω×𝑀 represents a genotype matrix counting the number of alleles designated ‘1’ for the 𝑁th individual for the 𝑀th locus, so the problem objective can be expressed as: 𝑓(𝐱) = 𝐮̃′𝐙′𝐱 𝐙′𝐱 calculates the number of ‘1’ alleles for the selection decision vector 𝐱. If we scale 𝑍′𝑥 by inverse of the product of the ploidy and the number of selected individuals, 1 Φ𝐽 , then we have calculated the selection allele frequency 𝛑. The problem objective becomes: 𝑓(𝐱) = 𝐮̃′𝐙′𝐱 = (Φ𝑁Ξ)𝐮̃′ ( 1 Φ𝑁Ξ ) 𝐙′𝐱 = Φ𝑁Ξ𝐮̃′𝛑 𝑀 = Φ𝑁Ξ ∑ 𝑢̃𝑚𝜋𝑚 𝑚=1 By the ordering property of real numbers, we know that maximizing a function is equivalent to minimizing the negated function, max 𝐱 𝑓(𝐱) ≡ min 𝐱 −𝑓(𝐱). Additionally, we also know that in an optimization problem scaling by a constant factor 𝜆 and shifting by a constant factor 𝜅 results in the same solution, min 𝐱 𝑓(𝐱) ≡ min 𝐱 𝜆𝑓(𝐱) + 𝜅. With these two facts, we can rewrite the above as: 𝑀 max 𝐱 𝑓(𝐱) ≡ min 𝐱 Φ𝑁Ξ ∑ −𝑢̃𝑚𝜋𝑚 𝑚=1 71 𝑀 ≡ min 𝐱 𝜆 ( ∑ −𝑢̃𝑚𝜋𝑚 ) + 𝜅 𝑚=1 For constants 𝜆 = Φ𝑁Ξ and 𝜅 = 0. Now, we divert our attention to the weighted 𝐿1-norm metric to see if we can cast its minimization to the same form as above. We first start by noting that: 𝑀 ‖𝛑 − 𝛕‖1|𝐰 = (∑ 𝑤𝑚|𝜋𝑚 − 𝜏𝑚|1 𝑚=1 1/1 ) 𝑀 = ∑ 𝑤𝑚|𝜋𝑚 − 𝜏𝑚| 𝑚=1 In CGS and its variants, we seek to fix all favorable alleles and purge all deleterious alleles. The target allele frequencies 𝛕 can be used to encode this preference information in this metric. We begin by splitting markers into a favorable set ℱ and a deleterious set 𝒟. If the ‘1’ allele at the 𝑚th locus is favorable, 𝑢̃𝑚 ≥ 0, then we put it into the favorable set and assign the target allele frequency as complete fixation of the ‘1’ allele, 𝜏𝑚 = 1. If the ‘1’ allele at the 𝑚th locus is deleterious, 𝑢̃𝑚 < 0, then we put it into the deleterious set and assign the target allele frequency as complete fixation of the ‘0’ allele, 𝜏𝑚 = 0. We let the weight designated to each marker be determined as 𝑤𝑚 = |𝑢̃𝑚|. Thus, the 𝐿1-norm metric can be expressed as: ‖𝛑 − 𝛕‖1|𝐰 = ∑ 𝑤𝑚|𝜋𝑚 − 0| 𝑚∈ℱ + ∑ 𝑤𝑚|𝜋𝑚 − 1| 𝑚∈𝒟 For each locus, if 𝜏𝑚 = 0, then 𝑤𝑚|𝜋𝑚 − 0| = { 𝑖𝑓 (𝜋𝑚 − 0) ≥ 0 𝑤𝑚𝜋𝑚 −𝑤𝑚𝜋𝑚 𝑖𝑓 (𝜋𝑚 − 0) < 0 72 Since we know that the allele frequency is between 0 and 1, 𝜋𝑚 ∈ [0,1], the latter condition becomes impossible. Furthermore, we know that 𝑤𝑚 = −𝑢̃𝑚 since 𝑢̃𝑚 < 0. The expression simplifies to: At a locus, if 𝜏𝑚 = 1, then 𝑤𝑚|𝜋𝑚 − 0| = 𝑤𝑚𝜋𝑚 = −𝑢̃𝑚𝜋𝑚 𝑤𝑚|𝜋𝑚 − 1| = { 𝑖𝑓 (𝜋𝑚 − 1) ≥ 0 𝑤𝑚𝜋𝑚 − 𝑤𝑚 −𝑤𝑚𝜋𝑚 + 𝑤𝑚 𝑖𝑓 (𝜋𝑚 − 1) < 0 Again, since we know that 𝜋𝑚 ∈ [0,1], the former condition becomes impossible. Furthermore, we know that 𝑤𝑚 = 𝑢̃𝑚 since 𝑢̃𝑚 ≥ 0. The expression simplifies to: 𝑤𝑚|𝜋𝑚 − 1| = −𝑤𝑚𝜋𝑚 + 𝑤𝑚 = −𝑢̃𝑚𝜋𝑚 + 𝑢̃𝑚 We substitute these two facts into the modified 𝐿1-norm metric to get: ‖𝛑 − 𝛕‖1|𝐰 = ∑ 𝑤𝑚|𝜋𝑚 − 0| 𝑚∈ℱ + ∑ 𝑤𝑚|𝜋𝑚 − 1| 𝑚∈𝒟 = ∑ −𝑢̃𝑚𝜋𝑚 + ∑ (−𝑢̃𝑚𝜋𝑚 + 𝑢̃𝑚) 𝑚∈ℱ 𝑚∈𝒟 + ∑ 𝑢̃𝑚 𝑚∈𝒟 = ∑ −𝑢̃𝑚𝜋𝑚 + ∑ −𝑢̃𝑚𝜋𝑚 𝑚∈ℱ 𝑀 = ∑ −𝑢̃𝑚𝜋𝑚 𝑚=1 𝑀 𝑚∈𝒟 + ∑ 𝑢̃𝑚 𝑚∈𝒟 = 𝜆 (∑ −𝑢̃𝑚𝜋𝑚 𝑚=1 ) + 𝜅 For constants 𝜆 = 1 and 𝜅 = ∑ 𝑚∈𝒟 𝑢̃𝑚 . 73 Thus, optimization for CGS and its variants is a special case of minimizing of the weighted 𝐿1-norm distance metric where marker weights are assigned according to the absolute value of the marker effects and target allele frequencies are assigned as 1 for the favorable allele and 0 for the deleterious allele. 5.4.2. Inbreeding control and its variants as weighted 𝑳𝟐-norm distance minimization problems It is popular to control inbreeding using a quadratic function of a relationship matrix 𝐑 defining the relatedness between selection candidates as either an objective or constraint in a selection optimization problem. Specifically, this quadratic function is defined as: 𝑓(𝐱) = 𝐱′𝐑𝐱 where 𝐱 is a decision vector of length 𝑁 satisfying 𝟏𝐍 ′ 𝐱 = 1 and 𝑥𝑖 ≥ 0 ∀𝑖, and 𝐑 is a 𝑁 × 𝑁 positive, (semi-)definite relationship matrix. The relationship matrix in this function can be an additive relationship matrix 𝐀, a kinship matrix 𝐊, or a genomic relationship matrix 𝐆. The common interpretation of this quadratic function is that it represents the mean or a multiple of the mean additive, kinship, or genomic relationship for a proposed selection decision. Here, we propose that this quadratic function can alternatively, and perhaps more precisely, be interpreted as the squared weighted 𝐿2-norm distance between a selection allele frequency vector and a target allele frequency or utopian vector. Mathematically, this is stated as: min 𝐱 𝐱′𝐑𝐱 ≡ min 𝐱 ‖𝛑 − 𝛕‖2|𝐰 2 The proof for this assertion is straightforward and involves simple expansion of the definition of the weighted 𝐿2-norm. To begin, we start with the squared weighted 𝐿2-norm definition and put it into matrix notation: 𝑀 ‖𝛑 − 𝛕‖2|𝐰 2 = ∑ 𝑤𝑚(𝜋𝑚 − 𝜏𝑚)2 𝑚=1 74 = (𝛑 − 𝛕)′𝐃𝐰(𝛑 − 𝛕) Where weights assigned to each marker are represented by the diagonal matrix 𝐷𝑤. As seen in the 𝐿1-norm proof, we can represent the selection allele frequency vector as 𝛑 = ( 1 Φ𝑁Ξ ) 𝐙′𝐱. We substitute this value into the expression and rearrange some of the terms. ‖𝛑 − 𝛕‖2|𝐰 2 = (𝛑 − 𝛕)′𝐃𝐰(𝛑 − 𝛕) = (( 1 Φ𝑁Ξ ′ ) 𝐙′𝐱 − 𝛕) 𝐃𝐰 (( 1 Φ𝑁Ξ ) 𝐙′𝐱 − 𝛕) = ( 2 ) 1 Φ𝑁Ξ (𝐙′𝐱 − 𝛕)′𝐃𝐰(𝐙′𝐱 − 𝛕) Since we know that 𝟏𝐍 ′ 𝐱 = 1, we can multiply 𝛕 by 𝟏𝐍 ′ 𝐱 and continue simplifying: ‖𝛑 − 𝛕‖2|𝐰 2 = ( 2 ) 1 Φ𝑁Ξ (𝐙′𝐱 − 𝛕)′𝐃𝐰(𝐙′𝐱 − 𝛕) = ( 2 ) 1 Φ𝑁Ξ = ( 2 ) 1 Φ𝑁Ξ = ( 2 ) 1 Φ𝑁Ξ (𝐙′𝐱 − 𝛕𝟏𝐍 ′ 𝐱 )′𝐃𝐰(𝐙′𝐱 − 𝛕𝟏𝐍 ′ 𝐱 ) ((𝐙′ − 𝛕𝟏𝐍 ′ )𝐱) ′ 𝐃𝐰((𝐙′ − 𝛕𝟏𝐍 ′ )𝐱) 𝐱′(𝐙 − 𝟏𝐍𝛕′)𝐃𝐰(𝐙 − 𝟏𝐍𝛕′)′𝐱 The 𝐙 − 𝟏𝐍𝛕′ and 𝐃𝐰 terms are of particular interest. If we allow 𝛕 to represent the mean allele frequency of the selection candidate population and 𝐃𝐰 to be an identity matrix 𝐈, then the calculation of (𝐙 − 𝟏𝐍𝛕′)𝐃𝐰(𝐙 − 𝟏𝐍𝛕′)′ is proportional to a genomic relationship matrix calculated using the VanRaden method (VanRaden, 2008). If 𝛕 = 𝟏/𝟐 and 𝐃𝐰 = 𝐈, then the metric is proportional to an identity-by-state kinship matrix (Allier, Lehermeier, et al., 2019). Finally, if 𝛕 contains the mean allele frequencies of the selected set and 𝐃𝐰 contains squared 75 marker effects, then the metric is proportional to a weighted VanRaden genomic relationship matrix (Fragomeni et al., 2017; VanRaden, 2008). Continuing, if we let 𝐙̃ = 𝐙 − 𝟏𝐍𝛕′ represent a target centered marker matrix and 𝐑𝐰 represent a weighted marker target relationship matrix, then the weighted 𝐿2-norm metric simplifies to the familiar quadratic form: ‖𝛑 − 𝛕‖2|𝐰 2 = ( 1 Φ𝑁Ξ = ( 1 Φ𝑁Ξ = ( 1 Φ𝑁Ξ 2 ) 2 ) 2 ) 𝐱′(𝐙 − 𝟏𝐍𝛕′)𝐃𝐰(𝐙 − 𝟏𝐍𝛕′)′𝐱 𝐱′𝐙̃𝐃𝐰𝐙̃ ′𝐱 𝐱′𝐑𝐰𝐱 = 𝜆𝐱′𝐑𝐰𝐱 + 𝜅 For 𝜆 = ( 2 1 Φ𝑁Ξ ) and 𝜅 = 0. Since scaling and shifting an objective function does not change the nature of an optimization problem, then it can be said that minimizing the squared weighted 𝐿2-norm distance between a selection allele frequency vector and a target allele frequency vector is equivalent to minimizing a corresponding quadratic function: min 𝐱 ‖𝛑 − 𝛕‖2|𝐰 2 ≡ min 𝐱 𝐱′𝐑𝐱 This result has important implications for breeding optimizations. The equivalence of these two optimization functions means that the way an additive, kinship, or genomic relationship is calculated determines the target allele frequencies which the optimization is attempting to achieve. For example, using a VanRaden genomic relationship matrix means that the optimization is attempting to select a subset of individuals which have allele frequencies as close as possible to the current population allele frequencies. If an identity-by-state kinship 76 matrix is used, then the optimization is attempting to select a subset of individuals which have allele frequencies as close as possible to 0.5. Finally, if a weighted VanRaden genomic relationship matrix is used, then the optimization is attempting to maintain current allele frequencies using weights to determine the preference strength for each allele. 5.4.3. Beyond weighted 𝑳𝟏- and 𝑳𝟐-norm distance metrics As elucidated above, objectives and constraints in several established selection strategies can be transformed into weighted 𝐿1- or 𝐿2-norm distance minimization problems. To our knowledge, only weighted 𝐿1-, and 𝐿2-norms have been used to design selection criteria, which means that there are many more weighted 𝐿𝑝-norms which can be explored for use in selection. We suggest that due to the gradient of the norm metric, weighted 𝐿𝑝-norms where 𝑝 ≥ 1 will prove most useful for selection, including those with non-integer 𝑝 constants. We speculate that weighted 𝐿𝑝-norms with 1 < 𝑝 < 2 may produce hybrid selection strategies that balance genetic gain and genetic diversity nicely. We also speculate that weighted 𝐿3- and 𝐿4-norms may prove useful as diversity maintenance functions since their curvatures and allele loss penalizations are more extreme than that of the 𝐿2-norm. In application of weights, we suggest that weights should be assigned as 𝑤𝑚 = |𝑢̃𝑚|𝑝 where 𝑢̃𝑚 is the marker effect. Thus the 𝐿𝑝-norm metric becomes: 𝑀 ‖𝛑 − 𝛕‖𝑝|𝐰 𝑝 = ∑ 𝑤𝑚|𝜋𝑚 − 𝜏𝑚|𝑝 𝑚=1 𝑀 = ∑ |𝑢̃𝑚|𝑝|𝜋𝑚 − 𝜏𝑚|𝑝 𝑚=1 77 5.5. Relationship between EMBVS and UCS The evaluation of expected maximum breeding values for use in EMBVS can be particularly computationally expensive, especially if the number of mating configurations is large and the number of simulated progenies is large. We propose that if progeny trait values are assumed to be normally distributed, then expected maximum breeding values are directly proportional to the usefulness criterion for some selection intensity. Computationally expensive progeny simulations can be exchanged for potentially less expensive progeny variance calculations (Allier, Moreau, et al., 2019). Below is the proof for this proposition. Let 𝑋 be a random variable drawn from 𝑁(𝜇, 𝜎) representing the breeding values of progenies for a specific mating configuration. Let 𝑋𝑟,𝑛 be a random variable representing the 𝑟th order statistic for a sample of size 𝑛 drawn from 𝑁(𝜇, 𝜎). Values of 𝑋𝑟,𝑛 represent the 𝑟th best breeding value resulting from a mating configuration. The expected value of 𝑋𝑟,𝑛 is defined as: E[𝑋𝑟,𝑛] = 𝑛! (𝑟 − 1)! (𝑛 − 𝑟)! ∞ ∫ 𝑥(1 − F(𝑥)) −∞ 𝑟−1 F(𝑥)𝑛−𝑟𝑓(𝑥)𝑑𝑥 , where F(⋅) is the cumulative distribution function for the distribution 𝑁(𝜇, 𝜎) and 𝑓(⋅) is the probability density function for the distribution 𝑁(𝜇, 𝜎). To calculate the expected maximum breeding value for 𝑛 progenies derived from a mating configuration, we can calculate E[𝑋1,𝑛]. If we standardize this expected value with respect to the mean and variance of the distribution from which it is drawn, we arrive at the familiar form for the usefulness criterion: 𝑣 = E[𝑋1,𝑛] − 𝜇 𝜎 E[𝑋1,𝑛] = 𝜇 + 𝑣𝜎 78 In other words, if progeny values can be assumed to follow a normal distribution, there is a 1 to 1 correlation between the expected maximum breeding value and the usefulness criterion. Now, the question becomes whether a normality assumption is appropriate. Simulation studies have revealed that progeny breeding value distributions are very close to normal for quantitative traits (Bernardo, 2022). Progeny distributions do appear to exhibit slightly less kurtosis compared to a normal distribution (Bernardo, 2022), but practically speaking, this deviation is negligible. Collectively, these findings mean that UCS can be used as a potentially faster alternative to EMBVS. 5.6. Mating configuration resource allocation To date, there has been little research focusing on optimizing resource allocations for specific mating configurations. Hunter and McClosky (2016) explicitly worked on resource allocation for mating configurations and Moeinizade et al. (2019) proposed a mating configuration resource allocation heuristic. Additionally, integer variants of OCS for mating configurations have been used, but not extensively studied (Gorjanc et al., 2018a). To our knowledge, mating configuration resource allocation remains an underexplored topic of research. Continued research in this area would be very helpful to the breeding community as it would provide breeders with targeted insights on how to allocate resources to specific mating configurations. Improved resource allocation could also lead to enhanced long-term genetic gain or better maintenance of diversity. 6. Conclusion In this review article, we have reviewed 27 different selection strategies, ranging from simple index selection strategies, to complex, simulation-based, mating configuration optimization strategies. From the surveyed literature, we find that time-cognizant, progenitive- 79 population selection strategies are among the best selection strategies for long-term genetic gain. These selection strategies take into consideration the merits of progenies produced from specific mating configurations rather than simply the merits of parental candidates and incorporate some measure of population merit or genetic diversity into decision-making. Additionally, they consider time in their decision-making processes, allowing for their selection decisions to be dependent on and optimized for a specific, finite time horizon. Selection methodology remains an active area of research, and improvements in selection methodology have the potential to significantly improve plant and animal species, given the centrality and importance of selection in breeding. We suggest that weighted 𝐿𝑝-norms and, especially, mating configuration resource allocation may be fruitful avenues of research. Ideally, novel selection strategies should be tested against a suite of other well characterized selection strategies in a variety of simulated breeding scenarios. We suggest that as a bare minimum, CGS, GOCS, and random selection should be used as experimental controls in simulation experiments due to their popularity or, in the case of random selection, as a minimum standard. Simulated breeding scenarios should consider both overlapping and non-overlapping generation structures to examine how proposed selection strategies react to situations involving line recycling and genetic bottlenecking. Simulations should also consider different genetic architectures and a variety of heritabilities. At a bare minimum, a strictly additive model of genetic control should be considered, but simulations under dominance and epistatic assumptions would also be useful. Finally, we suggest that novel selection strategies should be tested in scenarios where simulated quantitative trait loci are known and unknown to understand their efficacy in best- and practical- case scenarios, respectively. 80 ) 6 3 9 1 , h t i m S ; 3 4 9 1 , l e z a H ( ) 2 6 9 1 , s m a i l l i W ( ) 3 6 9 1 , n o t s l E ( ) 9 6 9 1 , r e k a B & k e š e P ( ) 8 7 9 1 , k c o M & a b m a l u M ( n o i t p m u s s A e n o N e n o N e n o N e n o N e n o N ) 1 0 0 2 , . l a t e n e s s i w u e M ( ) 0 1 0 2 , k n i n n a J ( ) 2 1 0 2 , . l a t e n o s s e n o S ( ) 2 1 0 2 , . l a t e r e p m e K ( ) 5 1 0 2 , . l a t e u i L ( ) 5 1 0 2 , . l a t e r e l y w t e a D ( e n o N e n o N l a m i s e t i n i f n I e n o N e n o N e n o N ) 7 9 9 1 , n e s s i w u e M ( l a m i s e t i n i f n I ) 6 1 0 2 , y k s o l C c M & r e t n u H ( ) 6 1 0 2 , z e h c n á S & r i m e d k A ( l a m i s e t i n i f n I l a m i s e t i n i f n I ) 7 1 0 2 ) 7 1 0 2 , . l a , . l a t e t e n o f f i o G ( n o f f i o G ( e n o N e n o N ) 7 1 0 2 , . l a t e r e i e m r e h e L ( l a m i s e t i n i f n I ) 7 1 0 2 , . l a t e r e a l e k u e B e D ( ) 8 1 0 2 , . l a t e r e l l ü M ( ) 9 1 0 2 ) 9 1 0 2 , . l a , . l a t e t e e d a z i n i e o M ( e d a z i n i e o M ( ) 9 1 0 2 ) 9 1 0 2 ) 9 1 0 2 , . l a , . l a , . l a t e t e t e r i m e d k A ( r i m e d k A ( r i m e d k A ( e n o N e n o N e n o N e n o N l a m i s e t i n i f n I l a m i s e t i n i f n I e n o N ) 9 1 0 2 , . l a t e , r e i e m r e h e L , r e i l l A ( l a m i s e t i n i f n I ) 0 2 0 2 , . l a t e e d a z i n i e o M ( ) 2 2 0 2 , g n a W & g n a h Z ( ) 2 2 0 2 , . l a t e i n i m A ( e n o N e n o N e n o N e p y T e n o N e n o N e n o N e n o N e n o N t n e r a P e n o N e n o N t n e r a P e n o N e n o N e n o N s s o r C t n e r a P e n o N e n o N e n o N e n o N e n o N s s o r C e n o N t n e r a P t n e r a P e n o N e n o N s s o r C s s o r C e n o N ) s ( e c n e r e f e R c i t e n e G l e d o M e c r u o s e R n o i t a c o l l A e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l g n i S e l p i t l u M e l p i t l u M e l p i t l u M e l g n i S e l p i t l u M e l g n i S e l g n i S e l g n i S e l g n i S n o i t a l u p o P - t n e r a P n o i t a l u p o P - t n e r a P y n e g o r P e l p i t l u M n o i t a l u p o P - t n e r a P e l g n i S e l g n i S e l g n i S e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l g n i S y n e g o r P n o i t a l u p o P - y n e g o r P n o i t a l u p o P - y n e g o r P n o i t a l u p o P - t n e r a P n o i t a l u p o P - y n e g o r P t n e r a P n o i t a l u p o P - y n e g o r P n o i t a l u p o P - y n e g o r P n o i t a l u p o P - y n e g o r P G M - S B G S V P O S C U S A R S V B M E S A L X - S A L S C O - T M M G - T M S D N S C P C U S A L - T M S A L - V P S S L e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l p i t l u M e l g n i S e l g n i S e l p i t l u M e l g n i S e l g n i S e l g n i S e l g n i S t n e r a P t n e r a P t n e r a P t n e r a P t n e r a P n o i t a l u p o P - t n e r a P t n e r a P t n e r a P n o i t a l u p o P - t n e r a P n o i t a l u p o P - t n e r a P t n e r a P y n e g o r P S I O S I B S I F W S I G D S I S R S C O S G C S G W S C O G K K - S B G S G W D S V H O n o i t a l u p o P - y n e g o r P S V B M E A R e l p i t l u M n o i t a l u p o P - y n e g o r P M G 81 t i a r T r e b m u N e v i t c e j b O r e b m u N n o i t c e l e S s t i n U n o i t c e l e S y g e t a r t S e l p i t l u M e l p i t l u M n o i t a l u p o P - t n e r a P . r e p a p s i h t n i d e w e i v e r s e i g e t a r t s n o i t c e l e s d e h s i l b u p f o y r a m m u S : 3 . 1 e l b a T CHAPTER 2: PYBROPS: A PYTHON PACKAGE FOR BREEDING PROGRAM SIMULATION AND OPTIMIZATION FOR MULTI-OBJECTIVE BREEDING 1. Introduction For this chapter, please refer to our published paper, Shrote & Thompson (2024). 82 CHAPTER 3: TOWARDS MULTI-OBJECTIVE GENOMIC SELECTION AND GENOMIC MATING 1. Introduction 1.1. Genomic selection and diversity preservation The genetic improvement of crops has been a practice which humanity has been practicing since the domestication of the first crop species approximately 10,000 years ago. In the last century, the process of breeding has been more formally and mathematically defined beginning with R. A. Fisher’s famous 1918 paper which simultaneously invented the statistical technique of analysis of variance and demonstrated that quantitative traits could be explained by many small effect genes each adhering to patterns of Mendelian inheritance (Fisher, 1918). Despite the great complexity of breeding programs, all breeding programs can be summarized into a single intuitive equation known as “the breeder’s equation” (Bernardo, 2020a). This equation is: Δ𝐺 = 𝜎𝐴𝑖ℎ 𝑡 , where Δ𝐺 is the rate of genetic gain, 𝜎𝐴 is the amount of heritable genetic diversity in a breeding population, 𝑖 is the intensity of selection, ℎ is the accuracy of selection, and 𝑡 is the amount of time it takes to complete a breeding cycle. Breeders manipulate terms in this equation to improve the rate of genetic gain and achieve breeding goals. Among the terms in this equation, reducing the time 𝑡 to complete a breeding cycle is highly effective at increasing genetic gain, owing to its asymptotic nature as it decreases towards zero. Recent research into rapid cycle breeding programs have, at least in simulated scenarios, demonstrated the efficacy of this technique (Gorjanc et al., 2018b, 2018a). The selection intensity 𝑖, has also increased in recent years, enabled by the advent of genomic selection (Bernardo, 2020a; Meuwissen et al., 2001). 83 Unfortunately, rapid cycling and increased selection intensity can rapidly deplete genetic diversity (Gorjanc et al., 2018b, 2018a), which is required for long-term success of a breeding program (Sanchez et al., 2023). Maintaining or improving genetic diversity is desirable for multiple reasons. First, genetic diversity is a precondition for genetic gain. Populations with low genetic diversity may have reduced genetic gains (Swarup et al., 2021) and populations with no genetic diversity can have no genetic gain as per the breeder’s equation. Second, genetic diversity is essential for the resilience and adaptability of a breeding population (Swarup et al., 2021). Populations with sufficient genetic diversity are more likely to contain alleles needed to adapt to new abiotic and biotic challenges, and new breeding goals (Sanchez et al., 2023). Third and finally, genetic diversity is required to prevent inbreeding depression (Sanchez et al., 2023). This is especially important for crops that mostly outcross and contain many deleterious, recessive alleles. To combat the loss of genetic diversity, several genomic selection variants have been proposed including weighted genomic selection (Jannink, 2010; WGS), genomic optimal contribution selection (Sonesson et al., 2012; GOCS), genotype building selection (Kemper et al., 2012; GBS), dynamic weighted genomic selection (Liu et al., 2015; DWGS), optimal haploid value selection (Daetwyler et al., 2015; OHV), genomic mating (Akdemir & Sánchez, 2016; GM), optimal population value selection (Goiffon et al., 2017; OPV), usefulness criterion selection (Lehermeier et al., 2017; UCS), expected maximum breeding value selection (Müller et al., 2018; EMBV), look ahead selection (Moeinizade et al., 2019, 2020; LAS), usefulness criterion parental contribution selection (Allier et al., 2019; UCPC), and present value look ahead selection (Zhang & Wang, 2022; PV-LAS). These genomic selection variants can be grouped into their diversity preservation mechanisms. Diversity preservation mechanisms include those which 84 upweight rare, favorable alleles (WGS, DWGS), control inbreeding by adding a diversity constraint (GOCS, GM, UCPC), better preserve favorable haplotype blocks (GBS, OHV, OPV), account for progeny diversity (UCS, UCPC), or use simulations to estimate long-term selection repercussions (LAS, PV-LAS). 1.2. Tested selection methods background and formulations as optimization problems As described above, many selection methods have been developed over the years by different research groups to combat the loss of genetic diversity and improve genetic gains in the long-term. Here, we briefly describe several of the selection strategies relevant to this chapter. 1.2.1. Estimated breeding value (EBV) selection and parental mean estimated breeding value (pmEBV) selection Estimated breeding value (EBV) selection is a parental selection strategy that seeks to maximize the sum of EBVs for a subset of 𝑁Ξ individuals selected from 𝑁Ω parental candidates. EBVs for parental candidates may be calculated using a variety of techniques including linear modeling and linear mixed modeling. Mathematically, the optimization problem is a ranking and sorting problem and can be expressed as: Subject to: max 𝐱 ′ 𝐲𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is included in the selected subset and 𝐲𝐄𝐁𝐕 is a vector of length 𝑁Ω containing estimated breeding values for parental candidates. 85 A variant of estimated breeding value selection is parental mean estimated breeding value (pmEBV) selection. pmEBV selection is a progenitive selection strategy that seeks to maximize the sum of pmEBVs for a subset of 𝑁Ξ mating configurations selected from 𝑁Ω mating configuration candidates. pmEBVs for mating configurations are calculated as a sum of parental EBVs, weighted by the expected genome contribution of the parents. In two-way crosses, this is equivalent to taking the mean of the parents; in three-way crosses, two parents are weighted as 0.25 and one as 0.5; etc. Like EBV selection, pmEBV selection is also a ranking and sorting problem, but its decision space grows by 𝒪(𝑁𝑑), where 𝑁 is the number of parental candidates and 𝑑 is the order of the cross. For low cross orders and low 𝑁, the search space is manageable. Mathematically, pmEBV selection is defined as: Subject to: max 𝐱 ′ 𝐲𝐩𝐦𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω. where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) mating configuration is included in the selected subset and 𝐲𝐩𝐦𝐄𝐁𝐕 is a vector of length 𝑁Ω containing parental mean estimated breeding values for mating configurations. 1.2.2. Genomic estimated breeding value (GEBV) selection and parental mean genomic estimated breeding value (pmGEBV) selection Genomic estimated breeding value (GEBV) selection is a parental selection strategy that seeks to maximize the GEBVs for a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates. GEBVs for individuals may be calculated as a linear sum of estimated allele effects using a genomic prediction model (Meuwissen et al., 2001). From an optimization standpoint, GEBV 86 selection is identical to EBV selection except GEBVs are used in place of EBVs. Mathematically, GEBV selection is defined as: Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is included in the selected subset and 𝐲𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing GEBVs for parental candidates. Parental mean genomic estimated breeding value (pmGEBV) selection is a variant of GEBV selection, that seeks to maximize the sum of pmGEBVs for a subset of 𝑁Ξ mating configurations from 𝑁Ω candidate mating configurations. pmGEBVs are calculated in a manner identical to their pmEBV counterparts, except GEBVs are used in place of EBVs. Mathematically, pmGEBV is identical in form to pmEBV and is stated as: Subject to: max 𝐱 ′ 𝐲𝐩𝐦𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) a mating configuration is included in the selected subset and 𝐲𝐩𝐦𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing parental mean genomic estimated breeding values for mating configurations. 87 1.2.3. Optimal contribution selection (OCS), parental mean optimal contribution selection (pmOCS), and usefulness criterion optimal contribution selection (ucOCS) Optimal contribution selection (OCS) is a selection strategy that seeks to maximize the GEBVs for a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates subject to a quadratic inbreeding constraint. The OCS strategy used in this chapter is a variant of the original (Meuwissen, 1997) that uses an identity-by-state kinship relationship matrix (Allier, Lehermeier, et al., 2019) to govern its quadratic inbreeding constraint and operates in a binary decision space. Mathematically, OCS is defined as: Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 1 2 𝐱′𝐊𝐱 ≤ 𝐶̅𝑡+1 𝑁Ξ ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected, 𝐲𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing genomic estimated breeding values for parental candidates, 𝐊 is an 𝑁Ω × 𝑁Ω identity-by-state kinship relationship matrix for parental candidates, and 𝐶̅𝑡+1 is the maximum allowable mean kinship allowed in the next generation. Parental mean optimal contribution selection (pmOCS) is a variant of regular OCS adapted to select mating configurations instead of individuals. pmOCS seeks to maximize the pmGEBVs for a subset of 𝑁Ξ mating configurations from 𝑁Ω mating configuration candidates, subject to an inbreeding constraint. Like pmEBV and pmGEBV selection, the number of 88 decision variables for pmOCS grows according to 𝑁𝑑, where 𝑁 is the number of parental candidates and 𝑑 is the order of the cross. Mathematically, pmOCS is defined as: Subject to: max 𝐱 ′ 𝐲𝐩𝐦𝐆𝐄𝐁𝐕 𝐱 1 2 𝐱′𝐐𝔼 𝑁Ξ ′ 𝐊𝐐𝔼𝐱 ≤ 𝐶̅𝑡+1 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) a mating configuration is selected, 𝐲𝐩𝐦𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing pmGEBVs for mating configuration candidates, 𝐐𝔼 is a 𝑁 × 𝑁Ω matrix containing expected parental contributions for each of the 𝑁 parents contributing to each of the 𝑁Ω mating configuration candidates, and 𝐶̅𝑡+1 is the maximum allowable mean kinship allowed in the next generation. Elements in 𝐐𝔼 are 0 if the parent does not contribute to the corresponding cross, 0.5 if the parent contributes to the corresponding biparental cross, etc. A final variant of OCS tested in this chapter is usefulness criterion optimal contribution selection (ucOCS). Like pmOCS, ucOCS selects mating configurations, but in ucOCS, the goal is to maximize the usefulness criteria for a subset of 𝑁Ξ mating configurations from 𝑁Ω mating configuration candidates, subject to an inbreeding constraint. Subject to: max 𝐱 ′ 𝐱 𝐲𝐔𝐂 1 2 𝐱′𝐐𝔼 𝑁Ξ ′ 𝐊𝐐𝔼𝐱 ≤ 𝐶̅𝑡+1 89 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω 1.2.4. Optimal haploid value (OHV) selection Optimal haploid value (OHV) selection is a selection strategy that seeks to maximize the optimal haploid values (OHVs) for a subset of 𝑁Ξ mating configurations from 𝑁Ω mating configuration candidates. OHVs are calculated by breaking up the genome into haplotype blocks, calculating the values of these haplotype blocks in mating configuration candidates, and taking twice the sum of the best haplotype blocks in a mating configuration for all mating configuration candidates (Daetwyler et al., 2015). Mathematically, OHV selection is defined as: Subject to: max 𝐱 ′ 𝐲𝐎𝐇𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) a mating configuration is selected and 𝐲𝐎𝐇𝐕 is a vector of length 𝑁Ω containing OHVs for candidate mating configurations. 1.2.5. Optimal population value (OPV) selection Optimal population value (OPV) selection is a selection strategy bearing resemblance to OHV selection. In OPV selection, the goal is to select a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates the maximizes the optimal population value (OPV) of the selected subset. 𝐵 max 𝐱 Such that: Φ ∑ max 𝑛∈{𝑖∈{1,…,𝑁}|𝑥𝑖=1} (𝐵𝑚𝑎𝑥)𝑛,𝑏 𝑏=1 90 ′ 𝐱 = 𝑁Ξ 𝟏𝐍 𝐱 ∈ 𝔹𝑁, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected, Φ is the ploidy of the organism, and (𝐵𝑚𝑎𝑥)𝑛,𝑏 is the best haplotype block value in the 𝑛th individual at the 𝑏th chromosome segment. 1.2.6. Weighted genomic selection (WGS) Weighted genomic selection (WGS) is a variant of GEBV selection that upweights marker effects based on the frequency of the favorable allele and selects individuals based on the sum of upweighted marker effects (Goddard, 2009; Jannink, 2010). The sum of upweighted marker effects for an individual is known as its weighted genomic estimated breeding value (wGEBV). Like GEBV selection, WGS seeks to identify a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates that maximizes the sum of wGEBVs. Mathematically, WGS is defined as: Subject to: max 𝐱 ′ 𝐲𝐰𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected and 𝐲𝐰𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing wGEBVs for parental candidates. 1.2.7. Usefulness criterion selection (UCS) Usefulness criterion selection (UCS) is a selection strategy that seeks to maximize the usefulness criteria for a subset of 𝑁Ξ mating configurations from 𝑁Ω mating configuration candidates. Mathematically, UCS is defined as: max 𝐱 ′ 𝐱 𝐲𝐔𝐂 91 Subject to: ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) a mating configuration is selected and 𝐲𝐔𝐂 is a vector of length 𝑁Ω containing usefulness criteria for mating configuration candidates. 1.2.8. Mean expected heterozygosity selection (MEHS) and mean genomic relationship selection (MGRS) Mean expected heterozygosity selection (MEHS) is variant of OCS that removes the GEBV objective and makes the minimization of inbreeding the only objective. The goal of MEHS is to select a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates the minimizes the mean identity-by-state kinship relationship. Mathematically, MEHS is defined as: Subject to: min 𝐱 1 2 𝐱′𝐊𝐱 𝑁Ξ ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected and 𝐊 is an 𝑁Ω × 𝑁Ω identity-by-state kinship relationship matrix for parental candidates. Mean genomic relationship selection is a variant of MEHS, that uses a VanRaden genomic relationship matrix (VanRaden, 2008) to define genomic relationships. Mathematically, MGRS is defined as: 92 Subject to: min 𝐱 1 2 𝐱′𝐆𝐱 𝑁Ξ ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected and 𝐆 is an 𝑁Ω × 𝑁Ω VanRaden genomic relationship matrix for parental candidates. 1.2.9. Random selection (RS) As the name suggests, in random selection individuals are randomly selected to serve as parents for the next generation. From a set of 𝑁Ω parental candidates, a random subset of 𝑁Ξ individuals is selected to serve as parents for the next generation. 1.3. Outline of this chapter In this chapter, we introduce two new multi-objective selection strategies called multi- objective genomic selection (MOGS) and multi-objective genomic mating (MOGM), with the goal of assessing their efficacies in long-term selection scenarios. We begin by first describing the objective function formulations for these two strategies. Since MOGS and MOGM are formulated in a manner that allows for generic population allele frequency manipulation, we describe two simulation experiments: an allele frequency alteration simulation experiment, and a breeding program simulation experiment. The former experiment seeks to diversify alleles, while the latter experiment seeks to fix favorable alleles. We also briefly describe some of the optimization algorithms used in this chapter. After presenting the methods, we present the results in two parts: each part corresponding to each experiment. Finally, we offer some discussion on the tested selection strategies and provide a conclusion. 93 2. Methods 2.1. Two new multi-objective methodologies 2.1.1. A new multi-objective genomic selection methodology The first novel selection methodology we introduce is called multi-objective genomic selection (MOGS). MOGS is composed of two objectives: a population allele frequency distance (PAFD) objective which controls genetic gain and a population allele unavailability (PAU) objective which controls genetic diversity. The former PAFD objective seeks to minimize the weighted Manhattan distance between the allele frequency of the selected set and a desired, target allele frequency. The latter PAU objective seeks to minimize the loss of alleles in the selected set needed to attain the desired, target allele frequency. Mathematically, MOGS is defined as: Such that: min 𝐱 𝐰′ (( 1 𝛷𝑁Ξ |⋅| 𝐙′𝐱 − 𝛕) ) min 𝐱 𝑀 ∑ 𝑤𝑚𝐼PAU ( 𝑚=1 1 𝛷𝑁Ξ ′ 𝐱, 𝜏𝑚) 𝐙∗,𝑚 𝟏′𝐱 = 𝑁Ξ 𝐱 ∈ 𝔹𝑁Ω Here, 𝐱 is a binary decision vector of length 𝑁 containing whether the 𝑛th parental candidate is selected (1) or not (0). 𝐱 is constrained such that its sum must be equal to 𝑁Ξ, the number of selected individuals. 𝐙 is a 𝑁 × 𝑀 matrix containing allele dosage information for each of 𝑁 parental candidates and 𝑀 genomic markers. Elements within 𝐙 must be integer values such that 𝑧𝑛,𝑚 ∈ {0,1, … , 𝛷} where Φ is the ploidy number. 𝐰 is a genomic marker weight vector of length 𝑀. Genomic marker weights for the 𝑚th marker are assigned according to user preference and 94 are most practically assigned as the absolute value of their linear effect estimates: 𝑤𝑚 = |𝑢𝑚|. Linear effects may be estimated using a linear genomic prediction model of the user’s choice. 𝛕 is a target allele frequency vector of length 𝑀. Target allele frequencies must be in the range [0,1] and are set according to user preferences. In many selection scenarios, fixation of the favorable allele is desirable, so these are set to 0 or 1. (⋅)|⋅| denotes the elementwise absolute value of a vector. 𝐙∗,𝐦 is vector of length 𝑁 corresponding to the allele dosages for each of 𝑁 parental candidates at the 𝑚th locus. Finally, 𝐼PAU(𝜔, 𝜏) is an indicator function which scores alleles at a locus as being available for selection (0) or unavailable for selection (1) for an input selection allele frequency 𝜔 and target allele frequency 𝜏. Indicator function values are determined using Table 3.1 below: 𝑰𝑷𝑨𝑼(𝝎, 𝝉) value 𝝎 value 0 1 0 1 0 0 0 𝝉 value 0 0 < 𝜏 ≤ 1 0 < 𝜔 < 1 0 ≤ 𝜏 ≤ 1 0 ≤ 𝜏 < 1 1 1 1 Table 3.1: Summary of indicator function values for the range of possible subset allele frequency and target allele frequency inputs. Since the MOGS problem specification is multi-objective in nature, its two objectives must be reduced to a single objective so that a single selection decision can be made. Previous selection methodologies have used techniques such as the weight sum method to combine multiple objectives (Akdemir et al., 2019; Akdemir & Sánchez, 2016; De Beukelaer et al., 2017) or the ε-constraint method to convert objectives into constraints (Allier, Lehermeier, et al., 2019; Moeinizade et al., 2020). Here, we utilize a pseudoweight method to reduce multiple objectives to a single objective. This pseudoweight method is related to the angle method used by Gorjanc & Hickey (2018). For our peudoweight method, we first estimate the Pareto frontier using a multi-objective genetic algorithm (in our case, an NSGA-III variant; described in section 2.6.3) 95 and identify a set of non-dominated solutions representing optimal selection decisions for the PAFD and PAU objectives. Next, we normalize the objective values in the non-dominated solution set to have a range of [0,1] for each objective. Then given a preference vector 𝐯, we identify the solution whose normalized point lies closest to the preference vector. This singular, non-dominated point is used to make selection decisions. By setting an appropriate preference vector, we can make selection decisions which correspond to relative weightings of objectives. This helps reduce the decision-making burden since exact, a priori weights and constraints are not needed as they would be in the weight sum method and ε-constraint methods, respectively. 2.1.2. A new multi-objective genomic mating methodology The second novel selection methodology we introduce is called multi-objective genomic mating (MOGM). MOGM is composed of the exact same objectives and constraints as MOGS, but it adds an additional mate pairing step after a suitable set of parents has been identified. The mate pairing problem is described as follows: given 𝑁Ξ individuals, pair them into 1 2 𝑁Ξ mate pairs to maximize the sum of their values. For MOGM, we adopt the philosophy that the value of a mate pair should be assigned according to the expected additive variance of its progeny. By maximizing the variance of the offspring, more extreme progenies can be selected. We adopt the methodology described by Allier, Moreau, et al. (2019) and Osthushenrich et al. (2017) to calculate progeny additive genetic variances from a linear genomic prediction model. The mate pairing problem above is recognizable as a maximum weighted matching problem. If we model the selected set of parents as vertices 𝑉, the possible mate pairings as edges 𝐸, and the expected additive variance of the progenies as weights 𝜎𝐴 2, then we can construct a weighted graph 𝐺 = (𝑉, 𝐸, 𝜎𝐴 2) representing the possible pairings and their values. To 96 maximize the mate pairings, we can solve the following optimization problem using the blossom algorithm: Such that: max ∑(𝜎𝐴 𝑒∈𝐸 2)𝑒𝑥𝑒 ∑ 𝑥𝑒 ≤ 1 𝑒∈𝛿(𝑣) ∀𝑣 ∈ 𝑉 𝑥𝑒 ∈ {0,1} ∀𝑒 ∈ 𝐸, where 𝑥𝑒 is a decision variable for whether (1) or not (0) the 𝑒th edge (mate pairing) is selected, (𝜎𝐴 2)𝑒 is the weight of the 𝑒th edge (expected progeny additive variance for a mate pair), and 𝛿(𝑣) denotes the set of edges incident to the 𝑣th vertex. 2.2. Allele frequency alteration simulation protocols The MOGS and MOGM objectives are formulated in a manner such that they allow for the selection of populations with custom allele frequencies. To test the efficacy of the MOGS and MOGM objectives in attaining their target allele frequency goals, we devised a simulation scenario where the goal was to shift allele frequencies to a target of 0.5 for all loci. 2.2.1. Empirical marker source As an empirical marker source, we used SNP data from the Wisconsin maize diversity panel 942 (Hirsch et al., 2014; Mazaheri et al., 2019) and linearly interpolated genetic map positions for the SNPs in the dataset using the US NAM consensus genetic map (McMullen et al., 2009). After interpolation, we randomly selected 40 founder individuals and sampled 1000 loci with minor allele frequencies ≥ 0.2 and consecutive genetic map distances ≥ 0.2 cM. These 1000 sampled loci served as targets for selection in the allele frequency alteration experiments. 97 2.2.2. Population foundation and burn-in simulations Following founder and SNP marker sampling, we created a founding population by randomly pairing the 40 founders to form 20 biparental crosses. From these 20 biparental crosses, we derived 80 hybrid progenies per cross, resulting in 1600 progenies total. These 1600 hybrid progenies were randomly intermated with each other in biparental crosses for 20 generations to form the founding population. At each intermating step, 3200 biparental crosses were formed with all individuals contributing to exactly two crosses. Each biparental cross produced exactly one progeny so that the population size was kept at a constant size of 1600. Following the establishment of the founding population, five bootstrap cohorts were derived from the foundation population to create the starting point for the burn-in simulations. Bootstrap cohorts were created by randomly selecting 40 individuals from the founding population, randomly pairing them into 20 biparental crosses, and deriving 4 doubled haploid progenies from the cross, for a total of 80 progenies per cohort. An overlapping cohort structure breeding program was established like that described by Allier, Lehermeier, et al. (2019). Briefly, the breeding population was divided into five different cohorts: the three oldest of which served as candidates for selection and the two youngest of which represented breeding candidates under development. Each year, members of the three oldest cohorts were pooled. From the 240 pooled candidates, 40 were selected and randomly paired to form 20 biparental crosses. 4 doubled haploid progenies were derived from each biparental cross to form a new cohort containing 80 progenies. Following the creation of the new cohort, the oldest cohort was discarded, so that a constant of five cohorts were maintained. Random selection was performed until the mean expected heterozygosity (MEH) was just under 0.25. 98 2.2.3. Main simulation The main simulation proceeded in a manner identical to the burn-in, except that instead of random selection, tested selection strategies were used instead. We tested several selection methodologies including MEHS, MGRS, RS, and our two novel strategies, MOGS and MOGM. For MOGS and MOGM, we set the target allele frequency as 0.5 and marker weight as 1 for the PAFD and PAU objectives for all genomic loci. The target allele frequency of 0.5 specified that we sought to maintain major and minor allele states in equal proportions at each biallelic genomic locus. The marker weight of 1 assigned to all genomic loci specified that we preferred each genomic locus equally, regardless of the allele frequencies present at each locus. We tested multiple preference weightings for PAFD and PAU objectives and empirically determined that a 90% preference for PAFD and a 10% preference for PAU were suitable settings for long term selection. In addition to these selection strategies, we tested PAFD and PAU objectives individually to characterize their performance. We simulated 60 generations of selection and replicated each selection methodology 40 times. Throughout the simulations, we collected population statistics including MEH, number of polymorphic loci, and the Manhattan (L1-norm) and Euclidean (L2-norm) distances between the population allele frequencies and the target allele frequencies. 2.3. Breeding simulation protocols MOGS and MOGM can also be adapted to breeding programs. To test the efficacy of the MOGS and MOGM, we devised a breeding program simulation scenario where the goal was to maximize long-term genetic gain over the course of 60 generations. 99 2.3.1. Empirical marker source We used SNP data from the Wisconsin maize diversity panel 942 (Hirsch et al., 2014; Mazaheri et al., 2019) as an empirical source of markers for all breeding program experiments. We linearly interpolated the genetic map positions for all SNP markers using the US NAM consensus genetic map (McMullen et al., 2009). From this dataset, we randomly selected 40 individuals to serve as founders for in silico simulations. After selecting 40 founders, we randomly sampled 3000 SNPs with minor allele frequencies ≥ 0.2 and consecutive genetic map distances ≥ 0.2 cM. We assigned 1000 of these SNPs to serve as quantitative trait loci (QTLs) for a simulated, quantitative trait. We assigned additive effects to QTLs following a normal distribution with a mean of 0 and standard deviation of 0.01. The remaining 2000 SNPs were designated as non-causal loci and were assigned an additive effect of zero. 2.3.2. Founding population simulation Following the selection of founders and genetic markers, we randomly paired the founders and created 80 hybrid progenies for each founder pairing. These resulting 1600 hybrid progenies were randomly intermated with each other so that each hybrid produced a single progeny. Resulting progenies served as the parents of the next generation and were randomly intermated to each produce a single progeny. This pattern of random intermating was repeated for a total of 20 generations to form the founding population. From the founding population, the narrow sense heritability for the simulated, quantitative trait was set as 0.4. 2.3.3. Burn-in simulation Following the establishment of the founding population, an overlapping cohort structure and burn-in protocol was created like that described in Allier, Lehermeier, et al. (2019). Briefly, the breeding population was broken into five cohorts, with each cohort containing doubled 100 haploid (DH) progenies produced during a single year. The two youngest cohorts contained DH progenies that were under development and represented the time needed to generate DH lines from an initial cross. The three oldest cohorts represented breeding materials which had been developed as lines and were eligible for phenotyping and selection. To bootstrap the simulation, five bootstrap cohorts were created by selecting 40 random individuals from the founding population to form 20 biparental crosses. Each biparental cross produced 80 doubled haploid (DH) progenies for a total of 1600 progenies per bootstrap cohort. The burn-in protocol is as follows. Each year, members of the three oldest cohorts underwent phenotyping. Each cohort member was tested in four replications under the assumption of sufficient seed for testing and no missing data. Phenotypes were simulated using the QTL effects established at the beginning of the simulation and by adding random errors in accordance with a narrow sense heritability of 0.4 in the founder population. Genotype by environment interaction was not simulated. After phenotyping the three oldest cohorts, phenotypic means for individuals were calculated and the top 5% within each biparental progeny family (4 individuals) were selected to serve as parental candidates for a total of 240 parental candidates. From these 240 parental candidates, the top 40 individuals were selected on phenotypic means and randomly mated to form 20 biparental crosses. Each cross generated 80 doubled haploid progenies to create a new cohort of 1600 progenies. The new cohort was added to the breeding population as its youngest cohort, and the oldest cohort was removed from the population. In summary, the time between the creation of a cohort and the first testing of a cohort was three years, after which the cohort was phenotyped for three years and finally removed (Fig. 3.1). The burn-in simulation lasted until the MEH of the QTL reduced to just under 0.25. In our case, this corresponded to 31 generations. 101 Figure 3.1: Diagram of the breeding program simulation strategy used in this chapter. At generation 𝓉, the oldest three cohorts are combined to form a population. From this combined population, the top 5% of individuals (4 individuals) are selected based on phenotypic means to serve as parental candidates. From the parental candidates, parents are selected according to a selection strategy. In the burn-in stage, this selection strategy is based on phenotypic means, but in the main simulation, this is the selection strategy which is being tested. Parents are intermated to form a new cohort and the new cohort is pushed to the queue while the oldest cohort is discarded from the queue. The cycle continues until the end of the simulation. 2.3.4. Main simulation The main simulation proceeded very similarly to the burn-in and used the five cohorts produced in the burn-in as a starting point. The only difference between the burn-in protocols and the main simulation protocols was the selection of parents used to create the next cohort. In the main simulation, the top 5% of individuals within each biparental progeny family were selected as parental candidates as before, but from the 240 candidates, the tested selection methodology was used to select the 40 individuals from which to derive the next cohort. We 102 tested several selection methodologies including EBV, GEBV, pmEBV, pmGEBV, OCS, pmOCS, UCS, ucOCS, OHV, OPV, WGS, RS, and our two novel strategies, MOGS and MOGM. For MOGS and MOGM, we tested multiple preference weightings for PAFD and PAU objectives and empirically determined that a 10% preference for PAFD and a 90% preference for PAU were suitable settings for long term selection. We simulated 60 generations of selection and replicated each selection methodology 40 times. Each strategy was tested underneath two selection scenarios. The first selection scenario was the true (TRUE) scenario. In the TRUE scenario, we assumed that all QTL locations and effects were known, and the tested selection methodologies used this information to formulate their decisions. The TRUE scenario represents the upper bound of the selection methodology since in all real-world scenarios, QTL locations are not known and/or their effects are estimated. The second scenario was the estimated (EST) scenario. In the EST scenario, we assumed that all QTL locations and effects were unknown and estimated. To simulate this, we masked the 1000 QTL established at the beginning of the simulation and used the 2000 linked, non-causal loci to inform the tested selection methodologies. The EST scenario represents the realistic performance of the selection methodology in real-world scenarios. We fit a ridge regression model (Meuwissen et al., 2001) using the EMMA method (Kang et al., 2008) to estimate effects of the 2000 non-causal loci. These effect estimates were also used to inform the tested selection methodologies. Several of the tested selection methodologies required specialized algorithms for optimization and/or hyperparameters to be set. EBV, GEBV, pmEBV, pmGEBV, UCS, OHV, and WGS were the most straightforward. We exhaustively computed values for each parental candidate or parental candidate cross, sorted these values from largest to smallest and selected 103 the top 40 individuals or 20 crosses, respectively. For EBV, GEBV, and WGS, we randomly paired the top 40 selected individuals to form 20 crosses. OCS, pmOCS, ucOCS, and OPV required more specialized algorithms. We used an exhaustive subset hill climbing algorithm (described in section 2.6.1) to optimize for OCS and OPV. We used a neighborhood subset hill climbing algorithm (described in section 2.6.2) to optimize for pmOCS and ucOCS since an exhaustive hill climbing strategy was too computationally challenging. For the neighborhood subset hill climber, we defined the neighborhood of a selected cross as all other crosses sharing a parent with the selected cross plus an additional 100 randomly selected crosses. For OCS, pmOCS, and ucOCS, we set the mean kinship constraint to begin at 0.855 in the first generation and gradually relaxed it to 1 (complete inbreeding) throughout the 60 tested generations. For OHV and OPV, we broke the genome into 50 equally sized haplotype blocks based on genetic map distances between markers, calculated corresponding haplotype block values using our genomic prediction model, and computed OHV and OPV scores using the haplotype block values. Throughout the simulations, we collected population statistics including mean expected heterozygosity (MEH), additive genetic and genic variances, Bulmer effect, lower and upper selection limits (LSL and USL, respectively), minimum, mean, and maximum true breeding values (TBVs), number of polymorphic loci, number of fixed deleterious, neutral, and favorable alleles, and number of polymorphic deleterious, neutral, and favorable alleles. All population statistics were collected on the three oldest cohorts in the breeding program. Mean expected heterozygosity was calculated as 1 𝑀 ∑ 𝑀 𝑚=1 2𝑝𝑚(1 − 𝑝𝑚) where 𝑀 is the number of markers and 𝑝𝑚 is the allele frequency of the 𝑚th marker (Allier, Lehermeier, et al., 2019). Additive genetic variance, 𝜎𝐴 2, was calculated as the variance of true breeding values for individuals within the 104 population. Genic variance was calculated as 𝜎𝑎 2 = ∑ 𝑀 𝑚=1 4𝛼𝑚 2 𝑝𝑚(1 − 𝑝𝑚) where 𝑀 is the number of markers, 𝑝𝑚 is the allele frequency of the 𝑚th marker, and 𝛼𝑚 is the additive effect of the 𝑚th QTL (Allier, Lehermeier, et al., 2019). The Bulmer effect was calculated as the ratio of additive genetic variance over additive genic variance 𝜎𝐴 2/𝜎𝑎 2 (Allier, Lehermeier, et al., 2019; Bulmer, 1971). Lower and upper selection limits were calculated as the breeding values of individuals having the worst and best, respectively, attainable allele combinations, given the current population. 2.4. Characterization of MOGS and MOGM objectives For both allele frequency alteration and breeding simulation experiments, we sought to characterize the MOGS and MOGM objectives for the starting population resulting from the burn-in simulations. We randomly sampled 1000 random selection decisions for MOGS and MOGM objectives for all experiments. In the breeding simulation experiment, we evaluated MOGS and MOGM objectives under both TRUE and EST scenarios and regressed PAU objective values on PAFD objective values using simple linear regression. This was done to see if there was any relationship between the objectives. 2.5. Validation of NSGA-III performance on MOGS and MOGM objectives One question which arises for the MOGS and MOGM strategies is whether the NSGA-III algorithm has correctly converged to a set of nondominated and presumably Pareto optimal points. To validate the convergence and spread of nondominated points found by NSGA-III along the Pareto frontier, we used two separate strategies. First, we compared the optimization results of NSGA-III on the MOGS and MOGM objectives against the optimization results for NSGA-II. For NSGA-II, we created a variant of the original algorithm that used reduced exchange crossover (Correa et al., 2001) and reduced exchange mutation operators (Correa et al., 105 2001) to traverse the subset search space. We used a population size of 100 and evolved this population for 1500 generations. Second, we performed several single-objective optimizations using the exhaustive subset hill climber algorithm described in section 2.6.1 and compared these results to points identified by NSGA-III. To validate NSGA-III, we optimized for each objective separately using the hill climber algorithm and then used the ε-constraint method to validate sections of the Pareto frontier identified by NSGA-III. 2.6. Algorithms used 2.6.1. Exhaustive subset hill climber algorithm We crafted a hill climber algorithm to search for at least locally optimal solutions to fixed size subset optimization problems. Briefly, the algorithm first starts by randomly selecting a decision vector in the appropriate search space and evaluates the solution for its objective and constraint functions. This initial solution is marked as the current best solution. For each element in the current best solution, the algorithm performs a local search by exchanging all element options in the search space, testing these neighboring solutions for an improvement to the current best solution, and identifying the best neighboring solution. An improvement is defined as a solution that has a smaller constraint violation or, if constraint violations are equivalent, a better objective value. If the best neighboring solution improves upon the current best solution, then the best neighboring solution becomes the current best solution, and the algorithm performs another local search with the new current best solution. If no improvements can be made on the current best solution in its neighborhood, then the algorithm terminates and returns the best solution it found. 106 2.6.2. Neighborhood subset hill climber algorithm For discrete, subset search spaces with large numbers of options, we developed a variant of the exhaustive subset hill climber algorithm described above that non-exhaustively tests nearby solutions. The algorithm is identical to the exhaustive algorithm except that for each element in the current best solution, instead of exchanging all element options in the search space, the algorithm exchanges a limited subset of options called neighboring options. Neighboring options are determined by the exact element being exchanged which allows for known relationships between elements in the search space to be exploited. 2.6.3. Subset NSGA-III algorithm For multi-objective optimization in discrete, subset search spaces, we crafted a variant of NSGA-III from Deb and Jain (2014) by modifying the recombination and mutation operators. We used the reduced exchange crossover and reduced exchange mutation operators developed by Correa et al. (2001) in place of the original operators proposed by Deb and Jain (2014). We used a population size of 100 with 96 evenly spaced reference points in two dimensions as parameters to our NSGA-III variant. We evolved this population for 1500 generations, which permitted suitable algorithm convergence. 2.7. Simulation data analysis We fit numerous linear models to analyze the collected simulation metrics. Since the data are extensive, we only analyzed statistical differences between simulation metrics at generations 15, 30, 45, and 60. For each simulation metric at each selected generation number, we fit the model: 𝑦𝑖𝑗 = 𝜇 + 𝑠𝑖 + 𝜀𝑖𝑗 𝜀𝑖𝑗~𝑁(0, 𝜎𝜀 2) 107 Here, 𝑦𝑖𝑗 is the observed simulation metric for the 𝑖th selection strategy for the 𝑗th simulation replicate, 𝜇 is the simulation metric mean, 𝑠𝑖 is the fixed effect of the 𝑖th simulation metric, and 𝜀𝑖𝑗 is the simulation metric error, assumed to follow a normal distribution with mean 0 and variance 𝜎𝜀 2. For each model fitting, we calculated 95% confidence intervals using Tukey’s multiple test correction (Tukey, 1949) and identified statistical groupings using the emmeans (Lenth, 2024) and multcompView (Graves et al., 2024) packages in R (R Core Team, 2024). 3. Results 3.1. Allele frequency alteration simulation results 3.1.1. Characterization of MOGS and MOGM objectives A regression of randomly sampled selection decisions revealed that there was a significant positive relationship between the PAFD and PAU objectives (Fig. 3.2). For every unit increment in PAU, PAFD increased by 0.136 on average (Table 3.2). Although there was a significant relationship between PAFD and PAU, a great deal of variability still existed between the two objectives. A simple linear model with PAU could only explain about 12.5% of the variance in PAFD (model 𝑅2 = 0.1251). Since MOGS and MOGM seek to minimize both PAFD and PAU objectives, PAFD and PAU objectives appeared to be largely non-competing in nature, at least in early stages of optimization. This trend observed in randomly sampled selection decisions, however, did not persist at the boundaries of the search space. In the following section, section 3.1.2, we were able to identify a Pareto frontier (Fig. 3.3), indicating that these two objectives were competing in nature. 108 Figure 3.2: Regression of PAU objective values on PAFD objective values for 1000 random selection decisions in the allele frequency alteration experiment. A slight positive correlation was observed for these two objectives. Parameter Estimate Std. Error 275.023 Intercept 3.449465 0.135863 0.011374 PAU p-value t-value 79.72919 0 11.94521 7.77E-31 Table 3.2: Summary of the regression model fit by regressing PAU objective values on PAFD objective values for 1000 random selection decisions in the allele frequency alteration experiment. 3.1.2. Validation of NSGA-III performance on MOGS and MOGM objectives Multi-objective optimization of the PAFD and PAU objectives used by MOGS and MOGM for the allele frequency alteration experiments revealed a relatively small Pareto frontier for the optimization problem (Fig. 3.3). NSGA-III appeared to provide better convergence than NSGA-II. The use of a hillclimber algorithm and the ε-constraint method to validate points along 109 the Pareto frontier revealed that NSGA-III converged well but suffered from difficulties in identifying points extreme for both PAFD and PAU objectives (Fig. 3.3). Figure 3.3: Pareto frontier for the PAFD and PAU objectives in MOGS/MOGM using NSGA-II (blue circles) and NGSA-III (orange X’s). Validation points for the hill climber with ε-constraint (black tripoints) correspond to minimizing PAFD unrestricted, PAU unrestricted, minimizing PAU such that PAFD ≤ 303, and minimizing PAU such that PAFD ≤ 301.5. 3.1.3. Number of polymorphic marker results All selection strategies were able to maintain a high number of polymorphic loci throughout the duration of the simulation, though to varying degrees (Fig. 3.4). PAU, MOGS, and MOGM were statistically tied for the greatest number of polymorphic loci maintained after 60 generations (Table 3.3). MEHS performed the next best, followed by PAFD, MGRS, and RS in order of decreasing ability (Table 3.3). Performance rankings changed were somewhat stable 110 across multiple generations (Appx. A, Table A.1-3). PAU, MOGS, and MOGM strategies remained the top strategies across all generations, but the other four strategies changed ranks. Notably, PAU was able to maintain an almost constant number of polymorphic markers over time (Appx. A, Table A.1-3). In early generations, MGRS outperformed MEH (Appx. A, Table A.1), but in later generations, the loss of alleles plateaued for MEH (Fig. 3.4), allowing for MEH to overtake MGRS. In early generations, RS was the second-worst selection strategy, surpassing PAFD in ability at generation 15 (Appx. A, Table A.15), but as time progressed, RS sank to the lowest rank (Appx. A, Table A.3). Figure 3.4: Number of polymorphic loci over 60 generations by selection strategy in the allele frequency alteration experiment. 111 Mean Pop. Selection No. Poly. Markers Strategy 733.8500 PAU MOGS10 732.5250 MOGM10 732.4000 704.0750 MEHS 684.6500 PAFD 681.6500 MGRS 660.2000 RS DF Generation 60 95% Std. Error Lower CI 0.70918 273 732.4538 0.70918 273 731.1288 0.70918 273 731.0038 0.70918 273 702.6788 0.70918 273 683.2538 0.70918 273 680.2538 0.70918 273 658.8038 Statistical Grouping 95% Upper CI 735.2462 E 733.9212 E 733.7962 E 705.4712 D 686.0462 C 683.0462 B 661.5962 A Table 3.3: Number of polymorphic loci at generation 60 by selection strategy in the allele frequency alteration experiment. 3.1.4. Mean expected heterozygosity results With respect to the MEH diversity metric, the MEHS, MOGS, MOGM, and PAFD selection strategies all increased population MEH over the 60 generations of selection (Fig. 3.5). MEHS was the best selection strategy at improving population MEH, followed by MOGS and MOGM, which were statistically tied, and PAFD (Fig. 3.5; Table 3.4). PAU, MGRS, and RS were all unable to improve MEH diversity metrics. Over 60 generations, population MEH slightly decreased with PAU, MGRS, and RS selection strategies (Fig. 3.5). Between the PAU and MGRS, PAU created populations with slightly higher MEH than MGRS. RS performed the worst out of all selection strategies (Table 3.4). Relative rankings of selection strategies were relatively stable over time, primarily changing in the magnitudes of their differences (Appx. A, Tables A.4-6). 112 Figure 3.5: Population mean expected heterozygosity over 60 generations by selection strategy in the allele frequency alteration experiment. Generation 60 DF 95% Lower CI Mean Pop. MEH Selection Strategy MEHS 0.3236 MOGM10 0.3142 MOGS10 0.3132 0.3033 PAFD 0.2418 PAU 0.2363 MGRS 0.2253 RS Std. Error 0.00038 273 0.3229 0.00038 273 0.3134 0.00038 273 0.3124 0.00038 273 0.3026 0.00038 273 0.2411 0.00038 273 0.2355 0.00038 273 0.2246 Table 3.4: Population mean expected heterozygosity at generation 60 by selection strategy in the allele frequency alteration experiment. Statistical Grouping F E E D C B A 95% Upper CI 0.3244 0.3149 0.3139 0.3041 0.2426 0.2370 0.2261 3.1.5. Manhattan (L1-norm) distance results For the Manhattan distance between the target allele frequency of 0.5 and the population allele frequency, MEHS was the most performant selection strategy (Table 3.5). MOGS and MOGM were the next best selection strategies and were statistically tied in their abilities. PAFD was the next best, followed by PAU and MGRS. RS was the worst selection strategy. The PAU, 113 MGRS, and RS selection strategies increased the Manhattan distance between the population and target allele frequencies (Fig. 3.6; Table 3.5). The increase in distance was most dramatic with RS (Fig. 3.6). Like the results for population MEH, relative rankings of selection strategies were relatively stable over time, primarily changing in the magnitudes of their differences (Appx. A, Tables A.7-9). Figure 3.6: Manhattan distance between the population allele frequency and a target allele frequency of 0.5 over 60 generations by selection strategy in the allele frequency alteration experiment. 114 Mean Pop. Selection Man. Dist. Strategy 330.0147 RS 321.3064 MGRS 319.8331 PAU PAFD 237.9261 MOGS10 234.1722 MOGM10 232.8772 226.2925 MEHS Generation 60 DF 95% Std. Error Lower CI 0.36541 273 329.2953 0.36541 273 320.5870 0.36541 273 319.1137 0.36541 273 237.2068 0.36541 273 233.4528 0.36541 273 232.1578 0.36541 273 225.5731 Statistical Grouping 95% Upper CI 330.7341 E 322.0257 D 320.5525 D 238.6455 C 234.8916 B 233.5966 B 227.0119 A Table 3.5: Manhattan distance between the population allele frequency and a target allele frequency of 0.5 at generation 60 by selection strategy in the allele frequency alteration experiment. 3.1.6. Euclidean (L2-norm) distance results Results for the Euclidean distance between the population allele frequency and a target allele frequency of 0.5 were very similar to the Manhattan distance results. MEHS was the best selection strategy for improving this metric, followed by MOGS and MOGM which were statistically tied, followed by PAFD (Table 3.6). PAU, MGRS, and RS increased this metric, resulting in less diverse populations (Fig. 3.7). Among these three strategies, PAU was the least unsatisfactory, followed by MGRS and RS. Like the Manhattan distance results, the relative rankings of selection strategies were relatively stable over time (Appx. A, Tables A.10-12). 115 Figure 3.7: Euclidean distance between the population allele frequency and a target allele frequency of 0.5 over 60 generations by selection strategy in the allele frequency alteration experiment. Mean Pop. Selection Eucl. Dist Strategy 137.3491 RS 131.8709 MGRS 129.0850 PAU PAFD 98.3333 MOGS10 93.4112 MOGM10 92.9116 88.1833 MEHS Generation 60 DF Std. 95% Lower CI Error 0.19004 273 136.9750 0.19004 273 131.4967 0.19004 273 128.7109 0.19004 273 97.9592 0.19004 273 93.0371 0.19004 273 92.5375 0.19004 273 87.8091 Statistical Grouping 95% Upper CI 137.7232 F 132.2450 E 129.4592 D C 98.7074 B 93.7853 B 93.2858 A 88.5574 Table 3.6: Euclidean distance between the population allele frequency and a target allele frequency of 0.5 at generation 60 by selection strategy in the allele frequency alteration experiment. 3.2. Breeding simulation results We provide an abridged version of our results since the analysis is extensive. In our abridged analysis, we focus on genetic gain as measured by population mean TBV, and genetic diversity as measured by population MEH and population USL at generation 60. Additional 116 simulation metrics are summarized, and additional figures and tables may be viewed in Appendix A. 3.2.1. Characterization of MOGS and MOGM objectives A regression of randomly sampled selection decisions under both TRUE and EST scenarios revealed that there were no significant correlations between PAU and PAFD objectives, at least at the start of the simulations. Regression results may be viewed in Figs. 3.8 and 3.9 and Tables 3.7 and 3.8 below. Figure 3.8: Regression of PAU objective values on PAFD objective values for 1000 random selection decisions in the TRUE scenario. No statistical correlation was observed for these two objectives. 117 Parameter Estimate Std. Error Intercept PAU 2.168959 0.003642 -0.01927 0.016449 p-value t-value 595.5368 0 -1.17164 0.241622 Table 3.7: Regression of PAU objective values on PAFD objective values for 1000 random selection decisions in the TRUE scenario. Figure 3.9: Regression of PAU objective values on PAFD objective values for 1000 random selection decisions in the EST scenario. No statistical correlation was observed for these two objectives. Parameter Estimate Std. Error Intercept PAU 13.41068 0.002323 0.001795 0.001133 p-value t-value 5773.504 0 1.583865 0.113541 Table 3.8: Regression of PAU objective values on PAFD objective values for 1000 random selection decisions in the EST scenario. 3.2.2. Validation of NSGA-III performance on MOGS and MOGM objectives Multi-objective optimization of the PAFD and PAU objectives in the TRUE scenario revealed a small Pareto frontier using NSGA-III with a population size of 100 (Fig. 3.10). 118 NSGA-III appeared to converge better than NSGA-II for the two objectives (Fig. 3.10). Four separate hill climbs – two on PAFD and PAU separately, and two using the ε-constraint method – revealed that NSGA-III appeared to converge well with respect to the Pareto frontier. It did, however, exhibit difficulties in identifying points along the edges of the Pareto frontier, especially for extreme PAU values (Fig. 3.10). Figure 3.10: Pareto frontier for PAFD and PAU objectives in the TRUE scenario using NSGA-II (blue circles) and NGSA-III (orange X’s). Validation points for the hill climber with ε-constraint (black tripoints) correspond to minimizing PAFD unrestricted, PAU unrestricted, minimizing PAU such that PAFD ≤ 2.084, and minimizing PAU such that PAFD ≤ 2.078. Multi-objective optimization of the PAFD and PAU objectives in the EST scenario proved to be more challenging than in the TRUE scenario. Both NSGA-II and NSGA-III identified a Pareto frontier, but several separate hill climbs revealed that this was a false frontier (Fig. 3.11). NGSA-II and NSGA-III appeared to have either found a local optimum or 119 prematurely converged for the optimization problem presented in the EST scenario. In particular, NSGA-II and NGSA-III had difficulties minimizing the PAFD objective. Since 2000 loci linked to the 1000 causal loci were used for optimization in the EST scenario instead of the 1000 causal loci used in the TRUE scenario, this suggests that the optimization difficulty of PAFD increases as the number of loci increases. Figure 3.11: Pareto frontier for PAFD and PAU objectives in the TRUE scenario using NSGA-II and NGSA-III. Validation points corresponded to minimizing PAFD unrestricted, PAU unrestricted, minimizing PAU such that PAFD ≤ 5.440, and minimizing PAU such that PAFD ≤ 5.430. 3.2.3. TRUE scenario results 3.2.3.1. Genetic gain results Under scenarios where the true effects of QTL were known, ucOCS improved the population mean TBV the most among all other tested selection strategies after 60 generations of 120 selection (Fig. 3.12; Table 3.9). Selection with WGS was the second best and was statistically tied with pmOCS (Table 3.9). MOGM performed similarly to pmOCS and outperformed OCS and its MOGS counterpart (Table 3.9). OCS slightly outperformed MOGS, and MOGS performance was comparable to OHV (Table 3.9). In the lower half of long-term selection strategies were GEBV, EBV, UCS, OPV pmEBV, pmGEBV, and RS (Table 3.9). Ranking and statistical grouping results for improvements in the population maximum and minimum TBV at generation 60 were similar to results for improvements in mean TBVs. At generation 60, WGS and ucOCS were the best strategies for improving maximum TBV (Appx. A, Fig. A.1; Appx. A, Table A.19). MOGM and pmOCS, which were statistically tied with each other, were the next best selection strategies (Appx. A, Table A.19). OCS and MOGS formed the third best statistical grouping for this metric (Appx. A, Table A.19). Interestingly, RS outperformed pmEBV and pmGEBV in long-term maximum TBV (Appx. A, Table A.19). For minimum TBVs at generation 60, ucOCS and pmOCS had the best and second-best rankings, respectively (Appx. A, Fig. A.2; Appx. A, Table A.23). MOGM and WGS were in the third-best statistical grouping for this metric, followed by OCS and OHV in the fourth-best grouping, and MOGS and GEBV in the fifth-best grouping (Appx. A, Table A.23). RS was the worst selection strategy for improving population minimum TBV (Appx. A, Table A.23). Selection strategy rankings for genetic gain changed over time. In early generations, UCS, ucOCS, pmGEBV, pmEBV, and OHV strategies tended to be the best selection strategies for improving population mean, maximum, and minimum TBVs (Appx. A, Tables A.13, A.16, A.20). At generation 15, UCS was the best strategy or tied with the best strategy for improving these three metrics (Appx. A, Tables A.13, A.16, A.20). Except for ucOCS, the rankings for these 121 five strategies reduced over time as they depleted their populations’ genetic diversity (Appx. A, Tables A.13-23). EBV and GEBV selections strategies were decidedly mediocre in their performances, being mid-ranking in population mean, maximum, and minimum TBV metrics at most time points throughout the simulation (Table 3.9; Appx. A, Tables A.13-23). OPV performed poorly overall in improving the three TBV metrics, exhibiting poor performance in early generations and slightly less poor performance in later generations (Fig. 3.12; Appx. A, Fig. A.1-2; Table 3.9; Appx. A, Tables A.13-23). RS exhibited the poorest performance, performing poorly in every genetic gain metric at every examined time point (Fig. 3.12; Appx. A, Figs. A.1-2; Table 3.9; Appx. A, Tables A.13-23). Figure 3.12: Mean true breeding value over 60 generations by selection strategy in the TRUE scenario. 122 Generation 60 DF 95% Std. Lower CI Error 0.00818 546 106.5327 0.00818 546 106.4562 0.00818 546 106.4091 0.00818 546 106.3916 0.00818 546 106.3219 0.00818 546 106.2798 0.00818 546 106.2757 0.00818 546 106.2088 0.00818 546 106.1922 0.00818 546 106.0208 0.00818 546 105.9708 0.00818 546 105.6887 0.00818 546 105.6578 0.00818 546 105.6392 Table 3.9: Mean true breeding value at generation 60 by selection strategy in the TRUE scenario. Mean Pop. Selection Mean TBV Strategy 106.5487 ucOCS 106.4723 WGS pmOCS 106.4252 MOGM90 106.4077 106.3379 OCS MOGS90 106.2959 106.2918 OHV50 106.2249 GEBV 106.2083 EBV 106.0369 UCS 105.9869 OPV50 105.7048 pmEBV pmGEBV 105.6738 105.6553 RS Statistical 95% Grouping Upper CI J 106.5648 106.4884 I 106.4413 H 106.4237 H 106.3540 G 106.3120 F 106.3079 F 106.2409 E 106.2244 E 106.0530 D 106.0029 C 105.7209 B 105.6899 AB 105.6714 A 3.2.3.2. Mean expected heterozygosity results After 60 generations of selection under the assumption of known QTL effects, RS proved to be the selection strategy that maintained the highest MEH (Fig. 3.13; Table 3.10). The second- and third-best selection strategies for maintaining MEH were OPV and WGS, respectively (Table 3.10). OCS was the next best selection strategy for preserving population MEH and was statistically tied with MOGS (Table 3.10). MOGS and MOGM exhibited statistically equivalent measures of MEH and were in the fifth-best statistical grouping for this metric (Table 3.10). GEBV and EBV were statistically equivalent to each other and performed worse than MOGS and MOGM (Table 3.10). Selection strategies which paired individuals like ucOCS, pmOCS, OHV, UCS, pmEBV, and pmGEBV performed worse than GEBV and EBV over the long term (Table 3.10). Rankings for the selection strategies were relatively stable throughout time, except for ucOCS and pmOCS (Fig. 3.13; Appx. A, Tables A.24-26). These two selection strategies expended their genetic diversity towards the end of the simulation resulting in a substantial drop in rank (Appx. A, Table A.24-26; Table 3.10). 123 Figure 3.13: Population mean expected heterozygosity over 60 generations by selection strategy in the TRUE scenario. Generation 60 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.1345 RS 0.1256 OPV50 0.1028 WGS 0.0695 OCS MOGS90 0.0679 MOGM90 0.0647 0.0549 GEBV 0.0539 EBV 0.0394 ucOCS 0.0366 pmOCS 0.0262 OHV50 0.0076 UCS pmEBV 0.0029 pmGEBV 0.0028 Std. Error 0.00081 546 0.1329 0.00081 546 0.1240 0.00081 546 0.1012 0.00081 546 0.0679 0.00081 546 0.0663 0.00081 546 0.0632 0.00081 546 0.0534 0.00081 546 0.0523 0.00081 546 0.0378 0.00081 546 0.0350 0.00081 546 0.0246 0.00081 546 0.0060 0.00081 546 0.0013 0.00081 546 0.0012 Table 3.10: Population mean expected heterozygosity at generation 60 by selection strategy in the TRUE scenario. Statistical Grouping J I H G FG F E E D D C B A A 95% Upper CI 0.1361 0.1272 0.1044 0.0711 0.0695 0.0663 0.0565 0.0555 0.0410 0.0382 0.0278 0.0092 0.0045 0.0044 124 3.2.3.3. Selection limit results WGS was found to be the best selection strategy at generation 60 for maintaining the USL by a large margin when QTL effects were known (Fig. 3.14; Table 3.11). OPV and RS were the second- and third-best selection strategies for maintaining population USL (Table 3.11). MOGM and MOGS were the fourth- and fifth-best selection strategies, respectively (Table 3.11). OCS and ucOCS were grouped together and outperformed pmOCS (Table 3.11). GEBV and EBV were statistically similar and mediocre in their performances (Fig. 3.14; Table 3.11). OHV and UCS performed worse than GEBV and EBV long-term, with OHV outperforming UCS (Table 3.11). Finally, pmEBV and pmGEBV were statistically the worst long-term selection strategies at generation 60 (Table 3.11). Like the MEH metric, rankings for the population USL remained very stable throughout the course of the simulations, with rankings at generation 15, 30, and 45 being almost identical to those in generation 60 (Fig. 3.14; Appx. A, Tables A.27-29; Table 3.11). In the analysis of the LSL, the results were almost opposite of those for the USL. At generation 60, RS, OPV, and WGS had the lowest, second-lowest, and third-lowest LSL metrics, respectively (Appx. A, Fig. A.3; Appx. A, Table A.33). MOGS, OCS, and MOGM were also among the lower half of selection strategies for this metric. ucOCS delivered the highest LSL at generation 60, followed by pmOCS and UCS (Appx. A, Table A.33). Over the 60 simulated generations, there appeared to be more rank changes for the LSL metric, especially for ucOCS and pmOCS. In early generations, pmGEBV, pmEBV, and UCS were the three strategies with the highest LSLs (Appx. A, Tables A.30-32), but in later generations, these three strategies were overtaken by ucOCS and pmOCS (Appx. A, Table A.33). 125 Figure 3.14: Population upper selection limit over 60 generations by selection strategy in the TRUE scenario. Mean Pop. Selection USL Strategy 107.1527 WGS 106.9878 OPV50 RS 106.9037 MOGM90 106.8362 MOGS90 106.7792 106.7032 OCS 106.6750 ucOCS 106.5814 pmOCS 106.4885 GEBV 106.4632 EBV 106.3521 OHV50 106.0398 UCS pmEBV 105.7057 pmGEBV 105.6743 Generation 60 DF 95% Std. Error Lower CI 0.00994 546 107.1332 0.00994 546 106.9682 0.00994 546 106.8841 0.00994 546 106.8167 0.00994 546 106.7596 0.00994 546 106.6836 0.00994 546 106.6554 0.00994 546 106.5618 0.00994 546 106.4690 0.00994 546 106.4436 0.00994 546 106.3326 0.00994 546 106.0202 0.00994 546 105.6862 0.00994 546 105.6547 Statistical Grouping 95% Upper CI 107.1722 K J 107.0073 106.9232 I 106.8558 H 106.7987 G 106.7227 F 106.6945 F 106.6009 E 106.5081 D 106.4827 D 106.3717 C 106.0593 B 105.7252 A 105.6938 A Table 3.11: Population upper selection limit at generation 60 by selection strategy in the TRUE scenario. 126 3.2.3.4. Other diversity metrics Genetic and genic variances largely mirrored the trends observed in MEH over time, with selection strategy rankings remaining mostly the same over time (Appx. A, Figs. A.4-5; Appx. A, Tables A.34-41). Notably, OPV, RS, and WGS were good long-term selection strategies for maintaining these two metrics (Appx. A, Tables A.37, 41). With respect to the Bulmer effect, OHV, OPV, UCS, and ucOCS tended to maintain a higher ratio of additive genetic variance to additive genic variance throughout the duration of the simulation, while MOGS, MOGM, pmOCS, RS, WGS, EBV, OCS, and GEBV tended to maintain a lower ratio (Appx. A, Fig. A.6; Appx. A, Tables A.42-45). These groupings indicated that MOGS, MOGM, pmOCS, RS, WGS, EBV, OCS, and GEBV tended to have a higher degree of genetic diversity that was temporarily inaccessible to selection due to linkage disequilibrium. pmEBV and pmGEBV were unique in that their Bulmer effects were comparatively low for most of the simulation but then substantially increased in later generations (Appx. A, Fig. A.6; Appx. A, Table A.45). Raw allele diversity metrics tended to mirror the trends observed in the USL and LSL performance metrics. Overall, selection strategies like OPV, RS, WGS, MOGS, and MOGM tended to preserve many polymorphic loci and fix fewer alleles regardless of whether they were beneficial or deleterious (Appx. A, Figs. A.7-11; Appx. A, Tables A.46-65). 3.2.4. EST scenario results 3.2.4.1. Genetic gain results We observed several major rank changes in selection strategy genetic gain performance under scenarios where the QTL effects were unknown compared to when they were known. At generation 60, pmOCS was identified as the best strategy at improving population mean TBVs (Fig. 3.15; Table 3.12). ucOCS, OCS, and MOGM were statistically tied as the next best 127 selection strategies for improving this metric (Table 3.12). OCS, MOGM, and GEBV were in the third-best statistical grouping (Table 3.12). For GEBV, this was a noticeable rank change since when true QTL effects were known, it exhibited a mediocre performance. MOGS was in the fourth-best statistical grouping and was statistically tied with GEBV with respect to improving mean TBVs (Table 3.12). EBV, OHV, and UCS were statistically similar and exhibited mediocre performance, worse than MOGS. pmGEBV outperformed pmEBV but performed worse than UCS (Table 3.12). OPV was in the second-worst statistical grouping for long-term genetic gain and outperformed WGS and RS (Table 3.12). WGS was statistically similar to RS and performed very poorly. This was a substantial change for WGS since in the TRUE scenario, WGS was among the top performers (Table 3.9). Selection strategy rankings for population maximum and minimum TBVs closely mirrored those for the population mean TBV (Appx. A, Figs. A.12-13; Appx. A, Table A.69-76). At generation 60, pmOCS, MOGM, OCS, and ucOCS were statistically grouped as the best selection strategies for improving the population maximum TBV (Appx. A, Table A.72), and pmOCS was statistically determined as the best selection strategy for improving the population minimum TBV, with ucOCS and OCS as a close second (Appx. A, Table A.76). Several major rank changes were observed throughout the 60 simulated generations. For example, pmGEBV, UCS, and pmEBV were among the best selection strategies at generation 15, but then reduced in their ranking as the simulated progressed (Appx. A, Table A.66-68). OCS, pmOCS, ucOCS, MOGS, and MOGM were intermediately ranked in early generations but increased in their rankings as the generation number increased. pmOCS performed quite well over the duration of the simulation. At generation 15, it was an upper mid-tier strategy, but then remained as the dominant strategy at generations 30, 45, and 60 (Appx. A, Table A.66-68). 128 Figure 3.15: Population mean true breeding value over 60 generations by selection strategy in the EST scenario. Mean Pop. Selection Mean TBV Strategy 105.9185 pmOCS 105.8494 ucOCS OCS 105.8453 MOGM90 105.8255 GEBV 105.8052 MOGS90 105.7785 105.6377 EBV 105.6360 OHV50 UCS 105.6295 pmGEBV 105.5872 105.3037 pmEBV 105.1604 OPV50 105.0042 WGS 104.9997 RS Generation 60 DF 95% Std. Lower CI Error 0.00845 546 105.9019 0.00845 546 105.8328 0.00845 546 105.8287 0.00845 546 105.8089 0.00845 546 105.7886 0.00845 546 105.7619 0.00845 546 105.6211 0.00845 546 105.6194 0.00845 546 105.6129 0.00845 546 105.5706 0.00845 546 105.2871 0.00845 546 105.1438 0.00845 546 104.9876 0.00845 546 104.9831 95% Statistical Upper CI Grouping I 105.9351 105.8660 H 105.8619 GH 105.8421 GH 105.8218 FG 105.7951 F 105.6543 E 105.6526 E 105.6461 E 105.6038 D 105.3203 C 105.1770 B 105.0208 A 105.0163 A Table 3.12: Population mean true breeding value at generation 60 by selection strategy in the EST scenario. 129 3.2.4.2. Mean expected heterozygosity results Results for selection strategy long-term MEH preservation in the EST scenario were similar to the results in the TRUE scenario. At generation 60, WGS exhibited the best long-term MEH preservation by a large margin (Fig. 3.16; Table 3.13). OPV and RS were the second- and third-best selection strategies for maintaining population MEH (Table 3.13). MOGM, MOGS, and OHV exhibited the fourth-best performance for this metric (Table 3.13). Notably, the ranking for OHV in the EST scenario was a large improvement compared to its performance in the TRUE scenario. OCS, GEBV, and EBV exhibited similar performances but performed worse than MOGM, MOGS, and OHV (Table 3.13). ucOCS exhibited a poor performance, underperforming compared to OCS, GEBV, and EBV, but beating UCS and pmOCS (Table 3.13). UCS and pmOCS performed similarly to each other (Table 3.13). pmEBV and pmGEBV were the worst selection strategies for preserving population MEH. MEH preservation ranking changes did not change much over time except for ucOCS and pmOCS, which started good, but lost substantial diversity by the end of the simulation (Fig. 3.16; Appx. A, Table A.77-79). The diversity loss by ucOCS and pmOCS closely mirrored the same trends observed during the TRUE scenario. 130 Figure 3.16: Population mean expected heterozygosity over 60 generations by selection strategy in the EST scenario. Generation 60 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2401 WGS 0.1899 OPV50 RS 0.1723 MOGM90 0.1139 MOGS90 0.1139 0.1128 OHV50 0.0951 OCS 0.0939 GEBV 0.0907 EBV 0.0760 ucOCS 0.0572 pmOCS 0.0550 UCS pmEBV 0.0296 pmGEBV 0.0293 Std. Error 0.00097 546 0.2382 0.00097 546 0.1880 0.00097 546 0.1704 0.00097 546 0.1120 0.00097 546 0.1120 0.00097 546 0.1109 0.00097 546 0.0932 0.00097 546 0.0919 0.00097 546 0.0888 0.00097 546 0.0741 0.00097 546 0.0553 0.00097 546 0.0531 0.00097 546 0.0276 0.00097 546 0.0273 Table 3.13: Population mean expected heterozygosity at generation 60 by selection strategy in the EST scenario. Statistical Grouping H G F E E E D D D C B B A A 95% Upper CI 0.2420 0.1918 0.1742 0.1158 0.1158 0.1147 0.0971 0.0958 0.0926 0.0779 0.0591 0.0569 0.0315 0.0312 131 3.2.4.3. Selection limit results Long-term preservation of USL under the EST scenario was, again, very similar to the trends observed in the TRUE scenario. WGS proved to be the best strategy (Fig. 3.17; Table 3.14). OPV and RS were the second- and third-best selection strategies for maintaining this metric (Table 3.14). MOGM and MOGS were the fourth-best selection strategies for preserving USL and were statistically grouped together (Table 3.14). OCS and OHV statistically grouped together and followed MOGM and MOGS in performance ranking (Table 3.14). GEBV performed at an intermediate level and was statistically grouped with OHV (Table 3.14). EBV and ucOCS were statistically similar to each other and performed worse than OHV, GEBV, and OCS (Table 3.14). pmOCS performed worse than EBV and ucOCS (Table 3.14). UCS performed poorly in its ability at preserving USL, worse than pmOCS (Table 3.14). Finally, pmGEBV and pmEBV, were the worst two strategies for preserving USL (Table 3.14). USL rankings for each of the tested selection strategies were relatively stable across generations (Appx. A, Table A.80- 82). Like in the TRUE scenario, rankings for selection strategies in their ability to increase the LSL at generation 60 were almost completely opposite of their rankings for maintaining the USL (Appx. A, Fig. A.14; Appx. A, Table A.86). Selection strategies that excelled at maintaining their USLs tended to exhibit reduced LSLs. Furthermore, ranking for LSL improvement were relatively stable across generations (Appx. A, Fig. A.14; Appx. A, Tables A.83-86). 132 Figure 3.17: Population upper selection limit over 60 generations by selection strategy in the EST scenario. Mean Pop. Selection USL Strategy 107.1853 WGS 107.1255 OPV50 RS 106.9880 MOGM90 106.8380 MOGS90 106.8345 106.6507 OCS 106.6048 OHV50 106.5900 GEBV 106.4934 EBV 106.4856 ucOCS 106.3626 pmOCS UCS 106.1115 pmGEBV 105.8108 105.6159 pmEBV Generation 60 DF 95% Std. Error Lower CI 0.01182 546 107.1621 0.01182 546 107.1023 0.01182 546 106.9648 0.01182 546 106.8148 0.01182 546 106.8113 0.01182 546 106.6275 0.01182 546 106.5816 0.01182 546 106.5667 0.01182 546 106.4702 0.01182 546 106.4624 0.01182 546 106.3394 0.01182 546 106.0882 0.01182 546 105.7876 0.01182 546 105.5927 Statistical Grouping 95% Upper CI 107.2086 K J 107.1488 107.0112 I 106.8612 H 106.8577 H 106.6739 G 106.6280 FG 106.6132 F 106.5166 E 106.5088 E 106.3859 D 106.1347 C 105.8341 B 105.6391 A Table 3.14: Population upper selection limit at generation 60 by selection strategy in the EST scenario. 133 3.2.4.4. Other diversity metrics Trends in population genetic and genic variances closely followed the trends observed in MEH over time, with selection strategy rankings remaining very similar over time (Appx. A, Figs. A.15-16; Appx. A, Tables A.87-94). At generation 60, WGS, OPV, and RS were the top three strategies for maintaining population genetic and genic variance (Appx. A, Tables A.90, 94). With respect to the Bulmer effect, OHV, OPV, UCS, and ucOCS tended to maintain a higher ratio of additive genetic variance to additive genic variance throughout the duration of the simulation, like was observed in the TRUE scenario (Appx. A, Fig. A.17). Statistical groupings were murkier, however, with many overlapping statistical groupings (Appx. A, Tables A.95-98). Like in the TRUE scenario, MOGS, MOGM, pmOCS, WGS, EBV, OCS, GEBV tended to maintain a lower Bulmer effect, indicating that these strategies had a higher degree of genetic diversity temporarily inaccessible to selection due to linkage disequilibrium. Unlike in the TRUE scenario, pmEBV and pmGEBV did not increase in their Bulmer effects in later generations (Appx. A, Fig. A.17; Appx. A, Tables A.95-98). Like in the TRUE scenario, raw allele diversity metrics tended to mirror the trends observed in the upper and LSL performance metrics in the EST scenario (Appx. A, Figs. A.18-22; Appx. A, Tables A.99-118). Additionally, the WGS, OPV, RS, MOGS, and MOGM selection strategies tended to preserve many polymorphic loci and fix a fewer number of QTL alleles regardless of whether they were beneficial or deleterious in the EST scenario (Appx. A, Tables A.99-118). 134 4. Discussion 4.1. Allele frequency alteration simulation experiment 4.1.1. MOGS and MOGM allele diversity preservation performance We find that MOGS and MOGM can be used as effective diversity preservation selection strategies. With respect to preservation of polymorphic loci, MOGS and MOGM were among the top performing strategies. Based on the 10% PAFD, 90% PAU pseudo-weights given to MOGS and MOGM objectives and on the individual performances of both objectives, it appears that the PAU objective is extremely effective at preserving the number of polymorphic loci in a population. PAFD, while preserving many polymorphic loci, does not do as effective of a job as PAU. Due to its exceptional performance, we suggest that the PAU objective could serve as an alternative diversity constraint to the typical quadratic inbreeding constraints used in the optimal contribution selection family of selection strategies. With respect to their ability at preserving and improving the MEH of a population, we find that MOGS and MOGM are capable selection strategies, underperforming only MEHS. Compared to their comprising objectives, PAFD and PAU, MOGS and MOGM outperform both objectives individually, suggesting that there is a synergistic effect of selecting towards a target allele frequency, which PAFD was designed to accomplish, and preserving raw allele diversity, which PAU was designed to accomplish. Mathematically, PAFD and MEHS are optimization problems that seek to minimize the weighted L1- and L2-norm distance, respectively, between the selection allele frequency and a target allele frequency, which in both cases was 0.5. Comparing these two strategies, we find that minimizing the weighted L2-norm distance is a more efficient strategy than its L1-norm counterpart in both preserving raw allele diversity and improving MEH. The L2-norm appears to 135 more heavily penalize deviations from target allele frequencies than the L1-norm in its mathematical formulation, leading to better preservation of allele diversity and attainment of MEH. We suggest that replacing the PAFD objective in MOGS and MOGM with an equivalent L2-norm minimization objective may be a way to improve upon MOGS and MOGM. 4.1.2. MEHS and MGRS allele diversity preservation performance Though related in their mathematical forms, MEHS and MGRS exhibited divergent performance in both the number of polymorphic loci preserved and MEH. This relates to their mathematical formulation. In MEHS, using an identity-by-state kinship matrix to determine inbreeding relationships implicitly established the optimization problem to one where the goal was to minimize the L2-norm distance between the selection allele frequency and a target allele frequency of 0.5. In MGRS, using a VanRaden genomic relationship matrix implicitly established the optimization problem to one where the goal was to minimize the L2-norm distance between the selection allele frequency and the current population allele frequency. Thus, the goal of MEHS was to shift all allele frequencies to 0.5, while the goal of MGRS was to maintain current allele frequencies. This major difference between MEHS and MGRS can be observed in the MEH performance data. MGRS experienced only a slight decrease in MEH across generations, while MEHS improved it. We suspect that the decrease in MEH exhibited by MGRS is likely due to genetic drift rather than a failure of the method. Overall, these results can help serve as guidance for breeders seeking to maintain genetic diversity with quadratic constraint strategies: choice of genomic relationship matrix governs how population allele frequencies change over time and more importantly, to what allele frequencies towards which a population will be pushed. 136 4.1.3. MOGS and MOGM distance metric minimization performance In minimizing the Manhattan and Euclidean distance between the population allele frequency and a target allele frequency of 0.5, we find that MOGS and MOGM are capable strategies but do not perform as well as MEHS. MOGS and MOGM performed better than both of their constituent functions, suggesting again that there is a synergistic effect between PAFD and PAU. The superior performance of MEHS in improving the Manhattan and Euclidean distance suggests that L2-penalization is a more effective strategy for altering allele frequencies than an L1-penalization strategy. MOGS and MOGM may be able to be improved by replacing the L1-norm based, PAFD objective with an L2-norm based objective. 4.2. Breeding program simulation experiment 4.2.1. Remarks on general selection strategy behaviors In our simulations, we tested a diverse panel of selection strategies with the intent of benchmarking our own selection strategies as well as better understanding the behavior of previously published selection strategies. From these results, we observe that selection strategies fall into a spectrum of behaviors. At extremes of this spectrum, selection strategies may be described as maximally exploitative, maximally preservative, or controlled exploitative. Maximally exploitative selection strategies tend to quickly exploit genetic diversity in their behavior. In the long-term, maximally exploitative selection strategies deplete population genetic diversity and are unable to sustain genetic gains due to a lack of diversity. In our study, we identify selection strategies like GEBV, EBV, UCS, pmEBV, and pmGEBV as tending to be more maximally exploitative. Maximally preservative selection strategies tend to preserve as much genetic diversity as possible in their behavior. In the long-term, maximally preservative selection strategies maintain population genetic diversity and can sustain genetic gains as a 137 result. WGS, OPV, MOGM, and MOGS are examples of selection strategies that tend to exhibit these behaviors. Finally, controlled exploitative selection strategies tend to take a middle ground approach and constrain the exploitation of genetic diversity according to some timescale. OCS, pmOCS, and ucOCS tended to exhibit this behavior because of their inbreeding constraints, which became more relaxed as time progressed. 4.2.2. Consequences of selecting 40 unique parents versus 20 unique mate pairs The selection strategies that we tested in our simulations can be classified into two groups: those which select 40 unique parents and those which select 20 unique mate pairs. In the former strategy, all parents must be unique while in the latter strategy, it is possible for a parent to be used in multiple mate pairings. WGS, MOGM, MOGS, GEBV, OCS, EBV, OPV, and RS fall into the former category, while OHV, ucOCS, pmOCS, UCS, pmGEBV, and pmEBV fall into the latter category. We observed that in the absence of diversity preservation mechanisms, selection strategies which selected 40 unique parents tended to have better long-term success compared to their mate pair selection counterparts. As evidence of this, EBV and GEBV selection strategies outperformed pmEBV and pmGEBV, respectively, in long-term genetic gain and diversity metrics in both TRUE and EST scenarios. This finding is unsurprising, given that it is well known that maintaining genetic diversity is essential to sustaining long-term genetic gains. In the presence of diversity preservation mechanisms, we observed that selection strategies which selected 20 unique mate pairs tended to outperform strategies which selected 40 unique parents with respect to genetic gain. For example, ucOCS and pmOCS tended to outperform OCS in genetic gain in both TRUE and EST scenarios. These increases in genetic 138 gain came at the cost of genetic diversity, however. In the long-term, OCS tended to select for more diverse populations compared to ucOCS and pmOCS. 4.2.3. Consequences of using variance estimates to inform selection decisions In our study, we observed that using progeny variance estimates to inform selection decisions had positive to mixed results. In scenarios where QTL locations and effects were known, using progeny variances to make selection decisions unambiguously improved genetic gain and in several cases, genetic diversity. For example, in the TRUE scenario at generation 60, ucOCS outperformed its counterpart, pmOCS, in improving population mean breeding value. Similarly, UCS also outperformed its counterpart, pmGEBV, in this same metric. MOGM also improved its genetic gain metrics over MOGS. With respect to improving MEH and USL, selection methods incorporating progeny variances were either neutral compared to their non- variance incorporating counterparts or improved these metrics. For example, UCS improved both diversity metrics over pmGEBV and ucOCS improved over pmOCS in only the USL metric. MOGM and MOGS exhibited similar diversity metric results. Unlike the TRUE scenario, using progeny variance estimates in the EST scenario had mixed results, and we recommend caution in using progeny variance estimates to make breeding decisions. In our long-term genetic gain results, ucOCS underperformed pmOCS, UCS outperformed pmGEBV, and MOGM outperformed MOGS. We believe that this is because progeny variance, a second-order statistic, is more challenging to estimate than progeny mean, a first-order statistic. Any errors made in estimating marker effects will be squared when calculating progeny variance. Indeed, in empirical research studies with real traits, progeny variances have been found to be somewhat challenging to predict (Adeyemo & Bernardo, 2019; Neyhart et al., 2019; Wartha & Lorenz, 2024), especially in traits with low heritability (Neyhart 139 et al., 2019). The additional error introduced in estimating progeny variance may reduce long- term genetic gains through reduced selection accuracy or increase long-term genetic gains through increased genetic diversity preservation, depending on the selection strategy. For ucOCS which had diversity preservation techniques employed in its methodology, the additional error introduced in the progeny variance estimate reduced selection accuracy and consequently reduced long-term genetic gains and increased genetic diversity relative to pmOCS. For UCS which had no diversity preservation technique employed, the additional error reduced selection accuracy and resulted in poorer short-term genetic gains (Appx. A, Table A.66-67) relative to the TRUE scenario at the same time points (Appx. A, Table A.13-14), but also improved population genetic diversity, allowing for better long-term genetic gains relative to pmGEBV. Finally, in the case of MOGM, it seems like the negative effects of progeny variance errors were largely mitigated by segregating the selection of individuals and the pairing of individuals into two different steps. In MOGM, selection accuracy was not reduced by erroneous progeny variance estimates, and any accuracy in progeny variance estimates could be maximally exploited in the pairing step. 4.2.4. MOGS and MOGM performance Overall, MOGS and MOGM performed well. While not performing the best in every category, they demonstrated themselves to be in the top half of tested selection strategies for genetic gain and genetic diversity metrics. These findings support the efficacy of the two objectives utilized by MOGS and MOGM. The mate pairing strategy according to the estimated progeny variance in MOGM had an overall beneficial effect on selection strategy performance relative to MOGS. In the TRUE scenario, the mate pairing strategy increased the LSL, mean TBV, maximum TBV, minimum TBV, number of fixed favorable alleles, and number of 140 polymorphic favorable alleles. The mate pairing strategy also decreased the number of fixed deleterious alleles, number of polymorphic deleterious alleles, and the genic variance. In the EST scenario, the mate pairing strategy increased the population mean TBV, minimum TBV, and LSL. This suggests that mate pairing based on the predicted progeny variance of mate pairs may be of benefit in practical scenarios. As mentioned in the preceding section, using progeny variance estimates to make selections come with risks, but these risks appear to be mitigated by separating parental selection from parental pairing. If the correlation between estimated and true progeny variances is positive, then the benefit of mate pairing will be proportional to the correlation strength. If there is no correlation between estimated and true progeny variances, then mate pairing will be no better than random. Finally, if the correlation between estimated and true progeny variances is negative, then the mate pairing strategy may work antagonistically with selection goals. To our knowledge, MOGM is the first proposed formulation of a mate pairing problem as a case of maximum weighted matching described in the literature. We submit that this mate pairing strategy may be useful for deciding mate pairs using metrics other than estimated progeny variance, if the breeder is uncomfortable with the associated error. For example, Akdemir & Sánchez (2016) construct a “risk” objective to assess the desirability of a proposed mate pairing. This metric is agnostic of any marker effect estimates and only relies on observed genomic marker data which are presumed to be measured with certainty. First order statistics may be reliable enough to assess the merit of a proposed mate pair, too. For example, Moeinizade et al. (2019) allocated resources to mate pairs according to the range of progenies which could possibly be observed using marker effect estimates. 141 4.2.5. Potential improvements to MOGS and MOGM Although MOGS and MOGM performed well, we propose that they can be further improved in three manners. First, we propose that MOGS and MOGM may be improved by improving the NSGA-III algorithm used to map the Pareto frontier for their two objectives. In the TRUE scenario, it appears that our NSGA-III algorithm performed well, but for the EST scenario, the same algorithm got trapped in a local optimum. We believe that this is due to the number of markers examined. In the TRUE scenario, 1000 markers were considered in the PAFD and PAU objectives, while in the EST scenario, 2000 markers were considered. In general, combinatorics problems are challenging to solve, and in our case, it appears that the PAFD and PAU problem challenge increases with the number of markers considered. We propose that improving the recombination operator or perhaps adding a local search operator to our NSGA-III algorithm will improve its performance and consequently the performance of MOGS and MOGM. Second, optimizing for both MOGS and MOGM was computationally difficult compared to many of the other selection strategies we tested. In selection scenarios where quick optimization times are required, MOGS and MOGM may be too slow. Since genetic algorithms are known to be slower optimization algorithms, it may be better to convert either the PAFD or PAU objective into a constraint and conduct a single-objective optimization using a faster optimization algorithm, like a hillclimber. Third and finally, based on the performance in the allele frequency alteration experiment, replacing the L1-norm based, PAFD objective with an L2-norm based objective may provide better performance for MOGS and MOGM both in terms of genetic gain and genetic diversity preservation. 142 4.2.6. Future studies on the effects of genetic architecture on MOGS and MOGM performance In our study, we only investigated the performance of MOGS and MOGM for selection of a single, additive, quantitative trait controlled by many QTL. Since we only studied the behavior of MOGS and MOGM under this specific genetic architecture, much is unknown about the efficacy of MOGS and MOGM with trait controlled by few to intermediate numbers of QTL, and traits exhibiting dominance and/or epistatic effects. Currently, both the PAFD and PAU objectives in MOGS and MOGM implicitly assume an additive genetic architecture in their formulation. We are unsure how well this implicit assumption would impact the performance of MOGS and MOGM in scenarios where genetic architecture was not strictly additive in nature. Future studies should seek to answer this question. 4.2.7. Remarks on WGS performance Perhaps one of the most interesting and surprising results from these experiments were the results from WGS. In the TRUE scenario, WGS was the top strategy or among the top strategies in many metrics. In the long-term, WGS was the best in maximum TBV, second-best in mean TBV, and third-best in minimum TBV. WGS was also exceedingly competent in its ability to maintain genetic diversity over the long-term. It was third-best in MEH, best in USL, third- best in genetic variance, and third-best in genic variance. It accomplished this by maintaining the highest levels of favorable and deleterious polymorphic loci and by fixing the least amount of favorable and deleterious alleles. In the EST scenario, WGS was the worst selection strategy at delivering genetic gain and tied with RS. WGS was the best selection strategy at maintaining genetic diversity as measured by population MEH and USL, however. These results are highly curious and suggest that WGS is highly sensitive to marker effect estimate errors. The 143 upweighting strategy used by WGS seems to magnify the marker effect errors thereby significantly reducing the efficacy of selection. The error magnification does not seem to affect the ability of WGS to maintain diversity. Previously, WGS was shown to outperform selection on GEBV (Goiffon et al., 2017; Jannink, 2010). We believe that the differences in results between our study and others may be caused by differences in population structure. In our simulations, we adopt an overlapping cohort framework whereas in other simulations, authors have opted for non-overlapping cohort frameworks. Non-overlapping cohort frameworks induce high levels of genetic bottlenecking which emphasize the importance of maintaining genetic diversity. In these scenarios, WGS may have been able to outperform other selections strategies because of its superior ability to maintain genetic diversity. To improve genetic gain metrics in WGS, we speculate that a more moderate upweighting strategy may reduce the magnification of errors thereby permitting improved genetic gain metrics. We also speculate that reducing the magnitude of upweighting will also result in a reduction in the strategy’s ability to maintain genetic diversity as a necessary tradeoff. 4.2.8. Remarks on OPV performance In our study, OPV demonstrated behaviors divergent from what has been previously published (Goiffon et al., 2017). In our study, OPV was among the worst selection strategy for long-term genetic gain metrics in both TRUE and EST scenarios. It was common for OPV to only outperform RS at many time points. OPV did however excel at maintaining genetic diversity in both TRUE and EST scenarios. In many instances, it was only rivaled by WGS and RS. These results disagree substantially with the results published by Goiffon et al. (2017) who found that OPV was able to generate the most genetic gain and preserve the most genetic diversity when compared with other strategies. We believe that these results are due to the 144 different simulation frameworks used between our studies. Goiffon et al. (2017) utilized a non- overlapping cohort population structure, which induced extreme bottlenecking pressures. In our study, we made use of an overlapping cohort population structure, which mitigated extreme bottlenecking effects. Since OPV scores proposed parental selections using the best haplotype blocks found in the selected subset, we speculate that OPV’s objective function specification excels at maintaining valuable diversity but is ineffective at increasing valuable haplotype block frequencies. Intuitively, these objective function characteristics would be advantageous in selection scenarios where there was a high probability of losing valuable haplotype blocks and/or alleles, as what would be experienced in extreme genetic bottlenecking scenarios. We speculate that in extreme bottlenecking scenarios, genetic drift coupled with the maintenance of valuable haplotype blocks provided by OPV may work synergistically to purge deleterious alleles and increase genetic gain relative to other selection strategies. In scenarios where genetic diversity is more abundant and the bottlenecking effect less pronounced, as in our simulation scenarios, these synergistic effects may be substantially reduced, resulting in reduced genetic gain, but continued maintenance of genetic diversity. 5. Conclusion In this study, we presented multi-objective genomic selection (MOGS) and multi- objective genomic mating (MOGM). We find that MOGS and MOGM are performant and robust selection strategies capable of altering population allele frequencies to an arbitrary target and to drive genetic gain in breeding programs. Though not the best selection strategies, MOGS and MOGM are competitive and offer high genetic gains with higher genetic diversity metrics compared to many other selection strategies. Novel to the MOGM selection strategy is a mate pairing step which solves a maximum weighted matching problem. We propose that this mate 145 pairing step may be useful in practical breeding scenarios and could be applied as a step on top of existing selection techniques to further improve genetic gains. 146 CHAPTER 4: TOWARDS THE DEVELOPMENT OF MULTI-OBJECTIVE, TIME- COGNIZANT SELECTION STRATEGIES 1. Introduction 1.1. Multi-objective and time-cognizant selection strategies In plant and animal breeding, a breeder is concerned with the genetic improvement of a plant or animal species for human benefit (Bernardo, 2020a). Genetic improvement of a species is primarily accomplished through selection (Falconer & Mackay, 1996). Since selection has profound short- and long-term consequences on a breeding population, a breeder must choose a selection methodology carefully. Two important considerations when formulating a selection methodology are: 1) how the selection methodology should handle multiple traits simultaneously and 2) how the selection methodology should change across time. For the former consideration, most breeding programs are inherently multi-objective in nature. Traits such as yield, biomass, biotic and abiotic stress resistance, maturity, adaptation to mechanization, and quality attributes all serve as potential targets of selection (Fehr, 1991). Genetic diversity of a breeding population may also be a consideration (Meuwissen, 1997). For the latter consideration, presumably the constitution of a breeding population changes over time as selection occurs, thereby presenting new challenges to the breeding program. A selection methodology should account for these future challenges and make better selection decisions in the present to poise the breeding program to make better selection decisions in the future. Multi-objective and time-cognizant selection methodologies have been frequently studied for use in breeding programs. Selection on multiple traits has been a topic which has been studied since at least the 1930s. In 1936 and 1943, Smith and Hazel, respectively, described an optimal selection index selection methodology for multiple traits. This selection methodology, 147 often referred to as Smith-Hazel index selection, takes into consideration a set of economic weights, heritabilities, and coheritabilities for a set of traits and identifies a linear index which maximizes the probability of selecting individuals with the best genotypic values according to the provided economic weights. Many other index selection methodologies have also been proposed including base index selection (Williams, 1962), weight-free index selection (Elston, 1963), desired gains index selection (Pešek & Baker, 1969), and rank sum index selection (Mulamba & Mock, 1978). Outside of index selection, techniques such as tandem selection and independent culling have been proposed as methods for improving multiple traits simultaneously (Bernardo, 2020a). Index selection techniques, however, are generally regarded as being better than tandem selection and independent culling (Bernardo, 2020a). Outside of selection indices, several techniques have been proposed that incorporate measures of genetic diversity as objectives or objective components (Akdemir et al., 2019; Akdemir & Sánchez, 2016; Allier, Lehermeier, et al., 2019; De Beukelaer et al., 2017; Gorjanc et al., 2018a; Meuwissen, 1997; Pryce et al., 2012; Sanchez et al., 2023; Sonesson et al., 2012). Popular among these techniques is optimal contribution selection, which seeks to maximize the breeding value of selected individuals subject to an inbreeding constraint (Meuwissen, 1997). With the advent of cheap genotyping technology and genomic prediction techniques, there has been a resurging interest in multi-objective and multi-trait selection methodologies. Genotypic information has a broad range of uses. Notably, it can be used to make more accurate genotypic and breeding value predictions (Calus et al., 2008; Habier et al., 2007; Meuwissen et al., 2001) and to more accurately calculate kinship relationships between individuals (Bernardo, 2020a). Genotypic information can also be leveraged to perform selection strategies not previously possible. For example, genotypic information has been used to improve optimal 148 contribution selection strategies in both single- (Sonesson et al., 2012) and multi- (Akdemir et al., 2019) trait scenarios. It has also been used to inform multi-trait look-ahead selection strategies (Han et al., 2017; Moeinizade et al., 2019, 2020; Zhang & Wang, 2022). Time-cognizant selection techniques are a more recent innovation in selection methodology. In many selection techniques, it is implicitly considered. In optimal contribution selection, time may be incorporated into a selection strategy by gradually reducing the inbreeding constraint over time. Allier, Lehermeier, et al. (2019) considered linear reductions in the inbreeding constraint in a long-term optimal contribution selection scenario but noted that other inbreeding constraint trajectories are possible. In optimal haploid value (Daetwyler et al., 2015) and optimal population value (Goiffon et al., 2017) selection, the number of haplotype blocks into which the genome is broken is determined using empirical simulations and is proportional to the breeding horizon. A higher number of haplotype blocks corresponds to better long-term performance for both strategies. In other selection techniques, time is explicitly considered as a factor influencing selection decisions. Selection strategies which upweight marker effects according to some criterion may incorporate time as a criterion factor, such as the dynamically upweighted selection strategy proposed by Liu et al. (2015). Liu et al. (2015) found dynamically upweighting genomic marker effects could improve long-term selection trajectories. In the simulation-based, look- ahead family of selection strategies (Moeinizade et al., 2019, 2020; Zhang & Wang, 2022), the objective functions for all family members explicitly take time to a deadline into consideration. The consideration of time to a deadline causes basic look-ahead selection strategies to manifest unique properties. Single- and multi-trait look-ahead selection strategies tend to accumulate and conserve genetic diversity in early generations, but then rapidly exploit genetic diversity in later 149 generations (Moeinizade et al., 2019, 2020). In present-value look-ahead selection, this behavior was altered by considering the present-value of the best simulated individuals for a proposed selection decision across a customizable time window. This resulted in better short term genetic gains compared to ordinary, single-trait look-ahead selection at a slight cost in long-term genetic gains (Zhang & Wang, 2022). 1.2. Tested selection methods background and formulation as optimization problems As introduced above, there are many selection strategies which have been proposed that consider multiple traits or objectives and explicitly or implicitly consider time as an input in decision-making. Below, we briefly describe several of the selection strategies relevant to this set of experiments. 1.2.1. Genomic estimated breeding value (GEBV) selection Genomic estimated breeding value (GEBV) selection is a parental selection strategy proposed by Meuwissen et al. (2001) that seeks to maximize the sum of GEBVs for a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates. The GEBV for an individual may be calculated as a sum of allele effects for the individual’s unique genotype using allele effect estimates from a genomic prediction model (Meuwissen et al., 2001). Fundamentally, selection on GEBV for a single trait is a ranking and sorting optimization problem, mathematically stated as: Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, 150 where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is included in the selected subset and 𝐲𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing GEBVs for parental candidates. For multiple traits, it is possible to assign economic weights 𝐞 and use base index selection (Williams, 1962) to select a subset of individuals with the best indices for multiple traits. Multi-trait GEBV selection can be mathematically expressed as: Subject to: max 𝐱 ′ 𝐞𝐘𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐞 is a vector containing economic weights for 𝑇 traits, 𝐘𝐆𝐄𝐁𝐕 is a 𝑁Ω × 𝑇 matrix containing genomic estimated breeding values for parental candidates, and all other symbols are as before. 1.2.2. Weighted genomic selection (WGS) Weighted genomic selection (WGS) is a variant of GEBV selection that upweights favorable alleles according to the frequency of the favorable allele (Goddard, 2009; Jannink, 2010). The goal of WGS is to maximize the sum of weighted genomic estimated breeding values (wGEBVs) in a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates. Like GEBV selection, WGS is a ranking and sorting optimization problem and is mathematically stated as: Subject to: max 𝐱 ′ 𝐲𝐰𝐆𝐄𝐁𝐕 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, 151 where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is included in the selected subset and 𝐲𝐰𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing wGEBVs for parental candidates. 1.2.3. Optimal contribution selection (OCS) Optimal contribution selection (OCS) is a parental selections strategy that seeks to maximize the breeding values of selected individuals, subject to an inbreeding constraint (Meuwissen, 1997). There are many variants of OCS, but for the purposes of this study, we seek to maximize the sum of GEBVs for a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates subject to an average identity-by-state kinship relationship constraint like what was described in Allier, Lehermeier, et al. (2019). Mathematically, OCS is defined as: Subject to: max 𝐱 ′ 𝐲𝐆𝐄𝐁𝐕 𝐱 1 2 𝐱′𝐊𝐱 ≤ 𝐶̅𝑡+1 𝑁Ξ ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected, 𝐲𝐆𝐄𝐁𝐕 is a vector of length 𝑁Ω containing GEBVs for parental candidates, 𝐊 is an 𝑁Ω × 𝑁Ω identity-by-state kinship relationship matrix for parental candidates, and 𝐶̅𝑡+1 is the maximum allowable mean kinship allowed in the next generation. Similar to multi-trait GEBV selection, it is also possible to describe a multi-trait variant of OCS using base index selection (Williams, 1962), like what was done in Akdemir et al. (2019). Multi-trait OCS using a base index can be described as: 152 Subject to: max 𝐱 ′ 𝐞𝐘𝐆𝐄𝐁𝐕 𝐱 1 2 𝐱′𝐊𝐱 ≤ 𝐶̅𝑡+1 𝑁Ξ ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐞 is a vector containing economic weights for 𝑇 traits, 𝐘𝐆𝐄𝐁𝐕 is a 𝑁Ω × 𝑇 matrix containing genomic estimated breeding values for parental candidates, and all other symbols are as before. 1.2.4. Random selection (RS) As the name suggests, individuals are randomly selected to serve as parents in random selection. Specifically, a random subset of 𝑁Ξ individuals is selected from a set of 𝑁Ω parental candidates to serve as parents for the next generation. 1.3. Goal and outline of this chapter The goal of this chapter is to develop two variants of WGS and determine if they are effective selection strategies compared against established GEBV and OCS methods. The first WGS variant is multi-trait in nature with adjustable upweighting parameters, and the second WGS variant is multi-trait and time-cognizant with adjustable upweighting parameters. In the following sections, we describe our methods, present results characterizing the effects of upweighting in long-term selection with our proposed selection strategies, present results for single- and multi-trait versions of our WGS variants, offer discussion on the performances of the proposed selection strategies, and finally conclude. 153 2. Methods 2.1. Two new multi-trait selection methodologies 2.1.1. A new, multi-trait, generalized weighted genomic selection methodology We introduce a new multi-trait, generalized weighted genomic selection (GWGS) strategy that is a generalization of WGS (Goddard, 2009; Jannink, 2010). We first begin by observing that in WGS, Jannink (2010) upweights marker effects for the 𝑡th trait according to the following approximation: 𝜋 2 𝑢̂𝑚,𝑡 = − sin−1(√𝑝̃𝑚,𝑡) 𝑢𝑚,𝑡 √𝑝̃𝑚,𝑡(1 − 𝑝̃𝑚,𝑡) ≈ 1 √𝑝̃𝑚,𝑡 𝑢𝑚,𝑡 ≈ 𝑝̃𝑚,𝑡 −0.5𝑢𝑚,𝑡, where 𝑢𝑚,𝑡 is the marker effect at the 𝑚th locus for the 𝑡th trait, 𝑝̃𝑚,𝑡 is the favorable allele frequency at the 𝑚th locus for the 𝑡th trait, and 𝑢̂𝑚,𝑡 is the upweighted marker effect at the 𝑚th locus for the 𝑡th trait. We note that the upweighting factor of Jannink’s (2010) inverse square root approximation to Goddard’s (2009) ideal weighting can be adjusted by modifying the exponent of the favorable allele frequency. We propose that marker effects can be more generally upweighted according to: 𝑢̂𝑚,𝑡 = 𝑝̃𝑚,𝑡 −𝛼𝑡𝑢𝑚,𝑡, where 𝛼𝑡 is an upweighting hyperparameter for the 𝑡th trait established by the user. The range of the 𝛼𝑡 hyperparameter is [0, ∞) with 0 being equivalent to selection on GEBVs and upweighting increasing as 𝛼𝑡 → ∞. For practical and experimental purposes, we suggest that the 𝛼𝑡 range be restricted to [0,1]. 154 Using the generalized marker effect upweighting scheme described above, generalized weighted genomic estimated breeding values (gwGEBVs) for individuals and traits may be calculated as 𝐘𝐠𝐰𝐆𝐄𝐁𝐕(𝛂) = 𝐙𝐔̂, where 𝐘𝐠𝐰𝐆𝐄𝐁𝐕(𝛂) is a 𝑁Ω × 𝑇 matrix containing the gwGEBVs for each of 𝑁Ω parental candidates and 𝑇 traits for a set of trait alpha values 𝛂, 𝐙 is an 𝑁Ω × 𝑀 genomic marker matrix for each of 𝑁Ω parental candidates and 𝑀 markers, and 𝐔̂ is a 𝑀 × 𝑇 matrix containing generalized upweighted marker effects for each of 𝑀 markers and 𝑇 traits calculated using the provided alpha values 𝛂. Stated as an optimization problem, the goal of GWGS is to select a subset of 𝑁Ξ individuals from 𝑁Ω parental candidates to maximize the sum of gwGEBVs for each trait of interest, given a set of 𝛼𝑡 values established a priori. Mathematically, GWGS is stated as the following multi-objective problem: Subject to: max 𝐱 ′ 𝐘𝐠𝐰𝐆𝐄𝐁𝐕(𝛂) 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω, where 𝐱 is a binary decision vector of length 𝑁Ω indicating whether (1) or not (0) an individual is selected, and all other terms have been defined above. In the degenerate case where a single trait is under consideration, the optimization problem reduces to a single objective problem which can be solved by sorting individuals based on gwGEBVs. Since GWGS is multi-objective in nature, a method is needed to reduce the multi- objective problem to a single-objective, thereby permitting for a single decision to be made. For this task, we assign a vector of economic weights 𝐞 and utilize the weight sum method to reduce 155 multiple objectives into a single objective. Of note, the optimization problem presented by GWGS is non-convex in nature since its search space is discrete in nature. Depending on the gwGEBVs for individuals, there may exist Pareto optimal solutions that do not exist on the convex hull of the search space. These Pareto optimal solutions will be numerically impossible to identify using the weight sum method. We recognize this shortcoming, and remark that the choice to use the weight sum method was for the sake of simplicity and based on the properties of the Pareto frontier. As will be seen in results section 3.3.1, the GWGS Pareto frontier in our simulation scenarios appeared to be convex at the macro-scale, suggesting that the shortcomings of the weight sum method would minimally affect selection decisions. By applying these economic weightings, the optimization problem becomes: Subject to: max 𝐱 ′ 𝐞′𝐘𝐠𝐰𝐆𝐄𝐁𝐕(𝛂) 𝐱 ′ 𝐱 = 𝑁Ξ 𝟏𝐍𝛀 𝐱 ∈ 𝔹𝑁Ω 2.1.2. A new, multi-trait, temporally weighted genomic selection methodology We introduce a new temporally weighted genomic selection (TWGS) strategy, which serves as a temporally cognizant variant of GWGS. TWGS is identical to GWGS except that 𝛼𝑡 upweighting hyperparameters are varied across time according to user preference. Given some function 𝑓(⋅), upweighting hyperparameters may be calculated as 𝛼𝑡 = 𝑓𝑡(𝓉) where 𝓉 is the current time point or generation. For our simulations, we utilize a linear function to decrease the upweighting hyperparameter from an initial hyperparameter setting 𝛼𝑡,0 to zero over the course of the simulation. This is stated as 𝛼𝑡 = 𝑓𝑡(𝓉) = 𝛼𝑡,0 (1 − 𝓉 𝒯 ) where 𝒯 is the number of generations in the simulation. 156 2.2. Single-trait breeding program simulation protocols 2.2.1. Empirical marker source For our simulations, we used the SNP marker set from the Wisconsin maize diversity panel 942 (Hirsch et al., 2014; Mazaheri et al., 2019) as an empirical source of SNP markers. We used the US NAM consensus genetic map (McMullen et al., 2009) to linearly interpolate genetic map positions for each of the SNP markers in the dataset. Following genetic map interpolation, we randomly selected 40 founder individuals and sampled 3000 genetic loci with minor allele frequencies ≥ 0.2 and consecutive genetic map distances ≥ 0.2 cM as was done in Allier et al. (2019). After sampling genetic loci, we assigned marker effects to create a single, simulated quantitative trait. 1000 of the sampled loci were designated as being quantitative trait loci (QTL) and the remaining 2000 loci were designated as having no effect on the simulated quantitative trait. We randomly assigned additive effects for each of the 1000 QTL according to a normal distribution with mean 0 and standard deviation 0.01. 2.2.2. Founding population simulation Following founder and marker sampling, we created a randomly mating population to serve as a founding population. We randomly paired the 40 selected founders to create 20 hybrid crosses and produced 80 hybrid progenies from each cross. The resulting 1600 progenies were randomly intermated for 20 generations. At each generation, each population member produced a single progeny, so that the size of the randomly mating population remained at a constant 1600. No overlap of generations occurred in the random mating step. The resulting population after 20 generations of random intermating was designated as the founding population, and we used the founding population to assign a narrow sense heritability of 0.4 for the simulated quantitative trait. 157 2.2.3. Burn-in simulation Following the establishment of the founding population and quantitative trait heritability, we performed a burn-in simulation to establish a breeding population with a linkage disequilibrium structure like what one might see in a real breeding program. We established an overlapping cohort structure like that described in Allier et al. (2019). Briefly, the breeding program was broken into five doubled haploid progeny cohorts. Each cohort had a different age and purpose. The oldest three cohorts contained developed breeding materials and were eligible for phenotyping and selection as parents. The youngest two cohorts contained developing breeding materials and were ineligible for phenotyping or selection as parents. To bootstrap the simulation, bootstrap cohorts were created by randomly selecting 40 members of the founding population to form 20 biparental crosses and generating 80 doubled haploid progenies per cross. In total, each cohort consisted of 1600 individuals from 20 biparental families. Following the creation of the bootstrap cohorts, the burn-in protocol closely followed that described in Allier et al. (2019). At each cycle of the burn-in, the three oldest cohorts were phenotyped in four replications without genotype by environment interactions, assuming sufficient seed for each tested line and no missing data. Phenotypes were simulated using the established QTL and by adding random errors corresponding to a narrow sense heritability of 0.4 in the founding population. The random error added to the QTL effects was kept constant throughout the simulation, meaning that heritability decreased as the genotypic variance decreased. After phenotyping the three oldest cohorts, we calculated the phenotypic mean for the tested lines and selected the top 5% (4 lines) within each biparental family to serve as parental candidates for the next cohort. In total, 240 lines were considered as parental candidates. The top 40 lines were selected on their phenotypic mean and randomly paired to form 20 biparental 158 crosses. Each cross produced 80 doubled haploid progenies to create a new cohort containing 1600 lines. The new cohort was added to the breeding population as the youngest cohort, and the oldest cohort was removed from the breeding population. From this cohort structure, the time between the creation of a line to the first instance of its testing was three generations. A line was tested for three generations before its removal. The burn-in simulation was conducted until the mean expected heterozygosity of the QTL was just under 0.25. In our case, this corresponded to 32 generations. The population generated from the burn-in was archived, designated as the starting population, and served as the starting point for all single-trait data-collecting simulations. 2.2.4. Characterization of upweighting consequences on population metrics After creating a starting population, we wanted to characterize the effect of the upweighting hyperparameter 𝛼𝑡 in GWGS and TWGS on genetic gain and genetic diversity metrics in long-term selection scenarios. To characterize the effects of upweighting, we conducted many long-term breeding program simulations using the starting population created in the burn-in as an initial population. The breeding simulation protocols were identical to those described in the burn-in, except that the 40 parents selected from the 240 candidates were selected on gwGEBVs instead of phenotypic means. The upweighting hyperparameter 𝛼𝑡 used to calculate gwGEBVs was randomly assigned from a uniform distribution, 𝛼𝑡~𝑈𝑛𝑖𝑓(0,1), at each generation. The breeding program was simulated for 60 generations for 1000 random 𝛂 trajectories. Random 𝛂 trajectories were only replicated once. Throughout the simulation, we collected the 𝛼𝑡 value at each generation and various population statistics including mean true breeding value, maximum true breeding value, mean expected heterozygosity (MEH), additive genetic and genic variances, Bulmer effect (Bulmer, 1971), and lower and upper selection limits (LSL and USL, respectively). All population statistics were calculated using the three oldest 159 cohorts in the simulated breeding program. MEH was calculated using the definition by Allier, Lehermeier, et al. (2019), as 1 𝑀 ∑ 𝑀 𝑚=1 2𝑝𝑚(1 − 𝑝𝑚) where 𝑀 is the number of markers and 𝑝𝑚 is the allele frequency of the 𝑚th marker. Additive genetic variance, 𝜎𝐴 2, was calculated as the variance of true breeding values, and genic variance was calculated as 𝜎𝑎 2 = ∑ 𝑀 𝑚=1 4𝛼𝑚 2 𝑝𝑚(1 − 𝑝𝑚), where 𝑀 is the number of markers, 𝑝𝑚 is the allele frequency of the 𝑚th marker, and 𝛼𝑚 is the additive effect of the 𝑚th QTL (Allier, Lehermeier, et al., 2019). The Bulmer effect was calculated as the ratio of additive genetic and genic variances, 𝜎𝐴 2/𝜎𝑎 2, as defined in Allier, Lehermeier, et al. (2019). Lower and upper selection limits were calculated as the theoretical breeding values of individuals having the worst and best, respectively, possible additive allele combination, given the alleles accessible to the current population. We considered two different scenarios for the simulation protocols described above. In the first scenario, the effects and state of the 1000 QTL were known. This scenario was labeled as the true (TRUE) scenario and represented the upper bound of the efficacy of the 𝛂 trajectory. In the second scenario, the effects and state of the 1000 QTL were unknown. We masked the 1000 causal QTL established at the beginning of the simulation and used the 2000 non-causal loci to inform selection decisions. To estimate marker effects and make selection decisions, we fit a ridge regression model (Meuwissen et al., 2001) using the EMMA method (Kang et al., 2008) to estimate the genetic variance. The ridge regression model was fit every generation using phenotypic and genotypic data from the three oldest cohorts. To characterize the effect the upweighting hyperparameter 𝛼𝑡 on a given genetic gain or genetic diversity statistic in the terminal generation, we used a two-part analysis. In the first step of our analysis, we extracted the 𝛼𝑡 values used at each generation of the 1000 simulations and 160 corresponding generation 60 population genetic gain and diversity metrics. Then for each metric, we fit a regression model of the form: 𝒯 𝑦𝑡,𝑖 = 𝜇 + ∑ 𝛽𝛼𝑡,𝓉 + 𝜀𝑖, 𝓉=1 where 𝑦𝑡,𝑖 is the population genetic gain or diversity metric at generation 60 for the 𝑡th trait (in this case, only a single trait) for the 𝑖th simulated 𝛂 trajectory, 𝜇 is the overall mean, 𝛽𝛼𝑡,𝓉 is the effect of the upweighting hyperparameter 𝛼𝑡 at the 𝓉th generation, and 𝜀𝑖 is the error for the 𝑖th 𝛂 trajectory. In the second step of our analysis, we took the effect estimates for the upweighting hyperparameter at each generation and regressed them against their corresponding generation number. This was done to examine how the effect of the upweighting hyperparameter on the examined genetic gain or genetic diversity metric changed over time. The model for this secondary analysis was: 𝛽̂ 𝛼𝑡,𝓉 = 𝜇 + 𝛾 + 𝜀𝓉, where 𝛽̂ 𝛼𝑡,𝓉 is the estimated effect of the upweighting hyperparameter 𝛼𝑡 at the 𝓉th generation estimated in the first part, 𝜇 is the model intercept, 𝛾 is the effect of the generation number on the estimated hyperparameter effect, and 𝜀𝓉 is the random error for the 𝓉th estimated hyperparameter effect. 2.2.5. Main breeding program simulation After characterizing the effects of the upweighting hyperparameter on long-term genetic gain and diversity metrics, we more rigorously tested GWGS and TWGS strategies for constant and linear 𝛂 trajectories, respectively. To do this, we performed breeding simulations identical to the breeding simulations described in the upweighting characterization experiment, except we 161 used constant and linear 𝛂 trajectories instead of random trajectories. For GWGS, we tested constant 𝛼𝑡 values from 0.05 to 0.5 by steps of 0.05. These strategies are abbreviated as gwGEBV05 for 𝛼𝑡 = 0.05, gwGEBV10 for 𝛼𝑡 = 0.10, …, and gwGEBV50 𝛼𝑡 = 0.50. For TWGS, we tested initial 𝛼𝑡,0 values from 0.10 to 1.00 by steps of 0.10 and decreased the 𝛼𝑡 values to zero in the linear manner described in the TWGS section above. These strategies are abbreviated as gwGEBV10d for 𝛼𝑡,0 = 0.10, gwGEBV20d for 𝛼𝑡,0 = 0.20, …, and gwGEBV100d for 𝛼𝑡 = 1.00. These 𝛼𝑡,0 values in TWGS were chosen so that the mean 𝛼𝑡 value throughout the duration of the simulation was equivalent to their GWGS counterparts. This permitted a fairer comparison between gwGEBV05 and gwGEBV10d, for example. We collected the same population genetic gain and diversity metrics as the upweighting hyperparameter experiment throughout the duration of the simulation and replicated each selection strategy 80 times. As in the hyperparameter upweighting characterization experiment, we examined scenarios where QTL locations and effects were known (TRUE scenario) and where QTL locations were masked and effects unknown (EST scenario). 2.3. Multi-trait breeding program simulation protocols 2.3.1. Empirical marker source We used the same marker set in our multi-trait breeding program experiments as in our single-trait breeding program simulations described previously. From the 3000 sampled loci, we assigned 1000 loci as being trait QTL and the remaining 2000 loci as being neutral markers. Next, we assigned additive marker effects corresponding to two traits for each of the 1000 QTL. Marker effects for the two traits were randomly drawn from a multivariate normal distribution with a mean of 𝛍 = [ ] and covariance structure of 𝚺 = [ 0 0 0.0001 −0.00004 −0.00004 0.0001 ]. This 162 covariance structure corresponded to two traits having a genetic correlation of -0.4. We named the simulated quantitative traits “Trait 1” and “Trait 2,” respectively. 2.3.2. Founding population simulation The protocol to construct the founding population in the multi-trait breeding program experiments was identical to that of the single-trait breeding program experiments. We used the resulting founding population to assign a narrow sense heritability of 0.4 for both simulated traits. In back-solving for the error variance, we assumed that errors in one trait did not impact the other trait. 2.3.3. Burn-in simulation Our burn-in simulation in the multi-trait breeding program experiments was almost identical to that described in the single-trait breeding program experiments. The only difference was in how individuals were selected in the within-family selection and parental selection steps. Since two traits were under selection, we used a linear index weighing each trait equally to determine the merit of individuals. The burn-in was run until the mean expected heterozygosity for the QTL of both traits decreased beneath 0.25, and the resulting starting population was archived for use in all subsequent simulations. 2.3.4. Characterization of multi-trait GWGS and TWGS search spaces and Pareto frontiers We characterized GWGS and TWGS in two ways. First, we randomly sampled 1000 selection decisions and calculated mean gwGEBVs for the sampled selection decision. We fit a regression between these two objectives. Second, we used an NSGA-III variant with subset recombination and mutation operators (described in section 2.4.2) to estimate the Pareto frontier for GWGS and TWGS in our bi-trait selection scenario. We visually confirmed the convergence of the Pareto frontier by comparing the NSGA-III results against NSGA-II results. Additionally, 163 we used an exhaustive subset hill climber algorithm (described in section 2.4.1) to perform several single-objective optimizations using the ε-constraint method at various points along the Pareto frontier. Furthermore, we identified the best selection decision for a single trait by sorting parental candidates based on their gwGEBVs and selecting the 40 individuals with the top gwGEBVs. 2.3.5. Main breeding program simulation Breeding program simulations in the multi-trait scenario were identical to those in the burn-in simulations, except in the selection methodology. Within-family selection was performed as before, but parental candidates were selected in GWGS and TWGS by weighing gwGEBVs for Traits 1 and 2 equally using a linear index. The simulation was conducted for 60 generations with 80 replications for all examined selection strategies. We examined scenarios where QTL locations and effects were known (TRUE scenario) and where QTL locations and effects were unknown (EST scenario). 2.4. Optimization algorithms 2.4.1. Exhaustive subset hill climber algorithm We created a hill climber algorithm capable of optimizing constrained and unconstrained single-objective subset optimization problems. Briefly, the hill climber algorithm starts at a random solution in the search space. This random starting solution is evaluated according to the optimization problem’s objective and constraint functions and is assigned as the current best solution. Next, the algorithm exhaustively searches the neighborhood around the current best solution by exchanging single elements in the current best solution vector with other elements available in the search space and evaluating the neighboring solutions. The best neighboring solution is kept track of during the neighborhood search. A solution is determined as being better 164 than another solution if its constraint violation is less than another solution, or if its constraint violation is equal and its objective function value is better than another solution. The best neighboring solution is compared to the current best solution. If the best neighboring solution is better than the current best solution, then the best neighboring solution replaces the current best solution, and the hill climber performs another iteration of neighborhood search. If the best neighboring solution is not better than the current best solution, then the algorithm terminates and returns the current best solution. 2.4.2. Subset NSGA-II and NSGA-III algorithms We created NSGA-II (Deb et al., 2002) and NSGA-III (Deb & Jain, 2014) algorithm variants to handle discrete, subset search spaces. For both our algorithm variants, we replaced the original recombination and mutation operators with the reduced exchange crossover and reduced exchange mutation operators proposed by Correa et al. (2001). For both NSGA-II and NSGA-III, we used a population size of 100 and evolved this population for 1500 generations. For NSGA- III specifically, we used 96 evenly spaced reference points to direct the algorithm in bi-objective problems and 91 evenly spaced reference points in tri-objective problems. 2.5. Simulation data analysis Since the data are extensive, we only analyzed data for collected metrics at generations 15, 30, 45, and 60. For each simulation metric and time point, we fit the following linear model: 𝑦𝑖𝑗 = 𝜇 + 𝑠𝑖 + 𝜀𝑖𝑗 𝜀𝑖𝑗~𝑁(0, 𝜎𝜀 2), where, 𝑦𝑖𝑗 is the observed simulation metric for the 𝑖th selection strategy for the 𝑗th simulation replicate, 𝜇 is the overall mean for the simulation metric, 𝑠𝑖 is the fixed effect of the 𝑖th 165 simulation metric, and 𝜀𝑖𝑗 is random error, assumed to follow a normal distribution with mean 0 and variance 𝜎𝜀 2. For each linear model, we calculated 95% confidence intervals for selection strategy effect estimates. We used the emmeans (Lenth, 2024) and multcompView (Graves et al., 2024) packages in R (R Core Team, 2024) to statistically group selection strategies and perform multiple test corrections using Tukey’s test (Tukey, 1949). 3. Results 3.1. Characterization of the effects of marker upweighting in long-term, single-trait selection 3.1.1. TRUE scenario 3.1.1.1. Effects of upweighting on genetic gain metrics For the TRUE scenario, regressing all 60 upweighting factors on the mean true breeding value at generation 60 yielded results that were largely not statistically significant. The effect of the upweighting factor at a particular generation on the mean population true breeding value at generation 60 tended to be positive in early generations, and negative in later generations (Fig. 4.1A), but most of these effect estimates were not statistically significant (Fig. 4.1B). When regressing the effect estimates against time, however, there was a strongly significant, slight negative relationship between the generation number and the effect estimate (Fig. 4.1A; Table 4.1). In other words, while we are not able to individually discern the effect of increasing the upweighting factor at a particular generation on the mean true breeding value at generation 60, the effect estimates appeared to decrease with time. 166 Figure 4.1: A) Scatterplot and regression of estimated upweighting factor effects on population mean true breeding value at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation 0.007159 0.001613 -0.000293 0.000046 t-value p-value 4.437591 0.000041 -6.378099 0.000000 Table 4.1: Parameter estimates for a regression model fitting estimated upweighting factor effect on population mean true breeding value at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. An identical analysis on the maximum population true breeding value yielded very similar results to the mean population true breeding value. The effects of upweighting factors at individual generations were almost all statistically not significant, but collectively, there was a strongly significant, negative trend in the upweighting effect coefficients across time (Appx. B, Fig. B.1; Appx. B, Table B.1). 167 3.1.1.2. Effects of upweighting on mean expected heterozygosity Regressing all 60 upweighting factors on the population mean expected heterozygosity in generation 60 in the TRUE scenario yielded significant results for several generation time points. In generations 45-60, many of the upweighting factors exhibited statistically significant and slightly positive effects (Fig. 4.2A-B). In these generations, increasing the upweighting factor increased the population mean expected heterozygosity at generation 60. In generation 1-40, we observed a handful of time points that exhibited positive, statistically significant effects on population mean expected heterozygosity. There did not appear to be a pattern among these significant time points. Regression of the effect estimates against time revealed a strong, positive relationship (Fig. 4.2A; Table 4.2) indicating that the effect of the upweighting factor on population mean heterozygosity at generation 60 increased as the generation approached generation 60. 168 Figure 4.2: A) Scatterplot and regression of estimated upweighting factor effects on population mean expected heterozygosity at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept 0.000277 0.000296 Generation 0.000039 0.000008 p-value t-value 0.934894 0.353719 4.633839 0.000021 Table 4.2: Parameter estimates for a regression model fitting estimated upweighting factor effect on population mean expected heterozygosity at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 3.1.1.3. Effects of upweighting on the upper selection limit In the TRUE scenario, regressing upweighting factors for all 60 generations yielded many statistically significant results. In generations 1-30, almost all upweighting factors had a strong, positive effect on the population upper selection limit at generation 60 (Fig. 4.3A-B). Increasing the upweighting factor in these generations increased the upper selection limit in the long-term. 169 In later generations (31-60), these effects were largely not statistically significant (Fig. 4.3B). Regression of estimated upweighting effect estimates against generation revealed a strongly significant, negative relationship between upweighting effect and generation number (Fig. 4.3A; Table 4.3). The effect of upweighting on the population upper selection limit at generation 60 decreased over time. Figure 4.3: A) Scatterplot and regression of estimated upweighting factor effects on population upper selection limit at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation 0.022297 0.001443 -0.000257 0.000041 t-value p-value 15.449436 0.000000 -6.239366 0.000000 Table 4.3: Parameter estimates for a regression model fitting estimated upweighting factor effect on population upper selection limit at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 170 3.1.1.4. Effects of upweighting on other diversity metrics Results for the effect of the upweighting factor on the additive genetic variance at generation 60 in the TRUE scenario were mostly statistically insignificant. In extremely late generations (55-60), there was a significant, positive relationship between upweighting and population additive genetic variance at generation 60, but other than this, no other trends were observed (Appx. B, Fig. B.2; Appx. B, Table B.1). The effects of upweighting on population additive genic variance at generation 60 in the TRUE scenario mirrored those of population mean expected heterozygosity. In later generations (45-60), we observed many significant, positive relationships for the effect of upweighting on population mean expected heterozygosity at generation 60, and we observed a significant positive trend in the upweighting effect estimates across time (Appx. B, Fig. B.3; Appx. B, Table B.3). Results for the effect of upweighting on the Bulmer effect at generation 60 in the TRUE scenario mirrored those for population additive genetic variance. In extremely late generations (55-60), there was a significant, positive relationship between the upweighting factor and the Bulmer effect at generation 60, but we observed no other trends otherwise (Appx. B, Fig. B.4; Appx. B, Table B.4). 3.1.2. EST scenario results 3.1.2.1. Effects of upweighting on genetic gain metrics Results for the effect of the upweighting factor on the population mean true breeding value in the EST scenario were very similar to the results in the TRUE scenario. Like in the TRUE scenario, many of the upweighting effect estimates at individual generations were not statistically significant (Fig. 4.4B). In the generation 51-60 range, several upweighting effect 171 estimates exhibited negative effects (Fig. 4.4A) that were highly significant (Fig. 4.4B). For significant generations in this range, increasing the upweighting factor decreased the population mean true breeding value at generation 60. There appeared to be a handful of generations in the generation 1-50 range exhibiting statistically significant, negative effects (Fig. 4.4A-B), though there did not appear to be any trend. Regressing upweighting effect estimates against the generation number revealed that there was a statistically significant, negative trend in the effect estimates (Table 4.4). As generation number increased, the effect of the upweighting factor became more negative (Fig. 4.4A). Figure 4.4: A) Scatterplot and regression of estimated upweighting factor effects on population mean true breeding value at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. 172 Parameter Estimate Std. Error Intercept Generation -0.004809 0.002571 -0.000318 0.000073 t-value p-value -1.870845 0.066414 -4.335269 0.000059 Table 4.4: Parameter estimates for a regression model fitting estimated upweighting factor effect on population mean true breeding value at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. An identical analysis conducted on the population maximum true breeding value metric revealed similar results. In the last 10 generations, many of the upweighting effects on the population maximum true breeding value at generation 60 were statistically significant with negative effect estimates (Appx. B, Fig. B.5). Regression of estimated upweighting effect estimates on generation number revealed a statistically significant, negative relationship between the two variables. As generation number increased, the effect of upweighting on the population maximum true breeding value at generation 60 became more negative (Appx. B, Table B.5). 3.1.2.2. Effects of upweighting on mean expected heterozygosity In the EST scenario, results for the effect of upweighting factor on the population mean expected heterozygosity in generation 60 were very similar to the results in the TRUE scenario. Regressing the 60 upweighting factors on the population mean expected heterozygosity at generation 60 revealed statistically significant, positive effects in latter generations (51-60) (Fig. 4.5A). Applying a more extreme upweighting factor in later generations increased the population mean expected heterozygosity in generation 60. Regressing estimated upweighting effects against generation number revealed a statistically significant positive relationship between generation number and effect estimate. As generation number increased, the upweighting effect on population mean expected heterozygosity at generation 60 became more positive (Fig. 4.5A). 173 Figure 4.5: A) Scatterplot and regression of estimated upweighting factor effects on population mean expected heterozygosity at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept 0.000746 0.000197 Generation 0.000016 0.000006 p-value t-value 3.781608 0.000371 2.790729 0.007107 Table 4.5: Parameter estimates for a regression model fitting estimated upweighting factor effect on population mean expected heterozygosity at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 3.1.2.3. Effects of upweighting on population upper selection limit In the EST scenario, results for the effect of upweighting on population upper selection limit at generation 60 differed substantially from the results for the TRUE scenario. Upweighting did not have any effect on population upper selection limit at generation 60 for any generation (Fig. 4.6B). We did not observe any significant relationship between upweighting effect 174 estimates and generation number (Fig. 4.6A; Table 4.6). This stood in contrast to the TRUE scenario, where positive upweighting effects were observed in early generations (Fig. 4.3B), with a decreasing trend in the effect (Fig. 4.3A). Figure 4.6: A) Scatterplot of estimated upweighting factor effects on population upper selection limit at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). Regression results were not statistically significant. B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation 0.004245 0.001151 -0.000020 0.000033 t-value p-value 3.686372 0.000503 -0.614676 0.541173 Table 4.6: Parameter estimates for a regression model fitting estimated upweighting factor effect on population upper selection limit at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 175 3.1.2.4. Effects of upweighting on other diversity metrics The effects of upweighting on population additive genetic variance, additive genic variance, and the Bulmer effect at generation 60 in the EST scenario were similar to the results for the TRUE scenario. For population additive genetic variance at generation 60, upweighting effects for several time points in the generation 51-60 range were negative and statistically significant (Appx. B, Fig. B.B.6). There also appeared to be a negative relationship between the upweighting effect estimate and the generation number (Appx. B, Table B.6). In other words, as generation number increased, the effect of upweighting became more negative. Results for the population additive genic variance in the EST scenario closely mirrored the results for population mean expected heterozygosity. In later generations (51-60), the effect of upweighting at several generations was positive and statistically significant (Appx. B, Fig. B.7). Furthermore, there appeared to be a positive trend between the upweighting effect and the generation (Appx. B, Table B.7). As generation increased, the effect of upweighting became more positive. Finally, the effects of upweighting on the Bulmer effect at generation 60 closely mirrored the trends observed for population additive genetic variance. The effect of upweighting the Bulmer effect at generation 60 for several time points was negative and statistically significant (Appx. B, Fig. B.8). There appeared to be a significant negative trend between the upweighting effect estimates and the generation number, suggesting that as generation number increased, the effect of upweighting on the Bulmer effect at generation 60 became more negative (Appx. B, Table B.8). 176 3.2. Single-trait breeding program results 3.2.1. TRUE scenario 3.2.1.1. Genetic gain metrics There was a great deal of statistical and trajectory overlap among the tested selection methods (Fig. 4.7). In the TRUE scenario, the best methods at improving the population mean true breeding values at generation 60, were gwGEBV70d, gwGEBV80d, gwGEBV60d, gwGEBV90d, gwGEBV50d, and gwGEBV50 (Table 4.7). These six methods were statistically tied as the best methods. Following these top strategies were gwGEBV100d, gwGEBV40, gwGEBV45, gwGEBV35, gwGEBV30, gwGEBV40d, gwGEBV25, gwGEBV20, gwGEBV30d, gwGEBV15, and gwGEBV20d in order of decreasing rank and at varying levels of statistical grouping (Table 4.7). OCS was inferior to most of the tested GWGS and TWGS strategies and was among the lower ranking half of selection strategies. OCS was statistically similar to gwGEBV20d (Table 4.7). OCS significantly outperformed selection on GEBV (Table 4.7), validating its effectiveness as a long-term selection strategy. Ranked between OCS and GEBV were gwGEBV10, gwGEBV10d, and gwGEBV05 (Table 4.7). GEBV was the second worst selection strategy, and the RS control was the worst selection strategy by a large margin (Table 4.7). Several of the TWGS selection strategies outperformed their GWGS selection counterparts. The TWGS strategies gwGEBV80d, gwGEBV70d, gwGEBV60d, gwGEBV50d, gwGEBV40d, gwGEBV30d and gwGEBV20d significantly outperformed their GWGS strategy counterparts gwGEBV40, gwGEBV35, gwGEBV30, gwGEBV25, gwGEBV20, gwGEBV15, and gwGEBV10, respectively (Table 4.7). Additionally, two of the TWGS strategies exhibited a higher population mean true breeding value at generation 60 when compared to their GWGS 177 strategy counterparts, but the difference was not statistically different. These TWGS strategies included gwGEBV90d and gwGEBV10d. Throughout the duration of the simulation, selection strategy rankings changed dramatically. At generation 15, the best selection strategies were gwGEBV10d, gwGEBV15, gwGEBV05, gwGEBV10, gwGEBV20d, gwGEBV20, and GEBV (Appx. B, Table B.9). OCS was the fifth worst strategy at this time point and RS was the worst (Appx. B, Table B.9). At generation 30, GEBV selection lost its top ranking and several of the TWGS and GWGS strategies with higher upweighting factors made their way into the top ranking. The top strategies at generation 30 were gwGEBV30d, gwGEBV40d, gwGEBV25, gwGEBV20, gwGEBV20d, gwGEBV30, and gwGEBV15 (Appx. B, Table B.10). GEBV decreased to a middle rank and was slightly better than OCS at this time point (Appx. B, Table B.10). RS remained the worst performing strategy at this time point (Appx. B, Table B.10). At generation 45, selection strategy rankings changed again, with gwGEBV50d and gwGEBV60d being statistically tied as the best strategies (Appx. B, Table B.11). The ranking for GEBV selection decreased to second worst, only outperforming RS (Appx. B, Table B.11). OCS ranking remained low among the tested selection strategies and was statistically tied with gwGEBV10, gwGEBV100d, and gwGEBV10d (Appx. B, Table B.11). 178 Figure 4.7: Population mean true breeding value by selection strategy over 60 generations in the single-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 179 Mean Pop. Selection Mean TBV Strategy 106.4895 gwGEBV70d 106.4878 gwGEBV80d 106.4865 gwGEBV60d 106.4809 gwGEBV90d 106.4780 gwGEBV50d gwGEBV50 106.4748 gwGEBV100d 106.4704 106.4631 gwGEBV40 106.4623 gwGEBV45 106.4482 gwGEBV35 106.4335 gwGEBV30 106.4202 gwGEBV40d 106.4155 gwGEBV25 106.3875 gwGEBV20 106.3838 gwGEBV30d 106.3598 gwGEBV15 106.3415 gwGEBV20d 106.3389 OCS 106.3149 gwGEBV10 106.2905 gwGEBV10d 106.2731 gwGEBV05 106.2208 GEBV 105.6561 RS Generation 60 95% Lower CL DF Std. Error 0.00373 1817 106.4822 0.00373 1817 106.4805 0.00373 1817 106.4792 0.00373 1817 106.4736 0.00373 1817 106.4707 0.00373 1817 106.4675 0.00373 1817 106.4631 0.00373 1817 106.4558 0.00373 1817 106.4550 0.00373 1817 106.4409 0.00373 1817 106.4261 0.00373 1817 106.4129 0.00373 1817 106.4082 0.00373 1817 106.3802 0.00373 1817 106.3765 0.00373 1817 106.3525 0.00373 1817 106.3342 0.00373 1817 106.3315 0.00373 1817 106.3076 0.00373 1817 106.2832 0.00373 1817 106.2658 0.00373 1817 106.2135 0.00373 1817 105.6488 Statistical Grouping LM LM 95% Upper CL 106.4968 M 106.4951 106.4938 106.4882 KLM 106.4853 KLM 106.4821 KLM 106.4777 KL JK 106.4704 JK 106.4697 106.4555 IJ 106.4408 HI 106.4275 H 106.4229 H 106.3948 G 106.3911 G F 106.3671 EF 106.3488 106.3462 E 106.3222 D 106.2978 C 106.2805 C 106.2281 B 105.6634 A Table 4.7: Population mean true breeding value by selection strategy at generation 60 in the single-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. Results for the population maximum true breeding value were very similar to the results observed for the population mean true breeding value. At generation 15, GWGS and TWGS strategies with lower upweighting factors (𝛼𝑡 ∈ [0.05,0.4]) were among the best selection strategies (Appx. B, Table B.12). Selection on GEBV was in the second-best statistical grouping, and OCS was the fourth worst selection strategy at this time point (Appx. B, Table B.12). These rankings changed as generation number increased, however. At generation 60, GWGS and 180 TWGS strategies with higher upweighting factors (𝛼𝑡 ∈ [0.4,1.0]) were among the best selection strategies (Appx. B, Table B.15). Specifically, gwGEBV50, gwGEBV80d, gwGEBV90d, gwGEBV70d, gwGEBV100d, and gwGEBV45 were statistically tied as the best methods to improve population maximum true breeding value (Appx. B, Table B.15). Several of the TWGS strategies significantly outperformed their GWGS counterparts at generation 60. Specifically, gwGEBV70d, gwGEBV60d, gwGEBV50d, gwGEBV40d, gwGEBV20d, and gwGEBV10d significantly outperformed their GWGS counterparts gwGEBV35, gwGEBV30, gwGEBV25, gwGEBV20, gwGEBV10, and gwGEBV05, respectively (Appx. B, Table B.15). 3.2.1.2. Mean expected heterozygosity metric In the TRUE scenario, the best method for sustaining long-term genetic diversity as measured by mean expected heterozygosity at generation 60 was, surprisingly, RS (Fig. 4.8; Table 4.8). gwGEBV50 and gwGEBV45 were the second- and third-best selection strategies, followed by gwGEBV40, gwGEBV100d, and gwGEBV35, which were all statistically grouped together (Table 4.8). OCS maintained mean expected heterozygosity at an intermediate level at generation 60, grouping with gwGEBV50d, gwGEBV40d, and gwGEBV15 strategies (Table 4.8). Finally, selection on GEBV was the worst selection strategy at maintaining mean expected heterozygosity (Table 4.8). In the long-term, GWGS strategies tended to maintain mean expected heterozygosity better than their TWGS counterparts. Specifically, the GWGS selection strategies gwGEBV50, gwGEBV45, gwGEBV40, gwGEBV35, gwGEBV30, gwGEBV25, and gwGEBV20 statistically outperformed their TWGS counterparts gwGEBV100d, gwGEBV90d, gwGEBV80d, gwGEBV70d, gwGEBV60d, gwGEBV50d, and gwGEBV40d, respectively (Table 4.8). Though not statistically significant, several additional GWGS strategies exhibited higher mean expected 181 heterozygosity estimates than their TWGS counterparts. These strategies included gwGEBV15 and gwGEBV10 (Table 4.8). Rankings for population mean expected heterozygosity across time were stable within selection strategy families but changed considerably when considering all selection strategies (Fig. 4.8). Within the GWGS strategy family, selection strategies with higher upweighting factors achieved better mean expected heterozygosity rankings than those with lower upweighting factors. The order of rankings was stable across many generations (Fig. 4.8; Appx. B, Tables B.16-18; Table 4.8). Ranking within the TWGS strategy family was like that of GWGS. TWGS strategies with higher initial upweighting factors achieved better mean expected heterozygosity metrics across all generations (Fig. 4.8; Appx. B, Tables 16-18; Table 8). OCS was able to improve mean expected heterozygosity in early generations, but its ranking dropped considerably as time progressed (Appx. B, Tables 16-18). In early generations, RS ranked well in its ability to maintain population mean expected heterozygosity (Appx. B, Tables 16), and in later generations, it further improved in ranking (Fig. 4.8; Appx. B, Tables 17-18; Table 4.8). TWGS strategies generally exhibited more linear decreases in their mean expected heterozygosity metrics than their GWGS counterparts which exhibited more curved trajectories (Fig. 4.8). This resulted in many rank changes across generations. 182 Figure 4.8: Population mean expected heterozygosity by selection strategy over 60 generations in the single-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 183 Generation 60 DF Selection Strategy 95% Lower CL Mean Pop. MEH 0.1349 RS 0.1026 gwGEBV50 0.0977 gwGEBV45 gwGEBV40 0.0928 gwGEBV100d 0.0906 0.0894 gwGEBV35 0.0857 gwGEBV90d 0.0847 gwGEBV30 0.0831 gwGEBV80d 0.0825 gwGEBV70d 0.0799 gwGEBV25 0.0798 gwGEBV60d 0.0764 gwGEBV20 0.0752 gwGEBV50d 0.0718 OCS 0.0712 gwGEBV40d 0.0697 gwGEBV15 0.0683 gwGEBV30d 0.0644 gwGEBV10 0.0642 gwGEBV20d 0.0611 gwGEBV10d 0.0606 gwGEBV05 0.0553 GEBV Std. Error 0.00067 1817 0.1336 0.00067 1817 0.1013 0.00067 1817 0.0964 0.00067 1817 0.0915 0.00067 1817 0.0893 0.00067 1817 0.0881 0.00067 1817 0.0844 0.00067 1817 0.0834 0.00067 1817 0.0817 0.00067 1817 0.0812 0.00067 1817 0.0786 0.00067 1817 0.0785 0.00067 1817 0.0751 0.00067 1817 0.0739 0.00067 1817 0.0705 0.00067 1817 0.0699 0.00067 1817 0.0684 0.00067 1817 0.0670 0.00067 1817 0.0631 0.00067 1817 0.0629 0.00067 1817 0.0598 0.00067 1817 0.0593 0.00067 1817 0.0540 Table 4.8: Population mean expected heterozygosity by selection strategy at generation 60 in the single-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 95% Upper CL 0.1362 0.1039 0.0990 0.0941 0.0919 0.0907 0.0870 0.0860 0.0844 0.0838 0.0812 0.0811 0.0777 0.0765 0.0731 0.0725 0.0710 0.0696 0.0657 0.0655 0.0624 0.0619 0.0566 Statistical Grouping N M L K K K J J IJ IJ I HI GH FG EF DE DE D C C BC B A 3.2.1.3. Upper selection limit metric The best selection strategies for maintaining population upper selection limit in the TRUE scenario at generation 60 were gwGEBV50 and gwGEBV100d (Fig. 4.9; Table 4.9). The second-best selection strategies were gwGEBV90d, gwGEBV45, and gwGEBV80d (Table 4.9). OCS maintained the upper selection limit at a lower, intermediate level relative to all other tested selection strategies (Table 4.9). Selection on GEBV was the worst selection strategy for maintaining population upper selection limit (Table 4.9). Surprisingly, RS demonstrated 184 intermediate performance for maintaining population upper selection limit (Table 4.9). Many TWGS strategies and their GWGS counterparts grouped together statistically at generation 60. For instance, gwGEBV100d, gwGEBV90d, gwGEBV40d, gwGEBV30d, and gwGEBV10d strategies grouped with their counterparts gwGEBV50, gwGEBV45, gwGEBV20, gwGEBV15, and gwGEBV05, respectively (Table 4.9). Like with population mean expected heterozygosity, the rankings for maintaining population upper selection limit were stable within selection strategy families but noticeably changed when considering all selection strategies. Within the GWGS strategy family, selection strategies with higher upweighting factors better maintained their upper selection limits than strategies with lower upweighting factors (Fig. 4.9; Appx. B, Tables B.19-21; Table 4.9). The TWGS strategy family also exhibited similar behaviors (Fig. 4.9; Appx. B, Tables B.19-21; Table 4.9). OCS maintained the population upper selection limit at an intermediate level in early generations (Appx. B, Tables B.19) and reduced slightly in its ranking as generation number increased (Appx. B, Tables B.20-21). Selection on GEBV was always the worst strategy throughout the 60 simulated generations, and RS performed at an intermediate level throughout the simulation (Fig. 4.9; Appx. B, Tables B.19-21; Table 4.9). 185 Figure 4.9: Population upper selection limit by selection strategy over 60 generations in the single-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 186 Mean Pop. Selection USL Strategy 107.1497 gwGEBV50 gwGEBV100d 107.1445 107.1059 gwGEBV90d 107.0995 gwGEBV45 107.0811 gwGEBV80d 107.0457 gwGEBV70d 107.0395 gwGEBV40 107.0089 gwGEBV60d 106.9926 gwGEBV35 106.9500 gwGEBV50d 106.9380 gwGEBV30 106.9031 RS 106.8878 gwGEBV25 106.8518 gwGEBV40d 106.8336 gwGEBV20 106.7755 gwGEBV30d 106.7500 gwGEBV15 106.7204 OCS 106.6855 gwGEBV20d 106.6566 gwGEBV10 106.6013 gwGEBV10d 106.5751 gwGEBV05 106.4865 GEBV Generation 60 95% Lower CL DF Std. Error 0.00531 1817 107.1393 0.00531 1817 107.1341 0.00531 1817 107.0955 0.00531 1817 107.0891 0.00531 1817 107.0707 0.00531 1817 107.0353 0.00531 1817 107.0291 0.00531 1817 106.9985 0.00531 1817 106.9822 0.00531 1817 106.9396 0.00531 1817 106.9276 0.00531 1817 106.8926 0.00531 1817 106.8774 0.00531 1817 106.8413 0.00531 1817 106.8231 0.00531 1817 106.7651 0.00531 1817 106.7396 0.00531 1817 106.7100 0.00531 1817 106.6751 0.00531 1817 106.6461 0.00531 1817 106.5909 0.00531 1817 106.5647 0.00531 1817 106.4761 Statistical Grouping 95% Upper CL 107.1601 M 107.1549 M L 107.1163 L 107.1100 L 107.0915 107.0561 K 107.0499 K J 107.0194 J 107.0030 I 106.9605 106.9484 I 106.9135 H 106.8982 H 106.8622 G 106.8440 G F 106.7859 F 106.7605 106.7309 E 106.6960 D 106.6670 C 106.6117 B 106.5855 B 106.4969 A Table 4.9: Population upper selection limit by selection strategy at generation 60 in the single- trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 3.2.1.4. Other diversity metrics Results for population additive genetic and genic variance metrics were similar to those for population mean expected heterozygosity and upper selection limit. In general, the TWGS strategies with high initial upweighting factor parameters produced populations with high additive genetic and genic variance (Appx. B, Figs. B.10-11; Appx. B, Tables B.22-29). In generation 15, gwGEBV100d was the best method for both metrics (Appx. B, Tables B.22, 26). As time progressed, the rankings of the TWGS strategies reduced somewhat for these metrics 187 and were overtaken by some of the GWGS strategies and RS (Appx. B, Tables B.22-25, 27-29). OCS started at an intermediate level for these population metrics and decreased slightly as the generation number increased (Appx. B, Tables B.22-29). GEBV was consistently the worst selection strategy for these two metrics across all generations, while RS was the best long-term selection strategy, surprisingly (Appx. B, Figs. B.10-11; Appx. B, Tables B.22-29). Following RS, gwGEBV50 was the second-best strategy for maintaining long-term population additive genetic and genic variance (Appx. B, Tables B.25, 29). Results for the Bulmer effect metric were mostly inconclusive. Most selection strategies statistically overlapped with each other throughout the 60 simulated generations (Appx. B, Fig. B.12; Appx. B, Tables 30-33). 3.2.2. EST scenario 3.2.2.1. Genetic gain metrics In the EST scenario, the best long-term selection strategies at generation 60 were gwGEBV10d and OCS (Fig. 4.10; Table 4.10). This result was substantially different from the result in the TRUE scenario where GWGS and TWGS strategies with higher upweighting factors were among the best and OCS performed at a lower, intermediate level. GEBV selection was in the third best statistical grouping and performed about the same as gwGEBV05 and gwGEBV20d (Table 4.10). RS remained the worst strategy, like in the TRUE scenario, but also was statistically tied with gwGEBV45 and gwGEBV50. Rankings for GWGS and TWGS strategies with respect to their upweighting factors were generally the opposite of those observed in the TRUE scenario. GWGS and TWGS strategies with higher upweighting factors were ranked poorer than those with lower upweighting factors (Table 4.10). Furthermore, TWGS strategies tended to outperform their GWGS counterparts at generation 60 (Table 4.10), but in earlier generations, GWGS strategies tended to outperform their TWGS counterparts (Appx. B, 188 Tables B.34-35). Collectively, the rankings of selection strategies across time were stable except for the TWGS strategies (Appx. B, Tables B.34-36). In later generations, several TWGS strategies exhibited noticeable inflection points in which their genetic gain increased at a faster rate (Fig. 4.10). The increase seemed to be more extreme in strategies with greater initial upweighting factors (Fig. 4.10). Figure 4.10: Population mean true breeding value by selection strategy over 60 generations in the single-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 189 Mean Pop. Selection Mean TBV Strategy 105.8511 gwGEBV10d 105.8351 OCS 105.8178 gwGEBV05 105.8044 GEBV 105.7917 gwGEBV20d 105.7220 gwGEBV10 105.7064 gwGEBV30d 105.6330 gwGEBV40d 105.5785 gwGEBV15 105.5600 gwGEBV50d 105.4898 gwGEBV60d 105.4376 gwGEBV20 105.4333 gwGEBV70d 105.3796 gwGEBV80d 105.3336 gwGEBV90d gwGEBV25 105.2971 gwGEBV100d 105.2958 105.2101 gwGEBV30 105.1390 gwGEBV35 105.0865 gwGEBV40 105.0215 gwGEBV45 104.9993 RS 104.9986 gwGEBV50 Generation 60 95% Lower CL DF Std. Error 0.00463 1817 105.8420 0.00463 1817 105.8260 0.00463 1817 105.8087 0.00463 1817 105.7953 0.00463 1817 105.7826 0.00463 1817 105.7129 0.00463 1817 105.6973 0.00463 1817 105.6239 0.00463 1817 105.5694 0.00463 1817 105.5509 0.00463 1817 105.4807 0.00463 1817 105.4286 0.00463 1817 105.4243 0.00463 1817 105.3705 0.00463 1817 105.3246 0.00463 1817 105.2881 0.00463 1817 105.2867 0.00463 1817 105.2010 0.00463 1817 105.1300 0.00463 1817 105.0775 0.00463 1817 105.0124 0.00463 1817 104.9903 0.00463 1817 104.9895 Statistical Grouping P 95% Upper CL 105.8602 105.8441 OP 105.8269 NO 105.8135 MN 105.8007 M L 105.7311 105.7155 L 105.6421 K J 105.5876 J 105.5690 105.4989 I 105.4467 H 105.4424 H 105.3886 G F 105.3427 E 105.3062 105.3048 E 105.2191 D 105.1481 C 105.0956 B 105.0306 A 105.0084 A 105.0077 A Table 4.10: Population mean true breeding value by selection strategy at generation 60 in the single-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. Results for genetic gain as measured by the population maximum true breeding value were very similar to the population mean true breeding value results. gwGEBV10d and gwGEBV05 strategies were observed to be the best strategies at improving this metric at generation 60 (Appx. B, Fig. B.13; Appx. B, Table B.40). gwGEBV20d and OCS were also competitive, statistically tying with gwGEBV05 (Appx. B, Table B.40). As with the results for the mean, GWGS and TWGS strategies with lower upweighting factors tended to outperform strategies with higher upweighting factors, within their respective selection strategy families 190 (Appx. B, Tables B.37-40). Like with the population mean true breeding value metric, we observed an inflection point for TWGS strategies with the population maximum true breeding value metric (Appx. B, Fig. B.13). In earlier generations, GWGS strategies tended to outperform their TWGS counterparts (Appx. B, Tables B.37-39), while in later generations (> 45), the rate of genetic gain increased for TWGS strategies, permitting many to outperform their GWGS counterparts (Appx. B, Fig. B.13; Appx. B, Table B.40). 3.2.2.2. Mean expected heterozygosity metric Results for the preservation of population mean expected heterozygosity in the EST scenario were somewhat similar to the results for the TRUE scenario. At generation 60, the gwGEBV50 and gwGEBV45 selection strategies were the best at maintaining population mean expected heterozygosity (Fig. 4.11; Table 4.11). This result contrasted with the TRUE scenario, where RS was the best long-term selection strategy for maintaining population mean expected heterozygosity. OCS, and GEBV were the two worst selection strategies for maintaining this diversity metric, with OCS outperforming GEBV (Table 4.11). RS performed at a lower, intermediate level, above that of OCS and GEBV (Table 4.11). For both GWGS and TWGS strategies, a higher upweighting factor resulted in a higher population mean expected heterozygosity (Table 4.11). Rankings for the selection strategies were somewhat stable across time. Within individual GWGS and TWGS families, population mean expected heterozygosity rankings were stable throughout the duration of the simulation (Fig. 4.11; Appx. B, Table B.41-43; Table 4.11). In early generations, several TWGS strategies were able to outperform their GWGS counterparts (Appx. B, Table B.41-42). Furthermore, several of the TWGS strategies exhibited inflection points at later stages of the simulation where they experienced a rapid decline in population 191 mean expected heterozygosity, resulting in major rank changes (Fig. 4.11). OCS was able to slightly increase population mean expected heterozygosity (Fig. 4.11), but it rapidly lost this advantage as the simulation progressed (Appx. B, Tables B.41-43). Figure 4.11: Population mean expected heterozygosity by selection strategy over 60 generations in the single-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 192 Mean Pop. MEH Selection Strategy 0.2401 gwGEBV50 0.2394 gwGEBV45 0.2368 gwGEBV40 0.2336 gwGEBV35 0.2285 gwGEBV30 gwGEBV25 0.2223 gwGEBV100d 0.2098 0.2093 gwGEBV20 0.2067 gwGEBV90d 0.2027 gwGEBV80d 0.1976 gwGEBV70d 0.1933 gwGEBV15 0.1922 gwGEBV60d 0.1848 gwGEBV50d 0.1751 gwGEBV40d 0.1722 RS 0.1676 gwGEBV10 0.1638 gwGEBV30d 0.1472 gwGEBV20d 0.1324 gwGEBV05 0.1240 gwGEBV10d 0.0966 OCS 0.0930 GEBV Generation 60 95% Lower CL DF Std. Error 0.00053 1817 0.2391 0.00053 1817 0.2383 0.00053 1817 0.2358 0.00053 1817 0.2325 0.00053 1817 0.2274 0.00053 1817 0.2212 0.00053 1817 0.2088 0.00053 1817 0.2082 0.00053 1817 0.2056 0.00053 1817 0.2016 0.00053 1817 0.1966 0.00053 1817 0.1923 0.00053 1817 0.1911 0.00053 1817 0.1837 0.00053 1817 0.1740 0.00053 1817 0.1712 0.00053 1817 0.1665 0.00053 1817 0.1628 0.00053 1817 0.1462 0.00053 1817 0.1314 0.00053 1817 0.1230 0.00053 1817 0.0955 0.00053 1817 0.0920 95% Upper CL 0.2412 0.2404 0.2379 0.2346 0.2295 0.2233 0.2109 0.2103 0.2077 0.2037 0.1987 0.1944 0.1932 0.1858 0.1761 0.1733 0.1686 0.1648 0.1483 0.1334 0.1251 0.0976 0.0941 Statistical Grouping T ST S R Q P O NO N M L K K J I H G F E D C B A Table 4.11: Population mean expected heterozygosity by selection strategy at generation 60 in the single-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 3.2.2.3. Upper selection limit metric Upper selection limit results were similar to the population mean expected heterozygosity results but were less statistically distinguishable. At generation 60 in the EST scenario, the best selection strategies for maintaining the upper selection limit were gwGEBV50, gwGEBV45, gwGEBV40, and gwGEBV35 (Fig. 4.12; Table 4.12). GEBV and OCS were the worst and second worst selection strategies for maintaining the upper selection limit at generation 60 (Fig. 4.12; Table 4.12). RS performed at a lower, intermediate level for this genetic diversity metric 193 (Table 4.12). Like with population mean expected heterozygosity, the rankings for maintaining population upper selection limit were relatively stable across time. Within the GWGS and TWGS strategy families, selection strategies with higher upweighting factors maintained their upper selection limits better than strategies with lower upweighting factors (Fig. 4.12; Appx. B, Tables B.44-46; Table 4.12). GEBV and OCS were consistently the worst selection strategies for maintaining the population upper selection limit relative to all other tested selection strategies (Appx. B, Tables B.44-46; Table 4.12). RS consistently performed at a lower intermediate level throughout the simulation (Fig. 4.12; Appx. B, Tables B.44-46; Table 4.12). Figure 4.12: Population upper selection limit by selection strategy over 60 generations in the single-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 194 Mean Pop. Selection USL Strategy 107.1811 gwGEBV50 107.1717 gwGEBV45 107.1695 gwGEBV40 107.1570 gwGEBV35 107.1463 gwGEBV90d gwGEBV30 107.1452 gwGEBV100d 107.1398 107.1363 gwGEBV80d 107.1352 gwGEBV25 107.1236 gwGEBV70d 107.1182 gwGEBV60d 107.1087 gwGEBV50d 107.0966 gwGEBV20 107.0765 gwGEBV40d 107.0635 gwGEBV15 107.0333 gwGEBV30d 106.9915 RS 106.9787 gwGEBV10 106.9663 gwGEBV20d 106.8435 gwGEBV10d 106.8264 gwGEBV05 106.6519 OCS 106.5861 GEBV Generation 60 95% Lower CL DF Std. Error 0.00502 1817 107.1713 0.00502 1817 107.1619 0.00502 1817 107.1596 0.00502 1817 107.1471 0.00502 1817 107.1365 0.00502 1817 107.1354 0.00502 1817 107.1299 0.00502 1817 107.1264 0.00502 1817 107.1253 0.00502 1817 107.1138 0.00502 1817 107.1084 0.00502 1817 107.0988 0.00502 1817 107.0867 0.00502 1817 107.0667 0.00502 1817 107.0537 0.00502 1817 107.0235 0.00502 1817 106.9817 0.00502 1817 106.9689 0.00502 1817 106.9565 0.00502 1817 106.8337 0.00502 1817 106.8166 0.00502 1817 106.6421 0.00502 1817 106.5762 Statistical Grouping 95% Upper CL 107.1910 O 107.1816 NO 107.1793 MNO 107.1668 LMNO 107.1562 KLMN 107.1551 KLM JKL 107.1496 JKL 107.1461 JKL 107.1450 107.1335 IJK 107.1281 HIJ 107.1185 HI 107.1064 GH FG 107.0864 F 107.0734 107.0432 E 107.0014 D 106.9886 D 106.9762 D 106.8533 C 106.8363 C 106.6618 B 106.5959 A Table 4.12: Population upper selection limit by selection strategy at generation 60 in the single- trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 3.2.2.4. Other diversity metrics Trends in population additive genetic and genic variance closely mirrored the trends observed for population mean expected heterozygosity. gwGEBV50, gwGEBV45, and gwGEBV40 were the top three selection strategies for these two metrics at generation 60 (Appx. B, Tables B.50, 54). Rankings within selection strategy families were generally stable across time (Appx. B, Figs. B.14-15; Appx. B, Tables B.47-54). Like with population mean expected heterozygosity, GWGS and TWGS selection strategies with higher upweighting factors tended to 195 preserve more additive genetic and genic variance across time (Appx. B, Tables B.47-54). Additionally, many of the TWGS selection strategies exhibited inflection points where additive genetic and genic variance rapidly decreased in later generations (Appx. B, Figs. B.14-15). OCS and GEBV were consistently the two worst strategies for preserving additive genetic and genic variance, while RS consistently produced intermediate performance results (Appx. B, Figs. B.14- 15; Appx. B, Tables B.47-54). Results for the Bulmer effect metric were difficult to discern due to high degrees of statistical overlap. GEBV, OCS, gwGEBV05, and gwGEBV10d tended to exhibit lower ratios of genetic variance to genic variance across time (Appx. B, Fig. B.16; Appx. B, Tables B.55-58). Other selection strategies exhibited a high degree of statistical overlap with each other. The TWGS strategies appeared to exhibit a rapid decrease in the Bulmer effect in later generations, and this was more extreme for TWGS strategies with higher initial upweighting factors (Appx. B, Fig. B.16). 3.3. Multi-trait breeding program results 3.3.1. Characterization of objectives 3.3.1.1. Characterization of GWGS and TWGS objectives Though technically non-convex by virtue of the discrete nature of the search space, the Pareto frontiers for the selection of 40 individuals based on the gwGEBVs for traits 1 and 2 appeared to be generally convex in both TRUE and EST scenarios and in all examined upweighting factor levels. Examples of Pareto frontiers can be viewed in Figs. 4.13 and 4.14. NSGA-II and NSGA-III mapped the central regions of these Pareto frontiers, missing the edges, but the algorithms converged well as demonstrated by their agreement with each other and with the independent single-objective optimizations using the ε-constraint method (Figs. 4.13-14). 196 Figure 4.13: Example Pareto frontier of gwGEBVs for the selection of 40 individuals in the multi-trait, TRUE scenario. gwGEBVs for both traits were calculated with an upweighting factor of 𝛼𝑡 = 0.05. Results for multi-objective optimization using NGSA-II (blue dots) and NGSA-III (orange ‘x’s) are plotted alongside the results from four separate single-objective optimizations (black tripoints). 197 Figure 4.14: Example Pareto frontier of gwGEBVs for the selection of 40 individuals in the multi-trait, EST scenario. gwGEBVs for both traits were calculated with an upweighting factor of 𝛼𝑡 = 0.05. Results for multi-objective optimization using NGSA-II (blue dots) and NGSA-III (orange ‘x’s) are plotted alongside the results from four separate single-objective optimizations (black tripoints). 3.3.1.2. Characterization of OCS objectives Again, though technically non-convex in nature, the Pareto frontiers for multi-trait OCS appeared to be generally convex in both TRUE and EST scenarios. Examples of Pareto frontiers can be viewed in Figs. 4.15 and 4.16. NSGA-II performed poorly at mapping these Pareto frontiers, exhibiting irregular distributions of points across the Pareto frontier (Figs. 4.15-16). NSGA-III performed substantially better in both its distribution and convergence along the Pareto frontier (Figs. 4.15-16). Like in the multi-trait gwGEBV case, NSGA-II and NSGA-III 198 exhibited difficulties around the edges of the Pareto frontier, as revealed by several independent single-objective optimizations using the ε-constraint method (Figs. 4.13-14). Figure 4.15: Example Pareto frontier for optimal contribution selection for multi-trait OCS in the TRUE scenario. Results for multi-objective optimization using NGSA-II (blue dots) and NGSA- III (orange ‘x’s) are plotted alongside the results from six separate single-objective optimizations (black tripoints). 199 Figure 4.16: Example Pareto frontier for optimal contribution selection for multi-trait OCS in the EST scenario. Results for multi-objective optimization using NGSA-II (blue dots) and NGSA-III (orange ‘x’s) are plotted alongside the results from six separate single-objective optimizations (black tripoints). 3.3.2. Multi-trait breeding program results: TRUE scenario 3.3.2.1. Genetic gain results In the multi-trait scenario, genetic gain results for quantitative traits Trait 1 and Trait 2 were somewhat similar to each other (Fig. 4.17). For Trait 1 at generation 60, the best selection strategies were gwGEBV40d, gwGEBV50d, gwGEBV30d, and gwGEBV60d, while for Trait 2 at generation 60, the best strategies were gwGEBV30d, OCS, gwGEBV20d, gwGEBV10d, gwGEBV50d, gwGEBV15, gwGEBV40d, and gwGEBV10 (Table 4.13). The best selection 200 strategies for both traits at generation 60 were gwGEBV30d, gwGEBV40d, and gwGEBV50d (Table 4.13), which was different from the single-trait selection scenario (Table 4.7). While in the single-trait, TRUE scenario, TWGS strategies with higher initial upweighting performed well, TWGS strategies with moderate initial upweighting factors appeared to perform better in the bi- trait, TRUE scenario. OCS results were somewhat mixed. For Trait 1, OCS performed at a lower- intermediate level, while for Trait 2, OCS was one of the best selection strategies (Table 4.13). GEBV performed at a lower level for both traits and underperformed relative to OCS for both traits (Table 4.13). RS exhibited the worst performance at generation 60 for both traits (Table 4.13). gwGEBV45 and gwGEBV50 performed poorly and were only better than RS at generation 60 (Table 4.13). This was surprising since gwGEBV50 and gwGEBV45 were strategies that performed well and moderately well, respectively, in the single-trait scenario (Table 4.7). Like in the single-trait scenario, TWGS strategies tended to outperform their GWGS counterparts in both traits. This trend was most apparent for TWGS and GWGS strategies with higher upweighting factors. For example, the TWGS strategies gwGEBV50d, gwGEBV60d, gwGEBV70d, gwGEBV80d, gwGEBV90d, and gwGEBV100d significantly outperformed their GWGS counterparts in both traits at generation 60. Ranking trends across time in the multi-trait scenario in the TRUE scenario were also like those observed in the single-trait scenario. In early generations, selection strategies with low upweighting factors were favored, and in later generations, selection strategies with higher upweighting factors tended to supplant these strategies (Appx. B, Tables B.59-61). 201 Figure 4.17: Population mean true breeding value by selection strategy over 60 generations in the multi-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 202 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T F E H G I H I H I H I H I H G I H G F I H E H G G F D C F E C B D E B F E I A F E D G F E I H G K J I J I H L K J I H G ] 0 6 8 9 . 3 0 1 , 3 6 5 9 . 3 0 1 [ ] 9 0 8 5 . 3 0 1 , 3 2 5 5 . 3 0 1 [ ] 1 3 0 0 . 4 0 1 , 5 3 7 9 . 3 0 1 [ ] 6 9 8 5 . 3 0 1 , 0 1 6 5 . 3 0 1 [ ] 5 3 9 9 . 3 0 1 , 8 3 6 9 . 3 0 1 [ ] 0 9 1 6 . 3 0 1 , 4 0 9 5 . 3 0 1 [ ] 3 3 1 0 . 4 0 1 , 6 3 8 9 . 3 0 1 [ ] 8 5 3 6 . 3 0 1 , 2 7 0 6 . 3 0 1 [ ] 0 8 9 9 . 3 0 1 , 4 8 6 9 . 3 0 1 [ ] 8 9 2 6 . 3 0 1 , 2 1 0 6 . 3 0 1 [ ] 5 5 2 0 . 4 0 1 , 9 5 9 9 . 3 0 1 [ ] 5 3 6 6 . 3 0 1 , 9 4 3 6 . 3 0 1 [ ] 6 7 7 9 . 3 0 1 , 0 8 4 9 . 3 0 1 [ ] 6 2 2 6 . 3 0 1 , 0 4 9 5 . 3 0 1 [ E D ] 5 7 1 9 . 3 0 1 , 9 7 8 8 . 3 0 1 [ ] 5 8 6 5 . 3 0 1 , 9 9 3 5 . 3 0 1 [ I H G F ] 5 1 5 9 . 3 0 1 , 9 1 2 9 . 3 0 1 [ ] 4 0 1 6 . 3 0 1 , 8 1 8 5 . 3 0 1 [ L ] 0 7 9 9 . 3 0 1 , 4 7 6 9 . 3 0 1 [ ] 3 2 9 6 . 3 0 1 , 7 3 6 6 . 3 0 1 [ I H G L K J L K ] 0 3 0 0 . 4 0 1 , 4 3 7 9 . 3 0 1 [ ] 2 7 6 6 . 3 0 1 , 7 8 3 6 . 3 0 1 [ ] 5 2 0 9 . 3 0 1 , 8 2 7 8 . 3 0 1 [ ] 5 8 1 6 . 3 0 1 , 9 9 8 5 . 3 0 1 [ ] 5 0 8 9 . 3 0 1 , 9 0 5 9 . 3 0 1 [ ] 0 1 6 6 . 3 0 1 , 4 2 3 6 . 3 0 1 [ H G F E ] 1 1 6 8 . 3 0 1 , 4 1 3 8 . 3 0 1 [ ] 7 6 9 5 . 3 0 1 , 1 8 6 5 . 3 0 1 [ K J I D C I H G C B ] 8 2 5 9 . 3 0 1 , 2 3 2 9 . 3 0 1 [ ] 2 8 3 6 . 3 0 1 , 6 9 0 6 . 3 0 1 [ ] 1 3 4 8 . 3 0 1 , 5 3 1 8 . 3 0 1 [ ] 1 5 4 5 . 3 0 1 , 5 6 1 5 . 3 0 1 [ ] 7 5 2 9 . 3 0 1 , 1 6 9 8 . 3 0 1 [ ] 5 2 2 6 . 3 0 1 , 9 3 9 5 . 3 0 1 [ ] 3 9 1 8 . 3 0 1 , 7 9 8 7 . 3 0 1 [ ] 5 5 2 5 . 3 0 1 , 9 6 9 4 . 3 0 1 [ I H G F ] 2 7 0 9 . 3 0 1 , 6 7 7 8 . 3 0 1 [ ] 8 0 1 6 . 3 0 1 , 2 2 8 5 . 3 0 1 [ E D C G F E ] 7 5 1 9 . 3 0 1 , 1 6 8 8 . 3 0 1 [ ] 7 1 6 5 . 3 0 1 , 1 3 3 5 . 3 0 1 [ ] 4 5 2 0 . 4 0 1 , 8 5 9 9 . 3 0 1 [ ] 9 1 9 5 . 3 0 1 , 3 3 6 5 . 3 0 1 [ A ] 2 3 6 5 . 3 0 1 , 6 3 3 5 . 3 0 1 [ ] 4 7 4 3 . 3 0 1 , 8 8 1 3 . 3 0 1 [ B ] 9 1 9 7 . 3 0 1 , 3 2 6 7 . 3 0 1 [ ] 7 7 9 4 . 3 0 1 , 1 9 6 4 . 3 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 7 2 0 9 . 3 0 1 2 1 7 9 . 3 0 1 3 8 8 9 . 3 0 1 6 8 7 9 . 3 0 1 5 8 9 9 . 3 0 1 2 3 8 9 . 3 0 1 7 0 1 0 . 4 0 1 8 2 6 9 . 3 0 1 2 2 8 9 . 3 0 1 7 6 3 9 . 3 0 1 2 8 8 9 . 3 0 1 6 7 8 8 . 3 0 1 7 5 6 9 . 3 0 1 2 6 4 8 . 3 0 1 0 8 3 9 . 3 0 1 3 8 2 8 . 3 0 1 9 0 1 9 . 3 0 1 5 4 0 8 . 3 0 1 4 2 9 8 . 3 0 1 1 7 7 7 . 3 0 1 9 0 0 9 . 3 0 1 6 0 1 0 . 4 0 1 4 8 4 5 . 3 0 1 1 t i a r T 2 4 5 5 . 3 0 1 6 6 6 5 . 3 0 1 3 5 7 5 . 3 0 1 7 4 0 6 . 3 0 1 5 1 2 6 . 3 0 1 5 5 1 6 . 3 0 1 2 9 4 6 . 3 0 1 3 8 0 6 . 3 0 1 0 8 7 6 . 3 0 1 1 6 9 5 . 3 0 1 9 2 5 6 . 3 0 1 2 4 0 6 . 3 0 1 7 6 4 6 . 3 0 1 4 2 8 5 . 3 0 1 9 3 2 6 . 3 0 1 8 0 3 5 . 3 0 1 2 8 0 6 . 3 0 1 2 1 1 5 . 3 0 1 5 6 9 5 . 3 0 1 4 3 8 4 . 3 0 1 4 7 4 5 . 3 0 1 6 7 7 5 . 3 0 1 1 3 3 3 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R 203 s e t a c i d n i S C O , s V B E G n o n o i t c e l e s s e t a c i d n i V B E G , e m i t r e v o y l r a e n i l d e s a e r c e d h c i h w 1 0 . 0 × # # f o s e u l a v α g n i t r a t s h t i w s e i g e t a r t s S G W T s e t a c i d n i d } # # { V B E G w g , 1 0 . 0 × # # f o s e u l a v α d e x i f h t i w s e i g e t a r t s S G W G s e t a c i d n i } # # { V B E G w g n r e t t a p n o i t a i v e r b b a e h T . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 3 1 . 4 e l b a T . n o i t c e l e s m o d n a r s e t a c i d n i S R d n a , t n i a r t s n o c g n i d e e r b n i d e x a l e r y l r a e n i l a h t i w S C O g n i s u n o i t c e l e s Results for the population maximum true breeding value were less precise, resulting in substantial statistical overlap between the tested selection strategies. At generation 60, ten selection strategies were statistically grouped together in the top group for Trait 1. They were: gwGEBV35, gwGEBV30, gwGEBV60d, gwGEBV70d, gwGEBV25, gwGEBV40, gwGEBV80d, gwGEBV90d, gwGEBV50d, and gwGEBV40d (Appx. B, Table B.65). For Trait 2 at generation 60, twelve selection strategies were in the top performing statistical grouping. They were: gwGEBV60d, gwGEBV20, gwGEBV25, gwGEBV50d, gwGEBV30, gwGEBV70d, gwGEBV100d, gwGEBV40, gwGEBV90d, gwGEBV80d, gwGEBV15, and gwGEBV35 (Appx. B, Table B.65). OCS and GEBV were ranked poorly for population maximum true breeding value at generation 60 for both traits, but they did outperform RS in almost all cases (Appx. B, Table B.65). Ranking trends over time were similar to those observed in the population mean true breeding value metric: in early generations, selections strategies with low upweighting factors were favored and in later generations, selection strategies with moderate to high upweighting factors were favored (Appx. B, Fig. B.17; Appx. B, Tables B.62-65). 3.3.2.2. Mean expected heterozygosity results Results for mean expected heterozygosity in the multi-trait, TRUE scenario were like those observed in the single-trait, TRUE scenario. At generation 60, gwGEBV50 was the best selection method for maintaining long-term mean expected heterozygosity (Fig. 4.18, Table 4.14). gwGEBV45 was the second-best selection method, followed by gwGEBV40 and RS, which were statistically grouped together (Table 4.14). GEBV was the worst strategy at maintaining long-term mean expected heterozygosity (Table 4.14). OCS exhibited a slight increase in mean expected heterozygosity in very early generations (Fig. 4.18), but it lost genetic diversity quickly as its diversity constraint relaxed throughout time. OCS nonetheless 204 outperformed GEBV at generation 60, but it too was ranked poorly among the tested selection strategies (Table 4.14). Rankings within selection strategy families were stable across time, like in the single-trait scenario. Within the GWGS and TWGS strategy families, selection strategies with higher upweighting factors maintained greater population mean expected heterozygosity at all time points (Fig. 4.18). Comparisons across all selection strategies revealed several rank changes. In earlier generations, TWGS strategies outperformed their GWGS counterparts with respect to population mean expected heterozygosity (Appx. B, Table B.66-67) but as time progressed, GWGS strategies tended to perform better than their TWGS counterparts, especially in late generations (Appx. B, Table B.68; Table 4.14). Figure 4.18: Population mean expected heterozygosity by selection strategy over 60 generations in the multi-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 205 Generation 60 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.0510 GEBV 0.0654 gwGEBV05 0.0629 gwGEBV10d 0.0795 gwGEBV10 0.0723 gwGEBV20d 0.0919 gwGEBV15 0.0820 gwGEBV30d 0.1036 gwGEBV20 0.0873 gwGEBV40d 0.1114 gwGEBV25 0.0956 gwGEBV50d 0.1197 gwGEBV30 0.1021 gwGEBV60d 0.1246 gwGEBV35 0.1067 gwGEBV70d 0.1329 gwGEBV40 0.1128 gwGEBV80d 0.1394 gwGEBV45 0.1166 gwGEBV90d gwGEBV50 0.1441 gwGEBV100d 0.1197 0.0690 OCS 0.1305 RS [0.0498, 0.0522] A [0.0642, 0.0666] B [0.0617, 0.0641] B [0.0783, 0.0807] E [0.0711, 0.0735] D [0.0907, 0.0931] G [0.0808, 0.0832] E [0.1024, 0.1048] IJ [0.0861, 0.0885] F [0.1102, 0.1126] K [0.0944, 0.0968] H [0.1185, 0.1209] L [0.1009, 0.1033] I [0.1234, 0.1258] M [0.1055, 0.1079] J [0.1317, 0.1341] N [0.1116, 0.1140] K [0.1382, 0.1406] O [0.1154, 0.1178] L [0.1429, 0.1453] P [0.1185, 0.1209] L [0.0678, 0.0702] C [0.1293, 0.1317] N DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table 4.14: Population mean expected heterozygosity by selection strategy at generation 60 in the multi-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 3.3.2.3. Upper selection limit results Upper selection limit results in the TRUE scenario were similar to the population mean expected heterozygosity results (Fig. 4.19). For both traits, gwGEBV50 was the best selection strategy for maintaining the upper selection limit at generation 60, followed by gwGEBV45 in second place, and gwGEBV40 in third place (Table 4.15). OCS and GEBV were statistically grouped as the second worst and worst strategies, respectively, at maintaining upper selection 206 limit for both traits (Table 4.15). RS maintained upper selection limit at intermediate levels for both traits with respect to all tested selection strategies (Table 4.15). Like with population mean expected heterozygosity, rankings for selection strategies were stable across time within selection strategy families. Within the GWGS and TWGS families, rankings proceeded according to the upweighting factor. GWGS and TWGS strategies with higher upweighting factors exhibited better long-term maintenance of the upper selection limit (Fig. 4.19; Table 4.15). Comparing across all selection strategies, TWGS strategies tended to exhibit better upper selection limit metrics in earlier generations compared to their GWGS counterparts (Appx. B, Table B.69-71). In later generations, TWGS strategies exhibited a slight inflection point (Fig. 4.19) and their GWGS counterparts supplanted them in their rankings (Table 4.15). 207 Figure 4.19: Population upper selection limit by selection strategy over 60 generations in the multi-trait, TRUE scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 208 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B B D C F E G F I H J I A C ] 1 4 8 5 . 4 0 1 , 6 9 3 5 . 4 0 1 [ ] 1 5 7 2 . 4 0 1 , 1 1 3 2 . 4 0 1 [ ] 4 3 5 9 . 4 0 1 , 8 8 0 9 . 4 0 1 [ ] 7 4 1 6 . 4 0 1 , 6 0 7 5 . 4 0 1 [ C B ] 2 3 2 9 . 4 0 1 , 7 8 7 8 . 4 0 1 [ ] 7 7 6 5 . 4 0 1 , 7 3 2 5 . 4 0 1 [ E D G F H G I H K I ] 5 7 8 2 . 5 0 1 , 9 2 4 2 . 5 0 1 [ ] 1 3 7 9 . 4 0 1 , 0 9 2 9 . 4 0 1 [ ] 2 1 5 1 . 5 0 1 , 7 6 0 1 . 5 0 1 [ ] 1 6 4 8 . 4 0 1 , 0 2 0 8 . 4 0 1 [ ] 9 0 6 5 . 5 0 1 , 4 6 1 5 . 5 0 1 [ ] 1 5 8 2 . 5 0 1 , 1 1 4 2 . 5 0 1 [ ] 5 3 2 4 . 5 0 1 , 0 9 7 3 . 5 0 1 [ ] 4 6 3 1 . 5 0 1 , 3 2 9 0 . 5 0 1 [ ] 5 0 8 7 . 5 0 1 , 0 6 3 7 . 5 0 1 [ ] 2 0 1 5 . 5 0 1 , 1 6 6 4 . 5 0 1 [ ] 2 6 9 5 . 5 0 1 , 6 1 5 5 . 5 0 1 [ ] 2 1 4 3 . 5 0 1 , 1 7 9 2 . 5 0 1 [ ] 5 9 5 9 . 5 0 1 , 0 5 1 9 . 5 0 1 [ ] 8 1 9 6 . 5 0 1 , 7 7 4 6 . 5 0 1 [ ] 9 6 4 8 . 5 0 1 , 4 2 0 8 . 5 0 1 [ ] 6 0 2 5 . 5 0 1 , 5 6 7 4 . 5 0 1 [ ] 9 1 3 1 . 6 0 1 , 3 7 8 0 . 6 0 1 [ ] 6 6 7 8 . 5 0 1 , 5 2 3 8 . 5 0 1 [ ] 1 0 0 0 . 6 0 1 , 5 5 5 9 . 5 0 1 [ ] 0 2 6 6 . 5 0 1 , 0 8 1 6 . 5 0 1 [ L K M ] 2 4 7 2 . 6 0 1 , 7 9 2 2 . 6 0 1 [ ] 4 6 9 9 . 5 0 1 , 3 2 5 9 . 5 0 1 [ M J K N L O M B H G J N K O ] 2 1 1 1 . 6 0 1 , 7 6 6 0 . 6 0 1 [ ] 7 8 6 7 . 5 0 1 , 7 4 2 7 . 5 0 1 [ ] 6 8 2 4 . 6 0 1 , 1 4 8 3 . 6 0 1 [ ] 0 3 2 1 . 6 0 1 , 9 8 7 0 . 6 0 1 [ ] 4 3 2 2 . 6 0 1 , 9 8 7 1 . 6 0 1 [ ] 1 5 5 8 . 5 0 1 , 0 1 1 8 . 5 0 1 [ ] 8 9 7 5 . 6 0 1 , 2 5 3 5 . 6 0 1 [ ] 5 4 3 2 . 6 0 1 , 4 0 9 1 . 6 0 1 [ L K ] 5 2 0 3 . 6 0 1 , 9 7 5 2 . 6 0 1 [ ] 0 3 0 9 . 5 0 1 , 9 8 5 8 . 5 0 1 [ M L ] 5 0 8 3 . 6 0 1 , 9 5 3 3 . 6 0 1 [ ] 7 2 5 9 . 5 0 1 , 7 8 0 9 . 5 0 1 [ P ] 9 3 7 6 . 6 0 1 , 4 9 2 6 . 6 0 1 [ ] 4 2 2 3 . 6 0 1 , 3 8 7 2 . 6 0 1 [ B H ] 9 2 4 9 . 4 0 1 , 3 8 9 8 . 4 0 1 [ ] 0 3 5 5 . 4 0 1 , 9 8 0 5 . 4 0 1 [ ] 8 1 3 8 . 5 0 1 , 3 7 8 7 . 5 0 1 [ ] 7 8 5 5 . 5 0 1 , 6 4 1 5 . 5 0 1 [ . p o P n a e M L S U 2 t i a r T 9 1 6 5 . 4 0 1 1 1 3 9 . 4 0 1 9 0 0 9 . 4 0 1 2 5 6 2 . 5 0 1 9 8 2 1 . 5 0 1 7 8 3 5 . 5 0 1 2 1 0 4 . 5 0 1 3 8 5 7 . 5 0 1 9 3 7 5 . 5 0 1 2 7 3 9 . 5 0 1 7 4 2 8 . 5 0 1 6 9 0 1 . 6 0 1 8 7 7 9 . 5 0 1 9 1 5 2 . 6 0 1 0 9 8 0 . 6 0 1 4 6 0 4 . 6 0 1 2 1 0 2 . 6 0 1 5 7 5 5 . 6 0 1 2 0 8 2 . 6 0 1 6 1 5 6 . 6 0 1 2 8 5 3 . 6 0 1 6 0 2 9 . 4 0 1 6 9 0 8 . 5 0 1 1 t i a r T 1 3 5 2 . 4 0 1 6 2 9 5 . 4 0 1 7 5 4 5 . 4 0 1 1 1 5 9 . 4 0 1 0 4 2 8 . 4 0 1 1 3 6 2 . 5 0 1 4 4 1 1 . 5 0 1 2 8 8 4 . 5 0 1 2 9 1 3 . 5 0 1 7 9 6 6 . 5 0 1 6 8 9 4 . 5 0 1 6 4 5 8 . 5 0 1 0 0 4 6 . 5 0 1 4 4 7 9 . 5 0 1 7 6 4 7 . 5 0 1 9 0 0 1 . 6 0 1 0 3 3 8 . 5 0 1 4 2 1 2 . 6 0 1 0 1 8 8 . 5 0 1 4 0 0 3 . 6 0 1 7 0 3 9 . 5 0 1 9 0 3 5 . 4 0 1 7 6 3 5 . 5 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R 209 n o i t a i v e r b b a e h T . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 5 1 . 4 e l b a T h t i w s e i g e t a r t s S G W T s e t a c i d n i d } # # { V B E G w g , 1 0 . 0 × # # f o s e u l a v α d e x i f h t i w s e i g e t a r t s S G W G s e t a c i d n i } # # { V B E G w g n r e t t a p g n i s u n o i t c e l e s s e t a c i d n i S C O , s V B E G n o n o i t c e l e s s e t a c i d n i V B E G , e m i t r e v o y l r a e n i l d e s a e r c e d h c i h w 1 0 . 0 × # # f o s e u l a v α g n i t r a t s . n o i t c e l e s m o d n a r s e t a c i d n i S R d n a , t n i a r t s n o c g n i d e e r b n i d e x a l e r y l r a e n i l a h t i w S C O 3.3.2.4. Other diversity metrics Results for population additive genetic and genic variance were very similar to the results for population mean expected heterozygosity and upper selection limit. At generation 60, gwGEBV50, gwGEBV45, and gwGEBV40 were the top three strategies for both genetic diversity metrics in both traits (Appx. B, Figs. B.18-19; Appx. B, Tables B.75, B.79). GEBV was the worst selection strategy for these metrics in all cases, and OCS was the second worst, frequently statistically grouping with gwGEBV05 and gwGEBV10d (Appx. B, Tables B.75, B.79). RS exhibited an intermediate performance at generation 60 compared to all other tested selection strategies (Appx. B, Tables B.75, B.79). Within their respective families, GWGS and TWGS strategies with higher upweighting factors tended to perform better than strategies with lower upweighting factors for both diversity metrics in both traits (Appx. B, Tables B.72-79). In early generations, TWGS strategies tended to outperform their GWGS counterparts, but in later generations, TWGS strategies experienced an inflection point leading to them having poorer long-term performance with respect to their GWGS counterparts (Appx. B, Figs. B.18-19). Results for the Bulmer effect were inconclusive since there was a great deal of statistical overlap. On visual inspection, GEBV, OCS, and RS did seem to exhibit lower ratios of genetic variance to genic variance for both traits (Appx. B, Fig. B.20), but the error variances were too large to make any significance claims (Appx. B, Tables B.80-83). 3.3.3. EST scenario 3.3.3.1. Genetic gain results Genetic gain results, as measured by the population mean true breeding value, in the multi-trait, EST scenario were similar to those in the single-trait scenario, but there were some key differences. For Trait 1 at generation 60, GEBV and OCS were statistically tied as the top 210 selection strategies (Fig. 4.20; Table 4.16). gwGEBV10d also performed well for Trait 1, grouping with OCS in the second-best statistical group (Table 4.16). For Trait 2 at generation 60, the best strategies were OCS and gwGEBV10d (Table 4.16). The next best strategies were gwGEBV05 and GEBV, which were also statistically grouped with gwGEBV10. RS performed better in the multi-trait scenario than the single-trait scenario relative to other tested selection strategies. For Trait 1 at generation 60, RS outperformed several GWGS strategies including gwGEBV25, gwGEBV30, gwGEBV35, gwGEBV40, gwGEBV45, and gwGEBV50 (Table 4.16). For Trait 2 at generation 60, RS outperformed gwGEBV40, gwGEBV45, and gwGEBV50. This deviated significantly from the single-trait scenario, since in the single-trait scenario, RS was among the worst strategies and performed statistically the same as gwGEBV45 and gwGEBV50 (Table 4.10). Ranking trends within families were similar to those in the single-trait scenario. Within GWGS and TWGS strategy families, selection strategies with higher upweighting factors tended to perform poorer than selection strategies with lower upweighting factors. Rankings were generally stable within selection families across time (Appx. B, Tables B.84-86). The TWGS strategy family generally underperformed relative to their GWGS counterparts in early generations and exhibited an upward inflection in genetic gain in later generations, permitting them to outperform their GWGS counterparts (Fig. 4.20; Appx. B, Tables B.84-86). 211 Figure 4.20: Population mean true breeding value by selection strategy over 60 generations in the multi-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 212 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T N N O N L M J L H G K F J E J I D C I H C B H G B A G A G F O E D M L N M K J ] 3 7 6 5 . 3 0 1 , 8 0 4 5 . 3 0 1 [ ] 2 3 9 2 . 3 0 1 , 6 7 6 2 . 3 0 1 [ ] 5 3 9 5 . 3 0 1 , 0 7 6 5 . 3 0 1 [ ] 0 0 1 3 . 3 0 1 , 4 4 8 2 . 3 0 1 [ ] 1 9 2 4 . 3 0 1 , 6 2 0 4 . 3 0 1 [ ] 5 3 7 1 . 3 0 1 , 9 7 4 1 . 3 0 1 [ O ] 7 6 6 5 . 3 0 1 , 2 0 4 5 . 3 0 1 [ ] 0 0 6 3 . 3 0 1 , 5 4 3 3 . 3 0 1 [ L H K E J D I C H C B H G B A G F F E A A E ] 7 1 8 4 . 3 0 1 , 2 5 5 4 . 3 0 1 [ ] 4 1 6 2 . 3 0 1 , 8 5 3 2 . 3 0 1 [ ] 5 1 8 2 . 3 0 1 , 0 5 5 2 . 3 0 1 [ ] 1 6 6 0 . 3 0 1 , 5 0 4 0 . 3 0 1 [ ] 6 5 1 4 . 3 0 1 , 1 9 8 3 . 3 0 1 [ ] 5 8 8 1 . 3 0 1 , 0 3 6 1 . 3 0 1 [ ] 4 5 8 1 . 3 0 1 , 9 8 5 1 . 3 0 1 [ ] 4 5 8 9 . 2 0 1 , 9 9 5 9 . 2 0 1 [ ] 2 6 3 3 . 3 0 1 , 7 9 0 3 . 3 0 1 [ ] 4 6 4 1 . 3 0 1 , 8 0 2 1 . 3 0 1 [ ] 1 1 2 1 . 3 0 1 , 6 4 9 0 . 3 0 1 [ ] 5 3 2 9 . 2 0 1 , 0 8 9 8 . 2 0 1 [ ] 3 3 8 2 . 3 0 1 , 8 6 5 2 . 3 0 1 [ ] 5 8 0 1 . 3 0 1 , 9 2 8 0 . 3 0 1 [ ] 9 9 5 0 . 3 0 1 , 3 3 3 0 . 3 0 1 [ ] 6 0 8 8 . 2 0 1 , 1 5 5 8 . 2 0 1 [ ] 5 9 4 2 . 3 0 1 , 0 3 2 2 . 3 0 1 [ ] 2 0 7 0 . 3 0 1 , 6 4 4 0 . 3 0 1 [ ] 3 6 1 0 . 3 0 1 , 8 9 8 9 . 2 0 1 [ ] 2 5 6 8 . 2 0 1 , 7 9 3 8 . 2 0 1 [ ] 0 5 1 2 . 3 0 1 , 5 8 8 1 . 3 0 1 [ ] 7 1 5 0 . 3 0 1 , 1 6 2 0 . 3 0 1 [ ] 7 2 8 9 . 2 0 1 , 2 6 5 9 . 2 0 1 [ ] 2 8 3 8 . 2 0 1 , 6 2 1 8 . 2 0 1 [ ] 2 2 8 1 . 3 0 1 , 7 5 5 1 . 3 0 1 [ ] 8 6 2 0 . 3 0 1 , 3 1 0 0 . 3 0 1 [ ] 0 6 7 9 . 2 0 1 , 5 9 4 9 . 2 0 1 [ ] 6 6 1 8 . 2 0 1 , 0 1 9 7 . 2 0 1 [ ] 8 3 6 1 . 3 0 1 , 2 7 3 1 . 3 0 1 [ ] 4 3 0 0 . 3 0 1 , 9 7 7 9 . 2 0 1 [ ] 0 8 4 9 . 2 0 1 , 4 1 2 9 . 2 0 1 [ ] 0 2 1 8 . 2 0 1 , 4 6 8 7 . 2 0 1 [ ] 5 1 5 1 . 3 0 1 , 0 5 2 1 . 3 0 1 [ ] 0 5 7 9 . 2 0 1 , 5 9 4 9 . 2 0 1 [ O N ] 2 8 1 6 . 3 0 1 , 7 1 9 5 . 3 0 1 [ ] 0 3 3 3 . 3 0 1 , 5 7 0 3 . 3 0 1 [ E ] 0 0 5 0 . 3 0 1 , 5 3 2 0 . 3 0 1 [ ] 0 7 8 9 . 2 0 1 , 4 1 6 9 . 2 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 4 3 5 5 . 3 0 1 0 4 5 5 . 3 0 1 2 0 8 5 . 3 0 1 8 5 1 4 . 3 0 1 4 8 6 4 . 3 0 1 3 8 6 2 . 3 0 1 3 2 0 4 . 3 0 1 2 2 7 1 . 3 0 1 0 3 2 3 . 3 0 1 9 7 0 1 . 3 0 1 1 0 7 2 . 3 0 1 6 6 4 0 . 3 0 1 3 6 3 2 . 3 0 1 1 3 0 0 . 3 0 1 8 1 0 2 . 3 0 1 4 9 6 9 . 2 0 1 9 8 6 1 . 3 0 1 7 2 6 9 . 2 0 1 5 0 5 1 . 3 0 1 7 4 3 9 . 2 0 1 2 8 3 1 . 3 0 1 9 4 0 6 . 3 0 1 8 6 3 0 . 3 0 1 1 t i a r T 2 7 4 3 . 3 0 1 4 0 8 2 . 3 0 1 2 7 9 2 . 3 0 1 7 0 6 1 . 3 0 1 6 8 4 2 . 3 0 1 3 3 5 0 . 3 0 1 8 5 7 1 . 3 0 1 7 2 7 9 . 2 0 1 6 3 3 1 . 3 0 1 7 0 1 9 . 2 0 1 7 5 9 0 . 3 0 1 8 7 6 8 . 2 0 1 4 7 5 0 . 3 0 1 5 2 5 8 . 2 0 1 9 8 3 0 . 3 0 1 4 5 2 8 . 2 0 1 1 4 1 0 . 3 0 1 8 3 0 8 . 2 0 1 7 0 9 9 . 2 0 1 2 9 9 7 . 2 0 1 2 2 6 9 . 2 0 1 3 0 2 3 . 3 0 1 2 4 7 9 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R 213 s e t a c i d n i S C O , s V B E G n o n o i t c e l e s s e t a c i d n i V B E G , e m i t r e v o y l r a e n i l d e s a e r c e d h c i h w 1 0 . 0 × # # f o s e u l a v α g n i t r a t s h t i w s e i g e t a r t s S G W T s e t a c i d n i d } # # { V B E G w g , 1 0 . 0 × # # f o s e u l a v α d e x i f h t i w s e i g e t a r t s S G W G s e t a c i d n i } # # { V B E G w g n r e t t a p n o i t a i v e r b b a e h T . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 6 1 . 4 e l b a T . n o i t c e l e s m o d n a r s e t a c i d n i S R d n a , t n i a r t s n o c g n i d e e r b n i d e x a l e r y l r a e n i l a h t i w S C O g n i s u n o i t c e l e s Results for the population maximum true breeding value were like the results for the population mean true breeding value, except there was slightly more standard error leading to more statistical overlap. For Trait 1 at generation 60, gwGEBV05, gwGEBV10d, gwGEBV20d, GEBV, and gwGEBV10 were identified as the best selection strategies, and for Trait 2 at generation 60, gwGEBV10d, gwGEBV05, and OCS were identified as the best selection strategies (Appx. B, Table B.90). Generally, GWGS and TWGS strategies with lower upweighting factors tended to perform better than strategies with higher upweighting factors (Appx. B, Fig. B.21; Appx. B, Tables B.87-90). In earlier generations, GWGS strategies tended to outperform their TWGS counterparts, but in later generations, TWGS strategies experienced an increase in their genetic gain rate and tended to outperform their GWGS counterparts (Appx. B, Tables B.87-90). 3.3.3.2. Mean expected heterozygosity results At generation 60, gwGEBV50, gwGEBV45, and gwGEBV40 were the best selection strategies for maintaining population mean expected heterozygosity (Fig. 4.21; Table 4.17). RS ranked poorly as the fifth worst selection strategy but performed better than OCS and selection on GEBVs (Table 4.17). OCS was able to increase population mean expected heterozygosity in very early generations, but lost these gains, ultimately resulting in the second worst ranking (Fig. 4.21; Table 4.17). GEBV was the worst ranked selection strategy at all generations (Fig. 4.21; Appx. B, Tables B.91-93; Table 4.17). Within GWGS and TWGS strategy families at generation 60, selection strategies with higher upweighting factors exhibited higher population mean expected heterozygosity than strategies with lower upweighting factors (Table 4.17). Ranking patterns were consistent across generations, with this same trend being observed in generations prior to generation 60 (Fig. 4.21; Appx. B, Tables B.91-93). GWGS strategies tended to 214 outperform their TWGS strategy counterparts, especially in later generations (Appx. B, Tables B.91-93; Table 4.17). TWGS strategies exhibited an inflection point where mean expected heterozygosity dropped, dramatically in some cases (Fig. 4.21). The inflection point beginning the increased drop in population mean expected heterozygosity occurred in later generations. Figure 4.21: Population mean expected heterozygosity by selection strategy over 60 generations in the multi-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 215 Generation 60 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.1004 GEBV 0.1648 gwGEBV05 0.1518 gwGEBV10d 0.2069 gwGEBV10 0.1794 gwGEBV20d 0.2289 gwGEBV15 0.1959 gwGEBV30d 0.2407 gwGEBV20 0.2064 gwGEBV40d 0.2477 gwGEBV25 0.2150 gwGEBV50d 0.2528 gwGEBV30 0.2206 gwGEBV60d 0.2554 gwGEBV35 0.2247 gwGEBV70d 0.2569 gwGEBV40 0.2288 gwGEBV80d 0.2578 gwGEBV45 0.2320 gwGEBV90d gwGEBV50 0.2587 gwGEBV100d 0.2339 0.1080 OCS 0.1746 RS [0.0996, 0.1013] A [0.1640, 0.1657] D [0.1509, 0.1526] C [0.2060, 0.2078] H [0.1785, 0.1802] F [0.2280, 0.2298] L [0.1950, 0.1968] G [0.2399, 0.2416] N [0.2056, 0.2073] H [0.2469, 0.2486] O [0.2141, 0.2159] I [0.2519, 0.2537] P [0.2197, 0.2215] J [0.2545, 0.2562] Q [0.2238, 0.2256] K [0.2561, 0.2578] QR [0.2279, 0.2296] L [0.2569, 0.2587] R [0.2311, 0.2328] M [0.2578, 0.2596] R [0.2331, 0.2348] M [0.1071, 0.1088] B [0.1738, 0.1755] E DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table 4.17: Population mean expected heterozygosity by selection strategy at generation 60 in the multi-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 3.3.3.3. Upper selection limit results Upper selection limit results in the EST scenario were very similar to those observed in the TRUE scenario. For Trait 1 at generation 60, gwGEBV50, gwGEBV45, gwGEBV40, and gwGEBV100d were the best selection strategies for maintaining the upper selection limit (Table 4.18). For Trait 2 at the same time point, the best selection strategies were almost the same: gwGEBV50, gwGEBV45, and gwGEBV40 (Table 4.18). For both traits, GEBV maintained the lowest upper selection limit at generation 60 (Table 4.18) and across time (Fig. 4.22; Appx. B, 216 Tables B.94-96). OCS maintained the upper selection limit for both traits at levels higher than that of GEBV but underperformed relative to all other tested selection strategies (Fig. 4.22; Appx. B, Tables B.94-96; Table 4.18). Within the GWGS and TWGS strategy families, selection strategies with higher upweighting factors maintained a higher upper selection limit at generation 60 (Table 4.18) and across multiple generations for both Trait 1 and Trait 2 (Appx. B, Tables B.94-96). In early generations, TWGS strategies tended to outperform their GWGS counterparts (Appx. B, Tables B.94-96), but in later generations, TWGS strategies experienced an increase in the reduction of the upper selection limit, resulting in GWGS strategies tending to outperform their TWGS counterparts (Fig. 4.22; Table 4.18). 217 Figure 4.22: Population upper selection limit by selection strategy over 60 generations in the multi-trait, EST scenario. The abbreviation pattern gwGEBV{##} indicates GWGS strategies with fixed α values of ## × 0.01, gwGEBV{##}d indicates TWGS strategies with starting α values of ## × 0.01 which decreased linearly over time, GEBV indicates selection on GEBVs, OCS indicates selection using OCS with a linearly relaxed inbreeding constraint, and RS indicates random selection. 218 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A D C G E J I G N M L I L K H A D C F E H F J I G L K I H ] 8 1 4 3 . 5 0 1 , 0 6 0 3 . 5 0 1 [ ] 2 3 1 1 . 5 0 1 , 1 7 7 0 . 5 0 1 [ ] 5 9 2 1 . 6 0 1 , 7 3 9 0 . 6 0 1 [ ] 9 7 2 8 . 5 0 1 , 8 1 9 7 . 5 0 1 [ ] 0 1 8 0 . 6 0 1 , 2 5 4 0 . 6 0 1 [ ] 7 2 7 7 . 5 0 1 , 6 6 3 7 . 5 0 1 [ ] 5 4 4 5 . 6 0 1 , 7 8 0 5 . 6 0 1 [ ] 2 4 5 1 . 6 0 1 , 1 8 1 1 . 6 0 1 [ ] 4 1 9 3 . 6 0 1 , 6 5 5 3 . 6 0 1 [ ] 2 9 4 0 . 6 0 1 , 1 3 1 0 . 6 0 1 [ ] 9 8 2 7 . 6 0 1 , 1 3 9 6 . 6 0 1 [ ] 7 3 3 3 . 6 0 1 , 6 7 9 2 . 6 0 1 [ ] 3 7 4 5 . 6 0 1 , 5 1 1 5 . 6 0 1 [ ] 3 3 8 1 . 6 0 1 , 2 7 4 1 . 6 0 1 [ ] 2 1 1 8 . 6 0 1 , 4 5 7 7 . 6 0 1 [ ] 0 3 8 3 . 6 0 1 , 9 6 4 3 . 6 0 1 [ ] 5 4 5 6 . 6 0 1 , 7 8 1 6 . 6 0 1 [ ] 5 6 8 2 . 6 0 1 , 4 0 5 2 . 6 0 1 [ ] 0 2 4 8 . 6 0 1 , 3 6 0 8 . 6 0 1 [ ] 1 2 5 4 . 6 0 1 , 0 6 1 4 . 6 0 1 [ ] 2 4 2 7 . 6 0 1 , 4 8 8 6 . 6 0 1 [ ] 8 1 5 3 . 6 0 1 , 7 5 1 3 . 6 0 1 [ P O N M N M L ] 0 7 7 8 . 6 0 1 , 2 1 4 8 . 6 0 1 [ ] 5 3 8 4 . 6 0 1 , 4 7 4 4 . 6 0 1 [ P O N L K Q P O K J M L Q P O N M ] 7 3 8 8 . 6 0 1 , 9 7 4 8 . 6 0 1 [ ] 6 0 0 5 . 6 0 1 , 5 4 6 4 . 6 0 1 [ P O N M L K ] 2 8 0 9 . 6 0 1 , 4 2 7 8 . 6 0 1 [ ] 9 8 2 5 . 6 0 1 , 8 2 9 4 . 6 0 1 [ ] 5 1 3 8 . 6 0 1 , 7 5 9 7 . 6 0 1 [ ] 3 5 6 4 . 6 0 1 , 1 9 2 4 . 6 0 1 [ L K ] 1 5 1 8 . 6 0 1 , 3 9 7 7 . 6 0 1 [ ] 0 5 4 4 . 6 0 1 , 9 8 0 4 . 6 0 1 [ P O ] 8 1 2 9 . 6 0 1 , 0 6 8 8 . 6 0 1 [ ] 1 4 3 5 . 6 0 1 , 0 8 9 4 . 6 0 1 [ K J ] 3 2 7 7 . 6 0 1 , 5 6 3 7 . 6 0 1 [ ] 8 8 1 4 . 6 0 1 , 7 2 8 3 . 6 0 1 [ O N M N M L ] 0 0 7 8 . 6 0 1 , 2 4 3 8 . 6 0 1 [ ] 4 5 8 4 . 6 0 1 , 3 9 4 4 . 6 0 1 [ P O Q B F P O N M ] 4 9 8 8 . 6 0 1 , 6 3 5 8 . 6 0 1 [ ] 5 1 1 5 . 6 0 1 , 4 5 7 4 . 6 0 1 [ P ] 7 6 4 9 . 6 0 1 , 9 0 1 9 . 6 0 1 [ ] 6 6 5 5 . 6 0 1 , 4 0 2 5 . 6 0 1 [ B F ] 1 7 8 4 . 5 0 1 , 3 1 5 4 . 5 0 1 [ ] 6 0 0 2 . 5 0 1 , 5 4 6 1 . 5 0 1 [ ] 2 7 5 4 . 6 0 1 , 4 1 2 4 . 6 0 1 [ ] 5 1 8 1 . 6 0 1 , 4 5 4 1 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 9 3 2 3 . 5 0 1 6 1 1 1 . 6 0 1 1 3 6 0 . 6 0 1 6 6 2 5 . 6 0 1 5 3 7 3 . 6 0 1 0 1 1 7 . 6 0 1 4 9 2 5 . 6 0 1 3 3 9 7 . 6 0 1 6 6 3 6 . 6 0 1 1 4 2 8 . 6 0 1 3 6 0 7 . 6 0 1 1 9 5 8 . 6 0 1 4 4 5 7 . 6 0 1 8 5 6 8 . 6 0 1 2 7 9 7 . 6 0 1 3 0 9 8 . 6 0 1 6 3 1 8 . 6 0 1 9 3 0 9 . 6 0 1 1 2 5 8 . 6 0 1 8 8 2 9 . 6 0 1 5 1 7 8 . 6 0 1 2 9 6 4 . 5 0 1 3 9 3 4 . 6 0 1 1 t i a r T 2 5 9 0 . 5 0 1 8 9 0 8 . 5 0 1 6 4 5 7 . 5 0 1 2 6 3 1 . 6 0 1 2 1 3 0 . 6 0 1 7 5 1 3 . 6 0 1 2 5 6 1 . 6 0 1 9 4 6 3 . 6 0 1 4 8 6 2 . 6 0 1 0 4 3 4 . 6 0 1 8 3 3 3 . 6 0 1 5 5 6 4 . 6 0 1 7 0 0 4 . 6 0 1 5 2 8 4 . 6 0 1 9 6 2 4 . 6 0 1 9 0 1 5 . 6 0 1 2 7 4 4 . 6 0 1 1 6 1 5 . 6 0 1 3 7 6 4 . 6 0 1 5 8 3 5 . 6 0 1 5 3 9 4 . 6 0 1 6 2 8 1 . 5 0 1 5 3 6 1 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R 219 g n i s u n o i t c e l e s s e t a c i d n i S C O , s V B E G n o n o i t c e l e s s e t a c i d n i V B E G , e m i t r e v o y l r a e n i l d e s a e r c e d h c i h w 1 0 . 0 × # # f o s e u l a v α g n i t r a t s n o i t a i v e r b b a e h T . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 8 1 . 4 e l b a T h t i w s e i g e t a r t s S G W T s e t a c i d n i d } # # { V B E G w g , 1 0 . 0 × # # f o s e u l a v α d e x i f h t i w s e i g e t a r t s S G W G s e t a c i d n i } # # { V B E G w g n r e t t a p . n o i t c e l e s m o d n a r s e t a c i d n i S R d n a , t n i a r t s n o c g n i d e e r b n i d e x a l e r y l r a e n i l a h t i w S C O 3.3.3.4. Other diversity metrics Results for population additive genetic and genic variance in the EST scenario were very similar to the results for population mean expected heterozygosity. gwGEBV50, gwGEBV45, gwGEBV35, and gwGEBV40 were the best selection strategies for maintaining population genetic variance for both traits at generation 60, and gwGEBV50 and gwGEBV45 were the best selection strategies for maintaining population genic variance for both traits at generation 60 (Appx. B, Tables B.100, B.104). Within GWGS and TWGS strategy families, selection strategies with higher upweighting factors tended to maintain higher levels of population genetic and genic variance across time for both traits than selection strategies with lower upweighting factors (Appx. B, Figs. B.22-23; Appx. B, Tables B.97-104). TWGS strategies exhibited sharp reductions in population additive genetic and genic variance in later generations leading them to underperform in these metrics relative to their GWGS counterparts (Appx. B, Figs. B.22-23; Appx. B, Tables B.100, B.104). GEBV was the worst selection strategy for maintaining these additive genetic and genic variance metrics for both traits across almost all time points (Appx. B, Figs. B.22-23; Appx. B, Tables B.97-104). OCS was the second worst selection strategy for maintaining these metrics for both traits (Appx. B, Figs. B.22-23; Appx. B, Tables B.97-104). Bulmer effect results in the EST scenario were inconclusive for both traits. We observed a high degree of statistical overlapping across all generations (Appx. B, Tables B.105-108). On visual inspection, GEBV, OCS, and RS appeared to exhibit lower ratios of additive genetic variance to genic variance ratios than TWGS and GWGS strategies (Appx. B, Fig. B.24), but there was not a great degree of separation between these selection strategies and the GWGS and TWGS strategies. 220 4. Discussion 4.1. Remarks on the effects of marker upweighting on long-term selection and an ideal long-term upweighting strategy In our assessment, the simulation results characterizing the effects of marker upweighting on long-term, single-trait selection were mostly inconclusive. Indeed, we were able to identify many time points for which the upweighting factor value significantly affected a population genetic gain or genetic diversity metric at generation 60, but most of the timepoints were not statistically significant after correcting for multiple tests. Stochastic breeding simulations always have some degree of error, and this error increases as the number of simulated generations increases. Perhaps for these experiments, 10000 random upweighting factor trajectories was not enough to discern the effects of the upweighting factor on many of the examined metrics. Furthermore, though we were able to identify several significant, linear relationships between upweighting factor effect estimates and generation number, we urge extreme caution in their interpretation. Given that most of the upweighting factor effect estimates were not statistically significant, it is possible that the trends we observed could be an artifact of our first model. Additional simulations may provide better upweighting factor effect estimates which could reveal a constant, quadratic, or even non-linear trend in the upweighting factor effects across time. From what conclusive results we have, we observe that increasing the upweighting factor, and by extension the preference for genetic diversity, in later generations appears to have a detrimental effect on long-term genetic gain results. In the TRUE scenario, the only significant regression coefficients for genetic gain metrics occurred at generations 5, 45, 56, and 57. At generation 5, increasing the upweighting factor increased the population maximum true breeding 221 value and at generations 45, 56, and 57, increasing the upweighting factor decreased the population mean true breeding value. In the EST scenario, many significant time points existed. At generations 24, 33-34, 38-40, 42, 45, 51-53, and 56-58, increasing the upweighting factor decreased the population mean true breeding value at generation 60. At generations 46, 53, and 55-58, increasing the upweighting factor decreased the population maximum true breeding value at generation 60. These results suggest that an ideal selection strategy to maximize genetic gain should decrease its priority on preservation of genetic diversity in later generations. The rate at which this priority should be reduced, however, is still largely unknown. From the conclusive results we have on the effects of the upweighting factor on population mean expected heterozygosity, it appears that upweighting and by extension genetic diversity preference is important throughout the duration of a breeding program and is especially important in later generations. In the TRUE scenario, generations 11, 14, 22-23, 45-48, 50-51, 53-54, 56-58, and in the EST scenario, generations 4, 23-24, 38-40, 51-53, and 56-58 were significant. At all these time points, increasing the upweighting factor significantly increased the population mean expected heterozygosity at generation 60, but this effect was especially pronounced in generations 56-58. These results suggest that maintaining genetic diversity is important at all time points in a breeding program, and that it may be possible to recover genetic diversity as measured by population mean expected heterozygosity very late in a breeding program. Finally, our most conclusive results for the effect of the upweighting factor on the upper selection limit at generation 60 indicates that the upweighting factor, and by extension the preference for genetic diversity, in early generations significantly affects the upper selection limit in the long-term. In the TRUE scenario, most upweighting factor effect coefficients in 222 generations 1-30 were statistically significant, suggesting that it is crucial to maintain genetic diversity in early generations of a closed, long-term breeding program. Once genetic diversity is lost, it cannot be recovered. In the EST scenario, none of the upweighting factor effect coefficients were statistically significant. We believe that the additional variance introduced in the EST scenario made it more difficult to distinguish between different random upweighting trajectories, leading to the negative results. 4.2. Remarks on error multiplication for gwGEBV-based selection strategies 4.2.1. Peculiar observations for gwGEBV-based selection strategies In our single- and multi-trait experiments, we observed that when marker effects and locations were known, GWGS and TWGS selection strategies exhibited superior long-term genetic gain and genetic diversity metrics compared to OCS, GEBV, and RS. Generally, GWGS and TWGS strategies with higher upweighting performed better in these metrics. When marker effects and locations were unknown, however, we observed the opposite to be true regarding genetic gain metrics. GWGS and TWGS strategies tended to underperform in genetic gain relative to OCS and GEBV in these scenarios, and GWGS and TWGS strategies with lower upweighting factors tended to deliver higher genetic gains. GWGS and TWGS strategies remained effective at maintaining genetic diversity, however. These peculiar results merit further examination and explanation. We propose that the contrasting genetic gain properties exhibited by GWGS and TWGS in the TRUE and EST scenarios can be explained by a magnification of error stemming from the estimation of the favorable allele state. We provide mathematical proof of this proposition below. 223 4.2.2. gwGEBV error multiplication at a single locus for a single trait To begin, let us first define several assumptions and variables. For our derivation, we assume that a QTL is biallelic in nature and acts in a strictly additive manner. Let 𝑢𝑡,𝑖 represent the true additive allele effect for trait 𝑡 at the 𝑖th locus, 𝜀𝑡,𝑖 represent the effect estimation error associated for trait 𝑡 at the 𝑖th locus, and 𝑢̂𝑡,𝑖 = 𝑢𝑡,𝑖 + 𝜀𝑡,𝑖 represent the estimated additive allele effect for trait 𝑡 at the 𝑖th locus. Next, let 𝑝𝑡,𝑖 represent the true population favorable allele frequency for trait 𝑡 at the 𝑖th locus, 𝛿𝑡,𝑖 represent the estimation error associated with the true population favorable allele frequency for trait 𝑡 at the 𝑖th locus, and 𝑝̂𝑡,𝑖 = 𝑝𝑡,𝑖 + 𝛿𝑡,𝑖 represent the estimated population favorable allele frequency for trait 𝑡 at the 𝑖th locus. Favorable allele frequencies are estimated by identifying the beneficial allele state using the sign of 𝑢̂𝑡,𝑖. Finally, let 𝑢̃𝑡,𝑖 = 𝑝̂𝑡,𝑖 −𝛼𝑡𝑢̂𝑡,𝑖 represent the upweighted additive allele effect for trait 𝑡 at the 𝑖th locus for the given upweighting factor 𝛼𝑡. We can expand the upweighted additive effect as an expression of true values and their errors: 𝑢̃𝑡,𝑖 = 𝑝̂𝑡,𝑖 −𝛼𝑡𝑢̂𝑡,𝑖 = (𝑝𝑡,𝑖 + 𝛿𝑡,𝑖) −𝛼𝑡(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) For our favorable allele frequency estimation, we have two options: either we estimated the favorable allele frequency correctly from the sign of 𝑢̂𝑡,𝑖, or we did not. In the former case, 𝛿𝑡,𝑖 = 0, and in the latter case, 𝛿𝑡,𝑖 ≠ 0. If we estimated the favorable allele frequency correctly, then 𝑝̂𝑡,𝑖 = 𝑝𝑡,𝑖 and our upweighted additive effect is: 𝑢̃𝑡,𝑖 = 𝑝𝑡,𝑖 −𝛼𝑡(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) = 𝑝𝑡,𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖 224 If we estimated the favorable allele frequency incorrectly, then our upweighting becomes slightly more complicated. Since our estimate of the favorable allele frequency is incorrect, then 𝑝̂𝑡,𝑖 = 1 − 𝑝𝑡,𝑖 since we assumed only two alleles. Our upweighted additive effect then becomes: 𝑢̃𝑡,𝑖 = (1 − 𝑝𝑡,𝑖) −𝛼𝑡(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) We can add 0 = 𝑝𝑡,𝑖 −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 to (1 − 𝑝𝑡,𝑖) −𝛼𝑡 and factor out an upweighted favorable allele frequency error as 𝜉𝑡,𝑖 = (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 to get an expression of the added error: 𝑢̃𝑡,𝑖 = (1 − 𝑝𝑡,𝑖) −𝛼𝑡(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) = ((1 − 𝑝𝑡,𝑖) −𝛼𝑡 + 𝑝𝑡,𝑖 −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡)(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) = (𝑝𝑡,𝑖 −𝛼𝑡 + (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡)(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) = (𝑝𝑡,𝑖 −𝛼𝑡 + 𝜉𝑡,𝑖)(𝑢𝑡,𝑖 + 𝜀𝑡,𝑖) = 𝑝𝑡,𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖 + 𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖 As seen above, in the case where we correctly estimate the favorable allele frequency, we succeed in upweighting our allele effect, and we also unavoidably upweight the error associated with the allele effect. In the case where we incorrectly estimate the favorable allele frequency, we add additional error to the upweighted allele effects. The upweighted favorable allele frequency error extracted above has a couple of important properties which we will briefly describe and then mathematically prove. First, when 𝑝𝑡,𝑖 < 0.5, the sign of the error is negative, and when 𝑝𝑡,𝑖 > 0.5, the sign of the error is positive. This results in underweighting and overweighting of upweights, respectively, relative to if we had correctly estimated the favorable allele frequency. Furthermore, when the favorable allele frequency is 0.5, the upweighted favorable allele frequency error is always zero. Second, the upweighted favorable allele frequency error explodes to negative infinity or infinity as the true favorable allele frequency approaches 0 or 1, 225 respectively. This potentially has grave consequences for breeding, since it is presumed that the breeder wishes to fix the favorable allele. Finally, the upweighted favorable allele frequency error also exponentially grows to negative infinity or infinity as the upweighting factor increases to infinity when 𝑝𝑡,𝑖 < 0.5 or 𝑝𝑡,𝑖 > 0.5, respectively. This potentially has severe consequences for breeding since the upweighting factor also controls the degree to which genetic diversity is preserved. Regardless of the upweighted favorable allele frequency error source, the consequence of these additional errors is reduced selection accuracy. The first claim about the properties related to the upweighted favorable allele frequency error is proved below. Suppose that the upweighting error 𝜉𝑡,𝑖 is positive, the true favorable allele frequency is between 0 and 1, 𝑝𝑡,𝑖 ∈ (0,1), and the upweighting factor is positive, 𝛼𝑡 > 0, then: 𝜉𝑡,𝑖 > 0 (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 > 0 (1 − 𝑝𝑡,𝑖) −𝛼𝑡 > 𝑝𝑡,𝑖 −𝛼𝑡 (1 − 𝑝𝑡,𝑖) 𝛼𝑡 < 𝑝𝑡,𝑖 𝛼𝑡 The statement (1 − 𝑝𝑡,𝑖) 𝛼𝑡 < 𝑝𝑡,𝑖 𝛼𝑡 with 𝛼𝑡 > 0 is only true if 1 − 𝑝𝑡,𝑖 < 𝑝𝑡,𝑖. We can see that: 1 − 𝑝𝑡,𝑖 < 𝑝𝑡,𝑖 1 < 2𝑝𝑡,𝑖 0.5 < 𝑝𝑡,𝑖 𝑝𝑡,𝑖 > 0.5 Thus, 𝜉𝑡,𝑖 is positive if 𝑝𝑡,𝑖 > 0.5 and the upweighting factor 𝛼𝑡 is positive. Now, suppose that the upweighting error is negative, the true favorable allele frequency is between 0 and 1, 𝑝𝑡,𝑖 ∈ (0,1), and the upweighting factor is positive, 𝛼𝑡 > 0, then: 226 𝜉𝑡,𝑖 < 0 (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 < 0 (1 − 𝑝𝑡,𝑖) −𝛼𝑡 < 𝑝𝑡,𝑖 −𝛼𝑡 (1 − 𝑝𝑡,𝑖) 𝛼𝑡 > 𝑝𝑡,𝑖 𝛼𝑡 The statement (1 − 𝑝𝑡,𝑖) 𝛼𝑡 > 𝑝𝑡,𝑖 𝛼𝑡 with 𝛼𝑡 > 0 is only true if 1 − 𝑝𝑡,𝑖 > 𝑝𝑡,𝑖. Like the positive case, we can see that: 1 − 𝑝𝑡,𝑖 > 𝑝𝑡,𝑖 1 > 2𝑝𝑡,𝑖 0.5 > 𝑝𝑡,𝑖 𝑝𝑡,𝑖 < 0.5 Thus, 𝜉𝑡,𝑖 is negative if 𝑝𝑡,𝑖 < 0.5 and the upweighting factor 𝛼𝑡 is positive. Now, finally suppose that the favorable allele frequency is 0.5 and the upweighting factor is positive. The proof that the upweight factor error is zero for any 𝛼𝑡 > 0 is straightforward: 𝜉𝑡,𝑖 = (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 = (1 − 0.5)−𝛼𝑡 − 0.5−𝛼𝑡 = 0.5−𝛼𝑡 − 0.5−𝛼𝑡 = 0 Proof for the second claim about the properties of the upweighted favorable allele frequency error term is established by taking the limit of the upweighted favorable allele frequency error term as 𝑝𝑡,𝑖 → 0 or 𝑝𝑡,𝑖 → 1. In the former case, we have: lim 𝑝𝑡,𝑖→0 ((1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡) = lim 𝑝𝑡,𝑖→0 1 (1 − 𝑝𝑡,𝑖) 𝛼𝑡 − lim 𝑝𝑡,𝑖→0 1 𝛼𝑡 𝑝𝑡,𝑖 227 = 1 − ∞ = −∞ And in the latter case, we have: lim 𝑝𝑡,𝑖→1 ((1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡) = lim 𝑝𝑡,𝑖→1 1 (1 − 𝑝𝑡,𝑖) 𝛼𝑡 − lim 𝑝𝑡,𝑖→1 1 𝛼𝑡 𝑝𝑡,𝑖 = ∞ − 1 = ∞ Thus, the upweighted favorable allele frequency error increases to negative infinity and infinity as the true favorable allele frequency approaches 0 and 1, respectively. Finally, proof for the third claim about the upweighted favorable allele frequency error is demonstrated by taking the limit as 𝛼𝑡 → ∞, assuming the true favorable allele frequency is between 0 and 1, 𝑝𝑡,𝑖 ∈ (0,1), and the upweighting factor is positive, 𝛼𝑡 > 0. We can use the results from the proof of the first upweighted favorable allele frequency error property to direct this proof. If 𝑝𝑡,𝑖 > 0.5, then we know the upweighted favorable allele frequency error must be greater than zero for any 𝛼𝑡 > 0: (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 > 0. The limit as 𝛼𝑡 → ∞ therefore must go to infinity: ((1 − 𝑝𝑡,𝑖) lim 𝛼𝑡→∞ 𝑝𝑡,𝑖>0.5 −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡) = ∞ Similarly, if 𝑝𝑡,𝑖 < 0.5, then we know the upweighted favorable allele frequency error must be less than zero for any 𝛼𝑡 > 0: (1 − 𝑝𝑡,𝑖) −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡 < 0, and the limit of the upweighted favorable allele frequency error as 𝛼𝑡 → ∞ must go to negative infinity: ((1 − 𝑝𝑡,𝑖) lim 𝛼𝑡→∞ 𝑝𝑡,𝑖<0.5 −𝛼𝑡 − 𝑝𝑡,𝑖 −𝛼𝑡) = −∞ 228 Thus, the upweighted favorable allele frequency error exponentially grows to negative infinity and infinity as 𝛼𝑡 → ∞ when 𝑝𝑡,𝑖 < 0.5 and 𝑝𝑡,𝑖 > 0.5, respectively. 4.2.3. gwGEBV error multiplication in the multi-locus, single-trait case The calculations in the preceding section are for single loci. Now, suppose that we consider many loci as is done in the calculation of gwGEBVs. Let 𝑧𝑖 denote the allele state at the 𝑖th QTL, 𝒟𝑡 denote the set of loci for which the deleterious allele frequency was identified instead of the favorable allele frequency for trait 𝑡, 𝒟𝑡 𝑐 denote the complement of 𝒟𝑡, the set of loci for which the favorable allele frequency was correctly identified for trait 𝑡, and 𝒜 = 𝒟𝑡 ∪ 𝑐 denote the set of all alleles. The gwGEBVs can be expressed as: 𝒟𝑡 𝑦𝑔𝑤𝐺𝐸𝐵𝑉𝑡 = ∑ (𝑝𝑡,𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 𝑐 𝑖∈𝒟𝑡 = ∑ (𝑝𝑡,𝑖 𝑐 𝑖∈𝒟𝑡 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 + ∑ (𝑝𝑡,𝑖 𝑖∈𝒟𝑡 + ∑ (𝑝𝑡,𝑖 𝑖∈𝒟𝑡 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖 + 𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 + ∑ (𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 𝑖∈𝒟𝑡 = ∑(𝑝𝑡,𝑖 𝑖∈𝒜 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 + ∑ (𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 𝑖∈𝒟𝑡 As seen above, gwGEBVs can be separated into two components. The first component relates to the upweighted estimation of allele effects, and the second component relates to the upweighted estimation of the favorable allele frequency. The upweighted favorable allele frequency error component inherits all the error inflation properties described in the previous section. Additionally, it is straightforward to see that as the set of loci for which the deleterious allele frequency was identified instead of the favorable allele frequency decreases to zero, the upweighted favorable allele frequency error component decreases to zero: 229 lim |𝒟𝑡|→0 ∑ (𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 𝑖∈𝒟𝑡 = 0 The size of the set 𝒟𝑡 is related to the correlation between true and estimated allele effects. For the sake of simplicity, suppose that true allele effects, 𝑢𝑡,𝑖, and estimated allele effects, 𝑢̂𝑡,𝑖, follow a bivariate normal distribution with mean zero and some covariance structure. The combined density where 𝑢𝑡,𝑖 and 𝑢̂𝑡,𝑖 are both positive and both negative determines the probability 𝜋𝑡 with which the favorable allele frequency will be correctly estimated. If we assume for the sake of simplicity that each locus exhibits independence and the same probability of correct estimation, then the size of 𝒟𝑡 can be modeled as a binomial distribution with an expected size of |𝒜|(1 − 𝜋𝑡): |𝒟𝑡|~𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙(|𝒜|, 1 − 𝜋𝑡) 𝐸[|𝒟𝑡|] = |𝒜|(1 − 𝜋𝑡) In other words, the expected size of 𝒟𝑡 approaches zero as the correlation between true and estimated allele effects approaches one. Conversely, the expected size of 𝒟𝑡 approaches the size of 𝒜 as the correlation between true and estimated allele effects approaches negative one. 4.2.4. gwGEBV error multiplication in the multi-locus, multi-trait case Now, let us consider multiple traits where we take a weighted sum of gwGEBVs for 𝑇 traits, as was considered in the multi-trait experiments of this study. Let 𝑤𝑡 represent the weight assigned to the 𝑡th trait. The index constructed using this weighted sum can be expressed as follows: 𝑇 𝑦𝐼𝑛𝑑𝑒𝑥 = ∑ 𝑤𝑡𝑦𝑔𝑤𝐺𝐸𝐵𝑉𝑡 𝑡=1 230 𝑇 = ∑ 𝑤𝑡 (∑(𝑝𝑡,𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 + ∑ (𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 ) 𝑡=1 𝑖∈𝒜 𝑇 𝑖∈𝒟𝑡 𝑇 = ∑ 𝑤𝑡 ∑(𝑝𝑡,𝑖 −𝛼𝑡𝑢𝑡,𝑖 + 𝑝𝑡,𝑖 −𝛼𝑡𝜀𝑡,𝑖)𝑧𝑖 + ∑ 𝑤𝑡 ∑ (𝜉𝑡,𝑖𝑢𝑡,𝑖 + 𝜉𝑡,𝑖𝜀𝑡,𝑖)𝑧𝑖 𝑡=1 𝑖∈𝒜 𝑡=1 𝑖∈𝒟𝑡 Like the single-trait case, we see that the multi-trait, gwGEBV index can be separated into a component related to the upweighted estimation of allele effects and a component related to the upweighted estimation of favorable allele frequencies. Presumably, there may be overlaps between trait-specific sets of markers for which the upweighted favorable allele frequency was incorrectly estimated. The union of these sets, therefore, denotes the set of loci for which at least one upweighted favorable allele frequency estimation error was made, ⋃ 𝒟𝑡 𝑇 𝑡=1 . It is reasonable to suppose that this union of sets increases as more traits are added. If we assume that upweighted favorable allele frequency estimation errors between traits are independent, we can model the number of loci for which at least one error was made according to a binomial distribution: 𝑇 |⋃ 𝒟𝑡 𝑡=1 𝑇 | ~𝐵𝑖𝑛𝑜𝑚𝑖𝑎𝑙 (|𝒜|, 1 − ∏ 𝜋𝑡 ), 𝑡=1 where 𝜋𝑡 is the probability that the upweighted favorable allele frequency is estimated correctly, defined in the single-trait case above. The expected value then becomes: 𝑇 𝐸 [|⋃ 𝒟𝑡 𝑡=1 𝑇 |] = |𝒜| (1 − ∏ 𝜋𝑡 ) 𝑡=1 Furthermore, assuming at least some degree of error is made in estimating the upweighted favorable allele frequency for each trait, 𝜋𝑡 < 1 ∀𝑡 ∈ {1, … , 𝑇}, the expected size of ⋃ 𝒟𝑡 𝑇 𝑡=1 approaches the size of 𝒜 as the number of traits approaches infinity: 231 lim 𝑇→∞ 𝑇 𝐸 [|⋃ 𝒟𝑡 𝑡=1 |] = lim 𝑇→∞ |𝒜| (1 − ∏ 𝜋𝑡 ) 𝑇 𝑡=1 𝑇 ∏ 𝜋𝑡 𝑡=1 ) = |𝒜| (1 − lim 𝑇→∞ = |𝒜|(1 − 0) = |𝒜| Putting all these items together, we see that errors are introduced at more loci as the number of traits increases, until eventually all loci have some degree of upweighted favorable allele frequency error. Selection accuracy will decrease as the number of traits increases. 4.2.5. Summary of gwGEBV error multiplication These mathematical results explain our observations in single- and multi-trait scenarios. In the EST scenario, we observed lower genetic gain with higher 𝛼𝑡 for both GWGS and TWGS strategies. Furthermore, we observed improved genetic gain results in the TWGS strategies in later generations, which corresponded to the temporal reduction in 𝛼𝑡 values. The mathematical results above predict that selection accuracy will decrease with higher 𝛼𝑡 due to greater error magnification, agreeing with our observations. When we compare EST scenario, GWGS and TWGS performances between single- and multi-trait cases, we see that several of the GWGS strategies in the multi-trait case underperform relative to RS for both traits. In the single-trait case, these same selection strategies performed better than or equal to RS. Again, these observations align with our mathematical predictions which indicate that selection accuracy will decrease as the number of traits increases. Finally, in the TRUE scenario we had zero error which allowed for GWGS and TWGS strategies to be differentiated based on the strength of their 232 upweighting factors with respect to the initial population genetic diversity and the duration of selection. 4.3. Recommendations for selection strategies From the simulation and mathematical results above, we recommend allele effect upweighting in only specific circumstances. If marker effects are known with high accuracy, selection on gwGEBVs may be a suitable long-term selection strategy. In practical scenarios, we rarely have highly accurate marker effects, except for maybe a handful of loci, thereby limiting the practical use of gwGEBVs in breeding programs. If marker effects are not known with high accuracy, we recommend using conventional selection strategies like GEBV and OCS or a gwGEBV strategy with a low upweighting factor. In our simulation results, gwGEBV05 and gwGEBV10d delivered similar genetic gains to GEBV and OCS yet offered superior long-term genetic diversity metrics. Depending on the breeder’s goals, a GWGS strategy may be preferable to a TWGS strategy if the breeder desires to maintain greater population mean expected heterozygosity at the end of a specific breeding window. 4.4. Future avenues of research for marker upweighting based selection strategies In our experiments, we observed that GWGS and TWGS selection strategies demonstrated an exceptional ability to maintain genetic diversity, even with modest upweighting factors and in scenarios with estimated marker effects. These results suggest that upweighted selection indices may offer a promising avenue for maintenance of genetic diversity. We suggest that gwGEBVs may prove useful as diversity constraints similar to the diversity constraint imposed by a kinship or genomic relationship matrix in OCS. Using gwGEBVs instead of a kinship or genomic relationship matrix in a constrained optimization could offer speed benefits for large-scale selection problems. In OCS, the time complexity to evaluate the average kinship 233 or genomic relationship for a proposed solution is 𝒪(𝑛2), while the time complexity to evaluate the average gwGEBV for a proposed solution is 𝒪(𝑛). This difference represents a substantial computational cost reduction and merits further exploration. From our mathematical results, we observed that the upweighted favorable allele frequency error introduced in the calculation of gwGEBVs depends on the frequency of the favorable allele, and the magnitude of error introduced increases to infinity as the favorable allele frequency approaches 0 or 1. This exploding error term may be able to be controlled by modifying the gwGEBVs calculation method. Specifically, it may be possible to mitigate errors by upweighting allele effects for loci within a specific range of allele frequency values and by using normal GEBV calculations for allele frequencies outside of this range. We suggest that upweighting within the range 𝑝𝑡,𝑖 ∈ [0.1,0.9] may be appropriate, but additional computer simulations would be required to test this hypothesis. Finally, in our mathematical and empirical results, we observed that weighted sums of gwGEBVs for multiple traits introduce additional error. For multi-trait scenarios, it may better to use marker effect estimates for a single composite index rather than from multiple indices to mitigate the additional upweighted favorable allele frequency error introduced by considering multiple traits. 5. Conclusion Our characterization of the effects of upweighting in GWGS and TWGS were not entirely conclusive but gave clues suggesting that upweighting was detrimental to long-term genetic gain in later generations. Upweighting in GWGS and TWGS also appears to strongly increase long- term genetic diversity as measured by mean expected heterozygosity in later generations. At least 234 in scenarios where QTL locations and effects were known, upweighting appeared to significantly preserve the upper selection limit of a breeding population. Based on simulation results from this study, we find that the proposed GWGS and TWGS strategies need improvement if they are to be applied in practical scenarios. In scenarios where the locations and effects for causal QTL are known, GWGS and TWGS strategies perform very well, in many cases delivering higher genetic gains and genetic diversity when compared to OCS and selection on GEBVs. However, in realistic scenarios where the locations and effects for causal QTL are unknown, GWGS and TWGS strategies struggle to perform as well as OCS and GEBV selection. This is caused by error magnification resulting from incorrect estimation of the favorable allele frequency and, in the case of multiple traits, resulting from the existence of multiple traits. We suggest that error magnification may be mitigated by restricting the application of upweighting to loci with allele frequencies within a specific range. More research is needed to test this hypothesis, however. 235 CHAPTER 5: PREDICTION OF PROGENY MEAN AND VARIANCE FROM PARENTAL INFORMATION 1. Introduction In plant breeding, it is normal cadence to cross two elite parents together, derive progenies from the resulting cross, and select the best progenies to release as cultivars and/or serve as parents for the next generation. Unfortunately, the number of potential biparental crosses one could perform increases quadratically with the number of parental candidates. Even for modest numbers of parental candidates, the number of cross combinations is usually larger than the number of crosses a breeding program can feasibly evaluate. For example, 20 parents can be combined into 190 unique crosses. Evaluation metrics are needed to rank and prioritize crosses since not all crosses can be evaluated. There are two fundamental progeny statistics that are of importance when selecting which crosses to pursue: the expected mean trait value of the progenies and expected variance of trait values in the progenies. The expected progeny mean is often of primary importance and the expected progeny variance of secondary importance when selecting which crosses to perform (Bernardo, 2020a). Additionally, the usefulness criterion (Schnell & Utz, 1975), a statistic derived from the expected progeny mean and variance statistics, is often cited as a statistic useful in evaluating the merit of a proposed cross (Adeyemo & Bernardo, 2019; Lian et al., 2015). The usefulness criterion of a cross is calculated as 𝑈𝐶𝑘 = 𝜇 + 𝑖𝑘ℎ𝜎𝐺, where 𝑈𝐶𝑘 is the usefulness criterion for a cross for a proportion of candidates, 𝑘, selected, 𝜇 is the expected progeny mean, 𝑖𝑘 is the standardized selection differential for a proportion of candidates, 𝑘, selected, ℎ is the square root of the heritability, and 𝜎𝐺 is the genetic standard deviation of the progenies (Schnell & Utz, 1975). 236 Several studies have examined the predictability of progeny mean, progeny variance, and cross usefulness. Progeny mean is relatively easy to predict and can be reliably estimated as the mean performance of the constituting parents (Adeyemo & Bernardo, 2019; Lian et al., 2015; Miller et al., 2023; Neyhart & Smith, 2019; Oget-Ebrad et al., 2024; Wartha & Lorenz, 2024; Wolfe et al., 2021). Progeny variance and cross usefulness are more difficult statistics to estimate, however, and almost all studies report that the correlation between predicted and observed progeny variances or cross usefulnesses are less than the correlations observed for progeny means (Adeyemo & Bernardo, 2019; Lian et al., 2015; Oget-Ebrad et al., 2024; Tiede et al., 2015; Wartha & Lorenz, 2024; Wolfe et al., 2021). This is because variance is a second-order statistic and any errors in estimation are squared. Various metrics have been proposed as potential predictors of progeny variance. These include the mean variance of related, half-sib families to the proposed cross (Lian et al., 2015), phenotypic distance (Souza & Sorrells, 1991; Tiede et al., 2015), molecular marker or kinship (dis)similarity metrics (Beckett et al., 2019; Lian et al., 2015; Souza & Sorrells, 1991; Tiede et al., 2015), and estimates of genetic variance derived by coupling genomic prediction models (Meuwissen et al., 2001) with either simulations of progeny (Abed & Belzile, 2019; Adeyemo & Bernardo, 2019; Beckett et al., 2019; Lian et al., 2015; Miller et al., 2023; Tiede et al., 2015) or deterministic, analytical matrix formulae for progeny variance (Allier, Moreau, et al., 2019; Lehermeier et al., 2017; Neyhart et al., 2019; Neyhart & Smith, 2019; Oget-Ebrad et al., 2024; Osthushenrich et al., 2017, 2018; Wartha & Lorenz, 2024; Wolfe et al., 2021). Not all predictive metrics that have been proposed in the literature have equal predictive capabilities in real breeding populations. In Lian et al. (2015), the authors found that using the mean progeny variance of related, half-sib families to the proposed cross was an effective 237 predictor of progeny variance. Tiede et al. (2015) and Souza & Sorrells (1991) found that the phenotypic distance between two individuals in a proposed cross was a poor or insignificant predictor of the variance of progenies generated by the cross. Metrics measuring molecular marker or kinship (dis)similarity have been mixed in their predictive capabilities. Souza & Sorrells (1991) found that only one out of four parentage similarity metrics were significant for predicting progeny variance of a cross in the yield trait they were examining. Lian et al. (2015) found genetic similarity to be predictive of progeny variance for two out of the three traits they examined. Finally, Tiede et al. (2015) found genetic dissimilarity to be an insignificant predictor of progeny variance for the Fusarium head blight resistance trait they were examining. Metrics using genomic prediction models to estimate progeny variance through either simulations or analytical formulae have been mostly successful in empirical studies and have typically been more successful than other cited predictive methods. Lian et al. (2015), Tiede et al. (2015), Neyhart & Smith (2019), Wolfe et al. (2021), and Wartha & Lorenz (2024) were all successful or mostly successful in predicting progeny variance using genomic prediction modeling techniques for the traits they were examining. Oget-Ebrad et al. (2024) reported mixed results for progeny variance estimates and were only able to predict progeny variance for two out of four examined traits. Adeyemo & Bernardo (2019) were completely unsuccessful at predicting progeny variance for any of the three traits they examined. This outcome, however, may have been due to the relatedness their training population. In Adeyemo & Bernardo (2019), the authors used a diversity panel of mostly unrelated individuals to construct a genomic prediction model, while all other cited studied have used breeding populations of related individuals or populations of half- sib families to construct genomic prediction models. 238 Several factors appear to influence the prediction accuracy of progeny variance estimations using genomic prediction modeling methods. First and foremost is the relatedness of the genomic prediction training population to the progenies derived from a cross. Greater relatedness of the training population to the cross progenies improves progeny variance predictions (Adeyemo & Bernardo, 2019; Miller et al., 2023). Second, progeny variance predictions are sensitive to trait heritability. Progeny variance for traits with high heritability are easier to predict than traits with lower heritability (Neyhart et al., 2019; Wartha & Lorenz, 2024) and it has been shown that the drop in variance prediction accuracy is more severely impacted by trait heritability than the drop in prediction accuracy observed for progeny mean or cross usefulness (Oget-Ebrad et al., 2024). The genetic architecture of a trait can impact progeny variance prediction accuracies (Neyhart et al., 2019; Oget-Ebrad et al., 2024). In particular, the progeny variance prediction accuracy decreases substantially as the number of quantitative trait loci (QTL) controlling a trait increases (Oget-Ebrad et al., 2024). Finally, the number of progenies derived from a cross can impact the predictive performance of progeny variance estimations. The accuracy of progeny variance predictions improves as the number of progenies derived from a cross increase (Oget-Ebrad et al., 2024). In this study, we sought to predict the mean and variance of progeny families from a diverse set of crosses and empirically validate the results of previous studies. Specifically, we phenotyped a panel of diverse maize inbreds for six traits, developed a genomic prediction model using information from the diversity panel, and predicted the expected progeny mean and variance for a set of crosses using members of this panel. We then performed those crosses and derived progenies from them, phenotyped the progenies, and examined whether our mean and variance predictions aligned with our progeny observations. 239 2. Methods 2.1. Parental populations 2.1.1. Parental plant material and testing A subset of 802 inbred individuals from the Wisconsin Maize Diversity Panel 942 (WiDiv-942) (Hirsch et al., 2014; Mazaheri et al., 2019) were grown at the Michigan State University Agronomy Farm (N 42° 42’ 30.96”, W 84° 28’ 5.88”) in the 2018-2022 growing seasons. The subset of individuals used in this study was determined on maturity and adaptation to Michigan growing environments and is referred to the parental population. In the years 2018- 2021, maize varieties were tested in randomized complete block designs with two replicates. In these years, plants were grown in 10-foot long, two row plots with 30-inch row spacing at a density of 34,800 plants per acre. In 2022, maize varieties were tested in a randomized complete block design, with two blocks. During this year, one block was given normal nitrogen rates, while the other block was given reduced nitrogen rates. Additionally, plants were grown in 30- foot long, two row plots with 30-inch row spacing at a density of 34,800 plants per acre. Many, but not all varieties were tested in each year. Table 5.1 below summarizes the number of WiDiv- 942 members which were tested each year. Year(s) 2018 2019 2020 2021 2022 2018-2022 Number of unique WiDiv-942 members tested 612 760 766 766 246 802 Table 5.1: A summary of the number of unique WiDiv-942 panel members tested 2018-2022. 240 2.1.2. Phenotypic data collection Anthesis day (AD), silking day (SD), ear height (EH), flag height (FH), ear leaf number (ELN), and total leaf number (TLN) were recorded for each plot. AD and SD were measured on a per-plot basis, while EH, FH, ELN, and TLN were measured on two marked, median-sized plants. AD was measured as the number of days after planting on which 50% of plants in the plot shed pollen for at least 50% of their main tassel branch. SD was measured as the number of days after planting on which 50% of plants in the plot exhibited silks protruding from their uppermost ear. EH was measured as the distance from the plant base to the stalk node supporting the uppermost ear. FH was measured as the distance from the plant base to the leaf collar of the flag leaf, the uppermost leaf exposed beneath the tassel. For ELN and TLN, leaf numbers were tracked throughout the growing season by counting and labeling the V3, V6, V10, and V13 leaves. ELN was measured as the leaf number at the uppermost ear. TLN was measured as the leaf number at the flag leaf. 2.1.3. BLUE Modeling A two-part statistical model was used to estimate best linear unbiased estimators (BLUEs) for the 802 tested WiDiv-942 members in all six examined traits. In the first part, we fit custom spatial models for all trait-year combinations using the SpATS package (Rodríguez- Álvarez et al., 2018) in R (R Core Team, 2024). A spatial model was preferred because the sizes of our fields were large enough such that there were pockets of field variability that were large enough to be discerned with the human eye. The generic spatial model was of the form: 𝑦𝑖𝑗𝑘𝑙𝑚 = 𝜇 + 𝐺𝑖 + 𝑏𝑗 + 𝑆(𝑘, 𝑙) + 𝜀𝑖𝑗𝑘𝑙𝑚 𝐛~𝑁(𝟎, 𝜎𝑏 2𝐈) 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐈), 241 where 𝑦𝑖𝑗𝑘𝑙𝑚 is the trait observation for the 𝑖th genotype in the 𝑗th block at the 𝑘th row and 𝑙th column for the 𝑚th plot or plant, 𝜇 is the overall mean, 𝐺𝑖 is the fixed effect of the 𝑖th genotype, 𝑏𝑗 is the random effect of 𝑗th block, 𝑆(𝑘, 𝑙) is the P-spline effect at row 𝑘 and column 𝑙, and 𝜀𝑖𝑗𝑘𝑙𝑚 is random residual error. For 2022 data, the block effect was treated as fixed instead of random since varying nitrogen rates were applied in that year. Since the SpATS package did not have tools to assess the significance of model effect terms, we gauged which model terms to include by fitting an ordinary linear mixed model using the lme4 package (Bates et al., 2015) in R. For each trait-year combination, we fit a generic linear mixed model using the residual maximum likelihood (REML) method. The generic linear mixed model formula was: 𝑦𝑖𝑗𝑘𝑙𝑚 = 𝜇 + 𝐺𝑖 + 𝑏𝑗 + 𝑟𝑘 + 𝑐𝑙 + 𝜀𝑖𝑗𝑘𝑙𝑚 𝐛~𝑁(𝟎, 𝜎𝑏 2𝐈) 𝐫~𝑁(𝟎, 𝜎𝑟 2𝐈) 𝐜~𝑁(𝟎, 𝜎𝑐 2𝐈) 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐈), where 𝑦𝑖𝑗𝑘𝑙𝑚 is the trait observation for the 𝑖th genotype in the 𝑗th block at the 𝑘th row and 𝑙th column for the 𝑚th plot or plant, 𝜇 is the overall mean, 𝐺𝑖 is the fixed effect of the 𝑖th genotype, 𝑏𝑗 is the random effect of 𝑗th block, 𝑟𝑘 is the random effect of the 𝑘th row in the field, 𝑐𝑙 is the random effect of the 𝑙th column in the field, and 𝜀𝑖𝑗𝑘𝑙𝑚 is random error. For 2022 models, block effect was treated as fixed instead of random to account for different nitrogen application rates. We tested the significance of each random effect model term using an exact restricted likelihood ratio (RLR) test (Crainiceanu & Ruppert, 2004) with 10,000 simulated values using the RLRsim (Scheipl et al., 2008) package in R (R Core Team, 2024). An effect was designated 242 as significant if the p-value was less than 0.05. If the block effect was significant, it was included in the spatial model. If either the row or column effect was significant, the P-spline term was included in the spatial model. After determining the significance of block, row, and column effects, we fit an appropriate model for each trait-year combination and calculated genotype BLUEs. Final models are summarized in Table 5.2. 243 Year Trait 2018 2019 2020 2021 2022 AD SD EH FH ELN TLN AD SD EH FH ELN TLN AD SD EH FH ELN TLN AD SD EH FH ELN TLN AD SD EH FH ELN TLN Model Terms Genotype Block Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed – – – – – – – – Spatial P-spline P-spline P-spline Random P-spline P-spline P-spline Random P-spline P-spline Random P-spline Random P-spline P-spline P-spline Random P-spline Random P-spline Random P-spline Random P-spline P-spline P-spline P-spline P-spline Random P-spline Random P-spline Random P-spline Random P-spline P-spline P-spline P-spline P-spline – – Fixed Fixed Fixed Fixed Fixed Fixed – – – – Table 5.2: Summary of final models fit in the first step of our two-step analysis. In the Genotype, Block, and Spatial columns, “Fixed” indicates that the model term was fit as a fixed effect, “Random” indicates that the model term was fit as a random effect, “–” indicates that the model term was not used, and “P-spline” indicates that a P-spline was used to account for spatial variation. For the second part of our two-step statistical analysis, we took our trait BLUEs calculated for each year and fit the following weighted linear mixed model: 𝑦𝑖𝑗 = 𝜇 + 𝐺𝑖 + 𝑡𝑗 + 𝜀𝑖𝑗 𝐭~𝑁(𝟎, 𝜎𝑦 2𝐈) 244 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐃) where 𝑦𝑖𝑗 is the trait BLUE for the 𝑖th genotype in the 𝑗th year, 𝜇 is the overall mean, 𝐺𝑖 is the fixed effect of the 𝑖th genotype, 𝑡𝑗 is the random effect of the 𝑗th year, 𝜀𝑖𝑗 is random error, and 𝐷 is a diagonal matrix of which diagonal elements are the inverse of the number of observations used to estimate the trait BLUEs calculated in the first modeling step. A final set of multi-year trait BLUEs were extracted from the model above for all traits. This set of BLUEs is denoted as the parental BLUE set. Parental BLUEs were used to fit genomic predictions models and inform predictions of progeny mean and variance (discussed in sections below). 2.1.4. Heritability calculations 2.1.4.1. Single-year trait heritability calculations We evaluated the heritability of AD, SD, EH, FH, ELN, and TLN on an annual basis and collectively across the five tested years. To calculate the heritability of traits within a single year, we fit a generic linear mixed model defined below using the lme4 R package (Bates et al., 2015) and used an exact RLR test (Crainiceanu & Ruppert, 2004) with 10,000 simulated values to determine the significance of various model terms using the RLRsim (Scheipl et al., 2008) package in R. Model terms were determined as significant if their exact RLR test p-value was less than 0.05. Final models (summarized in Table 5.3) used in calculating heritability only contained significant terms and were fit using the REML method. The generic linear mixed model we fit was: 𝑦𝑖𝑗𝑘𝑙𝑚 = 𝜇 + 𝑔𝑖 + 𝑏𝑗 + 𝑟𝑘 + 𝑐𝑙 + 𝜀𝑖𝑗𝑘𝑙𝑚 𝐠~𝑁(𝟎, 𝜎𝑔 2𝐈) 𝐛~𝑁(𝟎, 𝜎𝑏 2𝐈) 245 𝐫~𝑁(𝟎, 𝜎𝑟 2𝐈) 𝐜~𝑁(𝟎, 𝜎𝑐 2𝐈) 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐈), where 𝑦𝑖𝑗𝑘𝑙𝑚 is the trait observation for the 𝑖th genotype in the 𝑗th block at row 𝑘 and column 𝑙 for the 𝑚th measured plant or plot, 𝜇 is the overall mean, 𝑔𝑖 is the random effect of the 𝑖th genotype, 𝑏𝑗 is the random effect of 𝑗th block, 𝑟𝑘 is the random effect of the 𝑘th row in the field, 𝑐𝑙 is the random effect of the 𝑙th column in the field, and 𝜀𝑖𝑗𝑘𝑙𝑚 is random error. Like with the BLUE estimation protocols, block effect was treated as a fixed effect for 2022 data to account for different nitrogen application rates. 246 Year Trait Model Terms – – – – – – – – Row Column Genotype Block AD Random Random Random SD Random Random Random EH Random Random Random FH Random Random Random Random ELN Random Random TLN Random Random Random AD Random Random Random Random SD Random Random Random Random EH Random Random Random Random FH Random Random Random Random ELN Random Random Random TLN Random Random Random AD Random Random Random Random SD Random Random Random Random EH Random Random Random Random FH Random Random Random Random ELN Random Random Random TLN Random Random Random Random AD Random Random Random Random Random SD Random Random Random Random EH FH Random Random Random Random ELN Random Random Random Random TLN Random Random Random Random Random Fixed Random Random AD Random Fixed Random Random SD Random Fixed Random Random EH Fixed Random Random FH Random – Fixed ELN Random – Fixed TLN Random – – – – – – 2018 2019 2020 2021 2022 Table 5.3: A summary of the final models fit to calculate single-year trait heritabilities. In the Genotype, Block, Row, and Column model term columns, “Fixed” indicates that the model term was fit as a fixed effect, “Random” indicates that the model term was fit as a random effect, and “–” indicates that the model term was not used because it was insignificant. Using the single-year linear mixed models described above, single-year broad-sense, trait heritabilities were calculated as: 𝐻2 = 2 𝜎𝑔 𝜎𝑔 2 + 2 𝜎𝜀 𝑛𝑜𝑏𝑠 , 247 where 𝐻2 is the broad sense heritability, 𝜎𝑔 2 is the estimated genotypic variance, 𝜎𝜀 2 is the estimated error variance, and 𝑛𝑜𝑏𝑠 is the number of observations for the trait. For AD and SD, 𝑛𝑜𝑏𝑠 = 2 since two plots were measured each year. For EH, FH, ELN, and TLN, 𝑛𝑜𝑏𝑠 = 4 since two plants were measured in two plots each year. 2.1.4.2. Multi-year trait heritability calculations For multi-year trait heritabilities, we fit a linear mixed model considering all data collected over the five years. The model was defined as: 𝑦𝑖𝑗𝑘𝑙𝑚 = 𝜇 + 𝑔𝑖 + 𝑡𝑗 + (𝑔𝑡)𝑖𝑗 + 𝑏𝑘(𝑗) + 𝑟𝑙(𝑗) + 𝑐𝑚(𝑗) + 𝜀𝑖𝑗𝑘𝑙𝑚 𝐠~𝑁(𝟎, 𝜎𝑔 2𝐈) 𝐭~𝑁(𝟎, 𝜎𝑡 2𝐈) 𝐠𝐭~𝑁(𝟎, 𝜎𝑔𝑡 2 𝐈) 𝐛~𝑁(𝟎, 𝜎𝑏 2𝐈) 𝐫~𝑁(𝟎, 𝜎𝑟 2𝐈) 𝐜~𝑁(𝟎, 𝜎𝑐 2𝐈) 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐈), where 𝑦𝑖𝑗𝑘𝑙𝑚 is the trait observation for the 𝑖th genotype in the 𝑗th year at the 𝑘th block nested within the 𝑗th year at the 𝑙th row nested within the 𝑗th year and at the 𝑚th column nested within the 𝑗th year, 𝜇 is the overall mean, 𝑔𝑖 is the random effect of the 𝑖th genotype, 𝑡𝑗 is the random effect of the 𝑗th year, 𝑏𝑘(𝑗) is the random effect of 𝑘th block nested within the 𝑗th year, 𝑟𝑙(𝑗) is the random effect of the 𝑙th row nested within the 𝑗th year, 𝑐𝑚(𝑗) is the random effect of the 𝑚th column nested within the 𝑗th year, and 𝜀𝑖𝑗𝑘𝑙𝑚 is random error. 248 Multi-year broad-sense, trait heritabilities were calculated using variance components estimated from the multi-year, trait models described above. Specifically, heritabilities were calculated as: 𝐻2 = 2 𝜎𝑔 2 + 𝜎𝑔 2 𝜎𝑔𝑡 𝑛𝑦𝑒𝑎𝑟 + 2 𝜎𝜀 𝑛𝑦𝑒𝑎𝑟 × 𝑛𝑜𝑏𝑠 , where 𝐻2 is the broad sense heritability, 𝜎𝑔 2 is the estimated genotypic variance, 𝜎𝑔𝑡 2 is the genotype-by-year interaction variance, 𝜎𝜀 2 is the estimated error variance, 𝑛𝑦𝑒𝑎𝑟 is the number of years tested, and 𝑛𝑜𝑏𝑠 is the number of observations for the trait. For all traits, 𝑛𝑦𝑒𝑎𝑟 = 5. For AD and SD, 𝑛𝑜𝑏𝑠 = 2, and for EH, FH, ELN, and TLN, 𝑛𝑜𝑏𝑠 = 4. 2.1.5. Genomic predictions We used the WiDiv-942 marker datasets published by Hirsch et al. (2014) and Mazaheri et al. (2019) as a source of genotypic markers for our genomic predictions. We selected genomic markers for the 802 WiDiv-942 panel members we tested and removed markers with minor allele frequencies less than 0.03 using BCFtools (Danecek et al., 2021; H. Li, 2011). Next, we linearly interpolated the genetic map positions of these remaining markers using the US NAM consensus genetic map (McMullen et al., 2009) and randomly selected 10,000 markers >0.05 cM apart to serve as markers for genomic prediction. Using the selected genomic data and calculated trait BLUEs, we fit an RR-BLUP (Meuwissen et al., 2001) genomic prediction model using the rrBLUP package (Endelman, 2011) in R. All data was used to fit the model and marker effect estimates from this model were used in subsequent parental BLUP calculations, progeny mean estimates, and progeny variance estimates. Additionally, a 10-fold cross validation (CV) was conducted on the data to estimate the accuracy of the RR-BLUP model. 249 2.2. Progeny populations 2.2.1. Progeny family creation We acquired or created thirteen biparental, doubled haploid (DH) progeny families using 24 unique parents found in the 802 tested WiDiv-942 panel members. These thirteen families are summarized in Table 5.4. Most DH families were derived from the F1 of a biparental cross, but for four of these families, DH lines were derived from the F2 (Table 5.4). All DH families had greater than 15 constituting members, with a maximum of 50 constituting members (Table 5.4). Several of the DH families had low family member counts due to poor DH induction, inbred sterility, or poor inbred survivability. Parent 1 Parent 2 DK3IIH6 PHK76 LH205 PHT22 ZS1791 LH188 NC230 787 52220 PHK56 LH145 N6 PHT11 Oh43 B73 B73 B73 C102 CI 91B DKHBA1 H84 LH82 MoG NC236 PHJ65 PHN11 Family Type F2 F1 F1 F1 F1 F1 F1 F1 F2 F2 F1 F1 F2 Number of Family Members 50 50 50 44 20 15 19 17 50 48 27 16 49 Table 5.4: A summary of the biparental, doubled haploid (DH) families created from members of the WiDiv-942 panel. Most DH families were derived from F1 hybrid individuals. Four DH families were derived from F2 individuals. The targeted number of members per family was 50, however many of the families had fewer members, going down to 15 in one case. 2.2.2. Progeny family testing Progeny families were tested in the 2022-2024 field seasons at the Michigan State University Agronomy Farm in the same fields as their parents were tested. Progeny families were tested using different statistical designs across years, and progeny families were not tested in all 250 years (Table 5.5). In 2022, we used a randomized complete block design with two replicates and repeated B73 spatial checks. In 2023 and 2024, we used Latin square designs with two replicates and repeated B73 as a check. In 2023, we broke our field up into two replicate blocks, each with five subblocks. Each subblock contained a randomized, 10×10 Latin square balanced by family (9 families + B73 check) in the row and column directions. In 2024, we broke our field into two replicate blocks, each with four subblocks. Each subblock contained a randomized, 12×12 Latin square balanced by family (11 families + B73 check) in the row and column directions. Of note, the number of families tested in 2022 and 2023 do not align with those listed in Table 5.5. This is because, we tested two additional families which had to be excluded from subsequent analyses due to lack of genotypic information. In all years, plants were grown in 10-foot long, two row plots with 30-inch row spacing at a density of 34,800 plants per acre. Family Years Tested DK3IIH6 × PHK76 2022, 2023 2023, 2024 B73 × LH205 2023, 2024 B73 × PHT22 2023, 2024 B73 × ZS1791 2024 C102 × LH188 2024 CI 91B × NC230 2024 DKHBA1 × 787 2024 H84 × 52220 2022, 2023 LH82 × PHK56 2022, 2023 MoG × LH145 2024 NC236 × N6 2024 PHJ65 × PHT11 2022, 2023 PHN11 × Oh43 Table 5.5: A summary of progeny families and the years in which progeny families were tested. Progeny families were tested for 1-2 years. 2.2.3. Phenotypic data collection The same set of traits measured on the 802 tested WiDiv-942 panel members in the parental population were measured in the progeny families. Phenotypic evaluation of progeny families was done in a manner identical to that of the parental population. Additionally, we 251 collected germination delay data for only the 2023 field season. In 2023, we experienced an early season drought which delayed germination for many plots. The germination delay severity varied based on plot. For AD and SD, we visually rated individual plots according to their germination delay percentage. Delay percentage ratings could take one of five categorical percentage ratings: 0%, 25%, 50%, 75%, or 100% delayed. For EH, FH, ELN, and TLN, we scored individually marked plants as “not delayed” or “delayed” depending on whether they germinated shortly after planting or approximately one month after planting when rains arrived, respectively. 2.2.4. BLUE Modeling We used a two-step modeling approach to estimate progeny family member phenotypic BLUEs, like with the parental population. We computed 2022 and 2024 single-year, progeny family member phenotypic BLUEs in a manner nearly identical to the protocols described for the parental population. The only difference in the analyses was that in 2024, the subblock effect was substituted for the block effect in the base model since we used a Latin square design in that year. Single-year analysis for 2023 data required adjustments due to differences in experimental design and additional environmental effects. The models we used are summarized in Table 5.6. In 2023, we fit spatial models accounting for the delay percentage in the case of AD and SD, and plant delay in the case of EH, FH, ELN, and TLN. In most cases, we used the SpATS package (Rodríguez-Álvarez et al., 2018) to fit P-spline based spatial models. For some traits, SpATS exhibited difficulties fitting a P-spline, creating unrealistic phenotypic BLUEs. We suspect this might have been caused by weed pressure along the field borders. In these scenarios, we replaced the P-spline effect with simple row and column effects. Like for the parental datasets, we used an exact RLR test (Crainiceanu & Ruppert, 2004) to determine the significance 252 of random effect model terms and estimate the significance of the P-spline. In sum, our generic spatial model was of the form: 𝑦𝑖𝑗𝑘𝑙𝑚𝑛 = 𝜇 + 𝐷𝑖 + 𝐺𝑗 + 𝑏𝑘 + 𝑆(𝑙, 𝑚) + 𝜀𝑖𝑗𝑘𝑙𝑚𝑛 𝐛~𝑁(𝟎, 𝜎𝑏 2𝐈) 𝛆~𝑁(𝟎, 𝜎𝜀 2𝐈), where 𝑦𝑖𝑗𝑘𝑙𝑚 is the trait observation for the 𝑖th genotype in the 𝑗th block at the 𝑘th row and 𝑙th column for the 𝑚th plot or plant, 𝜇 is the overall mean, 𝐷𝑖 is the fixed effect for the 𝑖th delay percentage or plant delay level, 𝐺𝑗 is the fixed effect of the 𝑗th genotype, 𝑏𝑘 is the random effect of 𝑘th subblock, 𝑆(𝑙, 𝑚) is either the P-spline effect for the 𝑙th row and 𝑚th column or random row and column effects (𝑟𝑙 + 𝑐𝑚) for the 𝑙th row and 𝑚th column, respectively, and 𝜀𝑖𝑗𝑘𝑙𝑚 is random residual error. 253 Year Trait Genotype 2022 2023 2024 AD SD EH FH ELN TLN AD SD EH FH ELN TLN AD SD EH FH ELN TLN Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Delay Percent N/A N/A N/A N/A N/A N/A Fixed Fixed N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Model Terms Spatial – – – – – – Block Subblock N/A N/A N/A N/A N/A N/A P-spline P-spline P-spline P-spline – P-spline – Plant Delay N/A N/A N/A N/A N/A N/A N/A N/A Random N/A N/A Random Row × Column Fixed N/A Random Fixed N/A Random Fixed N/A Random Fixed N/A Random Row × Column N/A N/A Random N/A N/A N/A N/A Random N/A N/A Random N/A N/A Random N/A N/A Random P-spline P-spline P-spline P-spline P-spline P-spline P-spline P-spline P-spline – Table 5.6: A summary of the final models fit to calculate single-year trait BLUEs for the progeny population. In the Genotype, Delay Percent, Delay Plant, Block, Subblock, and Spatial model term columns, “Fixed” indicates that the model term was fit as a fixed effect, “Random” indicates that the model term was fit as a random effect, “P-spline” indicates that a P-spline was fit to account for spatial variation, “Row × Column” indicates that row and column effects were fit to account for spatial variation, “–” indicates that the model term was not used because it was insignificant, and “N/A” indicates that the model term was not applicable to the trait-year combination. For the second part of our two-step statistical analysis, we took single-year trait BLUEs and fit an appropriate weighted linear mixed model identical in form to the one described for the parental population. 2.2.5. Heritability calculations 2.2.5.1. Single-year trait heritability calculations We calculated single-year trait heritabilities in a manner nearly identical to that described for the parental population. The only differences were that for 2023 and 2024 data, the subblock effect was substituted for the block effect, and for 2023, an additional delay percentage or plant 254 delay fixed effect was added, like that described in the BLUE estimation protocols above. A summary of the models we fit to calculate heritability can be found in Table 5.7. Model Terms Year Trait Genotype 2022 2023 2024 Random AD Random SD Random EH FH Random ELN Random TLN Random Random AD Random SD Random EH FH Random ELN Random TLN Random Random AD Random SD Random EH FH Random ELN Random TLN Random Delay Percent N/A N/A N/A N/A N/A N/A Fixed Fixed N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A – – – – – – – – Random Random N/A N/A N/A N/A N/A N/A Block Subblock Row Column Random Random Random Random Random Random Random Random Plant Delay N/A N/A N/A N/A N/A N/A N/A N/A Random N/A N/A Random Random Random Fixed N/A Random Random Random Fixed N/A Random Random Random Fixed N/A Random Random Random Fixed N/A Random N/A N/A Random Random Random N/A N/A Random Random N/A N/A Random Random Random N/A N/A Random Random Random N/A N/A Random Random Random N/A N/A Random Random Random – – – – – Table 5.7: A summary of the final models fit to calculate single-year trait heritabilities for the progeny population. In the Genotype, Delay Percent, Delay Plant, Block, Subblock, Row, and Column model term columns, “Fixed” indicates that the model term was fit as a fixed effect, “Random” indicates that the model term was fit as a random effect, “–” indicates that the model term was not used because it was insignificant, and “N/A” indicates that the model term was not applicable to the trait-year combination. 2.2.5.2. Multi-year trait heritability calculations We calculated multi-year trait heritabilities in an almost identical manner to that described for the parental population. The only difference was that we added a fixed effect accounting for the delay percentage or plant delay into the model. Plots and plants in years 2022 and 2024 were recorded as having no delay. Multi-year broad-sense, trait heritabilities were calculated as: 255 𝐻2 = 2 𝜎𝑔 2 + 𝜎𝑔 2 𝜎𝑔𝑡 𝑛𝑦𝑒𝑎𝑟 + 2 𝜎𝜀 𝑛𝑦𝑒𝑎𝑟/𝑔𝑒𝑛𝑜 × 𝑛𝑜𝑏𝑠/𝑔𝑒𝑛𝑜 , where 𝐻2 is the broad sense heritability, 𝜎𝑔 2 is the estimated genotypic variance, 𝜎𝑔𝑡 2 is the genotype-by-year interaction variance, 𝜎𝜀 2 is the estimated error variance, 𝑛𝑦𝑒𝑎𝑟 is the number of years tested, 𝑛𝑦𝑒𝑎𝑟/𝑔𝑒𝑛 is the number of years for which each genotype was tested, and 𝑛𝑜𝑏𝑠/𝑔𝑒𝑛𝑜 is the number of observations per genotype in a given year for a given trait. For all traits, 𝑛𝑦𝑒𝑎𝑟 = 3 and 𝑛𝑦𝑒𝑎𝑟/𝑔𝑒𝑛𝑜 = 2 since not all progeny family members were tested in all years. For AD and SD, 𝑛𝑜𝑏𝑠/𝑔𝑒𝑛𝑜 = 2, and for EH, FH, ELN, and TLN, 𝑛𝑜𝑏𝑠/𝑔𝑒𝑛𝑜 = 4. 2.3. Parent-progeny analysis 2.3.1. Progeny mean predictions After calculating trait BLUE values for all tested progenies, we calculated mean progeny BLUE values within each family for all traits. Progeny mean trait BLUE values served as the value which we sought to predict. Additionally, we calculated mean parental BLUE and BLUP values within each family for all traits. Parental mean trait BLUEs and BLUPs served as predictors for progeny mean trait BLUEs. For each trait and predictor combination, we fit a weighted linear model predicting progeny mean BLUE values for the appropriate trait. Weights were assigned according to the inverse of the number of family members. We used a simple t-test to determine the significance of the slope of the regression model. 2.3.2. Progeny variance predictions In addition to calculating mean progeny BLUE values for families, we calculated the variance of progeny BLUE values within each family for all traits. We sought to predict the variance of progeny trait BLUE values using five different predictors. Our five predictors were the magnitude of the difference between parental BLUEs, the magnitude of the difference 256 between parental BLUPs, the predicted variance of the progenies using our RR-BLUP genomic prediction models, the VanRaden genomic relationship between the two parents, and the identity- by-state (IBS) genomic relationship between the two parents. For our first two predictors, we calculated the magnitude of the difference between parental BLUEs and BLUPs as the absolute value of the difference between the BLUE and BLUP values for the two parents, respectively. For our progeny variance predictors, we calculated the expected progeny variance using the deterministic matrix calculations proposed by Allier, Moreau, et al. (2019) and Osthushenrich et al. (2017). We used the marker effect estimates from the RR-BLUP models we fit for the parental population and the linearly interpolated genetic map positions for markers as inputs to the variance calculations. For our final two predictors, we calculated VanRaden and IBS genomic relationships using the methods described by VanRaden (2008) and Allier, Lehermeier, et al. (2019), respectively. Like with progeny mean predictions, we fit a weighted linear model predicting the variance in progeny BLUE values for each trait and predictor combination. Weights were assigned according to the squared inverse of the number of family members. The squared inverse was used because variance is a second order statistic. We used a simple t-test to determine the significance of the slope of the regression model. In our variance prediction analysis for EH and FH, we dropped observations for the H84 × 52220 family. This was done because the 52220 parent harbored a major dwarfing allele which significantly affected the variance of EH and FH in the progenies. On examining the residuals for our EH and FH models, this family exhibited high statistical leverage, impacting the quality of the regression models. 257 3. Results 3.1. Parental population statistics 3.1.1. Parental trait BLUEs Parental BLUEs for all traits were roughly normally distributed in the parental population and significantly positively correlated with each other (Fig. 5.1). AD-SD and ELN-TLN were the two most highly correlated trait pairs, having correlations of 0.970 and 0.934, respectively (Fig. 5.1). FH-ELN and SD-FH were the two least correlated trait pairs, having correlations of 0.476 and 0.524, respectively (Fig. 5.1). Most other trait pairs had correlations falling in the range of 0.6-0.8. 258 Figure 5.1: A correlogram of AD, SD, EH, FH, ELN, and TLN trait BLUEs in the parental population. All traits followed a roughly normal distribution in the parental population and were significantly and positively correlated with each other, though to varying degrees. 3.1.2. Parental trait heritabilities Single-year trait heritabilities were high for all examined traits. In almost all years, heritability exceeded 0.9 for all traits (Table 5.8). 2021 was the only year for which at least some traits exhibited heritabilities less than 0.9. In 2021, AD and SD heritabilities were both 0.829, 259 which was still high (Table 5.8). Trait heritabilities across all years were also extremely high. All multi-year trait heritabilities exceeded 0.9 (Table 5.8). Year Trait Heritability SD EH 2018 2019 2020 2021 2022 AD FH ELN TLN 0.980 0.977 0.952 0.957 0.969 0.974 0.981 0.973 0.951 0.944 0.969 0.973 0.981 0.975 0.952 0.944 0.973 0.978 0.829 0.829 0.932 0.941 0.950 0.957 0.935 0.918 0.963 0.971 0.978 0.982 2018-2022 0.978 0.975 0.961 0.955 0.981 0.984 Table 5.8: A summary of trait heritabilities for the 802 WiDiv-942 maize varieties tested in this study. Values for individual years represent the heritability calculated within a single year, while values for multiple years represent heritabilities calculated across multiple years and consider genotype-by-environment interactions. 3.1.3. Parental genomic prediction model performance RR-BLUP model performance varied by trait. AD and SD were the two traits easiest to predict and were predicted with a similar accuracy (Fig. 5.2; Table 5.9). The mean Pearson correlation coefficients for AD and SD predictions in the testing set were 0.843 and 0.835, respectively. ELN and TLN were the next easiest traits to predict, with mean Pearson correlation coefficients for testing set prediction at 0.773 and 0.774, respectively (Fig. 5.2; Table 5.9). EH and FH were the most difficult traits to predict. EH had a mean Pearson correlation coefficient of 0.643 for the testing set in the cross-validation, while FH had a mean of 0.590 (Fig. 5.2; Table 5.9). 260 Figure 5.2: 10-fold cross validation results for RR-BLUP model performance on AD, SD, EH, FH, ELN, and TLN. The left panel depicts model performance as measured by the Pearson correlation coefficient, while the right panel depicts model performance as measured by the coefficient of determination. Error bars represent the standard deviation of the estimate. Trait 𝒓 𝑹𝟐 Mean St. Dev. Mean St. Dev 0.057 0.843 AD 0.057 0.835 SD 0.119 0.643 EH 0.127 0.590 FH 0.055 ELN 0.773 0.086 TLN 0.774 0.034 0.034 0.097 0.113 0.036 0.056 Table 5.9: 10-fold cross valid results for RR-BLUP model performance on AD, SD, EH, EH, FH, ELN, and TLN. Listed are the mean fold Pearson correlation coefficients and mean fold coefficient of determination for all traits. Additionally, the standard deviation of metric for the 10 folds is provided. 0.712 0.699 0.422 0.360 0.599 0.602 261 3.2. Progeny Population statistics 3.2.1. Progeny trait BLUEs Unlike the parental population, progeny trait BLUEs were slightly skewed when considering all progeny families (Fig. 5.3). At the individual family level, there was a wide range of trait distributions (Fig. 5.4). Many families exhibited roughly normally distributed trait BLUE values, as expected (Fig. 5.4). Other families exhibited skewed or bimodal distributions (Fig. 5.4). All trait BLUEs were significantly and positively correlated with each other, though to a lesser degree when compared to parental traits (Fig. 5.1; Fig. 5.3). Like in the parental population, the two most correlated trait pairs were AD-SD and ELN-TLN. These two trait pairs had correlations of 0.936 and 0.913, respectively (Fig. 5.3). FH-ELN and SD-FH were also the two least correlated trait pairs, like what was observed in the parental data, and had correlations of 0.299 and 0.338, respectively (Fig. 5.3). Most other trait pairs had correlations falling in the range of 0.4-0.8. 262 Figure 5.3: A correlogram of AD, SD, EH, FH, ELN, and TLN trait BLUEs in the progeny population. Several of the traits had slightly skewed distributions, collectively across all families in the progeny population. Trait BLUEs were significantly and positively correlated with each other, though to varying degrees. 263 Figure 5.4: Distributions of AD, SD, EH, FH, ELN, and TLN separated by family. Many distributions were unimodal and normally distributed, while other distributions were skewed or bimodally distributed. 3.2.2. Progeny trait heritabilities We observed high single- and multi-year heritabilities for EH, FH, ELN, and TLN. Across all years, heritabilities for these four traits exceeded 0.9 (Table 5.10). AD and SD exhibited lower heritabilities, however. In 2022, AD and SD heritabilities were in the 0.80-0.84 264 range (Table 5.10), while in 2023, heritabilities were lower, in the 0.52-0.55 range (Table 5.10). The poor AD and SD heritability in 2023 was caused by the early season drought, which caused seedling emergence nonuniformity. Year Trait Heritability ELN TLN EH SD AD 0.833 0.807 0.920 0.953 0.946 0.949 2022 0.546 0.523 0.931 0.949 0.954 0.960 2023 2024 0.955 0.959 0.953 0.968 0.965 0.967 2022-2024 0.815 0.846 0.945 0.960 0.961 0.969 FH Table 5.10: A summary of trait heritabilities for the 13 progeny families tested in this study. Values for individual years represent the heritability calculated within a single year, while values for multiple years represent heritabilities calculated across multiple years and consider genotype- by-environment interactions. 3.3. Parent-progeny predictions 3.3.1. Progeny mean predictions Prediction of progeny means using only parental data was successful for all traits. Mean parental BLUEs and RR-BLUP predictions were both positively correlated with and highly significant in their ability to predict observed progeny mean trait BLUEs (Fig. 5.5; Table 5.11). The Pearson correlations coefficient for most predictions exceeded 0.9 (Table 5.11). EH was the most difficult trait to predict from parental BLUEs and BLUPs. For this trait, the Pearson correlation coefficient was 0.713 and 0.814 for BLUEs and BLUPs, respectively (Table 5.11). For most traits, parental BLUEs were a slightly more accurate predictor of progeny mean BLUEs. Only with EH were parental BLUPs a more accurate predictor than parental BLUEs (Table 5.11). 265 Figure 5.5: A correlogram of progeny mean predictor values (x-axis) versus observed progeny means (y-axis) for the six examined traits. All regressions between progeny mean predictor and progeny mean were statistically significant. Corresponding, significant regressions are depicted by the red regression lines. 266 Trait Mean Parental BLUE 𝒓 p-value Mean Parental RR-BLUP 𝒓 p-value 0.960 2.14 × 10−7 0.947 9.35 × 10−7 AD 0.952 5.17 × 10−7 0.951 6.09 × 10−7 SD 0.713 6.17 × 10−3 0.814 7.02 × 10−4 EH 0.937 2.25 × 10−6 0.927 5.06 × 10−6 FH ELN 0.910 1.61 × 10−5 0.900 2.76 × 10−5 TLN 0.940 1.74 × 10−6 0.936 2.52 × 10−6 Table 5.11: A summary of correlation coefficients and p-values for the regressions performed between progeny mean predictors and the observed progeny mean. Highlighted in green are the progeny mean predictor-trait combinations that were significant at a level of 0.05. 3.3.2. Progeny variance predictions Predicting progeny variance proved to be extremely challenging. Predictions of progeny variance from estimated marker effects from a parental RR-BLUP model did not correlate well with observed variances (Fig. 5.6). For this prediction metric, only ELN and TLN variance predictions were statistically significant (Table 5.12). Using the difference between parental BLUEs as a predictor of progeny variance was very successful, however. We observed significant correlations between this predictive metric and observed progeny traits variances for all traits except SD (Table 5.12). For traits where there was a significant relationship, the Pearson correlation coefficient was greater than 0.8 (Table 5.12). Prediction of progeny variance using the difference in parental BLUPs calculated from an RR-BLUP model were largely not significant (Fig. 5.6; Table 5.12). Only ELN variance was significantly correlated with this metric (Table 5.12). The predictive performance of parental VanRaden and IBS genomic relationship statistics were very similar to each other. Both statistics were significantly negatively correlated with FH (Table 5.12). Additionally, parental IBS genomic relationships were significantly negatively correlated with the observed progeny SD variance (Table 5.12). 267 Figure 5.6: Correlogram of progeny variance predictor values (x-axis) versus observed progeny variances (y-axis) for the six examined traits. In subplots without regression lines, there was not a significant regression coefficient for the corresponding progeny variance predictor and trait. In subplots with regression lines, there was a significant relationship. 268 Predicted Progeny Variance Parental BLUE Difference Trait 𝒓 p-value 𝒓 p-value AD 0.254 0.402 0.852 2.19 × 10−4 Parental RR-BLUP Difference p- value 𝒓 0.343 0.251 SD 0.135 0.661 0.371 0.212 0.194 0.525 EH 0.437 0.156 0.951 FH - 0.069 ELN 0.836 0.831 0.841 3.74 × 10−4 0.904 TLN 0.626 0.022 0.906 2.06 × 10−6 6.12 × 10−4 2.20 × 10−5 1.99 × 10−5 - 0.142 - 0.013 0.660 0.969 0.739 0.004 0.207 0.497 VanRaden Genomic Relationship IBS Genomic Relationship 𝒓 - 0.355 - 0.440 - 0.321 - 0.619 - 0.174 - 0.230 p- value 0.234 0.133 0.309 0.032 0.571 0.451 p- value 0.300 0.038 0.337 0.029 0.676 0.573 𝒓 - 0.312 - 0.579 - 0.304 - 0.628 - 0.128 - 0.173 Table 5.12: A summary of correlation coefficients and p-values for the regressions performed between progeny variance predictors and the observed progeny variance. Highlighted in green are the progeny variance predictor-trait combinations that were significant at a level of 0.05. 4. Discussion 4.1. Progeny mean predictions From our results, we find that the mean progeny trait value for a cross can be reliably predicted using either mean parental phenotypic BLUEs or mean parental genotypic BLUPs. For all trait-prediction metric combinations we examined, we were able to identify a significant correlation between predicted parental means and observed progeny means. The magnitude of the correlation appeared to mirror the heritability of the trait, like was found in Adeyemo & Bernardo (2019). These results are consistent with previously published results which found that mean progeny performance can be predicted using parental means (Adeyemo & Bernardo, 2019; Miller et al., 2023; Neyhart & Smith, 2019; Oget-Ebrad et al., 2024; Wartha & Lorenz, 2024; Wolfe et al., 2021). For all traits except for EH, using mean parental phenotypic BLUEs to predict progeny means appeared to be slightly more effective than using mean parental genomic BLUPs. This may be due to the shrinkage introduced in the BLUP calculation which biases 269 estimates in favor of reducing the variance surrounding the estimate. For this reason, we recommend that mean parental phenotypic BLUEs be used to estimate mean progeny performance. 4.2. Progeny variance predictions Overall, we found that progeny variance was extremely difficult to predict in the populations we examined. Of all the predictive metrics we tested, the magnitude of difference between the parental BLUEs was the most effective at predicting progeny variance. The magnitude of difference between parental BLUEs was significantly correlated with five out of six traits: AD, EH, FH, ELN, and TLN. For these traits, this metric exhibited a high correlation with the observed progeny variance, in all five cases exceeding 0.8. We believe this result may be an artifact of the crosses we selected for testing. Many of our crosses had parents which had large phenotypic differences for the traits we examined. For AD, SD, EH, FH, ELN, and TLN the minimum differences between parents in a cross across all examined crosses were 6.5 days, 9.2 days, 27.7 cm, 34.3 cm, 2.2 leaves, and 2.4 leaves, respectively. We did not sample crosses for parents which were similar phenotypically, so our results may not apply to crosses between parents with similar performance, especially if the two parents are distantly related. We found that the magnitude of difference between parental genotypic BLUPs was not an effective predictor of progeny variance for the traits we examined. This predictive metric was only significantly correlated with ELN, and it had a poorer correlation with progeny variance than its phenotypic BLUE counterpart. Like for the progeny mean predictions, we believe that the BLUP shrinkage may have introduced errors into the estimates of the magnitude of difference, resulting in poorer predictive performance. 270 We also found that the genomic relationship between parents in a cross was not a reliable predictor of the variance of progeny resulting from the cross for most traits. This result agreed with the results of Souza & Sorrells (1991) and Tiede et al. (2015). We were able to identify a significant negative relationship between VanRaden and IBS genomic relationships and FH progeny variance as well as IBS genomic relationships and SD progeny variance, but we suggest that these relationships may be spurious. For these correlations, there appeared to be two crosses which exhibited genomic relationships far outside the normal range of genomic relationship values and influenced the regression outcomes. Specifically, these two crosses were B73 × LH205 and B73 × ZS1791. Both LH205 and ZS1791 shared ancestry with B73 (Mazaheri et al., 2019), making these two crosses narrower than the other crosses we performed. Finally, we found that progeny variance predictions using the formulae by Allier, Moreau, et al. (2019) and Osthushenrich et al. (2017) were largely ineffective at predicting progeny variance in this population. In our variance predictions, we were only able to predict ELN and TLN progeny variance. This negative result was similar to that which was reported by Adeyemo & Bernardo (2019). We believe that our negative result was in part caused by two of the same conditions that were experienced by Adeyemo & Bernardo. First, like Adeyemo & Bernardo, we utilized a diversity panel to train a genomic prediction model for predicting progeny variances. Even though we had a significantly larger training set than Adeyemo & Bernardo (802 vs. 284), we believe that the diversity panel simply contained too diverse of materials to accurately estimate genomic marker effect coefficients for many of our traits. This, of course, resulted in poor progeny variance predictions. Second, like Adeyemo & Bernardo, we tested a small number of progeny families (our 13 vs. their 8). The small number of families we tested had low statistical power, making it difficult for us to detect correlations between our progeny variance 271 predictions and our observed progeny variances. In addition to these two factors, we believe that additive-by-additive epistatic effects and small family sizes for several of our crosses may have made progeny variances more difficult to predict. When testing the MoG × LH145 family, we observed that several progeny lineages exhibited reduced height, spindly, deformed leaves, and low fertility, atypical of the median progeny phenotype. Since all progenies were inbred, we speculate that there were several deleterious epistatic effects that manifest themselves when the MoG and LH145 genomes were recombined in the progenies. With respect to family size, it has been shown that small family size decreases the predictive ability of progeny variance estimates (Oget-Ebrad et al., 2024). Several of the crosses which we tested may not have had enough progenies in them to reliably estimate the progeny variance. 5. Conclusion We find that parental mean trait values can reliably estimate progeny mean trait values, in accordance with what has been previously published (Adeyemo & Bernardo, 2019; Miller et al., 2023; Neyhart & Smith, 2019; Oget-Ebrad et al., 2024; Wartha & Lorenz, 2024; Wolfe et al., 2021). We find that progeny variances are more difficult to estimate for several predictive metrics, even with high trait heritabilities, and that the most reliable estimate of the variance in progeny trait values was the magnitude of the difference in parental trait values. We were unable to predict progeny variance using analytical formulae in our experiment, unlike what has been previously reported (Oget-Ebrad et al., 2024; Wartha & Lorenz, 2024; Wolfe et al., 2021). We believe that these negative results were caused by our experimental design, which used an extremely diverse set of maize lines as a training population for genomic prediction models and tested a small number of families, several of which contained a small number of progenies. We submit that in future experiments, several improvements should be made to improve the chances 272 of predicting progeny variance. 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Error Lower CI 0.43499 273 732.9936 0.43499 273 731.6686 0.43499 273 731.5186 0.43499 273 712.5936 0.43499 273 709.2186 0.43499 273 708.6186 0.43499 273 701.4936 Statistical Grouping 95% Upper CI 734.7064 D 733.3814 D 733.2314 D 714.3064 C 710.9314 B 710.3314 B 703.2064 A Table A.1: Population number of polymorphic loci at generation 15 by selection strategy in the allele frequency alteration experiment. Mean Pop. Selection No. Poly. Markers Strategy PAU 733.8500 MOGS10 732.5000 MOGM10 732.4000 706.3000 MEHS 702.1750 MGRS 694.3250 RS 694.0250 PAFD DF Generation 30 95% Std. Error Lower CI 0.51111 273 732.8438 0.51111 273 731.4938 0.51111 273 731.3938 0.51111 273 705.2938 0.51111 273 701.1688 0.51111 273 693.3188 0.51111 273 693.0188 Statistical Grouping 95% Upper CI 734.8562 D 733.5062 D 733.4062 D 707.3062 C 703.1812 B 695.3312 A 695.0312 A Table A.2: Population number of polymorphic loci at generation 30 by selection strategy in the allele frequency alteration experiment. 284 Mean Pop. Selection No. Poly. Markers Strategy 733.8500 PAU MOGS10 732.5250 MOGM10 732.4000 704.5750 MEHS 692.1500 MGRS 688.5250 PAFD 676.7750 RS DF Generation 45 95% Std. Error Lower CI 0.59535 273 732.6779 0.59535 273 731.3529 0.59535 273 731.2279 0.59535 273 703.4029 0.59535 273 690.9779 0.59535 273 687.3529 0.59535 273 675.6029 Statistical Grouping 95% Upper CI 735.0221 E 733.6971 E 733.5721 E 705.7471 D 693.3221 C 689.6971 B 677.9471 A Table A.3: Population number of polymorphic loci at generation 45 by selection strategy in the allele frequency alteration experiment. 1.2. Mean expected heterozygosity Generation 15 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2815 MEHS PAFD 0.2751 MOGM10 0.2747 MOGS10 0.2741 0.2480 PAU 0.2466 MGRS 0.2437 RS Std. Error 0.00023 273 0.2810 0.00023 273 0.2746 0.00023 273 0.2742 0.00023 273 0.2737 0.00023 273 0.2475 0.00023 273 0.2461 0.00023 273 0.2433 Table A.4: Population mean expected heterozygosity at generation 15 by selection strategy in the allele frequency alteration experiment. Statistical Grouping E D D D C B A 95% Upper CI 0.2819 0.2756 0.2751 0.2746 0.2485 0.2471 0.2442 Generation 30 DF 95% Lower CI Mean Pop. MEH Selection Strategy MEHS 0.3008 MOGM10 0.2923 MOGS10 0.2916 0.2887 PAFD 0.2461 PAU 0.2430 MGRS 0.2376 RS Std. Error 0.00031 273 0.3002 0.00031 273 0.2917 0.00031 273 0.2910 0.00031 273 0.2881 0.00031 273 0.2455 0.00031 273 0.2424 0.00031 273 0.2370 Table A.5: Population mean expected heterozygosity at generation 30 by selection strategy in the allele frequency alteration experiment. Statistical Grouping F E E D C B A 95% Upper CI 0.3014 0.2929 0.2923 0.2893 0.2467 0.2436 0.2382 285 Generation 45 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.3140 MEHS MOGM10 0.3047 MOGS10 0.3037 0.2971 PAFD 0.2441 PAU 0.2397 MGRS 0.2313 RS Std. Error 0.00034 273 0.3133 0.00034 273 0.3040 0.00034 273 0.3030 0.00034 273 0.2964 0.00034 273 0.2434 0.00034 273 0.2390 0.00034 273 0.2306 Table A.6: Population mean expected heterozygosity at generation 45 by selection strategy in the allele frequency alteration experiment. Statistical Grouping F E E D C B A 95% Upper CI 0.3147 0.3054 0.3043 0.2978 0.2447 0.2404 0.2320 1.3. Manhattan (L1-norm) distance Mean Pop. Selection Man. Dist. Strategy 315.5255 RS 313.5748 PAU MGRS 313.0854 MOGS10 283.0769 MOGM10 282.4342 278.7164 MEHS 278.3327 PAFD Generation 15 DF 95% Std. Error Lower CI 0.23728 273 315.0584 0.23728 273 313.1077 0.23728 273 312.6183 0.23728 273 282.6097 0.23728 273 281.9670 0.23728 273 278.2492 0.23728 273 277.8656 Statistical Grouping 95% Upper CI 315.9927 D 314.0419 C 313.5525 C 283.5440 B 282.9013 B 279.1835 A 278.7998 A Table A.7: Manhattan distance between the population allele frequency and a target allele frequency of 0.5 at generation 15 by selection strategy in the allele frequency alteration experiment. Mean Pop. Selection Man. Dist. Strategy 320.4614 RS 315.9944 MGRS PAU 315.6188 MOGS10 261.2229 MOGM10 260.3170 259.0159 PAFD 255.9898 MEHS Generation 30 DF 95% Std. Error Lower CI 0.30949 273 319.8521 0.30949 273 315.3851 0.30949 273 315.0095 0.30949 273 260.6136 0.30949 273 259.7077 0.30949 273 258.4066 0.30949 273 255.3805 Statistical Grouping 95% Upper CI 321.0707 E 316.6037 D 316.2280 D 261.8322 C 260.9263 C 259.6252 B 256.5991 A Table A.8: Manhattan distance between the population allele frequency and a target allele frequency of 0.5 at generation 30 by selection strategy in the allele frequency alteration experiment. 286 Mean Pop. Selection Man. Dist. Strategy 325.3269 RS 318.5864 MGRS 317.5271 PAU PAFD 247.0191 MOGS10 246.0803 MOGM10 244.8695 239.6273 MEHS Generation 45 DF 95% Std. Error Lower CI 0.34089 273 324.6558 0.34089 273 317.9152 0.34089 273 316.8560 0.34089 273 246.3479 0.34089 273 245.4092 0.34089 273 244.1984 0.34089 273 238.9562 Statistical Grouping 95% Upper CI 325.9980 E 319.2575 D 318.1982 D 247.6902 C 246.7514 BC 245.5406 B 240.2984 A Table A.9: Manhattan distance between the population allele frequency and a target allele frequency of 0.5 at generation 45 by selection strategy in the allele frequency alteration experiment. 1.4. Euclidean (L2-norm) distance Mean Pop. Selection Eucl. Dist. Strategy 128.1266 RS 126.7018 MGRS 125.9961 PAU MOGS10 112.9388 MOGM10 112.6716 112.4536 PAFD 109.2566 MEHS Generation 15 DF Std. 95% Lower CI Error 0.11683 273 127.8966 0.11683 273 126.4718 0.11683 273 125.7660 0.11683 273 112.7088 0.11683 273 112.4416 0.11683 273 112.2236 0.11683 273 109.0266 Statistical Grouping 95% Upper CI 128.3566 E 126.9318 D 126.2261 C 113.1688 B 112.9016 B 112.6836 B 109.4866 A Table A.10: Euclidean distance between the population allele frequency and a target allele frequency of 0.5 at generation 15 by selection strategy in the allele frequency alteration experiment. Mean Pop. Selection Eucl. Dist. Strategy 131.1792 RS 128.4958 MGRS 126.9605 PAU PAFD 105.6533 MOGS10 104.1772 MOGM10 103.8514 99.6085 MEHS Generation 30 DF Std. 95% Lower CI Error 0.15440 273 130.8752 0.15440 273 128.1918 0.15440 273 126.6565 0.15440 273 105.3493 0.15440 273 103.8732 0.15440 273 103.5475 0.15440 273 99.3045 Statistical Grouping 95% Upper CI 131.4832 F 128.7998 E 127.2645 D 105.9573 C 104.4812 B 104.1554 B A 99.9125 Table A.11: Euclidean distance between the population allele frequency and a target allele frequency of 0.5 at generation 30 by selection strategy in the allele frequency alteration experiment. 287 Mean Pop. Selection Eucl. Dist. Strategy 134.3400 RS 130.1497 MGRS 127.9732 PAU PAFD 101.4399 MOGS10 98.1664 MOGM10 97.6489 92.9940 MEHS Generation 45 DF 95% Std. Error Lower CI 0.17235 273 134.0007 0.17235 273 129.8103 0.17235 273 127.6339 0.17235 273 101.1006 0.17235 273 97.8271 0.17235 273 97.3096 0.17235 273 92.6546 Statistical Grouping 95% Upper CI 134.6793 F 130.4890 E 128.3125 D 101.7792 C B 98.5057 B 97.9882 A 93.3333 Table A.12: Euclidean distance between the population allele frequency and a target allele frequency of 0.5 at generation 45 by selection strategy in the allele frequency alteration experiment. 2. Breeding simulation supplementary results 2.1. TRUE scenario results 2.1.1. Population mean true breeding value Mean Pop. Selection Mean TBV Strategy UCS 104.7079 pmGEBV 104.6265 104.6222 pmEBV OHV50 104.5597 MOGM90 104.5189 104.4722 EBV GEBV 104.4682 MOGS90 104.4455 104.4438 ucOCS 104.4150 pmOCS 104.3838 WGS 104.3717 OCS 104.0815 OPV50 104.0279 RS Generation 15 DF 95% Std. Lower CI Error 0.00298 546 104.7021 0.00298 546 104.6207 0.00298 546 104.6164 0.00298 546 104.5539 0.00298 546 104.5130 0.00298 546 104.4664 0.00298 546 104.4623 0.00298 546 104.4396 0.00298 546 104.4380 0.00298 546 104.4091 0.00298 546 104.3780 0.00298 546 104.3659 0.00298 546 104.0756 0.00298 546 104.0221 95% Statistical Upper CI Grouping 104.7138 J 104.6324 I I 104.6280 104.5656 H 104.5247 G 104.4781 F 104.4740 F 104.4513 E 104.4497 E 104.4208 D 104.3897 C 104.3776 C 104.0873 B 104.0337 A Table A.13: Population mean true breeding value at generation 15 by selection strategy in the TRUE scenario. 288 Mean Pop. Selection Mean TBV Strategy 105.5374 UCS 105.5016 ucOCS OHV50 105.4998 MOGM90 105.4139 105.4121 pmOCS 105.3206 OCS 105.3199 EBV 105.3182 GEBV pmEBV 105.3120 pmGEBV 105.3080 MOGS90 105.3052 105.2931 WGS 104.8391 OPV50 104.6842 RS Generation 30 DF 95% Std. Lower CI Error 0.00498 546 105.5277 0.00498 546 105.4918 0.00498 546 105.4901 0.00498 546 105.4041 0.00498 546 105.4023 0.00498 546 105.3108 0.00498 546 105.3101 0.00498 546 105.3084 0.00498 546 105.3022 0.00498 546 105.2982 0.00498 546 105.2954 0.00498 546 105.2833 0.00498 546 104.8293 0.00498 546 104.6745 Statistical Grouping 95% Upper CI 105.5472 G 105.5114 F 105.5096 F 105.4236 E 105.4219 E 105.3303 D 105.3297 D 105.3280 D 105.3218 CD 105.3177 CD 105.3150 CD 105.3029 C 104.8489 B 104.6940 A Table A.14: Population mean true breeding value at generation 30 by selection strategy in the TRUE scenario. Selection Mean Pop. Strategy Mean TBV ucOCS 106.1897 pmOCS 106.0642 106.0368 OHV50 MOGM90 106.0135 105.9786 WGS 105.9452 OCS UCS 105.9321 MOGS90 105.8970 105.8798 GEBV 105.8708 EBV pmEBV 105.6334 pmGEBV 105.6131 105.4836 OPV50 105.2207 RS Generation 45 DF 95% Std. Lower CI Error 0.00657 546 106.1768 0.00657 546 106.0513 0.00657 546 106.0239 0.00657 546 106.0006 0.00657 546 105.9657 0.00657 546 105.9323 0.00657 546 105.9192 0.00657 546 105.8841 0.00657 546 105.8670 0.00657 546 105.8579 0.00657 546 105.6205 0.00657 546 105.6002 0.00657 546 105.4707 0.00657 546 105.2078 Statistical 95% Grouping Upper CI 106.2026 I 106.0771 H 106.0497 GH 106.0263 G 105.9915 F 105.9581 E 105.9450 E 105.9099 D 105.8927 D 105.8837 D 105.6463 C 105.6260 C 105.4965 B 105.2336 A Table A.15: Population mean true breeding value at generation 45 by selection strategy in the TRUE scenario. 289 2.1.1.1. Population maximum true breeding value Figure A.1: Population maximum true breeding value over 60 generations by selection strategy in the TRUE scenario. Mean Pop. Selection Max TBV Strategy 105.0269 UCS 104.9901 OHV50 ucOCS 104.9086 MOGM90 104.8805 pmEBV 104.8642 pmGEBV 104.8610 104.8219 pmOCS 104.8122 EBV 104.8037 GEBV MOGS90 104.7924 104.7823 WGS 104.7646 OCS 104.5562 OPV50 104.4660 RS Generation 15 DF 95% Std. Error Lower CI 0.00641 546 105.0143 0.00641 546 104.9775 0.00641 546 104.8960 0.00641 546 104.8679 0.00641 546 104.8516 0.00641 546 104.8485 0.00641 546 104.8093 0.00641 546 104.7996 0.00641 546 104.7911 0.00641 546 104.7798 0.00641 546 104.7697 0.00641 546 104.7520 0.00641 546 104.5436 0.00641 546 104.4535 Statistical 95% Grouping Upper CI 105.0395 I 105.0027 H 104.9212 G 104.8931 FG 104.8768 F 104.8736 F 104.8345 E 104.8248 DE 104.8163 DE 104.8050 CDE 104.7949 CD 104.7772 C 104.5688 B 104.4786 A Table A.16: Population maximum true breeding value at generation 15 by selection strategy in the TRUE scenario. 290 Mean Pop. Selection Max TBV Strategy 105.7889 ucOCS 105.7676 OHV50 105.7021 UCS pmOCS 105.6794 MOGM90 105.6619 105.6006 WGS OCS 105.5847 MOGS90 105.5560 105.5554 EBV 105.5529 GEBV pmEBV 105.4404 pmGEBV 105.4364 105.2514 OPV50 105.0360 RS Generation 30 DF 95% Std. Error Lower CI 0.00659 546 105.7760 0.00659 546 105.7547 0.00659 546 105.6892 0.00659 546 105.6665 0.00659 546 105.6490 0.00659 546 105.5876 0.00659 546 105.5717 0.00659 546 105.5431 0.00659 546 105.5424 0.00659 546 105.5399 0.00659 546 105.4274 0.00659 546 105.4235 0.00659 546 105.2385 0.00659 546 105.0231 Statistical 95% Grouping Upper CI I 105.8019 105.7805 I 105.7151 H 105.6923 GH 105.6748 G 105.6135 F 105.5976 EF 105.5690 DE 105.5683 DE 105.5658 D 105.4533 C 105.4494 C 105.2643 B 105.0490 A Table A.17: Population maximum true breeding value at generation 30 by selection strategy in the TRUE scenario. Selection Mean Pop. Strategy Max TBV ucOCS 106.3458 pmOCS 106.2079 106.2029 WGS MOGM90 106.1814 106.1775 OHV50 106.1119 OCS MOGS90 106.0629 106.0280 GEBV 106.0164 EBV 105.9940 UCS 105.8074 OPV50 pmEBV 105.6735 pmGEBV 105.6508 105.5027 RS Generation 45 DF 95% Std. Error Lower CI 0.00764 546 106.3308 0.00764 546 106.1929 0.00764 546 106.1879 0.00764 546 106.1664 0.00764 546 106.1625 0.00764 546 106.0968 0.00764 546 106.0479 0.00764 546 106.0130 0.00764 546 106.0014 0.00764 546 105.9790 0.00764 546 105.7924 0.00764 546 105.6585 0.00764 546 105.6358 0.00764 546 105.4877 Statistical Grouping 95% Upper CI 106.3608 H 106.2229 G 106.2179 G 106.1964 G 106.1925 G 106.1269 F 106.0779 E 106.0430 DE 106.0314 D 106.0090 D 105.8224 C 105.6885 B 105.6658 B 105.5177 A Table A.18: Population maximum true breeding value at generation 45 by selection strategy in the TRUE scenario. 291 Mean Pop. Selection Max TBV Strategy 106.6233 WGS ucOCS 106.6063 MOGM90 106.5119 106.4792 pmOCS 106.4358 OCS MOGS90 106.4036 106.3387 OHV50 106.3047 GEBV 106.2898 EBV 106.2379 OPV50 106.0397 UCS 105.8788 RS pmEBV 105.7056 pmGEBV 105.6743 Generation 60 DF 95% Std. Error Lower CI 0.00854 546 106.6065 0.00854 546 106.5895 0.00854 546 106.4952 0.00854 546 106.4624 0.00854 546 106.4190 0.00854 546 106.3868 0.00854 546 106.3219 0.00854 546 106.2880 0.00854 546 106.2731 0.00854 546 106.2212 0.00854 546 106.0229 0.00854 546 105.8620 0.00854 546 105.6888 0.00854 546 105.6575 Statistical 95% Grouping Upper CI I 106.6401 106.6231 I 106.5287 H 106.4960 H 106.4526 G 106.4204 G 106.3555 F 106.3215 EF 106.3066 E 106.2547 D 106.0565 C 105.8955 B 105.7224 A 105.6910 A Table A.19: Population maximum true breeding value at generation 60 by selection strategy in the TRUE scenario. 2.1.1.2. Population minimum true breeding value Figure A.2: Population minimum true breeding value over 60 generations by selection strategy in the TRUE scenario. 292 Mean Pop. Min TBV Selection Strategy pmGEBV 104.3606 104.3536 pmEBV UCS 104.3272 MOGM90 104.1301 104.1202 GEBV 104.1147 EBV OHV50 104.0880 MOGS90 104.0584 103.9736 pmOCS 103.9648 OCS 103.9455 WGS 103.9036 ucOCS 103.5982 OPV50 103.5773 RS Generation 15 DF 95% Std. Error Lower CI 0.00767 546 104.3455 0.00767 546 104.3385 0.00767 546 104.3121 0.00767 546 104.1150 0.00767 546 104.1052 0.00767 546 104.0997 0.00767 546 104.0729 0.00767 546 104.0434 0.00767 546 103.9585 0.00767 546 103.9498 0.00767 546 103.9304 0.00767 546 103.8886 0.00767 546 103.5831 0.00767 546 103.5622 Statistical Grouping 95% Upper CI 104.3756 G 104.3686 G 104.3422 G 104.1452 F 104.1353 EF 104.1298 EF 104.1030 DE 104.0735 D 103.9887 C 103.9799 C 103.9605 C 103.9187 B 103.6133 A 103.5923 A Table A.20: Population minimum true breeding value at generation 15 by selection strategy in the TRUE scenario. Mean Pop. Selection Min TBV Strategy 105.3305 UCS OHV50 105.1875 pmGEBV 105.1683 105.1677 pmEBV ucOCS 105.1535 MOGM90 105.1366 105.1136 pmOCS 105.0755 GEBV EBV 105.0749 105.0419 OCS MOGS90 105.0254 104.9523 WGS 104.4299 OPV50 104.3304 RS Generation 30 DF 95% Std. Error Lower CI 0.00692 546 105.3169 0.00692 546 105.1739 0.00692 546 105.1547 0.00692 546 105.1542 0.00692 546 105.1399 0.00692 546 105.1230 0.00692 546 105.1000 0.00692 546 105.0619 0.00692 546 105.0613 0.00692 546 105.0283 0.00692 546 105.0118 0.00692 546 104.9387 0.00692 546 104.4163 0.00692 546 104.3168 Statistical 95% Grouping Upper CI 105.3441 I 105.2011 H 105.1819 GH 105.1813 GH 105.1671 G 105.1502 FG 105.1272 F 105.0891 E 105.0885 E 105.0555 D 105.0390 D 104.9659 C 104.4435 B 104.3440 A Table A.21: Population minimum true breeding value at generation 30 by selection strategy in the TRUE scenario. 293 Mean Pop. Selection Min TBV Strategy 105.9925 ucOCS 105.8986 pmOCS 105.8634 OHV50 UCS 105.8463 MOGM90 105.8357 105.7719 OCS 105.7313 WGS 105.7247 GEBV MOGS90 105.7177 105.7171 EBV pmEBV 105.5827 pmGEBV 105.5667 105.1349 OPV50 104.9299 RS Generation 45 DF 95% Std. Error Lower CI 0.00671 546 105.9794 0.00671 546 105.8854 0.00671 546 105.8502 0.00671 546 105.8331 0.00671 546 105.8225 0.00671 546 105.7587 0.00671 546 105.7181 0.00671 546 105.7115 0.00671 546 105.7045 0.00671 546 105.7040 0.00671 546 105.5695 0.00671 546 105.5535 0.00671 546 105.1217 0.00671 546 104.9167 Statistical Grouping 95% Upper CI 106.0057 H 105.9117 G 105.8765 F 105.8594 F 105.8489 F 105.7851 E 105.7444 D 105.7379 D 105.7308 D 105.7303 D 105.5959 C 105.5799 C 105.1480 B 104.9431 A Table A.22: Population minimum true breeding value at generation 45 by selection strategy in the TRUE scenario. Mean Pop. Selection Min TBV Strategy 106.4709 ucOCS pmOCS 106.3638 MOGM90 106.2947 106.2942 WGS 106.2348 OCS 106.2226 OHV50 MOGS90 106.1739 106.1382 GEBV 106.1221 EBV 106.0310 UCS 105.7251 OPV50 pmEBV 105.7031 pmGEBV 105.6730 105.4191 RS Generation 60 DF 95% Std. Error Lower CI 0.00823 546 106.4547 0.00823 546 106.3477 0.00823 546 106.2785 0.00823 546 106.2780 0.00823 546 106.2186 0.00823 546 106.2065 0.00823 546 106.1578 0.00823 546 106.1221 0.00823 546 106.1060 0.00823 546 106.0148 0.00823 546 105.7089 0.00823 546 105.6869 0.00823 546 105.6569 0.00823 546 105.4029 Statistical 95% Grouping Upper CI J 106.4870 106.3800 I 106.3108 H 106.3103 H 106.2510 G 106.2388 G 106.1901 F 106.1544 EF 106.1383 E 106.0472 D 105.7412 C 105.7193 BC 105.6892 B 105.4352 A Table A.23: Population minimum true breeding value at generation 60 by selection strategy in the TRUE scenario. 294 2.1.2. Genetic diversity metrics 2.1.2.1. Population mean expected heterozygosity Generation 15 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2273 pmOCS 0.2264 ucOCS 0.2259 OCS 0.2221 OPV50 0.2214 RS WGS 0.2211 MOGS90 0.1948 MOGM90 0.1888 0.1885 GEBV 0.1857 EBV 0.1749 OHV50 0.1365 UCS pmEBV 0.1254 pmGEBV 0.1208 Std. Error 0.00111 546 0.2251 0.00111 546 0.2242 0.00111 546 0.2237 0.00111 546 0.2199 0.00111 546 0.2192 0.00111 546 0.2189 0.00111 546 0.1927 0.00111 546 0.1866 0.00111 546 0.1863 0.00111 546 0.1835 0.00111 546 0.1727 0.00111 546 0.1343 0.00111 546 0.1232 0.00111 546 0.1186 Table A.24: Population mean expected heterozygosity at generation 15 by selection strategy in the TRUE scenario. Statistical Grouping H GH FGH FGH FG F E D D D C B A A 95% Upper CI 0.2294 0.2286 0.2281 0.2243 0.2235 0.2233 0.1970 0.1910 0.1907 0.1879 0.1771 0.1387 0.1276 0.1230 Generation 30 DF 95% Lower CI Mean Pop. MEH Selection Strategy RS 0.1871 OPV50 0.1867 WGS 0.1755 OCS 0.1615 pmOCS 0.1612 0.1600 ucOCS MOGS90 0.1389 MOGM90 0.1330 0.1297 GEBV 0.1267 EBV 0.1015 OHV50 UCS 0.0625 0.0502 pmEBV pmGEBV 0.0452 Std. Error 0.00106 546 0.1850 0.00106 546 0.1846 0.00106 546 0.1734 0.00106 546 0.1594 0.00106 546 0.1591 0.00106 546 0.1579 0.00106 546 0.1368 0.00106 546 0.1309 0.00106 546 0.1276 0.00106 546 0.1247 0.00106 546 0.0994 0.00106 546 0.0605 0.00106 546 0.0481 0.00106 546 0.0431 Table A.25: Population mean expected heterozygosity at generation 30 by selection strategy in the TRUE scenario. Statistical Grouping J J I H H H G F EF E D C B A 95% Upper CI 0.1892 0.1888 0.1776 0.1635 0.1633 0.1621 0.1409 0.1351 0.1318 0.1288 0.1036 0.0646 0.0523 0.0472 295 Generation 45 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.1585 RS 0.1547 OPV50 0.1365 WGS OCS 0.1071 MOGS90 0.0965 0.0947 pmOCS ucOCS 0.0932 MOGM90 0.0927 0.0861 GEBV 0.0843 EBV 0.0554 OHV50 0.0245 UCS pmEBV 0.0139 pmGEBV 0.0133 Std. Error 0.00084 546 0.1569 0.00084 546 0.1531 0.00084 546 0.1349 0.00084 546 0.1055 0.00084 546 0.0948 0.00084 546 0.0931 0.00084 546 0.0916 0.00084 546 0.0910 0.00084 546 0.0844 0.00084 546 0.0826 0.00084 546 0.0537 0.00084 546 0.0229 0.00084 546 0.0123 0.00084 546 0.0116 Table A.26: Population mean expected heterozygosity at generation 45 by selection strategy in the TRUE scenario. Statistical Grouping H H G F E E E E D D C B A A 95% Upper CI 0.1602 0.1564 0.1382 0.1088 0.0981 0.0964 0.0949 0.0943 0.0877 0.0859 0.0570 0.0262 0.0156 0.0149 2.1.2.2. Population upper selection limit Generation 15 DF Statistical Grouping Mean Pop. Selection USL Strategy 107.2664 WGS 107.2342 OPV50 RS 107.2293 MOGM90 107.2186 MOGS90 107.2176 107.1943 OCS 107.1864 ucOCS 107.1579 pmOCS 107.0067 GEBV 106.9905 EBV 106.8582 OHV50 106.6032 UCS pmEBV 106.4196 pmGEBV 106.4135 95% Std. Error Lower CI 0.00851 546 107.2497 0.00851 546 107.2175 0.00851 546 107.2126 0.00851 546 107.2018 0.00851 546 107.2008 0.00851 546 107.1775 0.00851 546 107.1697 0.00851 546 107.1412 0.00851 546 106.9900 0.00851 546 106.9738 0.00851 546 106.8415 0.00851 546 106.5864 0.00851 546 106.4029 0.00851 546 106.3968 Table A.27: Population upper selection limit at generation 15 by selection strategy in the TRUE scenario. 95% Upper CI 107.2831 H 107.2509 GH 107.2461 GH 107.2353 FG 107.2343 FG 107.2110 EFG 107.2032 EF 107.1746 E 107.0234 D 107.0072 D 106.8749 C 106.6199 B 106.4364 A 106.4302 A 296 Generation 30 DF Statistical Grouping J I Mean Pop. Selection USL Strategy 107.2133 WGS 107.1143 OPV50 RS 107.0716 MOGM90 107.0491 MOGS90 107.0267 106.9682 OCS 106.9640 ucOCS 106.9139 pmOCS 106.7404 GEBV 106.7061 EBV 106.5090 OHV50 106.1584 UCS pmEBV 105.8782 pmGEBV 105.8176 95% Std. Error Lower CI 0.01035 546 107.1930 0.01035 546 107.0940 0.01035 546 107.0512 0.01035 546 107.0288 0.01035 546 107.0063 0.01035 546 106.9478 0.01035 546 106.9436 0.01035 546 106.8936 0.01035 546 106.7200 0.01035 546 106.6858 0.01035 546 106.4887 0.01035 546 106.1380 0.01035 546 105.8579 0.01035 546 105.7973 Table A.28: Population upper selection limit at generation 30 by selection strategy in the TRUE scenario. 95% Upper CI 107.2336 107.1346 107.0919 HI 107.0695 H 107.0470 H 106.9885 G 106.9843 G 106.9342 F 106.7607 E 106.7265 E 106.5293 D 106.1787 C 105.8985 B 105.8379 A Generation 45 DF Selection Mean Pop. Strategy USL WGS 107.1782 OPV50 107.0335 106.9779 RS MOGM90 106.9129 MOGS90 106.8751 106.7906 OCS 106.7745 ucOCS 106.7181 pmOCS 106.5707 GEBV 106.5394 EBV 106.3808 OHV50 106.0497 UCS 105.7231 pmEBV pmGEBV 105.6895 95% Std. Error Lower CI 0.01008 546 107.1584 0.01008 546 107.0137 0.01008 546 106.9581 0.01008 546 106.8931 0.01008 546 106.8553 0.01008 546 106.7708 0.01008 546 106.7547 0.01008 546 106.6983 0.01008 546 106.5509 0.01008 546 106.5196 0.01008 546 106.3610 0.01008 546 106.0299 0.01008 546 105.7033 0.01008 546 105.6697 Table A.29: Population upper selection limit at generation 45 by selection strategy in the TRUE scenario. Statistical 95% Grouping Upper CI J 107.1980 107.0533 I 106.9977 H 106.9327 G 106.8949 G 106.8104 F 106.7943 F 106.7379 E 106.5905 D 106.5592 D 106.4006 C 106.0695 B 105.7429 A 105.7093 A 297 2.1.2.3. Population lower selection limit Figure A.3: Population lower selection limit over 60 generations by selection strategy in the TRUE scenario. Generation 15 DF Statistical Grouping Mean Pop. Selection Strategy LSL pmGEBV 101.5923 101.5623 pmEBV 100.9800 UCS 99.4103 OHV50 EBV 99.0059 99.0048 GEBV MOGM90 98.6678 MOGS90 98.5063 98.2705 pmOCS 98.0167 ucOCS 97.8768 OCS 97.8286 WGS 97.2658 OPV50 96.9796 RS 95% Std. Error Lower CI 0.03278 546 101.5280 0.03278 546 101.4979 0.03278 546 100.9156 0.03278 546 99.3459 0.03278 546 98.9415 0.03278 546 98.9404 0.03278 546 98.6035 0.03278 546 98.4419 0.03278 546 98.2061 0.03278 546 97.9523 0.03278 546 97.8124 0.03278 546 97.7642 0.03278 546 97.2014 0.03278 546 96.9152 Table A.30: Population lower selection limit at generation 15 by selection strategy in the TRUE scenario. 95% Upper CI 101.6567 K 101.6267 K J 101.0444 I 99.4747 H 99.0703 H 99.0692 G 98.7322 F 98.5707 E 98.3349 D 98.0811 CD 97.9412 C 97.8930 B 97.3302 A 97.0440 298 Generation 30 DF Mean Pop. Selection Strategy LSL pmGEBV 104.4390 104.3571 pmEBV 104.1728 UCS 102.7513 OHV50 102.0064 EBV 101.9300 GEBV pmOCS 101.7803 MOGM90 101.7423 ucOCS 101.5980 MOGS90 101.4792 101.0401 OCS 100.3283 WGS 99.3918 OPV50 99.1089 RS 95% Std. Error Lower CI 0.02954 546 104.3810 0.02954 546 104.2990 0.02954 546 104.1148 0.02954 546 102.6932 0.02954 546 101.9484 0.02954 546 101.8720 0.02954 546 101.7223 0.02954 546 101.6843 0.02954 546 101.5400 0.02954 546 101.4212 0.02954 546 100.9821 0.02954 546 100.2703 0.02954 546 99.3337 0.02954 546 99.0509 Table A.31: Population lower selection limit at generation 30 by selection strategy in the TRUE scenario. Statistical 95% Grouping Upper CI J 104.4970 J 104.4151 104.2308 I 102.8093 H 102.0644 G 101.9880 G 101.8384 F 101.8003 F 101.6560 E 101.5372 E 101.0982 D 100.3863 C B 99.4498 A 99.1670 Generation 45 DF Mean Pop. Selection LSL Strategy UCS 105.5724 pmGEBV 105.4631 105.4481 pmEBV 104.8586 OHV50 104.6043 ucOCS 104.5674 pmOCS 104.2079 GEBV EBV 104.1920 MOGM90 104.0813 MOGS90 103.7903 103.7779 OCS 102.5272 WGS 101.1565 OPV50 100.8816 RS 95% Std. Error Lower CI 0.02231 546 105.5286 0.02231 546 105.4193 0.02231 546 105.4042 0.02231 546 104.8148 0.02231 546 104.5605 0.02231 546 104.5236 0.02231 546 104.1640 0.02231 546 104.1482 0.02231 546 104.0375 0.02231 546 103.7465 0.02231 546 103.7341 0.02231 546 102.4834 0.02231 546 101.1127 0.02231 546 100.8377 Table A.32: Population lower selection limit at generation 45 by selection strategy in the TRUE scenario. 95% Statistical Upper CI Grouping 105.6162 J 105.5069 I I 105.4919 104.9025 H 104.6481 G 104.6113 G 104.2517 F 104.2358 F 104.1252 E 103.8342 D 103.8217 D 102.5710 C 101.2003 B 100.9254 A 299 Generation 60 DF Statistical Grouping J I Mean Pop. Selection LSL Strategy 106.2003 ucOCS 106.0928 pmOCS 106.0275 UCS 105.9580 OHV50 105.7018 pmEBV pmGEBV 105.6729 105.5370 GEBV 105.5139 EBV MOGM90 105.4643 OCS 105.3764 MOGS90 105.2392 104.3866 WGS 102.7812 OPV50 102.3655 RS 95% Std. Error Lower CI 0.01834 546 106.1642 0.01834 546 106.0568 0.01834 546 105.9914 0.01834 546 105.9219 0.01834 546 105.6657 0.01834 546 105.6368 0.01834 546 105.5010 0.01834 546 105.4779 0.01834 546 105.4282 0.01834 546 105.3404 0.01834 546 105.2031 0.01834 546 104.3506 0.01834 546 102.7452 0.01834 546 102.3295 Table A.33: Population lower selection limit at generation 60 by selection strategy in the TRUE scenario. 95% Upper CI 106.2363 106.1288 106.0635 HI 105.9940 H 105.7378 G 105.7089 G 105.5730 F 105.5499 F 105.5003 F 105.4124 E 105.2752 D 104.4227 C 102.8173 B 102.4015 A 2.1.2.4. Population additive genetic variance Figure A.4: Population additive genetic variance over 60 generations by selection strategy in the TRUE scenario. 300 Mean Pop. Selection Genetic Var. Strategy 0.0209 ucOCS 0.0178 OPV50 0.0166 OHV50 0.0153 RS 0.0153 pmOCS 0.0136 WGS OCS 0.0134 MOGM90 0.0115 UCS 0.0106 MOGS90 0.0105 0.0093 EBV 0.0093 GEBV pmGEBV 0.0057 0.0057 pmEBV Generation 15 95% Lower CI DF Std. Error 0.00024 546 0.0205 0.00024 546 0.0173 0.00024 546 0.0161 0.00024 546 0.0148 0.00024 546 0.0148 0.00024 546 0.0131 0.00024 546 0.0129 0.00024 546 0.0110 0.00024 546 0.0101 0.00024 546 0.0100 0.00024 546 0.0088 0.00024 546 0.0088 0.00024 546 0.0052 0.00024 546 0.0052 95% Upper CI 0.0214 0.0183 0.0171 0.0158 0.0158 0.0141 0.0139 0.0119 0.0111 0.0110 0.0098 0.0097 0.0062 0.0061 Statistical Grouping H G F E E D D C C C B B A A Table A.34: Population additive genetic variance at generation 15 by selection strategy in the TRUE scenario. Generation 30 Mean Pop. Selection Genetic Var. Strategy 0.0131 OPV50 0.0099 RS 0.0087 ucOCS 0.0085 WGS 0.0070 OHV50 0.0067 pmOCS OCS 0.0058 MOGM90 0.0057 MOGS90 0.0055 0.0047 EBV 0.0046 GEBV 0.0033 UCS 0.0019 pmEBV pmGEBV 0.0018 95% Lower CI DF Std. Error 0.00014 546 0.0128 0.00014 546 0.0096 0.00014 546 0.0084 0.00014 546 0.0082 0.00014 546 0.0067 0.00014 546 0.0064 0.00014 546 0.0055 0.00014 546 0.0054 0.00014 546 0.0053 0.00014 546 0.0044 0.00014 546 0.0043 0.00014 546 0.0030 0.00014 546 0.0017 0.00014 546 0.0015 95% Upper CI 0.0133 0.0102 0.0090 0.0088 0.0073 0.0070 0.0061 0.0059 0.0058 0.0049 0.0048 0.0035 0.0022 0.0020 Statistical Grouping H G F F E E D D D C C B A A Table A.35: Population additive genetic variance at generation 30 by selection strategy in the TRUE scenario. 301 Mean Pop. Selection Genetic Var. Strategy 0.0090 OPV50 0.0065 RS 0.0045 WGS ucOCS 0.0027 MOGM90 0.0024 MOGS90 0.0023 0.0023 OCS 0.0022 OHV50 0.0021 pmOCS 0.0019 GEBV 0.0018 EBV 0.0006 UCS pmEBV 0.0003 pmGEBV 0.0002 Generation 45 95% Lower CI DF Std. Error 0.00008 546 0.0089 0.00008 546 0.0063 0.00008 546 0.0044 0.00008 546 0.0026 0.00008 546 0.0023 0.00008 546 0.0022 0.00008 546 0.0021 0.00008 546 0.0020 0.00008 546 0.0020 0.00008 546 0.0018 0.00008 546 0.0017 0.00008 546 0.0005 0.00008 546 0.0001 0.00008 546 0.0001 95% Upper CI 0.0092 0.0066 0.0047 0.0029 0.0026 0.0025 0.0024 0.0023 0.0023 0.0021 0.0020 0.0008 0.0004 0.0004 Statistical Grouping H G F E DE D D CD CD C C B AB A Table A.36: Population additive genetic variance at generation 45 by selection strategy in the TRUE scenario. Generation 60 Selection Mean Pop. Strategy Genetic Var. OPV50 0.0052 RS 0.0043 0.0022 WGS MOGS90 0.0010 MOGM90 0.0010 0.0008 OCS 0.0006 GEBV 0.0006 EBV 0.0004 ucOCS 0.0003 pmOCS 0.0003 OHV50 0.0000 UCS 0.0000 pmEBV pmGEBV 0.0000 95% Lower CI DF Std. Error 0.00004 546 0.0051 0.00004 546 0.0042 0.00004 546 0.0021 0.00004 546 0.0010 0.00004 546 0.0009 0.00004 546 0.0007 0.00004 546 0.0005 0.00004 546 0.0005 0.00004 546 0.0004 0.00004 546 0.0003 0.00004 546 0.0003 0.00004 546 -0.0001 0.00004 546 -0.0001 0.00004 546 -0.0001 95% Upper CI 0.0052 0.0044 0.0023 0.0011 0.0011 0.0009 0.0007 0.0007 0.0005 0.0004 0.0004 0.0001 0.0001 0.0001 Statistical Grouping H G F E DE D C C BC B B A A A Table A.37: Population additive genetic variance at generation 60 by selection strategy in the TRUE scenario. 302 2.1.2.5. Population additive genic variance Figure A.5: Population additive genic variance over 60 generations by selection strategy in the TRUE scenario. Generation 15 Selection Mean Pop. Strategy Genic Var. WGS 0.0270 OPV50 0.0265 RS 0.0259 ucOCS 0.0249 OCS 0.0248 0.0247 pmOCS MOGS90 0.0208 0.0201 OHV50 0.0200 GEBV MOGM90 0.0198 0.0197 EBV UCS 0.0142 0.0129 pmEBV pmGEBV 0.0124 95% Lower CI DF Std. Error 0.00012 546 0.0267 0.00012 546 0.0262 0.00012 546 0.0256 0.00012 546 0.0247 0.00012 546 0.0246 0.00012 546 0.0244 0.00012 546 0.0206 0.00012 546 0.0199 0.00012 546 0.0197 0.00012 546 0.0196 0.00012 546 0.0195 0.00012 546 0.0140 0.00012 546 0.0126 0.00012 546 0.0121 95% Upper CI 0.0272 0.0267 0.0261 0.0251 0.0251 0.0249 0.0210 0.0204 0.0202 0.0200 0.0200 0.0145 0.0131 0.0126 Statistical Grouping G G F E E E D C C C C B A A Table A.38: Population additive genic variance at generation 15 by selection strategy in the TRUE scenario. 303 Mean Pop. Selection Genic Var. Strategy 0.0188 OPV50 0.0183 RS 0.0163 WGS 0.0118 OCS 0.0112 pmOCS ucOCS 0.0107 MOGS90 0.0107 0.0095 GEBV MOGM90 0.0094 0.0093 EBV 0.0079 OHV50 0.0039 UCS pmEBV 0.0032 pmGEBV 0.0030 Generation 30 95% Lower CI DF Std. Error 0.00010 546 0.0186 0.00010 546 0.0181 0.00010 546 0.0161 0.00010 546 0.0116 0.00010 546 0.0110 0.00010 546 0.0105 0.00010 546 0.0105 0.00010 546 0.0093 0.00010 546 0.0092 0.00010 546 0.0091 0.00010 546 0.0078 0.00010 546 0.0037 0.00010 546 0.0031 0.00010 546 0.0028 95% Upper CI 0.0190 0.0185 0.0165 0.0120 0.0114 0.0109 0.0108 0.0097 0.0096 0.0095 0.0081 0.0040 0.0034 0.0032 Statistical Grouping I I H G F E E D D D C B A A Table A.39: Population additive genic variance at generation 30 by selection strategy in the TRUE scenario. Generation 45 Selection Mean Pop. Strategy Genic Var. RS 0.0125 OPV50 0.0120 0.0088 WGS MOGS90 0.0047 OCS 0.0047 MOGM90 0.0041 0.0037 GEBV 0.0037 pmOCS 0.0036 EBV 0.0032 ucOCS 0.0024 OHV50 0.0006 UCS 0.0004 pmEBV pmGEBV 0.0003 95% Lower CI DF Std. Error 0.00007 546 0.0124 0.00007 546 0.0119 0.00007 546 0.0087 0.00007 546 0.0045 0.00007 546 0.0045 0.00007 546 0.0039 0.00007 546 0.0035 0.00007 546 0.0035 0.00007 546 0.0035 0.00007 546 0.0031 0.00007 546 0.0023 0.00007 546 0.0005 0.00007 546 0.0003 0.00007 546 0.0002 95% Upper CI 0.0126 0.0122 0.0090 0.0048 0.0048 0.0042 0.0038 0.0038 0.0037 0.0034 0.0025 0.0007 0.0005 0.0005 Statistical Grouping I H G F F E D D D C B A A A Table A.40: Population additive genic variance at generation 45 by selection strategy in the TRUE scenario. 304 Mean Pop. Selection Genic Var. Strategy 0.0079 RS 0.0069 OPV50 WGS 0.0042 MOGS90 0.0020 0.0016 OCS MOGM90 0.0016 0.0011 EBV 0.0011 GEBV 0.0006 pmOCS 0.0005 ucOCS 0.0003 OHV50 0.0000 UCS pmEBV 0.0000 pmGEBV 0.0000 Generation 60 95% Lower CI DF Std. Error 0.00005 546 0.0078 0.00005 546 0.0068 0.00005 546 0.0041 0.00005 546 0.0019 0.00005 546 0.0015 0.00005 546 0.0015 0.00005 546 0.0010 0.00005 546 0.0010 0.00005 546 0.0005 0.00005 546 0.0004 0.00005 546 0.0002 0.00005 546 -0.0001 0.00005 546 -0.0001 0.00005 546 -0.0001 95% Upper CI 0.0079 0.0070 0.0043 0.0021 0.0017 0.0016 0.0012 0.0012 0.0007 0.0006 0.0004 0.0001 0.0001 0.0001 Statistical Grouping I H G F E E D D C BC B A A A Table A.41: Population additive genic variance at generation 60 by selection strategy in the TRUE scenario. 2.1.2.6. Population Bulmer effect Figure A.6: Population Bulmer effect over 60 generations by selection strategy in the TRUE scenario. 305 Mean Pop. Selection Bulmer Effect Strategy 0.8413 ucOCS 0.8227 OHV50 0.7487 UCS 0.6735 OPV50 0.6203 pmOCS RS 0.5915 MOGM90 0.5787 0.5395 OCS WGS 0.5049 MOGS90 0.5040 EBV 0.4706 pmGEBV 0.4691 0.4642 GEBV 0.4410 pmEBV Generation 15 95% Lower CI DF Std. Error 0.01403 546 0.8138 0.01403 546 0.7951 0.01403 546 0.7211 0.01403 546 0.6459 0.01403 546 0.5928 0.01403 546 0.5639 0.01403 546 0.5511 0.01403 546 0.5119 0.01403 546 0.4774 0.01403 546 0.4765 0.01403 546 0.4430 0.01403 546 0.4415 0.01403 546 0.4367 0.01403 546 0.4135 95% Upper CI 0.8689 0.8502 0.7762 0.7010 0.6479 0.6190 0.6062 0.5670 0.5325 0.5316 0.4981 0.4966 0.4918 0.4686 Statistical Grouping G G F E DE CD CD BC AB AB A A A A Table A.42: Population Bulmer effect at generation 15 by selection strategy in the TRUE scenario. Generation 30 Mean Pop. Selection Bulmer Effect Strategy 0.8869 OHV50 0.8518 UCS 0.8105 ucOCS OPV50 0.6955 MOGM90 0.6040 0.5970 pmEBV pmOCS 0.5961 pmGEBV 0.5756 RS 0.5403 0.5231 WGS MOGS90 0.5218 0.5030 EBV 0.4907 OCS 0.4823 GEBV 95% Lower CI DF Std. Error 0.01768 546 0.8522 0.01768 546 0.8171 0.01768 546 0.7758 0.01768 546 0.6608 0.01768 546 0.5693 0.01768 546 0.5623 0.01768 546 0.5614 0.01768 546 0.5408 0.01768 546 0.5056 0.01768 546 0.4884 0.01768 546 0.4870 0.01768 546 0.4682 0.01768 546 0.4560 0.01768 546 0.4476 95% Upper CI 0.9216 0.8865 0.8453 0.7303 0.6387 0.6317 0.6308 0.6103 0.5751 0.5578 0.5565 0.5377 0.5255 0.5170 Statistical Grouping E E E D C C C BC ABC ABC ABC AB A A Table A.43: Population Bulmer effect at generation 30 by selection strategy in the TRUE scenario. 306 Mean Pop. Selection Bulmer Effect Strategy 1.0276 UCS 0.9146 OHV50 0.8578 ucOCS 0.7511 OPV50 0.7477 pmEBV pmGEBV 0.6903 MOGM90 0.6027 0.5801 pmOCS 0.5263 GEBV 0.5187 RS 0.5140 WGS 0.5135 EBV MOGS90 0.5021 0.4918 OCS Generation 45 95% Lower CI DF Std. Error 0.02742 545 0.9737 0.02742 545 0.8607 0.02742 545 0.8039 0.02742 545 0.6973 0.02742 545 0.6938 0.02777 545 0.6357 0.02742 545 0.5488 0.02742 545 0.5262 0.02742 545 0.4724 0.02742 545 0.4649 0.02742 545 0.4601 0.02742 545 0.4596 0.02742 545 0.4482 0.02742 545 0.4379 95% Upper CI 1.0815 0.9684 0.9117 0.8050 0.8016 0.7448 0.6566 0.6339 0.5802 0.5726 0.5678 0.5674 0.5560 0.5456 Statistical Grouping F EF DE CD CD BC AB AB A A A A A A Table A.44: Population Bulmer effect at generation 45 by selection strategy in the TRUE scenario. Generation 60 Mean Pop. Bulmer Effect Selection Strategy pmGEBV 1.1605 1.0329 UCS 0.9948 OHV50 0.9810 pmEBV 0.9515 ucOCS 0.7494 OPV50 MOGM90 0.6454 0.5919 pmOCS 0.5503 RS 0.5461 GEBV EBV 0.5427 MOGS90 0.5363 0.5284 OCS 0.5163 WGS 95% Lower CI DF Std. Error 0.05869 482 1.0452 0.02553 482 0.9828 0.02455 482 0.9465 0.04483 482 0.8929 0.02455 482 0.9032 0.02455 482 0.7011 0.02455 482 0.5972 0.02455 482 0.5436 0.02455 482 0.5021 0.02455 482 0.4978 0.02455 482 0.4944 0.02455 482 0.4880 0.02455 482 0.4802 0.02455 482 0.4680 95% Upper CI 1.2759 1.0831 1.0430 1.0691 0.9997 0.7976 0.6937 0.6401 0.5986 0.5943 0.5909 0.5845 0.5767 0.5645 Statistical Grouping D D D D D C BC AB AB AB AB AB AB A Table A.45: Population Bulmer effect at generation 60 by selection strategy in the TRUE scenario. 307 2.1.3. Allele metrics 2.1.3.1. Number of polymorphic loci Figure A.7: Population number of polymorphic loci over 60 generations by selection strategy in the TRUE scenario. Generation 15 Mean Pop. Selection Poly. Alleles Strategy 2330.2000 RS 2287.1750 OPV50 2228.5250 OCS 2197.0000 ucOCS 2185.8750 WGS pmOCS 2165.7000 MOGS90 2092.2250 MOGM90 2067.4500 1982.0250 GEBV 1975.9500 EBV 1808.4250 OHV50 1463.5500 UCS pmEBV 1309.2500 pmGEBV 1294.2750 Statistical Grouping DF 95% Upper CI 95% Std. Lower CI Error 7.19261 546 2316.0714 2344.3286 I 7.19261 546 2273.0464 2301.3036 H 7.19261 546 2214.3964 2242.6536 G 7.19261 546 2182.8714 2211.1286 FG 7.19261 546 2171.7464 2200.0036 F 7.19261 546 2151.5714 2179.8286 F 7.19261 546 2078.0964 2106.3536 E 7.19261 546 2053.3214 2081.5786 E 7.19261 546 1967.8964 1996.1536 D 7.19261 546 1961.8214 1990.0786 D 7.19261 546 1794.2964 1822.5536 C 7.19261 546 1449.4214 1477.6786 B 7.19261 546 1295.1214 1323.3786 A 7.19261 546 1280.1464 1308.4036 A Table A.46: Population number of polymorphic loci at generation 15 by selection strategy in the TRUE scenario. 308 Generation 30 DF 95% Upper CI Statistical Grouping Mean Pop. Selection Poly. Alleles Strategy 2026.1000 RS 1968.4750 OPV50 1789.5000 WGS 1722.0000 OCS 1628.4250 ucOCS MOGS90 1583.2250 pmOCS 1574.1750 MOGM90 1549.2750 1441.6000 GEBV 1410.2250 EBV 1101.3250 OHV50 677.9250 UCS pmEBV 531.4500 pmGEBV 479.7250 95% Std. Lower CI Error 9.04158 546 2008.3395 2043.8605 K 9.04158 546 1950.7145 1986.2355 J 9.04158 546 1771.7395 1807.2605 I 9.04158 546 1704.2395 1739.7605 H 9.04158 546 1610.6645 1646.1855 G 9.04158 546 1565.4645 1600.9855 F 9.04158 546 1556.4145 1591.9355 F 9.04158 546 1531.5145 1567.0355 F 9.04158 546 1423.8395 1459.3605 E 9.04158 546 1392.4645 1427.9855 E 9.04158 546 1083.5645 1119.0855 D 695.6855 C 9.04158 546 660.1645 549.2105 B 9.04158 546 513.6895 497.4855 A 9.04158 546 461.9645 Table A.47: Population number of polymorphic loci at generation 30 by selection strategy in the TRUE scenario. Generation 45 DF 95% Upper CI Statistical Grouping Mean Pop. Selection Poly. Alleles Strategy 1752.9000 RS 1678.7250 OPV50 1440.4750 WGS OCS 1198.3000 MOGS90 1134.9000 MOGM90 1107.6500 1000.9500 ucOCS 974.8250 GEBV 962.1750 pmOCS 953.8500 EBV 620.6750 OHV50 275.4250 UCS 161.2500 pmEBV pmGEBV 145.6750 95% Std. Lower CI Error 7.67103 546 1737.8317 1767.9683 J 7.67103 546 1663.6567 1693.7933 I 7.67103 546 1425.4067 1455.5433 H 7.67103 546 1183.2317 1213.3683 G 7.67103 546 1119.8317 1149.9683 F 7.67103 546 1092.5817 1122.7183 F 1016.0183 E 7.67103 546 985.8817 989.8933 DE 7.67103 546 959.7567 977.2433 D 7.67103 546 947.1067 968.9183 D 7.67103 546 938.7817 635.7433 C 7.67103 546 605.6067 290.4933 B 7.67103 546 260.3567 176.3183 A 7.67103 546 146.1817 160.7433 A 7.67103 546 130.6067 Table A.48: Population number of polymorphic loci at generation 45 by selection strategy in the TRUE scenario. 309 Generation 60 DF 95% Upper CI Statistical Grouping Mean Pop. Selection Poly. Alleles Strategy 1516.3750 RS 1404.7750 OPV50 1096.0500 WGS OCS 788.3000 MOGS90 781.0500 MOGM90 761.8250 618.9250 GEBV 605.1750 EBV 431.7250 ucOCS 398.4500 pmOCS 301.8000 OHV50 77.0750 UCS pmEBV 31.9250 pmGEBV 28.3500 95% Std. Lower CI Error 6.82732 546 1502.9640 1529.7860 J 6.82732 546 1391.3640 1418.1860 I 6.82732 546 1082.6390 1109.4610 H 801.7110 G 6.82732 546 774.8890 794.4610 G 6.82732 546 767.6390 775.2360 G 6.82732 546 748.4140 F 632.3360 6.82732 546 605.5140 F 618.5860 6.82732 546 591.7640 445.1360 E 6.82732 546 418.3140 411.8610 D 6.82732 546 385.0390 315.2110 C 6.82732 546 288.3890 B 90.4860 6.82732 546 63.6640 A 45.3360 6.82732 546 18.5140 A 41.7610 6.82732 546 14.9390 Table A.49: Population number of polymorphic loci at generation 60 by selection strategy in the TRUE scenario. 2.1.3.2. Number of fixed favorable alleles Figure A.8: Population number of fixed favorable alleles over 60 generations by selection strategy in the TRUE scenario. 310 Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 475.8750 474.1500 pmEBV 438.9750 UCS 351.6500 OHV50 317.8500 EBV GEBV 317.5000 MOGM90 298.8750 MOGS90 292.1750 275.6000 pmOCS 264.4000 ucOCS 261.4750 WGS 256.8250 OCS 232.6500 OPV50 218.2750 RS DF Generation 15 95% Std. Error Lower CI 1.83648 546 472.2676 1.83648 546 470.5426 1.83648 546 435.3676 1.83648 546 348.0426 1.83648 546 314.2426 1.83648 546 313.8926 1.83648 546 295.2676 1.83648 546 288.5676 1.83648 546 271.9926 1.83648 546 260.7926 1.83648 546 257.8676 1.83648 546 253.2176 1.83648 546 229.0426 1.83648 546 214.6676 Statistical 95% Grouping Upper CI I 479.4824 477.7574 I 442.5824 H 355.2574 G 321.4574 F 321.1074 F 302.4824 E 295.7824 E 279.2074 D 268.0074 C 265.0824 C 260.4324 C 236.2574 B 221.8824 A Table A.50: Population number of fixed favorable alleles at generation 15 by selection strategy in the TRUE scenario. Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 659.6250 653.5750 pmEBV 632.9750 UCS 543.3250 OHV50 480.9000 EBV 476.1250 GEBV MOGM90 461.6000 pmOCS 459.1750 MOGS90 448.4750 447.2750 ucOCS 417.3500 OCS 388.7500 WGS 334.8500 OPV50 317.5000 RS DF Generation 30 95% Std. Error Lower CI 1.97561 546 655.7443 1.97561 546 649.6943 1.97561 546 629.0943 1.97561 546 539.4443 1.97561 546 477.0193 1.97561 546 472.2443 1.97561 546 457.7193 1.97561 546 455.2943 1.97561 546 444.5943 1.97561 546 443.3943 1.97561 546 413.4693 1.97561 546 384.8693 1.97561 546 330.9693 1.97561 546 313.6193 95% Statistical Upper CI Grouping 663.5057 J 657.4557 J I 636.8557 547.2057 H 484.7807 G 480.0057 G 465.4807 F 463.0557 F 452.3557 E 451.1557 E 421.2307 D 392.6307 C 338.7307 B 321.3807 A Table A.51: Population number of fixed favorable alleles at generation 30 by selection strategy in the TRUE scenario. 311 Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 738.5500 738.2000 pmEBV 737.2750 UCS 676.1000 OHV50 634.6500 pmOCS 634.0000 ucOCS 613.9000 EBV 613.2750 GEBV MOGM90 599.7500 MOGS90 584.5250 575.2500 OCS 504.4750 WGS 427.1750 OPV50 408.0000 RS DF Generation 45 95% Std. Error Lower CI 1.61845 546 735.3708 1.61845 546 735.0208 1.61845 546 734.0958 1.61845 546 672.9208 1.61845 546 631.4708 1.61845 546 630.8208 1.61845 546 610.7208 1.61845 546 610.0958 1.61845 546 596.5708 1.61845 546 581.3458 1.61845 546 572.0708 1.61845 546 501.2958 1.61845 546 423.9958 1.61845 546 404.8208 Statistical 95% Grouping Upper CI J 741.7292 J 741.3792 J 740.4542 679.2792 I 637.8292 H 637.1792 H 617.0792 G 616.4542 G 602.9292 F 587.7042 E 578.4292 D 507.6542 C 430.3542 B 411.1792 A Table A.52: Population number of fixed favorable alleles at generation 45 by selection strategy in the TRUE scenario. Mean Pop. Selection Fixed Fav. Alleles Strategy 791.1750 UCS 775.0750 ucOCS 768.0000 pmEBV pmOCS 767.5250 pmGEBV 766.2500 763.5500 OHV50 713.2500 GEBV EBV 711.9250 MOGM90 700.6750 692.2500 OCS MOGS90 685.5000 617.4500 WGS 516.4250 OPV50 487.5750 RS DF Generation 60 95% Std. Error Lower CI 1.50685 546 788.2151 1.50685 546 772.1151 1.50685 546 765.0401 1.50685 546 764.5651 1.50685 546 763.2901 1.50685 546 760.5901 1.50685 546 710.2901 1.50685 546 708.9651 1.50685 546 697.7151 1.50685 546 689.2901 1.50685 546 682.5401 1.50685 546 614.4901 1.50685 546 513.4651 1.50685 546 484.6151 Statistical 95% Grouping Upper CI 794.1349 I 778.0349 H 770.9599 GH 770.4849 G 769.2099 G 766.5099 G 716.2099 F 714.8849 F 703.6349 E 695.2099 D 688.4599 D 620.4099 C 519.3849 B 490.5349 A Table A.53: Population number of fixed favorable alleles at generation 60 by selection strategy in the TRUE scenario. 312 2.1.3.3. Number fixed deleterious alleles Figure A.9: Population number of fixed deleterious alleles over 60 generations by selection strategy in the TRUE scenario. Mean Pop. Fixed Del. Alleles Selection Strategy pmGEBV 137.8750 136.4500 pmEBV 118.9000 UCS 94.0500 OHV50 75.7000 EBV 74.0750 GEBV pmOCS 55.1750 MOGM90 53.4500 MOGS90 53.3250 53.0500 ucOCS 51.2250 OCS 47.9250 RS 47.7250 WGS 47.3500 OPV50 DF Generation 15 95% Std. Error Lower CI 0.83282 546 136.2391 0.83282 546 134.8141 0.83282 546 117.2641 0.83282 546 92.4141 0.83282 546 74.0641 0.83282 546 72.4391 0.83282 546 53.5391 0.83282 546 51.8141 0.83282 546 51.6891 0.83282 546 51.4141 0.83282 546 49.5891 0.83282 546 46.2891 0.83282 546 46.0891 0.83282 546 45.7141 Statistical Grouping 95% Upper CI 139.5109 F 138.0859 F 120.5359 E D 95.6859 C 77.3359 C 75.7109 B 56.8109 B 55.0859 B 54.9609 B 54.6859 AB 52.8609 A 49.5609 A 49.3609 A 48.9859 Table A.54: Population number of fixed deleterious alleles at generation 15 by selection strategy in the TRUE scenario. 313 Mean Pop. Fixed Del. Alleles Selection Strategy pmGEBV 208.0500 201.7000 pmEBV 179.0250 UCS 143.0750 OHV50 112.5250 EBV 109.5500 GEBV 89.5000 pmOCS 84.0500 ucOCS MOGS90 81.6750 OCS 81.1500 MOGM90 80.1500 66.1250 RS 63.2750 OPV50 59.8000 WGS DF Generation 30 95% Std. Error Lower CI 1.11009 546 205.8694 1.11009 546 199.5194 1.11009 546 176.8444 1.11009 546 140.8944 1.11009 546 110.3444 1.11009 546 107.3694 1.11009 546 87.3194 1.11009 546 81.8694 1.11009 546 79.4944 1.11009 546 78.9694 1.11009 546 77.9694 1.11009 546 63.9444 1.11009 546 61.0944 1.11009 546 57.6194 Statistical 95% Grouping Upper CI I 210.2306 203.8806 H 181.2056 G 145.2556 F 114.7056 E 111.7306 E D 91.6806 C 86.2306 C 83.8556 C 83.3306 C 82.3306 B 68.3056 AB 65.4556 A 61.9806 Table A.55: Population number of fixed deleterious alleles at generation 30 by selection strategy in the TRUE scenario. Mean Pop. Fixed Del. Alleles Selection Strategy pmGEBV 229.0750 226.0500 pmEBV 200.0000 UCS 165.9750 OHV50 139.4500 EBV 136.1000 GEBV 123.0000 pmOCS 115.9750 ucOCS OCS 109.4250 MOGS90 106.8000 MOGM90 103.2750 79.6250 RS 76.6250 OPV50 69.8750 WGS DF Generation 45 95% Std. Error Lower CI 1.07765 546 226.9582 1.07765 546 223.9332 1.07765 546 197.8832 1.07765 546 163.8582 1.07765 546 137.3332 1.07765 546 133.9832 1.07765 546 120.8832 1.07765 546 113.8582 1.07765 546 107.3082 1.07765 546 104.6832 1.07765 546 101.1582 1.07765 546 77.5082 1.07765 546 74.5082 1.07765 546 67.7582 95% Statistical Upper CI Grouping 231.1918 J 228.1668 J I 202.1168 168.0918 H 141.5668 G 138.2168 G 125.1168 F 118.0918 E 111.5418 D 108.9168 CD 105.3918 C B 81.7418 B 78.7418 A 71.9918 Table A.56: Population number of fixed deleterious alleles at generation 45 by selection strategy in the TRUE scenario. 314 Mean Pop. Fixed Del. Alleles Selection Strategy pmGEBV 233.1500 230.5500 pmEBV 204.1750 UCS 174.5250 OHV50 156.3000 EBV 153.0750 GEBV 152.8500 pmOCS 140.5250 ucOCS OCS 128.7250 MOGS90 124.4750 MOGM90 119.0750 91.2250 RS 86.5250 OPV50 78.6750 WGS DF Generation 60 95% Std. Error Lower CI 1.04561 546 231.0961 1.04561 546 228.4961 1.04561 546 202.1211 1.04561 546 172.4711 1.04561 546 154.2461 1.04561 546 151.0211 1.04561 546 150.7961 1.04561 546 138.4711 1.04561 546 126.6711 1.04561 546 122.4211 1.04561 546 117.0211 1.04561 546 89.1711 1.04561 546 84.4711 1.04561 546 76.6211 Statistical 95% Grouping Upper CI I 235.2039 232.6039 I 206.2289 H 176.5789 G 158.3539 F 155.1289 F 154.9039 F 142.5789 E 130.7789 D 126.5289 D 121.1289 C B 93.2789 B 88.5789 A 80.7289 Table A.57: Population number of fixed deleterious alleles at generation 60 by selection strategy in the TRUE scenario. 2.1.3.4. Number of polymorphic favorable alleles Figure A.10: Population number of polymorphic favorable alleles over 60 generations by selection strategy in the TRUE scenario. 315 Mean Pop. Selection Poly. Fav. Alleles Strategy 733.8000 RS 720.0000 OPV50 691.9500 OCS 690.8000 WGS 682.5500 ucOCS pmOCS 669.2250 MOGS90 654.5000 MOGM90 647.6750 608.4250 GEBV 606.4500 EBV 554.3000 OHV50 442.1250 UCS pmEBV 389.4000 pmGEBV 386.2500 DF Generation 15 95% Std. Error Lower CI 2.46594 546 728.9561 2.46594 546 715.1561 2.46594 546 687.1061 2.46594 546 685.9561 2.46594 546 677.7061 2.46594 546 664.3811 2.46594 546 649.6561 2.46594 546 642.8311 2.46594 546 603.5811 2.46594 546 601.6061 2.46594 546 549.4561 2.46594 546 437.2811 2.46594 546 384.5561 2.46594 546 381.4061 Statistical 95% Grouping Upper CI I 738.6439 724.8439 H 696.7939 G 695.6439 G 687.3939 G 674.0689 F 659.3439 E 652.5189 E 613.2689 D 611.2939 D 559.1439 C 446.9689 B 394.2439 A 391.0939 A Table A.58: Population number of polymorphic favorable alleles at generation 15 by selection strategy in the TRUE scenario. Mean Pop. Selection Poly. Fav. Alleles Strategy 616.3750 RS 601.8750 OPV50 551.4500 WGS OCS 501.5000 MOGS90 469.8500 468.6750 ucOCS MOGM90 458.2500 451.3250 pmOCS 414.3250 GEBV 406.5750 EBV 313.6000 OHV50 188.0000 UCS 144.7250 pmEBV pmGEBV 132.3250 DF Generation 30 95% Std. Error Lower CI 2.79661 546 610.8816 2.79661 546 596.3816 2.79661 546 545.9566 2.79661 546 496.0066 2.79661 546 464.3566 2.79661 546 463.1816 2.79661 546 452.7566 2.79661 546 445.8316 2.79661 546 408.8316 2.79661 546 401.0816 2.79661 546 308.1066 2.79661 546 182.5066 2.79661 546 139.2316 2.79661 546 126.8316 Statistical 95% Grouping Upper CI J 621.8684 607.3684 I 556.9434 H 506.9934 G 475.3434 F 474.1684 F 463.7434 EF 456.8184 E 419.8184 D 412.0684 D 319.0934 C 193.4934 B 150.2184 A 137.8184 A Table A.59: Population number of polymorphic favorable alleles at generation 30 by selection strategy in the TRUE scenario. 316 Mean Pop. Selection Poly. Fav. Alleles Strategy 512.3750 RS 496.2000 OPV50 425.6500 WGS OCS 315.3250 MOGS90 308.6750 MOGM90 296.9750 250.6250 GEBV 250.0250 ucOCS 246.6500 EBV 242.3500 pmOCS 157.9250 OHV50 62.7250 UCS pmEBV 35.7500 pmGEBV 32.3750 DF Generation 45 95% Std. Error Lower CI 2.28742 546 507.8818 2.28742 546 491.7068 2.28742 546 421.1568 2.28742 546 310.8318 2.28742 546 304.1818 2.28742 546 292.4818 2.28742 546 246.1318 2.28742 546 245.5318 2.28742 546 242.1568 2.28742 546 237.8568 2.28742 546 153.4318 2.28742 546 58.2318 2.28742 546 31.2568 2.28742 546 27.8818 Statistical 95% Grouping Upper CI I 516.8682 500.6932 H 430.1432 G 319.8182 F 313.1682 F 301.4682 E 255.1182 D 254.5182 D 251.1432 D 246.8432 D 162.4182 C B 67.2182 A 40.2432 A 36.8682 Table A.60: Population number of polymorphic favorable alleles at generation 45 by selection strategy in the TRUE scenario. Selection Mean Pop. Strategy Poly. Fav. Alleles RS 421.2000 OPV50 397.0500 303.8750 WGS MOGS90 190.0250 MOGM90 180.2500 179.0250 OCS 133.6750 GEBV 131.7750 EBV 84.4000 ucOCS 79.6250 pmOCS 61.9250 OHV50 4.6500 UCS 1.4500 pmEBV pmGEBV 0.6000 DF Generation 60 95% Std. Error Lower CI 1.95044 546 417.3687 1.95044 546 393.2187 1.95044 546 300.0437 1.95044 546 186.1937 1.95044 546 176.4187 1.95044 546 175.1937 1.95044 546 129.8437 1.95044 546 127.9437 1.95044 546 80.5687 1.95044 546 75.7937 1.95044 546 58.0937 1.95044 546 0.8187 1.95044 546 -2.3813 1.95044 546 -3.2313 Statistical 95% Grouping Upper CI 425.0313 I 400.8813 H 307.7063 G 193.8563 F 184.0813 E 182.8563 E 137.5063 D 135.6063 D C 88.2313 C 83.4563 B 65.7563 A 8.4813 A 5.2813 A 4.4313 Table A.61: Population number of polymorphic favorable alleles at generation 60 by selection strategy in the TRUE scenario. 317 2.1.3.5. Number of polymorphic deleterious alleles Figure A.11: Population number of polymorphic deleterious alleles over 60 generations by selection strategy in the TRUE scenario. Mean Pop. Selection Poly. Del. Alleles Strategy 733.8000 RS 720.0000 OPV50 691.9500 OCS 690.8000 WGS 682.5500 ucOCS pmOCS 669.2250 MOGS90 654.5000 MOGM90 647.6750 608.4250 GEBV 606.4500 EBV 554.3000 OHV50 442.1250 UCS pmEBV 389.4000 pmGEBV 386.2500 DF Generation 15 95% Std. Lower CI Error 2.46594 546 728.9561 2.46594 546 715.1561 2.46594 546 687.1061 2.46594 546 685.9561 2.46594 546 677.7061 2.46594 546 664.3811 2.46594 546 649.6561 2.46594 546 642.8311 2.46594 546 603.5811 2.46594 546 601.6061 2.46594 546 549.4561 2.46594 546 437.2811 2.46594 546 384.5561 2.46594 546 381.4061 Statistical 95% Grouping Upper CI 738.6439 I 724.8439 H 696.7939 G 695.6439 G 687.3939 G 674.0689 F 659.3439 E 652.5189 E 613.2689 D 611.2939 D 559.1439 C 446.9689 B 394.2439 A 391.0939 A Table A.62: Population number of polymorphic deleterious alleles at generation 15 by selection strategy in the TRUE scenario. 318 Mean Pop. Selection Poly. Del. Alleles Strategy 616.3750 RS 601.8750 OPV50 551.4500 WGS OCS 501.5000 MOGS90 469.8500 ucOCS 468.6750 MOGM90 458.2500 451.3250 pmOCS 414.3250 GEBV 406.5750 EBV 313.6000 OHV50 188.0000 UCS pmEBV 144.7250 pmGEBV 132.3250 DF Generation 30 95% Std. Error Lower CI 2.79661 546 610.8816 2.79661 546 596.3816 2.79661 546 545.9566 2.79661 546 496.0066 2.79661 546 464.3566 2.79661 546 463.1816 2.79661 546 452.7566 2.79661 546 445.8316 2.79661 546 408.8316 2.79661 546 401.0816 2.79661 546 308.1066 2.79661 546 182.5066 2.79661 546 139.2316 2.79661 546 126.8316 Statistical 95% Grouping Upper CI J 621.8684 607.3684 I 556.9434 H 506.9934 G 475.3434 F 474.1684 F 463.7434 EF 456.8184 E 419.8184 D 412.0684 D 319.0934 C 193.4934 B 150.2184 A 137.8184 A Table A.63: Population number of polymorphic deleterious alleles at generation 30 by selection strategy in the TRUE scenario. Mean Pop. Selection Poly. Del. Alleles Strategy 512.3750 RS 496.2000 OPV50 425.6500 WGS OCS 315.3250 MOGS90 308.6750 MOGM90 296.9750 250.6250 GEBV 250.0250 ucOCS 246.6500 EBV 242.3500 pmOCS 157.9250 OHV50 62.7250 UCS 35.7500 pmEBV pmGEBV 32.3750 DF Generation 45 95% Std. Error Lower CI 2.28742 546 507.8818 2.28742 546 491.7068 2.28742 546 421.1568 2.28742 546 310.8318 2.28742 546 304.1818 2.28742 546 292.4818 2.28742 546 246.1318 2.28742 546 245.5318 2.28742 546 242.1568 2.28742 546 237.8568 2.28742 546 153.4318 2.28742 546 58.2318 2.28742 546 31.2568 2.28742 546 27.8818 Statistical 95% Grouping Upper CI 516.8682 I 500.6932 H 430.1432 G 319.8182 F 313.1682 F 301.4682 E 255.1182 D 254.5182 D 251.1432 D 246.8432 D 162.4182 C B 67.2182 A 40.2432 A 36.8682 Table A.64: Population number of polymorphic deleterious alleles at generation 45 by selection strategy in the TRUE scenario. 319 Mean Pop. Selection Poly. Del. Alleles Strategy 421.2000 RS 397.0500 OPV50 WGS 303.8750 MOGS90 190.0250 MOGM90 180.2500 179.0250 OCS 133.6750 GEBV 131.7750 EBV 84.4000 ucOCS 79.6250 pmOCS 61.9250 OHV50 4.6500 UCS pmEBV 1.4500 pmGEBV 0.6000 DF Generation 60 95% Std. Error Lower CI 1.95044 546 417.3687 1.95044 546 393.2187 1.95044 546 300.0437 1.95044 546 186.1937 1.95044 546 176.4187 1.95044 546 175.1937 1.95044 546 129.8437 1.95044 546 127.9437 1.95044 546 80.5687 1.95044 546 75.7937 1.95044 546 58.0937 1.95044 546 0.8187 1.95044 546 -2.3813 1.95044 546 -3.2313 Statistical 95% Grouping Upper CI I 425.0313 400.8813 H 307.7063 G 193.8563 F 184.0813 E 182.8563 E 137.5063 D 135.6063 D C 88.2313 C 83.4563 B 65.7563 A 8.4813 A 5.2813 A 4.4313 Table A.65: Population number of polymorphic deleterious alleles at generation 60 by selection strategy in the TRUE scenario. 2.2. EST scenario results 2.2.1. Genetic gain metrics 2.2.1.1. Population mean true breeding value Mean Pop. Mean TBV Selection Strategy pmGEBV 104.4521 104.3921 UCS 104.3342 pmEBV 104.3147 pmOCS 104.2964 ucOCS GEBV 104.2811 MOGM90 104.2800 OCS 104.2647 MOGS90 104.2306 104.2297 EBV 104.1698 OHV50 103.8538 OPV50 103.8249 RS 103.7999 WGS Generation 15 DF 95% Std. Lower CI Error 0.00485 546 104.4426 0.00485 546 104.3825 0.00485 546 104.3246 0.00485 546 104.3051 0.00485 546 104.2869 0.00485 546 104.2716 0.00485 546 104.2705 0.00485 546 104.2552 0.00485 546 104.2210 0.00485 546 104.2202 0.00485 546 104.1603 0.00485 546 103.8442 0.00485 546 103.8154 0.00485 546 103.7903 Statistical Grouping 95% Upper CI 104.4617 K J 104.4016 104.3437 I 104.3242 HI 104.3059 GH 104.2906 FG 104.2895 FG 104.2742 F 104.2401 E 104.2393 E 104.1793 D 103.8633 C 103.8344 B 103.8094 A Table A.66: Population mean true breeding value at generation 15 by selection strategy in the EST scenario. 320 Mean Pop. Selection Mean TBV Strategy 105.1232 pmOCS ucOCS 105.0892 pmGEBV 105.0743 105.0332 UCS 105.0012 OCS MOGM90 104.9873 GEBV 104.9809 MOGS90 104.9191 104.8906 EBV 104.8892 pmEBV 104.8505 OHV50 104.3522 OPV50 104.2912 RS 104.2578 WGS Generation 30 DF 95% Std. Lower CI Error 0.00616 546 105.1111 0.00616 546 105.0771 0.00616 546 105.0622 0.00616 546 105.0211 0.00616 546 104.9891 0.00616 546 104.9752 0.00616 546 104.9689 0.00616 546 104.9070 0.00616 546 104.8785 0.00616 546 104.8771 0.00616 546 104.8384 0.00616 546 104.3401 0.00616 546 104.2791 0.00616 546 104.2457 Statistical 95% Grouping Upper CI J 105.1353 I 105.1013 105.0864 I 105.0453 H 105.0133 G 104.9994 G 104.9930 G 104.9312 F 104.9027 EF 104.9013 E 104.8626 D 104.3643 C 104.3033 B 104.2699 A Table A.67: Population mean true breeding value at generation 30 by selection strategy in the EST scenario. Selection Mean Pop. Strategy Mean TBV pmOCS 105.6434 ucOCS 105.5704 105.5087 OCS MOGM90 105.4824 GEBV 105.4711 MOGS90 105.4186 pmGEBV 105.4120 105.4012 UCS 105.3370 EBV 105.3074 OHV50 105.1655 pmEBV 104.7911 OPV50 104.6769 RS 104.6633 WGS Generation 45 DF 95% Std. Lower CI Error 0.00738 546 105.6289 0.00738 546 105.5559 0.00738 546 105.4942 0.00738 546 105.4679 0.00738 546 105.4566 0.00738 546 105.4041 0.00738 546 105.3975 0.00738 546 105.3867 0.00738 546 105.3225 0.00738 546 105.2929 0.00738 546 105.1510 0.00738 546 104.7766 0.00738 546 104.6624 0.00738 546 104.6488 Statistical 95% Grouping Upper CI 105.6579 I 105.5849 H 105.5232 G 105.4969 FG 105.4856 F 105.4331 E 105.4265 E 105.4158 E 105.3516 D 105.3219 D 105.1800 C 104.8056 B 104.6914 A 104.6778 A Table A.68: Population mean true breeding value at generation 45 by selection strategy in the EST scenario. 321 2.2.1.2. Population maximum true breeding value Figure A.12: Population maximum true breeding value over 60 generations by selection strategy in the EST scenario. Mean Pop. Max TBV Selection Strategy pmGEBV 104.7752 104.7569 UCS ucOCS 104.7506 104.7269 pmOCS MOGM90 104.6973 104.6710 pmEBV 104.6704 GEBV 104.6650 OCS OHV50 104.6334 MOGS90 104.6320 104.6207 EBV 104.3474 OPV50 104.3215 WGS 104.3160 RS Generation 15 DF 95% Std. Lower CI Error 0.00789 546 104.7597 0.00789 546 104.7414 0.00789 546 104.7351 0.00789 546 104.7114 0.00789 546 104.6818 0.00789 546 104.6555 0.00789 546 104.6549 0.00789 546 104.6495 0.00789 546 104.6179 0.00789 546 104.6165 0.00789 546 104.6052 0.00789 546 104.3319 0.00789 546 104.3060 0.00789 546 104.3005 Statistical Grouping 95% Upper CI 104.7907 H 104.7724 GH 104.7661 GH 104.7424 FG 104.7128 EF 104.6865 E 104.6859 DE 104.6805 CDE 104.6489 BCD 104.6475 BC 104.6362 B 104.3629 A 104.3370 A 104.3315 A Table A.69: Population maximum true breeding value at generation 15 by selection strategy in the EST scenario. 322 Mean Pop. Selection Max TBV Strategy 105.4114 ucOCS pmOCS 105.4081 MOGM90 105.3140 105.3055 UCS 105.3047 OCS pmGEBV 105.2788 GEBV 105.2788 MOGS90 105.2424 105.2155 OHV50 105.1953 EBV 105.1051 pmEBV 104.7952 OPV50 104.7262 WGS 104.7143 RS Generation 30 DF 95% Std. Error Lower CI 0.00800 546 105.3957 0.00800 546 105.3924 0.00800 546 105.2983 0.00800 546 105.2898 0.00800 546 105.2890 0.00800 546 105.2631 0.00800 546 105.2630 0.00800 546 105.2267 0.00800 546 105.1998 0.00800 546 105.1796 0.00800 546 105.0894 0.00800 546 104.7795 0.00800 546 104.7105 0.00800 546 104.6986 Statistical Grouping 95% Upper CI 105.4271 H 105.4238 H 105.3298 G 105.3212 G 105.3204 G 105.2945 FG 105.2945 FG 105.2581 EF 105.2313 DE 105.2110 D 105.1208 C 104.8109 B 104.7420 A 104.7300 A Table A.70: Population maximum true breeding value at generation 30 by selection strategy in the EST scenario. Selection Mean Pop. Strategy Max TBV pmOCS 105.8272 ucOCS 105.7959 105.7351 OCS MOGM90 105.7308 GEBV 105.6945 MOGS90 105.6865 105.6015 OHV50 105.5934 UCS EBV 105.5782 pmGEBV 105.5441 105.3007 pmEBV 105.1997 OPV50 105.1216 WGS 105.0638 RS Generation 45 DF 95% Std. Error Lower CI 0.00872 546 105.8101 0.00872 546 105.7788 0.00872 546 105.7180 0.00872 546 105.7137 0.00872 546 105.6773 0.00872 546 105.6694 0.00872 546 105.5843 0.00872 546 105.5763 0.00872 546 105.5611 0.00872 546 105.5270 0.00872 546 105.2836 0.00872 546 105.1826 0.00872 546 105.1045 0.00872 546 105.0467 Statistical 95% Grouping Upper CI I 105.8443 105.8130 I 105.7522 H 105.7479 H 105.7116 GH 105.7036 G 105.6186 F 105.6105 F 105.5953 EF 105.5612 E 105.3179 D 105.2168 C 105.1387 B 105.0809 A Table A.71: Population maximum true breeding value at generation 45 by selection strategy in the EST scenario. 323 Mean Pop. Selection Max TBV Strategy 106.0360 pmOCS MOGM90 106.0271 106.0235 OCS ucOCS 106.0161 MOGS90 105.9871 105.9805 GEBV 105.8732 OHV50 105.8290 EBV UCS 105.7664 pmGEBV 105.6703 105.5246 OPV50 105.4134 WGS 105.4031 pmEBV 105.3517 RS Generation 60 DF 95% Std. Error Lower CI 0.00943 546 106.0175 0.00943 546 106.0086 0.00943 546 106.0049 0.00943 546 105.9976 0.00943 546 105.9686 0.00943 546 105.9620 0.00943 546 105.8547 0.00943 546 105.8104 0.00943 546 105.7479 0.00943 546 105.6518 0.00943 546 105.5060 0.00943 546 105.3949 0.00943 546 105.3846 0.00943 546 105.3332 Statistical Grouping I 95% Upper CI 106.0545 106.0457 HI 106.0420 GHI 106.0347 GHI 106.0056 GH 105.9990 G 105.8917 F 105.8475 F 105.7850 E 105.6888 D 105.5431 C 105.4319 B 105.4216 B 105.3702 A Table A.72: Population maximum true breeding value at generation 60 by selection strategy in the EST scenario. 2.2.1.3. Population minimum true breeding value Figure A.13: Population minimum true breeding value over 60 generations by selection strategy in the EST scenario. 324 Mean Pop. Min TBV Selection Strategy pmGEBV 104.0877 103.9740 UCS 103.9651 pmEBV 103.8627 GEBV 103.8447 pmOCS 103.8253 OCS EBV 103.8078 MOGM90 103.8050 ucOCS 103.7842 MOGS90 103.7669 103.6511 OHV50 103.3323 OPV50 103.3158 RS 103.2460 WGS Generation 15 DF 95% Std. Error Lower CI 0.00996 546 104.0682 0.00996 546 103.9545 0.00996 546 103.9455 0.00996 546 103.8431 0.00996 546 103.8252 0.00996 546 103.8058 0.00996 546 103.7883 0.00996 546 103.7855 0.00996 546 103.7647 0.00996 546 103.7473 0.00996 546 103.6315 0.00996 546 103.3127 0.00996 546 103.2962 0.00996 546 103.2265 Statistical 95% Grouping Upper CI I 104.1073 103.9936 H 103.9847 H 103.8822 G 103.8643 FG 103.8449 EFG 103.8274 DEF 103.8246 DEF 103.8038 DE 103.7864 D 103.6707 C 103.3518 B 103.3353 B 103.2656 A Table A.73: Population minimum true breeding value at generation 15 by selection strategy in the EST scenario. Mean Pop. Min TBV Selection Strategy pmGEBV 104.8278 104.7836 pmOCS 104.7122 UCS 104.7028 ucOCS 104.6776 OCS 104.6556 GEBV pmEBV 104.6449 MOGM90 104.6107 EBV 104.5605 MOGS90 104.5368 104.4421 OHV50 103.8712 OPV50 103.8381 RS 103.7408 WGS Generation 30 DF 95% Std. Error Lower CI 0.00920 546 104.8097 0.00920 546 104.7655 0.00920 546 104.6941 0.00920 546 104.6848 0.00920 546 104.6596 0.00920 546 104.6375 0.00920 546 104.6268 0.00920 546 104.5927 0.00920 546 104.5424 0.00920 546 104.5187 0.00920 546 104.4241 0.00920 546 103.8532 0.00920 546 103.8201 0.00920 546 103.7228 Statistical 95% Grouping Upper CI 104.8459 I 104.8016 H 104.7302 G 104.7209 G 104.6957 FG 104.6736 F 104.6629 EF 104.6288 E 104.5786 D 104.5549 D 104.4602 C 103.8893 B 103.8562 B 103.7589 A Table A.74: Population minimum true breeding value at generation 30 by selection strategy in the EST scenario. 325 Mean Pop. Selection Min TBV Strategy 105.4251 pmOCS 105.3110 ucOCS OCS 105.2581 pmGEBV 105.2560 105.2157 GEBV MOGM90 105.1961 UCS 105.1714 MOGS90 105.1117 105.0729 EBV 105.0049 pmEBV 104.9743 OHV50 104.3694 OPV50 104.2772 RS 104.1873 WGS Generation 45 DF 95% Std. Error Lower CI 0.00894 546 105.4076 0.00894 546 105.2934 0.00894 546 105.2405 0.00894 546 105.2385 0.00894 546 105.1982 0.00894 546 105.1786 0.00894 546 105.1538 0.00894 546 105.0942 0.00894 546 105.0553 0.00894 546 104.9873 0.00894 546 104.9567 0.00894 546 104.3518 0.00894 546 104.2597 0.00894 546 104.1698 Statistical 95% Grouping Upper CI J 105.4427 105.3285 I 105.2757 H 105.2736 H 105.2333 GH 105.2137 FG 105.1890 F 105.1293 E 105.0905 E 105.0225 D 104.9919 D 104.3869 C 104.2948 B 104.2049 A Table A.75: Population minimum true breeding value at generation 45 by selection strategy in the EST scenario. Mean Pop. Selection Min TBV Strategy 105.7800 pmOCS 105.6567 ucOCS 105.6463 OCS GEBV 105.6068 MOGM90 105.5927 MOGS90 105.5279 pmGEBV 105.4841 105.4642 UCS 105.4249 EBV 105.3591 OHV50 105.1901 pmEBV 104.7686 OPV50 104.6347 RS 104.5647 WGS Generation 60 DF 95% Std. Error Lower CI 0.00944 546 105.7615 0.00944 546 105.6381 0.00944 546 105.6277 0.00944 546 105.5883 0.00944 546 105.5742 0.00944 546 105.5094 0.00944 546 105.4655 0.00944 546 105.4457 0.00944 546 105.4063 0.00944 546 105.3406 0.00944 546 105.1715 0.00944 546 104.7500 0.00944 546 104.6161 0.00944 546 104.5462 Statistical Grouping 95% Upper CI 105.7986 L 105.6752 K JK 105.6648 IJ 105.6254 105.6113 I 105.5464 H 105.5026 GH 105.4828 FG 105.4434 F 105.3776 E 105.2086 D 104.7871 C 104.6532 B 104.5833 A Table A.76: Population minimum true breeding value at generation 60 by selection strategy in the EST scenario. 326 2.2.2. Genetic diversity metrics 2.2.2.1. Population mean expected heterozygosity Generation 15 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2612 WGS 0.2387 OPV50 0.2308 RS 0.2202 ucOCS 0.2184 pmOCS OCS 0.2154 MOGS90 0.2120 0.2116 OHV50 MOGM90 0.2077 0.2032 EBV 0.2022 GEBV 0.1678 UCS pmEBV 0.1511 pmGEBV 0.1504 Std. Error 0.00095 546 0.2593 0.00095 546 0.2368 0.00095 546 0.2289 0.00095 546 0.2183 0.00095 546 0.2165 0.00095 546 0.2135 0.00095 546 0.2101 0.00095 546 0.2097 0.00095 546 0.2058 0.00095 546 0.2013 0.00095 546 0.2004 0.00095 546 0.1659 0.00095 546 0.1492 0.00095 546 0.1486 Table A.77: Population mean expected heterozygosity at generation 15 by selection strategy in the EST scenario. Statistical Grouping K J I H GH FG EF EF DE CD C B A A 95% Upper CI 0.2631 0.2406 0.2326 0.2221 0.2203 0.2172 0.2139 0.2134 0.2096 0.2050 0.2041 0.1697 0.1529 0.1523 Generation 30 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2564 WGS 0.2200 OPV50 RS 0.2081 MOGS90 0.1685 OHV50 0.1683 MOGM90 0.1643 0.1603 OCS 0.1585 ucOCS 0.1543 pmOCS 0.1522 EBV 0.1521 GEBV UCS 0.1084 pmGEBV 0.0816 0.0806 pmEBV Std. Error 0.00112 546 0.2542 0.00112 546 0.2178 0.00112 546 0.2059 0.00112 546 0.1664 0.00112 546 0.1661 0.00112 546 0.1621 0.00112 546 0.1581 0.00112 546 0.1563 0.00112 546 0.1521 0.00112 546 0.1500 0.00112 546 0.1500 0.00112 546 0.1062 0.00112 546 0.0794 0.00112 546 0.0784 Table A.78: Population mean expected heterozygosity at generation 30 by selection strategy in the EST scenario. Statistical Grouping J I H G G FG EF DE CD C C B A A 95% Upper CI 0.2586 0.2222 0.2103 0.1707 0.1705 0.1664 0.1625 0.1606 0.1565 0.1544 0.1543 0.1106 0.0838 0.0828 327 Generation 45 DF 95% Lower CI Mean Pop. MEH Selection Strategy 0.2486 WGS 0.2038 OPV50 RS 0.1887 MOGS90 0.1369 0.1366 OHV50 MOGM90 0.1344 0.1218 OCS 0.1178 GEBV 0.1156 EBV 0.1074 ucOCS 0.0939 pmOCS 0.0766 UCS pmGEBV 0.0465 0.0459 pmEBV Std. Error 0.00107 546 0.2465 0.00107 546 0.2017 0.00107 546 0.1866 0.00107 546 0.1348 0.00107 546 0.1345 0.00107 546 0.1323 0.00107 546 0.1197 0.00107 546 0.1157 0.00107 546 0.1135 0.00107 546 0.1053 0.00107 546 0.0918 0.00107 546 0.0745 0.00107 546 0.0444 0.00107 546 0.0438 Table A.79: Population mean expected heterozygosity at generation 45 by selection strategy in the EST scenario. Statistical Grouping J I H G G G F EF E D C B A A 95% Upper CI 0.2507 0.2059 0.1908 0.1390 0.1387 0.1365 0.1239 0.1199 0.1177 0.1095 0.0960 0.0787 0.0486 0.0480 2.2.2.2. Population upper selection limit Mean Pop. Selection USL Strategy 107.3054 OPV50 107.3022 WGS RS 107.2758 MOGM90 107.1821 MOGS90 107.1802 107.1318 OCS 107.1139 ucOCS 107.0785 pmOCS 107.0664 GEBV 107.0659 OHV50 107.0343 EBV UCS 106.7742 pmGEBV 106.6071 106.5602 pmEBV Generation 15 DF 95% Std. Error Lower CI 0.00869 546 107.2883 0.00869 546 107.2852 0.00869 546 107.2587 0.00869 546 107.1651 0.00869 546 107.1631 0.00869 546 107.1147 0.00869 546 107.0968 0.00869 546 107.0615 0.00869 546 107.0493 0.00869 546 107.0488 0.00869 546 107.0172 0.00869 546 106.7571 0.00869 546 106.5900 0.00869 546 106.5431 Statistical 95% Grouping Upper CI I 107.3224 I 107.3193 107.2928 I 107.1992 H 107.1973 H 107.1489 G 107.1309 FG 107.0956 EF 107.0835 DE 107.0829 DE 107.0514 D 106.7912 C 106.6242 B 106.5772 A Table A.80: Population upper selection limit at generation 15 by selection strategy in the EST scenario. 328 Mean Pop. Selection USL Strategy 107.2485 WGS 107.2281 OPV50 RS 107.1584 MOGM90 107.0177 MOGS90 107.0152 106.8997 OCS 106.8427 OHV50 106.8311 GEBV 106.8279 ucOCS 106.7843 EBV 106.7725 pmOCS 106.4232 UCS pmGEBV 106.1290 106.0183 pmEBV Generation 30 DF 95% Std. Error Lower CI 0.01198 546 107.2249 0.01198 546 107.2046 0.01198 546 107.1348 0.01198 546 106.9942 0.01198 546 106.9917 0.01198 546 106.8762 0.01198 546 106.8191 0.01198 546 106.8075 0.01198 546 106.8044 0.01198 546 106.7608 0.01198 546 106.7490 0.01198 546 106.3997 0.01198 546 106.1054 0.01198 546 105.9948 Statistical 95% Grouping Upper CI J 107.2720 J 107.2517 107.1819 I 107.0412 H 107.0387 H 106.9232 G 106.8662 FG 106.8546 EF 106.8514 DEF 106.8078 DE 106.7960 D 106.4467 C 106.1525 B 106.0418 A Table A.81: Population upper selection limit at generation 30 by selection strategy in the EST scenario. Selection Mean Pop. Strategy USL WGS 107.2085 OPV50 107.1657 107.0664 RS MOGS90 106.9086 MOGM90 106.9041 106.7465 OCS 106.7044 OHV50 106.6788 GEBV 106.6220 ucOCS 106.6109 EBV 106.5228 pmOCS UCS 106.2194 pmGEBV 105.8956 105.7330 pmEBV Generation 45 DF 95% Std. Error Lower CI 0.01202 546 107.1849 0.01202 546 107.1420 0.01202 546 107.0428 0.01202 546 106.8850 0.01202 546 106.8805 0.01202 546 106.7229 0.01202 546 106.6808 0.01202 546 106.6552 0.01202 546 106.5983 0.01202 546 106.5873 0.01202 546 106.4992 0.01202 546 106.1958 0.01202 546 105.8719 0.01202 546 105.7094 Statistical Grouping 95% Upper CI 107.2321 K 107.1893 K J 107.0900 I 106.9322 106.9277 I 106.7701 H 106.7280 GH 106.7024 FG 106.6456 EF 106.6345 E 106.5464 D 106.2430 C 105.9192 B 105.7566 A Table A.82: Population upper selection limit at generation 45 by selection strategy in the EST scenario. 329 2.2.2.3. Population lower selection limit Figure A.14: Population lower selection limit over 60 generations by selection strategy in the EST scenario. Mean Pop. Selection LSL Strategy pmEBV 100.5729 pmGEBV 100.5703 99.7790 UCS 98.4316 pmOCS 98.2664 EBV 98.2363 GEBV 98.1416 ucOCS 98.0919 OHV50 OCS 97.8291 MOGM90 97.5721 MOGS90 97.4980 96.3795 RS 96.1419 OPV50 95.9906 WGS Generation 15 DF 95% Std. Lower CI Error 0.03301 546 100.5081 0.03301 546 100.5055 0.03301 546 99.7142 0.03301 546 98.3668 0.03301 546 98.2016 0.03301 546 98.1715 0.03301 546 98.0768 0.03301 546 98.0270 0.03301 546 97.7642 0.03301 546 97.5073 0.03301 546 97.4331 0.03301 546 96.3147 0.03301 546 96.0770 0.03301 546 95.9257 95% Upper CI 100.6377 100.6351 99.8439 98.4965 98.3312 98.3012 98.2064 98.1567 97.8939 97.6369 97.5628 96.4444 96.2067 96.0554 Statistical Grouping I I H G F EF EF E D C C B A A Table A.83: Population lower selection limit at generation 15 by selection strategy in the EST scenario. 330 Mean Pop. Selection Strategy LSL pmGEBV 103.2046 103.0436 pmEBV 102.3785 UCS 101.5549 pmOCS 101.0817 ucOCS 100.7206 EBV 100.6476 GEBV 100.4162 OCS OHV50 100.3324 MOGM90 99.7760 MOGS90 99.6612 97.8804 RS 97.5934 OPV50 97.0836 WGS Generation 30 DF 95% Std. Error Lower CI 0.03293 546 103.1399 0.03293 546 102.9789 0.03293 546 102.3138 0.03293 546 101.4902 0.03293 546 101.0170 0.03293 546 100.6559 0.03293 546 100.5829 0.03293 546 100.3515 0.03293 546 100.2678 0.03293 546 99.7113 0.03293 546 99.5966 0.03293 546 97.8157 0.03293 546 97.5287 0.03293 546 97.0189 Statistical Grouping 95% Upper CI 103.2693 K J 103.1083 102.4432 I 101.6196 H 101.1464 G 100.7853 F 100.7123 F 100.4809 E 100.3971 E D 99.8407 D 99.7259 C 97.9451 B 97.6581 A 97.1483 Table A.84: Population lower selection limit at generation 30 by selection strategy in the EST scenario. Mean Pop. Selection Strategy LSL pmGEBV 104.5091 104.2273 pmEBV 103.8076 UCS 103.7965 pmOCS 103.2346 ucOCS 102.4630 GEBV 102.4385 EBV 102.3663 OCS OHV50 101.9464 MOGM90 101.5874 MOGS90 101.3947 99.1268 RS 98.7931 OPV50 98.0455 WGS Generation 45 DF 95% Std. Error Lower CI 0.02938 546 104.4514 0.02938 546 104.1696 0.02938 546 103.7499 0.02938 546 103.7388 0.02938 546 103.1769 0.02938 546 102.4053 0.02938 546 102.3808 0.02938 546 102.3086 0.02938 546 101.8887 0.02938 546 101.5297 0.02938 546 101.3370 0.02938 546 99.0691 0.02938 546 98.7354 0.02938 546 97.9878 Statistical Grouping 95% Upper CI 104.5668 K J 104.2850 I 103.8653 103.8542 I 103.2923 H 102.5207 G 102.4962 G 102.4240 G 102.0041 F 101.6451 E 101.4524 D C 99.1846 B 98.8508 A 98.1033 Table A.85: Population lower selection limit at generation 45 by selection strategy in the EST scenario. 331 Mean Pop. Selection Strategy LSL pmGEBV 105.1346 105.0279 pmOCS 104.7738 pmEBV 104.6439 UCS 104.4602 ucOCS 103.7549 GEBV 103.7195 OCS 103.5859 EBV OHV50 103.1782 MOGM90 102.9436 MOGS90 102.7854 100.1803 RS 99.8214 OPV50 98.8312 WGS Generation 60 DF 95% Std. Error Lower CI 0.02653 546 105.0825 0.02653 546 104.9758 0.02653 546 104.7217 0.02653 546 104.5918 0.02653 546 104.4081 0.02653 546 103.7028 0.02653 546 103.6674 0.02653 546 103.5338 0.02653 546 103.1261 0.02653 546 102.8915 0.02653 546 102.7333 0.02653 546 100.1282 0.02653 546 99.7693 0.02653 546 98.7790 Statistical Grouping 95% Upper CI 105.1868 L 105.0801 L 104.8260 K J 104.6960 I 104.5123 103.8070 H 103.7716 H 103.6381 G 103.2303 F 102.9957 E 102.8375 D 100.2325 C B 99.8735 A 98.8833 Table A.86: Population lower selection limit at generation 60 by selection strategy in the EST scenario. 2.2.2.4. Population genetic variance Figure A.15: Population additive genetic variance over 60 generations by selection strategy in the EST scenario. 332 Mean Pop. Selection Genetic Var. Strategy 0.0225 WGS 0.0207 OPV50 0.0201 ucOCS 0.0200 OHV50 0.0196 RS pmOCS 0.0160 MOGM90 0.0154 MOGS90 0.0150 0.0139 OCS 0.0137 EBV 0.0133 UCS 0.0125 GEBV pmEBV 0.0105 pmGEBV 0.0100 Generation 15 95% Lower CI DF Std. Error 0.00040 546 0.0217 0.00040 546 0.0199 0.00040 546 0.0193 0.00040 546 0.0192 0.00040 546 0.0188 0.00040 546 0.0152 0.00040 546 0.0146 0.00040 546 0.0142 0.00040 546 0.0132 0.00040 546 0.0129 0.00040 546 0.0126 0.00040 546 0.0117 0.00040 546 0.0098 0.00040 546 0.0092 95% Upper CI 0.0232 0.0214 0.0209 0.0208 0.0203 0.0168 0.0161 0.0158 0.0147 0.0145 0.0141 0.0133 0.0113 0.0108 Statistical Grouping G FG F F F E DE CDE BCD BCD BC B A A Table A.87: Population additive genetic variance at generation 15 by selection strategy in the EST scenario. Generation 30 Mean Pop. Selection Genetic Var. Strategy 0.0195 WGS 0.0164 OPV50 0.0151 RS 0.0129 OHV50 ucOCS 0.0112 MOGS90 0.0098 MOGM90 0.0098 0.0082 UCS 0.0081 EBV 0.0079 pmOCS 0.0078 OCS GEBV 0.0075 pmGEBV 0.0046 0.0045 pmEBV 95% Lower CI DF Std. Error 0.00029 546 0.0189 0.00029 546 0.0158 0.00029 546 0.0146 0.00029 546 0.0123 0.00029 546 0.0106 0.00029 546 0.0093 0.00029 546 0.0092 0.00029 546 0.0076 0.00029 546 0.0075 0.00029 546 0.0073 0.00029 546 0.0073 0.00029 546 0.0070 0.00029 546 0.0040 0.00029 546 0.0039 95% Upper CI 0.0201 0.0170 0.0157 0.0135 0.0118 0.0104 0.0104 0.0088 0.0087 0.0084 0.0084 0.0081 0.0052 0.0050 Statistical Grouping G F F E D CD C B B B B B A A Table A.88: Population additive genetic variance at generation 30 by selection strategy in the EST scenario. 333 Mean Pop. Selection Genetic Var. Strategy 0.0171 WGS 0.0136 OPV50 0.0126 RS OHV50 0.0083 MOGS90 0.0066 MOGM90 0.0057 0.0052 ucOCS 0.0051 EBV 0.0046 OCS 0.0045 GEBV 0.0040 UCS 0.0035 pmOCS pmGEBV 0.0018 0.0018 pmEBV Generation 45 95% Lower CI DF Std. Error 0.00017 546 0.0168 0.00017 546 0.0133 0.00017 546 0.0123 0.00017 546 0.0080 0.00017 546 0.0062 0.00017 546 0.0054 0.00017 546 0.0048 0.00017 546 0.0048 0.00017 546 0.0043 0.00017 546 0.0041 0.00017 546 0.0037 0.00017 546 0.0032 0.00017 546 0.0015 0.00017 546 0.0015 95% Upper CI 0.0174 0.0139 0.0130 0.0086 0.0069 0.0060 0.0055 0.0054 0.0049 0.0048 0.0043 0.0038 0.0021 0.0021 Statistical Grouping J I H G F E DE DE CD CD BC B A A Table A.89: Population additive genetic variance at generation 45 by selection strategy in the EST scenario. Generation 60 Mean Pop. Selection Genetic Var. Strategy 0.0144 WGS 0.0115 OPV50 0.0103 RS OHV50 0.0055 MOGS90 0.0040 MOGM90 0.0038 0.0033 EBV 0.0028 ucOCS 0.0027 OCS 0.0027 GEBV 0.0021 UCS 0.0014 pmOCS 0.0010 pmEBV pmGEBV 0.0008 95% Lower CI DF Std. Error 0.00013 546 0.0142 0.00013 546 0.0113 0.00013 546 0.0100 0.00013 546 0.0053 0.00013 546 0.0038 0.00013 546 0.0036 0.00013 546 0.0030 0.00013 546 0.0026 0.00013 546 0.0025 0.00013 546 0.0025 0.00013 546 0.0018 0.00013 546 0.0011 0.00013 546 0.0008 0.00013 546 0.0005 95% Upper CI 0.0147 0.0118 0.0105 0.0058 0.0043 0.0041 0.0035 0.0031 0.0030 0.0030 0.0023 0.0016 0.0013 0.0010 Statistical Grouping J I H G F EF DE D D D C B AB A Table A.90: Population additive genetic variance at generation 60 by selection strategy in the EST scenario. 334 2.2.2.5. Population genic variance Figure A.16: Population additive genic variance over 60 generations by selection strategy in the EST scenario. Generation 15 DF 95% Lower CI Mean Pop. Selection Genic Var. Strategy 0.0326 WGS 0.0294 OPV50 0.0283 RS 0.0248 OHV50 0.0245 ucOCS 0.0241 OCS pmOCS 0.0240 MOGS90 0.0238 MOGM90 0.0232 0.0228 EBV 0.0225 GEBV UCS 0.0183 0.0166 pmEBV pmGEBV 0.0161 Std. Error 0.00013 546 0.0323 0.00013 546 0.0291 0.00013 546 0.0281 0.00013 546 0.0246 0.00013 546 0.0242 0.00013 546 0.0238 0.00013 546 0.0237 0.00013 546 0.0235 0.00013 546 0.0230 0.00013 546 0.0225 0.00013 546 0.0222 0.00013 546 0.0180 0.00013 546 0.0163 0.00013 546 0.0159 Table A.91: Population additive genic variance at generation 15 by selection strategy in the EST scenario. Statistical Grouping K J I H GH FG FG EF DE CD C B A A 95% Upper CI 0.0329 0.0296 0.0286 0.0251 0.0248 0.0243 0.0242 0.0241 0.0235 0.0231 0.0227 0.0186 0.0168 0.0164 335 Generation 30 DF 95% Lower CI Mean Pop. Selection Genic Var. Strategy 0.0286 WGS 0.0241 OPV50 0.0229 RS OHV50 0.0162 MOGS90 0.0154 MOGM90 0.0147 0.0142 OCS 0.0140 EBV 0.0136 ucOCS 0.0135 GEBV 0.0128 pmOCS 0.0094 UCS pmEBV 0.0072 pmGEBV 0.0068 Std. Error 0.00014 546 0.0284 0.00014 546 0.0238 0.00014 546 0.0226 0.00014 546 0.0159 0.00014 546 0.0152 0.00014 546 0.0144 0.00014 546 0.0140 0.00014 546 0.0138 0.00014 546 0.0133 0.00014 546 0.0132 0.00014 546 0.0125 0.00014 546 0.0091 0.00014 546 0.0069 0.00014 546 0.0065 Table A.92: Population additive genic variance at generation 30 by selection strategy in the EST scenario. Statistical Grouping K J I H G F EF DEF DE D C B A A 95% Upper CI 0.0289 0.0244 0.0231 0.0165 0.0157 0.0149 0.0145 0.0143 0.0139 0.0138 0.0131 0.0097 0.0075 0.0071 Generation 45 DF 95% Lower CI Mean Pop. Selection Genic Var. Strategy 0.0244 WGS 0.0196 OPV50 0.0186 RS OHV50 0.0105 MOGS90 0.0096 MOGM90 0.0089 0.0084 EBV 0.0080 OCS 0.0077 GEBV 0.0067 ucOCS 0.0055 pmOCS 0.0051 UCS 0.0031 pmEBV pmGEBV 0.0027 Std. Error 0.00012 546 0.0241 0.00012 546 0.0194 0.00012 546 0.0183 0.00012 546 0.0103 0.00012 546 0.0094 0.00012 546 0.0086 0.00012 546 0.0082 0.00012 546 0.0078 0.00012 546 0.0075 0.00012 546 0.0064 0.00012 546 0.0052 0.00012 546 0.0049 0.00012 546 0.0029 0.00012 546 0.0025 Table A.93: Population additive genic variance at generation 45 by selection strategy in the EST scenario. Statistical Grouping K J I H G F EF DE D C B B A A 95% Upper CI 0.0246 0.0199 0.0188 0.0107 0.0098 0.0091 0.0086 0.0082 0.0079 0.0069 0.0057 0.0053 0.0033 0.0029 336 Generation 60 DF 95% Lower CI Mean Pop. Selection Genic Var. Strategy 0.0204 WGS 0.0157 OPV50 0.0150 RS OHV50 0.0068 MOGS90 0.0059 MOGM90 0.0056 0.0051 EBV 0.0045 OCS 0.0044 GEBV 0.0036 ucOCS 0.0027 UCS 0.0024 pmOCS pmEBV 0.0016 pmGEBV 0.0011 Std. Error 0.00009 546 0.0203 0.00009 546 0.0155 0.00009 546 0.0149 0.00009 546 0.0066 0.00009 546 0.0058 0.00009 546 0.0054 0.00009 546 0.0049 0.00009 546 0.0043 0.00009 546 0.0043 0.00009 546 0.0034 0.00009 546 0.0025 0.00009 546 0.0022 0.00009 546 0.0015 0.00009 546 0.0010 Table A.94: Population additive genic variance at generation 60 by selection strategy in the EST scenario. Statistical Grouping K J I H G G F E E D C C B A 95% Upper CI 0.0206 0.0159 0.0152 0.0069 0.0061 0.0058 0.0052 0.0047 0.0046 0.0038 0.0029 0.0025 0.0018 0.0013 2.2.2.6. Population Bulmer effect Figure A.17: Population Bulmer effect over 60 generations by selection strategy in the EST scenario. 337 Generation 15 DF 95% Lower CI Mean Pop. Selection Bulmer Effect Strategy 0.8197 ucOCS 0.8054 OHV50 0.7299 UCS 0.7034 OPV50 0.6902 RS 0.6882 WGS pmOCS 0.6680 MOGM90 0.6614 pmEBV 0.6421 MOGS90 0.6319 pmGEBV 0.6217 0.6013 EBV 0.5790 OCS 0.5556 GEBV Std. Error 0.01861 546 0.7832 0.01861 546 0.7688 0.01861 546 0.6933 0.01861 546 0.6668 0.01861 546 0.6537 0.01861 546 0.6517 0.01861 546 0.6314 0.01861 546 0.6248 0.01861 546 0.6056 0.01861 546 0.5954 0.01861 546 0.5851 0.01861 546 0.5647 0.01861 546 0.5424 0.01861 546 0.5190 Table A.95: Population Bulmer effect at generation 15 by selection strategy in the EST scenario. Statistical Grouping G FG EF DE DE CDE CDE BCDE ABCDE ABCD ABCD ABC AB A 95% Upper CI 0.8563 0.8419 0.7664 0.7399 0.7268 0.7248 0.7045 0.6979 0.6787 0.6685 0.6582 0.6378 0.6156 0.5922 Generation 30 DF 95% Lower CI Mean Pop. Selection Bulmer Effect Strategy 0.8763 UCS 0.8251 ucOCS 0.7970 OHV50 pmGEBV 0.6883 0.6806 WGS OPV50 0.6801 MOGM90 0.6685 RS 0.6623 MOGS90 0.6368 0.6325 pmEBV 0.6168 pmOCS 0.5775 EBV 0.5591 GEBV 0.5510 OCS Std. Error 0.02408 546 0.8290 0.02408 546 0.7778 0.02408 546 0.7497 0.02408 546 0.6409 0.02408 546 0.6332 0.02408 546 0.6328 0.02408 546 0.6212 0.02408 546 0.6150 0.02408 546 0.5895 0.02408 546 0.5852 0.02408 546 0.5695 0.02408 546 0.5302 0.02408 546 0.5118 0.02408 546 0.5037 Table A.96: Population Bulmer effect at generation 30 by selection strategy in the EST scenario. Statistical Grouping E E DE CD C C BC ABC ABC ABC ABC ABC AB A 95% Upper CI 0.9236 0.8724 0.8443 0.7356 0.7279 0.7274 0.7158 0.7096 0.6841 0.6798 0.6641 0.6248 0.6064 0.5983 338 Generation 45 DF 95% Lower CI Mean Pop. Selection Bulmer Effect Strategy 0.7948 OHV50 0.7828 UCS 0.7753 ucOCS 0.7019 WGS 0.6927 OPV50 pmGEBV 0.6879 MOGS90 0.6871 0.6801 RS MOGM90 0.6450 0.6407 pmOCS 0.6084 EBV 0.5863 pmEBV 0.5838 GEBV 0.5793 OCS Std. Error 0.01916 546 0.7572 0.01916 546 0.7451 0.01916 546 0.7377 0.01916 546 0.6643 0.01916 546 0.6551 0.01916 546 0.6502 0.01916 546 0.6495 0.01916 546 0.6425 0.01916 546 0.6074 0.01916 546 0.6031 0.01916 546 0.5707 0.01916 546 0.5487 0.01916 546 0.5462 0.01916 546 0.5416 Table A.97: Population Bulmer effect at generation 45 by selection strategy in the EST scenario. Statistical Grouping F EF DEF CDE BCDE BCD BCD BC ABC ABC AB A A A 95% Upper CI 0.8324 0.8204 0.8130 0.7396 0.7303 0.7255 0.7248 0.7178 0.6827 0.6784 0.6460 0.6240 0.6214 0.6169 Generation 60 DF 95% Lower CI Mean Pop. Selection Bulmer Effect Strategy 0.8192 OHV50 0.7881 ucOCS 0.7719 UCS OPV50 0.7329 pmGEBV 0.7095 WGS 0.7057 MOGM90 0.6854 RS 0.6823 MOGS90 0.6756 0.6616 pmEBV 0.6498 EBV 0.6161 GEBV 0.6131 OCS 0.6011 pmOCS Std. Error 0.02398 546 0.7721 0.02398 546 0.7410 0.02398 546 0.7248 0.02398 546 0.6858 0.02398 546 0.6624 0.02398 546 0.6585 0.02398 546 0.6383 0.02398 546 0.6351 0.02398 546 0.6285 0.02398 546 0.6145 0.02398 546 0.6027 0.02398 546 0.5690 0.02398 546 0.5659 0.02398 546 0.5540 Table A.98: Population Bulmer effect at generation 60 by selection strategy in the EST scenario. Statistical Grouping E DE CDE BCDE ABCDE ABCDE ABCD ABCD ABCD ABC AB A A A 95% Upper CI 0.8663 0.8352 0.8190 0.7801 0.7567 0.7528 0.7325 0.7294 0.7227 0.7087 0.6969 0.6632 0.6602 0.6483 339 2.2.3. Allele metrics 2.2.3.1. Number of polymorphic loci Figure A.18: Population number of polymorphic loci over 60 generations by selection strategy in the EST scenario. Generation 15 Mean Pop. Selection Poly. Alleles Strategy 2499.0500 WGS 2448.0750 OPV50 RS 2398.5000 MOGS90 2290.0250 MOGM90 2284.3750 2204.7500 OCS 2161.3250 ucOCS 2118.1000 GEBV 2116.3000 OHV50 2107.5750 pmOCS 2096.9750 EBV UCS 1770.0750 pmGEBV 1558.2250 1534.6000 pmEBV Statistical Grouping DF 95% Upper CI 95% Std. Lower CI Error 6.28785 546 2486.6987 2511.4013 I 6.28785 546 2435.7237 2460.4263 H 6.28785 546 2386.1487 2410.8513 G 6.28785 546 2277.6737 2302.3763 F 6.28785 546 2272.0237 2296.7263 F 6.28785 546 2192.3987 2217.1013 E 6.28785 546 2148.9737 2173.6763 D 6.28785 546 2105.7487 2130.4513 C 6.28785 546 2103.9487 2128.6513 C 6.28785 546 2095.2237 2119.9263 C 6.28785 546 2084.6237 2109.3263 C 6.28785 546 1757.7237 1782.4263 B 6.28785 546 1545.8737 1570.5763 A 6.28785 546 1522.2487 1546.9513 A Table A.99: Population number of polymorphic loci at generation 15 by selection strategy in the EST scenario. 340 Generation 30 Mean Pop. Selection Poly. Alleles Strategy 2408.3250 WGS 2290.0250 OPV50 RS 2197.1000 MOGS90 1960.4250 MOGM90 1943.1250 1757.4000 OCS 1721.3750 OHV50 1679.0750 GEBV 1634.4000 EBV 1626.8000 ucOCS 1520.8750 pmOCS 1176.5250 UCS pmGEBV 881.9500 867.3250 pmEBV Statistical Grouping DF 95% Upper CI 95% Std. Lower CI Error 9.04314 546 2390.5614 2426.0886 J 9.04314 546 2272.2614 2307.7886 I 9.04314 546 2179.3364 2214.8636 H 9.04314 546 1942.6614 1978.1886 G 9.04314 546 1925.3614 1960.8886 G 9.04314 546 1739.6364 1775.1636 F 9.04314 546 1703.6114 1739.1386 EF 9.04314 546 1661.3114 1696.8386 E 9.04314 546 1616.6364 1652.1636 D 9.04314 546 1609.0364 1644.5636 D 9.04314 546 1503.1114 1538.6386 C 9.04314 546 1158.7614 1194.2886 B 899.7136 A 9.04314 546 864.1864 885.0886 A 9.04314 546 849.5614 Table A.100: Population number of polymorphic loci at generation 30 by selection strategy in the EST scenario. Generation 45 Selection Mean Pop. Strategy Poly. Alleles WGS 2324.0000 OPV50 2140.4250 2009.1750 RS MOGS90 1673.2500 MOGM90 1651.6750 1411.6000 OHV50 1383.6750 OCS 1328.3250 GEBV 1273.7000 EBV 1160.4000 ucOCS 987.2750 pmOCS UCS 818.1750 pmGEBV 511.1000 498.0000 pmEBV Statistical Grouping DF 95% Upper CI 95% Std. Lower CI Error 8.40515 546 2307.4896 2340.5104 K 8.40515 546 2123.9146 2156.9354 J 8.40515 546 1992.6646 2025.6854 I 8.40515 546 1656.7396 1689.7604 H 8.40515 546 1635.1646 1668.1854 H 8.40515 546 1395.0896 1428.1104 G 8.40515 546 1367.1646 1400.1854 G 8.40515 546 1311.8146 1344.8354 F 8.40515 546 1257.1896 1290.2104 E 8.40515 546 1143.8896 1176.9104 D 1003.7854 C 8.40515 546 970.7646 834.6854 B 8.40515 546 801.6646 527.6104 A 8.40515 546 494.5896 514.5104 A 8.40515 546 481.4896 Table A.101: Population number of polymorphic loci at generation 45 by selection strategy in the EST scenario. 341 Generation 60 Mean Pop. Selection Poly. Alleles Strategy 2251.2750 WGS 2007.5750 OPV50 RS 1843.8500 MOGS90 1432.0000 MOGM90 1421.3750 1161.8250 OHV50 1102.4750 OCS 1063.1000 GEBV 1013.9250 EBV 828.8250 ucOCS 606.7250 pmOCS 589.5250 UCS pmEBV 323.2250 pmGEBV 317.7250 Statistical Grouping DF 95% Upper CI 95% Std. Lower CI Error 7.98097 546 2235.5978 2266.9522 K 7.98097 546 1991.8978 2023.2522 J 7.98097 546 1828.1728 1859.5272 I 7.98097 546 1416.3228 1447.6772 H 7.98097 546 1405.6978 1437.0522 H 7.98097 546 1146.1478 1177.5022 G 7.98097 546 1086.7978 1118.1522 F 7.98097 546 1047.4228 1078.7772 E 1029.6022 D 7.98097 546 998.2478 844.5022 C 7.98097 546 813.1478 622.4022 B 7.98097 546 591.0478 605.2022 B 7.98097 546 573.8478 338.9022 A 7.98097 546 307.5478 333.4022 A 7.98097 546 302.0478 Table A.102: Population number of polymorphic loci at generation 60 by selection strategy in the EST scenario. 2.2.3.2. Number of fixed favorable alleles Figure A.19: Population number of fixed favorable alleles over 60 generations by selection strategy in the EST scenario. 342 Mean Pop. Selection Fixed Fav. Alleles Strategy 415.5750 pmEBV pmGEBV 413.9250 365.7500 UCS 287.8500 pmOCS 282.8750 EBV 279.6000 GEBV 277.7500 OHV50 273.1500 ucOCS OCS 258.8250 MOGM90 241.7500 MOGS90 238.6000 192.4000 RS 180.2750 OPV50 171.0500 WGS DF Generation 15 95% Std. Error Lower CI 1.67236 546 412.2899 1.67236 546 410.6399 1.67236 546 362.4649 1.67236 546 284.5649 1.67236 546 279.5899 1.67236 546 276.3149 1.67236 546 274.4649 1.67236 546 269.8649 1.67236 546 255.5399 1.67236 546 238.4649 1.67236 546 235.3149 1.67236 546 189.1149 1.67236 546 176.9899 1.67236 546 167.7649 Statistical 95% Grouping Upper CI J 418.8601 J 417.2101 369.0351 I 291.1351 H 286.1601 GH 282.8851 FG 281.0351 FG 276.4351 F 262.1101 E 245.0351 D 241.8851 D 195.6851 C 183.5601 B 174.3351 A Table A.103: Population number of fixed favorable alleles at generation 15 by selection strategy in the EST scenario. Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 575.6500 569.3750 pmEBV 518.2500 UCS 458.3500 pmOCS 429.8250 ucOCS 411.9000 EBV 406.2000 GEBV 392.9750 OHV50 OCS 390.4000 MOGM90 351.7750 MOGS90 344.8500 260.1750 RS 241.6000 OPV50 215.7500 WGS DF Generation 30 95% Std. Error Lower CI 2.02912 546 571.6642 2.02912 546 565.3892 2.02912 546 514.2642 2.02912 546 454.3642 2.02912 546 425.8392 2.02912 546 407.9142 2.02912 546 402.2142 2.02912 546 388.9892 2.02912 546 386.4142 2.02912 546 347.7892 2.02912 546 340.8642 2.02912 546 256.1892 2.02912 546 237.6142 2.02912 546 211.7642 95% Statistical Upper CI Grouping 579.6358 J 573.3608 J I 522.2358 462.3358 H 433.8108 G 415.8858 F 410.1858 F 396.9608 E 394.3858 E 355.7608 D 348.8358 D 264.1608 C 245.5858 B 219.7358 A Table A.104: Population number of fixed favorable alleles at generation 30 by selection strategy in the EST scenario. 343 Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 661.1500 648.8250 pmEBV 607.3250 UCS 595.7250 pmOCS 557.7000 ucOCS 511.1000 EBV 507.8500 GEBV 499.5500 OCS OHV50 482.7500 MOGM90 445.9000 MOGS90 437.2500 319.6500 RS 296.0250 OPV50 258.0750 WGS DF Generation 45 95% Std. Error Lower CI 1.89558 546 657.4265 1.89558 546 645.1015 1.89558 546 603.6015 1.89558 546 592.0015 1.89558 546 553.9765 1.89558 546 507.3765 1.89558 546 504.1265 1.89558 546 495.8265 1.89558 546 479.0265 1.89558 546 442.1765 1.89558 546 433.5265 1.89558 546 315.9265 1.89558 546 292.3015 1.89558 546 254.3515 Statistical Grouping 95% Upper CI 664.8735 L 652.5485 K J 611.0485 599.4485 I 561.4235 H 514.8235 G 511.5735 FG 503.2735 F 486.4735 E 449.6235 D 440.9735 D 323.3735 C 299.7485 B 261.7985 A Table A.105: Population number of fixed favorable alleles at generation 45 by selection strategy in the EST scenario. Mean Pop. Fixed Fav. Alleles Selection Strategy pmGEBV 707.4500 687.1750 pmEBV 684.4500 pmOCS 664.1500 UCS 640.0250 ucOCS 584.5500 GEBV 581.2750 EBV 581.0250 OCS OHV50 555.0500 MOGM90 522.1500 MOGS90 515.2500 373.0250 RS 345.6000 OPV50 294.6500 WGS DF Generation 60 95% Std. Error Lower CI 1.81312 546 703.8885 1.81312 546 683.6135 1.81312 546 680.8885 1.81312 546 660.5885 1.81312 546 636.4635 1.81312 546 580.9885 1.81312 546 577.7135 1.81312 546 577.4635 1.81312 546 551.4885 1.81312 546 518.5885 1.81312 546 511.6885 1.81312 546 369.4635 1.81312 546 342.0385 1.81312 546 291.0885 95% Statistical Upper CI Grouping 711.0115 J 690.7365 I I 688.0115 667.7115 H 643.5865 G 588.1115 F 584.8365 F 584.5865 F 558.6115 E 525.7115 D 518.8115 D 376.5865 C 349.1615 B 298.2115 A Table A.106: Population number of fixed favorable alleles at generation 60 by selection strategy in the EST scenario. 344 2.2.3.3. Number of fixed deleterious alleles Figure A.20: Population number of fixed deleterious alleles over 60 generations by selection strategy in the EST scenario. Mean Pop. Selection Fixed Del. Alleles Strategy pmEBV 118.8750 pmGEBV 115.1750 96.0750 UCS 68.4250 EBV 64.9250 GEBV 64.8750 OHV50 64.1000 pmOCS 59.9750 ucOCS 57.6500 OCS MOGS90 53.1000 MOGM90 52.7000 42.9000 RS 39.6750 OPV50 39.0000 WGS DF Generation 15 95% Std. Error Lower CI 0.79772 546 117.3080 0.79772 546 113.6080 0.79772 546 94.5080 0.79772 546 66.8580 0.79772 546 63.3580 0.79772 546 63.3080 0.79772 546 62.5330 0.79772 546 58.4080 0.79772 546 56.0830 0.79772 546 51.5330 0.79772 546 51.1330 0.79772 546 41.3330 0.79772 546 38.1080 0.79772 546 37.4330 Statistical Grouping 95% Upper CI 120.4420 H 116.7420 H G 97.6420 F 69.9920 EF 66.4920 EF 66.4420 E 65.6670 D 61.5420 D 59.2170 C 54.6670 C 54.2670 B 44.4670 AB 41.2420 A 40.5670 Table A.107: Population number of fixed deleterious alleles at generation 15 by selection strategy in the EST scenario. 345 Mean Pop. Selection Fixed Del. Alleles Strategy 178.0250 pmEBV pmGEBV 171.9500 142.1250 UCS 105.7000 pmOCS 99.8750 EBV 98.1000 ucOCS 95.2500 GEBV 94.0500 OHV50 OCS 88.2250 MOGS90 75.4250 MOGM90 74.8500 55.5500 RS 48.1500 OPV50 45.0750 WGS DF Generation 30 95% Std. Error Lower CI 1.19194 546 175.6836 1.19194 546 169.6086 1.19194 546 139.7836 1.19194 546 103.3586 1.19194 546 97.5336 1.19194 546 95.7586 1.19194 546 92.9086 1.19194 546 91.7086 1.19194 546 85.8836 1.19194 546 73.0836 1.19194 546 72.5086 1.19194 546 53.2086 1.19194 546 45.8086 1.19194 546 42.7336 Statistical 95% Grouping Upper CI J 180.3664 174.2914 I 144.4664 H 108.0414 G 102.2164 F 100.4414 EF EF 97.5914 E 96.3914 D 90.5664 C 77.7664 C 77.1914 B 57.8914 A 50.4914 A 47.4164 Table A.108: Population number of fixed deleterious alleles at generation 30 by selection strategy in the EST scenario. Mean Pop. Selection Fixed Del. Alleles Strategy pmEBV 211.8500 pmGEBV 202.3500 169.4000 UCS 141.6500 pmOCS 128.7250 ucOCS 123.2250 EBV 116.1750 GEBV 114.0500 OHV50 OCS 110.4250 MOGM90 90.4750 MOGS90 90.2750 67.4250 RS 56.3250 OPV50 50.2250 WGS DF Generation 45 95% Std. Error Lower CI 1.13722 546 209.6161 1.13722 546 200.1161 1.13722 546 167.1661 1.13722 546 139.4161 1.13722 546 126.4911 1.13722 546 120.9911 1.13722 546 113.9411 1.13722 546 111.8161 1.13722 546 108.1911 1.13722 546 88.2411 1.13722 546 88.0411 1.13722 546 65.1911 1.13722 546 54.0911 1.13722 546 47.9911 Statistical Grouping 95% Upper CI 214.0839 L 204.5839 K J 171.6339 143.8839 I 130.9589 H 125.4589 G 118.4089 F 116.2839 EF 112.6589 E D 92.7089 D 92.5089 C 69.6589 B 58.5589 A 52.4589 Table A.109: Population number of fixed deleterious alleles at generation 45 by selection strategy in the EST scenario. 346 Mean Pop. Selection Fixed Del. Alleles Strategy 226.4250 pmEBV pmGEBV 215.3500 185.1750 UCS 167.1750 pmOCS 149.7250 ucOCS 140.7250 EBV 131.0250 GEBV 129.2500 OHV50 OCS 125.8000 MOGS90 102.1750 MOGM90 101.3750 77.6500 RS 62.2750 OPV50 54.2750 WGS DF Generation 60 95% Std. Error Lower CI 1.12301 546 224.2191 1.12301 546 213.1441 1.12301 546 182.9691 1.12301 546 164.9691 1.12301 546 147.5191 1.12301 546 138.5191 1.12301 546 128.8191 1.12301 546 127.0441 1.12301 546 123.5941 1.12301 546 99.9691 1.12301 546 99.1691 1.12301 546 75.4441 1.12301 546 60.0691 1.12301 546 52.0691 Statistical Grouping 95% Upper CI 228.6309 K J 217.5559 187.3809 I 169.3809 H 151.9309 G 142.9309 F 133.2309 E 131.4559 E 128.0059 E 104.3809 D 103.5809 D C 79.8559 B 64.4809 A 56.4809 Table A.110: Population number of fixed deleterious alleles at generation 60 by selection strategy in the EST scenario. 2.2.3.4. Number of polymorphic favorable alleles Figure A.21: Population number of polymorphic favorable alleles over 60 generations by selection strategy in the EST scenario. 347 Mean Pop. Selection Poly. Fav. Alleles Strategy 789.9500 WGS 780.0500 OPV50 RS 764.7000 MOGS90 708.3000 MOGM90 705.5500 683.5250 OCS 666.8750 ucOCS 657.3750 OHV50 655.4750 GEBV 648.7000 EBV 648.0500 pmOCS 538.1750 UCS pmGEBV 470.9000 465.5500 pmEBV DF Generation 15 95% Std. Error Lower CI 2.23617 546 785.5575 2.23617 546 775.6575 2.23617 546 760.3075 2.23617 546 703.9075 2.23617 546 701.1575 2.23617 546 679.1325 2.23617 546 662.4825 2.23617 546 652.9825 2.23617 546 651.0825 2.23617 546 644.3075 2.23617 546 643.6575 2.23617 546 533.7825 2.23617 546 466.5075 2.23617 546 461.1575 Statistical Grouping 95% Upper CI 794.3425 H 784.4425 H 769.0925 G 712.6925 F 709.9425 F 687.9175 E 671.2675 D 661.7675 CD 659.8675 C 653.0925 C 652.4425 C 542.5675 B 475.2925 A 469.9425 A Table A.111: Population number of polymorphic favorable alleles at generation 15 by selection strategy in the EST scenario. Selection Mean Pop. Strategy Poly. Fav. Alleles WGS 739.1750 OPV50 710.2500 684.2750 RS MOGS90 579.7250 MOGM90 573.3750 521.3750 OCS 512.9750 OHV50 498.5500 GEBV 488.2250 EBV 472.0750 ucOCS 435.9500 pmOCS 339.6250 UCS 252.6000 pmEBV pmGEBV 252.4000 DF Generation 30 95% Std. Error Lower CI 2.95413 546 733.3721 2.95413 546 704.4471 2.95413 546 678.4721 2.95413 546 573.9221 2.95413 546 567.5721 2.95413 546 515.5721 2.95413 546 507.1721 2.95413 546 492.7471 2.95413 546 482.4221 2.95413 546 466.2721 2.95413 546 430.1471 2.95413 546 333.8221 2.95413 546 246.7971 2.95413 546 246.5971 Statistical 95% Grouping Upper CI J 744.9779 716.0529 I 690.0779 H 585.5279 G 579.1779 G 527.1779 F 518.7779 F 504.3529 E 494.0279 E 477.8779 D 441.7529 C 345.4279 B 258.4029 A 258.2029 A Table A.112: Population number of polymorphic favorable alleles at generation 30 by selection strategy in the EST scenario. 348 Mean Pop. Selection Poly. Fav. Alleles Strategy 691.7000 WGS 647.6500 OPV50 RS 612.9250 MOGS90 472.4750 MOGM90 463.6250 403.2000 OHV50 390.0250 OCS 375.9750 GEBV 365.6750 EBV 313.5750 ucOCS 262.6250 pmOCS 223.2750 UCS pmEBV 139.3250 pmGEBV 136.5000 DF Generation 45 95% Std. Error Lower CI 2.68746 546 686.4210 2.68746 546 642.3710 2.68746 546 607.6460 2.68746 546 467.1960 2.68746 546 458.3460 2.68746 546 397.9210 2.68746 546 384.7460 2.68746 546 370.6960 2.68746 546 360.3960 2.68746 546 308.2960 2.68746 546 257.3460 2.68746 546 217.9960 2.68746 546 134.0460 2.68746 546 131.2210 Statistical Grouping 95% Upper CI 696.9790 K J 652.9290 618.2040 I 477.7540 H 468.9040 H 408.4790 G 395.3040 F 381.2540 E 370.9540 E 318.8540 D 267.9040 C 228.5540 B 144.6040 A 141.7790 A Table A.113: Population number of polymorphic favorable alleles at generation 45 by selection strategy in the EST scenario. Selection Mean Pop. Strategy Poly. Fav. Alleles WGS 651.0750 OPV50 592.1250 549.3250 RS MOGS90 382.5750 MOGM90 376.4750 315.7000 OHV50 293.1750 OCS 284.4250 GEBV 278.0000 EBV 210.2500 ucOCS 150.6750 UCS 148.3750 pmOCS 86.4000 pmEBV pmGEBV 77.2000 DF Generation 60 95% Std. Error Lower CI 2.52790 546 646.1094 2.52790 546 587.1594 2.52790 546 544.3594 2.52790 546 377.6094 2.52790 546 371.5094 2.52790 546 310.7344 2.52790 546 288.2094 2.52790 546 279.4594 2.52790 546 273.0344 2.52790 546 205.2844 2.52790 546 145.7094 2.52790 546 143.4094 2.52790 546 81.4344 2.52790 546 72.2344 Statistical 95% Grouping Upper CI J 656.0406 597.0906 I 554.2906 H 387.5406 G 381.4406 G 320.6656 F 298.1406 E 289.3906 DE 282.9656 D 215.2156 C 155.6406 B 153.3406 B A 91.3656 A 82.1656 Table A.114: Population number of polymorphic favorable alleles at generation 60 by selection strategy in the EST scenario. 349 2.2.3.5. Number of polymorphic deleterious alleles Figure A.22: Population number of polymorphic deleterious alleles over 60 generations by selection strategy in the EST scenario. Mean Pop. Selection Poly. Del. Alleles Strategy 789.9500 WGS 780.0500 OPV50 RS 764.7000 MOGS90 708.3000 MOGM90 705.5500 683.5250 OCS 666.8750 ucOCS 657.3750 OHV50 655.4750 GEBV 648.7000 EBV 648.0500 pmOCS UCS 538.1750 pmGEBV 470.9000 465.5500 pmEBV DF Generation 15 95% Std. Error Lower CI 2.23617 546 785.5575 2.23617 546 775.6575 2.23617 546 760.3075 2.23617 546 703.9075 2.23617 546 701.1575 2.23617 546 679.1325 2.23617 546 662.4825 2.23617 546 652.9825 2.23617 546 651.0825 2.23617 546 644.3075 2.23617 546 643.6575 2.23617 546 533.7825 2.23617 546 466.5075 2.23617 546 461.1575 Statistical Grouping 95% Upper CI 794.3425 H 784.4425 H 769.0925 G 712.6925 F 709.9425 F 687.9175 E 671.2675 D 661.7675 CD 659.8675 C 653.0925 C 652.4425 C 542.5675 B 475.2925 A 469.9425 A Table A.115: Population number of polymorphic deleterious alleles at generation 15 by selection strategy in the EST scenario. 350 Mean Pop. Selection Poly. Del. Alleles Strategy 739.1750 WGS 710.2500 OPV50 RS 684.2750 MOGS90 579.7250 MOGM90 573.3750 521.3750 OCS 512.9750 OHV50 498.5500 GEBV 488.2250 EBV 472.0750 ucOCS 435.9500 pmOCS 339.6250 UCS pmEBV 252.6000 pmGEBV 252.4000 DF Generation 30 95% Std. Error Lower CI 2.95413 546 733.3721 2.95413 546 704.4471 2.95413 546 678.4721 2.95413 546 573.9221 2.95413 546 567.5721 2.95413 546 515.5721 2.95413 546 507.1721 2.95413 546 492.7471 2.95413 546 482.4221 2.95413 546 466.2721 2.95413 546 430.1471 2.95413 546 333.8221 2.95413 546 246.7971 2.95413 546 246.5971 Statistical 95% Grouping Upper CI J 744.9779 716.0529 I 690.0779 H 585.5279 G 579.1779 G 527.1779 F 518.7779 F 504.3529 E 494.0279 E 477.8779 D 441.7529 C 345.4279 B 258.4029 A 258.2029 A Table A.116: Population number of polymorphic deleterious alleles at generation 30 by selection strategy in the EST scenario. Selection Mean Pop. Strategy Poly. Del. Alleles WGS 691.7000 OPV50 647.6500 612.9250 RS MOGS90 472.4750 MOGM90 463.6250 403.2000 OHV50 390.0250 OCS 375.9750 GEBV 365.6750 EBV 313.5750 ucOCS 262.6250 pmOCS 223.2750 UCS 139.3250 pmEBV pmGEBV 136.5000 DF Generation 45 95% Std. Error Lower CI 2.68746 546 686.4210 2.68746 546 642.3710 2.68746 546 607.6460 2.68746 546 467.1960 2.68746 546 458.3460 2.68746 546 397.9210 2.68746 546 384.7460 2.68746 546 370.6960 2.68746 546 360.3960 2.68746 546 308.2960 2.68746 546 257.3460 2.68746 546 217.9960 2.68746 546 134.0460 2.68746 546 131.2210 Statistical Grouping 95% Upper CI 696.9790 K 652.9290 J I 618.2040 477.7540 H 468.9040 H 408.4790 G 395.3040 F 381.2540 E 370.9540 E 318.8540 D 267.9040 C 228.5540 B 144.6040 A 141.7790 A Table A.117: Population number of polymorphic deleterious alleles at generation 45 by selection strategy in the EST scenario. 351 Mean Pop. Selection Poly. Del. Alleles Strategy 651.0750 WGS 592.1250 OPV50 RS 549.3250 MOGS90 382.5750 MOGM90 376.4750 315.7000 OHV50 293.1750 OCS 284.4250 GEBV 278.0000 EBV 210.2500 ucOCS 150.6750 UCS 148.3750 pmOCS pmEBV 86.4000 pmGEBV 77.2000 DF Generation 60 95% Std. Error Lower CI 2.52790 546 646.1094 2.52790 546 587.1594 2.52790 546 544.3594 2.52790 546 377.6094 2.52790 546 371.5094 2.52790 546 310.7344 2.52790 546 288.2094 2.52790 546 279.4594 2.52790 546 273.0344 2.52790 546 205.2844 2.52790 546 145.7094 2.52790 546 143.4094 2.52790 546 81.4344 2.52790 546 72.2344 Statistical 95% Grouping Upper CI J 656.0406 597.0906 I 554.2906 H 387.5406 G 381.4406 G 320.6656 F 298.1406 E 289.3906 DE 282.9656 D 215.2156 C 155.6406 B 153.3406 B A 91.3656 A 82.1656 Table A.118: Population number of polymorphic deleterious alleles at generation 60 by selection strategy in the EST scenario. 352 APPENDIX B: SUPPLEMENTAL FIGURES AND TABLES FOR CHAPTER 4: TOWARDS THE DEVELOPMENT OF MULTI-OBJECTIVE, TIME-COGNIZANT SELECTION STRATEGIES 1.1. Temporally weighted genomic selection characterization supplementary results 1.2. TRUE scenario results 1.2.1. Population maximum true breeding value Figure B.1: A) Scatterplot and regression of estimated upweighting factor effects on population maximum true breeding value at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. 353 Parameter Estimate Std. Error Intercept Generation 0.007465 0.001494 -0.000208 0.000043 t-value p-value 4.997043 0.000006 -4.893703 0.000008 Table B.1: Parameter estimates for a regression model fitting estimated upweighting factor effect on population maximum true breeding value at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 1.2.2. Population additive genetic variance Figure B.2: A) Scatterplot of estimated upweighting factor effects on population additive genetic variance at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). Regression results were not statistically significant. B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. 354 Parameter Estimate Std. Error Intercept 0.000028 0.000082 Generation 0.000003 0.000002 p-value t-value 0.339769 0.735258 1.208542 0.231743 Table B.2: Parameter estimates for a regression model fitting estimated upweighting factor effect on population additive genetic variance at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 1.2.3. Population additive genic variance Figure B.3: A) Scatterplot and regression of estimated upweighting factor effects on population additive genic variance at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. 355 Parameter Estimate Std. Error Intercept 0.000057 0.000024 Generation 0.000002 0.000001 p-value t-value 2.360265 0.021646 3.537095 0.000803 Table B.3: Parameter estimates for a regression model fitting estimated upweighting factor effect on population additive genic variance at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 1.2.4. Population Bulmer effect Figure B.4: A) Scatterplot of estimated upweighting factor effects on population Bulmer effect at generation 60 in the single-trait, TRUE scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). Regression results were not statistically significant. B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept -0.000721 0.016226 Generation 0.000282 0.000463 t-value p-value -0.044405 0.964734 0.610158 0.544141 Table B.4: Parameter estimates for a regression model fitting estimated upweighting factor effect on population Bulmer effect at generation 60 in the single-trait, TRUE scenario against the generation in which the upweighting factor was applied. 356 1.3. EST scenario results 1.3.1. Population maximum true breeding value Figure B.5: A) Scatterplot and regression of estimated upweighting factor effects on population maximum true breeding value at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation -0.001083 0.002577 -0.000370 0.000073 t-value p-value -0.420242 0.675861 -5.033949 0.000005 Table B.5: Parameter estimates for a regression model fitting estimated upweighting factor effect on population maximum true breeding value at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 357 1.3.2. Population additive genetic variance Figure B.6: A) Scatterplot and regression of estimated upweighting factor effects on population additive genetic variance at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation 0.000645 0.000195 -0.000021 0.000006 t-value p-value 3.307991 0.001618 -3.849329 0.000298 Table B.6: Parameter estimates for a regression model fitting estimated upweighting factor effect on population additive genetic variance at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 358 1.3.3. Population additive genic variance Figure B.7: A) Scatterplot and regression of estimated upweighting factor effects on population additive genic variance at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept 0.000117 0.000040 Generation 0.000004 0.000001 p-value t-value 2.932227 0.004810 3.152051 0.002566 Table B.7: Parameter estimates for a regression model fitting estimated upweighting factor effect on population additive genic variance at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 359 1.3.4. Population Bulmer effect Figure B.8: A) Scatterplot and regression of estimated upweighting factor effects on population Bulmer effect at generation 60 in the single-trait, EST scenario (y-axis) against the generation in which the upweighting factor was applied (x-axis). B) Corresponding statistical significance of estimated upweighting factor effects over 60 generations. Parameter Estimate Std. Error Intercept Generation 0.030527 0.011969 -0.001382 0.000341 t-value p-value 2.550442 0.013421 -4.050989 0.000153 Table B.8: Parameter estimates for a regression model fitting estimated upweighting factor effect on population Bulmer effect at generation 60 in the single-trait, EST scenario against the generation in which the upweighting factor was applied. 360 2. Single-trait breeding simulation supplementary results 2.1. TRUE scenario results 2.1.1. Population mean true breeding value Generation 15 Mean Pop. Selection Mean TBV Strategy 104.4753 gwGEBV10d 104.4745 gwGEBV15 104.4743 gwGEBV05 104.4743 gwGEBV10 104.4718 gwGEBV20d 104.4703 gwGEBV20 104.4677 GEBV 104.4654 gwGEBV25 104.4645 gwGEBV30d 104.4571 gwGEBV30 104.4486 gwGEBV40d 104.4446 gwGEBV35 104.4333 gwGEBV40 104.4141 gwGEBV50d 104.4010 gwGEBV45 104.3861 gwGEBV50 104.3829 gwGEBV60d 104.3449 gwGEBV70d 104.3389 OCS 104.3013 gwGEBV80d gwGEBV90d 104.2630 gwGEBV100d 104.2242 104.0306 RS 95% Lower CL DF Std. Error 0.00178 1817 104.4718 0.00178 1817 104.4710 0.00178 1817 104.4708 0.00178 1817 104.4708 0.00178 1817 104.4684 0.00178 1817 104.4669 0.00178 1817 104.4642 0.00178 1817 104.4619 0.00178 1817 104.4610 0.00178 1817 104.4536 0.00178 1817 104.4451 0.00178 1817 104.4411 0.00178 1817 104.4298 0.00178 1817 104.4107 0.00178 1817 104.3975 0.00178 1817 104.3826 0.00178 1817 104.3794 0.00178 1817 104.3414 0.00178 1817 104.3354 0.00178 1817 104.2978 0.00178 1817 104.2595 0.00178 1817 104.2207 0.00178 1817 104.0271 Statistical Grouping 95% Upper CL 104.4788 O 104.4779 NO 104.4778 NO 104.4778 NO 104.4753 MNO 104.4738 MNO 104.4712 MNO LMN 104.4689 104.4680 LM 104.4605 KL JK 104.4521 J 104.4481 I 104.4367 104.4176 H 104.4045 G F 104.3896 F 104.3864 E 104.3484 104.3424 E 104.3048 D 104.2665 C 104.2277 B 104.0341 A Table B.9: Population mean true breeding value by selection strategy at generation 15 in the single-trait, TRUE scenario. 361 Mean Pop. Selection Mean TBV Strategy 105.3727 gwGEBV30d 105.3663 gwGEBV40d 105.3650 gwGEBV25 105.3640 gwGEBV20 105.3616 gwGEBV20d 105.3612 gwGEBV30 105.3595 gwGEBV15 105.3547 gwGEBV50d 105.3517 gwGEBV35 105.3502 gwGEBV10 105.3481 gwGEBV10d 105.3425 gwGEBV40 105.3354 gwGEBV05 105.3262 gwGEBV60d 105.3185 GEBV 105.3120 gwGEBV45 105.3010 OCS 105.2995 gwGEBV70d 105.2967 gwGEBV50 105.2623 gwGEBV80d gwGEBV90d 105.2196 gwGEBV100d 105.1750 104.6862 RS Generation 30 95% Lower CL DF Std. Error 0.00293 1817 105.3669 0.00293 1817 105.3606 0.00293 1817 105.3592 0.00293 1817 105.3582 0.00293 1817 105.3559 0.00293 1817 105.3555 0.00293 1817 105.3538 0.00293 1817 105.3489 0.00293 1817 105.3459 0.00293 1817 105.3445 0.00293 1817 105.3424 0.00293 1817 105.3368 0.00293 1817 105.3296 0.00293 1817 105.3205 0.00293 1817 105.3128 0.00293 1817 105.3062 0.00293 1817 105.2952 0.00293 1817 105.2938 0.00293 1817 105.2909 0.00293 1817 105.2565 0.00293 1817 105.2139 0.00293 1817 105.1692 0.00293 1817 104.6804 Statistical Grouping LMN LMN 95% Upper CL 105.3784 N 105.3721 MN 105.3707 105.3697 105.3674 KLMN 105.3670 KLMN 105.3653 KLMN JKLM 105.3604 JKLM 105.3574 IJKL 105.3560 IJK 105.3539 IJ 105.3483 105.3411 HI 105.3320 GH 105.3243 G 105.3177 FG 105.3067 EF 105.3053 EF E 105.3024 105.2680 D 105.2254 C 105.1807 B 104.6919 A Table B.10: Population mean true breeding value by selection strategy at generation 30 in the single-trait, TRUE scenario. 362 Mean Pop. Selection Mean TBV Strategy 106.0340 gwGEBV50d 106.0209 gwGEBV60d 106.0104 gwGEBV70d 106.0044 gwGEBV40d 106.0009 gwGEBV40 105.9983 gwGEBV35 105.9971 gwGEBV30 105.9913 gwGEBV80d 105.9908 gwGEBV25 105.9863 gwGEBV30d 105.9830 gwGEBV50 105.9809 gwGEBV45 105.9737 gwGEBV20 105.9688 gwGEBV90d 105.9614 gwGEBV20d 105.9613 gwGEBV15 gwGEBV10 105.9375 gwGEBV100d 105.9372 105.9357 OCS 105.9250 gwGEBV10d 105.9139 gwGEBV05 105.8777 GEBV 105.2212 RS Generation 45 95% Lower CL DF Std. Error 0.00354 1817 106.0271 0.00354 1817 106.0139 0.00354 1817 106.0035 0.00354 1817 105.9974 0.00354 1817 105.9940 0.00354 1817 105.9914 0.00354 1817 105.9902 0.00354 1817 105.9844 0.00354 1817 105.9838 0.00354 1817 105.9793 0.00354 1817 105.9760 0.00354 1817 105.9740 0.00354 1817 105.9667 0.00354 1817 105.9618 0.00354 1817 105.9544 0.00354 1817 105.9544 0.00354 1817 105.9306 0.00354 1817 105.9303 0.00354 1817 105.9287 0.00354 1817 105.9181 0.00354 1817 105.9069 0.00354 1817 105.8707 0.00354 1817 105.2142 Statistical Grouping 95% Upper CL 106.0409 M 106.0278 LM 106.0173 KL JKL 106.0113 IJK 106.0079 106.0053 HIJK 106.0041 HIJK 105.9982 GHIJ 105.9977 GHIJ FGHIJ 105.9932 FGHI 105.9899 FGH 105.9878 EFG 105.9806 EF 105.9757 E 105.9683 105.9683 E 105.9445 D 105.9441 D 105.9426 D 105.9320 CD 105.9208 C 105.8846 B 105.2281 A Table B.11: Population mean true breeding value by selection strategy at generation 15 in the single-trait, TRUE scenario. 363 2.1.2. Population maximum true breeding value Figure B.9: Population maximum true breeding value by selection strategy over 60 generations in the single-trait, TRUE scenario. 364 Mean Pop. Selection Max TBV Strategy 104.8293 gwGEBV30d 104.8292 gwGEBV20d 104.8292 gwGEBV15 104.8271 gwGEBV30 104.8265 gwGEBV20 104.8242 gwGEBV25 104.8241 gwGEBV40d 104.8205 gwGEBV35 104.8191 gwGEBV40 104.8186 gwGEBV10 104.8178 gwGEBV10d 104.8140 gwGEBV05 104.8040 GEBV 104.8023 gwGEBV50d 104.7971 gwGEBV45 104.7843 gwGEBV60d 104.7820 gwGEBV50 104.7646 gwGEBV70d 104.7351 OCS 104.7333 gwGEBV80d gwGEBV90d 104.7046 gwGEBV100d 104.6782 104.4668 RS Generation 15 95% Lower CL DF Std. Error 0.00438 1817 104.8207 0.00438 1817 104.8206 0.00438 1817 104.8206 0.00438 1817 104.8185 0.00438 1817 104.8179 0.00438 1817 104.8157 0.00438 1817 104.8155 0.00438 1817 104.8119 0.00438 1817 104.8105 0.00438 1817 104.8100 0.00438 1817 104.8092 0.00438 1817 104.8054 0.00438 1817 104.7954 0.00438 1817 104.7937 0.00438 1817 104.7885 0.00438 1817 104.7758 0.00438 1817 104.7735 0.00438 1817 104.7560 0.00438 1817 104.7265 0.00438 1817 104.7248 0.00438 1817 104.6961 0.00438 1817 104.6697 0.00438 1817 104.4582 Statistical Grouping I I I I I 95% Upper CL 104.8379 104.8378 104.8378 104.8357 104.8351 104.8328 HI 104.8327 HI 104.8290 HI 104.8277 GHI 104.8272 GHI 104.8264 GHI 104.8226 GHI FGH 104.8126 FGH 104.8109 FG 104.8056 EF 104.7929 EF 104.7906 104.7732 E 104.7437 D 104.7419 D 104.7132 C 104.6868 B 104.4754 A Table B.12: Population maximum true breeding value by selection strategy at generation 15 in the single-trait, TRUE scenario. 365 Mean Pop. Selection Max TBV Strategy 105.6360 gwGEBV50d 105.6326 gwGEBV40d 105.6293 gwGEBV30d 105.6280 gwGEBV40 105.6275 gwGEBV30 105.6256 gwGEBV25 105.6246 gwGEBV35 105.6167 gwGEBV20 105.6136 gwGEBV60d 105.6119 gwGEBV20d 105.6090 gwGEBV15 105.6068 gwGEBV45 105.5996 gwGEBV70d 105.5960 gwGEBV50 105.5959 gwGEBV10 105.5892 gwGEBV10d 105.5729 gwGEBV05 105.5693 gwGEBV80d 105.5622 OCS 105.5543 GEBV gwGEBV90d 105.5413 gwGEBV100d 105.5103 105.0358 RS Generation 30 95% Lower CL DF Std. Error 0.00415 1817 105.6279 0.00415 1817 105.6244 0.00415 1817 105.6212 0.00415 1817 105.6198 0.00415 1817 105.6193 0.00415 1817 105.6175 0.00415 1817 105.6165 0.00415 1817 105.6085 0.00415 1817 105.6055 0.00415 1817 105.6037 0.00415 1817 105.6009 0.00415 1817 105.5987 0.00415 1817 105.5915 0.00415 1817 105.5879 0.00415 1817 105.5878 0.00415 1817 105.5810 0.00415 1817 105.5648 0.00415 1817 105.5611 0.00415 1817 105.5540 0.00415 1817 105.5462 0.00415 1817 105.5332 0.00415 1817 105.5021 0.00415 1817 105.0277 Statistical Grouping 95% Upper CL 105.6441 K JK 105.6407 105.6375 IJK 105.6361 HIJK 105.6356 HIJK 105.6337 HIJK 105.6328 HIJK 105.6248 GHIJK 105.6218 GHIJ 105.6200 GHIJ FGHI 105.6172 FGH 105.6150 FG 105.6078 FG 105.6042 FG 105.6041 105.5973 EF 105.5811 DE 105.5774 DE 105.5703 CD 105.5625 CD 105.5495 C 105.5184 B 105.0440 A Table B.13: Population maximum true breeding value by selection strategy at generation 30 in the single-trait, TRUE scenario. 366 Mean Pop. Selection Max TBV Strategy 106.2213 gwGEBV50d 106.2172 gwGEBV60d 106.2113 gwGEBV50 106.2088 gwGEBV70d 106.2047 gwGEBV40 106.2008 gwGEBV80d 106.1923 gwGEBV45 106.1895 gwGEBV35 106.1832 gwGEBV90d 106.1824 gwGEBV30 106.1778 gwGEBV40d 106.1680 gwGEBV25 gwGEBV100d 106.1676 106.1501 gwGEBV30d 106.1473 gwGEBV20 106.1289 gwGEBV15 106.1211 gwGEBV20d 106.1022 OCS 106.0937 gwGEBV10 106.0751 gwGEBV10d 106.0616 gwGEBV05 106.0241 GEBV 105.5017 RS Generation 45 95% Lower CL DF Std. Error 0.00408 1817 106.2133 0.00408 1817 106.2092 0.00408 1817 106.2033 0.00408 1817 106.2008 0.00408 1817 106.1967 0.00408 1817 106.1928 0.00408 1817 106.1843 0.00408 1817 106.1815 0.00408 1817 106.1752 0.00408 1817 106.1744 0.00408 1817 106.1698 0.00408 1817 106.1600 0.00408 1817 106.1596 0.00408 1817 106.1421 0.00408 1817 106.1393 0.00408 1817 106.1209 0.00408 1817 106.1131 0.00408 1817 106.0942 0.00408 1817 106.0857 0.00408 1817 106.0671 0.00408 1817 106.0536 0.00408 1817 106.0161 0.00408 1817 105.4937 Statistical Grouping 95% Upper CL 106.2293 O 106.2252 O 106.2193 NO 106.2168 MNO 106.2127 MNO 106.2088 LMNO 106.2003 KLMN 106.1975 KLM JKL 106.1912 JKL 106.1904 JK 106.1858 IJ 106.1760 IJ 106.1756 106.1581 I 106.1553 HI 106.1369 GH FG 106.1291 106.1102 EF 106.1017 DE 106.0831 CD 106.0696 C 106.0321 B 105.5097 A Table B.14: Population maximum true breeding value by selection strategy at generation 45 in the single-trait, TRUE scenario. 367 Mean Pop. Selection Max TBV Strategy 106.6251 gwGEBV50 106.6152 gwGEBV80d 106.6132 gwGEBV90d gwGEBV70d 106.6125 gwGEBV100d 106.6117 106.6072 gwGEBV45 106.6040 gwGEBV60d 106.5978 gwGEBV40 106.5897 gwGEBV50d 106.5760 gwGEBV35 106.5548 gwGEBV30 106.5338 gwGEBV25 106.5260 gwGEBV40d 106.5007 gwGEBV20 106.4841 gwGEBV30d 106.4637 gwGEBV15 106.4385 OCS 106.4351 gwGEBV20d 106.4110 gwGEBV10 106.3810 gwGEBV10d 106.3604 gwGEBV05 106.3021 GEBV 105.8817 RS Generation 60 95% Lower CL DF Std. Error 0.00401 1817 106.6173 0.00401 1817 106.6074 0.00401 1817 106.6053 0.00401 1817 106.6047 0.00401 1817 106.6038 0.00401 1817 106.5993 0.00401 1817 106.5962 0.00401 1817 106.5899 0.00401 1817 106.5818 0.00401 1817 106.5681 0.00401 1817 106.5470 0.00401 1817 106.5259 0.00401 1817 106.5182 0.00401 1817 106.4929 0.00401 1817 106.4762 0.00401 1817 106.4559 0.00401 1817 106.4306 0.00401 1817 106.4272 0.00401 1817 106.4032 0.00401 1817 106.3731 0.00401 1817 106.3526 0.00401 1817 106.2942 0.00401 1817 105.8738 Statistical Grouping 95% Upper CL 106.6330 N 106.6231 MN 106.6211 MN 106.6204 MN 106.6195 MN LMN 106.6151 LM 106.6119 LM 106.6057 106.5975 KL 106.5838 K J 106.5627 I 106.5416 106.5339 I 106.5086 H 106.4919 GH 106.4716 G F 106.4464 106.4429 F E 106.4189 106.3888 D 106.3683 C 106.3100 B 105.8896 A Table B.15: Population maximum true breeding value by selection strategy at generation 60 in the single-trait, TRUE scenario. 368 2.1.3. Population mean expected heterozygosity Generation 15 Selection Strategy Mean Pop. MEH gwGEBV100d 0.2322 0.2301 OCS 0.2294 gwGEBV90d 0.2269 gwGEBV80d 0.2241 gwGEBV70d 0.2212 RS 0.2211 gwGEBV60d 0.2211 gwGEBV50 0.2188 gwGEBV45 0.2168 gwGEBV50d 0.2145 gwGEBV40 0.2124 gwGEBV35 0.2115 gwGEBV40d 0.2101 gwGEBV30 0.2071 gwGEBV30d 0.2069 gwGEBV25 0.2042 gwGEBV20 0.2015 gwGEBV20d 0.1997 gwGEBV15 0.1965 gwGEBV10 0.1952 gwGEBV10d 0.1904 gwGEBV05 0.1881 GEBV 95% Lower CL DF Std. Error 0.00038 1817 0.2315 0.00038 1817 0.2293 0.00038 1817 0.2287 0.00038 1817 0.2262 0.00038 1817 0.2233 0.00038 1817 0.2205 0.00038 1817 0.2203 0.00038 1817 0.2203 0.00038 1817 0.2180 0.00038 1817 0.2160 0.00038 1817 0.2138 0.00038 1817 0.2117 0.00038 1817 0.2107 0.00038 1817 0.2094 0.00038 1817 0.2063 0.00038 1817 0.2062 0.00038 1817 0.2034 0.00038 1817 0.2008 0.00038 1817 0.1989 0.00038 1817 0.1958 0.00038 1817 0.1944 0.00038 1817 0.1896 0.00038 1817 0.1873 95% Upper CL 0.2330 0.2308 0.2302 0.2277 0.2248 0.2220 0.2218 0.2218 0.2195 0.2175 0.2153 0.2132 0.2122 0.2109 0.2078 0.2077 0.2049 0.2023 0.2004 0.1973 0.1959 0.1912 0.1888 Statistical Grouping P O O N M L L L K J I H GH G F F E D D C C B A Table B.16: Population mean expected heterozygosity by selection strategy at generation 15 in the single-trait, TRUE scenario. 369 Selection Strategy Mean Pop. MEH 0.1871 RS gwGEBV100d 0.1854 0.1812 gwGEBV90d 0.1759 gwGEBV80d 0.1749 gwGEBV50 0.1728 gwGEBV70d 0.1705 gwGEBV45 0.1684 gwGEBV60d 0.1657 gwGEBV40 0.1645 OCS 0.1622 gwGEBV50d 0.1614 gwGEBV35 0.1585 gwGEBV30 0.1553 gwGEBV40d 0.1537 gwGEBV25 0.1490 gwGEBV20 0.1489 gwGEBV30d 0.1447 gwGEBV15 0.1430 gwGEBV20d 0.1390 gwGEBV10 0.1359 gwGEBV10d 0.1341 gwGEBV05 0.1285 GEBV Generation 30 95% Lower CL DF Std. Error 0.00059 1817 0.1860 0.00059 1817 0.1843 0.00059 1817 0.1800 0.00059 1817 0.1747 0.00059 1817 0.1738 0.00059 1817 0.1717 0.00059 1817 0.1694 0.00059 1817 0.1673 0.00059 1817 0.1646 0.00059 1817 0.1634 0.00059 1817 0.1610 0.00059 1817 0.1603 0.00059 1817 0.1574 0.00059 1817 0.1541 0.00059 1817 0.1525 0.00059 1817 0.1478 0.00059 1817 0.1478 0.00059 1817 0.1436 0.00059 1817 0.1419 0.00059 1817 0.1378 0.00059 1817 0.1347 0.00059 1817 0.1330 0.00059 1817 0.1273 95% Upper CL 0.1883 0.1866 0.1824 0.1770 0.1761 0.1740 0.1717 0.1696 0.1669 0.1657 0.1633 0.1626 0.1597 0.1564 0.1548 0.1501 0.1501 0.1459 0.1442 0.1402 0.1370 0.1353 0.1296 Statistical Grouping Q Q P O NO MN LM KL JK IJ HI GH G F F E E D D C B B A Table B.17: Population mean expected heterozygosity by selection strategy at generation 30 in the single-trait, TRUE scenario. 370 Selection Strategy Mean Pop. MEH 0.1590 RS gwGEBV100d 0.1362 0.1356 gwGEBV50 0.1308 gwGEBV45 0.1305 gwGEBV90d 0.1264 gwGEBV80d 0.1258 gwGEBV40 0.1243 gwGEBV70d 0.1212 gwGEBV35 0.1202 gwGEBV60d 0.1175 gwGEBV30 0.1143 gwGEBV50d 0.1123 gwGEBV25 0.1099 OCS 0.1077 gwGEBV20 0.1073 gwGEBV40d 0.1030 gwGEBV30d 0.1014 gwGEBV15 0.0972 gwGEBV20d 0.0951 gwGEBV10 0.0916 gwGEBV10d 0.0913 gwGEBV05 0.0858 GEBV Generation 45 95% Lower CL DF Std. Error 0.00067 1817 0.1577 0.00067 1817 0.1349 0.00067 1817 0.1343 0.00067 1817 0.1295 0.00067 1817 0.1292 0.00067 1817 0.1251 0.00067 1817 0.1245 0.00067 1817 0.1230 0.00067 1817 0.1199 0.00067 1817 0.1189 0.00067 1817 0.1162 0.00067 1817 0.1130 0.00067 1817 0.1110 0.00067 1817 0.1086 0.00067 1817 0.1064 0.00067 1817 0.1060 0.00067 1817 0.1017 0.00067 1817 0.1001 0.00067 1817 0.0959 0.00067 1817 0.0938 0.00067 1817 0.0903 0.00067 1817 0.0900 0.00067 1817 0.0845 95% Upper CL 0.1603 0.1375 0.1370 0.1321 0.1318 0.1277 0.1271 0.1256 0.1225 0.1215 0.1189 0.1156 0.1136 0.1112 0.1090 0.1086 0.1043 0.1027 0.0985 0.0964 0.0929 0.0926 0.0871 Statistical Grouping O N N M M L L KL JK IJ HI GH FG EF E E D D C C B B A Table B.18: Population mean expected heterozygosity by selection strategy at generation 45 in the single-trait, TRUE scenario. 371 2.1.4. Population upper selection limit Generation 15 Selection Strategy Mean Pop. USL gwGEBV100d 107.3431 107.3287 gwGEBV90d 107.3163 gwGEBV80d 107.3009 gwGEBV70d 107.2747 gwGEBV60d 107.2714 gwGEBV50 107.2541 gwGEBV50d 107.2478 gwGEBV45 107.2287 RS 107.2174 gwGEBV40 107.2127 OCS 107.2002 gwGEBV35 107.1961 gwGEBV40d 107.1664 gwGEBV30 107.1462 gwGEBV30d 107.1436 gwGEBV25 107.1333 gwGEBV20 107.1110 gwGEBV20d 107.0980 gwGEBV15 107.0657 gwGEBV10d 107.0598 gwGEBV10 107.0280 gwGEBV05 107.0028 GEBV 95% Lower CL DF Std. Error 0.00359 1817 107.3360 0.00359 1817 107.3217 0.00359 1817 107.3093 0.00359 1817 107.2939 0.00359 1817 107.2677 0.00359 1817 107.2643 0.00359 1817 107.2471 0.00359 1817 107.2407 0.00359 1817 107.2216 0.00359 1817 107.2104 0.00359 1817 107.2057 0.00359 1817 107.1931 0.00359 1817 107.1891 0.00359 1817 107.1594 0.00359 1817 107.1391 0.00359 1817 107.1366 0.00359 1817 107.1262 0.00359 1817 107.1040 0.00359 1817 107.0910 0.00359 1817 107.0587 0.00359 1817 107.0527 0.00359 1817 107.0210 0.00359 1817 106.9958 Statistical Grouping 95% Upper CL 107.3501 O 107.3358 NO 107.3233 MN 107.3080 M 107.2818 L 107.2784 KL JK 107.2611 J 107.2548 107.2357 I 107.2245 HI 107.2198 GHI 107.2072 GH 107.2031 G F 107.1735 E 107.1532 E 107.1507 E 107.1403 107.1181 D 107.1050 D 107.0727 C 107.0668 C 107.0351 B 107.0099 A Table B.19: Population upper selection limit by selection strategy at generation 15 in the single- trait, TRUE scenario. 372 Selection Strategy Mean Pop. USL gwGEBV100d 107.2986 107.2788 gwGEBV90d 107.2581 gwGEBV80d 107.2308 gwGEBV70d 107.2111 gwGEBV50 107.1936 gwGEBV60d 107.1723 gwGEBV45 107.1523 gwGEBV50d 107.1300 gwGEBV40 107.0909 gwGEBV35 107.0733 RS 107.0580 gwGEBV40d 107.0500 gwGEBV30 107.0164 gwGEBV25 106.9999 OCS 106.9841 gwGEBV30d 106.9796 gwGEBV20 106.9220 gwGEBV15 106.9148 gwGEBV20d 106.8653 gwGEBV10 106.8411 gwGEBV10d 106.7851 gwGEBV05 106.7321 GEBV Generation 30 95% Lower CL DF Std. Error 0.00458 1817 107.2896 0.00458 1817 107.2698 0.00458 1817 107.2491 0.00458 1817 107.2218 0.00458 1817 107.2021 0.00458 1817 107.1846 0.00458 1817 107.1633 0.00458 1817 107.1433 0.00458 1817 107.1211 0.00458 1817 107.0819 0.00458 1817 107.0643 0.00458 1817 107.0490 0.00458 1817 107.0410 0.00458 1817 107.0074 0.00458 1817 106.9909 0.00458 1817 106.9752 0.00458 1817 106.9707 0.00458 1817 106.9130 0.00458 1817 106.9058 0.00458 1817 106.8563 0.00458 1817 106.8321 0.00458 1817 106.7762 0.00458 1817 106.7231 Statistical Grouping P 95% Upper CL 107.3076 107.2878 OP 107.2670 O 107.2397 N 107.2201 MN 107.2026 LM 107.1813 KL JK 107.1613 J 107.1390 107.0999 I 107.0823 HI 107.0670 H 107.0590 H 107.0254 G 107.0089 FG 106.9931 F 106.9886 F 106.9310 E E 106.9238 106.8743 D 106.8501 C 106.7941 B 106.7411 A Table B.20: Population upper selection limit by selection strategy at generation 30 in the single- trait, TRUE scenario. 373 Selection Strategy Mean Pop. USL gwGEBV100d 107.2369 107.2051 gwGEBV90d 107.1832 gwGEBV80d 107.1729 gwGEBV50 107.1421 gwGEBV70d 107.1258 gwGEBV45 107.1011 gwGEBV60d 107.0713 gwGEBV40 107.0443 gwGEBV50d 107.0282 gwGEBV35 106.9784 RS 106.9765 gwGEBV30 106.9384 gwGEBV40d 106.9341 gwGEBV25 106.8829 gwGEBV20 106.8605 gwGEBV30d 106.8196 OCS 106.8082 gwGEBV15 106.7673 gwGEBV20d 106.7225 gwGEBV10 106.6827 gwGEBV10d 106.6506 gwGEBV05 106.5664 GEBV Generation 45 95% Lower CL DF Std. Error 0.00517 1817 107.2268 0.00517 1817 107.1950 0.00517 1817 107.1731 0.00517 1817 107.1628 0.00517 1817 107.1319 0.00517 1817 107.1156 0.00517 1817 107.0910 0.00517 1817 107.0612 0.00517 1817 107.0341 0.00517 1817 107.0180 0.00517 1817 106.9682 0.00517 1817 106.9663 0.00517 1817 106.9282 0.00517 1817 106.9239 0.00517 1817 106.8728 0.00517 1817 106.8504 0.00517 1817 106.8095 0.00517 1817 106.7980 0.00517 1817 106.7571 0.00517 1817 106.7124 0.00517 1817 106.6726 0.00517 1817 106.6405 0.00517 1817 106.5562 Statistical 95% Grouping Upper CL P 107.2471 107.2153 O 107.1933 NO 107.1831 N 107.1522 M LM 107.1359 107.1113 L 107.0814 K J 107.0544 J 107.0383 I 106.9885 I 106.9866 106.9485 H 106.9442 H 106.8931 G 106.8707 G F 106.8298 106.8183 F E 106.7774 106.7327 D 106.6929 C 106.6607 B 106.5765 A Table B.21: Population upper selection limit by selection strategy at generation 45 in the single- trait, TRUE scenario. 374 2.1.5. Population additive genetic variance Figure B.10: Population additive genetic variance by selection strategy over 60 generations in the single-trait, TRUE scenario. 375 Selection Strategy Mean Pop. Genetic Var. gwGEBV100d 0.0180 0.0169 gwGEBV90d 0.0166 gwGEBV80d 0.0156 gwGEBV70d 0.0151 RS 0.0138 gwGEBV50 0.0138 gwGEBV60d 0.0136 gwGEBV45 0.0134 OCS 0.0130 gwGEBV50d 0.0126 gwGEBV40 0.0121 gwGEBV35 0.0121 gwGEBV40d 0.0115 gwGEBV30 0.0110 gwGEBV30d 0.0108 gwGEBV25 0.0106 gwGEBV20 0.0105 gwGEBV20d 0.0102 gwGEBV15 0.0099 gwGEBV10 0.0098 gwGEBV10d 0.0095 gwGEBV05 0.0093 GEBV Generation 15 95% Lower CL DF Std. Error 0.00014 1817 0.0177 0.00014 1817 0.0167 0.00014 1817 0.0163 0.00014 1817 0.0153 0.00014 1817 0.0148 0.00014 1817 0.0135 0.00014 1817 0.0135 0.00014 1817 0.0133 0.00014 1817 0.0131 0.00014 1817 0.0127 0.00014 1817 0.0123 0.00014 1817 0.0118 0.00014 1817 0.0118 0.00014 1817 0.0112 0.00014 1817 0.0107 0.00014 1817 0.0106 0.00014 1817 0.0104 0.00014 1817 0.0102 0.00014 1817 0.0099 0.00014 1817 0.0096 0.00014 1817 0.0095 0.00014 1817 0.0092 0.00014 1817 0.0090 95% Upper CL 0.0182 0.0172 0.0169 0.0158 0.0154 0.0141 0.0141 0.0139 0.0137 0.0133 0.0129 0.0123 0.0123 0.0118 0.0113 0.0111 0.0109 0.0108 0.0105 0.0102 0.0101 0.0098 0.0096 Statistical Grouping N M M L L K K JK JK IJ HI GH GH FG EF DEF DE CDE BCD ABC ABC AB A Table B.22: Population additive genetic variance by selection strategy at generation 15 in the single-trait, TRUE scenario. 376 Selection Strategy Mean Pop. Genetic Var. gwGEBV100d 0.0101 0.0099 RS 0.0093 gwGEBV90d 0.0086 gwGEBV80d 0.0081 gwGEBV50 0.0079 gwGEBV70d 0.0078 gwGEBV45 0.0073 gwGEBV60d 0.0072 gwGEBV40 0.0069 gwGEBV50d 0.0066 gwGEBV35 0.0062 gwGEBV30 0.0060 OCS 0.0060 gwGEBV40d 0.0060 gwGEBV25 0.0057 gwGEBV30d 0.0056 gwGEBV20 0.0055 gwGEBV15 0.0053 gwGEBV20d 0.0052 gwGEBV10 0.0050 gwGEBV10d 0.0049 gwGEBV05 0.0047 GEBV Generation 30 95% Lower CL DF Std. Error 0.00009 1817 0.0099 0.00009 1817 0.0097 0.00009 1817 0.0091 0.00009 1817 0.0084 0.00009 1817 0.0080 0.00009 1817 0.0077 0.00009 1817 0.0076 0.00009 1817 0.0072 0.00009 1817 0.0070 0.00009 1817 0.0067 0.00009 1817 0.0065 0.00009 1817 0.0061 0.00009 1817 0.0059 0.00009 1817 0.0058 0.00009 1817 0.0058 0.00009 1817 0.0056 0.00009 1817 0.0054 0.00009 1817 0.0053 0.00009 1817 0.0051 0.00009 1817 0.0050 0.00009 1817 0.0048 0.00009 1817 0.0047 0.00009 1817 0.0045 95% Upper CL 0.0103 0.0100 0.0095 0.0088 0.0083 0.0081 0.0080 0.0075 0.0074 0.0070 0.0068 0.0064 0.0062 0.0062 0.0062 0.0059 0.0058 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 Statistical Grouping O O N M LM L KL JK IJ HI GH FG EF EF EF DE CDE CD BCD BC AB AB A Table B.23: Population additive genetic variance by selection strategy at generation 30 in the single-trait, TRUE scenario. 377 Selection Strategy Mean Pop. Genetic Var. 0.0065 RS gwGEBV100d 0.0045 0.0044 gwGEBV50 0.0042 gwGEBV90d 0.0041 gwGEBV45 0.0039 gwGEBV80d 0.0036 gwGEBV40 0.0035 gwGEBV70d 0.0033 gwGEBV35 0.0033 gwGEBV60d 0.0031 gwGEBV30 0.0030 gwGEBV50d 0.0028 gwGEBV25 0.0026 gwGEBV40d 0.0026 gwGEBV20 0.0024 OCS 0.0024 gwGEBV15 0.0023 gwGEBV30d 0.0022 gwGEBV20d 0.0022 gwGEBV10 0.0020 gwGEBV05 0.0020 gwGEBV10d 0.0019 GEBV Generation 45 95% Lower CL DF Std. Error 0.00005 1817 0.0064 0.00005 1817 0.0044 0.00005 1817 0.0043 0.00005 1817 0.0041 0.00005 1817 0.0040 0.00005 1817 0.0038 0.00005 1817 0.0035 0.00005 1817 0.0034 0.00005 1817 0.0032 0.00005 1817 0.0032 0.00005 1817 0.0030 0.00005 1817 0.0029 0.00005 1817 0.0027 0.00005 1817 0.0025 0.00005 1817 0.0025 0.00005 1817 0.0023 0.00005 1817 0.0023 0.00005 1817 0.0022 0.00005 1817 0.0021 0.00005 1817 0.0021 0.00005 1817 0.0019 0.00005 1817 0.0019 0.00005 1817 0.0018 95% Upper CL 0.0065 0.0046 0.0045 0.0043 0.0042 0.0040 0.0037 0.0036 0.0034 0.0034 0.0032 0.0031 0.0029 0.0027 0.0027 0.0025 0.0025 0.0024 0.0023 0.0023 0.0021 0.0021 0.0020 Statistical Grouping O N MN LM L L K JK IJ IJ HI GH FG EF EF DE CDE CD BCD BC AB AB A Table B.24: Population additive genetic variance by selection strategy at generation 45 in the single-trait, TRUE scenario. 378 Selection Strategy Mean Pop. Genetic Var. 0.0043 RS 0.0021 gwGEBV50 gwGEBV45 0.0019 gwGEBV100d 0.0017 0.0017 gwGEBV40 0.0016 gwGEBV90d 0.0015 gwGEBV35 0.0014 gwGEBV80d 0.0014 gwGEBV70d 0.0013 gwGEBV30 0.0013 gwGEBV25 0.0012 gwGEBV60d 0.0011 gwGEBV50d 0.0011 gwGEBV20 0.0010 gwGEBV40d 0.0010 gwGEBV15 0.0009 OCS 0.0009 gwGEBV30d 0.0008 gwGEBV10 0.0008 gwGEBV20d 0.0007 gwGEBV10d 0.0007 gwGEBV05 0.0006 GEBV Generation 60 95% Lower CL DF Std. Error 0.00003 1817 0.0042 0.00003 1817 0.0021 0.00003 1817 0.0019 0.00003 1817 0.0017 0.00003 1817 0.0016 0.00003 1817 0.0015 0.00003 1817 0.0015 0.00003 1817 0.0014 0.00003 1817 0.0013 0.00003 1817 0.0013 0.00003 1817 0.0012 0.00003 1817 0.0012 0.00003 1817 0.0011 0.00003 1817 0.0011 0.00003 1817 0.0009 0.00003 1817 0.0009 0.00003 1817 0.0009 0.00003 1817 0.0008 0.00003 1817 0.0008 0.00003 1817 0.0007 0.00003 1817 0.0007 0.00003 1817 0.0006 0.00003 1817 0.0006 95% Upper CL 0.0043 0.0022 0.0020 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0014 0.0013 0.0013 0.0012 0.0012 0.0010 0.0010 0.0010 0.0009 0.0009 0.0008 0.0008 0.0007 0.0007 Statistical Grouping R Q P O NO MN LM KL JK JK IJ IJ HI GH FG EF EF DEF CDE BCD BC AB A Table B.25: Population additive genetic variance by selection strategy at generation 60 in the single-trait, TRUE scenario. 379 2.1.6. Population additive genic variance Figure B.11: Population additive genic variance by selection strategy over 60 generations in the single-trait, TRUE scenario. 380 Selection Strategy Mean Pop. Genic Var. gwGEBV100d 0.0300 0.0294 gwGEBV90d 0.0288 gwGEBV80d 0.0279 gwGEBV70d 0.0269 gwGEBV60d 0.0269 gwGEBV50 0.0262 gwGEBV45 0.0259 gwGEBV50d 0.0258 RS 0.0256 OCS 0.0251 gwGEBV40 0.0246 gwGEBV35 0.0244 gwGEBV40d 0.0240 gwGEBV30 0.0235 gwGEBV30d 0.0233 gwGEBV25 0.0227 gwGEBV20 0.0223 gwGEBV20d 0.0220 gwGEBV15 0.0213 gwGEBV10 0.0211 gwGEBV10d 0.0204 gwGEBV05 0.0199 GEBV Generation 15 95% Lower CL DF Std. Error 0.00006 1817 0.0298 0.00006 1817 0.0293 0.00006 1817 0.0287 0.00006 1817 0.0278 0.00006 1817 0.0268 0.00006 1817 0.0268 0.00006 1817 0.0261 0.00006 1817 0.0258 0.00006 1817 0.0257 0.00006 1817 0.0255 0.00006 1817 0.0250 0.00006 1817 0.0245 0.00006 1817 0.0243 0.00006 1817 0.0239 0.00006 1817 0.0234 0.00006 1817 0.0232 0.00006 1817 0.0226 0.00006 1817 0.0222 0.00006 1817 0.0218 0.00006 1817 0.0212 0.00006 1817 0.0210 0.00006 1817 0.0203 0.00006 1817 0.0198 95% Upper CL 0.0301 0.0295 0.0289 0.0280 0.0270 0.0270 0.0263 0.0261 0.0259 0.0257 0.0252 0.0247 0.0245 0.0241 0.0236 0.0234 0.0228 0.0224 0.0221 0.0214 0.0212 0.0205 0.0200 Statistical Grouping R Q P O N N M LM KL K J I I H G G F E D C C B A Table B.26: Population additive genic variance by selection strategy at generation 15 in the single-trait, TRUE scenario. 381 Selection Strategy Mean Pop. Genic Var. gwGEBV100d 0.0186 0.0183 RS 0.0178 gwGEBV90d 0.0169 gwGEBV80d 0.0162 gwGEBV50 0.0160 gwGEBV70d 0.0153 gwGEBV45 0.0150 gwGEBV60d 0.0143 gwGEBV40 0.0141 gwGEBV50d 0.0136 gwGEBV35 0.0130 gwGEBV30 0.0127 gwGEBV40d 0.0123 gwGEBV25 0.0123 OCS 0.0118 gwGEBV20 0.0118 gwGEBV30d 0.0112 gwGEBV15 0.0109 gwGEBV20d 0.0105 gwGEBV10 0.0102 gwGEBV10d 0.0101 gwGEBV05 0.0094 GEBV Generation 30 95% Lower CL DF Std. Error 0.00007 1817 0.0185 0.00007 1817 0.0182 0.00007 1817 0.0177 0.00007 1817 0.0167 0.00007 1817 0.0161 0.00007 1817 0.0159 0.00007 1817 0.0152 0.00007 1817 0.0149 0.00007 1817 0.0141 0.00007 1817 0.0139 0.00007 1817 0.0134 0.00007 1817 0.0128 0.00007 1817 0.0126 0.00007 1817 0.0122 0.00007 1817 0.0122 0.00007 1817 0.0116 0.00007 1817 0.0116 0.00007 1817 0.0110 0.00007 1817 0.0108 0.00007 1817 0.0104 0.00007 1817 0.0100 0.00007 1817 0.0100 0.00007 1817 0.0092 95% Upper CL 0.0188 0.0185 0.0180 0.0170 0.0163 0.0162 0.0155 0.0151 0.0144 0.0142 0.0137 0.0131 0.0128 0.0125 0.0125 0.0119 0.0119 0.0113 0.0111 0.0107 0.0103 0.0102 0.0095 Statistical Grouping O O N M L L K K J J I H GH FG F E E D D C B B A Table B.27: Population additive genic variance by selection strategy at generation 30 in the single-trait, TRUE scenario. 382 Selection Strategy Mean Pop. Genic Var. 0.0125 RS gwGEBV100d 0.0092 0.0087 gwGEBV50 0.0086 gwGEBV90d 0.0082 gwGEBV45 0.0080 gwGEBV80d 0.0075 gwGEBV70d 0.0074 gwGEBV40 0.0070 gwGEBV60d 0.0069 gwGEBV35 0.0064 gwGEBV30 0.0063 gwGEBV50d 0.0060 gwGEBV25 0.0056 gwGEBV20 0.0056 gwGEBV40d 0.0050 gwGEBV30d 0.0050 gwGEBV15 0.0049 OCS 0.0045 gwGEBV20d 0.0045 gwGEBV10 0.0041 gwGEBV10d 0.0041 gwGEBV05 0.0037 GEBV Generation 45 95% Lower CL DF Std. Error 0.00005 1817 0.0124 0.00005 1817 0.0091 0.00005 1817 0.0086 0.00005 1817 0.0085 0.00005 1817 0.0081 0.00005 1817 0.0079 0.00005 1817 0.0074 0.00005 1817 0.0072 0.00005 1817 0.0069 0.00005 1817 0.0068 0.00005 1817 0.0063 0.00005 1817 0.0062 0.00005 1817 0.0059 0.00005 1817 0.0055 0.00005 1817 0.0055 0.00005 1817 0.0049 0.00005 1817 0.0049 0.00005 1817 0.0048 0.00005 1817 0.0044 0.00005 1817 0.0044 0.00005 1817 0.0040 0.00005 1817 0.0040 0.00005 1817 0.0036 95% Upper CL 0.0126 0.0093 0.0088 0.0087 0.0083 0.0081 0.0076 0.0075 0.0071 0.0070 0.0065 0.0064 0.0061 0.0057 0.0057 0.0051 0.0051 0.0051 0.0046 0.0046 0.0042 0.0042 0.0038 Statistical Grouping M L K K J J I I H H G G F E E D D D C C B B A Table B.28: Population additive genic variance by selection strategy at generation 45 in the single-trait, TRUE scenario. 383 Selection Strategy Mean Pop. Genic Var. 0.0078 RS 0.0042 gwGEBV50 gwGEBV45 0.0039 gwGEBV100d 0.0036 0.0033 gwGEBV40 0.0032 gwGEBV90d 0.0031 gwGEBV35 0.0030 gwGEBV80d 0.0028 gwGEBV30 0.0028 gwGEBV70d 0.0026 gwGEBV60d 0.0025 gwGEBV25 0.0024 gwGEBV20 0.0023 gwGEBV50d 0.0020 gwGEBV40d 0.0020 gwGEBV15 0.0018 gwGEBV30d 0.0017 OCS 0.0016 gwGEBV10 0.0015 gwGEBV20d 0.0014 gwGEBV10d 0.0013 gwGEBV05 0.0011 GEBV Generation 60 95% Lower CL DF Std. Error 0.00004 1817 0.0078 0.00004 1817 0.0041 0.00004 1817 0.0039 0.00004 1817 0.0035 0.00004 1817 0.0033 0.00004 1817 0.0032 0.00004 1817 0.0030 0.00004 1817 0.0030 0.00004 1817 0.0027 0.00004 1817 0.0027 0.00004 1817 0.0025 0.00004 1817 0.0025 0.00004 1817 0.0023 0.00004 1817 0.0022 0.00004 1817 0.0019 0.00004 1817 0.0019 0.00004 1817 0.0017 0.00004 1817 0.0016 0.00004 1817 0.0016 0.00004 1817 0.0015 0.00004 1817 0.0013 0.00004 1817 0.0013 0.00004 1817 0.0011 95% Upper CL 0.0079 0.0043 0.0040 0.0036 0.0034 0.0033 0.0032 0.0031 0.0028 0.0028 0.0027 0.0026 0.0024 0.0024 0.0021 0.0020 0.0019 0.0018 0.0017 0.0016 0.0015 0.0014 0.0012 Statistical Grouping R Q P O N MN LM L K K JK IJ HI H G FG EF DE DE CD BC B A Table B.29: Population additive genic variance by selection strategy at generation 60 in the single-trait, TRUE scenario. 384 2.1.7. Population Bulmer effect Figure B.12: Population Bulmer effect by selection strategy over 60 generations in the single- trait, TRUE scenario. 385 Selection Strategy Mean Pop. Bulmer Effect gwGEBV100d 0.6000 0.5846 RS 0.5769 gwGEBV80d 0.5755 gwGEBV90d 0.5582 gwGEBV70d 0.5243 OCS 0.5181 gwGEBV45 0.5140 gwGEBV50 0.5132 gwGEBV60d 0.5023 gwGEBV40 0.5005 gwGEBV50d 0.4943 gwGEBV40d 0.4910 gwGEBV35 0.4790 gwGEBV30 0.4710 gwGEBV20d 0.4685 gwGEBV30d 0.4680 gwGEBV20 0.4674 GEBV 0.4657 gwGEBV25 0.4655 gwGEBV05 0.4651 gwGEBV10d 0.4646 gwGEBV10 0.4641 gwGEBV15 95% Lower CL DF Generation 15 Std. Error 0.00547 1817 0.5892 0.00547 1817 0.5738 0.00547 1817 0.5662 0.00547 1817 0.5648 0.00547 1817 0.5474 0.00547 1817 0.5136 0.00547 1817 0.5073 0.00547 1817 0.5033 0.00547 1817 0.5025 0.00547 1817 0.4916 0.00547 1817 0.4897 0.00547 1817 0.4836 0.00547 1817 0.4803 0.00547 1817 0.4683 0.00547 1817 0.4603 0.00547 1817 0.4577 0.00547 1817 0.4573 0.00547 1817 0.4567 0.00547 1817 0.4549 0.00547 1817 0.4548 0.00547 1817 0.4544 0.00547 1817 0.4539 0.00547 1817 0.4534 95% Upper CL 0.6107 0.5953 0.5876 0.5862 0.5689 0.5351 0.5288 0.5248 0.5239 0.5131 0.5112 0.5050 0.5018 0.4897 0.4817 0.4792 0.4787 0.4782 0.4764 0.4763 0.4758 0.4753 0.4748 Statistical Grouping G FG FG FG F E DE DE DE CDE CDE BCD ABCD ABC AB AB AB AB A A A A A Table B.30: Population Bulmer effect by selection strategy at generation 15 in the single-trait, TRUE scenario. 386 Selection Strategy Mean Pop. Bulmer Effect gwGEBV100d 0.5436 0.5371 RS 0.5231 gwGEBV90d 0.5114 gwGEBV80d 0.5084 gwGEBV45 0.5041 gwGEBV40 0.5034 gwGEBV50 0.4990 GEBV 0.4938 gwGEBV10 0.4937 gwGEBV70d 0.4922 gwGEBV15 0.4909 gwGEBV35 0.4897 OCS 0.4897 gwGEBV05 0.4896 gwGEBV10d 0.4894 gwGEBV60d 0.4887 gwGEBV30d 0.4875 gwGEBV50d 0.4864 gwGEBV25 0.4847 gwGEBV20d 0.4821 gwGEBV30 0.4771 gwGEBV20 0.4748 gwGEBV40d 95% Lower CL DF Generation 30 Std. Error 0.00660 1817 0.5307 0.00660 1817 0.5242 0.00660 1817 0.5101 0.00660 1817 0.4985 0.00660 1817 0.4954 0.00660 1817 0.4911 0.00660 1817 0.4905 0.00660 1817 0.4860 0.00660 1817 0.4809 0.00660 1817 0.4808 0.00660 1817 0.4792 0.00660 1817 0.4780 0.00660 1817 0.4767 0.00660 1817 0.4767 0.00660 1817 0.4767 0.00660 1817 0.4764 0.00660 1817 0.4758 0.00660 1817 0.4746 0.00660 1817 0.4735 0.00660 1817 0.4718 0.00660 1817 0.4692 0.00660 1817 0.4641 0.00660 1817 0.4619 95% Upper CL 0.5566 0.5501 0.5360 0.5243 0.5213 0.5170 0.5163 0.5119 0.5068 0.5067 0.5051 0.5039 0.5026 0.5026 0.5025 0.5023 0.5016 0.5004 0.4994 0.4977 0.4950 0.4900 0.4877 Statistical Grouping E DE CDE BCDE ABCD ABCD ABCD ABC ABC ABC ABC ABC ABC ABC ABC ABC AB AB AB AB AB A A Table B.31: Population Bulmer effect by selection strategy at generation 30 in the single-trait, TRUE scenario. 387 Selection Strategy Mean Pop. Bulmer Effect 0.5170 RS 0.5149 GEBV 0.5009 gwGEBV50 0.4987 gwGEBV05 0.4987 gwGEBV45 gwGEBV40 0.4944 gwGEBV100d 0.4941 0.4904 OCS 0.4893 gwGEBV80d 0.4872 gwGEBV35 0.4855 gwGEBV90d 0.4841 gwGEBV30 0.4832 gwGEBV10 0.4827 gwGEBV10d 0.4795 gwGEBV50d 0.4774 gwGEBV20d 0.4752 gwGEBV40d 0.4743 gwGEBV60d 0.4738 gwGEBV15 0.4702 gwGEBV20 0.4689 gwGEBV70d 0.4686 gwGEBV25 0.4644 gwGEBV30d 95% Lower CL DF Generation 45 Std. Error 0.00714 1817 0.5030 0.00714 1817 0.5009 0.00714 1817 0.4869 0.00714 1817 0.4847 0.00714 1817 0.4847 0.00714 1817 0.4804 0.00714 1817 0.4801 0.00714 1817 0.4764 0.00714 1817 0.4753 0.00714 1817 0.4732 0.00714 1817 0.4715 0.00714 1817 0.4701 0.00714 1817 0.4692 0.00714 1817 0.4687 0.00714 1817 0.4655 0.00714 1817 0.4634 0.00714 1817 0.4612 0.00714 1817 0.4603 0.00714 1817 0.4598 0.00714 1817 0.4562 0.00714 1817 0.4549 0.00714 1817 0.4546 0.00714 1817 0.4504 95% Upper CL 0.5310 0.5289 0.5149 0.5128 0.5127 0.5084 0.5081 0.5044 0.5033 0.5012 0.4995 0.4981 0.4972 0.4967 0.4935 0.4914 0.4892 0.4883 0.4878 0.4842 0.4829 0.4826 0.4784 Statistical Grouping C BC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC AB A A A A A A A A Table B.32: Population Bulmer effect by selection strategy at generation 45 in the single-trait, TRUE scenario. 388 Selection Strategy Mean Pop. Bulmer Effect 0.5508 GEBV 0.5468 OCS 0.5452 RS 0.5326 gwGEBV10d 0.5295 gwGEBV05 0.5129 gwGEBV20d 0.5118 gwGEBV10 0.5067 gwGEBV30d 0.5026 gwGEBV50d 0.5023 gwGEBV50 0.5005 gwGEBV25 0.4982 gwGEBV40 0.4954 gwGEBV40d 0.4928 gwGEBV45 0.4923 gwGEBV70d 0.4905 gwGEBV35 0.4896 gwGEBV15 0.4880 gwGEBV90d 0.4832 gwGEBV30 gwGEBV60d 0.4821 gwGEBV100d 0.4813 0.4743 gwGEBV20 0.4682 gwGEBV80d 95% Lower CL DF Generation 60 Std. Error 0.00827 1817 0.5346 0.00827 1817 0.5306 0.00827 1817 0.5290 0.00827 1817 0.5164 0.00827 1817 0.5133 0.00827 1817 0.4967 0.00827 1817 0.4956 0.00827 1817 0.4904 0.00827 1817 0.4863 0.00827 1817 0.4861 0.00827 1817 0.4843 0.00827 1817 0.4820 0.00827 1817 0.4792 0.00827 1817 0.4766 0.00827 1817 0.4761 0.00827 1817 0.4742 0.00827 1817 0.4734 0.00827 1817 0.4718 0.00827 1817 0.4670 0.00827 1817 0.4659 0.00827 1817 0.4651 0.00827 1817 0.4581 0.00827 1817 0.4520 95% Upper CL 0.5670 0.5630 0.5615 0.5488 0.5458 0.5291 0.5280 0.5229 0.5188 0.5185 0.5167 0.5144 0.5116 0.5090 0.5085 0.5067 0.5059 0.5042 0.4994 0.4983 0.4975 0.4905 0.4844 Statistical Grouping F EF EF DEF CDEF BCDEF BCDEF ABCDE ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABC ABC AB AB AB AB A Table B.33: Population Bulmer effect by selection strategy at generation 60 in the single-trait, TRUE scenario. 389 2.2. EST scenario results 2.2.1. Population mean true breeding value Generation 15 Selection Strategy Mean Pop. Mean TBV 104.2848 GEBV 104.2510 gwGEBV05 104.2476 OCS 104.1850 gwGEBV10d 104.1620 gwGEBV10 104.0646 gwGEBV15 104.0191 gwGEBV20d 103.9806 gwGEBV20 103.9252 gwGEBV25 103.9108 gwGEBV30d 103.8838 gwGEBV30 103.8505 gwGEBV40d 103.8491 gwGEBV35 103.8271 gwGEBV40 103.8247 RS 103.8142 gwGEBV50d 103.8067 gwGEBV45 103.7999 gwGEBV50 103.7919 gwGEBV60d 103.7717 gwGEBV70d 103.7626 gwGEBV80d 103.7541 gwGEBV90d gwGEBV100d 103.7463 95% Lower CL DF Std. Error 0.00251 1817 104.2799 0.00251 1817 104.2460 0.00251 1817 104.2426 0.00251 1817 104.1800 0.00251 1817 104.1571 0.00251 1817 104.0596 0.00251 1817 104.0142 0.00251 1817 103.9756 0.00251 1817 103.9203 0.00251 1817 103.9059 0.00251 1817 103.8789 0.00251 1817 103.8456 0.00251 1817 103.8442 0.00251 1817 103.8222 0.00251 1817 103.8198 0.00251 1817 103.8093 0.00251 1817 103.8018 0.00251 1817 103.7950 0.00251 1817 103.7870 0.00251 1817 103.7668 0.00251 1817 103.7577 0.00251 1817 103.7492 0.00251 1817 103.7414 Statistical Grouping 95% Upper CL 104.2897 R 104.2559 Q 104.2525 Q 104.1899 P 104.1670 O 104.0695 N 104.0241 M L 103.9855 103.9301 K J 103.9157 103.8887 I 103.8554 H 103.8540 H 103.8320 G 103.8296 G FG 103.8192 103.8116 EF 103.8049 DE 103.7968 D 103.7766 C 103.7676 BC 103.7590 AB 103.7512 A Table B.34: Population mean true breeding value by selection strategy at generation 15 in the single-trait, EST scenario. 390 Selection Strategy Mean Pop. Mean TBV 104.9952 OCS 104.9881 GEBV 104.9556 gwGEBV05 104.9121 gwGEBV10d 104.8435 gwGEBV10 104.7242 gwGEBV20d 104.6984 gwGEBV15 104.5732 gwGEBV20 104.5429 gwGEBV30d 104.4757 gwGEBV25 104.4218 gwGEBV40d 104.4058 gwGEBV30 104.3553 gwGEBV35 104.3471 gwGEBV50d 104.3111 gwGEBV40 104.2968 gwGEBV60d 104.2896 RS 104.2728 gwGEBV45 104.2591 gwGEBV50 104.2552 gwGEBV70d 104.2251 gwGEBV80d 104.2088 gwGEBV90d gwGEBV100d 104.1923 Generation 30 95% Lower CL DF Std. Error 0.00362 1817 104.9881 0.00362 1817 104.9810 0.00362 1817 104.9485 0.00362 1817 104.9050 0.00362 1817 104.8364 0.00362 1817 104.7171 0.00362 1817 104.6913 0.00362 1817 104.5661 0.00362 1817 104.5358 0.00362 1817 104.4686 0.00362 1817 104.4147 0.00362 1817 104.3987 0.00362 1817 104.3482 0.00362 1817 104.3400 0.00362 1817 104.3040 0.00362 1817 104.2897 0.00362 1817 104.2825 0.00362 1817 104.2657 0.00362 1817 104.2520 0.00362 1817 104.2481 0.00362 1817 104.2181 0.00362 1817 104.2017 0.00362 1817 104.1852 Statistical Grouping 95% Upper CL 105.0023 Q 104.9952 Q 104.9627 P 104.9192 O 104.8506 N 104.7313 M 104.7055 L 104.5803 K J 104.5500 104.4828 I 104.4289 H 104.4129 H 104.3624 G 104.3542 G F 104.3182 104.3039 EF 104.2967 DE 104.2799 CD 104.2662 C 104.2623 C 104.2322 B 104.2159 AB 104.1994 A Table B.35: Population mean true breeding value by selection strategy at generation 30 in the single-trait, EST scenario. 391 Selection Strategy Mean Pop. Mean TBV 105.4983 OCS 105.4756 GEBV 105.4626 gwGEBV05 105.4604 gwGEBV10d 105.3499 gwGEBV10 105.3273 gwGEBV20d 105.1984 gwGEBV15 105.1671 gwGEBV30d 105.0534 gwGEBV20 105.0384 gwGEBV40d 104.9351 gwGEBV50d 104.9335 gwGEBV25 104.8470 gwGEBV30 104.8459 gwGEBV60d 104.7846 gwGEBV35 104.7802 gwGEBV70d 104.7331 gwGEBV40 104.7189 gwGEBV80d 104.6831 gwGEBV90d 104.6750 RS 104.6744 gwGEBV45 104.6557 gwGEBV50 gwGEBV100d 104.6523 Generation 45 95% Lower CL DF Std. Error 0.00430 1817 105.4899 0.00430 1817 105.4672 0.00430 1817 105.4542 0.00430 1817 105.4519 0.00430 1817 105.3415 0.00430 1817 105.3188 0.00430 1817 105.1899 0.00430 1817 105.1586 0.00430 1817 105.0450 0.00430 1817 105.0299 0.00430 1817 104.9267 0.00430 1817 104.9250 0.00430 1817 104.8386 0.00430 1817 104.8375 0.00430 1817 104.7761 0.00430 1817 104.7717 0.00430 1817 104.7247 0.00430 1817 104.7105 0.00430 1817 104.6747 0.00430 1817 104.6666 0.00430 1817 104.6660 0.00430 1817 104.6473 0.00430 1817 104.6438 Statistical Grouping 95% Upper CL 105.5068 N 105.4841 M 105.4710 M 105.4688 M L 105.3583 105.3357 K J 105.2068 I 105.1755 105.0618 H 105.0468 H 104.9436 G 104.9419 G F 104.8554 F 104.8543 E 104.7930 104.7886 E 104.7416 D 104.7274 D 104.6916 C 104.6835 BC 104.6829 BC 104.6642 AB 104.6607 A Table B.36: Population mean true breeding value by selection strategy at generation 45 in the single-trait, EST scenario. 392 2.2.2. Population maximum true breeding value Figure B.13: Population maximum true breeding value by selection strategy over 60 generations in the single-trait, EST scenario. 393 Selection Strategy Mean Pop. Max TBV 104.6740 GEBV 104.6597 gwGEBV05 104.6585 OCS 104.6202 gwGEBV10d 104.6084 gwGEBV10 104.5398 gwGEBV15 104.5107 gwGEBV20d 104.4685 gwGEBV20 104.4258 gwGEBV25 104.4126 gwGEBV30d 104.3846 gwGEBV30 104.3616 gwGEBV40d 104.3576 gwGEBV35 104.3296 gwGEBV40 104.3278 gwGEBV50d 104.3158 gwGEBV50 104.3138 gwGEBV45 104.3085 RS 104.3045 gwGEBV60d 104.2796 gwGEBV70d 104.2758 gwGEBV80d 104.2729 gwGEBV90d gwGEBV100d 104.2659 Generation 15 95% Lower CL DF Std. Error 0.00594 1817 104.6624 0.00594 1817 104.6480 0.00594 1817 104.6468 0.00594 1817 104.6086 0.00594 1817 104.5968 0.00594 1817 104.5281 0.00594 1817 104.4991 0.00594 1817 104.4569 0.00594 1817 104.4142 0.00594 1817 104.4010 0.00594 1817 104.3730 0.00594 1817 104.3500 0.00594 1817 104.3459 0.00594 1817 104.3179 0.00594 1817 104.3162 0.00594 1817 104.3042 0.00594 1817 104.3022 0.00594 1817 104.2968 0.00594 1817 104.2929 0.00594 1817 104.2680 0.00594 1817 104.2641 0.00594 1817 104.2613 0.00594 1817 104.2542 Statistical 95% Grouping Upper CL L 104.6857 L 104.6713 104.6701 L 104.6319 K 104.6200 K J 104.5514 J 104.5224 I 104.4802 104.4375 H 104.4243 GH FG 104.3963 F 104.3733 104.3692 EF 104.3412 DE 104.3395 DE 104.3275 D 104.3255 D 104.3201 CD 104.3162 BCD 104.2913 ABC 104.2874 AB 104.2846 A 104.2775 A Table B.37: Population maximum true breeding value by selection strategy at generation 15 in the single-trait, EST scenario. 394 Selection Strategy Mean Pop. Max TBV 105.3003 OCS 105.2881 gwGEBV05 105.2852 GEBV 105.2562 gwGEBV10d 105.2196 gwGEBV10 105.1354 gwGEBV20d 105.1167 gwGEBV15 105.0105 gwGEBV20 105.0043 gwGEBV30d 104.9340 gwGEBV25 104.8905 gwGEBV40d 104.8716 gwGEBV30 104.8255 gwGEBV35 104.8170 gwGEBV50d 104.7929 gwGEBV40 104.7753 gwGEBV60d 104.7463 gwGEBV45 104.7391 gwGEBV70d 104.7371 gwGEBV50 104.7104 RS 104.7032 gwGEBV80d 104.6936 gwGEBV90d gwGEBV100d 104.6759 Generation 30 95% Lower CL DF Std. Error 0.00598 1817 105.2885 0.00598 1817 105.2764 0.00598 1817 105.2735 0.00598 1817 105.2445 0.00598 1817 105.2079 0.00598 1817 105.1237 0.00598 1817 105.1050 0.00598 1817 104.9988 0.00598 1817 104.9926 0.00598 1817 104.9223 0.00598 1817 104.8788 0.00598 1817 104.8599 0.00598 1817 104.8138 0.00598 1817 104.8053 0.00598 1817 104.7812 0.00598 1817 104.7636 0.00598 1817 104.7346 0.00598 1817 104.7274 0.00598 1817 104.7254 0.00598 1817 104.6987 0.00598 1817 104.6915 0.00598 1817 104.6818 0.00598 1817 104.6642 Statistical Grouping 95% Upper CL 105.3120 O 105.2998 O 105.2969 NO 105.2679 N 105.2313 M L 105.1471 105.1284 L 105.0223 K 105.0160 K J 104.9457 I 104.9023 I 104.8833 104.8372 H 104.8288 GH FG 104.8047 104.7871 EF 104.7581 DE 104.7509 CD 104.7488 CD 104.7221 BC 104.7150 AB 104.7053 AB 104.6876 A Table B.38: Population maximum true breeding value by selection strategy at generation 30 in the single-trait, EST scenario. 395 Selection Strategy Mean Pop. Max TBV 105.7307 OCS 105.7213 gwGEBV10d 105.7209 gwGEBV05 105.6995 GEBV 105.6639 gwGEBV10 105.6418 gwGEBV20d 105.5595 gwGEBV15 105.5207 gwGEBV30d 105.4536 gwGEBV20 105.4242 gwGEBV40d 105.3432 gwGEBV25 105.3417 gwGEBV50d 105.2787 gwGEBV60d 105.2633 gwGEBV30 105.2184 gwGEBV70d 105.2121 gwGEBV35 105.1725 gwGEBV40 105.1665 gwGEBV80d 105.1332 gwGEBV90d gwGEBV45 105.1192 gwGEBV100d 105.1048 105.0969 gwGEBV50 105.0617 RS Generation 45 95% Lower CL DF Std. Error 0.00586 1817 105.7192 0.00586 1817 105.7098 0.00586 1817 105.7094 0.00586 1817 105.6880 0.00586 1817 105.6524 0.00586 1817 105.6303 0.00586 1817 105.5480 0.00586 1817 105.5092 0.00586 1817 105.4421 0.00586 1817 105.4127 0.00586 1817 105.3317 0.00586 1817 105.3302 0.00586 1817 105.2672 0.00586 1817 105.2518 0.00586 1817 105.2069 0.00586 1817 105.2006 0.00586 1817 105.1610 0.00586 1817 105.1550 0.00586 1817 105.1217 0.00586 1817 105.1078 0.00586 1817 105.0933 0.00586 1817 105.0854 0.00586 1817 105.0502 Statistical Grouping 95% Upper CL 105.7422 M LM 105.7328 LM 105.7324 105.7110 L 105.6754 K 105.6533 K J 105.5710 I 105.5322 105.4651 H 105.4357 H 105.3547 G 105.3532 G F 105.2902 F 105.2748 E 105.2299 105.2236 E 105.1840 D 105.1780 D 105.1447 C 105.1307 BC 105.1163 BC 105.1084 B 105.0732 A Table B.39: Population maximum true breeding value by selection strategy at generation 45 in the single-trait, EST scenario. 396 Mean Pop. Selection Max TBV Strategy 106.0521 gwGEBV10d 106.0267 gwGEBV05 106.0141 gwGEBV20d 106.0102 OCS 105.9892 gwGEBV10 105.9779 GEBV 105.9551 gwGEBV30d 105.9057 gwGEBV40d 105.8871 gwGEBV15 105.8475 gwGEBV50d 105.7941 gwGEBV60d 105.7846 gwGEBV20 105.7460 gwGEBV70d 105.6983 gwGEBV80d 105.6619 gwGEBV25 gwGEBV90d 105.6589 gwGEBV100d 105.6370 105.5950 gwGEBV30 105.5357 gwGEBV35 105.4935 gwGEBV40 105.4252 gwGEBV45 105.4173 gwGEBV50 105.3505 RS Generation 60 95% Lower CL DF Std. Error 0.00562 1817 106.0411 0.00562 1817 106.0157 0.00562 1817 106.0031 0.00562 1817 105.9992 0.00562 1817 105.9782 0.00562 1817 105.9668 0.00562 1817 105.9440 0.00562 1817 105.8946 0.00562 1817 105.8761 0.00562 1817 105.8365 0.00562 1817 105.7831 0.00562 1817 105.7735 0.00562 1817 105.7350 0.00562 1817 105.6873 0.00562 1817 105.6509 0.00562 1817 105.6479 0.00562 1817 105.6260 0.00562 1817 105.5840 0.00562 1817 105.5246 0.00562 1817 105.4825 0.00562 1817 105.4142 0.00562 1817 105.4063 0.00562 1817 105.3395 Statistical Grouping P 95% Upper CL 106.0632 106.0378 OP 106.0252 NO 106.0212 NO 106.0002 MN LM 105.9889 105.9661 L 105.9167 K 105.8982 K J 105.8586 I 105.8052 I 105.7956 105.7570 H 105.7094 G F 105.6729 F 105.6700 F 105.6480 105.6061 E 105.5467 D 105.5045 C 105.4363 B 105.4284 B 105.3616 A Table B.40: Population maximum true breeding value by selection strategy at generation 60 in the single-trait, EST scenario. 397 2.2.3. Population mean expected heterozygosity Generation 15 Mean Pop. MEH Selection Strategy 0.2615 gwGEBV60d 0.2613 gwGEBV50 0.2609 gwGEBV70d 0.2608 gwGEBV45 0.2608 gwGEBV40 0.2608 gwGEBV50d 0.2600 gwGEBV35 0.2600 gwGEBV40d 0.2599 gwGEBV80d 0.2594 gwGEBV90d gwGEBV100d 0.2586 0.2581 gwGEBV30 0.2567 gwGEBV30d 0.2563 gwGEBV25 0.2524 gwGEBV20 0.2489 gwGEBV20d 0.2453 gwGEBV15 0.2352 gwGEBV10 0.2317 gwGEBV10d 0.2309 RS 0.2192 OCS 0.2189 gwGEBV05 0.2014 GEBV 95% Lower CL DF Std. Error 0.00027 1817 0.2609 0.00027 1817 0.2608 0.00027 1817 0.2604 0.00027 1817 0.2603 0.00027 1817 0.2603 0.00027 1817 0.2603 0.00027 1817 0.2594 0.00027 1817 0.2594 0.00027 1817 0.2594 0.00027 1817 0.2589 0.00027 1817 0.2580 0.00027 1817 0.2576 0.00027 1817 0.2562 0.00027 1817 0.2558 0.00027 1817 0.2518 0.00027 1817 0.2484 0.00027 1817 0.2448 0.00027 1817 0.2347 0.00027 1817 0.2312 0.00027 1817 0.2303 0.00027 1817 0.2187 0.00027 1817 0.2184 0.00027 1817 0.2009 95% Upper CL 0.2620 0.2618 0.2614 0.2614 0.2613 0.2613 0.2605 0.2605 0.2604 0.2599 0.2591 0.2586 0.2572 0.2569 0.2529 0.2495 0.2458 0.2357 0.2322 0.2314 0.2197 0.2194 0.2020 Statistical Grouping N MN LMN LMN LMN LMN KLM KLM JKL IJK IJ I H H G F E D C C B B A Table B.41: Population mean expected heterozygosity by selection strategy at generation 15 in the single-trait, EST scenario. 398 Mean Pop. MEH Selection Strategy 0.2563 gwGEBV80d 0.2562 gwGEBV50 0.2561 gwGEBV45 0.2559 gwGEBV70d 0.2558 gwGEBV90d gwGEBV100d 0.2554 0.2551 gwGEBV60d 0.2547 gwGEBV40 0.2529 gwGEBV50d 0.2528 gwGEBV35 0.2497 gwGEBV30 0.2488 gwGEBV40d 0.2457 gwGEBV25 0.2397 gwGEBV30d 0.2381 gwGEBV20 0.2267 gwGEBV15 0.2223 gwGEBV20d 0.2082 RS 0.2079 gwGEBV10 0.1938 gwGEBV10d 0.1821 gwGEBV05 0.1621 OCS 0.1513 GEBV Generation 30 95% Lower CL DF Std. Error 0.00037 1817 0.2556 0.00037 1817 0.2554 0.00037 1817 0.2553 0.00037 1817 0.2551 0.00037 1817 0.2551 0.00037 1817 0.2546 0.00037 1817 0.2544 0.00037 1817 0.2540 0.00037 1817 0.2522 0.00037 1817 0.2520 0.00037 1817 0.2490 0.00037 1817 0.2480 0.00037 1817 0.2449 0.00037 1817 0.2390 0.00037 1817 0.2374 0.00037 1817 0.2260 0.00037 1817 0.2216 0.00037 1817 0.2075 0.00037 1817 0.2072 0.00037 1817 0.1931 0.00037 1817 0.1814 0.00037 1817 0.1614 0.00037 1817 0.1506 95% Upper CL 0.2570 0.2569 0.2568 0.2566 0.2566 0.2561 0.2558 0.2555 0.2537 0.2535 0.2505 0.2495 0.2464 0.2405 0.2388 0.2275 0.2231 0.2089 0.2087 0.1946 0.1829 0.1629 0.1520 Statistical Grouping M M M M M M M LM KL K J J I H H G F E E D C B A Table B.42: Population mean expected heterozygosity by selection strategy at generation 30 in the single-trait, EST scenario. 399 Mean Pop. MEH Selection Strategy 0.2486 gwGEBV50 gwGEBV45 0.2483 gwGEBV100d 0.2467 0.2461 gwGEBV40 0.2458 gwGEBV90d 0.2445 gwGEBV80d 0.2428 gwGEBV35 0.2413 gwGEBV70d 0.2391 gwGEBV30 0.2381 gwGEBV60d 0.2334 gwGEBV25 0.2311 gwGEBV50d 0.2230 gwGEBV20 0.2219 gwGEBV40d 0.2085 gwGEBV15 0.2083 gwGEBV30d 0.1889 RS 0.1866 gwGEBV20d 0.1852 gwGEBV10 0.1568 gwGEBV10d 0.1541 gwGEBV05 0.1232 OCS 0.1172 GEBV Generation 45 95% Lower CL DF Std. Error 0.00043 1817 0.2477 0.00043 1817 0.2475 0.00043 1817 0.2459 0.00043 1817 0.2453 0.00043 1817 0.2450 0.00043 1817 0.2437 0.00043 1817 0.2419 0.00043 1817 0.2405 0.00043 1817 0.2382 0.00043 1817 0.2372 0.00043 1817 0.2326 0.00043 1817 0.2303 0.00043 1817 0.2221 0.00043 1817 0.2211 0.00043 1817 0.2077 0.00043 1817 0.2075 0.00043 1817 0.1881 0.00043 1817 0.1858 0.00043 1817 0.1843 0.00043 1817 0.1560 0.00043 1817 0.1532 0.00043 1817 0.1223 0.00043 1817 0.1163 95% Upper CL 0.2494 0.2492 0.2476 0.2470 0.2467 0.2454 0.2436 0.2422 0.2399 0.2389 0.2343 0.2320 0.2239 0.2228 0.2094 0.2092 0.1898 0.1875 0.1860 0.1577 0.1549 0.1240 0.1181 Statistical Grouping P OP NOP NO N MN LM L K K J I H H G G F E E D C B A Table B.43: Population mean expected heterozygosity by selection strategy at generation 45 in the single-trait, EST scenario. 400 2.2.4. Population upper selection limit Generation 15 Selection Strategy Mean Pop. USL gwGEBV100d 107.3109 107.3106 gwGEBV50d 107.3096 gwGEBV80d 107.3072 gwGEBV70d 107.3070 gwGEBV90d 107.3058 gwGEBV40 107.3057 gwGEBV50 107.3050 gwGEBV60d 107.3001 gwGEBV45 107.2968 gwGEBV40d 107.2950 gwGEBV30 107.2948 gwGEBV35 107.2882 gwGEBV25 107.2853 gwGEBV30d 107.2778 gwGEBV20 107.2722 RS 107.2635 gwGEBV15 107.2627 gwGEBV20d 107.2162 gwGEBV10d 107.2139 gwGEBV10 107.1615 OCS 107.1433 gwGEBV05 107.0659 GEBV 95% Lower CL DF Std. Error 0.00331 1817 107.3044 0.00331 1817 107.3041 0.00331 1817 107.3031 0.00331 1817 107.3007 0.00331 1817 107.3005 0.00331 1817 107.2994 0.00331 1817 107.2992 0.00331 1817 107.2986 0.00331 1817 107.2936 0.00331 1817 107.2903 0.00331 1817 107.2885 0.00331 1817 107.2883 0.00331 1817 107.2817 0.00331 1817 107.2788 0.00331 1817 107.2713 0.00331 1817 107.2657 0.00331 1817 107.2570 0.00331 1817 107.2562 0.00331 1817 107.2097 0.00331 1817 107.2074 0.00331 1817 107.1550 0.00331 1817 107.1368 0.00331 1817 107.0594 Statistical Grouping I I I I I I I 95% Upper CL 107.3174 107.3171 107.3161 107.3137 107.3135 107.3123 107.3122 107.3115 HI 107.3066 GHI 107.3033 GHI 107.3015 GHI 107.3013 GHI FGH 107.2947 FG 107.2918 EF 107.2843 EF 107.2787 E 107.2700 107.2692 E 107.2227 D 107.2204 D 107.1680 C 107.1498 B 107.0724 A Table B.44: Population upper selection limit by selection strategy at generation 15 in the single- trait, EST scenario. 401 Mean Pop. Selection USL Strategy 107.2578 gwGEBV90d gwGEBV100d 107.2563 107.2534 gwGEBV50 107.2512 gwGEBV80d 107.2494 gwGEBV60d 107.2493 gwGEBV70d 107.2464 gwGEBV50d 107.2459 gwGEBV40 107.2451 gwGEBV45 107.2356 gwGEBV35 107.2322 gwGEBV40d 107.2236 gwGEBV30 107.2233 gwGEBV25 107.1982 gwGEBV30d 107.1948 gwGEBV20 107.1657 gwGEBV15 107.1595 gwGEBV20d 107.1580 RS 107.1076 gwGEBV10 107.0629 gwGEBV10d 106.9901 gwGEBV05 106.9120 OCS 106.8314 GEBV Generation 30 95% Lower CL DF Std. Error 0.00401 1817 107.2499 0.00401 1817 107.2484 0.00401 1817 107.2455 0.00401 1817 107.2433 0.00401 1817 107.2416 0.00401 1817 107.2415 0.00401 1817 107.2386 0.00401 1817 107.2380 0.00401 1817 107.2372 0.00401 1817 107.2277 0.00401 1817 107.2244 0.00401 1817 107.2158 0.00401 1817 107.2155 0.00401 1817 107.1903 0.00401 1817 107.1870 0.00401 1817 107.1578 0.00401 1817 107.1517 0.00401 1817 107.1501 0.00401 1817 107.0997 0.00401 1817 107.0550 0.00401 1817 106.9823 0.00401 1817 106.9042 0.00401 1817 106.8236 Statistical Grouping 95% Upper CL 107.2657 K 107.2642 K JK 107.2613 IJK 107.2590 IJK 107.2573 IJK 107.2572 IJK 107.2543 IJK 107.2537 107.2529 IJK 107.2434 HIJ 107.2401 HI 107.2315 H 107.2312 H 107.2060 G 107.2027 G F 107.1736 F 107.1674 107.1659 F E 107.1154 107.0707 D 106.9980 C 106.9199 B 106.8393 A Table B.45: Population upper selection limit by selection strategy at generation 30 in the single- trait, EST scenario. 402 Mean Pop. Selection USL Strategy 107.2150 gwGEBV50 gwGEBV90d 107.2096 gwGEBV100d 107.2068 107.2045 gwGEBV80d 107.2035 gwGEBV45 107.2034 gwGEBV70d 107.2017 gwGEBV40 107.1960 gwGEBV50d 107.1916 gwGEBV60d 107.1906 gwGEBV35 107.1749 gwGEBV30 107.1681 gwGEBV25 107.1640 gwGEBV40d 107.1380 gwGEBV20 107.1222 gwGEBV30d 107.1050 gwGEBV15 107.0647 gwGEBV20d 107.0641 RS 107.0325 gwGEBV10 106.9432 gwGEBV10d 106.8947 gwGEBV05 106.7569 OCS 106.6823 GEBV Generation 45 95% Lower CL DF Std. Error 0.00460 1817 107.2060 0.00460 1817 107.2006 0.00460 1817 107.1978 0.00460 1817 107.1955 0.00460 1817 107.1945 0.00460 1817 107.1944 0.00460 1817 107.1926 0.00460 1817 107.1870 0.00460 1817 107.1826 0.00460 1817 107.1815 0.00460 1817 107.1659 0.00460 1817 107.1591 0.00460 1817 107.1549 0.00460 1817 107.1290 0.00460 1817 107.1132 0.00460 1817 107.0960 0.00460 1817 107.0557 0.00460 1817 107.0551 0.00460 1817 107.0235 0.00460 1817 106.9341 0.00460 1817 106.8857 0.00460 1817 106.7478 0.00460 1817 106.6733 Statistical Grouping LM LM LM LM LM LM 95% Upper CL 107.2241 M 107.2186 107.2158 107.2135 107.2125 107.2124 107.2107 107.2051 KLM JKLM 107.2006 JKL 107.1996 IJK 107.1839 IJ 107.1771 107.1730 I 107.1470 H 107.1312 GH 107.1140 G F 107.0738 107.0732 F E 107.0416 106.9522 D 106.9038 C 106.7659 B 106.6913 A Table B.46: Population upper selection limit by selection strategy at generation 45 in the single- trait, EST scenario. 403 2.2.5. Population additive genetic variance Figure B.14: Population additive genetic variance by selection strategy over 60 generations in the single-trait, EST scenario. 404 Mean Pop. Selection Genetic Var. Strategy 0.0227 gwGEBV50 0.0225 gwGEBV40d 0.0224 gwGEBV90d 0.0224 gwGEBV60d 0.0224 gwGEBV35 0.0224 gwGEBV80d 0.0223 gwGEBV25 0.0222 gwGEBV50d 0.0221 gwGEBV30 0.0221 gwGEBV30d 0.0221 gwGEBV40 0.0221 gwGEBV45 gwGEBV100d 0.0220 0.0220 gwGEBV70d 0.0220 gwGEBV20 0.0219 gwGEBV20d 0.0206 gwGEBV15 0.0194 RS 0.0185 gwGEBV10 0.0171 gwGEBV10d 0.0147 gwGEBV05 0.0143 OCS 0.0126 GEBV Generation 15 95% Lower CL DF Std. Error 0.00025 1817 0.0222 0.00025 1817 0.0220 0.00025 1817 0.0219 0.00025 1817 0.0219 0.00025 1817 0.0219 0.00025 1817 0.0219 0.00025 1817 0.0218 0.00025 1817 0.0217 0.00025 1817 0.0216 0.00025 1817 0.0216 0.00025 1817 0.0216 0.00025 1817 0.0216 0.00025 1817 0.0215 0.00025 1817 0.0215 0.00025 1817 0.0215 0.00025 1817 0.0214 0.00025 1817 0.0201 0.00025 1817 0.0189 0.00025 1817 0.0180 0.00025 1817 0.0166 0.00025 1817 0.0142 0.00025 1817 0.0138 0.00025 1817 0.0121 95% Upper CL 0.0232 0.0230 0.0229 0.0229 0.0229 0.0229 0.0228 0.0227 0.0226 0.0226 0.0226 0.0226 0.0225 0.0225 0.0225 0.0224 0.0211 0.0199 0.0190 0.0176 0.0152 0.0148 0.0131 Statistical Grouping F F F F F F F F F F F F F F F F E DE D C B B A Table B.47: Population additive genetic variance by selection strategy at generation 15 in the single-trait, EST scenario. 405 Mean Pop. Selection Genetic Var. Strategy 0.0202 gwGEBV60d gwGEBV70d 0.0196 gwGEBV100d 0.0196 0.0195 gwGEBV90d 0.0195 gwGEBV80d 0.0195 gwGEBV50d 0.0194 gwGEBV40 0.0193 gwGEBV50 0.0192 gwGEBV35 0.0191 gwGEBV40d 0.0190 gwGEBV45 0.0187 gwGEBV30 0.0186 gwGEBV25 0.0184 gwGEBV30d 0.0177 gwGEBV20 0.0161 gwGEBV15 0.0153 gwGEBV20d 0.0153 RS 0.0131 gwGEBV10 0.0110 gwGEBV10d 0.0097 gwGEBV05 0.0079 OCS 0.0075 GEBV Generation 30 95% Lower CL DF Std. Error 0.00022 1817 0.0197 0.00022 1817 0.0192 0.00022 1817 0.0191 0.00022 1817 0.0191 0.00022 1817 0.0191 0.00022 1817 0.0191 0.00022 1817 0.0190 0.00022 1817 0.0189 0.00022 1817 0.0188 0.00022 1817 0.0187 0.00022 1817 0.0185 0.00022 1817 0.0182 0.00022 1817 0.0182 0.00022 1817 0.0180 0.00022 1817 0.0172 0.00022 1817 0.0157 0.00022 1817 0.0149 0.00022 1817 0.0149 0.00022 1817 0.0126 0.00022 1817 0.0106 0.00022 1817 0.0093 0.00022 1817 0.0075 0.00022 1817 0.0070 95% Upper CL 0.0206 0.0201 0.0200 0.0200 0.0199 0.0199 0.0198 0.0197 0.0196 0.0195 0.0194 0.0191 0.0191 0.0188 0.0181 0.0165 0.0158 0.0158 0.0135 0.0115 0.0102 0.0083 0.0079 Statistical Grouping I HI HI HI GHI GHI GHI GHI GHI GHI GH FGH FGH FG F E E E D C B A A Table B.48: Population additive genetic variance by selection strategy at generation 30 in the single-trait, EST scenario. 406 Mean Pop. Selection Genetic Var. Strategy 0.0176 gwGEBV90d gwGEBV100d 0.0176 0.0175 gwGEBV80d 0.0175 gwGEBV70d 0.0169 gwGEBV50 0.0168 gwGEBV45 0.0167 gwGEBV60d 0.0166 gwGEBV40 0.0160 gwGEBV35 0.0158 gwGEBV50d 0.0156 gwGEBV30 0.0149 gwGEBV25 0.0143 gwGEBV40d 0.0140 gwGEBV20 0.0126 RS 0.0123 gwGEBV15 0.0117 gwGEBV30d 0.0093 gwGEBV10 0.0090 gwGEBV20d 0.0063 gwGEBV10d 0.0062 gwGEBV05 0.0047 OCS 0.0044 GEBV Generation 45 95% Lower CL DF Std. Error 0.00018 1817 0.0173 0.00018 1817 0.0172 0.00018 1817 0.0171 0.00018 1817 0.0171 0.00018 1817 0.0165 0.00018 1817 0.0164 0.00018 1817 0.0164 0.00018 1817 0.0162 0.00018 1817 0.0156 0.00018 1817 0.0155 0.00018 1817 0.0152 0.00018 1817 0.0146 0.00018 1817 0.0139 0.00018 1817 0.0136 0.00018 1817 0.0122 0.00018 1817 0.0120 0.00018 1817 0.0113 0.00018 1817 0.0089 0.00018 1817 0.0087 0.00018 1817 0.0059 0.00018 1817 0.0059 0.00018 1817 0.0043 0.00018 1817 0.0041 95% Upper CL 0.0180 0.0179 0.0179 0.0179 0.0173 0.0171 0.0171 0.0170 0.0164 0.0162 0.0159 0.0153 0.0147 0.0143 0.0129 0.0127 0.0121 0.0096 0.0094 0.0067 0.0066 0.0051 0.0048 Statistical Grouping L L KL KL JKL IJKL IJKL IJK HIJ GHI GH FG EF E D D D C C B B A A Table B.49: Population additive genetic variance by selection strategy at generation 45 in the single-trait, EST scenario. 407 Mean Pop. Selection Genetic Var. Strategy 0.0147 gwGEBV50 0.0143 gwGEBV45 0.0143 gwGEBV40 0.0133 gwGEBV35 0.0130 gwGEBV30 0.0121 gwGEBV25 gwGEBV20 0.0111 gwGEBV100d 0.0108 0.0104 gwGEBV90d 0.0104 RS 0.0097 gwGEBV80d 0.0090 gwGEBV15 0.0090 gwGEBV70d 0.0083 gwGEBV60d 0.0076 gwGEBV50d 0.0067 gwGEBV40d 0.0066 gwGEBV10 0.0056 gwGEBV30d 0.0045 gwGEBV20d 0.0040 gwGEBV05 0.0035 gwGEBV10d 0.0027 OCS 0.0027 GEBV Generation 60 95% Lower CL DF Std. Error 0.00012 1817 0.0145 0.00012 1817 0.0141 0.00012 1817 0.0141 0.00012 1817 0.0130 0.00012 1817 0.0127 0.00012 1817 0.0119 0.00012 1817 0.0108 0.00012 1817 0.0105 0.00012 1817 0.0102 0.00012 1817 0.0101 0.00012 1817 0.0095 0.00012 1817 0.0088 0.00012 1817 0.0087 0.00012 1817 0.0081 0.00012 1817 0.0073 0.00012 1817 0.0065 0.00012 1817 0.0064 0.00012 1817 0.0054 0.00012 1817 0.0043 0.00012 1817 0.0038 0.00012 1817 0.0033 0.00012 1817 0.0025 0.00012 1817 0.0024 95% Upper CL 0.0150 0.0146 0.0146 0.0135 0.0132 0.0123 0.0113 0.0110 0.0106 0.0106 0.0100 0.0093 0.0092 0.0085 0.0078 0.0070 0.0069 0.0059 0.0048 0.0043 0.0038 0.0030 0.0029 Statistical Grouping N N N M M L K JK J J I H H G F E E D C BC B A A Table B.50: Population additive genetic variance by selection strategy at generation 60 in the single-trait, EST scenario. 408 2.2.6. Population additive genic variance Figure B.15: Population additive genic variance by selection strategy over 60 generations in the single-trait, EST scenario. 409 Mean Pop. Selection Genetic Var. Strategy 0.0329 gwGEBV90d 0.0328 gwGEBV80d 0.0328 gwGEBV60d 0.0328 gwGEBV70d 0.0327 gwGEBV50 gwGEBV100d 0.0327 0.0325 gwGEBV45 0.0324 gwGEBV50d 0.0324 gwGEBV40 0.0321 gwGEBV40d 0.0321 gwGEBV35 0.0316 gwGEBV30 0.0312 gwGEBV30d 0.0310 gwGEBV25 0.0302 gwGEBV20 0.0295 gwGEBV20d 0.0288 gwGEBV15 0.0283 RS 0.0269 gwGEBV10 0.0264 gwGEBV10d 0.0245 OCS 0.0244 gwGEBV05 0.0223 GEBV Generation 15 95% Lower CL DF Std. Error 0.00006 1817 0.0328 0.00006 1817 0.0326 0.00006 1817 0.0326 0.00006 1817 0.0326 0.00006 1817 0.0326 0.00006 1817 0.0326 0.00006 1817 0.0324 0.00006 1817 0.0323 0.00006 1817 0.0323 0.00006 1817 0.0320 0.00006 1817 0.0320 0.00006 1817 0.0315 0.00006 1817 0.0311 0.00006 1817 0.0309 0.00006 1817 0.0301 0.00006 1817 0.0294 0.00006 1817 0.0287 0.00006 1817 0.0282 0.00006 1817 0.0268 0.00006 1817 0.0263 0.00006 1817 0.0244 0.00006 1817 0.0243 0.00006 1817 0.0222 95% Upper CL 0.0330 0.0329 0.0329 0.0329 0.0328 0.0328 0.0326 0.0325 0.0325 0.0322 0.0322 0.0317 0.0313 0.0312 0.0304 0.0296 0.0289 0.0285 0.0271 0.0265 0.0246 0.0245 0.0225 Statistical Grouping O NO NO NO MNO LMNO LMN LM KL K K J I I H G F E D C B B A Table B.51: Population additive genic variance by selection strategy at generation 15 in the single-trait, EST scenario. 410 Mean Pop. Selection Genetic Var. Strategy 0.0289 gwGEBV90d gwGEBV100d 0.0289 0.0288 gwGEBV80d 0.0286 gwGEBV50 0.0286 gwGEBV70d 0.0284 gwGEBV45 0.0281 gwGEBV60d 0.0279 gwGEBV40 0.0275 gwGEBV50d 0.0273 gwGEBV35 0.0267 gwGEBV30 0.0264 gwGEBV40d 0.0256 gwGEBV25 0.0246 gwGEBV30d 0.0242 gwGEBV20 0.0229 RS 0.0222 gwGEBV15 0.0215 gwGEBV20d 0.0193 gwGEBV10 0.0175 gwGEBV10d 0.0162 gwGEBV05 0.0143 OCS 0.0134 GEBV Generation 30 95% Lower CL DF Std. Error 0.00007 1817 0.0288 0.00007 1817 0.0288 0.00007 1817 0.0287 0.00007 1817 0.0285 0.00007 1817 0.0284 0.00007 1817 0.0283 0.00007 1817 0.0280 0.00007 1817 0.0278 0.00007 1817 0.0273 0.00007 1817 0.0272 0.00007 1817 0.0266 0.00007 1817 0.0263 0.00007 1817 0.0255 0.00007 1817 0.0245 0.00007 1817 0.0241 0.00007 1817 0.0228 0.00007 1817 0.0220 0.00007 1817 0.0214 0.00007 1817 0.0192 0.00007 1817 0.0174 0.00007 1817 0.0160 0.00007 1817 0.0142 0.00007 1817 0.0133 95% Upper CL 0.0291 0.0291 0.0290 0.0287 0.0287 0.0286 0.0282 0.0281 0.0276 0.0275 0.0268 0.0266 0.0258 0.0247 0.0243 0.0231 0.0223 0.0217 0.0194 0.0176 0.0163 0.0145 0.0136 Statistical Grouping R R QR PQR PQ OP NO N M M L L K J I H G F E D C B A Table B.52: Population additive genic variance by selection strategy at generation 30 in the single-trait, EST scenario. 411 Mean Pop. Selection Genetic Var. Strategy 0.0244 gwGEBV50 gwGEBV45 0.0242 gwGEBV100d 0.0241 0.0239 gwGEBV90d 0.0235 gwGEBV80d 0.0234 gwGEBV40 0.0226 gwGEBV70d 0.0226 gwGEBV35 0.0217 gwGEBV30 0.0217 gwGEBV60d 0.0204 gwGEBV25 0.0203 gwGEBV50d 0.0188 gwGEBV40d 0.0187 RS 0.0185 gwGEBV20 0.0165 gwGEBV30d 0.0161 gwGEBV15 0.0135 gwGEBV20d 0.0131 gwGEBV10 0.0103 gwGEBV10d 0.0101 gwGEBV05 0.0080 OCS 0.0076 GEBV Generation 45 95% Lower CL DF Std. Error 0.00007 1817 0.0242 0.00007 1817 0.0240 0.00007 1817 0.0240 0.00007 1817 0.0238 0.00007 1817 0.0233 0.00007 1817 0.0232 0.00007 1817 0.0225 0.00007 1817 0.0224 0.00007 1817 0.0216 0.00007 1817 0.0215 0.00007 1817 0.0202 0.00007 1817 0.0202 0.00007 1817 0.0186 0.00007 1817 0.0185 0.00007 1817 0.0183 0.00007 1817 0.0164 0.00007 1817 0.0160 0.00007 1817 0.0133 0.00007 1817 0.0129 0.00007 1817 0.0102 0.00007 1817 0.0100 0.00007 1817 0.0079 0.00007 1817 0.0075 95% Upper CL 0.0245 0.0243 0.0243 0.0241 0.0236 0.0235 0.0228 0.0227 0.0219 0.0218 0.0205 0.0205 0.0189 0.0188 0.0186 0.0166 0.0163 0.0136 0.0132 0.0104 0.0102 0.0081 0.0078 Statistical Grouping L KL KL K J J I I H H G G F F F E E D C B B A A Table B.53: Population additive genic variance by selection strategy at generation 45 in the single-trait, EST scenario. 412 Mean Pop. Selection Genetic Var. Strategy 0.0204 gwGEBV50 0.0200 gwGEBV45 0.0193 gwGEBV40 0.0185 gwGEBV35 0.0174 gwGEBV30 gwGEBV25 0.0161 gwGEBV100d 0.0153 0.0152 RS 0.0150 gwGEBV90d 0.0142 gwGEBV80d 0.0139 gwGEBV20 0.0135 gwGEBV70d 0.0127 gwGEBV60d 0.0117 gwGEBV15 0.0117 gwGEBV50d 0.0106 gwGEBV40d 0.0092 gwGEBV30d 0.0090 gwGEBV10 0.0076 gwGEBV20d 0.0064 gwGEBV05 0.0059 gwGEBV10d 0.0044 OCS 0.0044 GEBV Generation 60 95% Lower CL DF Std. Error 0.00007 1817 0.0202 0.00007 1817 0.0199 0.00007 1817 0.0191 0.00007 1817 0.0183 0.00007 1817 0.0173 0.00007 1817 0.0159 0.00007 1817 0.0152 0.00007 1817 0.0150 0.00007 1817 0.0149 0.00007 1817 0.0141 0.00007 1817 0.0138 0.00007 1817 0.0134 0.00007 1817 0.0125 0.00007 1817 0.0116 0.00007 1817 0.0115 0.00007 1817 0.0104 0.00007 1817 0.0090 0.00007 1817 0.0088 0.00007 1817 0.0075 0.00007 1817 0.0063 0.00007 1817 0.0058 0.00007 1817 0.0043 0.00007 1817 0.0042 95% Upper CL 0.0205 0.0201 0.0194 0.0186 0.0176 0.0162 0.0155 0.0153 0.0152 0.0144 0.0141 0.0136 0.0128 0.0119 0.0118 0.0107 0.0093 0.0091 0.0077 0.0065 0.0061 0.0046 0.0045 Statistical Grouping Q P O N M L K K K J J I H G G F E E D C B A A Table B.54: Population additive genic variance by selection strategy at generation 60 in the single-trait, EST scenario. 413 2.2.7. Population Bulmer effect Figure B.16: Population Bulmer effect by selection strategy over 60 generations in the single- trait, EST scenario. 414 Mean Pop. Selection Genic Var. Strategy 0.7443 gwGEBV20d 0.7266 gwGEBV20 0.7202 gwGEBV25 0.7159 gwGEBV15 0.7095 gwGEBV30d 0.7010 gwGEBV30 0.6997 gwGEBV40d 0.6969 gwGEBV35 0.6931 gwGEBV50 0.6861 gwGEBV10 0.6859 gwGEBV50d 0.6850 RS 0.6841 gwGEBV60d 0.6822 gwGEBV90d 0.6820 gwGEBV80d 0.6811 gwGEBV40 gwGEBV45 0.6782 gwGEBV100d 0.6746 0.6715 gwGEBV70d 0.6478 gwGEBV10d 0.6016 gwGEBV05 0.5835 OCS 0.5627 GEBV Generation 15 95% Lower CL DF Std. Error 0.00834 1817 0.7279 0.00834 1817 0.7103 0.00834 1817 0.7039 0.00834 1817 0.6996 0.00834 1817 0.6932 0.00834 1817 0.6847 0.00834 1817 0.6834 0.00834 1817 0.6806 0.00834 1817 0.6767 0.00834 1817 0.6698 0.00834 1817 0.6696 0.00834 1817 0.6686 0.00834 1817 0.6678 0.00834 1817 0.6659 0.00834 1817 0.6657 0.00834 1817 0.6647 0.00834 1817 0.6619 0.00834 1817 0.6582 0.00834 1817 0.6551 0.00834 1817 0.6315 0.00834 1817 0.5852 0.00834 1817 0.5671 0.00834 1817 0.5463 95% Upper CL 0.7606 0.7430 0.7366 0.7323 0.7259 0.7174 0.7161 0.7133 0.7095 0.7025 0.7023 0.7013 0.7005 0.6986 0.6984 0.6974 0.6946 0.6909 0.6879 0.6642 0.6180 0.5998 0.5791 Statistical Grouping G FG EFG DEFG CDEFG CDEF CDEF CDEF CDEF BCDEF BCDEF BCDEF BCDEF BCDE BCDE BCDE BCDE BCD BC B A A A Table B.55: Population Bulmer effect by selection strategy at generation 15 in the single-trait, EST scenario. 415 Mean Pop. Selection Genic Var. Strategy 0.7480 gwGEBV30d 0.7304 gwGEBV20 0.7278 gwGEBV15 0.7270 gwGEBV25 0.7228 gwGEBV40d 0.7176 gwGEBV60d 0.7130 gwGEBV20d 0.7100 gwGEBV50d 0.7021 gwGEBV35 0.6992 gwGEBV30 0.6949 gwGEBV40 0.6876 gwGEBV70d 0.6780 gwGEBV10 gwGEBV80d 0.6768 gwGEBV100d 0.6760 0.6757 gwGEBV50 0.6745 gwGEBV90d 0.6684 RS 0.6667 gwGEBV45 0.6295 gwGEBV10d 0.6016 gwGEBV05 0.5567 GEBV 0.5512 OCS Generation 30 95% Lower CL DF Std. Error 0.00890 1817 0.7305 0.00890 1817 0.7129 0.00890 1817 0.7103 0.00890 1817 0.7095 0.00890 1817 0.7054 0.00890 1817 0.7001 0.00890 1817 0.6956 0.00890 1817 0.6926 0.00890 1817 0.6847 0.00890 1817 0.6817 0.00890 1817 0.6774 0.00890 1817 0.6702 0.00890 1817 0.6605 0.00890 1817 0.6593 0.00890 1817 0.6585 0.00890 1817 0.6582 0.00890 1817 0.6571 0.00890 1817 0.6510 0.00890 1817 0.6493 0.00890 1817 0.6120 0.00890 1817 0.5842 0.00890 1817 0.5392 0.00890 1817 0.5337 95% Upper CL 0.7654 0.7478 0.7452 0.7444 0.7403 0.7350 0.7305 0.7275 0.7196 0.7166 0.7123 0.7051 0.6954 0.6942 0.6934 0.6931 0.6920 0.6859 0.6842 0.6469 0.6191 0.5741 0.5686 Statistical Grouping J IJ IJ IJ HIJ GHIJ FGHIJ EFGHIJ EFGHI EFGHI EFGHI EFGHI EFGH EFG EFG EFG DEFG DEF DE CD BC AB A Table B.56: Population Bulmer effect by selection strategy at generation 30 in the single-trait, EST scenario. 416 Mean Pop. Selection Genic Var. Strategy 0.7798 gwGEBV50d 0.7730 gwGEBV70d 0.7728 gwGEBV60d 0.7642 gwGEBV15 0.7617 gwGEBV40d 0.7566 gwGEBV20 0.7460 gwGEBV80d 0.7370 gwGEBV90d gwGEBV25 0.7330 gwGEBV100d 0.7296 0.7178 gwGEBV30 0.7117 gwGEBV30d 0.7106 gwGEBV40 0.7082 gwGEBV35 0.7077 gwGEBV10 0.6942 gwGEBV45 0.6934 gwGEBV50 0.6736 RS 0.6708 gwGEBV20d 0.6177 gwGEBV05 0.6125 gwGEBV10d 0.5885 OCS 0.5801 GEBV Generation 45 95% Lower CL DF Std. Error 0.00959 1817 0.7610 0.00959 1817 0.7542 0.00959 1817 0.7540 0.00959 1817 0.7454 0.00959 1817 0.7429 0.00959 1817 0.7378 0.00959 1817 0.7272 0.00959 1817 0.7182 0.00959 1817 0.7142 0.00959 1817 0.7108 0.00959 1817 0.6990 0.00959 1817 0.6929 0.00959 1817 0.6918 0.00959 1817 0.6894 0.00959 1817 0.6889 0.00959 1817 0.6754 0.00959 1817 0.6746 0.00959 1817 0.6548 0.00959 1817 0.6520 0.00959 1817 0.5989 0.00959 1817 0.5937 0.00959 1817 0.5697 0.00959 1817 0.5613 95% Upper CL 0.7986 0.7918 0.7916 0.7830 0.7805 0.7754 0.7648 0.7558 0.7518 0.7484 0.7366 0.7305 0.7294 0.7270 0.7265 0.7130 0.7122 0.6924 0.6896 0.6365 0.6313 0.6073 0.5990 Statistical Grouping G FG FG EFG EFG DEFG DEFG CDEFG CDEFG CDEF BCDE BCD BCD BCD BCD BC BC B B A A A A Table B.57: Population Bulmer effect by selection strategy at generation 45 in the single-trait, EST scenario. 417 Mean Pop. Selection Genic Var. Strategy 0.7954 gwGEBV20 0.7707 gwGEBV15 0.7537 gwGEBV25 0.7442 gwGEBV30 0.7433 gwGEBV40 0.7400 gwGEBV10 0.7222 gwGEBV50 0.7197 gwGEBV35 gwGEBV45 0.7175 gwGEBV100d 0.7037 0.6929 gwGEBV90d 0.6841 gwGEBV80d 0.6836 RS 0.6633 gwGEBV70d 0.6549 gwGEBV60d 0.6519 gwGEBV50d 0.6379 gwGEBV40d 0.6306 gwGEBV05 0.6153 gwGEBV30d 0.6147 GEBV 0.6139 OCS 0.6019 gwGEBV10d 0.5994 gwGEBV20d Generation 60 95% Lower CL DF Std. Error 0.00887 1817 0.7780 0.00887 1817 0.7533 0.00887 1817 0.7363 0.00887 1817 0.7268 0.00887 1817 0.7259 0.00887 1817 0.7226 0.00887 1817 0.7048 0.00887 1817 0.7023 0.00887 1817 0.7001 0.00887 1817 0.6863 0.00887 1817 0.6755 0.00887 1817 0.6667 0.00887 1817 0.6663 0.00887 1817 0.6459 0.00887 1817 0.6375 0.00887 1817 0.6346 0.00887 1817 0.6205 0.00887 1817 0.6132 0.00887 1817 0.5979 0.00887 1817 0.5973 0.00887 1817 0.5965 0.00887 1817 0.5845 0.00887 1817 0.5820 95% Upper CL 0.8128 0.7881 0.7711 0.7616 0.7607 0.7574 0.7396 0.7371 0.7349 0.7211 0.7103 0.7015 0.7010 0.6807 0.6723 0.6693 0.6553 0.6480 0.6327 0.6321 0.6313 0.6193 0.6168 Statistical Grouping J IJ HIJ GHI GHI GHI FGH FGH FGH EFG DEF DEF DEF CDE BCD BCD ABC ABC AB AB AB A A Table B.58: Population Bulmer effect by selection strategy at generation 60 in the single-trait, EST scenario. 3. Multi-trait breeding simulation supplementary results 3.1. TRUE scenario results 3.1.1. Population mean true breeding value 418 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T K J K J K K K J K J I K J H K J F I E H G D G C F B E B H G A O O O O ] 0 7 8 7 . 2 0 1 , 2 2 7 7 . 2 0 1 [ ] 6 6 0 8 . 2 0 1 , 1 2 9 7 . 2 0 1 [ ] 7 9 9 7 . 2 0 1 , 9 4 8 7 . 2 0 1 [ ] 9 7 9 7 . 2 0 1 , 3 3 8 7 . 2 0 1 [ ] 0 3 0 8 . 2 0 1 , 1 8 8 7 . 2 0 1 [ ] 5 1 9 7 . 2 0 1 , 9 6 7 7 . 2 0 1 [ ] 1 4 0 8 . 2 0 1 , 3 9 8 7 . 2 0 1 [ ] 0 8 8 7 . 2 0 1 , 4 3 7 7 . 2 0 1 [ N M ] 1 6 9 7 . 2 0 1 , 3 1 8 7 . 2 0 1 [ ] 3 1 6 7 . 2 0 1 , 7 6 4 7 . 2 0 1 [ L K M N I L ] 8 3 0 8 . 2 0 1 , 0 9 8 7 . 2 0 1 [ ] 9 6 6 7 . 2 0 1 , 4 2 5 7 . 2 0 1 [ ] 0 2 8 7 . 2 0 1 , 1 7 6 7 . 2 0 1 [ ] 9 1 1 7 . 2 0 1 , 3 7 9 6 . 2 0 1 [ ] 3 6 9 7 . 2 0 1 , 4 1 8 7 . 2 0 1 [ ] 6 4 4 7 . 2 0 1 , 0 0 3 7 . 2 0 1 [ ] 2 9 3 7 . 2 0 1 , 4 4 2 7 . 2 0 1 [ ] 4 1 7 6 . 2 0 1 , 8 6 5 6 . 2 0 1 [ ] 1 6 8 7 . 2 0 1 , 3 1 7 7 . 2 0 1 [ ] 9 7 1 7 . 2 0 1 , 4 3 0 7 . 2 0 1 [ H G ] 0 1 9 6 . 2 0 1 , 2 6 7 6 . 2 0 1 [ ] 9 5 3 6 . 2 0 1 , 3 1 2 6 . 2 0 1 [ K J F E J I D C C B G F H ] 0 3 6 7 . 2 0 1 , 2 8 4 7 . 2 0 1 [ ] 4 5 9 6 . 2 0 1 , 8 0 8 6 . 2 0 1 [ ] 1 7 5 6 . 2 0 1 , 2 2 4 6 . 2 0 1 [ ] 0 0 1 6 . 2 0 1 , 4 5 9 5 . 2 0 1 [ ] 7 9 2 7 . 2 0 1 , 8 4 1 7 . 2 0 1 [ ] 8 7 7 6 . 2 0 1 , 2 3 6 6 . 2 0 1 [ ] 5 5 2 6 . 2 0 1 , 6 0 1 6 . 2 0 1 [ ] 2 6 8 5 . 2 0 1 , 6 1 7 5 . 2 0 1 [ ] 4 4 1 7 . 2 0 1 , 5 9 9 6 . 2 0 1 [ ] 0 4 4 6 . 2 0 1 , 5 9 2 6 . 2 0 1 [ ] 0 3 0 6 . 2 0 1 , 2 8 8 5 . 2 0 1 [ ] 7 9 6 5 . 2 0 1 , 2 5 5 5 . 2 0 1 [ ] 2 0 9 6 . 2 0 1 , 3 5 7 6 . 2 0 1 [ ] 1 4 2 6 . 2 0 1 , 6 9 0 6 . 2 0 1 [ F E A L K E D ] 1 7 6 6 . 2 0 1 , 3 2 5 6 . 2 0 1 [ ] 2 6 0 6 . 2 0 1 , 6 1 9 5 . 2 0 1 [ ] 4 4 7 5 . 2 0 1 , 6 9 5 5 . 2 0 1 [ ] 9 2 4 5 . 2 0 1 , 3 8 2 5 . 2 0 1 [ ] 6 0 3 7 . 2 0 1 , 8 5 1 7 . 2 0 1 [ ] 9 1 1 7 . 2 0 1 , 4 7 9 6 . 2 0 1 [ ] 8 6 4 5 . 2 0 1 , 0 2 3 5 . 2 0 1 [ ] 4 2 9 5 . 2 0 1 , 9 7 7 5 . 2 0 1 [ B ] 2 2 8 5 . 2 0 1 , 4 7 6 5 . 2 0 1 [ ] 7 3 6 5 . 2 0 1 , 1 9 4 5 . 2 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 6 9 7 7 . 2 0 1 3 2 9 7 . 2 0 1 5 5 9 7 . 2 0 1 7 6 9 7 . 2 0 1 7 8 8 7 . 2 0 1 4 6 9 7 . 2 0 1 6 4 7 7 . 2 0 1 9 8 8 7 . 2 0 1 8 1 3 7 . 2 0 1 7 8 7 7 . 2 0 1 6 3 8 6 . 2 0 1 6 5 5 7 . 2 0 1 7 9 4 6 . 2 0 1 2 2 2 7 . 2 0 1 1 8 1 6 . 2 0 1 9 6 0 7 . 2 0 1 6 5 9 5 . 2 0 1 8 2 8 6 . 2 0 1 8 4 7 5 . 2 0 1 7 9 5 6 . 2 0 1 0 7 6 5 . 2 0 1 2 3 2 7 . 2 0 1 4 9 3 5 . 2 0 1 1 t i a r T 4 9 9 7 . 2 0 1 6 0 9 7 . 2 0 1 2 4 8 7 . 2 0 1 7 0 8 7 . 2 0 1 0 4 5 7 . 2 0 1 6 9 5 7 . 2 0 1 6 4 0 7 . 2 0 1 3 7 3 7 . 2 0 1 1 4 6 6 . 2 0 1 6 0 1 7 . 2 0 1 6 8 2 6 . 2 0 1 1 8 8 6 . 2 0 1 7 2 0 6 . 2 0 1 5 0 7 6 . 2 0 1 9 8 7 5 . 2 0 1 7 6 3 6 . 2 0 1 5 2 6 5 . 2 0 1 8 6 1 6 . 2 0 1 4 6 5 5 . 2 0 1 9 8 9 5 . 2 0 1 6 5 3 5 . 2 0 1 7 4 0 7 . 2 0 1 1 5 8 5 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 9 5 . B e l b a T 419 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T K J L K L L L L K L K J L K I J I H G I F H D G F C F E C B E D L K A B O N O N O N O N M N M L L K J L K J K J H I H G F H E D G C B F E J I ] 6 3 5 3 . 3 0 1 , 9 0 3 3 . 3 0 1 [ ] 5 8 1 2 . 3 0 1 , 5 6 9 1 . 3 0 1 [ ] 6 3 6 3 . 3 0 1 , 9 0 4 3 . 3 0 1 [ ] 0 4 1 2 . 3 0 1 , 0 2 9 1 . 3 0 1 [ ] 4 4 6 3 . 3 0 1 , 7 1 4 3 . 3 0 1 [ ] 3 2 1 2 . 3 0 1 , 3 0 9 1 . 3 0 1 [ ] 7 3 6 3 . 3 0 1 , 0 1 4 3 . 3 0 1 [ ] 0 8 9 1 . 3 0 1 , 9 5 7 1 . 3 0 1 [ ] 9 9 5 3 . 3 0 1 , 2 7 3 3 . 3 0 1 [ ] 6 3 9 1 . 3 0 1 , 6 1 7 1 . 3 0 1 [ ] 8 2 4 3 . 3 0 1 , 1 0 2 3 . 3 0 1 [ ] 8 8 6 1 . 3 0 1 , 8 6 4 1 . 3 0 1 [ ] 3 6 4 3 . 3 0 1 , 6 3 2 3 . 3 0 1 [ ] 6 6 6 1 . 3 0 1 , 5 4 4 1 . 3 0 1 [ ] 2 5 8 2 . 3 0 1 , 5 2 6 2 . 3 0 1 [ ] 4 3 4 1 . 3 0 1 , 4 1 2 1 . 3 0 1 [ ] 6 3 1 3 . 3 0 1 , 9 0 9 2 . 3 0 1 [ ] 1 3 5 1 . 3 0 1 , 0 1 3 1 . 3 0 1 [ ] 6 9 2 2 . 3 0 1 , 9 6 0 2 . 3 0 1 [ ] 5 2 9 0 . 3 0 1 , 5 0 7 0 . 3 0 1 [ ] 3 5 8 2 . 3 0 1 , 5 2 6 2 . 3 0 1 [ ] 4 9 1 1 . 3 0 1 , 3 7 9 0 . 3 0 1 [ ] 4 4 8 1 . 3 0 1 , 7 1 6 1 . 3 0 1 [ ] 0 2 5 0 . 3 0 1 , 0 0 3 0 . 3 0 1 [ ] 5 5 3 2 . 3 0 1 , 8 2 1 2 . 3 0 1 [ ] 3 7 9 0 . 3 0 1 , 3 5 7 0 . 3 0 1 [ ] 0 1 4 1 . 3 0 1 , 3 8 1 1 . 3 0 1 [ ] 4 1 1 0 . 3 0 1 , 4 9 8 9 . 2 0 1 [ ] 3 1 0 2 . 3 0 1 , 6 8 7 1 . 3 0 1 [ ] 5 3 6 0 . 3 0 1 , 4 1 4 0 . 3 0 1 [ ] 6 4 9 0 . 3 0 1 , 9 1 7 0 . 3 0 1 [ ] 1 2 8 9 . 2 0 1 , 0 0 6 9 . 2 0 1 [ ] 8 9 7 1 . 3 0 1 , 1 7 5 1 . 3 0 1 [ ] 2 1 3 0 . 3 0 1 , 2 9 0 0 . 3 0 1 [ D C ] 7 1 5 1 . 3 0 1 , 0 9 2 1 . 3 0 1 [ ] 3 7 9 9 . 2 0 1 , 3 5 7 9 . 2 0 1 [ A ] 2 0 6 0 . 3 0 1 , 5 7 3 0 . 3 0 1 [ ] 3 1 1 9 . 2 0 1 , 3 9 8 8 . 2 0 1 [ B ] 5 1 7 0 . 3 0 1 , 7 8 4 0 . 3 0 1 [ ] 4 7 5 9 . 2 0 1 , 4 5 3 9 . 2 0 1 [ M L K ] 4 2 5 3 . 3 0 1 , 7 9 2 3 . 3 0 1 [ ] 9 8 7 1 . 3 0 1 , 9 6 5 1 . 3 0 1 [ A ] 7 2 5 9 . 2 0 1 , 0 0 3 9 . 2 0 1 [ ] 0 2 2 9 . 2 0 1 , 0 0 0 9 . 2 0 1 [ O ] 1 1 3 3 . 3 0 1 , 4 8 0 3 . 3 0 1 [ ] 6 3 2 2 . 3 0 1 , 6 1 0 2 . 3 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 7 9 1 3 . 3 0 1 3 2 4 3 . 3 0 1 3 2 5 3 . 3 0 1 1 3 5 3 . 3 0 1 3 2 5 3 . 3 0 1 5 8 4 3 . 3 0 1 4 1 3 3 . 3 0 1 0 5 3 3 . 3 0 1 8 3 7 2 . 3 0 1 2 2 0 3 . 3 0 1 3 8 1 2 . 3 0 1 9 3 7 2 . 3 0 1 1 3 7 1 . 3 0 1 2 4 2 2 . 3 0 1 7 9 2 1 . 3 0 1 9 9 8 1 . 3 0 1 3 3 8 0 . 3 0 1 4 8 6 1 . 3 0 1 1 0 6 0 . 3 0 1 3 0 4 1 . 3 0 1 8 8 4 0 . 3 0 1 0 1 4 3 . 3 0 1 4 1 4 9 . 2 0 1 1 t i a r T 6 2 1 2 . 3 0 1 5 7 0 2 . 3 0 1 0 3 0 2 . 3 0 1 3 1 0 2 . 3 0 1 0 7 8 1 . 3 0 1 6 2 8 1 . 3 0 1 8 7 5 1 . 3 0 1 5 5 5 1 . 3 0 1 4 2 3 1 . 3 0 1 1 2 4 1 . 3 0 1 5 1 8 0 . 3 0 1 4 8 0 1 . 3 0 1 0 1 4 0 . 3 0 1 3 6 8 0 . 3 0 1 4 0 0 0 . 3 0 1 4 2 5 0 . 3 0 1 0 1 7 9 . 2 0 1 2 0 2 0 . 3 0 1 4 6 4 9 . 2 0 1 3 6 8 9 . 2 0 1 3 0 0 9 . 2 0 1 9 7 6 1 . 3 0 1 0 1 1 9 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 0 6 . B e l b a T 420 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T I H L K L K L K L K M L K J ] 9 8 8 6 . 3 0 1 , 3 2 6 6 . 3 0 1 [ ] 7 6 4 4 . 3 0 1 , 8 0 2 4 . 3 0 1 [ L K J I ] 1 6 4 7 . 3 0 1 , 6 9 1 7 . 3 0 1 [ ] 1 1 4 4 . 3 0 1 , 2 5 1 4 . 3 0 1 [ M L K J M L K ] 2 3 5 7 . 3 0 1 , 6 6 2 7 . 3 0 1 [ ] 1 2 5 4 . 3 0 1 , 2 6 2 4 . 3 0 1 [ ] 3 4 4 7 . 3 0 1 , 7 7 1 7 . 3 0 1 [ ] 0 3 6 4 . 3 0 1 , 1 7 3 4 . 3 0 1 [ M L ] 1 1 6 7 . 3 0 1 , 6 4 3 7 . 3 0 1 [ ] 1 5 6 4 . 3 0 1 , 2 9 3 4 . 3 0 1 [ L K J M L K ] 5 2 4 7 . 3 0 1 , 9 5 1 7 . 3 0 1 [ ] 6 0 6 4 . 3 0 1 , 7 4 3 4 . 3 0 1 [ L K K J J I I H H G G F F E E E D D C D C C B C B B L A L K J I ] 1 7 2 7 . 3 0 1 , 5 0 0 7 . 3 0 1 [ ] 5 0 4 4 . 3 0 1 , 5 4 1 4 . 3 0 1 [ M L ] 2 8 0 7 . 3 0 1 , 6 1 8 6 . 3 0 1 [ ] 3 0 7 4 . 3 0 1 , 3 4 4 4 . 3 0 1 [ M ] 5 8 4 7 . 3 0 1 , 0 2 2 7 . 3 0 1 [ ] 1 5 7 4 . 3 0 1 , 2 9 4 4 . 3 0 1 [ K J I H L K J I J I H I H G H G G F F E E D E D D C C B ] 6 0 9 6 . 3 0 1 , 1 4 6 6 . 3 0 1 [ ] 4 9 2 4 . 3 0 1 , 4 3 0 4 . 3 0 1 [ ] 9 1 7 6 . 3 0 1 , 4 5 4 6 . 3 0 1 [ ] 4 7 3 4 . 3 0 1 , 5 1 1 4 . 3 0 1 [ ] 5 3 4 6 . 3 0 1 , 0 7 1 6 . 3 0 1 [ ] 3 9 1 4 . 3 0 1 , 4 3 9 3 . 3 0 1 [ ] 9 2 3 6 . 3 0 1 , 3 6 0 6 . 3 0 1 [ ] 4 8 0 4 . 3 0 1 , 5 2 8 3 . 3 0 1 [ ] 5 5 9 5 . 3 0 1 , 9 8 6 5 . 3 0 1 [ ] 8 6 9 3 . 3 0 1 , 8 0 7 3 . 3 0 1 [ ] 5 4 8 5 . 3 0 1 , 9 7 5 5 . 3 0 1 [ ] 3 7 7 3 . 3 0 1 , 4 1 5 3 . 3 0 1 [ ] 7 4 6 5 . 3 0 1 , 1 8 3 5 . 3 0 1 [ ] 6 1 5 3 . 3 0 1 , 7 5 2 3 . 3 0 1 [ ] 5 0 4 5 . 3 0 1 , 0 4 1 5 . 3 0 1 [ ] 1 9 3 3 . 3 0 1 , 2 3 1 3 . 3 0 1 [ ] 8 5 3 5 . 3 0 1 , 2 9 0 5 . 3 0 1 [ ] 4 5 2 3 . 3 0 1 , 5 9 9 2 . 3 0 1 [ ] 1 5 1 5 . 3 0 1 , 6 8 8 4 . 3 0 1 [ ] 1 4 1 3 . 3 0 1 , 2 8 8 2 . 3 0 1 [ ] 5 3 1 5 . 3 0 1 , 9 6 8 4 . 3 0 1 [ ] 0 7 8 2 . 3 0 1 , 0 1 6 2 . 3 0 1 [ M L K J ] 5 9 6 7 . 3 0 1 , 0 3 4 7 . 3 0 1 [ ] 2 6 4 4 . 3 0 1 , 3 0 2 4 . 3 0 1 [ A ] 8 7 8 2 . 3 0 1 , 2 1 6 2 . 3 0 1 [ ] 9 2 7 1 . 3 0 1 , 9 6 4 1 . 3 0 1 [ B ] 0 8 9 4 . 3 0 1 , 4 1 7 4 . 3 0 1 [ ] 0 1 6 2 . 3 0 1 , 1 5 3 2 . 3 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 6 5 7 6 . 3 0 1 9 2 3 7 . 3 0 1 9 9 3 7 . 3 0 1 0 1 3 7 . 3 0 1 8 7 4 7 . 3 0 1 2 9 2 7 . 3 0 1 2 5 3 7 . 3 0 1 8 3 1 7 . 3 0 1 9 4 9 6 . 3 0 1 4 7 7 6 . 3 0 1 7 8 5 6 . 3 0 1 3 0 3 6 . 3 0 1 6 9 1 6 . 3 0 1 2 2 8 5 . 3 0 1 2 1 7 5 . 3 0 1 4 1 5 5 . 3 0 1 2 7 2 5 . 3 0 1 5 2 2 5 . 3 0 1 8 1 0 5 . 3 0 1 2 0 0 5 . 3 0 1 7 4 8 4 . 3 0 1 3 6 5 7 . 3 0 1 5 4 7 2 . 3 0 1 1 t i a r T 8 3 3 4 . 3 0 1 2 8 2 4 . 3 0 1 2 9 3 4 . 3 0 1 0 0 5 4 . 3 0 1 1 2 5 4 . 3 0 1 7 7 4 4 . 3 0 1 1 2 6 4 . 3 0 1 5 7 2 4 . 3 0 1 3 7 5 4 . 3 0 1 4 6 1 4 . 3 0 1 4 4 2 4 . 3 0 1 3 6 0 4 . 3 0 1 5 5 9 3 . 3 0 1 8 3 8 3 . 3 0 1 3 4 6 3 . 3 0 1 7 8 3 3 . 3 0 1 1 6 2 3 . 3 0 1 4 2 1 3 . 3 0 1 2 1 0 3 . 3 0 1 0 4 7 2 . 3 0 1 0 8 4 2 . 3 0 1 3 3 3 4 . 3 0 1 9 9 5 1 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 1 6 . B e l b a T 421 3.1.2. Population maximum true breeding value Figure B.17: Population maximum true breeding value by selection strategy over 60 generations in the multi-trait, TRUE scenario. 422 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T I H G F E J I H G F J I H D J I H J I H J I H J I J I H G J G F E D F E D J I H I H G F E H G F E G F E D C B C G F E D A C B E D B G G G G G G F G F G F G F G F E D G F ] 7 1 3 3 . 3 0 1 , 8 0 0 3 . 3 0 1 [ ] 7 9 4 3 . 3 0 1 , 7 8 1 3 . 3 0 1 [ ] 5 3 7 3 . 3 0 1 , 7 2 4 3 . 3 0 1 [ ] 9 7 5 3 . 3 0 1 , 9 6 2 3 . 3 0 1 [ ] 1 5 9 3 . 3 0 1 , 3 4 6 3 . 3 0 1 [ ] 4 9 5 3 . 3 0 1 , 4 8 2 3 . 3 0 1 [ ] 7 4 8 3 . 3 0 1 , 9 3 5 3 . 3 0 1 [ ] 7 9 5 3 . 3 0 1 , 7 8 2 3 . 3 0 1 [ ] 9 1 0 4 . 3 0 1 , 1 1 7 3 . 3 0 1 [ ] 9 3 5 3 . 3 0 1 , 9 2 2 3 . 3 0 1 [ ] 0 6 0 4 . 3 0 1 , 2 5 7 3 . 3 0 1 [ ] 3 8 4 3 . 3 0 1 , 3 7 1 3 . 3 0 1 [ ] 9 2 1 4 . 3 0 1 , 1 2 8 3 . 3 0 1 [ ] 2 2 3 3 . 3 0 1 , 1 1 0 3 . 3 0 1 [ ] 1 1 0 4 . 3 0 1 , 3 0 7 3 . 3 0 1 [ ] 8 5 4 3 . 3 0 1 , 8 4 1 3 . 3 0 1 [ ] 5 5 8 3 . 3 0 1 , 7 4 5 3 . 3 0 1 [ ] 4 3 2 3 . 3 0 1 , 4 2 9 2 . 3 0 1 [ ] 0 8 1 4 . 3 0 1 , 2 7 8 3 . 3 0 1 [ ] 0 9 3 3 . 3 0 1 , 0 8 0 3 . 3 0 1 [ ] 4 2 5 3 . 3 0 1 , 5 1 2 3 . 3 0 1 [ ] 3 6 7 2 . 3 0 1 , 3 5 4 2 . 3 0 1 [ ] 2 9 9 3 . 3 0 1 , 3 8 6 3 . 3 0 1 [ ] 1 9 2 3 . 3 0 1 , 0 8 9 2 . 3 0 1 [ E D C ] 5 4 4 3 . 3 0 1 , 7 3 1 3 . 3 0 1 [ ] 5 8 6 2 . 3 0 1 , 4 7 3 2 . 3 0 1 [ F E D C E D C B E D C B D C B A G F ] 1 3 7 3 . 3 0 1 , 3 2 4 3 . 3 0 1 [ ] 6 8 0 3 . 3 0 1 , 6 7 7 2 . 3 0 1 [ ] 6 4 8 2 . 3 0 1 , 8 3 5 2 . 3 0 1 [ ] 9 3 5 2 . 3 0 1 , 8 2 2 2 . 3 0 1 [ ] 4 2 7 3 . 3 0 1 , 6 1 4 3 . 3 0 1 [ ] 7 9 7 2 . 3 0 1 , 6 8 4 2 . 3 0 1 [ ] 0 8 7 2 . 3 0 1 , 1 7 4 2 . 3 0 1 [ ] 2 0 3 2 . 3 0 1 , 1 9 9 1 . 3 0 1 [ ] 6 2 5 3 . 3 0 1 , 7 1 2 3 . 3 0 1 [ ] 3 3 7 2 . 3 0 1 , 3 2 4 2 . 3 0 1 [ ] 1 6 6 2 . 3 0 1 , 3 5 3 2 . 3 0 1 [ ] 6 0 3 2 . 3 0 1 , 6 9 9 1 . 3 0 1 [ ] 8 6 3 3 . 3 0 1 , 0 6 0 3 . 3 0 1 [ ] 6 1 5 2 . 3 0 1 , 6 0 2 2 . 3 0 1 [ ] 5 2 4 2 . 3 0 1 , 7 1 1 2 . 3 0 1 [ ] 6 3 9 1 . 3 0 1 , 5 2 6 1 . 3 0 1 [ ] 6 2 5 3 . 3 0 1 , 7 1 2 3 . 3 0 1 [ ] 2 9 3 3 . 3 0 1 , 2 8 0 3 . 3 0 1 [ A ] 3 2 6 1 . 3 0 1 , 5 1 3 1 . 3 0 1 [ ] 9 6 8 1 . 3 0 1 , 9 5 5 1 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 3 6 1 3 . 3 0 1 1 8 5 3 . 3 0 1 7 9 7 3 . 3 0 1 3 9 6 3 . 3 0 1 5 6 8 3 . 3 0 1 6 0 9 3 . 3 0 1 5 7 9 3 . 3 0 1 7 5 8 3 . 3 0 1 1 0 7 3 . 3 0 1 6 2 0 4 . 3 0 1 9 6 3 3 . 3 0 1 7 3 8 3 . 3 0 1 1 9 2 3 . 3 0 1 7 7 5 3 . 3 0 1 2 9 6 2 . 3 0 1 0 7 5 3 . 3 0 1 5 2 6 2 . 3 0 1 1 7 3 3 . 3 0 1 7 0 5 2 . 3 0 1 4 1 2 3 . 3 0 1 1 7 2 2 . 3 0 1 1 7 3 3 . 3 0 1 9 6 4 1 . 3 0 1 1 t i a r T 2 4 3 3 . 3 0 1 4 2 4 3 . 3 0 1 9 3 4 3 . 3 0 1 2 4 4 3 . 3 0 1 4 8 3 3 . 3 0 1 8 2 3 3 . 3 0 1 7 6 1 3 . 3 0 1 3 0 3 3 . 3 0 1 9 7 0 3 . 3 0 1 5 3 2 3 . 3 0 1 8 0 6 2 . 3 0 1 5 3 1 3 . 3 0 1 9 2 5 2 . 3 0 1 1 3 9 2 . 3 0 1 4 8 3 2 . 3 0 1 2 4 6 2 . 3 0 1 6 4 1 2 . 3 0 1 8 7 5 2 . 3 0 1 1 5 1 2 . 3 0 1 1 6 3 2 . 3 0 1 0 8 7 1 . 3 0 1 7 3 2 3 . 3 0 1 4 1 7 1 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 2 6 . B e l b a T 423 l a c i t s i t a t S p u o r G I C % 5 9 0 3 n o i t a r e n e G F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T H G F E D C J I H G L K J I M L K M L K J M L M M L K J M L K J I H G F M L K J F E D K J I H G G F E D I H G F E D C I H G F E C B E D B E D C ] 3 4 4 7 . 3 0 1 , 9 9 0 7 . 3 0 1 [ ] 5 8 1 6 . 3 0 1 , 2 5 8 5 . 3 0 1 [ F E ] 6 9 9 7 . 3 0 1 , 1 5 6 7 . 3 0 1 [ ] 9 7 4 6 . 3 0 1 , 7 4 1 6 . 3 0 1 [ I H G F G F E I H G I H G I H I H ] 7 8 2 8 . 3 0 1 , 3 4 9 7 . 3 0 1 [ ] 6 7 5 6 . 3 0 1 , 3 4 2 6 . 3 0 1 [ ] 4 5 4 8 . 3 0 1 , 9 0 1 8 . 3 0 1 [ ] 9 1 8 6 . 3 0 1 , 7 8 4 6 . 3 0 1 [ ] 1 4 7 8 . 3 0 1 , 7 9 3 8 . 3 0 1 [ ] 1 8 9 6 . 3 0 1 , 8 4 6 6 . 3 0 1 [ ] 0 9 6 8 . 3 0 1 , 6 4 3 8 . 3 0 1 [ ] 8 2 9 6 . 3 0 1 , 6 9 5 6 . 3 0 1 [ ] 3 1 8 8 . 3 0 1 , 9 6 4 8 . 3 0 1 [ ] 2 9 0 7 . 3 0 1 , 0 6 7 6 . 3 0 1 [ ] 8 2 9 8 . 3 0 1 , 3 8 5 8 . 3 0 1 [ ] 8 0 1 7 . 3 0 1 , 6 7 7 6 . 3 0 1 [ I H G ] 4 0 7 8 . 3 0 1 , 0 6 3 8 . 3 0 1 [ ] 3 7 9 6 . 3 0 1 , 0 4 6 6 . 3 0 1 [ I ] 2 7 6 8 . 3 0 1 , 7 2 3 8 . 3 0 1 [ ] 2 9 1 7 . 3 0 1 , 0 6 8 6 . 3 0 1 [ I H G F I H G F F E D H G F F E D G F E D C F E ] 8 5 1 8 . 3 0 1 , 4 1 8 7 . 3 0 1 [ ] 1 7 7 6 . 3 0 1 , 9 3 4 6 . 3 0 1 [ ] 4 2 6 8 . 3 0 1 , 9 7 2 8 . 3 0 1 [ ] 1 2 8 6 . 3 0 1 , 9 8 4 6 . 3 0 1 [ ] 0 6 7 7 . 3 0 1 , 6 1 4 7 . 3 0 1 [ ] 6 2 4 6 . 3 0 1 , 3 9 0 6 . 3 0 1 [ ] 0 1 3 8 . 3 0 1 , 6 6 9 7 . 3 0 1 [ ] 7 4 7 6 . 3 0 1 , 4 1 4 6 . 3 0 1 [ ] 2 6 8 7 . 3 0 1 , 7 1 5 7 . 3 0 1 [ ] 3 9 3 6 . 3 0 1 , 1 6 0 6 . 3 0 1 [ ] 3 2 0 8 . 3 0 1 , 9 7 6 7 . 3 0 1 [ ] 4 8 5 6 . 3 0 1 , 1 5 2 6 . 3 0 1 [ ] 3 4 5 7 . 3 0 1 , 9 9 1 7 . 3 0 1 [ ] 6 2 0 6 . 3 0 1 , 3 9 6 5 . 3 0 1 [ ] 3 4 0 8 . 3 0 1 , 8 9 6 7 . 3 0 1 [ ] 2 6 4 6 . 3 0 1 , 9 2 1 6 . 3 0 1 [ E D C ] 2 0 7 7 . 3 0 1 , 8 5 3 7 . 3 0 1 [ ] 4 6 1 6 . 3 0 1 , 1 3 8 5 . 3 0 1 [ B ] 5 1 9 6 . 3 0 1 , 1 7 5 6 . 3 0 1 [ ] 5 5 3 5 . 3 0 1 , 3 2 0 5 . 3 0 1 [ C ] 3 1 1 7 . 3 0 1 , 9 6 7 6 . 3 0 1 [ ] 6 1 8 5 . 3 0 1 , 4 8 4 5 . 3 0 1 [ L K J I H G F E ] 5 3 4 8 . 3 0 1 , 0 9 0 8 . 3 0 1 [ ] 4 5 5 6 . 3 0 1 , 2 2 2 6 . 3 0 1 [ A A ] 9 3 9 4 . 3 0 1 , 4 9 5 4 . 3 0 1 [ ] 8 4 5 4 . 3 0 1 , 6 1 2 4 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 1 7 2 7 . 3 0 1 4 2 8 7 . 3 0 1 5 1 1 8 . 3 0 1 1 8 2 8 . 3 0 1 9 6 5 8 . 3 0 1 8 1 5 8 . 3 0 1 1 4 6 8 . 3 0 1 6 5 7 8 . 3 0 1 9 9 4 8 . 3 0 1 2 3 5 8 . 3 0 1 6 8 9 7 . 3 0 1 2 5 4 8 . 3 0 1 8 8 5 7 . 3 0 1 8 3 1 8 . 3 0 1 0 9 6 7 . 3 0 1 1 5 8 7 . 3 0 1 1 7 3 7 . 3 0 1 0 7 8 7 . 3 0 1 1 4 9 6 . 3 0 1 0 3 5 7 . 3 0 1 3 4 7 6 . 3 0 1 3 6 2 8 . 3 0 1 7 6 7 4 . 3 0 1 1 t i a r T 8 1 0 6 . 3 0 1 3 1 3 6 . 3 0 1 0 1 4 6 . 3 0 1 3 5 6 6 . 3 0 1 5 1 8 6 . 3 0 1 2 6 7 6 . 3 0 1 6 2 9 6 . 3 0 1 2 4 9 6 . 3 0 1 6 2 0 7 . 3 0 1 6 0 8 6 . 3 0 1 5 0 6 6 . 3 0 1 5 5 6 6 . 3 0 1 0 6 2 6 . 3 0 1 1 8 5 6 . 3 0 1 7 2 2 6 . 3 0 1 7 1 4 6 . 3 0 1 0 6 8 5 . 3 0 1 5 9 2 6 . 3 0 1 0 5 6 5 . 3 0 1 8 9 9 5 . 3 0 1 9 8 1 5 . 3 0 1 8 8 3 6 . 3 0 1 2 8 3 4 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 3 6 . B e l b a T 424 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r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t i a r T 4 4 7 9 . 3 0 1 7 4 7 0 . 4 0 1 3 8 8 0 . 4 0 1 8 4 2 1 . 4 0 1 5 5 3 1 . 4 0 1 0 0 6 1 . 4 0 1 2 8 6 1 . 4 0 1 4 1 8 1 . 4 0 1 6 3 5 1 . 4 0 1 2 8 6 1 . 4 0 1 2 3 5 1 . 4 0 1 7 6 4 1 . 4 0 1 1 2 5 1 . 4 0 1 1 7 1 1 . 4 0 1 0 4 1 1 . 4 0 1 6 9 9 0 . 4 0 1 8 1 8 0 . 4 0 1 1 3 8 0 . 4 0 1 3 6 7 0 . 4 0 1 8 8 7 0 . 4 0 1 7 8 5 0 . 4 0 1 0 4 0 1 . 4 0 1 9 9 4 7 . 3 0 1 1 t i a r T 7 5 2 7 . 3 0 1 4 5 6 7 . 3 0 1 8 0 8 7 . 3 0 1 0 2 3 8 . 3 0 1 5 5 3 8 . 3 0 1 2 1 7 8 . 3 0 1 3 2 9 8 . 3 0 1 6 2 8 8 . 3 0 1 1 8 2 9 . 3 0 1 4 6 9 8 . 3 0 1 5 6 1 9 . 3 0 1 8 0 1 9 . 3 0 1 7 0 2 9 . 3 0 1 3 0 1 9 . 3 0 1 2 9 9 8 . 3 0 1 1 7 8 8 . 3 0 1 8 4 7 8 . 3 0 1 5 7 7 8 . 3 0 1 4 1 6 8 . 3 0 1 2 0 5 8 . 3 0 1 1 6 1 8 . 3 0 1 7 6 6 7 . 3 0 1 7 0 0 6 . 3 0 1 l a c i t s i t a t S p u o r G I C % 5 9 5 4 n o i t a r e n e G . p o P n a e M V B T x a M n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 4 6 . B e l b a T 425 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T B C C E D D C H G F E G F E F E D H H G F H G H H H G F E H G F H G F E H G F E H G F E G F E H G F E D C A A B B ] 6 2 3 1 . 4 0 1 , 6 7 9 0 . 4 0 1 [ ] 8 8 7 7 . 3 0 1 , 9 4 4 7 . 3 0 1 [ ] 2 0 5 2 . 4 0 1 , 3 5 1 2 . 4 0 1 [ ] 1 6 4 8 . 3 0 1 , 3 2 1 8 . 3 0 1 [ ] 1 5 5 2 . 4 0 1 , 2 0 2 2 . 4 0 1 [ ] 6 1 4 8 . 3 0 1 , 8 7 0 8 . 3 0 1 [ D C ] 4 1 2 3 . 4 0 1 , 4 6 8 2 . 4 0 1 [ ] 5 8 4 9 . 3 0 1 , 6 4 1 9 . 3 0 1 [ C ] 6 2 9 2 . 4 0 1 , 6 7 5 2 . 4 0 1 [ ] 8 8 1 9 . 3 0 1 , 0 5 8 8 . 3 0 1 [ F E E D G F E H G F H G H G ] 6 7 5 3 . 4 0 1 , 7 2 2 3 . 4 0 1 [ ] 4 2 0 0 . 4 0 1 , 6 8 6 9 . 3 0 1 [ ] 1 5 4 3 . 4 0 1 , 2 0 1 3 . 4 0 1 [ ] 3 1 9 9 . 3 0 1 , 5 7 5 9 . 3 0 1 [ ] 5 2 9 3 . 4 0 1 , 6 7 5 3 . 4 0 1 [ ] 4 9 2 0 . 4 0 1 , 6 5 9 9 . 3 0 1 [ ] 7 7 3 3 . 4 0 1 , 8 2 0 3 . 4 0 1 [ ] 0 0 4 0 . 4 0 1 , 2 6 0 0 . 4 0 1 [ ] 2 2 9 3 . 4 0 1 , 2 7 5 3 . 4 0 1 [ ] 6 3 5 0 . 4 0 1 , 8 9 1 0 . 4 0 1 [ ] 6 4 8 3 . 4 0 1 , 7 9 4 3 . 4 0 1 [ ] 7 7 4 0 . 4 0 1 , 9 3 1 0 . 4 0 1 [ H G ] 0 3 9 3 . 4 0 1 , 0 8 5 3 . 4 0 1 [ ] 9 6 6 0 . 4 0 1 , 1 3 3 0 . 4 0 1 [ H ] 0 2 5 3 . 4 0 1 , 0 7 1 3 . 4 0 1 [ ] 3 3 8 0 . 4 0 1 , 5 9 4 0 . 4 0 1 [ H ] 7 8 7 3 . 4 0 1 , 8 3 4 3 . 4 0 1 [ ] 5 2 8 0 . 4 0 1 , 7 8 4 0 . 4 0 1 [ H G H G H G G F H G ] 4 6 7 3 . 4 0 1 , 5 1 4 3 . 4 0 1 [ ] 3 6 5 0 . 4 0 1 , 5 2 2 0 . 4 0 1 [ ] 7 5 6 3 . 4 0 1 , 8 0 3 3 . 4 0 1 [ ] 5 1 5 0 . 4 0 1 , 7 7 1 0 . 4 0 1 [ ] 2 3 6 3 . 4 0 1 , 2 8 2 3 . 4 0 1 [ ] 6 0 5 0 . 4 0 1 , 8 6 1 0 . 4 0 1 [ ] 2 6 4 3 . 4 0 1 , 2 1 1 3 . 4 0 1 [ ] 3 8 3 0 . 4 0 1 , 5 4 0 0 . 4 0 1 [ ] 0 5 6 3 . 4 0 1 , 1 0 3 3 . 4 0 1 [ ] 1 8 4 0 . 4 0 1 , 2 4 1 0 . 4 0 1 [ G F E ] 5 6 2 3 . 4 0 1 , 5 1 9 2 . 4 0 1 [ ] 6 1 3 0 . 4 0 1 , 8 7 9 9 . 3 0 1 [ F E ] 3 2 7 3 . 4 0 1 , 3 7 3 3 . 4 0 1 [ ] 5 3 0 0 . 4 0 1 , 7 9 6 9 . 3 0 1 [ B A ] 6 4 7 2 . 4 0 1 , 7 9 3 2 . 4 0 1 [ ] 9 0 4 8 . 3 0 1 , 1 7 0 8 . 3 0 1 [ ] 8 3 8 9 . 3 0 1 , 9 8 4 9 . 3 0 1 [ ] 9 6 3 7 . 3 0 1 , 1 3 0 7 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 1 5 1 1 . 4 0 1 8 2 3 2 . 4 0 1 7 7 3 2 . 4 0 1 9 3 0 3 . 4 0 1 1 5 7 2 . 4 0 1 2 0 4 3 . 4 0 1 7 7 2 3 . 4 0 1 1 5 7 3 . 4 0 1 3 0 2 3 . 4 0 1 7 4 7 3 . 4 0 1 2 7 6 3 . 4 0 1 2 1 6 3 . 4 0 1 5 5 7 3 . 4 0 1 5 4 3 3 . 4 0 1 9 8 5 3 . 4 0 1 2 8 4 3 . 4 0 1 7 5 4 3 . 4 0 1 7 8 2 3 . 4 0 1 5 7 4 3 . 4 0 1 0 9 0 3 . 4 0 1 8 4 5 3 . 4 0 1 1 7 5 2 . 4 0 1 3 6 6 9 . 3 0 1 1 t i a r T 9 1 6 7 . 3 0 1 2 9 2 8 . 3 0 1 7 4 2 8 . 3 0 1 6 1 3 9 . 3 0 1 9 1 0 9 . 3 0 1 5 5 8 9 . 3 0 1 4 4 7 9 . 3 0 1 5 2 1 0 . 4 0 1 1 3 2 0 . 4 0 1 7 6 3 0 . 4 0 1 8 0 3 0 . 4 0 1 6 5 6 0 . 4 0 1 0 0 5 0 . 4 0 1 4 6 6 0 . 4 0 1 4 9 3 0 . 4 0 1 6 4 3 0 . 4 0 1 7 3 3 0 . 4 0 1 4 1 2 0 . 4 0 1 1 1 3 0 . 4 0 1 7 4 1 0 . 4 0 1 6 6 8 9 . 3 0 1 0 4 2 8 . 3 0 1 0 0 2 7 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 5 6 . B e l b a T 426 3.1.3. Population mean expected heterozygosity Generation 15 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.1824 GEBV 0.1901 gwGEBV05 0.1948 gwGEBV10d 0.1964 gwGEBV10 0.2064 gwGEBV20d 0.2036 gwGEBV15 0.2168 gwGEBV30d 0.2100 gwGEBV20 0.2240 gwGEBV40d 0.2155 gwGEBV25 0.2311 gwGEBV50d 0.2207 gwGEBV30 0.2343 gwGEBV60d 0.2243 gwGEBV35 0.2360 gwGEBV70d 0.2281 gwGEBV40 0.2374 gwGEBV80d 0.2322 gwGEBV45 0.2389 gwGEBV90d 0.2343 gwGEBV50 gwGEBV100d 0.2379 0.2296 OCS 0.2165 RS [0.1818, 0.1830] A [0.1895, 0.1906] B [0.1942, 0.1954] C [0.1959, 0.1970] D [0.2058, 0.2070] F [0.2030, 0.2041] E [0.2162, 0.2174] H [0.2095, 0.2106] G [0.2234, 0.2246] J [0.2149, 0.2160] H [0.2306, 0.2317] M [0.2201, 0.2213] I [0.2337, 0.2349] N [0.2237, 0.2248] J [0.2354, 0.2366] O [0.2275, 0.2286] K [0.2369, 0.2380] OP [0.2317, 0.2328] M [0.2383, 0.2395] P [0.2337, 0.2348] N [0.2373, 0.2384] P [0.2290, 0.2302] L [0.2160, 0.2171] H DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.66: Population mean expected heterozygosity by selection strategy at generation 15 in the multi-trait, TRUE scenario. 427 Generation 30 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.1192 GEBV 0.1336 gwGEBV05 0.1386 gwGEBV10d 0.1444 gwGEBV10 0.1521 gwGEBV20d 0.1561 gwGEBV15 0.1667 gwGEBV30d 0.1652 gwGEBV20 0.1776 gwGEBV40d 0.1722 gwGEBV25 0.1876 gwGEBV50d 0.1799 gwGEBV30 0.1941 gwGEBV60d 0.1849 gwGEBV35 0.1992 gwGEBV70d 0.1906 gwGEBV40 0.2032 gwGEBV80d 0.1958 gwGEBV45 0.2063 gwGEBV90d gwGEBV50 0.2001 gwGEBV100d 0.2076 0.1636 OCS 0.1816 RS [0.1183, 0.1201] A [0.1327, 0.1345] B [0.1377, 0.1395] C [0.1435, 0.1453] D [0.1513, 0.1530] E [0.1552, 0.1570] F [0.1658, 0.1676] H [0.1643, 0.1661] GH [0.1767, 0.1785] J [0.1713, 0.1731] I [0.1867, 0.1885] M [0.1790, 0.1808] JK [0.1932, 0.1950] O [0.1840, 0.1858] L [0.1983, 0.2001] P [0.1897, 0.1915] N [0.2023, 0.2041] Q [0.1949, 0.1967] O [0.2054, 0.2072] R [0.1992, 0.2010] P [0.2067, 0.2085] R [0.1627, 0.1645] G [0.1807, 0.1825] K DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.67: Population mean expected heterozygosity by selection strategy at generation 30 in the multi-trait, TRUE scenario. 428 Generation 45 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.0798 GEBV 0.0945 gwGEBV05 0.0964 gwGEBV10d 0.1078 gwGEBV10 0.1093 gwGEBV20d 0.1200 gwGEBV15 0.1224 gwGEBV30d 0.1309 gwGEBV20 0.1320 gwGEBV40d 0.1388 gwGEBV25 0.1423 gwGEBV50d 0.1478 gwGEBV30 0.1508 gwGEBV60d 0.1525 gwGEBV35 0.1571 gwGEBV70d 0.1595 gwGEBV40 0.1642 gwGEBV80d 0.1655 gwGEBV45 0.1684 gwGEBV90d gwGEBV50 0.1705 gwGEBV100d 0.1723 0.1064 OCS 0.1531 RS [0.0787, 0.0809] A [0.0934, 0.0956] B [0.0954, 0.0975] B [0.1067, 0.1089] CD [0.1082, 0.1104] D [0.1189, 0.1211] E [0.1213, 0.1235] E [0.1298, 0.1320] F [0.1309, 0.1331] F [0.1377, 0.1399] G [0.1412, 0.1434] H [0.1467, 0.1489] I [0.1497, 0.1519] J [0.1515, 0.1536] J [0.1560, 0.1582] K [0.1584, 0.1606] K [0.1631, 0.1653] L [0.1644, 0.1666] L [0.1674, 0.1695] M [0.1694, 0.1716] MN [0.1712, 0.1734] N [0.1053, 0.1074] C [0.1520, 0.1542] J DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.68: Population mean expected heterozygosity by selection strategy at generation 45 in the multi-trait, TRUE scenario. 429 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B C C E D G F E I F K G M I H N J O N L K P O M L P H I H A B C C D D G E H F J G K H ] 0 6 7 5 . 6 0 1 , 2 4 5 5 . 6 0 1 [ ] 0 5 8 2 . 6 0 1 , 9 2 6 2 . 6 0 1 [ ] 9 0 0 7 . 6 0 1 , 1 9 7 6 . 6 0 1 [ ] 8 6 7 3 . 6 0 1 , 7 4 5 3 . 6 0 1 [ ] 6 1 7 7 . 6 0 1 , 8 9 4 7 . 6 0 1 [ ] 1 6 6 4 . 6 0 1 , 9 3 4 4 . 6 0 1 [ ] 3 7 8 7 . 6 0 1 , 6 5 6 7 . 6 0 1 [ ] 6 5 8 4 . 6 0 1 , 5 3 6 4 . 6 0 1 [ ] 1 4 8 8 . 6 0 1 , 3 2 6 8 . 6 0 1 [ ] 3 4 7 5 . 6 0 1 , 1 2 5 5 . 6 0 1 [ ] 0 3 5 8 . 6 0 1 , 3 1 3 8 . 6 0 1 [ ] 9 8 4 5 . 6 0 1 , 8 6 2 5 . 6 0 1 [ ] 5 7 7 9 . 6 0 1 , 7 5 5 9 . 6 0 1 [ ] 6 2 2 7 . 6 0 1 , 5 0 0 7 . 6 0 1 [ ] 3 7 9 8 . 6 0 1 , 6 5 7 8 . 6 0 1 [ ] 4 9 1 6 . 6 0 1 , 3 7 9 5 . 6 0 1 [ ] 3 5 5 0 . 7 0 1 , 6 3 3 0 . 7 0 1 [ ] 9 8 0 8 . 6 0 1 , 7 6 8 7 . 6 0 1 [ ] 9 1 5 9 . 6 0 1 , 1 0 3 9 . 6 0 1 [ ] 4 4 8 6 . 6 0 1 , 3 2 6 6 . 6 0 1 [ ] 4 2 7 1 . 7 0 1 , 6 0 5 1 . 7 0 1 [ ] 3 3 9 8 . 6 0 1 , 2 1 7 8 . 6 0 1 [ ] 3 1 9 9 . 6 0 1 , 5 9 6 9 . 6 0 1 [ ] 2 8 4 7 . 6 0 1 , 1 6 2 7 . 6 0 1 [ ] 0 1 3 2 . 7 0 1 , 2 9 0 2 . 7 0 1 [ ] 8 0 4 9 . 6 0 1 , 7 8 1 9 . 6 0 1 [ ] 2 0 3 0 . 7 0 1 , 5 8 0 0 . 7 0 1 [ ] 8 3 9 7 . 6 0 1 , 7 1 7 7 . 6 0 1 [ L K ] 3 0 7 2 . 7 0 1 , 6 8 4 2 . 7 0 1 [ ] 0 1 5 9 . 6 0 1 , 8 8 2 9 . 6 0 1 [ I ] 8 5 0 1 . 7 0 1 , 0 4 8 0 . 7 0 1 [ ] 5 4 5 8 . 6 0 1 , 4 2 3 8 . 6 0 1 [ M L ] 4 8 9 2 . 7 0 1 , 6 6 7 2 . 7 0 1 [ ] 7 2 7 9 . 6 0 1 , 5 0 5 9 . 6 0 1 [ J ] 9 1 8 1 . 7 0 1 , 2 0 6 1 . 7 0 1 [ ] 8 3 9 8 . 6 0 1 , 7 1 7 8 . 6 0 1 [ N M ] 5 7 1 3 . 7 0 1 , 8 5 9 2 . 7 0 1 [ ] 4 0 0 0 . 7 0 1 , 3 8 7 9 . 6 0 1 [ K N E G ] 2 9 0 2 . 7 0 1 , 4 7 8 1 . 7 0 1 [ ] 2 1 4 9 . 6 0 1 , 1 9 1 9 . 6 0 1 [ ] 8 5 4 3 . 7 0 1 , 0 4 2 3 . 7 0 1 [ ] 7 1 1 0 . 7 0 1 , 6 9 8 9 . 6 0 1 [ ] 1 5 2 0 . 7 0 1 , 3 3 0 0 . 7 0 1 [ ] 1 2 2 6 . 6 0 1 , 0 0 0 6 . 6 0 1 [ ] 9 2 5 0 . 7 0 1 , 1 1 3 0 . 7 0 1 [ ] 1 7 3 7 . 6 0 1 , 0 5 1 7 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 1 5 6 5 . 6 0 1 0 0 9 6 . 6 0 1 7 0 6 7 . 6 0 1 4 6 7 7 . 6 0 1 2 3 7 8 . 6 0 1 1 2 4 8 . 6 0 1 6 6 6 9 . 6 0 1 4 6 8 8 . 6 0 1 5 4 4 0 . 7 0 1 0 1 4 9 . 6 0 1 5 1 6 1 . 7 0 1 4 0 8 9 . 6 0 1 1 0 2 2 . 7 0 1 3 9 1 0 . 7 0 1 5 9 5 2 . 7 0 1 9 4 9 0 . 7 0 1 5 7 8 2 . 7 0 1 0 1 7 1 . 7 0 1 6 6 0 3 . 7 0 1 3 8 9 1 . 7 0 1 9 4 3 3 . 7 0 1 2 4 1 0 . 7 0 1 0 2 4 0 . 7 0 1 1 t i a r T 9 3 7 2 . 6 0 1 7 5 6 3 . 6 0 1 0 5 5 4 . 6 0 1 5 4 7 4 . 6 0 1 2 3 6 5 . 6 0 1 9 7 3 5 . 6 0 1 5 1 1 7 . 6 0 1 3 8 0 6 . 6 0 1 8 7 9 7 . 6 0 1 3 3 7 6 . 6 0 1 2 2 8 8 . 6 0 1 2 7 3 7 . 6 0 1 7 9 2 9 . 6 0 1 7 2 8 7 . 6 0 1 9 9 3 9 . 6 0 1 4 3 4 8 . 6 0 1 6 1 6 9 . 6 0 1 7 2 8 8 . 6 0 1 3 9 8 9 . 6 0 1 1 0 3 9 . 6 0 1 7 0 0 0 . 7 0 1 1 1 1 6 . 6 0 1 1 6 2 7 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g d 0 6 V B E G w g 0 3 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 9 6 . B e l b a T 430 t i m i l n o i t c e l e s r e p p u n o i t a l u p o P . 4 . 1 . 3 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B C D F F H G J I L J M K N L O M P N Q E I A B C D F F H G J I H K I L J ] 2 5 4 6 . 5 0 1 , 7 1 1 6 . 5 0 1 [ ] 1 4 6 4 . 5 0 1 , 2 3 3 4 . 5 0 1 [ ] 2 8 0 9 . 5 0 1 , 6 4 7 8 . 5 0 1 [ ] 3 3 0 7 . 5 0 1 , 4 2 7 6 . 5 0 1 [ ] 9 6 0 0 . 6 0 1 , 4 3 7 9 . 5 0 1 [ ] 9 6 8 7 . 5 0 1 , 1 6 5 7 . 5 0 1 [ ] 0 9 1 1 . 6 0 1 , 5 5 8 0 . 6 0 1 [ ] 2 8 0 9 . 5 0 1 , 3 7 7 8 . 5 0 1 [ ] 6 4 1 3 . 6 0 1 , 1 1 8 2 . 6 0 1 [ ] 1 2 7 0 . 6 0 1 , 3 1 4 0 . 6 0 1 [ ] 1 8 2 3 . 6 0 1 , 6 4 9 2 . 6 0 1 [ ] 3 6 9 0 . 6 0 1 , 5 5 6 0 . 6 0 1 [ ] 1 7 4 5 . 6 0 1 , 6 3 1 5 . 6 0 1 [ ] 7 6 1 3 . 6 0 1 , 9 5 8 2 . 6 0 1 [ ] 1 0 8 4 . 6 0 1 , 6 6 4 4 . 6 0 1 [ ] 3 4 2 2 . 6 0 1 , 4 3 9 1 . 6 0 1 [ ] 2 5 0 7 . 6 0 1 , 7 1 7 6 . 6 0 1 [ ] 9 2 6 4 . 6 0 1 , 1 2 3 4 . 6 0 1 [ ] 4 2 9 5 . 6 0 1 , 9 8 5 5 . 6 0 1 [ ] 0 4 2 3 . 6 0 1 , 2 3 9 2 . 6 0 1 [ ] 2 3 9 8 . 6 0 1 , 6 9 5 8 . 6 0 1 [ ] 4 2 8 5 . 6 0 1 , 6 1 5 5 . 6 0 1 [ ] 4 2 8 6 . 6 0 1 , 8 8 4 6 . 6 0 1 [ ] 9 7 4 4 . 6 0 1 , 1 7 1 4 . 6 0 1 [ ] 7 6 8 9 . 6 0 1 , 2 3 5 9 . 6 0 1 [ ] 7 4 5 6 . 6 0 1 , 9 3 2 6 . 6 0 1 [ ] 3 9 6 7 . 6 0 1 , 8 5 3 7 . 6 0 1 [ ] 9 9 9 4 . 6 0 1 , 1 9 6 4 . 6 0 1 [ M ] 2 7 5 0 . 7 0 1 , 7 3 2 0 . 7 0 1 [ ] 7 7 0 7 . 6 0 1 , 9 6 7 6 . 6 0 1 [ K N L O M O E H ] 3 1 8 8 . 6 0 1 , 8 7 4 8 . 6 0 1 [ ] 5 2 9 5 . 6 0 1 , 7 1 6 5 . 6 0 1 [ ] 0 8 1 1 . 7 0 1 , 5 4 8 0 . 7 0 1 [ ] 4 6 6 7 . 6 0 1 , 6 5 3 7 . 6 0 1 [ ] 6 9 7 9 . 6 0 1 , 1 6 4 9 . 6 0 1 [ ] 8 6 6 6 . 6 0 1 , 9 5 3 6 . 6 0 1 [ ] 3 9 6 1 . 7 0 1 , 8 5 3 1 . 7 0 1 [ ] 9 5 1 8 . 6 0 1 , 1 5 8 7 . 6 0 1 [ ] 8 3 3 0 . 7 0 1 , 3 0 0 0 . 7 0 1 [ ] 7 6 1 7 . 6 0 1 , 9 5 8 6 . 6 0 1 [ ] 2 5 1 2 . 7 0 1 , 7 1 8 1 . 7 0 1 [ ] 3 7 4 8 . 6 0 1 , 5 6 1 8 . 6 0 1 [ ] 4 2 5 2 . 6 0 1 , 8 8 1 2 . 6 0 1 [ ] 9 0 8 9 . 5 0 1 , 0 0 5 9 . 5 0 1 [ ] 7 2 2 6 . 6 0 1 , 2 9 8 5 . 6 0 1 [ ] 9 8 2 3 . 6 0 1 , 1 8 9 2 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 4 8 2 6 . 5 0 1 4 1 9 8 . 5 0 1 1 0 9 9 . 5 0 1 3 2 0 1 . 6 0 1 8 7 9 2 . 6 0 1 4 1 1 3 . 6 0 1 3 0 3 5 . 6 0 1 4 3 6 4 . 6 0 1 5 8 8 6 . 6 0 1 6 5 7 5 . 6 0 1 4 6 7 8 . 6 0 1 6 5 6 6 . 6 0 1 9 9 6 9 . 6 0 1 5 2 5 7 . 6 0 1 5 0 4 0 . 7 0 1 5 4 6 8 . 6 0 1 3 1 0 1 . 7 0 1 9 2 6 9 . 6 0 1 5 2 5 1 . 7 0 1 1 7 1 0 . 7 0 1 5 8 9 1 . 7 0 1 6 5 3 2 . 6 0 1 9 5 0 6 . 6 0 1 1 t i a r T 7 8 4 4 . 5 0 1 9 7 8 6 . 5 0 1 5 1 7 7 . 5 0 1 7 2 9 8 . 5 0 1 7 6 5 0 . 6 0 1 9 0 8 0 . 6 0 1 3 1 0 3 . 6 0 1 8 8 0 2 . 6 0 1 5 7 4 4 . 6 0 1 6 8 0 3 . 6 0 1 0 7 6 5 . 6 0 1 5 2 3 4 . 6 0 1 3 9 3 6 . 6 0 1 5 4 8 4 . 6 0 1 3 2 9 6 . 6 0 1 1 7 7 5 . 6 0 1 0 1 5 7 . 6 0 1 3 1 5 6 . 6 0 1 5 0 0 8 . 6 0 1 3 1 0 7 . 6 0 1 9 1 3 8 . 6 0 1 5 5 6 9 . 5 0 1 5 3 1 3 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 0 7 . B e l b a T 431 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B B D E F G H I I K J L K M L N N O O P C I A B C D E F G G I ] 1 2 0 0 . 5 0 1 , 3 2 6 9 . 4 0 1 [ ] 7 3 7 7 . 4 0 1 , 7 5 3 7 . 4 0 1 [ ] 1 5 5 3 . 5 0 1 , 2 5 1 3 . 5 0 1 [ ] 5 4 7 0 . 5 0 1 , 5 6 3 0 . 5 0 1 [ ] 7 9 9 3 . 5 0 1 , 8 9 5 3 . 5 0 1 [ ] 7 5 4 1 . 5 0 1 , 7 7 0 1 . 5 0 1 [ ] 8 0 2 6 . 5 0 1 , 0 1 8 5 . 5 0 1 [ ] 0 8 7 3 . 5 0 1 , 0 0 4 3 . 5 0 1 [ ] 0 3 1 7 . 5 0 1 , 1 3 7 6 . 5 0 1 [ ] 1 4 9 4 . 5 0 1 , 1 6 5 4 . 5 0 1 [ ] 8 6 8 8 . 5 0 1 , 9 6 4 8 . 5 0 1 [ ] 6 6 6 6 . 5 0 1 , 5 8 2 6 . 5 0 1 [ ] 4 3 1 0 . 6 0 1 , 6 3 7 9 . 5 0 1 [ ] 3 3 0 8 . 5 0 1 , 3 5 6 7 . 5 0 1 [ ] 5 2 9 0 . 6 0 1 , 7 2 5 0 . 6 0 1 [ ] 4 1 4 8 . 5 0 1 , 4 3 0 8 . 5 0 1 [ ] 2 1 4 2 . 6 0 1 , 4 1 0 2 . 6 0 1 [ ] 8 6 1 0 . 6 0 1 , 8 8 7 9 . 5 0 1 [ I H ] 0 4 4 2 . 6 0 1 , 2 4 0 2 . 6 0 1 [ ] 6 0 9 9 . 5 0 1 , 5 2 5 9 . 5 0 1 [ J J K K L L M M N ] 6 3 7 4 . 6 0 1 , 8 3 3 4 . 6 0 1 [ ] 8 9 6 1 . 6 0 1 , 8 1 3 1 . 6 0 1 [ ] 6 0 8 3 . 6 0 1 , 8 0 4 3 . 6 0 1 [ ] 2 6 5 1 . 6 0 1 , 2 8 1 1 . 6 0 1 [ ] 8 2 2 6 . 6 0 1 , 9 2 8 5 . 6 0 1 [ ] 7 9 8 2 . 6 0 1 , 7 1 5 2 . 6 0 1 [ ] 2 9 0 5 . 6 0 1 , 4 9 6 4 . 6 0 1 [ ] 6 5 4 2 . 6 0 1 , 6 7 0 2 . 6 0 1 [ ] 8 9 0 7 . 6 0 1 , 0 0 7 6 . 6 0 1 [ ] 7 1 5 3 . 6 0 1 , 7 3 1 3 . 6 0 1 [ ] 1 6 4 6 . 6 0 1 , 3 6 0 6 . 6 0 1 [ ] 3 2 5 3 . 6 0 1 , 3 4 1 3 . 6 0 1 [ ] 6 1 9 7 . 6 0 1 , 7 1 5 7 . 6 0 1 [ ] 2 4 3 4 . 6 0 1 , 2 6 9 3 . 6 0 1 [ ] 5 2 8 7 . 6 0 1 , 6 2 4 7 . 6 0 1 [ ] 6 0 4 4 . 6 0 1 , 5 2 0 4 . 6 0 1 [ ] 4 5 7 8 . 6 0 1 , 5 5 3 8 . 6 0 1 [ ] 8 6 9 4 . 6 0 1 , 8 8 5 4 . 6 0 1 [ O N ] 6 6 6 8 . 6 0 1 , 7 6 2 8 . 6 0 1 [ ] 1 3 2 5 . 6 0 1 , 1 5 8 4 . 6 0 1 [ O C H ] 1 2 4 9 . 6 0 1 , 2 2 0 9 . 6 0 1 [ ] 7 6 4 5 . 6 0 1 , 7 8 0 5 . 6 0 1 [ ] 6 1 7 4 . 5 0 1 , 8 1 3 4 . 5 0 1 [ ] 3 5 7 1 . 5 0 1 , 3 7 3 1 . 5 0 1 [ ] 7 9 1 2 . 6 0 1 , 8 9 7 1 . 6 0 1 [ ] 7 1 5 9 . 5 0 1 , 7 3 1 9 . 5 0 1 [ . p o P n a e M L S U 2 t i a r T 2 2 8 9 . 4 0 1 2 5 3 3 . 5 0 1 8 9 7 3 . 5 0 1 9 0 0 6 . 5 0 1 0 3 9 6 . 5 0 1 8 6 6 8 . 5 0 1 5 3 9 9 . 5 0 1 6 2 7 0 . 6 0 1 3 1 2 2 . 6 0 1 1 4 2 2 . 6 0 1 7 3 5 4 . 6 0 1 7 0 6 3 . 6 0 1 8 2 0 6 . 6 0 1 3 9 8 4 . 6 0 1 9 9 8 6 . 6 0 1 2 6 2 6 . 6 0 1 7 1 7 7 . 6 0 1 6 2 6 7 . 6 0 1 4 5 5 8 . 6 0 1 7 6 4 8 . 6 0 1 1 2 2 9 . 6 0 1 7 1 5 4 . 5 0 1 8 9 9 1 . 6 0 1 1 t i a r T 7 4 5 7 . 4 0 1 5 5 5 0 . 5 0 1 7 6 2 1 . 5 0 1 0 9 5 3 . 5 0 1 1 5 7 4 . 5 0 1 5 7 4 6 . 5 0 1 3 4 8 7 . 5 0 1 4 2 2 8 . 5 0 1 8 7 9 9 . 5 0 1 5 1 7 9 . 5 0 1 8 0 5 1 . 6 0 1 2 7 3 1 . 6 0 1 7 0 7 2 . 6 0 1 6 6 2 2 . 6 0 1 7 2 3 3 . 6 0 1 3 3 3 3 . 6 0 1 2 5 1 4 . 6 0 1 6 1 2 4 . 6 0 1 8 7 7 4 . 6 0 1 1 4 0 5 . 6 0 1 7 7 2 5 . 6 0 1 3 6 5 1 . 5 0 1 7 2 3 9 . 5 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 1 7 . B e l b a T 432 3.1.5. Population additive genetic variance Figure B.18: Population additive genetic variance by selection strategy over 60 generations in the multi-trait, TRUE scenario. 433 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 1 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T B A C B C B D C A C G F E E D C H G F G F B A C B ] 6 8 2 0 . 0 , 7 6 2 0 . 0 [ ] 1 7 2 0 . 0 , 4 5 2 0 . 0 [ ] 6 0 3 0 . 0 , 7 8 2 0 . 0 [ ] 0 8 2 0 . 0 , 3 6 2 0 . 0 [ A ] 3 6 2 0 . 0 , 4 4 2 0 . 0 [ ] 1 5 2 0 . 0 , 4 3 2 0 . 0 [ D C B ] 0 1 3 0 . 0 , 1 9 2 0 . 0 [ ] 7 8 2 0 . 0 , 0 7 2 0 . 0 [ D C D C F E E D ] 4 2 3 0 . 0 , 5 0 3 0 . 0 [ ] 3 0 3 0 . 0 , 5 8 2 0 . 0 [ ] 6 1 3 0 . 0 , 7 9 2 0 . 0 [ ] 5 9 2 0 . 0 , 8 7 2 0 . 0 [ ] 1 5 3 0 . 0 , 2 3 3 0 . 0 [ ] 8 2 3 0 . 0 , 0 1 3 0 . 0 [ ] 7 2 3 0 . 0 , 9 0 3 0 . 0 [ ] 7 0 3 0 . 0 , 0 9 2 0 . 0 [ I H G F H G F ] 3 6 3 0 . 0 , 4 4 3 0 . 0 [ ] 0 4 3 0 . 0 , 3 2 3 0 . 0 [ ] 4 5 3 0 . 0 , 5 3 3 0 . 0 [ ] 4 3 3 0 . 0 , 7 1 3 0 . 0 [ J I H G K J I H G ] 2 7 3 0 . 0 , 4 5 3 0 . 0 [ ] 3 5 3 0 . 0 , 5 3 3 0 . 0 [ G F J I H H G F J I H I H G J I H J I J I H J I H J F E D E D C I H G F ] 4 6 3 0 . 0 , 5 4 3 0 . 0 [ ] 6 3 3 0 . 0 , 9 1 3 0 . 0 [ K ] 3 8 3 0 . 0 , 4 6 3 0 . 0 [ ] 9 6 3 0 . 0 , 2 5 3 0 . 0 [ J I H G F ] 9 6 3 0 . 0 , 1 5 3 0 . 0 [ ] 5 4 3 0 . 0 , 7 2 3 0 . 0 [ G F K J ] 4 5 3 0 . 0 , 5 3 3 0 . 0 [ ] 2 3 3 0 . 0 , 5 1 3 0 . 0 [ ] 7 8 3 0 . 0 , 8 6 3 0 . 0 [ ] 5 6 3 0 . 0 , 7 4 3 0 . 0 [ K J K J I ] 6 9 3 0 . 0 , 7 7 3 0 . 0 [ ] 6 6 3 0 . 0 , 9 4 3 0 . 0 [ ] 2 8 3 0 . 0 , 3 6 3 0 . 0 [ ] 7 5 3 0 . 0 , 0 4 3 0 . 0 [ K ] 2 9 3 0 . 0 , 3 7 3 0 . 0 [ ] 8 6 3 0 . 0 , 1 5 3 0 . 0 [ K J I ] 4 8 3 0 . 0 , 6 6 3 0 . 0 [ ] 8 5 3 0 . 0 , 1 4 3 0 . 0 [ K J I H ] 5 8 3 0 . 0 , 6 6 3 0 . 0 [ ] 6 5 3 0 . 0 , 9 3 3 0 . 0 [ G F E D ] 2 4 3 0 . 0 , 3 2 3 0 . 0 [ ] 2 3 3 0 . 0 , 5 1 3 0 . 0 [ ] 9 2 3 0 . 0 , 0 1 3 0 . 0 [ ] 7 0 3 0 . 0 , 0 9 2 0 . 0 [ 4 5 2 0 . 0 6 7 2 0 . 0 6 9 2 0 . 0 0 0 3 0 . 0 5 1 3 0 . 0 6 0 3 0 . 0 1 4 3 0 . 0 8 1 3 0 . 0 3 5 3 0 . 0 5 4 3 0 . 0 3 6 3 0 . 0 5 4 3 0 . 0 7 7 3 0 . 0 5 5 3 0 . 0 4 7 3 0 . 0 0 6 3 0 . 0 6 8 3 0 . 0 2 7 3 0 . 0 3 8 3 0 . 0 5 7 3 0 . 0 5 7 3 0 . 0 3 3 3 0 . 0 9 1 3 0 . 0 3 4 2 0 . 0 2 6 2 0 . 0 2 7 2 0 . 0 8 7 2 0 . 0 4 9 2 0 . 0 6 8 2 0 . 0 9 1 3 0 . 0 8 9 2 0 . 0 1 3 3 0 . 0 5 2 3 0 . 0 4 4 3 0 . 0 3 2 3 0 . 0 6 5 3 0 . 0 8 2 3 0 . 0 0 6 3 0 . 0 6 3 3 0 . 0 7 5 3 0 . 0 8 4 3 0 . 0 0 6 3 0 . 0 9 4 3 0 . 0 7 4 3 0 . 0 4 2 3 0 . 0 9 9 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 2 7 . B e l b a T 434 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 3 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B D C F E D A B F E H G H G I H K J J I J I E D C ] 0 1 2 0 . 0 , 3 9 1 0 . 0 [ ] 5 9 1 0 . 0 , 9 7 1 0 . 0 [ C B ] 1 9 1 0 . 0 , 4 7 1 0 . 0 [ ] 8 7 1 0 . 0 , 2 6 1 0 . 0 [ A B ] 0 5 1 0 . 0 , 3 3 1 0 . 0 [ ] 1 4 1 0 . 0 , 5 2 1 0 . 0 [ ] 0 8 1 0 . 0 , 3 6 1 0 . 0 [ ] 4 6 1 0 . 0 , 7 4 1 0 . 0 [ E D F E H G H G J I I H J J I ] 9 2 2 0 . 0 , 2 1 2 0 . 0 [ ] 3 1 2 0 . 0 , 7 9 1 0 . 0 [ ] 2 3 2 0 . 0 , 5 1 2 0 . 0 [ ] 6 1 2 0 . 0 , 0 0 2 0 . 0 [ ] 2 6 2 0 . 0 , 5 4 2 0 . 0 [ ] 0 5 2 0 . 0 , 4 3 2 0 . 0 [ ] 8 6 2 0 . 0 , 1 5 2 0 . 0 [ ] 8 4 2 0 . 0 , 1 3 2 0 . 0 [ ] 0 0 3 0 . 0 , 2 8 2 0 . 0 [ ] 3 8 2 0 . 0 , 7 6 2 0 . 0 [ ] 8 7 2 0 . 0 , 1 6 2 0 . 0 [ ] 6 6 2 0 . 0 , 0 5 2 0 . 0 [ ] 7 0 3 0 . 0 , 0 9 2 0 . 0 [ ] 7 9 2 0 . 0 , 0 8 2 0 . 0 [ ] 7 9 2 0 . 0 , 0 8 2 0 . 0 [ ] 3 8 2 0 . 0 , 6 6 2 0 . 0 [ M L K L K ] 4 2 3 0 . 0 , 7 0 3 0 . 0 [ ] 8 1 3 0 . 0 , 2 0 3 0 . 0 [ L K J O N L K J O N M L O O N M E D C G F O K J M K J M L M L M L M L D C G F ] 3 1 3 0 . 0 , 6 9 2 0 . 0 [ ] 8 9 2 0 . 0 , 2 8 2 0 . 0 [ ] 2 5 3 0 . 0 , 5 3 3 0 . 0 [ ] 2 4 3 0 . 0 , 5 2 3 0 . 0 [ ] 6 1 3 0 . 0 , 8 9 2 0 . 0 [ ] 8 9 2 0 . 0 , 1 8 2 0 . 0 [ ] 9 5 3 0 . 0 , 2 4 3 0 . 0 [ ] 4 4 3 0 . 0 , 8 2 3 0 . 0 [ ] 1 3 3 0 . 0 , 4 1 3 0 . 0 [ ] 0 2 3 0 . 0 , 4 0 3 0 . 0 [ ] 4 5 3 0 . 0 , 7 3 3 0 . 0 [ ] 1 3 3 0 . 0 , 5 1 3 0 . 0 [ ] 3 4 3 0 . 0 , 6 2 3 0 . 0 [ ] 5 2 3 0 . 0 , 8 0 3 0 . 0 [ ] 5 5 3 0 . 0 , 8 3 3 0 . 0 [ ] 4 3 3 0 . 0 , 8 1 3 0 . 0 [ ] 1 1 2 0 . 0 , 4 9 1 0 . 0 [ ] 3 9 1 0 . 0 , 7 7 1 0 . 0 [ ] 7 4 2 0 . 0 , 0 3 2 0 . 0 [ ] 5 3 2 0 . 0 , 8 1 2 0 . 0 [ 1 4 1 0 . 0 2 7 1 0 . 0 2 8 1 0 . 0 1 0 2 0 . 0 0 2 2 0 . 0 4 2 2 0 . 0 4 5 2 0 . 0 9 5 2 0 . 0 1 9 2 0 . 0 9 6 2 0 . 0 8 9 2 0 . 0 8 8 2 0 . 0 5 1 3 0 . 0 5 0 3 0 . 0 4 4 3 0 . 0 7 0 3 0 . 0 1 5 3 0 . 0 3 2 3 0 . 0 6 4 3 0 . 0 4 3 3 0 . 0 6 4 3 0 . 0 3 0 2 0 . 0 8 3 2 0 . 0 3 3 1 0 . 0 6 5 1 0 . 0 0 7 1 0 . 0 7 8 1 0 . 0 5 0 2 0 . 0 8 0 2 0 . 0 2 4 2 0 . 0 0 4 2 0 . 0 5 7 2 0 . 0 8 5 2 0 . 0 8 8 2 0 . 0 5 7 2 0 . 0 0 1 3 0 . 0 0 9 2 0 . 0 3 3 3 0 . 0 0 9 2 0 . 0 6 3 3 0 . 0 2 1 3 0 . 0 3 2 3 0 . 0 7 1 3 0 . 0 6 2 3 0 . 0 5 8 1 0 . 0 7 2 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 3 7 . B e l b a T 435 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 4 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B B C C D D E E F F G G H G I H J I L K J I K J I L K L K J L B E A B B C C D D E F E G F G H H ] 8 8 0 0 . 0 , 4 7 0 0 . 0 [ ] 0 8 0 0 . 0 , 7 6 0 0 . 0 [ ] 2 1 1 0 . 0 , 9 9 0 0 . 0 [ ] 5 0 1 0 . 0 , 1 9 0 0 . 0 [ ] 6 1 1 0 . 0 , 2 0 1 0 . 0 [ ] 8 0 1 0 . 0 , 5 9 0 0 . 0 [ ] 0 4 1 0 . 0 , 7 2 1 0 . 0 [ ] 3 3 1 0 . 0 , 0 2 1 0 . 0 [ ] 1 4 1 0 . 0 , 7 2 1 0 . 0 [ ] 1 3 1 0 . 0 , 8 1 1 0 . 0 [ ] 3 7 1 0 . 0 , 0 6 1 0 . 0 [ ] 5 6 1 0 . 0 , 2 5 1 0 . 0 [ ] 1 7 1 0 . 0 , 7 5 1 0 . 0 [ ] 6 6 1 0 . 0 , 2 5 1 0 . 0 [ ] 4 9 1 0 . 0 , 1 8 1 0 . 0 [ ] 5 8 1 0 . 0 , 1 7 1 0 . 0 [ ] 0 0 2 0 . 0 , 7 8 1 0 . 0 [ ] 2 9 1 0 . 0 , 9 7 1 0 . 0 [ ] 0 2 2 0 . 0 , 7 0 2 0 . 0 [ ] 9 0 2 0 . 0 , 6 9 1 0 . 0 [ ] 4 2 2 0 . 0 , 0 1 2 0 . 0 [ ] 3 1 2 0 . 0 , 0 0 2 0 . 0 [ ] 4 4 2 0 . 0 , 1 3 2 0 . 0 [ ] 5 3 2 0 . 0 , 1 2 2 0 . 0 [ ] 1 5 2 0 . 0 , 8 3 2 0 . 0 [ ] 2 4 2 0 . 0 , 8 2 2 0 . 0 [ I H ] 7 5 2 0 . 0 , 4 4 2 0 . 0 [ ] 5 4 2 0 . 0 , 2 3 2 0 . 0 [ J I J I K J K J K K K B ] 0 7 2 0 . 0 , 6 5 2 0 . 0 [ ] 2 6 2 0 . 0 , 8 4 2 0 . 0 [ ] 7 7 2 0 . 0 , 3 6 2 0 . 0 [ ] 2 6 2 0 . 0 , 9 4 2 0 . 0 [ ] 2 8 2 0 . 0 , 8 6 2 0 . 0 [ ] 3 7 2 0 . 0 , 0 6 2 0 . 0 [ ] 1 8 2 0 . 0 , 8 6 2 0 . 0 [ ] 5 7 2 0 . 0 , 1 6 2 0 . 0 [ ] 5 9 2 0 . 0 , 2 8 2 0 . 0 [ ] 3 8 2 0 . 0 , 0 7 2 0 . 0 [ ] 4 9 2 0 . 0 , 1 8 2 0 . 0 [ ] 5 8 2 0 . 0 , 2 7 2 0 . 0 [ ] 9 9 2 0 . 0 , 5 8 2 0 . 0 [ ] 8 8 2 0 . 0 , 4 7 2 0 . 0 [ ] 0 1 1 0 . 0 , 6 9 0 0 . 0 [ ] 3 0 1 0 . 0 , 9 8 0 0 . 0 [ E D ] 2 9 1 0 . 0 , 9 7 1 0 . 0 [ ] 9 7 1 0 . 0 , 5 6 1 0 . 0 [ 1 8 0 0 . 0 6 0 1 0 . 0 9 0 1 0 . 0 4 3 1 0 . 0 4 3 1 0 . 0 7 6 1 0 . 0 4 6 1 0 . 0 8 8 1 0 . 0 3 9 1 0 . 0 3 1 2 0 . 0 7 1 2 0 . 0 7 3 2 0 . 0 5 4 2 0 . 0 0 5 2 0 . 0 3 6 2 0 . 0 0 7 2 0 . 0 5 7 2 0 . 0 4 7 2 0 . 0 8 8 2 0 . 0 7 8 2 0 . 0 2 9 2 0 . 0 3 0 1 0 . 0 6 8 1 0 . 0 4 7 0 0 . 0 8 9 0 0 . 0 2 0 1 0 . 0 7 2 1 0 . 0 5 2 1 0 . 0 8 5 1 0 . 0 9 5 1 0 . 0 8 7 1 0 . 0 6 8 1 0 . 0 3 0 2 0 . 0 6 0 2 0 . 0 8 2 2 0 . 0 5 3 2 0 . 0 9 3 2 0 . 0 5 5 2 0 . 0 6 5 2 0 . 0 7 6 2 0 . 0 8 6 2 0 . 0 7 7 2 0 . 0 9 7 2 0 . 0 1 8 2 0 . 0 6 9 0 0 . 0 2 7 1 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 4 7 . B e l b a T 436 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 6 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B C B A D C E D F D H E I F J G F K H G L H L H B F C B A ] 5 4 0 0 . 0 , 5 3 0 0 . 0 [ ] 2 4 0 0 . 0 , 2 3 0 0 . 0 [ ] 9 6 0 0 . 0 , 8 5 0 0 . 0 [ ] 6 6 0 0 . 0 , 6 5 0 0 . 0 [ B D C E D ] 1 6 0 0 . 0 , 0 5 0 0 . 0 [ ] 8 5 0 0 . 0 , 8 4 0 0 . 0 [ ] 8 9 0 0 . 0 , 8 8 0 0 . 0 [ ] 5 9 0 0 . 0 , 5 8 0 0 . 0 [ ] 3 7 0 0 . 0 , 3 6 0 0 . 0 [ ] 2 7 0 0 . 0 , 2 6 0 0 . 0 [ ] 4 2 1 0 . 0 , 4 1 1 0 . 0 [ ] 9 1 1 0 . 0 , 0 1 1 0 . 0 [ ] 5 9 0 0 . 0 , 5 8 0 0 . 0 [ ] 2 9 0 0 . 0 , 3 8 0 0 . 0 [ I H G ] 4 5 1 0 . 0 , 3 4 1 0 . 0 [ ] 8 4 1 0 . 0 , 8 3 1 0 . 0 [ K J F E D L ] 6 0 1 0 . 0 , 5 9 0 0 . 0 [ ] 3 0 1 0 . 0 , 4 9 0 0 . 0 [ ] 8 7 1 0 . 0 , 8 6 1 0 . 0 [ ] 2 7 1 0 . 0 , 2 6 1 0 . 0 [ ] 1 3 1 0 . 0 , 1 2 1 0 . 0 [ ] 7 2 1 0 . 0 , 8 1 1 0 . 0 [ ] 8 9 1 0 . 0 , 7 8 1 0 . 0 [ ] 0 9 1 0 . 0 , 0 8 1 0 . 0 [ H G ] 8 4 1 0 . 0 , 8 3 1 0 . 0 [ ] 3 4 1 0 . 0 , 3 3 1 0 . 0 [ I H M J I L ] 1 1 2 0 . 0 , 1 0 2 0 . 0 [ ] 3 0 2 0 . 0 , 3 9 1 0 . 0 [ ] 9 5 1 0 . 0 , 8 4 1 0 . 0 [ ] 4 5 1 0 . 0 , 4 4 1 0 . 0 [ ] 0 3 2 0 . 0 , 9 1 2 0 . 0 [ ] 2 2 2 0 . 0 , 2 1 2 0 . 0 [ ] 9 6 1 0 . 0 , 9 5 1 0 . 0 [ ] 1 6 1 0 . 0 , 1 5 1 0 . 0 [ N M K J ] 5 4 2 0 . 0 , 4 3 2 0 . 0 [ ] 4 3 2 0 . 0 , 4 2 2 0 . 0 [ ] 8 7 1 0 . 0 , 8 6 1 0 . 0 [ ] 2 7 1 0 . 0 , 3 6 1 0 . 0 [ N K B ] 4 5 2 0 . 0 , 4 4 2 0 . 0 [ ] 7 4 2 0 . 0 , 7 3 2 0 . 0 [ ] 0 8 1 0 . 0 , 0 7 1 0 . 0 [ ] 5 7 1 0 . 0 , 6 6 1 0 . 0 [ ] 9 5 0 0 . 0 , 8 4 0 0 . 0 [ ] 7 5 0 0 . 0 , 7 4 0 0 . 0 [ G F ] 6 4 1 0 . 0 , 6 3 1 0 . 0 [ ] 6 3 1 0 . 0 , 6 2 1 0 . 0 [ 0 4 0 0 . 0 4 6 0 0 . 0 6 5 0 0 . 0 3 9 0 0 . 0 8 6 0 0 . 0 9 1 1 0 . 0 0 9 0 0 . 0 8 4 1 0 . 0 1 0 1 0 . 0 3 7 1 0 . 0 6 2 1 0 . 0 2 9 1 0 . 0 3 4 1 0 . 0 6 0 2 0 . 0 4 5 1 0 . 0 4 2 2 0 . 0 4 6 1 0 . 0 0 4 2 0 . 0 3 7 1 0 . 0 9 4 2 0 . 0 5 7 1 0 . 0 4 5 0 0 . 0 1 4 1 0 . 0 7 3 0 0 . 0 1 6 0 0 . 0 3 5 0 0 . 0 0 9 0 0 . 0 7 6 0 0 . 0 4 1 1 0 . 0 8 8 0 0 . 0 3 4 1 0 . 0 8 9 0 0 . 0 7 6 1 0 . 0 3 2 1 0 . 0 5 8 1 0 . 0 8 3 1 0 . 0 8 9 1 0 . 0 9 4 1 0 . 0 7 1 2 0 . 0 6 5 1 0 . 0 9 2 2 0 . 0 8 6 1 0 . 0 2 4 2 0 . 0 0 7 1 0 . 0 2 5 0 0 . 0 1 3 1 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 5 7 . B e l b a T 437 3.1.6. Population additive genic variance Figure B.19: Population additive genic variance by selection strategy over 60 generations in the multi-trait, TRUE scenario. 438 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 1 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B C C E D H F J H L I M J N K O N L O M O N G F A B C D F E I G K I M J O N Q P K ] 8 9 2 0 . 0 , 5 9 2 0 . 0 [ ] 5 6 2 0 . 0 , 2 6 2 0 . 0 [ ] 3 1 3 0 . 0 , 0 1 3 0 . 0 [ ] 1 8 2 0 . 0 , 8 7 2 0 . 0 [ ] 7 2 3 0 . 0 , 4 2 3 0 . 0 [ ] 2 9 2 0 . 0 , 9 8 2 0 . 0 [ ] 1 3 3 0 . 0 , 8 2 3 0 . 0 [ ] 7 9 2 0 . 0 , 4 9 2 0 . 0 [ ] 5 5 3 0 . 0 , 2 5 3 0 . 0 [ ] 1 2 3 0 . 0 , 8 1 3 0 . 0 [ ] 8 4 3 0 . 0 , 5 4 3 0 . 0 [ ] 4 1 3 0 . 0 , 1 1 3 0 . 0 [ ] 5 8 3 0 . 0 , 2 8 3 0 . 0 [ ] 7 4 3 0 . 0 , 4 4 3 0 . 0 [ ] 6 6 3 0 . 0 , 3 6 3 0 . 0 [ ] 9 2 3 0 . 0 , 6 2 3 0 . 0 [ ] 6 0 4 0 . 0 , 3 0 4 0 . 0 [ ] 9 6 3 0 . 0 , 6 6 3 0 . 0 [ ] 1 8 3 0 . 0 , 8 7 3 0 . 0 [ ] 5 4 3 0 . 0 , 2 4 3 0 . 0 [ ] 5 2 4 0 . 0 , 2 2 4 0 . 0 [ ] 5 8 3 0 . 0 , 2 8 3 0 . 0 [ ] 5 9 3 0 . 0 , 2 9 3 0 . 0 [ ] 8 5 3 0 . 0 , 5 5 3 0 . 0 [ ] 3 3 4 0 . 0 , 0 3 4 0 . 0 [ ] 1 9 3 0 . 0 , 8 8 3 0 . 0 [ ] 7 0 4 0 . 0 , 4 0 4 0 . 0 [ ] 7 6 3 0 . 0 , 4 6 3 0 . 0 [ ] 9 3 4 0 . 0 , 6 3 4 0 . 0 [ ] 6 9 3 0 . 0 , 3 9 3 0 . 0 [ R Q N M ] 2 4 4 0 . 0 , 9 3 4 0 . 0 [ ] 8 9 3 0 . 0 , 5 9 3 0 . 0 [ ] 7 2 4 0 . 0 , 4 2 4 0 . 0 [ ] 8 8 3 0 . 0 , 5 8 3 0 . 0 [ R ] 5 4 4 0 . 0 , 2 4 4 0 . 0 [ ] 1 0 4 0 . 0 , 8 9 3 0 . 0 [ L ] 7 1 4 0 . 0 , 4 1 4 0 . 0 [ ] 9 7 3 0 . 0 , 6 7 3 0 . 0 [ P O R Q H G ] 4 3 4 0 . 0 , 1 3 4 0 . 0 [ ] 2 9 3 0 . 0 , 9 8 3 0 . 0 [ ] 2 4 4 0 . 0 , 9 3 4 0 . 0 [ ] 7 9 3 0 . 0 , 4 9 3 0 . 0 [ ] 2 7 3 0 . 0 , 9 6 3 0 . 0 [ ] 8 3 3 0 . 0 , 5 3 3 0 . 0 [ ] 7 6 3 0 . 0 , 5 6 3 0 . 0 [ ] 0 3 3 0 . 0 , 7 2 3 0 . 0 [ 6 9 2 0 . 0 2 1 3 0 . 0 6 2 3 0 . 0 0 3 3 0 . 0 3 5 3 0 . 0 7 4 3 0 . 0 3 8 3 0 . 0 4 6 3 0 . 0 4 0 4 0 . 0 0 8 3 0 . 0 3 2 4 0 . 0 4 9 3 0 . 0 2 3 4 0 . 0 5 0 4 0 . 0 8 3 4 0 . 0 6 1 4 0 . 0 1 4 4 0 . 0 5 2 4 0 . 0 4 4 4 0 . 0 2 3 4 0 . 0 1 4 4 0 . 0 1 7 3 0 . 0 6 6 3 0 . 0 4 6 2 0 . 0 9 7 2 0 . 0 0 9 2 0 . 0 5 9 2 0 . 0 9 1 3 0 . 0 2 1 3 0 . 0 6 4 3 0 . 0 7 2 3 0 . 0 8 6 3 0 . 0 3 4 3 0 . 0 3 8 3 0 . 0 6 5 3 0 . 0 0 9 3 0 . 0 6 6 3 0 . 0 4 9 3 0 . 0 8 7 3 0 . 0 6 9 3 0 . 0 6 8 3 0 . 0 9 9 3 0 . 0 1 9 3 0 . 0 5 9 3 0 . 0 6 3 3 0 . 0 8 2 3 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 6 7 . B e l b a T 439 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 3 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B C D F G H H K J L K N L O M P N Q O Q E I A B C D E F H G J I K J M K O L P N Q ] 3 6 1 0 . 0 , 9 5 1 0 . 0 [ ] 1 4 1 0 . 0 , 8 3 1 0 . 0 [ ] 9 8 1 0 . 0 , 5 8 1 0 . 0 [ ] 4 6 1 0 . 0 , 0 6 1 0 . 0 [ ] 0 0 2 0 . 0 , 6 9 1 0 . 0 [ ] 4 7 1 0 . 0 , 1 7 1 0 . 0 [ ] 4 1 2 0 . 0 , 0 1 2 0 . 0 [ ] 7 8 1 0 . 0 , 3 8 1 0 . 0 [ ] 2 3 2 0 . 0 , 9 2 2 0 . 0 [ ] 5 0 2 0 . 0 , 1 0 2 0 . 0 [ ] 3 4 2 0 . 0 , 9 3 2 0 . 0 [ ] 2 1 2 0 . 0 , 9 0 2 0 . 0 [ ] 0 7 2 0 . 0 , 6 6 2 0 . 0 [ ] 1 4 2 0 . 0 , 7 3 2 0 . 0 [ ] 6 6 2 0 . 0 , 2 6 2 0 . 0 [ ] 5 3 2 0 . 0 , 1 3 2 0 . 0 [ ] 2 0 3 0 . 0 , 8 9 2 0 . 0 [ ] 1 7 2 0 . 0 , 7 6 2 0 . 0 [ ] 7 8 2 0 . 0 , 3 8 2 0 . 0 [ ] 4 5 2 0 . 0 , 0 5 2 0 . 0 [ ] 8 2 3 0 . 0 , 4 2 3 0 . 0 [ ] 5 9 2 0 . 0 , 2 9 2 0 . 0 [ ] 7 0 3 0 . 0 , 3 0 3 0 . 0 [ ] 5 7 2 0 . 0 , 1 7 2 0 . 0 [ ] 7 4 3 0 . 0 , 3 4 3 0 . 0 [ ] 2 1 3 0 . 0 , 8 0 3 0 . 0 [ ] 4 2 3 0 . 0 , 0 2 3 0 . 0 [ ] 2 9 2 0 . 0 , 9 8 2 0 . 0 [ ] 2 6 3 0 . 0 , 8 5 3 0 . 0 [ ] 6 2 3 0 . 0 , 3 2 3 0 . 0 [ ] 0 4 3 0 . 0 , 6 3 3 0 . 0 [ ] 5 0 3 0 . 0 , 2 0 3 0 . 0 [ ] 0 7 3 0 . 0 , 6 6 3 0 . 0 [ ] 2 3 3 0 . 0 , 9 2 3 0 . 0 [ ] 2 5 3 0 . 0 , 8 4 3 0 . 0 [ ] 9 1 3 0 . 0 , 5 1 3 0 . 0 [ ] 7 7 3 0 . 0 , 3 7 3 0 . 0 [ ] 9 3 3 0 . 0 , 6 3 3 0 . 0 [ P O ] 4 6 3 0 . 0 , 0 6 3 0 . 0 [ ] 9 2 3 0 . 0 , 5 2 3 0 . 0 [ Q D I ] 1 8 3 0 . 0 , 7 7 3 0 . 0 [ ] 3 4 3 0 . 0 , 9 3 3 0 . 0 [ ] 0 2 2 0 . 0 , 6 1 2 0 . 0 [ ] 2 9 1 0 . 0 , 8 8 1 0 . 0 [ ] 1 8 2 0 . 0 , 7 7 2 0 . 0 [ ] 1 5 2 0 . 0 , 7 4 2 0 . 0 [ 1 6 1 0 . 0 7 8 1 0 . 0 8 9 1 0 . 0 2 1 2 0 . 0 1 3 2 0 . 0 1 4 2 0 . 0 8 6 2 0 . 0 4 6 2 0 . 0 0 0 3 0 . 0 5 8 2 0 . 0 6 2 3 0 . 0 5 0 3 0 . 0 5 4 3 0 . 0 2 2 3 0 . 0 0 6 3 0 . 0 8 3 3 0 . 0 8 6 3 0 . 0 0 5 3 0 . 0 5 7 3 0 . 0 2 6 3 0 . 0 9 7 3 0 . 0 8 1 2 0 . 0 9 7 2 0 . 0 9 3 1 0 . 0 2 6 1 0 . 0 3 7 1 0 . 0 5 8 1 0 . 0 3 0 2 0 . 0 1 1 2 0 . 0 9 3 2 0 . 0 3 3 2 0 . 0 9 6 2 0 . 0 2 5 2 0 . 0 3 9 2 0 . 0 3 7 2 0 . 0 0 1 3 0 . 0 0 9 2 0 . 0 4 2 3 0 . 0 3 0 3 0 . 0 0 3 3 0 . 0 7 1 3 0 . 0 8 3 3 0 . 0 7 2 3 0 . 0 1 4 3 0 . 0 0 9 1 0 . 0 9 4 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 7 7 . B e l b a T 440 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 4 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B B C C D D E F G H I J K L M N O O P P B G A B B C C D E F G H I J K L M N O P P Q Q B G ] 9 8 0 0 . 0 , 5 8 0 0 . 0 [ ] 8 7 0 0 . 0 , 4 7 0 0 . 0 [ ] 2 1 1 0 . 0 , 8 0 1 0 . 0 [ ] 1 0 1 0 . 0 , 7 9 0 0 . 0 [ ] 5 1 1 0 . 0 , 1 1 1 0 . 0 [ ] 3 0 1 0 . 0 , 9 9 0 0 . 0 [ ] 1 4 1 0 . 0 , 6 3 1 0 . 0 [ ] 7 2 1 0 . 0 , 3 2 1 0 . 0 [ ] 1 4 1 0 . 0 , 7 3 1 0 . 0 [ ] 8 2 1 0 . 0 , 4 2 1 0 . 0 [ ] 8 6 1 0 . 0 , 3 6 1 0 . 0 [ ] 3 5 1 0 . 0 , 9 4 1 0 . 0 [ ] 2 7 1 0 . 0 , 7 6 1 0 . 0 [ ] 8 5 1 0 . 0 , 4 5 1 0 . 0 [ ] 4 9 1 0 . 0 , 9 8 1 0 . 0 [ ] 7 7 1 0 . 0 , 3 7 1 0 . 0 [ ] 1 0 2 0 . 0 , 7 9 1 0 . 0 [ ] 4 8 1 0 . 0 , 0 8 1 0 . 0 [ ] 7 1 2 0 . 0 , 3 1 2 0 . 0 [ ] 8 9 1 0 . 0 , 4 9 1 0 . 0 [ ] 8 2 2 0 . 0 , 3 2 2 0 . 0 [ ] 8 0 2 0 . 0 , 4 0 2 0 . 0 [ ] 0 4 2 0 . 0 , 6 3 2 0 . 0 [ ] 0 2 2 0 . 0 , 6 1 2 0 . 0 [ ] 1 5 2 0 . 0 , 6 4 2 0 . 0 [ ] 7 2 2 0 . 0 , 3 2 2 0 . 0 [ ] 8 5 2 0 . 0 , 4 5 2 0 . 0 [ ] 6 3 2 0 . 0 , 2 3 2 0 . 0 [ ] 0 7 2 0 . 0 , 5 6 2 0 . 0 [ ] 5 4 2 0 . 0 , 1 4 2 0 . 0 [ ] 6 7 2 0 . 0 , 2 7 2 0 . 0 [ ] 1 5 2 0 . 0 , 7 4 2 0 . 0 [ ] 4 8 2 0 . 0 , 9 7 2 0 . 0 [ ] 7 5 2 0 . 0 , 3 5 2 0 . 0 [ ] 0 9 2 0 . 0 , 5 8 2 0 . 0 [ ] 5 6 2 0 . 0 , 1 6 2 0 . 0 [ ] 4 9 2 0 . 0 , 0 9 2 0 . 0 [ ] 6 6 2 0 . 0 , 2 6 2 0 . 0 [ ] 1 0 3 0 . 0 , 7 9 2 0 . 0 [ ] 6 7 2 0 . 0 , 2 7 2 0 . 0 [ ] 6 0 3 0 . 0 , 1 0 3 0 . 0 [ ] 6 7 2 0 . 0 , 2 7 2 0 . 0 [ ] 4 1 1 0 . 0 , 0 1 1 0 . 0 [ ] 1 0 1 0 . 0 , 7 9 0 0 . 0 [ ] 2 1 2 0 . 0 , 8 0 2 0 . 0 [ ] 3 8 1 0 . 0 , 0 8 1 0 . 0 [ 7 8 0 0 . 0 0 1 1 0 . 0 3 1 1 0 . 0 8 3 1 0 . 0 9 3 1 0 . 0 6 6 1 0 . 0 0 7 1 0 . 0 2 9 1 0 . 0 9 9 1 0 . 0 5 1 2 0 . 0 5 2 2 0 . 0 8 3 2 0 . 0 9 4 2 0 . 0 6 5 2 0 . 0 7 6 2 0 . 0 4 7 2 0 . 0 1 8 2 0 . 0 8 8 2 0 . 0 2 9 2 0 . 0 9 9 2 0 . 0 3 0 3 0 . 0 2 1 1 0 . 0 0 1 2 0 . 0 6 7 0 0 . 0 9 9 0 0 . 0 1 0 1 0 . 0 5 2 1 0 . 0 6 2 1 0 . 0 1 5 1 0 . 0 6 5 1 0 . 0 5 7 1 0 . 0 2 8 1 0 . 0 6 9 1 0 . 0 6 0 2 0 . 0 8 1 2 0 . 0 5 2 2 0 . 0 4 3 2 0 . 0 3 4 2 0 . 0 9 4 2 0 . 0 5 5 2 0 . 0 3 6 2 0 . 0 4 6 2 0 . 0 4 7 2 0 . 0 4 7 2 0 . 0 9 9 0 0 . 0 1 8 1 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 8 7 . B e l b a T 441 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 6 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C B E D G E I F L H O I P J Q L K R M S N B K J A C B E D G E I F ] 2 4 0 0 . 0 , 8 3 0 0 . 0 [ ] 8 3 0 0 . 0 , 4 3 0 0 . 0 [ ] 4 6 0 0 . 0 , 0 6 0 0 . 0 [ ] 0 6 0 0 . 0 , 6 5 0 0 . 0 [ ] 7 5 0 0 . 0 , 3 5 0 0 . 0 [ ] 4 5 0 0 . 0 , 0 5 0 0 . 0 [ ] 2 9 0 0 . 0 , 8 8 0 0 . 0 [ ] 8 8 0 0 . 0 , 4 8 0 0 . 0 [ ] 1 7 0 0 . 0 , 7 6 0 0 . 0 [ ] 8 6 0 0 . 0 , 4 6 0 0 . 0 [ ] 8 1 1 0 . 0 , 4 1 1 0 . 0 [ ] 2 1 1 0 . 0 , 8 0 1 0 . 0 [ ] 1 9 0 0 . 0 , 7 8 0 0 . 0 [ ] 7 8 0 0 . 0 , 3 8 0 0 . 0 [ ] 5 4 1 0 . 0 , 1 4 1 0 . 0 [ ] 8 3 1 0 . 0 , 4 3 1 0 . 0 [ ] 6 0 1 0 . 0 , 1 0 1 0 . 0 [ ] 1 0 1 0 . 0 , 7 9 0 0 . 0 [ L K ] 7 6 1 0 . 0 , 3 6 1 0 . 0 [ ] 7 5 1 0 . 0 , 3 5 1 0 . 0 [ H N I O J P K Q L R M B I ] 6 2 1 0 . 0 , 2 2 1 0 . 0 [ ] 9 1 1 0 . 0 , 5 1 1 0 . 0 [ ] 8 8 1 0 . 0 , 4 8 1 0 . 0 [ ] 7 7 1 0 . 0 , 3 7 1 0 . 0 [ ] 1 4 1 0 . 0 , 7 3 1 0 . 0 [ ] 3 3 1 0 . 0 , 9 2 1 0 . 0 [ ] 5 0 2 0 . 0 , 1 0 2 0 . 0 [ ] 0 9 1 0 . 0 , 6 8 1 0 . 0 [ ] 5 5 1 0 . 0 , 0 5 1 0 . 0 [ ] 5 4 1 0 . 0 , 1 4 1 0 . 0 [ ] 4 2 2 0 . 0 , 0 2 2 0 . 0 [ ] 9 0 2 0 . 0 , 5 0 2 0 . 0 [ ] 5 6 1 0 . 0 , 0 6 1 0 . 0 [ ] 2 5 1 0 . 0 , 9 4 1 0 . 0 [ ] 9 3 2 0 . 0 , 4 3 2 0 . 0 [ ] 2 2 2 0 . 0 , 8 1 2 0 . 0 [ ] 3 7 1 0 . 0 , 9 6 1 0 . 0 [ ] 0 6 1 0 . 0 , 6 5 1 0 . 0 [ ] 0 5 2 0 . 0 , 6 4 2 0 . 0 [ ] 1 3 2 0 . 0 , 7 2 2 0 . 0 [ ] 2 8 1 0 . 0 , 7 7 1 0 . 0 [ ] 9 6 1 0 . 0 , 5 6 1 0 . 0 [ ] 6 5 0 0 . 0 , 2 5 0 0 . 0 [ ] 2 5 0 0 . 0 , 9 4 0 0 . 0 [ ] 9 5 1 0 . 0 , 5 5 1 0 . 0 [ ] 7 3 1 0 . 0 , 3 3 1 0 . 0 [ 0 4 0 0 . 0 2 6 0 0 . 0 5 5 0 0 . 0 0 9 0 0 . 0 9 6 0 0 . 0 6 1 1 0 . 0 9 8 0 0 . 0 3 4 1 0 . 0 3 0 1 0 . 0 5 6 1 0 . 0 4 2 1 0 . 0 6 8 1 0 . 0 9 3 1 0 . 0 3 0 2 0 . 0 3 5 1 0 . 0 2 2 2 0 . 0 2 6 1 0 . 0 6 3 2 0 . 0 1 7 1 0 . 0 8 4 2 0 . 0 9 7 1 0 . 0 4 5 0 0 . 0 7 5 1 0 . 0 6 3 0 0 . 0 8 5 0 0 . 0 2 5 0 0 . 0 6 8 0 0 . 0 6 6 0 0 . 0 0 1 1 0 . 0 5 8 0 0 . 0 6 3 1 0 . 0 9 9 0 0 . 0 5 5 1 0 . 0 7 1 1 0 . 0 5 7 1 0 . 0 1 3 1 0 . 0 8 8 1 0 . 0 3 4 1 0 . 0 7 0 2 0 . 0 1 5 1 0 . 0 0 2 2 0 . 0 8 5 1 0 . 0 9 2 2 0 . 0 7 6 1 0 . 0 0 5 0 0 . 0 5 3 1 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 9 7 . B e l b a T 442 3.1.7. Population Bulmer effect Figure B.20: Population Bulmer effect by selection strategy over 60 generations in the multi- trait, TRUE scenario. 443 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A A A A A A A A A A A A A A A A A A A A A A A C B A C B A C B A C B A C B A C B A C B A C B A C B A C B B A C B A C B A ] 8 9 7 8 . 0 , 8 1 3 8 . 0 [ ] 6 5 4 9 . 0 , 6 6 9 8 . 0 [ ] 6 0 1 9 . 0 , 6 2 6 8 . 0 [ ] 9 3 6 9 . 0 , 8 4 1 9 . 0 [ ] 3 4 3 9 . 0 , 3 6 8 8 . 0 [ ] 8 9 5 9 . 0 , 7 0 1 9 . 0 [ ] 8 4 3 9 . 0 , 8 6 8 8 . 0 [ ] 2 6 6 9 . 0 , 1 7 1 9 . 0 [ ] 7 4 1 9 . 0 , 7 6 6 8 . 0 [ ] 5 5 4 9 . 0 , 4 6 9 8 . 0 [ ] 0 7 0 9 . 0 , 0 9 5 8 . 0 [ ] 0 2 4 9 . 0 , 9 2 9 8 . 0 [ ] 0 5 1 9 . 0 , 0 7 6 8 . 0 [ ] 7 7 4 9 . 0 , 6 8 9 8 . 0 [ ] 2 7 9 8 . 0 , 2 9 4 8 . 0 [ ] 9 5 3 9 . 0 , 9 6 8 8 . 0 [ ] 6 7 9 8 . 0 , 6 9 4 8 . 0 [ ] 4 6 2 9 . 0 , 3 7 7 8 . 0 [ ] 6 1 3 9 . 0 , 6 3 8 8 . 0 [ ] 5 2 7 9 . 0 , 4 3 2 9 . 0 [ ] 2 1 8 8 . 0 , 2 3 3 8 . 0 [ ] 9 1 2 9 . 0 , 8 2 7 8 . 0 [ ] 2 9 9 8 . 0 , 2 1 5 8 . 0 [ ] 1 1 3 9 . 0 , 0 2 8 8 . 0 [ ] 1 8 9 8 . 0 , 1 0 5 8 . 0 [ ] 6 7 3 9 . 0 , 5 8 8 8 . 0 [ C B A ] 8 7 7 8 . 0 , 8 9 2 8 . 0 [ ] 5 8 3 9 . 0 , 4 9 8 8 . 0 [ C B A C B A C B A ] 0 0 0 9 . 0 , 0 2 5 8 . 0 [ ] 1 6 2 9 . 0 , 0 7 7 8 . 0 [ ] 0 9 9 8 . 0 , 9 0 5 8 . 0 [ ] 5 6 2 9 . 0 , 5 7 7 8 . 0 [ ] 5 6 8 8 . 0 , 5 8 3 8 . 0 [ ] 4 5 2 9 . 0 , 4 6 7 8 . 0 [ B A ] 9 9 8 8 . 0 , 9 1 4 8 . 0 [ ] 3 4 1 9 . 0 , 3 5 6 8 . 0 [ B A ] 3 9 9 8 . 0 , 3 1 5 8 . 0 [ ] 8 9 1 9 . 0 , 8 0 7 8 . 0 [ B A ] 6 1 9 8 . 0 , 6 3 4 8 . 0 [ ] 1 8 1 9 . 0 , 0 9 6 8 . 0 [ A C ] 0 6 7 8 . 0 , 0 8 2 8 . 0 [ ] 3 3 0 9 . 0 , 2 4 5 8 . 0 [ ] 2 2 2 9 . 0 , 2 4 7 8 . 0 [ ] 2 7 8 9 . 0 , 1 8 3 9 . 0 [ C B A ] 5 6 9 8 . 0 , 5 8 4 8 . 0 [ ] 5 4 3 9 . 0 , 4 5 8 8 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 8 5 5 8 . 0 6 6 8 8 . 0 3 0 1 9 . 0 8 0 1 9 . 0 7 0 9 8 . 0 0 3 8 8 . 0 0 1 9 8 . 0 2 3 7 8 . 0 6 3 7 8 . 0 6 7 0 9 . 0 2 7 5 8 . 0 2 5 7 8 . 0 1 4 7 8 . 0 3 5 7 8 . 0 8 3 5 8 . 0 9 5 6 8 . 0 0 6 7 8 . 0 9 4 7 8 . 0 5 2 6 8 . 0 6 7 6 8 . 0 0 2 5 8 . 0 2 8 9 8 . 0 5 2 7 8 . 0 1 1 2 9 . 0 4 9 3 9 . 0 2 5 3 9 . 0 7 1 4 9 . 0 9 0 2 9 . 0 5 7 1 9 . 0 1 3 2 9 . 0 4 1 1 9 . 0 8 1 0 9 . 0 0 8 4 9 . 0 3 7 9 8 . 0 6 6 0 9 . 0 0 3 1 9 . 0 3 5 9 8 . 0 0 4 1 9 . 0 8 9 8 8 . 0 5 1 0 9 . 0 0 2 0 9 . 0 9 0 0 9 . 0 5 3 9 8 . 0 8 8 7 8 . 0 7 2 6 9 . 0 9 9 0 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 0 8 . B e l b a T 444 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B A C B A B A C B C B C B A C B C B A C B C B A C B C B C B C B A C B C B A C B A C B A C B A C B A A C C B A B A B A B B ] 8 9 0 9 . 0 , 4 2 5 8 . 0 [ ] 6 5 8 9 . 0 , 0 4 2 9 . 0 [ ] 3 8 4 9 . 0 , 8 0 9 8 . 0 [ ] 8 0 9 9 . 0 , 3 9 2 9 . 0 [ ] 6 7 4 9 . 0 , 1 0 9 8 . 0 [ ] 0 6 1 0 . 1 , 4 4 5 9 . 0 [ ] 8 5 7 9 . 0 , 3 8 1 9 . 0 [ ] 6 9 3 0 . 1 , 1 8 7 9 . 0 [ ] 8 3 8 9 . 0 , 3 6 2 9 . 0 [ ] 6 3 4 0 . 1 , 1 2 8 9 . 0 [ B A ] 5 7 5 9 . 0 , 0 0 0 9 . 0 [ ] 9 6 1 0 . 1 , 3 5 5 9 . 0 [ B B B B ] 2 7 7 9 . 0 , 7 9 1 9 . 0 [ ] 2 7 4 0 . 1 , 6 5 8 9 . 0 [ ] 7 0 1 0 . 1 , 2 3 5 9 . 0 [ ] 6 7 5 0 . 1 , 1 6 9 9 . 0 [ ] 2 9 9 9 . 0 , 7 1 4 9 . 0 [ ] 7 2 5 0 . 1 , 1 1 9 9 . 0 [ ] 7 4 7 9 . 0 , 3 7 1 9 . 0 [ ] 5 3 5 0 . 1 , 0 2 9 9 . 0 [ B A ] 8 3 4 9 . 0 , 3 6 8 8 . 0 [ ] 8 3 1 0 . 1 , 2 2 5 9 . 0 [ B B B B ] 3 5 7 9 . 0 , 9 7 1 9 . 0 [ ] 4 5 3 0 . 1 , 8 3 7 9 . 0 [ ] 2 1 4 9 . 0 , 7 3 8 8 . 0 [ ] 6 0 3 0 . 1 , 1 9 6 9 . 0 [ ] 6 5 7 9 . 0 , 1 8 1 9 . 0 [ ] 4 8 2 0 . 1 , 8 6 6 9 . 0 [ ] 2 3 8 9 . 0 , 7 5 2 9 . 0 [ ] 3 9 5 0 . 1 , 8 7 9 9 . 0 [ B A ] 4 7 3 9 . 0 , 9 9 7 8 . 0 [ ] 3 5 8 9 . 0 , 8 3 2 9 . 0 [ B ] 4 2 8 9 . 0 , 9 4 2 9 . 0 [ ] 9 7 4 0 . 1 , 3 6 8 9 . 0 [ B A B A B A B A B A ] 6 0 5 9 . 0 , 1 3 9 8 . 0 [ ] 4 5 1 0 . 1 , 8 3 5 9 . 0 [ ] 7 0 5 9 . 0 , 2 3 9 8 . 0 [ ] 9 8 8 9 . 0 , 3 7 2 9 . 0 [ ] 0 4 5 9 . 0 , 5 6 9 8 . 0 [ ] 8 8 9 9 . 0 , 2 7 3 9 . 0 [ ] 9 2 4 9 . 0 , 4 5 8 8 . 0 [ ] 3 6 8 9 . 0 , 7 4 2 9 . 0 [ ] 4 7 5 9 . 0 , 9 9 9 8 . 0 [ ] 9 2 0 0 . 1 , 3 1 4 9 . 0 [ A ] 4 3 8 8 . 0 , 9 5 2 8 . 0 [ ] 2 0 4 9 . 0 , 7 8 7 8 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 1 1 8 8 . 0 5 9 1 9 . 0 9 8 1 9 . 0 1 7 4 9 . 0 0 5 5 9 . 0 8 8 2 9 . 0 5 8 4 9 . 0 0 2 8 9 . 0 4 0 7 9 . 0 0 6 4 9 . 0 0 5 1 9 . 0 6 6 4 9 . 0 4 2 1 9 . 0 8 6 4 9 . 0 4 4 5 9 . 0 7 8 0 9 . 0 7 3 5 9 . 0 9 1 2 9 . 0 9 1 2 9 . 0 3 5 2 9 . 0 1 4 1 9 . 0 7 8 2 9 . 0 7 4 5 8 . 0 8 4 5 9 . 0 0 0 6 9 . 0 2 5 8 9 . 0 9 8 0 0 . 1 9 2 1 0 . 1 1 6 8 9 . 0 4 6 1 0 . 1 9 6 2 0 . 1 9 1 2 0 . 1 8 2 2 0 . 1 0 3 8 9 . 0 6 4 0 0 . 1 9 9 9 9 . 0 6 7 9 9 . 0 5 8 2 0 . 1 5 4 5 9 . 0 1 7 1 0 . 1 6 4 8 9 . 0 1 8 5 9 . 0 0 8 6 9 . 0 5 5 5 9 . 0 1 2 7 9 . 0 5 9 0 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 1 8 . B e l b a T 445 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B A C B A C B C B C B C C B C B C B C B C B C B C B C B C B C B C B C B A C B C B A C B B A A B A B A B A B A B A ] 2 7 6 9 . 0 , 2 7 0 9 . 0 [ ] 2 7 0 0 . 1 , 1 4 4 9 . 0 [ ] 1 0 9 9 . 0 , 2 0 3 9 . 0 [ ] 4 4 2 0 . 1 , 3 1 6 9 . 0 [ ] 6 6 9 9 . 0 , 7 6 3 9 . 0 [ ] 8 5 3 0 . 1 , 7 2 7 9 . 0 [ ] 8 4 9 9 . 0 , 9 4 3 9 . 0 [ ] 5 2 4 0 . 1 , 4 9 7 9 . 0 [ ] 3 5 9 9 . 0 , 3 5 3 9 . 0 [ ] 7 3 2 0 . 1 , 6 0 6 9 . 0 [ B A B A B A ] 7 8 9 9 . 0 , 7 8 3 9 . 0 [ ] 5 0 5 0 . 1 , 4 7 8 9 . 0 [ ] 3 9 0 0 . 1 , 3 9 4 9 . 0 [ ] 1 8 4 0 . 1 , 0 5 8 9 . 0 [ ] 1 4 0 0 . 1 , 1 4 4 9 . 0 [ ] 4 2 5 0 . 1 , 3 9 8 9 . 0 [ B ] 9 2 2 0 . 1 , 0 3 6 9 . 0 [ ] 5 6 6 0 . 1 , 4 3 0 0 . 1 [ B A ] 1 4 9 9 . 0 , 1 4 3 9 . 0 [ ] 2 4 3 0 . 1 , 1 1 7 9 . 0 [ B ] 4 5 3 0 . 1 , 5 5 7 9 . 0 [ ] 1 0 8 0 . 1 , 0 7 1 0 . 1 [ B B ] 4 5 2 0 . 1 , 4 5 6 9 . 0 [ ] 7 6 7 0 . 1 , 6 3 1 0 . 1 [ ] 4 4 1 0 . 1 , 5 4 5 9 . 0 [ ] 7 6 7 0 . 1 , 6 3 1 0 . 1 [ B A ] 3 9 0 0 . 1 , 3 9 4 9 . 0 [ ] 7 3 5 0 . 1 , 6 0 9 9 . 0 [ B ] 5 3 1 0 . 1 , 6 3 5 9 . 0 [ ] 0 3 8 0 . 1 , 9 9 1 0 . 1 [ B A ] 8 6 1 0 . 1 , 8 6 5 9 . 0 [ ] 5 7 5 0 . 1 , 4 4 9 9 . 0 [ B ] 8 7 0 0 . 1 , 8 7 4 9 . 0 [ ] 2 9 7 0 . 1 , 1 6 1 0 . 1 [ B A ] 8 3 8 9 . 0 , 8 3 2 9 . 0 [ ] 7 8 4 0 . 1 , 6 5 8 9 . 0 [ B ] 5 7 1 0 . 1 , 6 7 5 9 . 0 [ ] 6 0 8 0 . 1 , 5 7 1 0 . 1 [ B A B A B A ] 0 2 9 9 . 0 , 0 2 3 9 . 0 [ ] 3 8 4 0 . 1 , 2 5 8 9 . 0 [ ] 9 2 9 9 . 0 , 9 2 3 9 . 0 [ ] 3 7 5 0 . 1 , 2 4 9 9 . 0 [ ] 5 0 5 9 . 0 , 5 0 9 8 . 0 [ ] 5 4 0 0 . 1 , 4 1 4 9 . 0 [ A ] 0 4 1 9 . 0 , 1 4 5 8 . 0 [ ] 1 9 7 9 . 0 , 0 6 1 9 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 2 7 3 9 . 0 1 0 6 9 . 0 6 6 6 9 . 0 9 4 6 9 . 0 3 5 6 9 . 0 4 5 0 0 . 1 7 8 6 9 . 0 3 9 7 9 . 0 1 4 7 9 . 0 9 2 9 9 . 0 1 4 6 9 . 0 4 5 9 9 . 0 5 4 8 9 . 0 3 9 7 9 . 0 6 3 8 9 . 0 8 6 8 9 . 0 8 7 7 9 . 0 8 3 5 9 . 0 6 7 8 9 . 0 0 2 6 9 . 0 9 2 6 9 . 0 5 0 2 9 . 0 0 4 8 8 . 0 7 5 7 9 . 0 8 2 9 9 . 0 3 4 0 0 . 1 9 0 1 0 . 1 1 2 9 9 . 0 6 8 4 0 . 1 0 9 1 0 . 1 5 6 1 0 . 1 9 0 2 0 . 1 9 4 3 0 . 1 6 2 0 0 . 1 2 5 4 0 . 1 1 5 4 0 . 1 1 2 2 0 . 1 5 1 5 0 . 1 0 6 2 0 . 1 7 7 4 0 . 1 2 7 1 0 . 1 1 9 4 0 . 1 7 6 1 0 . 1 8 5 2 0 . 1 9 2 7 9 . 0 6 7 4 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 2 8 . B e l b a T 446 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T B B B B B B B B B A B B B B B B B B B B B B A B A B A B A B A B A B A B A B A B A B A ] 8 0 4 0 . 1 , 3 4 7 9 . 0 [ ] 4 2 7 0 . 1 , 1 5 0 0 . 1 [ ] 0 1 5 0 . 1 , 5 4 8 9 . 0 [ ] 4 5 8 0 . 1 , 2 8 1 0 . 1 [ ] 6 9 3 0 . 1 , 1 3 7 9 . 0 [ ] 9 5 5 0 . 1 , 7 8 8 9 . 0 [ ] 9 4 6 0 . 1 , 4 8 9 9 . 0 [ ] 2 8 8 0 . 1 , 0 1 2 0 . 1 [ ] 2 9 2 0 . 1 , 7 2 6 9 . 0 [ ] 7 3 5 0 . 1 , 5 6 8 9 . 0 [ ] 7 7 5 0 . 1 , 2 1 9 9 . 0 [ ] 3 5 7 0 . 1 , 1 8 0 0 . 1 [ ] 8 5 4 0 . 1 , 3 9 7 9 . 0 [ ] 9 2 6 0 . 1 , 7 5 9 9 . 0 [ ] 8 2 7 0 . 1 , 3 6 0 0 . 1 [ ] 7 7 8 0 . 1 , 4 0 2 0 . 1 [ ] 5 4 0 0 . 1 , 0 8 3 9 . 0 [ ] 1 0 3 0 . 1 , 9 2 6 9 . 0 [ B A B A B A B A B A B A B A B A ] 5 8 4 0 . 1 , 0 2 8 9 . 0 [ ] 8 9 7 0 . 1 , 6 2 1 0 . 1 [ ] 8 6 6 0 . 1 , 3 0 0 0 . 1 [ ] 4 8 8 0 . 1 , 2 1 2 0 . 1 [ ] 6 1 6 0 . 1 , 2 5 9 9 . 0 [ ] 5 7 8 0 . 1 , 3 0 2 0 . 1 [ ] 9 9 4 0 . 1 , 4 3 8 9 . 0 [ ] 4 4 8 0 . 1 , 2 7 1 0 . 1 [ ] 0 0 4 0 . 1 , 5 3 7 9 . 0 [ ] 9 4 7 0 . 1 , 7 7 0 0 . 1 [ ] 7 4 4 0 . 1 , 2 8 7 9 . 0 [ ] 2 5 8 0 . 1 , 9 7 1 0 . 1 [ ] 0 2 4 0 . 1 , 5 5 7 9 . 0 [ ] 3 7 6 0 . 1 , 1 0 0 0 . 1 [ ] 8 6 4 0 . 1 , 3 0 8 9 . 0 [ ] 1 8 7 0 . 1 , 8 0 1 0 . 1 [ B A B A B A ] 1 7 3 0 . 1 , 6 0 7 9 . 0 [ ] 8 7 8 0 . 1 , 6 0 2 0 . 1 [ ] 2 9 0 0 . 1 , 7 2 4 9 . 0 [ ] 1 5 5 0 . 1 , 9 7 8 9 . 0 [ ] 8 0 2 0 . 1 , 3 4 5 9 . 0 [ ] 3 5 5 0 . 1 , 1 8 8 9 . 0 [ A ] 7 2 3 9 . 0 , 2 6 6 8 . 0 [ ] 3 2 0 0 . 1 , 1 5 3 9 . 0 [ B ] 0 6 4 0 . 1 , 5 9 7 9 . 0 [ ] 5 5 9 0 . 1 , 3 8 2 0 . 1 [ B ] 2 3 8 0 . 1 , 7 6 1 0 . 1 [ ] 8 1 1 1 . 1 , 6 4 4 0 . 1 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 6 7 0 0 . 1 7 7 1 0 . 1 3 6 0 0 . 1 7 1 3 0 . 1 0 6 9 9 . 0 5 4 2 0 . 1 5 2 1 0 . 1 6 9 3 0 . 1 3 1 7 9 . 0 9 9 4 0 . 1 2 5 1 0 . 1 6 3 3 0 . 1 4 8 2 0 . 1 7 6 1 0 . 1 7 6 0 0 . 1 4 1 1 0 . 1 8 8 0 0 . 1 5 3 1 0 . 1 7 2 1 0 . 1 8 3 0 0 . 1 0 6 7 9 . 0 6 7 8 9 . 0 5 9 9 8 . 0 7 8 3 0 . 1 8 1 5 0 . 1 3 2 2 0 . 1 6 4 5 0 . 1 1 0 2 0 . 1 7 1 4 0 . 1 3 9 2 0 . 1 1 4 5 0 . 1 5 6 9 9 . 0 2 8 7 0 . 1 2 6 4 0 . 1 8 4 5 0 . 1 9 3 5 0 . 1 8 0 5 0 . 1 3 1 4 0 . 1 6 1 5 0 . 1 7 3 3 0 . 1 5 4 4 0 . 1 9 1 6 0 . 1 2 4 5 0 . 1 5 1 2 0 . 1 7 1 2 0 . 1 7 8 6 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s E U R T , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 3 8 . B e l b a T 447 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T M L K K I J G F F E H G E D C G F D C B A C B A E D E D C B A K I H G ] 9 5 4 6 . 2 0 1 , 5 1 3 6 . 2 0 1 [ ] 4 0 6 6 . 2 0 1 , 7 5 4 6 . 2 0 1 [ ] 1 2 1 6 . 2 0 1 , 6 7 9 5 . 2 0 1 [ ] 0 0 9 5 . 2 0 1 , 4 5 7 5 . 2 0 1 [ ] 9 0 4 5 . 2 0 1 , 4 6 2 5 . 2 0 1 [ ] 7 3 2 5 . 2 0 1 , 0 9 0 5 . 2 0 1 [ ] 6 3 2 5 . 2 0 1 , 1 9 0 5 . 2 0 1 [ ] 7 1 0 5 . 2 0 1 , 0 7 8 4 . 2 0 1 [ E D ] 5 8 3 4 . 2 0 1 , 0 4 2 4 . 2 0 1 [ ] 7 0 2 4 . 2 0 1 , 1 6 0 4 . 2 0 1 [ E C D A C B A B A ] 2 1 6 4 . 2 0 1 , 7 6 4 4 . 2 0 1 [ ] 1 1 3 4 . 2 0 1 , 5 6 1 4 . 2 0 1 [ ] 7 2 8 3 . 2 0 1 , 2 8 6 3 . 2 0 1 [ ] 1 5 8 3 . 2 0 1 , 5 0 7 3 . 2 0 1 [ ] 6 9 1 4 . 2 0 1 , 1 5 0 4 . 2 0 1 [ ] 0 7 0 4 . 2 0 1 , 3 2 9 3 . 2 0 1 [ ] 7 5 6 3 . 2 0 1 , 2 1 5 3 . 2 0 1 [ ] 8 5 5 3 . 2 0 1 , 1 1 4 3 . 2 0 1 [ ] 8 4 9 3 . 2 0 1 , 3 0 8 3 . 2 0 1 [ ] 3 6 7 3 . 2 0 1 , 6 1 6 3 . 2 0 1 [ ] 5 4 5 3 . 2 0 1 , 0 0 4 3 . 2 0 1 [ ] 2 2 5 3 . 2 0 1 , 5 7 3 3 . 2 0 1 [ ] 4 1 8 3 . 2 0 1 , 9 6 6 3 . 2 0 1 [ ] 6 5 6 3 . 2 0 1 , 9 0 5 3 . 2 0 1 [ C B A ] 0 6 5 3 . 2 0 1 , 5 1 4 3 . 2 0 1 [ ] 2 6 6 3 . 2 0 1 , 6 1 5 3 . 2 0 1 [ A ] 9 3 4 3 . 2 0 1 , 4 9 2 3 . 2 0 1 [ ] 3 7 4 3 . 2 0 1 , 7 2 3 3 . 2 0 1 [ B A ] 1 1 5 3 . 2 0 1 , 6 6 3 3 . 2 0 1 [ ] 5 7 5 3 . 2 0 1 , 8 2 4 3 . 2 0 1 [ A ] 6 6 3 3 . 2 0 1 , 1 2 2 3 . 2 0 1 [ ] 3 2 5 3 . 2 0 1 , 7 7 3 3 . 2 0 1 [ A ] 6 9 2 3 . 2 0 1 , 1 5 1 3 . 2 0 1 [ ] 7 9 4 3 . 2 0 1 , 1 5 3 3 . 2 0 1 [ D C B A B A ] 9 0 4 3 . 2 0 1 , 4 6 2 3 . 2 0 1 [ ] 9 8 5 3 . 2 0 1 , 3 4 4 3 . 2 0 1 [ C B A B A B A L G B A ] 9 6 3 3 . 2 0 1 , 4 2 2 3 . 2 0 1 [ ] 3 7 5 3 . 2 0 1 , 6 2 4 3 . 2 0 1 [ A ] 3 3 3 3 . 2 0 1 , 8 8 1 3 . 2 0 1 [ ] 3 8 4 3 . 2 0 1 , 7 3 3 3 . 2 0 1 [ A J F ] 9 2 3 3 . 2 0 1 , 4 8 1 3 . 2 0 1 [ ] 9 1 5 3 . 2 0 1 , 2 7 3 3 . 2 0 1 [ ] 6 1 2 6 . 2 0 1 , 1 7 0 6 . 2 0 1 [ ] 9 9 2 6 . 2 0 1 , 2 5 1 6 . 2 0 1 [ ] 4 6 8 3 . 2 0 1 , 9 1 7 3 . 2 0 1 [ ] 5 6 5 4 . 2 0 1 , 8 1 4 4 . 2 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 7 8 3 6 . 2 0 1 9 4 0 6 . 2 0 1 7 3 3 5 . 2 0 1 3 6 1 5 . 2 0 1 3 1 3 4 . 2 0 1 0 4 5 4 . 2 0 1 5 5 7 3 . 2 0 1 3 2 1 4 . 2 0 1 4 8 5 3 . 2 0 1 6 7 8 3 . 2 0 1 2 7 4 3 . 2 0 1 1 4 7 3 . 2 0 1 7 6 3 3 . 2 0 1 7 8 4 3 . 2 0 1 3 9 2 3 . 2 0 1 8 3 4 3 . 2 0 1 4 2 2 3 . 2 0 1 6 3 3 3 . 2 0 1 0 6 2 3 . 2 0 1 7 9 2 3 . 2 0 1 7 5 2 3 . 2 0 1 4 4 1 6 . 2 0 1 2 9 7 3 . 2 0 1 1 t i a r T 0 3 5 6 . 2 0 1 7 2 8 5 . 2 0 1 3 6 1 5 . 2 0 1 4 4 9 4 . 2 0 1 4 3 1 4 . 2 0 1 8 3 2 4 . 2 0 1 8 7 7 3 . 2 0 1 7 9 9 3 . 2 0 1 5 8 4 3 . 2 0 1 0 9 6 3 . 2 0 1 8 4 4 3 . 2 0 1 3 8 5 3 . 2 0 1 0 0 4 3 . 2 0 1 9 8 5 3 . 2 0 1 0 5 4 3 . 2 0 1 1 0 5 3 . 2 0 1 4 2 4 3 . 2 0 1 6 1 5 3 . 2 0 1 0 1 4 3 . 2 0 1 9 9 4 3 . 2 0 1 5 4 4 3 . 2 0 1 5 2 2 6 . 2 0 1 1 9 4 4 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g d 0 2 V B E G w g 0 1 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g d 0 4 V B E G w g 0 2 V B E G w g d 0 5 V B E G w g d 0 6 V B E G w g 0 3 V B E G w g 5 2 V B E G w g d 0 7 V B E G w g 0 4 V B E G w g d 0 8 V B E G w g 5 4 V B E G w g d 0 9 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 4 8 . B e l b a T 448 e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P . 1 . 2 . 3 s t l u s e r o i r a n e c s T S E . 2 . 3 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T L K J I H H G G F F E D F O M L K J I G G F E F E D E D ] 8 6 6 0 . 3 0 1 , 9 6 4 0 . 3 0 1 [ ] 4 9 0 0 . 3 0 1 , 3 0 9 9 . 2 0 1 [ ] 4 0 3 0 . 3 0 1 , 5 0 1 0 . 3 0 1 [ ] 6 3 1 9 . 2 0 1 , 4 4 9 8 . 2 0 1 [ ] 2 2 7 9 . 2 0 1 , 3 2 5 9 . 2 0 1 [ ] 0 8 5 8 . 2 0 1 , 8 8 3 8 . 2 0 1 [ ] 7 1 0 9 . 2 0 1 , 9 1 8 8 . 2 0 1 [ ] 4 5 9 7 . 2 0 1 , 2 6 7 7 . 2 0 1 [ ] 4 1 0 8 . 2 0 1 , 6 1 8 7 . 2 0 1 [ ] 1 8 2 7 . 2 0 1 , 0 9 0 7 . 2 0 1 [ ] 7 1 9 7 . 2 0 1 , 8 1 7 7 . 2 0 1 [ ] 5 2 9 6 . 2 0 1 , 4 3 7 6 . 2 0 1 [ ] 6 2 0 7 . 2 0 1 , 8 2 8 6 . 2 0 1 [ ] 5 1 3 6 . 2 0 1 , 4 2 1 6 . 2 0 1 [ ] 0 2 1 7 . 2 0 1 , 1 2 9 6 . 2 0 1 [ ] 1 9 3 6 . 2 0 1 , 9 9 1 6 . 2 0 1 [ ] 1 8 3 6 . 2 0 1 , 2 8 1 6 . 2 0 1 [ ] 7 8 7 5 . 2 0 1 , 5 9 5 5 . 2 0 1 [ ] 5 3 6 6 . 2 0 1 , 6 3 4 6 . 2 0 1 [ ] 4 4 9 5 . 2 0 1 , 2 5 7 5 . 2 0 1 [ ] 1 2 0 6 . 2 0 1 , 2 2 8 5 . 2 0 1 [ ] 9 8 5 5 . 2 0 1 , 7 9 3 5 . 2 0 1 [ ] 0 0 4 6 . 2 0 1 , 1 0 2 6 . 2 0 1 [ ] 8 3 6 5 . 2 0 1 , 7 4 4 5 . 2 0 1 [ E D C D C B A ] 8 7 8 5 . 2 0 1 , 9 7 6 5 . 2 0 1 [ ] 8 9 3 5 . 2 0 1 , 7 0 2 5 . 2 0 1 [ E E D C ] 5 2 0 6 . 2 0 1 , 6 2 8 5 . 2 0 1 [ ] 3 6 5 5 . 2 0 1 , 2 7 3 5 . 2 0 1 [ D C B A E D C D C B ] 2 7 8 5 . 2 0 1 , 3 7 6 5 . 2 0 1 [ ] 0 2 4 5 . 2 0 1 , 8 2 2 5 . 2 0 1 [ B A ] 3 6 7 5 . 2 0 1 , 5 6 5 5 . 2 0 1 [ ] 1 8 2 5 . 2 0 1 , 0 9 0 5 . 2 0 1 [ E D C B C B A ] 7 0 8 5 . 2 0 1 , 8 0 6 5 . 2 0 1 [ ] 5 3 3 5 . 2 0 1 , 4 4 1 5 . 2 0 1 [ A B A ] 3 3 5 5 . 2 0 1 , 4 3 3 5 . 2 0 1 [ ] 5 0 3 5 . 2 0 1 , 4 1 1 5 . 2 0 1 [ C B A B A A L F B A B A A N H ] 0 2 5 5 . 2 0 1 , 1 2 3 5 . 2 0 1 [ ] 2 3 2 5 . 2 0 1 , 1 4 0 5 . 2 0 1 [ ] 5 2 6 5 . 2 0 1 , 6 2 4 5 . 2 0 1 [ ] 6 9 2 5 . 2 0 1 , 5 0 1 5 . 2 0 1 [ ] 7 8 5 5 . 2 0 1 , 9 8 3 5 . 2 0 1 [ ] 1 5 1 5 . 2 0 1 , 9 5 9 4 . 2 0 1 [ ] 6 4 8 0 . 3 0 1 , 7 4 6 0 . 3 0 1 [ ] 4 1 8 9 . 2 0 1 , 3 2 6 9 . 2 0 1 [ ] 7 6 4 6 . 2 0 1 , 9 6 2 6 . 2 0 1 [ ] 0 5 6 6 . 2 0 1 , 9 5 4 6 . 2 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 8 6 5 0 . 3 0 1 4 0 2 0 . 3 0 1 3 2 6 9 . 2 0 1 8 1 9 8 . 2 0 1 5 1 9 7 . 2 0 1 7 1 8 7 . 2 0 1 7 2 9 6 . 2 0 1 1 2 0 7 . 2 0 1 2 8 2 6 . 2 0 1 6 3 5 6 . 2 0 1 1 2 9 5 . 2 0 1 0 0 3 6 . 2 0 1 8 7 7 5 . 2 0 1 5 2 9 5 . 2 0 1 4 6 6 5 . 2 0 1 3 7 7 5 . 2 0 1 3 3 4 5 . 2 0 1 8 0 7 5 . 2 0 1 1 2 4 5 . 2 0 1 6 2 5 5 . 2 0 1 8 8 4 5 . 2 0 1 6 4 7 0 . 3 0 1 8 6 3 6 . 2 0 1 1 t i a r T 9 9 9 9 . 2 0 1 0 4 0 9 . 2 0 1 4 8 4 8 . 2 0 1 8 5 8 7 . 2 0 1 6 8 1 7 . 2 0 1 0 3 8 6 . 2 0 1 0 2 2 6 . 2 0 1 5 9 2 6 . 2 0 1 1 9 6 5 . 2 0 1 8 4 8 5 . 2 0 1 3 9 4 5 . 2 0 1 2 4 5 5 . 2 0 1 2 0 3 5 . 2 0 1 8 6 4 5 . 2 0 1 5 8 1 5 . 2 0 1 4 2 3 5 . 2 0 1 0 1 2 5 . 2 0 1 9 3 2 5 . 2 0 1 7 3 1 5 . 2 0 1 1 0 2 5 . 2 0 1 5 5 0 5 . 2 0 1 9 1 7 9 . 2 0 1 5 5 5 6 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 5 0 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g 0 1 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 5 4 V B E G w g d 0 9 V B E G w g 0 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 5 8 . B e l b a T 449 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T N M N M L K J J I I H G F E G F D C E D C B C B B A H L K K J J I I H H G F G E D F E ] 0 4 6 3 . 3 0 1 , 5 0 4 3 . 3 0 1 [ ] 7 1 2 2 . 3 0 1 , 1 9 9 1 . 3 0 1 [ ] 1 0 4 3 . 3 0 1 , 6 6 1 3 . 3 0 1 [ ] 1 4 3 1 . 3 0 1 , 6 1 1 1 . 3 0 1 [ ] 2 8 2 3 . 3 0 1 , 6 4 0 3 . 3 0 1 [ ] 2 5 1 1 . 3 0 1 , 7 2 9 0 . 3 0 1 [ ] 3 6 0 2 . 3 0 1 , 8 2 8 1 . 3 0 1 [ ] 3 5 0 0 . 3 0 1 , 8 2 8 9 . 2 0 1 [ ] 9 5 6 1 . 3 0 1 , 3 2 4 1 . 3 0 1 [ ] 3 2 1 0 . 3 0 1 , 8 9 8 9 . 2 0 1 [ ] 5 8 6 0 . 3 0 1 , 9 4 4 0 . 3 0 1 [ ] 2 1 0 9 . 2 0 1 , 7 8 7 8 . 2 0 1 [ ] 2 6 5 0 . 3 0 1 , 6 2 3 0 . 3 0 1 [ ] 8 2 1 9 . 2 0 1 , 3 0 9 8 . 2 0 1 [ ] 5 2 7 9 . 2 0 1 , 9 8 4 9 . 2 0 1 [ ] 3 8 2 8 . 2 0 1 , 8 5 0 8 . 2 0 1 [ ] 8 7 5 9 . 2 0 1 , 3 4 3 9 . 2 0 1 [ ] 3 0 4 8 . 2 0 1 , 8 7 1 8 . 2 0 1 [ ] 2 2 1 9 . 2 0 1 , 7 8 8 8 . 2 0 1 [ ] 5 1 7 7 . 2 0 1 , 0 9 4 7 . 2 0 1 [ ] 1 0 0 9 . 2 0 1 , 5 6 7 8 . 2 0 1 [ ] 4 4 9 7 . 2 0 1 , 9 1 7 7 . 2 0 1 [ ] 7 2 6 8 . 2 0 1 , 2 9 3 8 . 2 0 1 [ ] 7 4 3 7 . 2 0 1 , 2 2 1 7 . 2 0 1 [ ] 5 9 6 8 . 2 0 1 , 0 6 4 8 . 2 0 1 [ ] 5 8 4 7 . 2 0 1 , 0 6 2 7 . 2 0 1 [ E D C ] 4 2 2 8 . 2 0 1 , 8 8 9 7 . 2 0 1 [ ] 3 3 2 7 . 2 0 1 , 8 0 0 7 . 2 0 1 [ E D ] 7 5 3 8 . 2 0 1 , 2 2 1 8 . 2 0 1 [ ] 8 0 3 7 . 2 0 1 , 3 8 0 7 . 2 0 1 [ C B A D C B ] 3 3 0 8 . 2 0 1 , 7 9 7 7 . 2 0 1 [ ] 1 0 0 7 . 2 0 1 , 6 7 7 6 . 2 0 1 [ ] 9 4 0 8 . 2 0 1 , 4 1 8 7 . 2 0 1 [ ] 1 6 1 7 . 2 0 1 , 6 3 9 6 . 2 0 1 [ B A ] 1 0 9 7 . 2 0 1 , 5 6 6 7 . 2 0 1 [ ] 3 8 8 6 . 2 0 1 , 8 5 6 6 . 2 0 1 [ C B A C B A ] 7 1 9 7 . 2 0 1 , 1 8 6 7 . 2 0 1 [ ] 8 0 0 7 . 2 0 1 , 3 8 7 6 . 2 0 1 [ B A F E O A A A L H ] 5 4 6 7 . 2 0 1 , 0 1 4 7 . 2 0 1 [ ] 8 2 8 6 . 2 0 1 , 3 0 6 6 . 2 0 1 [ ] 7 3 8 7 . 2 0 1 , 1 0 6 7 . 2 0 1 [ ] 2 5 8 6 . 2 0 1 , 6 2 6 6 . 2 0 1 [ ] 7 9 9 3 . 3 0 1 , 2 6 7 3 . 3 0 1 [ ] 7 3 9 1 . 3 0 1 , 2 1 7 1 . 3 0 1 [ ] 3 6 6 8 . 2 0 1 , 7 2 4 8 . 2 0 1 [ ] 1 3 4 8 . 2 0 1 , 6 0 2 8 . 2 0 1 [ . p o P n a e M V B T n a e M 2 t i a r T 2 2 5 3 . 3 0 1 4 8 2 3 . 3 0 1 4 6 1 3 . 3 0 1 5 4 9 1 . 3 0 1 1 4 5 1 . 3 0 1 7 6 5 0 . 3 0 1 4 4 4 0 . 3 0 1 7 0 6 9 . 2 0 1 1 6 4 9 . 2 0 1 5 0 0 9 . 2 0 1 3 8 8 8 . 2 0 1 0 1 5 8 . 2 0 1 8 7 5 8 . 2 0 1 6 0 1 8 . 2 0 1 0 4 2 8 . 2 0 1 5 1 9 7 . 2 0 1 1 3 9 7 . 2 0 1 3 8 7 7 . 2 0 1 9 9 7 7 . 2 0 1 7 2 5 7 . 2 0 1 9 1 7 7 . 2 0 1 9 7 8 3 . 3 0 1 5 4 5 8 . 2 0 1 1 t i a r T 4 0 1 2 . 3 0 1 9 2 2 1 . 3 0 1 9 3 0 1 . 3 0 1 0 4 9 9 . 2 0 1 0 1 0 0 . 3 0 1 0 0 9 8 . 2 0 1 6 1 0 9 . 2 0 1 0 7 1 8 . 2 0 1 1 9 2 8 . 2 0 1 3 0 6 7 . 2 0 1 1 3 8 7 . 2 0 1 5 3 2 7 . 2 0 1 3 7 3 7 . 2 0 1 0 2 1 7 . 2 0 1 6 9 1 7 . 2 0 1 8 8 8 6 . 2 0 1 9 4 0 7 . 2 0 1 0 7 7 6 . 2 0 1 6 9 8 6 . 2 0 1 6 1 7 6 . 2 0 1 9 3 7 6 . 2 0 1 4 2 8 1 . 3 0 1 8 1 3 8 . 2 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t n a e m n o i t a l u p o P : 6 8 . B e l b a T 450 3.2.2. Population maximum true breeding value Figure B.21: Population maximum true breeding value by selection strategy over 60 generations in the multi-trait, EST scenario. 451 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T H G H G G F E F D C B F E D C B A E D C D C B C B A B A B A B A B A A B A B A B A B A H G B A H H G G F E D F E ] 1 4 4 2 . 3 0 1 , 1 1 1 2 . 3 0 1 [ ] 3 8 4 2 . 3 0 1 , 3 5 1 2 . 3 0 1 [ ] 6 0 6 2 . 3 0 1 , 6 7 2 2 . 3 0 1 [ ] 5 9 2 2 . 3 0 1 , 5 6 9 1 . 3 0 1 [ ] 5 5 1 2 . 3 0 1 , 6 2 8 1 . 3 0 1 [ ] 8 2 8 1 . 3 0 1 , 8 9 4 1 . 3 0 1 [ ] 7 6 0 2 . 3 0 1 , 8 3 7 1 . 3 0 1 [ ] 1 0 6 1 . 3 0 1 , 2 7 2 1 . 3 0 1 [ ] 0 4 3 1 . 3 0 1 , 1 1 0 1 . 3 0 1 [ ] 0 8 0 1 . 3 0 1 , 0 5 7 0 . 3 0 1 [ ] 5 3 4 1 . 3 0 1 , 6 0 1 1 . 3 0 1 [ ] 6 2 2 1 . 3 0 1 , 6 9 8 0 . 3 0 1 [ E D C B ] 3 1 8 0 . 3 0 1 , 4 8 4 0 . 3 0 1 [ ] 9 9 7 0 . 3 0 1 , 9 6 4 0 . 3 0 1 [ E D C C B A E D C ] 3 8 1 1 . 3 0 1 , 4 5 8 0 . 3 0 1 [ ] 1 3 9 0 . 3 0 1 , 1 0 6 0 . 3 0 1 [ ] 5 1 6 0 . 3 0 1 , 6 8 2 0 . 3 0 1 [ ] 7 4 6 0 . 3 0 1 , 8 1 3 0 . 3 0 1 [ ] 6 8 9 0 . 3 0 1 , 7 5 6 0 . 3 0 1 [ ] 0 7 8 0 . 3 0 1 , 1 4 5 0 . 3 0 1 [ B A ] 7 6 4 0 . 3 0 1 , 8 3 1 0 . 3 0 1 [ ] 3 3 4 0 . 3 0 1 , 3 0 1 0 . 3 0 1 [ D C B A ] 8 9 7 0 . 3 0 1 , 9 6 4 0 . 3 0 1 [ ] 3 2 7 0 . 3 0 1 , 4 9 3 0 . 3 0 1 [ D C B A ] 3 8 5 0 . 3 0 1 , 4 5 2 0 . 3 0 1 [ ] 3 7 6 0 . 3 0 1 , 3 4 3 0 . 3 0 1 [ C B A ] 8 1 4 0 . 3 0 1 , 9 8 0 0 . 3 0 1 [ ] 5 0 5 0 . 3 0 1 , 5 7 1 0 . 3 0 1 [ C B A C B A ] 3 2 4 0 . 3 0 1 , 4 9 0 0 . 3 0 1 [ ] 3 2 5 0 . 3 0 1 , 4 9 1 0 . 3 0 1 [ ] 4 7 4 0 . 3 0 1 , 5 4 1 0 . 3 0 1 [ ] 9 8 5 0 . 3 0 1 , 0 6 2 0 . 3 0 1 [ B A ] 7 8 2 0 . 3 0 1 , 8 5 9 9 . 2 0 1 [ ] 9 3 4 0 . 3 0 1 , 0 1 1 0 . 3 0 1 [ C B A ] 5 1 4 0 . 3 0 1 , 6 8 0 0 . 3 0 1 [ ] 9 0 6 0 . 3 0 1 , 9 7 2 0 . 3 0 1 [ B A B A ] 1 9 3 0 . 3 0 1 , 2 6 0 0 . 3 0 1 [ ] 7 1 4 0 . 3 0 1 , 7 8 0 0 . 3 0 1 [ ] 9 1 5 0 . 3 0 1 , 9 8 1 0 . 3 0 1 [ ] 5 3 4 0 . 3 0 1 , 5 0 1 0 . 3 0 1 [ H ] 0 8 4 2 . 3 0 1 , 1 5 1 2 . 3 0 1 [ ] 9 3 4 2 . 3 0 1 , 9 0 1 2 . 3 0 1 [ A ] 0 9 3 0 . 3 0 1 , 1 6 0 0 . 3 0 1 [ ] 4 9 2 0 . 3 0 1 , 4 6 9 9 . 2 0 1 [ E D C ] 3 0 5 0 . 3 0 1 , 4 7 1 0 . 3 0 1 [ ] 7 9 8 0 . 3 0 1 , 7 6 5 0 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 6 7 2 2 . 3 0 1 1 4 4 2 . 3 0 1 0 9 9 1 . 3 0 1 3 0 9 1 . 3 0 1 6 7 1 1 . 3 0 1 1 7 2 1 . 3 0 1 9 4 6 0 . 3 0 1 9 1 0 1 . 3 0 1 1 5 4 0 . 3 0 1 1 2 8 0 . 3 0 1 3 0 3 0 . 3 0 1 4 3 6 0 . 3 0 1 4 5 2 0 . 3 0 1 9 1 4 0 . 3 0 1 9 5 2 0 . 3 0 1 0 1 3 0 . 3 0 1 3 2 1 0 . 3 0 1 1 5 2 0 . 3 0 1 6 2 2 0 . 3 0 1 7 2 2 0 . 3 0 1 4 5 3 0 . 3 0 1 5 1 3 2 . 3 0 1 9 3 3 0 . 3 0 1 1 t i a r T 8 1 3 2 . 3 0 1 0 3 1 2 . 3 0 1 3 6 6 1 . 3 0 1 6 3 4 1 . 3 0 1 5 1 9 0 . 3 0 1 1 6 0 1 . 3 0 1 4 3 6 0 . 3 0 1 6 6 7 0 . 3 0 1 2 8 4 0 . 3 0 1 6 0 7 0 . 3 0 1 8 6 2 0 . 3 0 1 8 5 5 0 . 3 0 1 0 4 3 0 . 3 0 1 8 0 5 0 . 3 0 1 9 5 3 0 . 3 0 1 5 2 4 0 . 3 0 1 5 7 2 0 . 3 0 1 4 4 4 0 . 3 0 1 9 2 1 0 . 3 0 1 2 5 2 0 . 3 0 1 0 7 2 0 . 3 0 1 4 7 2 2 . 3 0 1 2 3 7 0 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 7 8 . B e l b a T 452 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T I H J J I H H G G F E F E D F E C B E D C B D C C B I I ] 2 8 6 5 . 3 0 1 , 8 2 3 5 . 3 0 1 [ ] 8 4 8 4 . 3 0 1 , 2 0 5 4 . 3 0 1 [ ] 6 4 1 6 . 3 0 1 , 1 9 7 5 . 3 0 1 [ ] 2 7 7 4 . 3 0 1 , 5 2 4 4 . 3 0 1 [ I H ] 3 0 7 5 . 3 0 1 , 8 4 3 5 . 3 0 1 [ ] 7 1 5 4 . 3 0 1 , 1 7 1 4 . 3 0 1 [ H G G F F ] 7 9 3 5 . 3 0 1 , 2 4 0 5 . 3 0 1 [ ] 0 4 2 4 . 3 0 1 , 3 9 8 3 . 3 0 1 [ ] 6 2 5 4 . 3 0 1 , 1 7 1 4 . 3 0 1 [ ] 3 6 6 3 . 3 0 1 , 7 1 3 3 . 3 0 1 [ ] 0 7 4 4 . 3 0 1 , 6 1 1 4 . 3 0 1 [ ] 8 8 3 3 . 3 0 1 , 2 4 0 3 . 3 0 1 [ ] 2 3 7 3 . 3 0 1 , 8 7 3 3 . 3 0 1 [ ] 8 2 9 2 . 3 0 1 , 1 8 5 2 . 3 0 1 [ ] 7 0 8 3 . 3 0 1 , 3 5 4 3 . 3 0 1 [ ] 9 0 9 2 . 3 0 1 , 3 6 5 2 . 3 0 1 [ F E ] 6 0 3 3 . 3 0 1 , 1 5 9 2 . 3 0 1 [ ] 1 5 6 2 . 3 0 1 , 5 0 3 2 . 3 0 1 [ E D C B A ] 6 2 8 2 . 3 0 1 , 2 7 4 2 . 3 0 1 [ ] 5 5 3 2 . 3 0 1 , 9 0 0 2 . 3 0 1 [ F E D C ] 4 2 4 3 . 3 0 1 , 9 6 0 3 . 3 0 1 [ ] 2 0 5 2 . 3 0 1 , 6 5 1 2 . 3 0 1 [ E D C B ] 5 0 3 3 . 3 0 1 , 0 5 9 2 . 3 0 1 [ ] 0 4 4 2 . 3 0 1 , 4 9 0 2 . 3 0 1 [ E D C B ] 8 0 9 2 . 3 0 1 , 3 5 5 2 . 3 0 1 [ ] 1 2 4 2 . 3 0 1 , 5 7 0 2 . 3 0 1 [ C B A ] 1 3 8 2 . 3 0 1 , 6 7 4 2 . 3 0 1 [ ] 4 8 0 2 . 3 0 1 , 7 3 7 1 . 3 0 1 [ C B A ] 8 1 8 2 . 3 0 1 , 3 6 4 2 . 3 0 1 [ ] 4 5 1 2 . 3 0 1 , 8 0 8 1 . 3 0 1 [ D C B D C B A ] 3 4 8 2 . 3 0 1 , 8 8 4 2 . 3 0 1 [ ] 6 9 1 2 . 3 0 1 , 9 4 8 1 . 3 0 1 [ B A B A A C B A C B A J I C B A D C B A ] 0 3 4 2 . 3 0 1 , 5 7 0 2 . 3 0 1 [ ] 0 7 1 2 . 3 0 1 , 4 2 8 1 . 3 0 1 [ C B A ] 1 1 4 2 . 3 0 1 , 7 5 0 2 . 3 0 1 [ ] 1 6 0 2 . 3 0 1 , 5 1 7 1 . 3 0 1 [ B A ] 7 2 3 2 . 3 0 1 , 2 7 9 1 . 3 0 1 [ ] 5 2 0 2 . 3 0 1 , 9 7 6 1 . 3 0 1 [ B A ] 2 7 5 2 . 3 0 1 , 7 1 2 2 . 3 0 1 [ ] 1 2 0 2 . 3 0 1 , 5 7 6 1 . 3 0 1 [ A ] 5 0 5 2 . 3 0 1 , 0 5 1 2 . 3 0 1 [ ] 2 5 9 1 . 3 0 1 , 5 0 6 1 . 3 0 1 [ I ] 0 1 0 6 . 3 0 1 , 6 5 6 5 . 3 0 1 [ ] 3 6 7 4 . 3 0 1 , 7 1 4 4 . 3 0 1 [ F E D ] 2 6 7 2 . 3 0 1 , 8 0 4 2 . 3 0 1 [ ] 0 2 6 2 . 3 0 1 , 3 7 2 2 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 5 0 5 5 . 3 0 1 8 6 9 5 . 3 0 1 5 2 5 5 . 3 0 1 9 1 2 5 . 3 0 1 9 4 3 4 . 3 0 1 3 9 2 4 . 3 0 1 5 5 5 3 . 3 0 1 0 3 6 3 . 3 0 1 8 2 1 3 . 3 0 1 6 4 2 3 . 3 0 1 9 4 6 2 . 3 0 1 7 2 1 3 . 3 0 1 1 4 6 2 . 3 0 1 1 3 7 2 . 3 0 1 3 5 6 2 . 3 0 1 6 6 6 2 . 3 0 1 9 4 1 2 . 3 0 1 3 5 2 2 . 3 0 1 4 3 2 2 . 3 0 1 8 2 3 2 . 3 0 1 5 9 3 2 . 3 0 1 3 3 8 5 . 3 0 1 5 8 5 2 . 3 0 1 1 t i a r T 5 7 6 4 . 3 0 1 9 9 5 4 . 3 0 1 4 4 3 4 . 3 0 1 6 6 0 4 . 3 0 1 0 9 4 3 . 3 0 1 5 1 2 3 . 3 0 1 5 5 7 2 . 3 0 1 6 3 7 2 . 3 0 1 8 7 4 2 . 3 0 1 9 2 3 2 . 3 0 1 2 8 1 2 . 3 0 1 7 6 2 2 . 3 0 1 1 8 9 1 . 3 0 1 8 4 2 2 . 3 0 1 0 1 9 1 . 3 0 1 3 2 0 2 . 3 0 1 2 5 8 1 . 3 0 1 7 9 9 1 . 3 0 1 8 8 8 1 . 3 0 1 8 7 7 1 . 3 0 1 8 4 8 1 . 3 0 1 0 9 5 4 . 3 0 1 7 4 4 2 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 8 8 . B e l b a T 453 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T J I L L K J I H H G G G F E F E D F E D G F D C B E D C C B A C B A C B A C B A B A L K A C B A I I ] 8 4 8 7 . 3 0 1 , 0 8 4 7 . 3 0 1 [ ] 9 1 4 6 . 3 0 1 , 0 7 0 6 . 3 0 1 [ ] 2 4 6 8 . 3 0 1 , 4 7 2 8 . 3 0 1 [ ] 9 5 3 6 . 3 0 1 , 9 0 0 6 . 3 0 1 [ I H ] 5 6 5 8 . 3 0 1 , 6 9 1 8 . 3 0 1 [ ] 9 3 2 6 . 3 0 1 , 9 8 8 5 . 3 0 1 [ H H G G F G F F E F E ] 1 3 9 7 . 3 0 1 , 3 6 5 7 . 3 0 1 [ ] 3 2 8 5 . 3 0 1 , 3 7 4 5 . 3 0 1 [ ] 6 3 4 7 . 3 0 1 , 8 6 0 7 . 3 0 1 [ ] 6 9 8 5 . 3 0 1 , 7 4 5 5 . 3 0 1 [ ] 7 1 8 6 . 3 0 1 , 8 4 4 6 . 3 0 1 [ ] 6 1 1 5 . 3 0 1 , 6 6 7 4 . 3 0 1 [ ] 1 7 7 6 . 3 0 1 , 3 0 4 6 . 3 0 1 [ ] 9 1 1 5 . 3 0 1 , 0 7 7 4 . 3 0 1 [ ] 9 3 9 5 . 3 0 1 , 1 7 5 5 . 3 0 1 [ ] 4 1 5 4 . 3 0 1 , 4 6 1 4 . 3 0 1 [ ] 9 0 9 5 . 3 0 1 , 1 4 5 5 . 3 0 1 [ ] 5 6 6 4 . 3 0 1 , 6 1 3 4 . 3 0 1 [ ] 1 1 7 5 . 3 0 1 , 3 4 3 5 . 3 0 1 [ ] 7 4 2 4 . 3 0 1 , 8 9 8 3 . 3 0 1 [ ] 1 3 5 5 . 3 0 1 , 3 6 1 5 . 3 0 1 [ ] 2 2 3 4 . 3 0 1 , 3 7 9 3 . 3 0 1 [ D C B A ] 5 0 4 5 . 3 0 1 , 7 3 0 5 . 3 0 1 [ ] 6 8 7 3 . 3 0 1 , 6 3 4 3 . 3 0 1 [ D C B A E D C B ] 1 5 9 4 . 3 0 1 , 3 8 5 4 . 3 0 1 [ ] 0 3 6 3 . 3 0 1 , 1 8 2 3 . 3 0 1 [ ] 5 6 0 5 . 3 0 1 , 6 9 6 4 . 3 0 1 [ ] 4 8 8 3 . 3 0 1 , 5 3 5 3 . 3 0 1 [ E D C ] 9 8 3 5 . 3 0 1 , 1 2 0 5 . 3 0 1 [ ] 5 4 9 3 . 3 0 1 , 6 9 5 3 . 3 0 1 [ D C B A ] 1 5 7 4 . 3 0 1 , 2 8 3 4 . 3 0 1 [ ] 7 1 6 3 . 3 0 1 , 7 6 2 3 . 3 0 1 [ B A ] 0 1 6 4 . 3 0 1 , 1 4 2 4 . 3 0 1 [ ] 1 4 4 3 . 3 0 1 , 2 9 0 3 . 3 0 1 [ C B A ] 7 6 8 4 . 3 0 1 , 8 9 4 4 . 3 0 1 [ ] 9 3 5 3 . 3 0 1 , 9 8 1 3 . 3 0 1 [ A ] 5 4 6 4 . 3 0 1 , 7 7 2 4 . 3 0 1 [ ] 2 2 4 3 . 3 0 1 , 2 7 0 3 . 3 0 1 [ B A I H E D A ] 8 6 4 4 . 3 0 1 , 9 9 0 4 . 3 0 1 [ ] 4 3 4 3 . 3 0 1 , 4 8 0 3 . 3 0 1 [ ] 5 5 5 4 . 3 0 1 , 7 8 1 4 . 3 0 1 [ ] 2 0 4 3 . 3 0 1 , 2 5 0 3 . 3 0 1 [ ] 5 8 3 8 . 3 0 1 , 7 1 0 8 . 3 0 1 [ ] 5 0 2 6 . 3 0 1 , 5 5 8 5 . 3 0 1 [ ] 5 0 6 4 . 3 0 1 , 7 3 2 4 . 3 0 1 [ ] 8 9 9 3 . 3 0 1 , 9 4 6 3 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 4 6 6 7 . 3 0 1 8 5 4 8 . 3 0 1 1 8 3 8 . 3 0 1 7 4 7 7 . 3 0 1 2 5 2 7 . 3 0 1 3 3 6 6 . 3 0 1 7 8 5 6 . 3 0 1 5 5 7 5 . 3 0 1 5 2 7 5 . 3 0 1 7 2 5 5 . 3 0 1 7 4 3 5 . 3 0 1 1 2 2 5 . 3 0 1 5 0 2 5 . 3 0 1 7 6 7 4 . 3 0 1 0 8 8 4 . 3 0 1 6 2 4 4 . 3 0 1 6 6 5 4 . 3 0 1 1 6 4 4 . 3 0 1 3 8 6 4 . 3 0 1 4 8 2 4 . 3 0 1 1 7 3 4 . 3 0 1 1 0 2 8 . 3 0 1 1 2 4 4 . 3 0 1 1 t i a r T 5 4 2 6 . 3 0 1 4 8 1 6 . 3 0 1 4 6 0 6 . 3 0 1 8 4 6 5 . 3 0 1 2 2 7 5 . 3 0 1 1 4 9 4 . 3 0 1 4 4 9 4 . 3 0 1 9 3 3 4 . 3 0 1 1 9 4 4 . 3 0 1 3 7 0 4 . 3 0 1 7 4 1 4 . 3 0 1 1 1 6 3 . 3 0 1 0 7 7 3 . 3 0 1 5 5 4 3 . 3 0 1 9 0 7 3 . 3 0 1 6 6 2 3 . 3 0 1 2 4 4 3 . 3 0 1 7 4 2 3 . 3 0 1 4 6 3 3 . 3 0 1 9 5 2 3 . 3 0 1 7 2 2 3 . 3 0 1 0 3 0 6 . 3 0 1 3 2 8 3 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 9 8 . B e l b a T 454 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T H J J I H I H G H E D G D G F C G F E C B F E B A E D C B A D A D J I A M L K ] 5 5 3 9 . 3 0 1 , 4 9 9 8 . 3 0 1 [ ] 3 6 1 7 . 3 0 1 , 0 1 8 6 . 3 0 1 [ M L K ] 6 9 7 9 . 3 0 1 , 5 3 4 9 . 3 0 1 [ ] 1 6 1 7 . 3 0 1 , 8 0 8 6 . 3 0 1 [ M M ] 4 4 3 0 . 4 0 1 , 3 8 9 9 . 3 0 1 [ ] 9 5 5 7 . 3 0 1 , 6 0 2 7 . 3 0 1 [ ] 1 2 4 0 . 4 0 1 , 0 6 0 0 . 4 0 1 [ ] 4 4 5 7 . 3 0 1 , 1 9 1 7 . 3 0 1 [ M L I H G L K J F E K J I E D J I H C B I H G D C B H G B A G F G F F E K J A A ] 2 6 7 9 . 3 0 1 , 1 0 4 9 . 3 0 1 [ ] 3 0 4 7 . 3 0 1 , 9 4 0 7 . 3 0 1 [ ] 9 7 6 8 . 3 0 1 , 8 1 3 8 . 3 0 1 [ ] 4 1 4 6 . 3 0 1 , 1 6 0 6 . 3 0 1 [ ] 9 4 4 9 . 3 0 1 , 8 8 0 9 . 3 0 1 [ ] 0 9 9 6 . 3 0 1 , 7 3 6 6 . 3 0 1 [ ] 0 7 8 7 . 3 0 1 , 9 0 5 7 . 3 0 1 [ ] 1 0 7 5 . 3 0 1 , 8 4 3 5 . 3 0 1 [ ] 3 0 7 8 . 3 0 1 , 2 4 3 8 . 3 0 1 [ ] 7 6 7 6 . 3 0 1 , 4 1 4 6 . 3 0 1 [ ] 8 2 6 7 . 3 0 1 , 7 6 2 7 . 3 0 1 [ ] 0 0 5 5 . 3 0 1 , 7 4 1 5 . 3 0 1 [ ] 3 1 4 8 . 3 0 1 , 2 5 0 8 . 3 0 1 [ ] 2 2 6 6 . 3 0 1 , 9 6 2 6 . 3 0 1 [ ] 8 1 7 6 . 3 0 1 , 7 5 3 6 . 3 0 1 [ ] 1 9 9 4 . 3 0 1 , 8 3 6 4 . 3 0 1 [ ] 3 5 2 8 . 3 0 1 , 2 9 8 7 . 3 0 1 [ ] 8 2 4 6 . 3 0 1 , 5 7 0 6 . 3 0 1 [ ] 1 3 6 6 . 3 0 1 , 0 7 2 6 . 3 0 1 [ ] 5 6 0 5 . 3 0 1 , 2 1 7 4 . 3 0 1 [ ] 2 0 1 8 . 3 0 1 , 1 4 7 7 . 3 0 1 [ ] 2 8 2 6 . 3 0 1 , 9 2 9 5 . 3 0 1 [ ] 4 4 2 6 . 3 0 1 , 4 8 8 5 . 3 0 1 [ ] 6 0 6 4 . 3 0 1 , 2 5 2 4 . 3 0 1 [ ] 4 1 8 7 . 3 0 1 , 3 5 4 7 . 3 0 1 [ ] 8 8 0 6 . 3 0 1 , 5 3 7 5 . 3 0 1 [ ] 6 8 2 6 . 3 0 1 , 5 2 9 5 . 3 0 1 [ ] 2 6 4 4 . 3 0 1 , 9 0 1 4 . 3 0 1 [ ] 6 9 4 7 . 3 0 1 , 5 3 1 7 . 3 0 1 [ ] 2 8 9 5 . 3 0 1 , 9 2 6 5 . 3 0 1 [ ] 2 4 0 6 . 3 0 1 , 1 8 6 5 . 3 0 1 [ ] 1 2 4 4 . 3 0 1 , 8 6 0 4 . 3 0 1 [ ] 9 9 4 7 . 3 0 1 , 8 3 1 7 . 3 0 1 [ ] 7 7 6 5 . 3 0 1 , 4 2 3 5 . 3 0 1 [ ] 2 4 0 0 . 4 0 1 , 1 8 6 9 . 3 0 1 [ ] 7 3 9 6 . 3 0 1 , 4 8 5 6 . 3 0 1 [ D C ] 4 7 9 5 . 3 0 1 , 3 1 6 5 . 3 0 1 [ ] 8 1 1 5 . 3 0 1 , 5 6 7 4 . 3 0 1 [ . p o P n a e M V B T x a M 2 t i a r T 5 7 1 9 . 3 0 1 3 6 1 0 . 4 0 1 0 4 2 0 . 4 0 1 6 1 6 9 . 3 0 1 2 8 5 9 . 3 0 1 8 9 4 8 . 3 0 1 8 6 2 9 . 3 0 1 9 8 6 7 . 3 0 1 2 2 5 8 . 3 0 1 8 4 4 7 . 3 0 1 2 3 2 8 . 3 0 1 7 3 5 6 . 3 0 1 3 7 0 8 . 3 0 1 0 5 4 6 . 3 0 1 1 2 9 7 . 3 0 1 4 6 0 6 . 3 0 1 3 3 6 7 . 3 0 1 6 0 1 6 . 3 0 1 5 1 3 7 . 3 0 1 1 6 8 5 . 3 0 1 9 1 3 7 . 3 0 1 1 6 8 9 . 3 0 1 4 9 7 5 . 3 0 1 1 t i a r T 7 8 9 6 . 3 0 1 3 8 3 7 . 3 0 1 7 6 3 7 . 3 0 1 5 8 9 6 . 3 0 1 6 2 2 7 . 3 0 1 7 3 2 6 . 3 0 1 4 1 8 6 . 3 0 1 5 2 5 5 . 3 0 1 1 9 5 6 . 3 0 1 4 2 3 5 . 3 0 1 6 4 4 6 . 3 0 1 4 1 8 4 . 3 0 1 1 5 2 6 . 3 0 1 8 8 8 4 . 3 0 1 6 0 1 6 . 3 0 1 9 2 4 4 . 3 0 1 2 1 9 5 . 3 0 1 6 8 2 4 . 3 0 1 5 0 8 5 . 3 0 1 5 4 2 4 . 3 0 1 0 0 5 5 . 3 0 1 1 6 7 6 . 3 0 1 1 4 9 4 . 3 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e u l a v g n i d e e r b e u r t m u m i x a m n o i t a l u p o P : 0 9 . B e l b a T 455 3.2.3. Population mean expected heterozygosity Generation 15 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.2009 GEBV 0.2300 gwGEBV05 0.2455 gwGEBV10d 0.2495 gwGEBV10 0.2605 gwGEBV20d 0.2588 gwGEBV15 0.2644 gwGEBV30d 0.2621 gwGEBV20 0.2653 gwGEBV40d 0.2644 gwGEBV25 0.2659 gwGEBV50d 0.2651 gwGEBV30 0.2657 gwGEBV60d 0.2662 gwGEBV35 0.2652 gwGEBV70d 0.2661 gwGEBV40 0.2645 gwGEBV80d 0.2660 gwGEBV45 0.2635 gwGEBV90d 0.2657 gwGEBV50 gwGEBV100d 0.2623 0.2202 OCS 0.2310 RS [0.2004, 0.2013] A [0.2296, 0.2305] C [0.2451, 0.2460] D [0.2491, 0.2500] E [0.2600, 0.2609] G [0.2583, 0.2592] F [0.2640, 0.2649] IJ [0.2617, 0.2626] H [0.2649, 0.2658] JKL [0.2639, 0.2648] IJ [0.2654, 0.2663] L [0.2647, 0.2656] JKL [0.2652, 0.2661] KL [0.2658, 0.2667] L [0.2647, 0.2656] JKL [0.2656, 0.2665] L [0.2641, 0.2650] IJK [0.2655, 0.2665] L [0.2631, 0.2640] I [0.2653, 0.2662] KL [0.2618, 0.2627] H [0.2197, 0.2206] B [0.2306, 0.2315] C DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.91: Population mean expected heterozygosity by selection strategy at generation 15 in the multi-trait, EST scenario. 456 Generation 30 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.1538 GEBV 0.2012 gwGEBV05 0.2166 gwGEBV10d 0.2322 gwGEBV10 0.2449 gwGEBV20d 0.2486 gwGEBV15 0.2564 gwGEBV30d 0.2559 gwGEBV20 0.2621 gwGEBV40d 0.2602 gwGEBV25 0.2637 gwGEBV50d 0.2625 gwGEBV30 0.2640 gwGEBV60d 0.2640 gwGEBV35 0.2646 gwGEBV70d 0.2645 gwGEBV40 0.2640 gwGEBV80d 0.2648 gwGEBV45 0.2637 gwGEBV90d gwGEBV50 0.2652 gwGEBV100d 0.2625 0.1663 OCS 0.2085 RS [0.1532, 0.1545] A [0.2005, 0.2018] C [0.2159, 0.2172] E [0.2315, 0.2328] F [0.2442, 0.2455] G [0.2479, 0.2492] H [0.2558, 0.2571] I [0.2552, 0.2566] I [0.2614, 0.2627] K [0.2596, 0.2609] J [0.2631, 0.2644] KLM [0.2618, 0.2632] KL [0.2633, 0.2646] LM [0.2634, 0.2647] LM [0.2640, 0.2653] M [0.2638, 0.2651] M [0.2633, 0.2646] LM [0.2642, 0.2655] M [0.2631, 0.2644] KLM [0.2646, 0.2659] M [0.2618, 0.2631] KL [0.1656, 0.1669] B [0.2078, 0.2092] D DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.92: Population mean expected heterozygosity by selection strategy at generation 30 in the multi-trait, EST scenario. 457 Generation 45 Selection Strategy Mean Pop. MEH 95% CI Statistical Grouping 0.1217 GEBV 0.1802 gwGEBV05 0.1847 gwGEBV10d 0.2181 gwGEBV10 0.2178 gwGEBV20d 0.2380 gwGEBV15 0.2358 gwGEBV30d 0.2478 gwGEBV20 0.2465 gwGEBV40d 0.2539 gwGEBV25 0.2526 gwGEBV50d 0.2580 gwGEBV30 0.2555 gwGEBV60d 0.2599 gwGEBV35 0.2578 gwGEBV70d 0.2608 gwGEBV40 0.2592 gwGEBV80d 0.2614 gwGEBV45 0.2599 gwGEBV90d gwGEBV50 0.2624 gwGEBV100d 0.2597 0.1310 OCS 0.1904 RS [0.1209, 0.1224] A [0.1794, 0.1809] C [0.1839, 0.1854] D [0.2173, 0.2188] F [0.2171, 0.2186] F [0.2373, 0.2387] H [0.2351, 0.2365] G [0.2471, 0.2486] I [0.2458, 0.2473] I [0.2531, 0.2546] JK [0.2518, 0.2533] J [0.2573, 0.2587] LM [0.2548, 0.2563] K [0.2592, 0.2607] MNO [0.2571, 0.2586] L [0.2601, 0.2615] NOP [0.2584, 0.2599] LMN [0.2606, 0.2621] OP [0.2591, 0.2606] MNO [0.2617, 0.2632] P [0.2589, 0.2604] LMNO [0.1302, 0.1317] B [0.1897, 0.1912] E DF 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 1817 Table B.93: Population mean expected heterozygosity by selection strategy at generation 45 in the multi-trait, EST scenario. 458 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T H G F G F E I H G H G F J I H E D I H G F J I H G J I H K J J I H M L K A C D J I H M L K J I M L K J M B F E H G F E ] 2 1 7 1 . 7 0 1 , 2 1 5 1 . 7 0 1 [ ] 7 7 5 8 . 6 0 1 , 1 4 3 8 . 6 0 1 [ E ] 4 6 5 1 . 7 0 1 , 4 6 3 1 . 7 0 1 [ ] 9 0 4 8 . 6 0 1 , 2 7 1 8 . 6 0 1 [ J I H G G F E L K J I I H G F N M L K J I H L K J I N M ] 7 4 7 1 . 7 0 1 , 7 4 5 1 . 7 0 1 [ ] 6 1 8 8 . 6 0 1 , 0 8 5 8 . 6 0 1 [ ] 9 1 7 1 . 7 0 1 , 9 1 5 1 . 7 0 1 [ ] 3 5 5 8 . 6 0 1 , 7 1 3 8 . 6 0 1 [ ] 8 4 8 1 . 7 0 1 , 8 4 6 1 . 7 0 1 [ ] 5 6 9 8 . 6 0 1 , 9 2 7 8 . 6 0 1 [ ] 2 3 7 1 . 7 0 1 , 2 3 5 1 . 7 0 1 [ ] 0 6 7 8 . 6 0 1 , 4 2 5 8 . 6 0 1 [ ] 7 1 9 1 . 7 0 1 , 7 1 7 1 . 7 0 1 [ ] 8 4 2 9 . 6 0 1 , 2 1 0 9 . 6 0 1 [ ] 4 1 8 1 . 7 0 1 , 3 1 6 1 . 7 0 1 [ ] 4 6 8 8 . 6 0 1 , 8 2 6 8 . 6 0 1 [ ] 0 1 0 2 . 7 0 1 , 9 0 8 1 . 7 0 1 [ ] 1 0 3 9 . 6 0 1 , 4 6 0 9 . 6 0 1 [ ] 4 8 8 1 . 7 0 1 , 4 8 6 1 . 7 0 1 [ ] 8 7 9 8 . 6 0 1 , 2 4 7 8 . 6 0 1 [ M L K ] 5 1 9 1 . 7 0 1 , 5 1 7 1 . 7 0 1 [ ] 5 3 1 9 . 6 0 1 , 9 9 8 8 . 6 0 1 [ O N ] 1 8 1 2 . 7 0 1 , 1 8 9 1 . 7 0 1 [ ] 3 0 5 9 . 6 0 1 , 7 6 2 9 . 6 0 1 [ O ] 2 8 2 2 . 7 0 1 , 1 8 0 2 . 7 0 1 [ ] 6 5 6 9 . 6 0 1 , 0 2 4 9 . 6 0 1 [ M L K J ] 7 8 9 1 . 7 0 1 , 6 8 7 1 . 7 0 1 [ ] 0 0 1 9 . 6 0 1 , 4 6 8 8 . 6 0 1 [ N M L ] 6 4 0 2 . 7 0 1 , 5 4 8 1 . 7 0 1 [ ] 3 0 2 9 . 6 0 1 , 7 6 9 8 . 6 0 1 [ O ] 1 8 3 2 . 7 0 1 , 1 8 1 2 . 7 0 1 [ ] 0 6 6 9 . 6 0 1 , 4 2 4 9 . 6 0 1 [ O B ] 2 2 4 2 . 7 0 1 , 1 2 2 2 . 7 0 1 [ ] 2 1 7 9 . 6 0 1 , 6 7 4 9 . 6 0 1 [ ] 4 0 9 9 . 6 0 1 , 3 0 7 9 . 6 0 1 [ ] 5 1 6 6 . 6 0 1 , 9 7 3 6 . 6 0 1 [ F E ] 6 7 4 1 . 7 0 1 , 5 7 2 1 . 7 0 1 [ ] 5 0 5 8 . 6 0 1 , 9 6 2 8 . 6 0 1 [ A C D D ] 7 5 2 8 . 6 0 1 , 7 5 0 8 . 6 0 1 [ ] 9 8 2 5 . 6 0 1 , 3 5 0 5 . 6 0 1 [ ] 3 0 4 0 . 7 0 1 , 3 0 2 0 . 7 0 1 [ ] 4 5 9 6 . 6 0 1 , 8 1 7 6 . 6 0 1 [ ] 2 2 1 1 . 7 0 1 , 1 2 9 0 . 7 0 1 [ ] 0 1 8 7 . 6 0 1 , 4 7 5 7 . 6 0 1 [ ] 0 1 3 1 . 7 0 1 , 9 0 1 1 . 7 0 1 [ ] 9 2 8 7 . 6 0 1 , 3 9 5 7 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 7 5 1 8 . 6 0 1 3 0 3 0 . 7 0 1 2 2 0 1 . 7 0 1 0 1 2 1 . 7 0 1 2 1 6 1 . 7 0 1 4 6 4 1 . 7 0 1 7 4 6 1 . 7 0 1 9 1 6 1 . 7 0 1 8 4 7 1 . 7 0 1 2 3 6 1 . 7 0 1 7 1 8 1 . 7 0 1 3 1 7 1 . 7 0 1 0 1 9 1 . 7 0 1 4 8 7 1 . 7 0 1 1 8 0 2 . 7 0 1 5 1 8 1 . 7 0 1 1 8 1 2 . 7 0 1 7 8 8 1 . 7 0 1 1 8 2 2 . 7 0 1 6 4 9 1 . 7 0 1 1 2 3 2 . 7 0 1 3 0 8 9 . 6 0 1 5 7 3 1 . 7 0 1 1 t i a r T 1 7 1 5 . 6 0 1 6 3 8 6 . 6 0 1 2 9 6 7 . 6 0 1 1 1 7 7 . 6 0 1 9 5 4 8 . 6 0 1 1 9 2 8 . 6 0 1 8 9 6 8 . 6 0 1 5 3 4 8 . 6 0 1 7 4 8 8 . 6 0 1 2 4 6 8 . 6 0 1 0 3 1 9 . 6 0 1 6 4 7 8 . 6 0 1 2 8 1 9 . 6 0 1 0 6 8 8 . 6 0 1 5 8 3 9 . 6 0 1 7 1 0 9 . 6 0 1 8 3 5 9 . 6 0 1 2 8 9 8 . 6 0 1 2 4 5 9 . 6 0 1 5 8 0 9 . 6 0 1 4 9 5 9 . 6 0 1 7 9 4 6 . 6 0 1 7 8 3 8 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g d 0 6 V B E G w g 0 3 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 4 9 . B e l b a T 459 t i m i l n o i t c e l e s r e p p u n o i t a l u p o P . 4 . 2 . 3 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C D E F F K J I H G I H G L K J I J I H G M L K J L K J I H O N M L M L K J I M L K J I O N M O N H G G A C D E F G F I H H G K J I J I H ] 4 2 8 1 . 6 0 1 , 5 5 5 1 . 6 0 1 [ ] 1 1 5 9 . 5 0 1 , 4 1 2 9 . 5 0 1 [ ] 1 6 1 7 . 6 0 1 , 2 9 8 6 . 6 0 1 [ ] 2 8 6 3 . 6 0 1 , 5 8 3 3 . 6 0 1 [ ] 5 1 6 8 . 6 0 1 , 6 4 3 8 . 6 0 1 [ ] 8 3 7 4 . 6 0 1 , 1 4 4 4 . 6 0 1 [ ] 4 9 3 9 . 6 0 1 , 6 2 1 9 . 6 0 1 [ ] 8 6 4 5 . 6 0 1 , 1 7 1 5 . 6 0 1 [ ] 1 1 2 0 . 7 0 1 , 2 4 9 9 . 6 0 1 [ ] 6 6 2 6 . 6 0 1 , 9 6 9 5 . 6 0 1 [ ] 5 1 2 0 . 7 0 1 , 6 4 9 9 . 6 0 1 [ ] 8 7 4 6 . 6 0 1 , 1 8 1 6 . 6 0 1 [ ] 9 0 6 0 . 7 0 1 , 0 4 3 0 . 7 0 1 [ ] 6 5 9 6 . 6 0 1 , 9 5 6 6 . 6 0 1 [ ] 8 6 5 0 . 7 0 1 , 9 9 2 0 . 7 0 1 [ ] 8 4 7 6 . 6 0 1 , 1 5 4 6 . 6 0 1 [ ] 7 2 8 0 . 7 0 1 , 8 5 5 0 . 7 0 1 [ ] 0 1 3 7 . 6 0 1 , 3 1 0 7 . 6 0 1 [ ] 1 7 6 0 . 7 0 1 , 2 0 4 0 . 7 0 1 [ ] 2 4 0 7 . 6 0 1 , 5 4 7 6 . 6 0 1 [ M L K ] 2 6 9 0 . 7 0 1 , 3 9 6 0 . 7 0 1 [ ] 5 1 6 7 . 6 0 1 , 8 1 3 7 . 6 0 1 [ K J I ] 8 4 7 0 . 7 0 1 , 0 8 4 0 . 7 0 1 [ ] 9 8 2 7 . 6 0 1 , 2 9 9 6 . 6 0 1 [ O N M ] 0 7 0 1 . 7 0 1 , 2 0 8 0 . 7 0 1 [ ] 1 1 8 7 . 6 0 1 , 4 1 5 7 . 6 0 1 [ L K J ] 5 3 9 0 . 7 0 1 , 6 6 6 0 . 7 0 1 [ ] 5 1 4 7 . 6 0 1 , 9 1 1 7 . 6 0 1 [ Q P O N ] 4 0 2 1 . 7 0 1 , 5 3 9 0 . 7 0 1 [ ] 3 3 0 8 . 6 0 1 , 6 3 7 7 . 6 0 1 [ M L K Q P O N M L ] 3 9 9 0 . 7 0 1 , 4 2 7 0 . 7 0 1 [ ] 7 6 5 7 . 6 0 1 , 1 7 2 7 . 6 0 1 [ ] 7 3 3 1 . 7 0 1 , 9 6 0 1 . 7 0 1 [ ] 5 6 1 8 . 6 0 1 , 9 6 8 7 . 6 0 1 [ ] 9 1 0 1 . 7 0 1 , 0 5 7 0 . 7 0 1 [ ] 0 6 7 7 . 6 0 1 , 3 6 4 7 . 6 0 1 [ Q P ] 5 5 4 1 . 7 0 1 , 6 8 1 1 . 7 0 1 [ ] 5 1 2 8 . 6 0 1 , 8 1 9 7 . 6 0 1 [ N M L K P O N M ] 5 7 1 1 . 7 0 1 , 6 0 9 0 . 7 0 1 [ ] 3 4 8 7 . 6 0 1 , 6 4 5 7 . 6 0 1 [ O B E Q B F ] 3 5 5 1 . 7 0 1 , 4 8 2 1 . 7 0 1 [ ] 1 1 3 8 . 6 0 1 , 4 1 0 8 . 6 0 1 [ ] 7 6 6 3 . 6 0 1 , 9 9 3 3 . 6 0 1 [ ] 6 5 8 0 . 6 0 1 , 9 5 5 0 . 6 0 1 [ ] 0 8 0 9 . 6 0 1 , 1 1 8 8 . 6 0 1 [ ] 4 6 1 6 . 6 0 1 , 7 6 8 5 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 9 8 6 1 . 6 0 1 7 2 0 7 . 6 0 1 0 8 4 8 . 6 0 1 0 6 2 9 . 6 0 1 6 7 0 0 . 7 0 1 0 8 0 0 . 7 0 1 5 7 4 0 . 7 0 1 4 3 4 0 . 7 0 1 2 9 6 0 . 7 0 1 6 3 5 0 . 7 0 1 7 2 8 0 . 7 0 1 4 1 6 0 . 7 0 1 6 3 9 0 . 7 0 1 0 0 8 0 . 7 0 1 0 7 0 1 . 7 0 1 8 5 8 0 . 7 0 1 3 0 2 1 . 7 0 1 5 8 8 0 . 7 0 1 0 2 3 1 . 7 0 1 0 4 0 1 . 7 0 1 9 1 4 1 . 7 0 1 3 3 5 3 . 6 0 1 5 4 9 8 . 6 0 1 1 t i a r T 2 6 3 9 . 5 0 1 3 3 5 3 . 6 0 1 0 9 5 4 . 6 0 1 0 2 3 5 . 6 0 1 7 1 1 6 . 6 0 1 9 2 3 6 . 6 0 1 8 0 8 6 . 6 0 1 0 0 6 6 . 6 0 1 1 6 1 7 . 6 0 1 4 9 8 6 . 6 0 1 7 6 4 7 . 6 0 1 1 4 1 7 . 6 0 1 2 6 6 7 . 6 0 1 7 6 2 7 . 6 0 1 5 8 8 7 . 6 0 1 9 1 4 7 . 6 0 1 7 1 0 8 . 6 0 1 1 1 6 7 . 6 0 1 7 6 0 8 . 6 0 1 4 9 6 7 . 6 0 1 2 6 1 8 . 6 0 1 7 0 7 0 . 6 0 1 5 1 0 6 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 5 9 . B e l b a T 460 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C D F G H H I J I J I K J I K J A C D E F G H G I H J I J K J K J ] 3 6 7 6 . 5 0 1 , 5 4 4 6 . 5 0 1 [ ] 7 7 7 4 . 5 0 1 , 8 4 4 4 . 5 0 1 [ ] 5 6 8 3 . 6 0 1 , 6 4 5 3 . 6 0 1 [ ] 4 9 6 0 . 6 0 1 , 6 6 3 0 . 6 0 1 [ ] 6 1 8 4 . 6 0 1 , 7 9 4 4 . 6 0 1 [ ] 8 0 5 1 . 6 0 1 , 9 7 1 1 . 6 0 1 [ ] 0 6 3 7 . 6 0 1 , 2 4 0 7 . 6 0 1 [ ] 8 9 3 3 . 6 0 1 , 9 6 0 3 . 6 0 1 [ ] 6 1 9 7 . 6 0 1 , 8 9 5 7 . 6 0 1 [ ] 8 6 9 3 . 6 0 1 , 9 3 6 3 . 6 0 1 [ ] 9 0 8 8 . 6 0 1 , 1 9 4 8 . 6 0 1 [ ] 1 3 8 4 . 6 0 1 , 2 0 5 4 . 6 0 1 [ ] 7 4 8 8 . 6 0 1 , 8 2 5 8 . 6 0 1 [ ] 2 8 9 4 . 6 0 1 , 4 5 6 4 . 6 0 1 [ ] 6 2 3 9 . 6 0 1 , 7 0 0 9 . 6 0 1 [ ] 0 9 2 5 . 6 0 1 , 1 6 9 4 . 6 0 1 [ ] 3 0 5 9 . 6 0 1 , 5 8 1 9 . 6 0 1 [ ] 8 0 6 5 . 6 0 1 , 0 8 2 5 . 6 0 1 [ ] 7 3 5 9 . 6 0 1 , 8 1 2 9 . 6 0 1 [ ] 5 5 7 5 . 6 0 1 , 6 2 4 5 . 6 0 1 [ ] 6 8 6 9 . 6 0 1 , 7 6 3 9 . 6 0 1 [ ] 0 8 9 5 . 6 0 1 , 2 5 6 5 . 6 0 1 [ ] 8 7 7 9 . 6 0 1 , 9 5 4 9 . 6 0 1 [ ] 7 0 0 6 . 6 0 1 , 8 7 6 5 . 6 0 1 [ N M L K N M L K ] 8 2 0 0 . 7 0 1 , 9 0 7 9 . 6 0 1 [ ] 2 7 3 6 . 6 0 1 , 3 4 0 6 . 6 0 1 [ M L K L K J N M L K O N M L N M L K O N O N M L ] 8 0 0 0 . 7 0 1 , 9 8 6 9 . 6 0 1 [ ] 2 7 5 6 . 6 0 1 , 3 4 2 6 . 6 0 1 [ M L K P O N ] 1 5 0 0 . 7 0 1 , 3 3 7 9 . 6 0 1 [ ] 7 0 3 6 . 6 0 1 , 9 7 9 5 . 6 0 1 [ ] 1 8 2 0 . 7 0 1 , 2 6 9 9 . 6 0 1 [ ] 2 8 7 6 . 6 0 1 , 4 5 4 6 . 6 0 1 [ O N M L ] 1 6 0 0 . 7 0 1 , 2 4 7 9 . 6 0 1 [ ] 5 8 4 6 . 6 0 1 , 6 5 1 6 . 6 0 1 [ L K ] 1 0 9 9 . 6 0 1 , 2 8 5 9 . 6 0 1 [ ] 8 9 1 6 . 6 0 1 , 9 6 8 5 . 6 0 1 [ P O ] 4 3 4 0 . 7 0 1 , 5 1 1 0 . 7 0 1 [ ] 7 9 8 6 . 6 0 1 , 8 6 5 6 . 6 0 1 [ O N M P O N M ] 0 4 3 0 . 7 0 1 , 1 2 0 0 . 7 0 1 [ ] 1 5 6 6 . 6 0 1 , 2 2 3 6 . 6 0 1 [ O B E P B ] 8 1 6 0 . 7 0 1 , 0 0 3 0 . 7 0 1 [ ] 2 2 0 7 . 6 0 1 , 4 9 6 6 . 6 0 1 [ ] 0 1 6 8 . 5 0 1 , 1 9 2 8 . 5 0 1 [ ] 1 6 9 5 . 5 0 1 , 2 3 6 5 . 5 0 1 [ F E ] 8 7 5 6 . 6 0 1 , 9 5 2 6 . 6 0 1 [ ] 5 8 7 3 . 6 0 1 , 6 5 4 3 . 6 0 1 [ . p o P n a e M L S U 2 t i a r T 4 0 6 6 . 5 0 1 5 0 7 3 . 6 0 1 6 5 6 4 . 6 0 1 1 0 2 7 . 6 0 1 7 5 7 7 . 6 0 1 0 5 6 8 . 6 0 1 7 8 6 8 . 6 0 1 6 6 1 9 . 6 0 1 4 4 3 9 . 6 0 1 7 7 3 9 . 6 0 1 6 2 5 9 . 6 0 1 8 1 6 9 . 6 0 1 9 6 8 9 . 6 0 1 1 4 7 9 . 6 0 1 9 4 8 9 . 6 0 1 2 9 8 9 . 6 0 1 1 2 1 0 . 7 0 1 1 0 9 9 . 6 0 1 5 7 2 0 . 7 0 1 0 8 1 0 . 7 0 1 9 5 4 0 . 7 0 1 0 5 4 8 . 5 0 1 9 1 4 6 . 6 0 1 1 t i a r T 2 1 6 4 . 5 0 1 0 3 5 0 . 6 0 1 4 4 3 1 . 6 0 1 3 3 2 3 . 6 0 1 4 0 8 3 . 6 0 1 7 6 6 4 . 6 0 1 8 1 8 4 . 6 0 1 6 2 1 5 . 6 0 1 4 4 4 5 . 6 0 1 0 9 5 5 . 6 0 1 6 1 8 5 . 6 0 1 2 4 8 5 . 6 0 1 7 0 2 6 . 6 0 1 3 3 0 6 . 6 0 1 8 0 4 6 . 6 0 1 3 4 1 6 . 6 0 1 8 1 6 6 . 6 0 1 1 2 3 6 . 6 0 1 2 3 7 6 . 6 0 1 7 8 4 6 . 6 0 1 8 5 8 6 . 6 0 1 6 9 7 5 . 5 0 1 0 2 6 3 . 6 0 1 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t i m i l n o i t c e l e s r e p p u n o i t a l u p o P : 6 9 . B e l b a T 461 3.2.5. Population additive genetic variance Figure B.22: Population additive genetic variance by selection strategy over 60 generations in the multi-trait, EST scenario. 462 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B E D A F E D G F E G F E G F E G F E G F E G F E G F E G F G F E G F E G F E G F E G F E G G G G B D C A B C D C D C D C D C D C ] 7 0 3 0 . 0 , 7 8 2 0 . 0 [ ] 7 9 2 0 . 0 , 7 7 2 0 . 0 [ ] 4 5 3 0 . 0 , 4 3 3 0 . 0 [ ] 4 4 3 0 . 0 , 4 2 3 0 . 0 [ ] 7 9 3 0 . 0 , 7 7 3 0 . 0 [ ] 0 9 3 0 . 0 , 0 7 3 0 . 0 [ ] 8 9 3 0 . 0 , 8 7 3 0 . 0 [ ] 3 9 3 0 . 0 , 4 7 3 0 . 0 [ ] 7 0 4 0 . 0 , 7 8 3 0 . 0 [ ] 4 0 4 0 . 0 , 4 8 3 0 . 0 [ ] 8 0 4 0 . 0 , 8 8 3 0 . 0 [ ] 5 0 4 0 . 0 , 5 8 3 0 . 0 [ ] 2 2 4 0 . 0 , 1 0 4 0 . 0 [ ] 3 0 4 0 . 0 , 3 8 3 0 . 0 [ ] 7 0 4 0 . 0 , 7 8 3 0 . 0 [ ] 0 1 4 0 . 0 , 1 9 3 0 . 0 [ D C D C ] 9 1 4 0 . 0 , 9 9 3 0 . 0 [ ] 4 1 4 0 . 0 , 5 9 3 0 . 0 [ ] 2 1 4 0 . 0 , 2 9 3 0 . 0 [ ] 6 0 4 0 . 0 , 6 8 3 0 . 0 [ D ] 2 2 4 0 . 0 , 2 0 4 0 . 0 [ ] 9 1 4 0 . 0 , 9 9 3 0 . 0 [ D ] 3 2 4 0 . 0 , 3 0 4 0 . 0 [ ] 6 1 4 0 . 0 , 6 9 3 0 . 0 [ D C D C D C ] 7 1 4 0 . 0 , 7 9 3 0 . 0 [ ] 7 0 4 0 . 0 , 7 8 3 0 . 0 [ ] 2 2 4 0 . 0 , 2 0 4 0 . 0 [ ] 1 1 4 0 . 0 , 2 9 3 0 . 0 [ ] 3 1 4 0 . 0 , 3 9 3 0 . 0 [ ] 7 0 4 0 . 0 , 7 8 3 0 . 0 [ D C ] 7 1 4 0 . 0 , 7 9 3 0 . 0 [ ] 3 0 4 0 . 0 , 3 8 3 0 . 0 [ D ] 1 2 4 0 . 0 , 0 0 4 0 . 0 [ ] 5 1 4 0 . 0 , 6 9 3 0 . 0 [ D D D C D C B B ] 7 2 4 0 . 0 , 7 0 4 0 . 0 [ ] 6 1 4 0 . 0 , 6 9 3 0 . 0 [ ] 9 2 4 0 . 0 , 9 0 4 0 . 0 [ ] 9 1 4 0 . 0 , 9 9 3 0 . 0 [ ] 5 2 4 0 . 0 , 4 0 4 0 . 0 [ ] 5 1 4 0 . 0 , 5 9 3 0 . 0 [ ] 1 3 4 0 . 0 , 1 1 4 0 . 0 [ ] 9 0 4 0 . 0 , 9 8 3 0 . 0 [ ] 8 3 3 0 . 0 , 8 1 3 0 . 0 [ ] 4 2 3 0 . 0 , 5 0 3 0 . 0 [ ] 8 7 3 0 . 0 , 7 5 3 0 . 0 [ ] 9 4 3 0 . 0 , 0 3 3 0 . 0 [ 7 9 2 0 . 0 4 4 3 0 . 0 7 8 3 0 . 0 8 8 3 0 . 0 7 9 3 0 . 0 8 9 3 0 . 0 2 1 4 0 . 0 7 9 3 0 . 0 2 1 4 0 . 0 9 0 4 0 . 0 2 0 4 0 . 0 3 1 4 0 . 0 7 0 4 0 . 0 2 1 4 0 . 0 3 0 4 0 . 0 1 1 4 0 . 0 7 0 4 0 . 0 7 1 4 0 . 0 9 1 4 0 . 0 5 1 4 0 . 0 1 2 4 0 . 0 8 2 3 0 . 0 8 6 3 0 . 0 7 8 2 0 . 0 4 3 3 0 . 0 0 8 3 0 . 0 4 8 3 0 . 0 4 9 3 0 . 0 5 9 3 0 . 0 3 9 3 0 . 0 0 0 4 0 . 0 9 0 4 0 . 0 4 0 4 0 . 0 6 9 3 0 . 0 6 0 4 0 . 0 7 9 3 0 . 0 2 0 4 0 . 0 7 9 3 0 . 0 5 0 4 0 . 0 3 9 3 0 . 0 6 0 4 0 . 0 9 0 4 0 . 0 5 0 4 0 . 0 9 9 3 0 . 0 4 1 3 0 . 0 0 4 3 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 7 9 . B e l b a T 463 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B C B E D F E G F E H G F I H G F I H G I H G I H I H I H G I H I H I H I H I H I H I H I A D C A B C B E D F E D G F E G F E H G ] 5 1 2 0 . 0 , 6 9 1 0 . 0 [ ] 2 0 2 0 . 0 , 3 8 1 0 . 0 [ ] 5 9 2 0 . 0 , 5 7 2 0 . 0 [ ] 6 7 2 0 . 0 , 8 5 2 0 . 0 [ ] 9 1 3 0 . 0 , 0 0 3 0 . 0 [ ] 0 0 3 0 . 0 , 1 8 2 0 . 0 [ ] 3 5 3 0 . 0 , 4 3 3 0 . 0 [ ] 3 3 3 0 . 0 , 4 1 3 0 . 0 [ ] 8 6 3 0 . 0 , 9 4 3 0 . 0 [ ] 7 5 3 0 . 0 , 8 3 3 0 . 0 [ ] 5 7 3 0 . 0 , 5 5 3 0 . 0 [ ] 2 6 3 0 . 0 , 4 4 3 0 . 0 [ ] 7 8 3 0 . 0 , 8 6 3 0 . 0 [ ] 8 7 3 0 . 0 , 9 5 3 0 . 0 [ ] 8 8 3 0 . 0 , 9 6 3 0 . 0 [ ] 6 7 3 0 . 0 , 7 5 3 0 . 0 [ ] 0 1 4 0 . 0 , 1 9 3 0 . 0 [ ] 6 9 3 0 . 0 , 8 7 3 0 . 0 [ H G F E ] 6 9 3 0 . 0 , 7 7 3 0 . 0 [ ] 1 8 3 0 . 0 , 2 6 3 0 . 0 [ H G H G ] 4 9 3 0 . 0 , 5 7 3 0 . 0 [ ] 7 8 3 0 . 0 , 8 6 3 0 . 0 [ ] 1 0 4 0 . 0 , 2 8 3 0 . 0 [ ] 0 9 3 0 . 0 , 2 7 3 0 . 0 [ H G F ] 7 9 3 0 . 0 , 8 7 3 0 . 0 [ ] 6 8 3 0 . 0 , 8 6 3 0 . 0 [ H G ] 3 0 4 0 . 0 , 4 8 3 0 . 0 [ ] 7 8 3 0 . 0 , 8 6 3 0 . 0 [ H ] 5 0 4 0 . 0 , 6 8 3 0 . 0 [ ] 4 0 4 0 . 0 , 5 8 3 0 . 0 [ H G H G H G H G H G H A C ] 7 0 4 0 . 0 , 8 8 3 0 . 0 [ ] 6 9 3 0 . 0 , 7 7 3 0 . 0 [ ] 2 0 4 0 . 0 , 3 8 3 0 . 0 [ ] 9 8 3 0 . 0 , 0 7 3 0 . 0 [ ] 2 0 4 0 . 0 , 3 8 3 0 . 0 [ ] 2 9 3 0 . 0 , 3 7 3 0 . 0 [ ] 7 0 4 0 . 0 , 8 8 3 0 . 0 [ ] 7 9 3 0 . 0 , 8 7 3 0 . 0 [ ] 7 0 4 0 . 0 , 8 8 3 0 . 0 [ ] 5 9 3 0 . 0 , 7 7 3 0 . 0 [ ] 3 1 4 0 . 0 , 4 9 3 0 . 0 [ ] 3 0 4 0 . 0 , 4 8 3 0 . 0 [ ] 7 3 2 0 . 0 , 8 1 2 0 . 0 [ ] 7 1 2 0 . 0 , 9 9 1 0 . 0 [ ] 4 3 3 0 . 0 , 5 1 3 0 . 0 [ ] 5 0 3 0 . 0 , 7 8 2 0 . 0 [ 6 0 2 0 . 0 5 8 2 0 . 0 0 1 3 0 . 0 3 4 3 0 . 0 9 5 3 0 . 0 5 6 3 0 . 0 8 7 3 0 . 0 9 7 3 0 . 0 0 0 4 0 . 0 6 8 3 0 . 0 5 8 3 0 . 0 1 9 3 0 . 0 7 8 3 0 . 0 3 9 3 0 . 0 5 9 3 0 . 0 8 9 3 0 . 0 3 9 3 0 . 0 3 9 3 0 . 0 8 9 3 0 . 0 7 9 3 0 . 0 3 0 4 0 . 0 7 2 2 0 . 0 4 2 3 0 . 0 3 9 1 0 . 0 7 6 2 0 . 0 0 9 2 0 . 0 3 2 3 0 . 0 7 4 3 0 . 0 3 5 3 0 . 0 8 6 3 0 . 0 6 6 3 0 . 0 7 8 3 0 . 0 1 7 3 0 . 0 8 7 3 0 . 0 1 8 3 0 . 0 7 7 3 0 . 0 7 7 3 0 . 0 4 9 3 0 . 0 6 8 3 0 . 0 9 7 3 0 . 0 3 8 3 0 . 0 7 8 3 0 . 0 6 8 3 0 . 0 4 9 3 0 . 0 8 0 2 0 . 0 6 9 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 8 9 . B e l b a T 464 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A B B C C D D E D E D G F F E G F G F G F G F G F G F G F G F G F G A C A B B ] 9 5 1 0 . 0 , 1 4 1 0 . 0 [ ] 9 4 1 0 . 0 , 2 3 1 0 . 0 [ ] 1 4 2 0 . 0 , 3 2 2 0 . 0 [ ] 8 2 2 0 . 0 , 1 1 2 0 . 0 [ ] 1 4 2 0 . 0 , 3 2 2 0 . 0 [ ] 6 2 2 0 . 0 , 8 0 2 0 . 0 [ D C ] 5 0 3 0 . 0 , 7 8 2 0 . 0 [ ] 4 8 2 0 . 0 , 7 6 2 0 . 0 [ D E E ] 3 0 3 0 . 0 , 5 8 2 0 . 0 [ ] 2 9 2 0 . 0 , 5 7 2 0 . 0 [ ] 8 3 3 0 . 0 , 0 2 3 0 . 0 [ ] 2 2 3 0 . 0 , 5 0 3 0 . 0 [ ] 4 3 3 0 . 0 , 6 1 3 0 . 0 [ ] 8 1 3 0 . 0 , 1 0 3 0 . 0 [ F E ] 3 5 3 0 . 0 , 4 3 3 0 . 0 [ ] 2 3 3 0 . 0 , 5 1 3 0 . 0 [ G F E I H G H G F I H I H ] 2 5 3 0 . 0 , 4 3 3 0 . 0 [ ] 7 3 3 0 . 0 , 0 2 3 0 . 0 [ ] 7 7 3 0 . 0 , 9 5 3 0 . 0 [ ] 0 6 3 0 . 0 , 3 4 3 0 . 0 [ ] 5 6 3 0 . 0 , 7 4 3 0 . 0 [ ] 1 5 3 0 . 0 , 4 3 3 0 . 0 [ ] 3 8 3 0 . 0 , 5 6 3 0 . 0 [ ] 1 6 3 0 . 0 , 4 4 3 0 . 0 [ ] 0 8 3 0 . 0 , 2 6 3 0 . 0 [ ] 5 6 3 0 . 0 , 8 4 3 0 . 0 [ I H G ] 1 8 3 0 . 0 , 3 6 3 0 . 0 [ ] 8 5 3 0 . 0 , 1 4 3 0 . 0 [ I H I H I H I H ] 9 7 3 0 . 0 , 1 6 3 0 . 0 [ ] 8 6 3 0 . 0 , 1 5 3 0 . 0 [ ] 7 7 3 0 . 0 , 9 5 3 0 . 0 [ ] 3 6 3 0 . 0 , 5 4 3 0 . 0 [ ] 1 8 3 0 . 0 , 3 6 3 0 . 0 [ ] 2 7 3 0 . 0 , 5 5 3 0 . 0 [ ] 6 8 3 0 . 0 , 8 6 3 0 . 0 [ ] 8 6 3 0 . 0 , 1 5 3 0 . 0 [ I ] 7 8 3 0 . 0 , 9 6 3 0 . 0 [ ] 8 7 3 0 . 0 , 1 6 3 0 . 0 [ I H I H A C ] 5 8 3 0 . 0 , 7 6 3 0 . 0 [ ] 1 7 3 0 . 0 , 4 5 3 0 . 0 [ ] 8 8 3 0 . 0 , 0 7 3 0 . 0 [ ] 4 6 3 0 . 0 , 7 4 3 0 . 0 [ ] 7 6 1 0 . 0 , 9 4 1 0 . 0 [ ] 4 5 1 0 . 0 , 7 3 1 0 . 0 [ ] 4 9 2 0 . 0 , 6 7 2 0 . 0 [ ] 7 6 2 0 . 0 , 0 5 2 0 . 0 [ 0 5 1 0 . 0 2 3 2 0 . 0 2 3 2 0 . 0 6 9 2 0 . 0 4 9 2 0 . 0 9 2 3 0 . 0 5 2 3 0 . 0 4 4 3 0 . 0 3 4 3 0 . 0 8 6 3 0 . 0 6 5 3 0 . 0 4 7 3 0 . 0 1 7 3 0 . 0 2 7 3 0 . 0 0 7 3 0 . 0 8 6 3 0 . 0 2 7 3 0 . 0 7 7 3 0 . 0 8 7 3 0 . 0 6 7 3 0 . 0 9 7 3 0 . 0 8 5 1 0 . 0 5 8 2 0 . 0 1 4 1 0 . 0 0 2 2 0 . 0 7 1 2 0 . 0 5 7 2 0 . 0 3 8 2 0 . 0 4 1 3 0 . 0 9 0 3 0 . 0 3 2 3 0 . 0 9 2 3 0 . 0 1 5 3 0 . 0 2 4 3 0 . 0 3 5 3 0 . 0 6 5 3 0 . 0 0 5 3 0 . 0 9 5 3 0 . 0 4 5 3 0 . 0 3 6 3 0 . 0 0 6 3 0 . 0 9 6 3 0 . 0 3 6 3 0 . 0 6 5 3 0 . 0 5 4 1 0 . 0 9 5 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 9 9 . B e l b a T 465 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G . p o P n a e M . r a V c i t e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B A E D B C C B A B F C ] 2 2 1 0 . 0 , 7 0 1 0 . 0 [ ] 4 1 1 0 . 0 , 9 9 0 0 . 0 [ ] 5 9 1 0 . 0 , 9 7 1 0 . 0 [ ] 5 8 1 0 . 0 , 0 7 1 0 . 0 [ ] 7 7 1 0 . 0 , 1 6 1 0 . 0 [ ] 6 6 1 0 . 0 , 1 5 1 0 . 0 [ ] 5 6 2 0 . 0 , 0 5 2 0 . 0 [ ] 3 5 2 0 . 0 , 8 3 2 0 . 0 [ ] 1 1 2 0 . 0 , 5 9 1 0 . 0 [ ] 1 0 2 0 . 0 , 7 8 1 0 . 0 [ I H G I H G ] 6 0 3 0 . 0 , 0 9 2 0 . 0 [ ] 0 9 2 0 . 0 , 5 7 2 0 . 0 [ I H E D L K F E K J G F D M L H G M L K I H G M I H M J I A E D D J I F E K J F L K G L H G L K ] 5 4 2 0 . 0 , 0 3 2 0 . 0 [ ] 7 2 2 0 . 0 , 2 1 2 0 . 0 [ ] 6 1 3 0 . 0 , 0 0 3 0 . 0 [ ] 7 0 3 0 . 0 , 2 9 2 0 . 0 [ ] 2 6 2 0 . 0 , 6 4 2 0 . 0 [ ] 1 5 2 0 . 0 , 6 3 2 0 . 0 [ ] 5 4 3 0 . 0 , 0 3 3 0 . 0 [ ] 4 2 3 0 . 0 , 9 0 3 0 . 0 [ ] 6 7 2 0 . 0 , 0 6 2 0 . 0 [ ] 2 6 2 0 . 0 , 7 4 2 0 . 0 [ ] 9 3 3 0 . 0 , 3 2 3 0 . 0 [ ] 0 3 3 0 . 0 , 5 1 3 0 . 0 [ ] 0 9 2 0 . 0 , 4 7 2 0 . 0 [ ] 3 8 2 0 . 0 , 8 6 2 0 . 0 [ ] 3 6 3 0 . 0 , 8 4 3 0 . 0 [ ] 8 4 3 0 . 0 , 3 3 3 0 . 0 [ ] 1 0 3 0 . 0 , 5 8 2 0 . 0 [ ] 7 8 2 0 . 0 , 2 7 2 0 . 0 [ ] 5 5 3 0 . 0 , 9 3 3 0 . 0 [ ] 0 4 3 0 . 0 , 5 2 3 0 . 0 [ I H G ] 9 0 3 0 . 0 , 3 9 2 0 . 0 [ ] 8 9 2 0 . 0 , 3 8 2 0 . 0 [ J I H ] 4 1 3 0 . 0 , 9 9 2 0 . 0 [ ] 4 0 3 0 . 0 , 0 9 2 0 . 0 [ L ] 7 6 3 0 . 0 , 2 5 3 0 . 0 [ ] 7 4 3 0 . 0 , 2 3 3 0 . 0 [ J I H E D A ] 1 2 3 0 . 0 , 6 0 3 0 . 0 [ ] 6 0 3 0 . 0 , 1 9 2 0 . 0 [ ] 2 3 1 0 . 0 , 6 1 1 0 . 0 [ ] 9 1 1 0 . 0 , 4 0 1 0 . 0 [ ] 7 5 2 0 . 0 , 2 4 2 0 . 0 [ ] 2 3 2 0 . 0 , 7 1 2 0 . 0 [ L ] 0 7 3 0 . 0 , 4 5 3 0 . 0 [ ] 4 4 3 0 . 0 , 0 3 3 0 . 0 [ 4 1 1 0 . 0 7 8 1 0 . 0 9 6 1 0 . 0 8 5 2 0 . 0 3 0 2 0 . 0 8 9 2 0 . 0 8 3 2 0 . 0 8 0 3 0 . 0 4 5 2 0 . 0 7 3 3 0 . 0 8 6 2 0 . 0 1 3 3 0 . 0 2 8 2 0 . 0 5 5 3 0 . 0 3 9 2 0 . 0 7 4 3 0 . 0 1 0 3 0 . 0 0 6 3 0 . 0 7 0 3 0 . 0 2 6 3 0 . 0 4 1 3 0 . 0 4 2 1 0 . 0 0 5 2 0 . 0 7 0 1 0 . 0 7 7 1 0 . 0 8 5 1 0 . 0 6 4 2 0 . 0 4 9 1 0 . 0 3 8 2 0 . 0 0 2 2 0 . 0 0 0 3 0 . 0 3 4 2 0 . 0 6 1 3 0 . 0 5 5 2 0 . 0 2 2 3 0 . 0 6 7 2 0 . 0 0 4 3 0 . 0 0 8 2 0 . 0 3 3 3 0 . 0 0 9 2 0 . 0 0 4 3 0 . 0 7 9 2 0 . 0 7 3 3 0 . 0 8 9 2 0 . 0 2 1 1 0 . 0 4 2 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i t e n e g e v i t i d d a n o i t a l u p o P : 0 0 1 . B e l b a T 466 3.2.6. Population additive genic variance Figure B.23: Population additive genic variance by selection strategy over 60 generations in the multi-trait, EST scenario. 467 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C D E G F J I H L K J M L K J I M L M M I M L K M L M M M M L B D A C E F G G I H ] 0 4 3 0 . 0 , 7 3 3 0 . 0 [ ] 2 0 3 0 . 0 , 0 0 3 0 . 0 [ ] 1 8 3 0 . 0 , 8 7 3 0 . 0 [ ] 9 4 3 0 . 0 , 6 4 3 0 . 0 [ ] 8 0 4 0 . 0 , 5 0 4 0 . 0 [ ] 5 7 3 0 . 0 , 2 7 3 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 1 8 3 0 . 0 , 9 7 3 0 . 0 [ ] 8 3 4 0 . 0 , 5 3 4 0 . 0 [ ] 2 0 4 0 . 0 , 9 9 3 0 . 0 [ ] 4 3 4 0 . 0 , 1 3 4 0 . 0 [ ] 9 9 3 0 . 0 , 7 9 3 0 . 0 [ ] 8 4 4 0 . 0 , 5 4 4 0 . 0 [ ] 0 1 4 0 . 0 , 7 0 4 0 . 0 [ ] 3 4 4 0 . 0 , 0 4 4 0 . 0 [ ] 6 0 4 0 . 0 , 4 0 4 0 . 0 [ K J I ] 1 5 4 0 . 0 , 8 4 4 0 . 0 [ ] 3 1 4 0 . 0 , 0 1 4 0 . 0 [ I H K K J I K J K K K J K J K J K J K J I B D ] 7 4 4 0 . 0 , 4 4 4 0 . 0 [ ] 9 0 4 0 . 0 , 7 0 4 0 . 0 [ ] 4 5 4 0 . 0 , 1 5 4 0 . 0 [ ] 6 1 4 0 . 0 , 3 1 4 0 . 0 [ ] 0 5 4 0 . 0 , 7 4 4 0 . 0 [ ] 3 1 4 0 . 0 , 0 1 4 0 . 0 [ ] 5 5 4 0 . 0 , 2 5 4 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 4 5 4 0 . 0 , 1 5 4 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 5 5 4 0 . 0 , 2 5 4 0 . 0 [ ] 6 1 4 0 . 0 , 3 1 4 0 . 0 [ ] 3 5 4 0 . 0 , 0 5 4 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 5 5 4 0 . 0 , 2 5 4 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 5 5 4 0 . 0 , 2 5 4 0 . 0 [ ] 5 1 4 0 . 0 , 2 1 4 0 . 0 [ ] 6 5 4 0 . 0 , 3 5 4 0 . 0 [ ] 4 1 4 0 . 0 , 1 1 4 0 . 0 [ ] 5 5 4 0 . 0 , 2 5 4 0 . 0 [ ] 6 1 4 0 . 0 , 3 1 4 0 . 0 [ ] 3 5 4 0 . 0 , 0 5 4 0 . 0 [ ] 1 1 4 0 . 0 , 9 0 4 0 . 0 [ ] 5 6 3 0 . 0 , 3 6 3 0 . 0 [ ] 2 3 3 0 . 0 , 9 2 3 0 . 0 [ ] 6 0 4 0 . 0 , 3 0 4 0 . 0 [ ] 3 6 3 0 . 0 , 0 6 3 0 . 0 [ 8 3 3 0 . 0 9 7 3 0 . 0 7 0 4 0 . 0 3 1 4 0 . 0 6 3 4 0 . 0 2 3 4 0 . 0 6 4 4 0 . 0 1 4 4 0 . 0 0 5 4 0 . 0 6 4 4 0 . 0 2 5 4 0 . 0 8 4 4 0 . 0 3 5 4 0 . 0 2 5 4 0 . 0 4 5 4 0 . 0 2 5 4 0 . 0 3 5 4 0 . 0 3 5 4 0 . 0 4 5 4 0 . 0 3 5 4 0 . 0 2 5 4 0 . 0 4 6 3 0 . 0 5 0 4 0 . 0 1 0 3 0 . 0 8 4 3 0 . 0 3 7 3 0 . 0 0 8 3 0 . 0 1 0 4 0 . 0 8 9 3 0 . 0 9 0 4 0 . 0 5 0 4 0 . 0 1 1 4 0 . 0 8 0 4 0 . 0 4 1 4 0 . 0 1 1 4 0 . 0 3 1 4 0 . 0 4 1 4 0 . 0 4 1 4 0 . 0 3 1 4 0 . 0 3 1 4 0 . 0 3 1 4 0 . 0 2 1 4 0 . 0 4 1 4 0 . 0 0 1 4 0 . 0 1 3 3 0 . 0 2 6 3 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 1 0 1 . B e l b a T 468 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C D E F G H H J I I K J M L K M L K L K M L K M L K L K M M M L B E A C D F G H I I ] 3 3 2 0 . 0 , 9 2 2 0 . 0 [ ] 6 0 2 0 . 0 , 2 0 2 0 . 0 [ ] 9 9 2 0 . 0 , 6 9 2 0 . 0 [ ] 9 6 2 0 . 0 , 5 6 2 0 . 0 [ ] 5 2 3 0 . 0 , 2 2 3 0 . 0 [ ] 1 9 2 0 . 0 , 7 8 2 0 . 0 [ ] 3 5 3 0 . 0 , 9 4 3 0 . 0 [ ] 8 1 3 0 . 0 , 4 1 3 0 . 0 [ ] 8 7 3 0 . 0 , 4 7 3 0 . 0 [ ] 1 4 3 0 . 0 , 7 3 3 0 . 0 [ ] 5 8 3 0 . 0 , 1 8 3 0 . 0 [ ] 8 4 3 0 . 0 , 4 4 3 0 . 0 [ ] 3 0 4 0 . 0 , 9 9 3 0 . 0 [ ] 5 6 3 0 . 0 , 2 6 3 0 . 0 [ ] 2 0 4 0 . 0 , 9 9 3 0 . 0 [ ] 5 6 3 0 . 0 , 1 6 3 0 . 0 [ K J ] 7 1 4 0 . 0 , 3 1 4 0 . 0 [ ] 9 7 3 0 . 0 , 5 7 3 0 . 0 [ J ] 2 1 4 0 . 0 , 8 0 4 0 . 0 [ ] 5 7 3 0 . 0 , 1 7 3 0 . 0 [ M L L K ] 3 2 4 0 . 0 , 0 2 4 0 . 0 [ ] 5 8 3 0 . 0 , 1 8 3 0 . 0 [ ] 8 1 4 0 . 0 , 4 1 4 0 . 0 [ ] 1 8 3 0 . 0 , 7 7 3 0 . 0 [ O N M ] 6 2 4 0 . 0 , 2 2 4 0 . 0 [ ] 7 8 3 0 . 0 , 4 8 3 0 . 0 [ M L O N N M O N ] 4 2 4 0 . 0 , 1 2 4 0 . 0 [ ] 4 8 3 0 . 0 , 0 8 3 0 . 0 [ ] 7 2 4 0 . 0 , 4 2 4 0 . 0 [ ] 0 9 3 0 . 0 , 7 8 3 0 . 0 [ ] 5 2 4 0 . 0 , 1 2 4 0 . 0 [ ] 7 8 3 0 . 0 , 3 8 3 0 . 0 [ ] 8 2 4 0 . 0 , 4 2 4 0 . 0 [ ] 0 9 3 0 . 0 , 6 8 3 0 . 0 [ O N M ] 6 2 4 0 . 0 , 3 2 4 0 . 0 [ ] 8 8 3 0 . 0 , 5 8 3 0 . 0 [ O N O N B E ] 0 3 4 0 . 0 , 7 2 4 0 . 0 [ ] 1 9 3 0 . 0 , 7 8 3 0 . 0 [ ] 9 2 4 0 . 0 , 5 2 4 0 . 0 [ ] 0 9 3 0 . 0 , 6 8 3 0 . 0 [ ] 8 4 2 0 . 0 , 4 4 2 0 . 0 [ ] 9 1 2 0 . 0 , 5 1 2 0 . 0 [ ] 9 4 3 0 . 0 , 5 4 3 0 . 0 [ ] 2 1 3 0 . 0 , 8 0 3 0 . 0 [ O ] 0 3 4 0 . 0 , 6 2 4 0 . 0 [ ] 2 9 3 0 . 0 , 8 8 3 0 . 0 [ 1 3 2 0 . 0 8 9 2 0 . 0 4 2 3 0 . 0 1 5 3 0 . 0 6 7 3 0 . 0 3 8 3 0 . 0 1 0 4 0 . 0 0 0 4 0 . 0 5 1 4 0 . 0 0 1 4 0 . 0 1 2 4 0 . 0 6 1 4 0 . 0 4 2 4 0 . 0 2 2 4 0 . 0 6 2 4 0 . 0 3 2 4 0 . 0 6 2 4 0 . 0 4 2 4 0 . 0 8 2 4 0 . 0 8 2 4 0 . 0 7 2 4 0 . 0 6 4 2 0 . 0 7 4 3 0 . 0 4 0 2 0 . 0 7 6 2 0 . 0 9 8 2 0 . 0 6 1 3 0 . 0 9 3 3 0 . 0 6 4 3 0 . 0 3 6 3 0 . 0 3 6 3 0 . 0 7 7 3 0 . 0 3 7 3 0 . 0 3 8 3 0 . 0 9 7 3 0 . 0 5 8 3 0 . 0 2 8 3 0 . 0 9 8 3 0 . 0 5 8 3 0 . 0 8 8 3 0 . 0 7 8 3 0 . 0 0 9 3 0 . 0 9 8 3 0 . 0 8 8 3 0 . 0 7 1 2 0 . 0 0 1 3 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 2 0 1 . B e l b a T 469 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A C D E E F F G G H H I I K J J I K K L K L K L K L B E A C C D D E E F F G G I H H ] 6 6 1 0 . 0 , 2 6 1 0 . 0 [ ] 5 4 1 0 . 0 , 1 4 1 0 . 0 [ ] 0 4 2 0 . 0 , 6 3 2 0 . 0 [ ] 4 1 2 0 . 0 , 0 1 2 0 . 0 [ ] 7 4 2 0 . 0 , 3 4 2 0 . 0 [ ] 8 1 2 0 . 0 , 4 1 2 0 . 0 [ ] 9 9 2 0 . 0 , 5 9 2 0 . 0 [ ] 9 6 2 0 . 0 , 5 6 2 0 . 0 [ ] 2 0 3 0 . 0 , 8 9 2 0 . 0 [ ] 0 7 2 0 . 0 , 6 6 2 0 . 0 [ ] 8 3 3 0 . 0 , 4 3 3 0 . 0 [ ] 5 0 3 0 . 0 , 1 0 3 0 . 0 [ ] 5 3 3 0 . 0 , 1 3 3 0 . 0 [ ] 1 0 3 0 . 0 , 8 9 2 0 . 0 [ ] 1 6 3 0 . 0 , 7 5 3 0 . 0 [ ] 5 2 3 0 . 0 , 1 2 3 0 . 0 [ ] 8 5 3 0 . 0 , 4 5 3 0 . 0 [ ] 3 2 3 0 . 0 , 0 2 3 0 . 0 [ ] 6 7 3 0 . 0 , 2 7 3 0 . 0 [ ] 9 3 3 0 . 0 , 5 3 3 0 . 0 [ ] 4 7 3 0 . 0 , 0 7 3 0 . 0 [ ] 7 3 3 0 . 0 , 3 3 3 0 . 0 [ ] 5 8 3 0 . 0 , 1 8 3 0 . 0 [ ] 9 4 3 0 . 0 , 5 4 3 0 . 0 [ ] 3 8 3 0 . 0 , 8 7 3 0 . 0 [ ] 5 4 3 0 . 0 , 2 4 3 0 . 0 [ K J I ] 3 9 3 0 . 0 , 9 8 3 0 . 0 [ ] 3 5 3 0 . 0 , 0 5 3 0 . 0 [ J I ] 8 8 3 0 . 0 , 3 8 3 0 . 0 [ ] 2 5 3 0 . 0 , 8 4 3 0 . 0 [ M L K ] 4 9 3 0 . 0 , 0 9 3 0 . 0 [ ] 8 5 3 0 . 0 , 4 5 3 0 . 0 [ L K J N M ] 3 9 3 0 . 0 , 9 8 3 0 . 0 [ ] 5 5 3 0 . 0 , 1 5 3 0 . 0 [ ] 7 9 3 0 . 0 , 3 9 3 0 . 0 [ ] 1 6 3 0 . 0 , 7 5 3 0 . 0 [ N M L ] 7 9 3 0 . 0 , 3 9 3 0 . 0 [ ] 9 5 3 0 . 0 , 5 5 3 0 . 0 [ N M L ] 8 9 3 0 . 0 , 3 9 3 0 . 0 [ ] 0 6 3 0 . 0 , 6 5 3 0 . 0 [ N ] 2 0 4 0 . 0 , 8 9 3 0 . 0 [ ] 4 6 3 0 . 0 , 0 6 3 0 . 0 [ B D ] 7 7 1 0 . 0 , 3 7 1 0 . 0 [ ] 5 5 1 0 . 0 , 1 5 1 0 . 0 [ ] 4 0 3 0 . 0 , 9 9 2 0 . 0 [ ] 1 7 2 0 . 0 , 7 6 2 0 . 0 [ 4 6 1 0 . 0 8 3 2 0 . 0 5 4 2 0 . 0 7 9 2 0 . 0 0 0 3 0 . 0 6 3 3 0 . 0 3 3 3 0 . 0 9 5 3 0 . 0 6 5 3 0 . 0 4 7 3 0 . 0 2 7 3 0 . 0 3 8 3 0 . 0 1 8 3 0 . 0 1 9 3 0 . 0 5 8 3 0 . 0 2 9 3 0 . 0 1 9 3 0 . 0 5 9 3 0 . 0 5 9 3 0 . 0 0 0 4 0 . 0 5 9 3 0 . 0 5 7 1 0 . 0 2 0 3 0 . 0 3 4 1 0 . 0 2 1 2 0 . 0 6 1 2 0 . 0 7 6 2 0 . 0 8 6 2 0 . 0 3 0 3 0 . 0 9 9 2 0 . 0 3 2 3 0 . 0 1 2 3 0 . 0 7 3 3 0 . 0 5 3 3 0 . 0 7 4 3 0 . 0 4 4 3 0 . 0 1 5 3 0 . 0 0 5 3 0 . 0 6 5 3 0 . 0 3 5 3 0 . 0 9 5 3 0 . 0 7 5 3 0 . 0 2 6 3 0 . 0 8 5 3 0 . 0 3 5 1 0 . 0 9 6 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 3 0 1 . B e l b a T 470 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G . p o P n a e M . r a V c i n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T A D C G E K J F M H N I O J P K Q P L R Q M R M B H A D C G E K F ] 3 2 1 0 . 0 , 9 1 1 0 . 0 [ ] 9 0 1 0 . 0 , 5 0 1 0 . 0 [ ] 5 9 1 0 . 0 , 1 9 1 0 . 0 [ ] 6 7 1 0 . 0 , 2 7 1 0 . 0 [ ] 9 7 1 0 . 0 , 5 7 1 0 . 0 [ ] 0 6 1 0 . 0 , 6 5 1 0 . 0 [ ] 7 5 2 0 . 0 , 3 5 2 0 . 0 [ ] 4 3 2 0 . 0 , 0 3 2 0 . 0 [ ] 9 1 2 0 . 0 , 5 1 2 0 . 0 [ ] 7 9 1 0 . 0 , 3 9 1 0 . 0 [ ] 9 9 2 0 . 0 , 4 9 2 0 . 0 [ ] 0 7 2 0 . 0 , 6 6 2 0 . 0 [ ] 6 4 2 0 . 0 , 2 4 2 0 . 0 [ ] 2 2 2 0 . 0 , 8 1 2 0 . 0 [ M ] 4 2 3 0 . 0 , 9 1 3 0 . 0 [ ] 2 9 2 0 . 0 , 8 8 2 0 . 0 [ H N I O J P L K Q P ] 5 6 2 0 . 0 , 1 6 2 0 . 0 [ ] 0 4 2 0 . 0 , 6 3 2 0 . 0 [ ] 1 4 3 0 . 0 , 7 3 3 0 . 0 [ ] 8 0 3 0 . 0 , 4 0 3 0 . 0 [ ] 3 8 2 0 . 0 , 9 7 2 0 . 0 [ ] 5 5 2 0 . 0 , 0 5 2 0 . 0 [ ] 3 5 3 0 . 0 , 9 4 3 0 . 0 [ ] 0 2 3 0 . 0 , 6 1 3 0 . 0 [ ] 5 9 2 0 . 0 , 1 9 2 0 . 0 [ ] 5 6 2 0 . 0 , 0 6 2 0 . 0 [ ] 1 6 3 0 . 0 , 7 5 3 0 . 0 [ ] 7 2 3 0 . 0 , 3 2 3 0 . 0 [ ] 1 0 3 0 . 0 , 7 9 2 0 . 0 [ ] 3 7 2 0 . 0 , 9 6 2 0 . 0 [ ] 6 6 3 0 . 0 , 2 6 3 0 . 0 [ ] 2 3 3 0 . 0 , 8 2 3 0 . 0 [ R Q ] 0 7 3 0 . 0 , 5 6 3 0 . 0 [ ] 7 3 3 0 . 0 , 2 3 3 0 . 0 [ L ] 9 0 3 0 . 0 , 5 0 3 0 . 0 [ ] 8 7 2 0 . 0 , 4 7 2 0 . 0 [ M R M B G ] 8 1 3 0 . 0 , 4 1 3 0 . 0 [ ] 7 8 2 0 . 0 , 3 8 2 0 . 0 [ ] 4 7 3 0 . 0 , 0 7 3 0 . 0 [ ] 8 3 3 0 . 0 , 3 3 3 0 . 0 [ ] 2 2 3 0 . 0 , 7 1 3 0 . 0 [ ] 2 9 2 0 . 0 , 7 8 2 0 . 0 [ ] 1 3 1 0 . 0 , 7 2 1 0 . 0 [ ] 5 1 1 0 . 0 , 1 1 1 0 . 0 [ ] 5 6 2 0 . 0 , 1 6 2 0 . 0 [ ] 3 3 2 0 . 0 , 9 2 2 0 . 0 [ 1 2 1 0 . 0 3 9 1 0 . 0 7 7 1 0 . 0 5 5 2 0 . 0 7 1 2 0 . 0 6 9 2 0 . 0 4 4 2 0 . 0 1 2 3 0 . 0 3 6 2 0 . 0 9 3 3 0 . 0 1 8 2 0 . 0 1 5 3 0 . 0 3 9 2 0 . 0 9 5 3 0 . 0 9 9 2 0 . 0 4 6 3 0 . 0 7 0 3 0 . 0 8 6 3 0 . 0 6 1 3 0 . 0 2 7 3 0 . 0 0 2 3 0 . 0 9 2 1 0 . 0 3 6 2 0 . 0 7 0 1 0 . 0 4 7 1 0 . 0 8 5 1 0 . 0 2 3 2 0 . 0 5 9 1 0 . 0 8 6 2 0 . 0 0 2 2 0 . 0 0 9 2 0 . 0 8 3 2 0 . 0 6 0 3 0 . 0 2 5 2 0 . 0 8 1 3 0 . 0 3 6 2 0 . 0 5 2 3 0 . 0 1 7 2 0 . 0 0 3 3 0 . 0 6 7 2 0 . 0 4 3 3 0 . 0 5 8 2 0 . 0 6 3 3 0 . 0 9 8 2 0 . 0 3 1 1 0 . 0 1 3 2 0 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b e c n a i r a v c i n e g e v i t i d d a n o i t a l u p o P : 4 0 1 . B e l b a T 471 3.2.7. Population Bulmer effect Figure B.24: Population Bulmer effect by selection strategy over 60 generations in the multi- trait, EST scenario. 472 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 1 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B A A C B C C B A C B A C B A C B A C B A C B A C B A C B A C B A B A B A C B A C B A C B A C B A C B A C B A C B A C B A C B A C B A ] 8 0 0 9 . 0 , 4 4 5 8 . 0 [ ] 8 8 7 9 . 0 , 1 9 2 9 . 0 [ ] 5 9 2 9 . 0 , 1 3 8 8 . 0 [ ] 6 4 8 9 . 0 , 9 4 3 9 . 0 [ C B ] 2 2 6 9 . 0 , 8 5 1 9 . 0 [ ] 9 3 3 0 . 1 , 2 4 8 9 . 0 [ C ] 4 4 7 9 . 0 , 0 8 2 9 . 0 [ ] 0 2 4 0 . 1 , 3 2 9 9 . 0 [ C B A C B A C B A C B A C B A C B A C B A C B A C B A C B A C B A C B A ] 1 3 3 9 . 0 , 7 6 8 8 . 0 [ ] 0 9 0 0 . 1 , 3 9 5 9 . 0 [ ] 5 4 4 9 . 0 , 1 8 9 8 . 0 [ ] 2 8 1 0 . 1 , 5 8 6 9 . 0 [ ] 8 5 4 9 . 0 , 4 9 9 8 . 0 [ ] 8 6 8 9 . 0 , 1 7 3 9 . 0 [ ] 9 2 2 9 . 0 , 5 6 7 8 . 0 [ ] 9 3 1 0 . 1 , 3 4 6 9 . 0 [ ] 0 9 3 9 . 0 , 6 2 9 8 . 0 [ ] 0 9 1 0 . 1 , 3 9 6 9 . 0 [ ] 9 9 3 9 . 0 , 5 3 9 8 . 0 [ ] 1 6 1 0 . 1 , 4 6 6 9 . 0 [ ] 8 1 1 9 . 0 , 4 5 6 8 . 0 [ ] 7 0 8 9 . 0 , 0 1 3 9 . 0 [ ] 7 4 4 9 . 0 , 3 8 9 8 . 0 [ ] 8 1 1 0 . 1 , 1 2 6 9 . 0 [ ] 3 1 2 9 . 0 , 9 4 7 8 . 0 [ ] 5 4 8 9 . 0 , 8 4 3 9 . 0 [ ] 8 3 3 9 . 0 , 4 7 8 8 . 0 [ ] 2 5 9 9 . 0 , 5 5 4 9 . 0 [ ] 1 1 1 9 . 0 , 7 4 6 8 . 0 [ ] 6 2 8 9 . 0 , 9 2 3 9 . 0 [ ] 9 1 3 9 . 0 , 5 5 8 8 . 0 [ ] 7 5 0 0 . 1 , 0 6 5 9 . 0 [ C B A C B A C B A C B A ] 1 3 4 9 . 0 , 7 6 9 8 . 0 [ ] 2 6 0 0 . 1 , 5 6 5 9 . 0 [ ] 7 5 4 9 . 0 , 3 9 9 8 . 0 [ ] 5 7 1 0 . 1 , 8 7 6 9 . 0 [ ] 4 7 3 9 . 0 , 0 1 9 8 . 0 [ ] 2 2 0 0 . 1 , 5 2 5 9 . 0 [ ] 9 4 5 9 . 0 , 5 8 0 9 . 0 [ ] 3 7 9 9 . 0 , 6 7 4 9 . 0 [ B A ] 7 1 2 9 . 0 , 3 5 7 8 . 0 [ ] 5 5 7 9 . 0 , 8 5 2 9 . 0 [ B A ] 3 5 2 9 . 0 , 9 8 7 8 . 0 [ ] 9 5 7 9 . 0 , 2 6 2 9 . 0 [ A ] 9 1 3 9 . 0 , 5 5 8 8 . 0 [ ] 5 3 6 9 . 0 , 8 3 1 9 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 6 7 7 8 . 0 3 6 0 9 . 0 2 1 5 9 . 0 0 9 3 9 . 0 9 9 0 9 . 0 3 1 2 9 . 0 6 2 2 9 . 0 7 9 9 8 . 0 8 5 1 9 . 0 7 6 1 9 . 0 6 8 8 8 . 0 5 1 2 9 . 0 1 8 9 8 . 0 6 0 1 9 . 0 9 7 8 8 . 0 7 8 0 9 . 0 5 8 9 8 . 0 9 9 1 9 . 0 5 2 2 9 . 0 2 4 1 9 . 0 7 1 3 9 . 0 1 2 0 9 . 0 7 8 0 9 . 0 9 3 5 9 . 0 8 9 5 9 . 0 2 7 1 0 . 1 0 9 0 0 . 1 2 4 8 9 . 0 4 3 9 9 . 0 9 1 6 9 . 0 1 9 8 9 . 0 1 4 9 9 . 0 3 1 9 9 . 0 9 5 5 9 . 0 9 6 8 9 . 0 6 9 5 9 . 0 4 0 7 9 . 0 7 7 5 9 . 0 8 0 8 9 . 0 6 0 5 9 . 0 3 1 8 9 . 0 7 2 9 9 . 0 4 7 7 9 . 0 4 2 7 9 . 0 0 1 5 9 . 0 6 8 3 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 1 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 5 0 1 . B e l b a T 473 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 3 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T C B C B A C C B A C B A C B A C B A C B A C B A B A C B A C B A C B A C B A C B A C B A C B A C B A C B A C B A B A C B D C B A D C B A D C D C ] 4 2 8 9 . 0 , 3 3 3 9 . 0 [ ] 4 7 2 0 . 1 , 0 5 7 9 . 0 [ ] 9 1 8 9 . 0 , 8 2 3 9 . 0 [ ] 6 1 3 0 . 1 , 2 9 7 9 . 0 [ ] 1 3 0 0 . 1 , 0 4 5 9 . 0 [ ] 7 0 5 0 . 1 , 2 8 9 9 . 0 [ ] 0 9 7 9 . 0 , 9 9 2 9 . 0 [ ] 7 1 5 0 . 1 , 2 9 9 9 . 0 [ D C B ] 8 6 7 9 . 0 , 7 7 2 9 . 0 [ ] 5 5 4 0 . 1 , 0 3 9 9 . 0 [ D C B A D C B A ] 9 6 6 9 . 0 , 8 7 1 9 . 0 [ ] 2 0 4 0 . 1 , 8 7 8 9 . 0 [ ] 5 0 7 9 . 0 , 4 1 2 9 . 0 [ ] 1 6 3 0 . 1 , 6 3 8 9 . 0 [ A ] 6 5 1 9 . 0 , 5 6 6 8 . 0 [ ] 7 3 7 9 . 0 , 2 1 2 9 . 0 [ D ] 8 9 8 9 . 0 , 7 0 4 9 . 0 [ ] 0 4 5 0 . 1 , 6 1 0 0 . 1 [ D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A ] 6 6 6 9 . 0 , 5 7 1 9 . 0 [ ] 1 2 2 0 . 1 , 6 9 6 9 . 0 [ ] 6 7 3 9 . 0 , 5 8 8 8 . 0 [ ] 3 2 1 0 . 1 , 9 9 5 9 . 0 [ ] 8 5 6 9 . 0 , 7 6 1 9 . 0 [ ] 0 2 3 0 . 1 , 6 9 7 9 . 0 [ ] 8 7 3 9 . 0 , 7 8 8 8 . 0 [ ] 8 4 0 0 . 1 , 4 2 5 9 . 0 [ ] 7 5 5 9 . 0 , 6 6 0 9 . 0 [ ] 8 3 1 0 . 1 , 4 1 6 9 . 0 [ ] 0 3 5 9 . 0 , 9 3 0 9 . 0 [ ] 2 1 4 0 . 1 , 7 8 8 9 . 0 [ ] 6 4 6 9 . 0 , 5 5 1 9 . 0 [ ] 6 9 2 0 . 1 , 2 7 7 9 . 0 [ ] 8 5 4 9 . 0 , 7 6 9 8 . 0 [ ] 0 4 0 0 . 1 , 5 1 5 9 . 0 [ ] 2 0 5 9 . 0 , 1 1 0 9 . 0 [ ] 8 5 1 0 . 1 , 4 3 6 9 . 0 [ ] 7 3 5 9 . 0 , 6 4 0 9 . 0 [ ] 9 9 1 0 . 1 , 5 7 6 9 . 0 [ ] 3 1 5 9 . 0 , 2 2 0 9 . 0 [ ] 4 7 1 0 . 1 , 0 5 6 9 . 0 [ ] 9 8 6 9 . 0 , 8 9 1 9 . 0 [ ] 6 0 4 0 . 1 , 1 8 8 9 . 0 [ C B A ] 4 8 4 9 . 0 , 3 9 9 8 . 0 [ ] 1 4 8 9 . 0 , 7 1 3 9 . 0 [ B A ] 4 8 5 9 . 0 , 3 9 0 9 . 0 [ ] 6 0 8 9 . 0 , 1 8 2 9 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 0 1 9 8 . 0 9 7 5 9 . 0 3 7 5 9 . 0 6 8 7 9 . 0 5 4 5 9 . 0 3 2 5 9 . 0 4 2 4 9 . 0 9 5 4 9 . 0 2 5 6 9 . 0 0 2 4 9 . 0 0 3 1 9 . 0 3 1 4 9 . 0 2 3 1 9 . 0 1 1 3 9 . 0 4 8 2 9 . 0 1 0 4 9 . 0 2 1 2 9 . 0 7 5 2 9 . 0 1 9 2 9 . 0 7 6 2 9 . 0 4 4 4 9 . 0 9 3 2 9 . 0 8 3 3 9 . 0 5 7 4 9 . 0 2 1 0 0 . 1 4 5 0 0 . 1 4 4 2 0 . 1 5 5 2 0 . 1 2 9 1 0 . 1 0 4 1 0 . 1 9 9 0 0 . 1 8 7 2 0 . 1 8 5 9 9 . 0 1 6 8 9 . 0 8 5 0 0 . 1 6 8 7 9 . 0 6 7 8 9 . 0 9 4 1 0 . 1 4 3 0 0 . 1 8 7 7 9 . 0 6 9 8 9 . 0 7 3 9 9 . 0 2 1 9 9 . 0 4 4 1 0 . 1 9 7 5 9 . 0 4 4 5 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g d 0 8 V B E G w g 0 4 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 5 3 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 3 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 6 0 1 . B e l b a T 474 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 5 4 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T B A C B C B A D C B ] 4 3 4 9 . 0 , 3 1 9 8 . 0 [ ] 9 0 1 0 . 1 , 0 6 5 9 . 0 [ ] 5 4 0 0 . 1 , 3 2 5 9 . 0 [ ] 4 2 6 0 . 1 , 6 7 0 0 . 1 [ C B A D C B A ] 3 5 7 9 . 0 , 1 3 2 9 . 0 [ ] 3 2 3 0 . 1 , 5 7 7 9 . 0 [ C B C B C B C C B A C B A C B C B A C B C B C B A C B A C B A C B A C B A C B A C B A C B A A C B A D C B ] 7 2 2 0 . 1 , 6 0 7 9 . 0 [ ] 4 0 6 0 . 1 , 5 5 0 0 . 1 [ D C ] 9 5 0 0 . 1 , 8 3 5 9 . 0 [ ] 0 5 6 0 . 1 , 1 0 1 0 . 1 [ D ] 4 6 0 0 . 1 , 3 4 5 9 . 0 [ ] 9 5 8 0 . 1 , 0 1 3 0 . 1 [ D C B A ] 6 3 8 9 . 0 , 4 1 3 9 . 0 [ ] 0 0 3 0 . 1 , 2 5 7 9 . 0 [ D C B ] 5 1 0 0 . 1 , 3 9 4 9 . 0 [ ] 6 0 6 0 . 1 , 8 5 0 0 . 1 [ D C B ] 4 8 8 9 . 0 , 2 6 3 9 . 0 [ ] 1 0 5 0 . 1 , 2 5 9 9 . 0 [ D C ] 5 9 0 0 . 1 , 3 7 5 9 . 0 [ ] 1 9 6 0 . 1 , 2 4 1 0 . 1 [ D C B ] 1 2 8 9 . 0 , 9 9 2 9 . 0 [ ] 0 9 4 0 . 1 , 1 4 9 9 . 0 [ D C B A ] 2 1 0 0 . 1 , 1 9 4 9 . 0 [ ] 1 5 4 0 . 1 , 3 0 9 9 . 0 [ D C B A ] 6 7 7 9 . 0 , 5 5 2 9 . 0 [ ] 9 2 2 0 . 1 , 0 8 6 9 . 0 [ D C B ] 5 7 8 9 . 0 , 4 5 3 9 . 0 [ ] 0 4 5 0 . 1 , 1 9 9 9 . 0 [ D C B A ] 9 4 6 9 . 0 , 7 2 1 9 . 0 [ ] 5 2 2 0 . 1 , 6 7 6 9 . 0 [ D C B ] 3 6 7 9 . 0 , 2 4 2 9 . 0 [ ] 5 4 5 0 . 1 , 6 9 9 9 . 0 [ D C B A ] 7 0 8 9 . 0 , 5 8 2 9 . 0 [ ] 7 0 3 0 . 1 , 8 5 7 9 . 0 [ D C B ] 0 4 8 9 . 0 , 9 1 3 9 . 0 [ ] 5 1 6 0 . 1 , 6 6 0 0 . 1 [ D C B A D C B A ] 9 5 6 9 . 0 , 8 3 1 9 . 0 [ ] 7 9 2 0 . 1 , 8 4 7 9 . 0 [ ] 2 5 8 9 . 0 , 0 3 3 9 . 0 [ ] 4 2 2 0 . 1 , 5 7 6 9 . 0 [ D C ] 1 1 0 0 . 1 , 9 8 4 9 . 0 [ ] 7 3 6 0 . 1 , 9 8 0 0 . 1 [ B A ] 7 0 7 9 . 0 , 5 8 1 9 . 0 [ ] 7 1 9 9 . 0 , 9 6 3 9 . 0 [ A ] 2 0 3 9 . 0 , 0 8 7 8 . 0 [ ] 4 6 7 9 . 0 , 5 1 2 9 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 3 7 1 9 . 0 4 8 7 9 . 0 2 9 4 9 . 0 7 6 9 9 . 0 4 0 8 9 . 0 9 9 7 9 . 0 4 5 7 9 . 0 5 7 5 9 . 0 3 2 6 9 . 0 4 3 8 9 . 0 0 6 5 9 . 0 1 5 7 9 . 0 0 5 7 9 . 0 6 1 5 9 . 0 4 1 6 9 . 0 8 8 3 9 . 0 2 0 5 9 . 0 6 4 5 9 . 0 9 7 5 9 . 0 9 9 3 9 . 0 1 9 5 9 . 0 1 4 0 9 . 0 6 4 4 9 . 0 4 3 8 9 . 0 0 5 3 0 . 1 9 4 0 0 . 1 9 2 3 0 . 1 5 8 5 0 . 1 5 7 3 0 . 1 2 3 3 0 . 1 6 2 0 0 . 1 6 2 2 0 . 1 7 1 4 0 . 1 6 1 2 0 . 1 7 7 1 0 . 1 3 6 3 0 . 1 5 5 9 9 . 0 6 6 2 0 . 1 1 5 9 9 . 0 1 7 2 0 . 1 2 3 0 0 . 1 1 4 3 0 . 1 3 2 0 0 . 1 9 4 9 9 . 0 9 8 4 9 . 0 3 4 6 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 0 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 5 4 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 7 0 1 . B e l b a T 475 F D 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 7 1 8 1 l a c i t s i t a t S g n i p u o r G I C % 5 9 0 6 n o i t a r e n e G 2 t i a r T 1 t i a r T 2 t i a r T 1 t i a r T B A B A B A B A B B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A C B A C B A C B A ] 4 1 7 9 . 0 , 8 8 1 9 . 0 [ ] 7 3 2 0 . 1 , 9 7 6 9 . 0 [ ] 1 5 9 9 . 0 , 5 2 4 9 . 0 [ ] 1 6 4 0 . 1 , 4 0 9 9 . 0 [ ] 4 0 8 9 . 0 , 8 7 2 9 . 0 [ ] 5 9 2 0 . 1 , 7 3 7 9 . 0 [ C ] 5 8 3 0 . 1 , 9 5 8 9 . 0 [ ] 1 8 8 0 . 1 , 3 2 3 0 . 1 [ C B A ] 3 1 6 9 . 0 , 7 8 0 9 . 0 [ ] 6 4 2 0 . 1 , 8 8 6 9 . 0 [ C B ] 4 1 3 0 . 1 , 8 8 7 9 . 0 [ ] 4 2 8 0 . 1 , 7 6 2 0 . 1 [ C B A C B A C B A C B A C B A C B A C B C B C B A C B A ] 9 2 0 0 . 1 , 3 0 5 9 . 0 [ ] 7 5 2 0 . 1 , 9 9 6 9 . 0 [ ] 4 4 8 9 . 0 , 8 1 3 9 . 0 [ ] 7 0 6 0 . 1 , 9 4 0 0 . 1 [ ] 5 1 9 9 . 0 , 9 8 3 9 . 0 [ ] 2 0 5 0 . 1 , 5 4 9 9 . 0 [ ] 4 1 2 0 . 1 , 8 8 6 9 . 0 [ ] 9 1 6 0 . 1 , 1 6 0 0 . 1 [ ] 7 1 8 9 . 0 , 1 9 2 9 . 0 [ ] 8 6 3 0 . 1 , 0 1 8 9 . 0 [ ] 9 9 6 9 . 0 , 3 7 1 9 . 0 [ ] 8 0 4 0 . 1 , 0 5 8 9 . 0 [ ] 9 8 8 9 . 0 , 3 6 3 9 . 0 [ ] 5 7 7 0 . 1 , 8 1 2 0 . 1 [ ] 8 5 1 0 . 1 , 2 3 6 9 . 0 [ ] 4 5 7 0 . 1 , 6 9 1 0 . 1 [ ] 3 7 0 0 . 1 , 7 4 5 9 . 0 [ ] 9 1 6 0 . 1 , 1 6 0 0 . 1 [ ] 7 8 7 9 . 0 , 1 6 2 9 . 0 [ ] 6 6 3 0 . 1 , 8 0 8 9 . 0 [ C B A C B A C B A C B A ] 0 5 0 0 . 1 , 4 2 5 9 . 0 [ ] 1 4 4 0 . 1 , 4 8 8 9 . 0 [ ] 5 6 9 9 . 0 , 9 3 4 9 . 0 [ ] 4 9 6 0 . 1 , 6 3 1 0 . 1 [ ] 4 8 9 9 . 0 , 8 5 4 9 . 0 [ ] 3 2 3 0 . 1 , 5 6 7 9 . 0 [ ] 9 7 0 0 . 1 , 3 5 5 9 . 0 [ ] 6 8 5 0 . 1 , 9 2 0 0 . 1 [ C B ] 4 6 0 0 . 1 , 8 3 5 9 . 0 [ ] 6 9 7 0 . 1 , 9 3 2 0 . 1 [ B A ] 2 6 8 9 . 0 , 6 3 3 9 . 0 [ ] 3 2 1 0 . 1 , 6 6 5 9 . 0 [ A ] 0 5 7 9 . 0 , 4 2 2 9 . 0 [ ] 0 9 9 9 . 0 , 2 3 4 9 . 0 [ . p o P n a e M t c e f f E r e m l u B 2 t i a r T 1 t i a r T 1 5 4 9 . 0 8 8 6 9 . 0 1 4 5 9 . 0 2 2 1 0 . 1 0 5 3 9 . 0 1 5 0 0 . 1 6 6 7 9 . 0 1 8 5 9 . 0 2 5 6 9 . 0 1 5 9 9 . 0 4 5 5 9 . 0 6 3 4 9 . 0 6 2 6 9 . 0 5 9 8 9 . 0 0 1 8 9 . 0 4 2 5 9 . 0 1 0 8 9 . 0 7 8 7 9 . 0 2 0 7 9 . 0 1 2 7 9 . 0 6 1 8 9 . 0 9 9 5 9 . 0 7 8 4 9 . 0 8 5 9 9 . 0 2 8 1 0 . 1 6 1 0 0 . 1 2 0 6 0 . 1 7 6 9 9 . 0 6 4 5 0 . 1 8 7 9 9 . 0 8 2 3 0 . 1 3 2 2 0 . 1 0 4 3 0 . 1 9 8 0 0 . 1 9 2 1 0 . 1 7 9 4 0 . 1 5 7 4 0 . 1 0 4 3 0 . 1 7 8 0 0 . 1 8 1 5 0 . 1 3 6 1 0 . 1 5 1 4 0 . 1 4 4 0 0 . 1 8 0 3 0 . 1 5 4 8 9 . 0 1 1 7 9 . 0 n o i t c e l e S y g e t a r t S d 0 1 V B E G w g 0 1 V B E G w g d 0 2 V B E G w g 5 1 V B E G w g d 0 3 V B E G w g 0 2 V B E G w g d 0 4 V B E G w g 5 2 V B E G w g d 0 5 V B E G w g 0 3 V B E G w g d 0 6 V B E G w g d 0 7 V B E G w g 5 3 V B E G w g d 0 8 V B E G w g d 0 9 V B E G w g 5 4 V B E G w g 0 4 V B E G w g 5 0 V B E G w g 0 5 V B E G w g V B E G d 0 0 1 V B E G w g S C O S R . o i r a n e c s T S E , t i a r t - i t l u m e h t n i 0 6 n o i t a r e n e g t a y g e t a r t s n o i t c e l e s y b t c e f f e r e m l u B n o i t a l u p o P : 8 0 1 . B e l b a T 476