WINIHIHHIHI HI» EiHWHiIlHH W W ‘9 W —3 All N 00 N —l .1 I (D MI 321 93 00602 4008 ' MWIMWM ZHOZ3H70 .. ~-“» 45‘ ‘ This is to certify that the dissertation entitled PREDICTION OF GENETIC CHANGES IN SMALL CLOSED CATTLE POPULATIONS EMPLOYING MULTIPLE OVULATION AND EMBRYO TRANSFER TECHNIQUES presented by Gwang-Joo Jeon has been accepted towards fulfillment of the requirements for Ph.D. degree in Animal Science @243 Major professor ///j’ /8¢ MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 LIBRARY Mkhigdn State University PLACE II RETURN BOX to remove thie ohedmut from your record. TOAVOD FINES retunonorbdoreddedue. DATE DUE r DATE DUE DATE DUE N56,! 0 7 i“. (19:); \! \l T's—T I MSU Is An Affirmative Action/Equel Opportunity Institution PREDICTION OF GENETIC CHANGES IN SHALL CLOSED CATTLE POPULATIONS EHPLOYINC HULTIPLE OVULATION AND EMBRYO TRANSFER TECHNIQUES By Gwang-Joo Jeon A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Animal Science 1989 - L \ (a 00400 ABSTRACT PREDICTION OF GENETIC CHANGES IN SHALL CLOSED CATTLE POPULATIONS EHPLOYING MULTIPLE OVULATION AND EMBRYO TRANSFER TECHNIQUES By Gwang-Joo Jeon Breeding schemes employing multiple ovulation and embryo transfer techniques promise a greater rate of genetic response than current AI progeny testing schemes. This is due to shorter generation intervals, higher intensity in selecting cows for replacements, more progeny from genetically superior females, and potential for more intensive control on selection criteria relative to large populations such as entire 0.8. This study examined genetic changes and random genetic drift in three small closed dairy cattle populations using a stochastic simulation model. Results from the stochastic simulation were compared to those from the deterministic models. Two populations with 88 breeding females and one population with 352 breeding females using multiple ovulation and embryo transfer breeding schemes were generated by stochastic simulation. Selection was strictly for first lactation milk yield. Ignoring and restricting inbred matings were also examined for their impact on genetic responses. In closed finite populations, effective population size, inbreeding, and linkage disequilibrium have major influences on genetic responses and genetic drift. The reduction in genetic variation due to inbreeding and linkage disequilibrium was taken into account in the simulation. The results indicated that strict restriction on inbreeding slowed genetic progress but was less of problem in a larger population. The smaller population, ignoring inbred matings, showed a rapid rate of inbreeding. Linkage disequilibrium reduced genetic variation as significantly as inbreeding in the three populations. Genetic responses and drift in small closed populations were also estimated by deterministic models and then compared with those from stochastic simulation results. In deterministic models, Rendel and Robertson's equation and gene flow model were modified to account for reduced accuracies and heritabilities due to inbreeding and linkage disequilibrium in each generation. Generally, deterministic models gave similar estimates to stochastic models for genetic responses. Reduction of genetic variation due to linkage disequilibrium is as important as that due to inbreeding. When conservative restriction on inbreeding was applied in the mating schemes to a small herd, deterministic methods did not give similar estimates to stochastic models for genetic responses in later generations. ACKNOWLEDGMENT I would like to express my gratitude toward my committee members, Dr. Ferris, Dr. Mao, Dr. Magee, and Dr. Gill, for their counseling and professional guidance. I am especially indebted to Dr. Ferris and Dr. Mao for their endless encouragement and support in my time at M.S.U. I will also miss my friends, Just, Stanley, Terri, Florah, Hancan, and Peter who have been sharing all the smiles and laughs together in Room 119, Anthony Hall. I also thank my mother, father, brother, and sister, who have never stopped their love during my study, for their patience and care. ii TABLE OF CONTENTS INTRODUCTION LITERATURE REVIEW 2.1 INTRODUCTION 2.2 MULTIPLE OVULATION AND EMBRYO TRANSFER (MOET) 2.2.1 SUPEROVULATION . 2.2.2 EMBRYO RECOVERY. 2.2.3 STORAGE OF EMBRYO. 2.2.4 RECIPIENTS . 2.3 MOET BREEDING SCHEMES . 2.3.1 ACCUMULATION OF INBREEDING . 2.3.2 LINKAGE DISEQUILIBRIUM . 2.3.3 RANDOM GENETIC DRIFT . 2.4 PREDICTION OF BREEDING VALUES . 2.5 PREDICTION OF GENETIC RESPONSES . CHAPTER 1: STOCHASTIC MODELING OF MULTIPLE OVULATION AND EMBRYO TRANSFER (MOET) BREEDING SCHEMES IN SMALL CLOSED DAIRY CATTLE POPULATIONS 3.1 ABSTRACT 3.2 INTRODUCTION 3.3 METHODS . 3.4 RESULTS . 3.5 CONCLUSIONS . 3.6 REFERENCES iii page 11 14 14 17 l9 19 19 21 27 38 4O CHAPTER 2: COMPARISON OF DETERMINISTIC AND STOCHASTIC MODELING FOR PREDICTING GENETIC CHANGES IN SMALL CLOSED DAIRY CATTLE POPULATIONS . . . . . . . . . . . . . . . . 42 4.1 ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 44 4.3 METHODS . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . 61 4.6 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 66 SUMMARY AND CONCLUSIONS. . . . . . . . . . . . . . . . . . . . 67 OVERALL REFERENCES . . . . . . . . . . . . . . . . . . . . . . 69 iv LIST OF TABLES page TABLE 1. Parameters used to simulate the three populations employing MOET breeding schemes . . . . . . . . . . . . 45 TABLE 2. Parameters averaged from the five replicates of each simulated MOET population that were used in the deterministic equations . . . . . . . . . . . . . . . . 46 TABLE 3. Description of modified Rendel and Robertson's equations (RRE) and Gene Flow models (GFM). . . . . . . . . . . . 47 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 10. ll. 12. 13. 14. 15. 16. LIST OF FIGURES Accumulation of inbreeding in the three MOET populations for 12 years . Changes in genetic variation in MOETl population for 12 years . . . . . . . . . Changes in genetic variation in MOET2 population for 12 years . . . . . . . . Changes in genetic variation in MOET3 population for 12 years . . . . . . . . . Annual genetic mean with genetic drift variation MOETI population for 12 years . Annual genetic mean with genetic drift variation MOET2 population for 12 years . Annual genetic mean with genetic drift variation MOET3 population for 12 years . Estimated genetic responses by RRE in comparison realized genetic responses in MOETl population. Estimated genetic responses by GFM in comparison realized genetic responses in MOETl population. Estimated genetic responses by RRE in comparison realized genetic responses in MOET2 population. Estimated genetic responses by GFM in comparison realized genetic responses in MOET2 population. Estimated genetic responses by RRE in comparison realized genetic responses in MOET3 population. Estimated genetic responses by GFM in comparison realized genetic responses in MOET3 population. in in in to to t0 to to to Estimated random genetic drift SD in comparison to realized random genetic drift SD in MOETl population. Estimated random genetic drift SD in comparison to realized random genetic drift SD in MOET2 population. Estimated random genetic drift SD in comparison to realized random genetic drift SD in MOET3 population. vi page 29 31 32 33 35 36 37 55 56 57 58 59 6O 63 64 65 1. INTRODUCTION Traditionally, the main concern of animal breeders have been maximum improvement of animals' genetic potential, which returns the most profit to them. The maximum improvement of genetic potential requires several factors such as proper statistical procedures to accurately rank animals and good managerial practices to allow animals to express their genetic ability. In general, any breeding program should be judged in several ways, not only the maximum improvement of the traits but also the monetary returns from the improved traits (Hill, 1971). Recently, new technology termed multiple ovulation and embryo transfer (MOET), has been developed with the potential to a faster genetic progress than artificial insemination (AI) progeny testing schemes. From theory of genetic progress formulized by Rendel and Robertson (1950), which was initially based on the selection index by Hazel (1943), genetic progress is described as a function of selection intensity, accuracy of the evaluation, genetic variation, and generation interval for each transmitting path of genetic materials. Among these factors, MOET breeding scheme should most benefit selection intensity and generation interval. A major advantage of MOET is that several progeny from selected parents utilizing genetically inferior cows as recipients. As a consequence, the selection intensity of cow to cow path becomes much higher than the conventional AI progeny testing scheme. The study of MOET breeding schemes in comparison to the conventional AI progeny testing scheme has been done using empirical simulation by several people. They showed that the genetic progress from a MOET scheme was much greater than that from the conventional AI breeding scheme. Many studies using the formula of Rendel and Robertson's equation or gene flow model using transition probability method in estimation of genetic responses has been neglected for the effect of inbreeding and linkage disequilibrium. The inbreeding and linkage disequilibrium, however, substantially reduce the genetic variation depending on the population size and selection intensity. This may partially explain the discrepancy between the realized and the estimated genetic changes (Ven Vleck, 1981). Especially, in a small finite population, inbreeding and linkage disequilibrium should be closely monitored. This study was divided into two investigations: (1) Stochastic simulation modeling of small closed populations using MOET techniques was studied to examine genetic changes considering the reduction in variance due to inbreeding and linkage disequilibrium. (2) Comparison between stochastic and deterministic models in estimation of genetic changes with and without consideration of inbreeding and linkage disequilibrium. 2. REVIEW OF LITERATURE 2.1 INTRODUCTION: In traditional AI progeny testing breeding schemes, selection of future parents requires two stages which takes approximately 6 years on average: In the first stage, parents are selected based on their pedigree information and in the second stage they are re-evaluated based on their own or progeny performance. Due to the limitation of single progeny from females in conventional AI progeny testing scheme, genetic improvement is achieved mainly through the use of thousands units of semen from selected sires. Recently, a new technology called MOET, termed by Nicholas and Smith (1983), has been developed and implemented in some commercial herds. MOET schemes have a promising feature based on theory. The main advantages of MOET application to a population are; 1) more offspring from selected females 2) reduced generation intervals 3) easier to transport embryos than adult animals 4) new borns have easier adaptation to the environment of herds than adult animals 5) quick test for a carrier of recessive traits due to short generation intervals 6) reduced risk of disease transmission 7) increase numbers of rare or endangered species. Several authors (proposed application of MOET breeding schemes and reported faster genetic responses than conventional AI progeny testing populations (Nicholas, 1977, Van Vleck, 1977, Nicholas and Smith, 1983, Ruane, 1988). 2.2 MULTIPLE OVULATION AND EMBRYO TRANSFER (MOET): The initial embryo transfer was conducted in a rabbit as early as 1891. Up to 1971, most embryo transfer work has been done as a laboratory tool for the study of reproduction. Since 1975, embryo transfer has become an acceptable tool for use in cattle breeding (Critser et al., 1980). This acceptability is partly due to the nonsurgical collection technique. Multiple ovulation and embryo transfer involves several procedures (Seidel, 1989). 2.2.1 SUPEROVULATION: When a heifer is born, the ovary contains about 200,000 oocytes. These oocytes are formed during fetal development. After birth, no new oocytes are made. those present degenerate and disappear from the ovary by puberty. This process of degeneration is called atresia, which continues throughout life. Superovulation is defined as the treatment of a female with the hormones that cause more ova to be ovulated at one time than normal. One hormone used is follicle-stimulating hormone (FSH) which is secreted by the pituitary gland located at the base of brain. Another is pregnant mare's serum gonadotropin (PMSG). Superovulation is also called multiple ovulation. Timing of superovulation depends on the estrous cycle which varies from cow to cow. The time to induce superovulation, for example, is day 15 if a cow will have a 19-day cycle, or at day 19 if she has a 23-day cycle. 2.2.2 EMBRYO RECOVERY: About 5 days after superovulation with FSH hormone, artificial insemination is conducted. If the semen and eggs meet at the proper time fertilization occurs. The fertilized egg is called an embryo. In cattle, embryos are recovered 6 to 8 days after estrus. After 9 days, recovery and pregnancy rates are slightly reduced. Embryo recovery is usually by a nonsurgical method. The success of embryo recovery depends not only on the age of embryo but also on the technique and the skill of the technician. About 50 to 80% of embryos are recovered. 2.2.3 STORAGE 0F EMBRYO: If recovered embryos must be immediately transferred, This should be done between 20 min to 24 hr. In most cases, it is necessary to store embryos until appropriate recipients are available. To maintain the viability of embryo is important. For short-term storage, they are usually kept under 0 to -10 degree Celsius for several days without much loss of viability. For long-term storage, they are deep-frozen in liquid nitrogen at -196 degree Celsius. 2.2.4 RECIPIENTS: The recipients are not necessarily genetically inferior cows. They must be in good health including fertility, conformation, and milking ability. In general, there are more losses of calves from heifer recipients than cow recipients. 2.3 MOET BREEDING SCHEMES: Ruane (1988) made a good review on various MOET breeding schemes. In the conventional AI progeny testing scheme, the bull to bull path contributes most to the genetic improvement. MOET breeding schemes improve the genetic progress through the increase in the reproductive rate of the female allowing a larger emphasis on selection of female candidates. As a consequence, selection intensity of the cow to bull path increases because fewer cows are required to obtain the bulls for progeny testing. Land and Hill (1975) examined the potential genetic progress of growth rate in beef cattle employing MOET. In their scheme, cows and bulls were assumed to have the first progeny at 2 years of age and 90 8 of cows calving any year survived to the following year. If the embryo does not survive, then, the recipient received a second transfer. All recipients were assumed fertile. The main advantage in the scheme was the number of calves reared from each donor cow. They reported that the growth rate by MOET can be almost twice the conventional performance testing program. Petersen and Hansen (1977) studied the MOET aspect in bull to cow path in dual cattle populations, where selection emphasis was on butterfat and growth rate. By doubling the number of sons per dam, which resulted in halving the number of selected cows, there was about 8% increase in butterfat yield. Nicholas (1979) first examined the potential genetic progress by MOET in dairy cattle. In his scheme, females were selected based on their dam's first lactation record and generation interval was assumed 2 years. This resulted in relatively a lower accuracy of .25. Males were selected based on their dam's first lactation record, or a family index using full-sib, half-sib, and dam's first record. All schemes obtained higher genetic responses than the conventional AI progeny testing scheme. Following Nicholas's work (1979), Nicholas and Smith (1983) were first to examine two MOET schemes that they termed Juvenile and Adult schemes. The basic principle of the juvenile and adult schemes are equivalent to the first and second stage selection, respectively, of conventional AI progeny testing scheme. The generation interval for juvenile scheme is slightly less than 2 years. This is about one third that of conventional AI progeny testing scheme. The generation interval for their adult scheme was 3.7 years. The results showed that by using various numbers of progeny per donor and numbers of donors per sire, the genetic responses from both juvenile and adult schemes, or combination of two schemes exceeded the genetic responses from the conventional AI progeny testing scheme by up to 80 percent. Powell (1981) studied the effects of embryo transfer resulting in additional progeny information on evaluation of cows and bulls. He showed that the repeatability of cow index increased from .43 for a cow having one daughter to .49 for 10 daughters. He also pointed out that ET can be used in cow evaluations to increase the number of full-sib and half-sib records, which eventually shorten the generation interval because the use of 3 full-sibs and 12 half-sibs gives about the same accuracy as cow's own 3 records (Ruane, 1988). McDaniel and Cassel (1981) investigated the impact of ET on genetic progress and concluded that ET can increase cow index dollars up to 17% when 10 offspring per dam were obtained versus one offspring. For herd replacements, percentage of cows to maintain herd size is significantly reduced to 3.5 % when 20 offspring per dam is possible. Juga and Haki-Tanila (1987) studied the effect of various number of donors per sire and number of sires used. They reported that selecting only one sire used on all cows obtained less than one percent of genetic progress more than conventional AI progeny testing breeding scheme per year. They suggested the optimum breeding design was adult MOET scheme with selection of 2 sires and 16 donors per sire, which resulted in 1.26 % increase per year. Wooliams and Smith (1988) re-examined the work of Nicholas and Smith (1983), where information on paternal pedigree was not included in the index. They suggested inclusion of this information increased the selection response in juvenile scheme 25 to 30%. They also studied the effect of including indicator traits. Indicator traits are defined as those traits which give indirect information on the traits being selected. For example, blood urea nitrogen (BUN) as indicator trait for milk yield. The value of indicator traits depends on the magnitude of the co-heritability which is defined as genetic correlation between two traits times the corresponding heritabilities of the two traits. The use of indicator traits may also allow earlier selection in both male and females, which makes the generation intervals shorter. Bradford and Kennedy (1980) pointed out that there exist some difficulties in selection of potential bull-dam donors because they are at the extreme edge of the phenotypic distribution. Cunningham (1976) mentioned that the underlying genetic distribution of selected bull- dams may not follow the normal distribution due to the intensive selection. 2.3.1 ACCUMULATION 0F INBREEDING: Since MOET breeding schemes produce more than one progeny from the selected parents, more full-sibs and half-sibs are expected than with conventional AI progeny testing schemes. This increases the rate of inbreeding. The effects of inbreeding are two: 1) reduction in variance and 2) inbreeding depression. The higher level of inbreeding in the population causes animals to be more related and thus, the population is less variable. Since the variation is key in selection, less variation may slow the rate of genetic progress. The inbreeding depression refers to the reduction of mean phenotypic value of the characteristics connected with reproduction or physiological efficiency. With the usual dominance model of inbreeding depression, there exist a linear relationship between inbreeding coefficient and performance in unselected populations (Hill, 1986). Hill also pointed out that the effect of population size ranging from 10 to 160 animals are trivial for 5 generations. The rate of inbreeding is directly associated with the effective population size. This was first introduced by Wright (1931). The restriction of population size increases the homozygosity within the population and is introduced in terms of the concept of the idealized random breeding population, which is known as the effective population size. Under selection and artificial insemination, the inbreeding coefficient in a population is much higher than that estimated from the random mating population of equal size, because parents do not contribute to the next generation equally (Toro et al., 1988). Robertson (1961) pointed out that inbreeding under individual selection is expected to be much greater than that calculated from the actual number of parents when both heritability of the trait and selection intensity is high. With no selection and random mating of parents, the rate of 10 inbreeding is simply defined as (Falconer, 1980): AF - 1/(4Nm) + 1/(4Nf) where Nm and Nf are number of selected males and females. Then, the h level of inbreeding in the tt generation becomes: t rt - l-(l-AF) where Ft is the average inbreeding in the tth generation. In reality, random mating without selection would not be practiced in commercial herds. Therefore, the inbreeding rate by the formula above is expected to be much less than the realized inbreeding rate. Another formula for annual expected inbreeding was given by Hill (1972): AF - (1/Nm + l/Nf)/(8xL2) where L is an average generation interval of males and females. These two formulae assume that the generations are discrete and selected parents have the equal probability of contributing to the next generation. However, the rate of inbreeding in overlapping generations equals the rate of inbreeding in discrete generations if the the number of individuals entering the population each generation and the variance of lifetime family size are equal (Fewson and Nitter, 1987). Johnson (1977) developed a method for estimation of inbreeding using a transition probability matrix method (Hill, 1974): F(t+1) - PFtP' + D where P is a matrix specifying the path of genes between the different age groups and has a stochastic nature; and D is a diagonal matrix whose elements depend on the number of individuals in each age group. This formula, however, does not take into account the complex situation 11 of the four pathways of transmitting genetic materials. Fewson and Nitter (1987) designed a formula to estimate the rate of inbreeding in a single cycle selection of the four pathways: AF - P'QP - [1/4 1/4 1/4 1/4] |l/2Nmm 1/2Nmf| | |1/4| :1/2Nmf l/2Nmf: 0 : |1/4| |1/2an l/2fol |1/4| l |1/2fo 1/2fol |1/4| - l/32(1/Nmm + 3/Nmf + l/me + 3/fo) where P can be extended such that for an example, male to male (mm) path can be subdivided into a group of young bulls (q proportion) and the proven bulls (l-q proportion) and young cows with a proportion of r and an old cows with a proportion of (l-r). Then, P' is redefined as: P' - [.253 .25(l-s)| .25q .25(l-q)| .25| .25r .25(l-r)] As a consequence, Q becomes a size of 7x7 matrix. Toro et a1. (1988) examined four different methods of mating policy for the minimization of inbreeding; 1) random mating (RM) 2) minimum coancestry (MC) 3) weighted selection (WS) and 4) the combination of MC and MS (MW). They found the MW system gives the lowest inbreeding coefficient of the methods. 2.3.2 LINKAGE DISEQUILIBRIUM: Selection in the parental generation creates a reduction of variance in the progeny generation. This is known as linkage disequilibrium, or gametic phase disequilibrium (Falconer, 1981). The consequence of reduced variance 12 due to parental selection can be simply viewed as the distribution theory. Since only the right tail-side of parental population is selected as parents, the distribution of these selected parents is no longer the same as the original population. The reduced variance due to selection can be denoted (Falconer, 1981): V(p)' - (1-k)V(p) where V(p)' is the phenotypic variance in the selected parents; V(p) is the phenotypic variance in the whole population; k is the reduction factor and redefined as i(i-x), where i is the selection intensity and x is the deviation of the truncation point from the population mean in standard deviation units. Then, the reduced genetic variance of V(g)’ equals (1-kh2)V(g). Bulmer (1971) derived the linkage disequilibrium in more detail by regressing the progeny on parents: y - a + bPl + bPz + e where a is an intercept; b is a regression weight; and e is error. Taking the variance (V), V(e) is (1-.5(h2)2)V(y), where V(y) is a total phenotypic variance. The equality of V(e) and (l-.5(h2)2)V(y) is defined by rewriting the above equation: y - a + b(P1 + P2) + e By knowing that the covariance between an offspring and one parent is (l/2)h2V(y), then, Cov(y,P1+P2) - h2V(y) V(P1+P2) - 2V(y), therefore, b - Cov(y,P1+P2)/V(P1+P2) - .5h2 13 Then, the residual variance can be computed; V(y) - b2V(P1+P2) + V(e) V(e) - V(y) - 2bZV(y) - (1-.5h“>V Finally, the variance in progeny generation after selection in parental generation becomes: V(y*) - b2V(P1) + b2V(P2) + V(e) - 2b2[v(y) + dV(y)1 + V(e) - V(y) + .5(h2)2dV/(1'E)°§<0) where 03(t) was the genetic variation at time t; 02(0) was the initial genetic variation in the base population; and F was the average inbreeding coefficient in the population at time t. With increasing selection intensity, a larger reduction of genetic variance due to linkage disequilibrium is expected. The MOET3 population has the largest number of breeding animals, which gave a higher selection intensity on males than MOETl and MOET2. This resulted in the largest reduction in genetic variance due to linkage disequilibrium of 20.5% for MOET3. The linkage disequilibrium in MOETl and MOET2 were 17% and 16.8%, respectively. The amount of genetic variation in each year varied as shown in 31 Figure 2, 3 and 4. In MOET2 and MOET3, if top ranking bulls could not be used because of restriction on inbreeding in the progeny, bulls from previous generations, who might not be intensively selected, were used, hence more genetic variation among progeny: This should explain why MOET2 showed more fluctuation of genetic variation than MOETl and MOET3. Genetic SD 1400 ‘*— mumflcso 1200 b -1- plus or minus one 80 HIKE 600" 400' 200‘ 0 l L l l L l l I l L l l l l 012 a 4 5 a 7 a 9 Year(MOET1) Figure 2. Change in genetic variation in MOETl population for 12 years 10 U 12 13 14 15 32 0 Genetic SD "' generic 80 -1- plus or mlnus SD M O O T 1 l l l 1 l 1 L l l l 0123456789101112131415 Year(MOET2) Figure 3. Change in genetic variation in MOET2 population for 12 years 33 Genetic SD 1400 * genetic so + plus or minus 80 1000; SEES I I 1200 I 800 600 400 200 O 1 L l 1 1 I L l I l l i l l 0123456789101112131415 Year(MOET8) Figure 4. Change in genetic variation in MOET3 population for 12 years 34 Genetic response The genetic changes from the three MOET schemes were compared to both theoretical and realized genetic progress from a conventional progeny testing AI population. The theoretical genetic progress was assumed to be 2% of pro-duction average or 150 kg per year (Van Vleck, 1981), and realized genetic gain was assumed to be one third of the theoretical genetic gain (Van Vleck, 1977) or 50 kg per year. The genetic progress over 12 years are shown in Figure 5, 6, and 7. The genetic means of MOETl population followed a smooth linear trend and fluctuated less than those of MOET2 and MOET3. This was due to no restriction on inbred matings in MOETl population. This always allowed the selection of best genetic material in each month. The selection of best animals was not always possible in MOET2 in order to meet the restricted inbreeding criteria, which hindered genetic progress. The same restriction on inbreeding was imposed in MOET3 population, but its genetic trend was similar to that of MOETl. Due to the larger population size, MOET3 population was less affected by the inbreeding restriction and had higher probability of selecting animals that were less related. The rate of genetic progress in either MOETl or MOET3 populations was greater than both theoretical and realized genetic gains from the current AI progeny testing population. However, the genetic gain in MOET2 population was less than the theoretical genetic gain from the current AI progeny testing population. This was because of the small number of breeding animals and inbreeding restriction in mating. 35 Genetic mean 3000 -—'oumucnm01 250° F + plus or minus one SO -8- Alitneorstioail 2°00 -)(— Aliresllzsd) I ' r 1500 - " 500 - /u ‘ llllllll -5000123456789101112131415 Figure 5. Annual genetic mean with genetic drift variation in MOETI population for 12 years 36 Genetic mean 3000 “'°" genetic mean 2500 _ + plus or minus one 80 -B- Alitheoretloal) 2000 P 9" Al(resllzsd) l I T 1 1500 l- 1000 - I. ‘ , J 500- / < ;/ . ,I... deal] "' -500 1‘1 1 i l l l l l l l l l l 0123456789101112131415 Year Figure 6. Annual genetic mean with genetic drift variation in MOET2 population for 12 years 37 Genetic mean 3000 "' geneucinean 2500 _ + plus or minus one SD -8- Alitheoretlcal) E 2000” 9(- Alireallzed) 3 1500' 1000' 500- < .. 4311/ . fl "" -500 1 1 1 1 1 1 4 1 1 1 l l 1 l 0123456789101112131415 Figure 7. Annual genetic mean with genetic drift variation in MOET3 population for 12 years 38 Genetic drift Many factors contribute to random genetic drift, but it is mainly related to effective population size. The random genetic drift was described in terms of variation in genetic means over five replications and was also shown in Figure 5, 6, and 7. For the coefficient of variation (CV) of response to be a after n generations, given selection intensity of i and heritability h“, the population size required can be approximated by Nicholas (1980): 1/na’i2h2 Therefore, imposing higher selection intensity on highly heritable traits for a fixed number of generations would require a smaller population size. On the other hand, for fixed intensity, heritability and size, for a to be small, relatively large population size would be required. Hence, after 24 years, the CV of genetic mean MOET3 population was the smallest, 4.69%. Those in MOETl and MOET2 populations were 9.68% and 13.38%, respectively. In MOET2 population, the selection intensity was lower than those in MOETl and MOET3 populations due to inbreeding restriction and smaller size, thus resulting in the highest CV of genetic mean. 3.5 CONCLUSIONS All three MOET breeding schemes studied achieved higher genetic responses than the realized genetic gain from the current AI progeny testing population. This was accomplished in populations in spite of their small sizes, the closed schemes, and in some cases restrictions on inbreeding. In fact, genetic gains in these MOET populations were higher than not only the realized but also the theoretical maximum 39 genetic gain possible in the current AI progeny testing schemes. This was true with the exception of the small population with inbreeding restriction. The small population, without restrictions to avoid inbreeding, accumulated a high level of inbreeding. No restriction on inbreeding did not appear to be worthwhile in terms of genetic gain for the time horizon studied. Beyond that, however, selection would become futile due to severe reduction in genetic variation because of inbreeding. Higher selection intensity regardless of population size lead to higher degree of linkage disequilibrium. The reduction in genetic variation due to linkage disequilibrium was as significant as that due to accumulation of inbreeding. Higher selection intensity and larger population size lead to lower random genetic drift, but genetic drift was not significant in all the populations studied. 40 3.6 REFERENCES Bulmer, M.G. 1971. The effect of selection on genetic variability. Am. Nat. 105:201. Christensen, L.G. and T. Liboriussen. 1986. Embryo transfer in the genetic improvement of dairy cattle. In exploiting new technologies in animal breeding (genetic development), pp. 163-169. Oxford Univ. Press. De Roo, G. 1988. Studies on breeding schemes in a closed pig population. A stochastic model to study breeding schemes in a small pig population. Agricultural Sys. 25:1. Hill, W.G. 1967. Monte Carlo genetics in animal breeding research. In Proceedings of Technical Committee Meeting NC-l, Improvement of Beef Cattle Through Breeding Methods, Wooster, Ohio. IMSL (1987). IMSL STAT/LIBRARY. IMSL, Houston, TX, U.S.A. Juga, J. and Maki-Tanila. 1987. Genetic change in nucleus breeding dairy herd using embryo transfer. Acta. Agric. Scand. 37:511. Nicholas, F.W. 1980. Size of population required for artificial selection. Genet. Res., Vol. 35:85. Nicholas, F.W. and C. Smith. 1983. Increased rates of genetic changes in dairy cattle by embryo transfer and splitting. Anim. Prod. 36:341. Rendel, J.M. and A. Robertson. 1950. Estimation of genetic gain in milk yield by selection in a closed herd of dairy cattle. J. Genetics 50:1. Ruane, J. 1988. Review of the use of embryo transfer in the genetic improvement of dairy cattle. Animal Breeding Abs. Vol. 56:437. 41 Seidel, G.E. and S.M. Seidel. 1981. The embryo transfer industry. In New Technologies in Animal Breeding, pp. 41-80. Academic Press, London. Van Vleck, L.D. 1977. Theoretical and actual genetic progress in dairy cattle. In Proc. Int. Conf. Quantitative Genetics (ed. E. Pollak, 0. Kempthorne and T.B. Baily Jr.), pp. 543-568. Iowa State University Press, Ames, Iowa. Van Vleck, L.D. 1981. Potential genetic impact of artificial insemination, sex selection, embryo transfer, cloning and selfing in dairy cattle. In New Technologies in Animal Breeding, pp. 221-242. Academic Press, London. 4. CHAPTER 2 Comparison of Deterministic and Stochastic Mbdeling for Genetic Responses in Small Closed Dairy Cattle Populations 4.1 ABSTRACT Genetic responses and drift in small closed populations were studied by stochastic and deterministic models. In closed finite populations, effective population size, inbreeding, and linkage disequilibrium have major influences on genetic responses and drift. Three multiple ovulation and embryo transfer breeding schemes covering a 12 year period were simulated by stochastic models. The results were compared to those from deterministic models. In deterministic models, Rendel and Robertson's equation and Gene Flow model were modified to account for reduced accuracies and heritabilities due to inbreeding and linkage disequilibrium in each generation. Selection intensity, generation interval, and accumulation of inbreeding used in deterministic models were obtained from stochastic models. Generally, the modified deterministic models gave estimates of genetic responses similar to stochastic models. Reduction of genetic variation due to linkage disequilibrium was as important as that due to inbreeding. However, in the population with a large accumulation of inbreeding, accounting for linkage disequilibrium alone was not as effective as that of inbreeding alone for deterministic models. When conservative restriction on inbreeding was applied in the mating schemes to a small size herd, deterministic methods did not give estimates of genetic responses similar to responses from stochastic models in later generations. 42 43 4.2 INTRODUCTION In designing a selective mating plan, an accurate prediction of genetic gain and an anticipation of genetic drift are essential. The deterministic equation by Rendel and Robertson (1950) for the prediction of genetic change in a breeding program is well known and popularly used. However, it is only asymptotically true when the rate of genetic change is in a steady state, which may take many generations. A method to account for the earlier fluctuation of genetic progress before reaching the steady state is the Gene Flow model using the probability transition matrix (Hill, 1976). When the rate of genetic change in a breeding program with a constant selection intensity over time becomes stable, then the two equations, RRE and GFM, would give the same result. In a small finite population, rate of inbreeding and linkage disequilibrium are major factors that should be closely monitored. These two factors substantially reduce genetic variation and result in slower genetic progress. This contributes to the discrepancy between realized genetic gains in a real population and estimated genetic gains from RRE and GFM. Also, the random genetic drift is essential in small finite populations. Both RRE and GFM are deterministic in nature and their theoretical formulas do not take into account inbreeding and linkage disequilibrium, or the Bulmer effect (1971), both of which lead to a reduction in genetic variation depending on population size, level of inbreeding, and selection intensity. This may be a partial explanation why only one third of the predicted genetic response has been achieved 44 in dairy populations (Van Vleck, 1981). The deterministic equation for estimation of random genetic drift given by Hill (1976) also assumes constant parameters over time, ignoring the reduced variance due to inbreeding and linkage disequilibrium. The deterministic models can be improved to avoid simplifying the assumptions such as heritability, selection accuracy, and variances kept constant throughout the period of breeding plan. The genetic changes can be more accurately studied by a stochastic simulation model. However, the stochastic approach is tedious, costly, and time demanding. The objectives of this study were: 1) to illustrate a modification in estimation equation for random genetic drift by Hill (4), and Rendel and Robertson's equation and Gene flow model for genetic response, which would account for reduced variances due to inbreeding and linkage disequilibrium; 2) to examine possible improvement in the accuracy of predicting genetic responses by the modified Rendel and Robertson's equation and Gene flow model, and random genetic drift by the modified Hill's equation; and 3) to compare both genetic responses and random genetic drift from the deterministic and stochastic models in three small closed dairy cattle populations employing multiple ovulation and embryo transfer (MOET) technique. 4.3 METHODS Stochastic model Breeding events in each of the three multiple ovulation and embryo transfer (MOET) populations were simulated monthly for a 12 year period using parameters shown in Table 1. Simulation of each population was 45 replicated five times. The structure and details of breeding events of the three MOET populations, MOETl, MOET2, and MOET3, were previously described in detail in CHAPTER 3. Table 1. Parameters used to simulate the three populations using MOET breeding schemes . Trait : milk yield Heritability (hz) : .4 Phenotypic SD : 1,498 kg Production mean : 7,500 kg Survival rate : .7 Conception rate : .7 Avg. no. eggs/superovulation : 5 (following Poisson distribution) No. of founder females ( age 14 mo.) : 88 for MOET 1 88 for MOET 2 352 for MOET 3 1Restriction in inbreeding with maximum of .0625 in the progeny was imposed in mating schemes of MOET2 and MOET3. For MOET 1, inbreeding was not considered. An infinitesimal model at an individual animal level was used to generate records: yi - p + ai + e1 where yi was the first lactation record of the ith animal; p was a constant overall mean; a1 was an additive genetic value of the ith animal; and 46 e1 was the random residual corresponding to the ith record. For genetic evaluation of animals, an animal model was used with a known complete relationship matrix. Accumulation of inbreeding, changes in genetic variance due to inbreeding and linkage disequilibrium, and genetic responses with drift variation were computed each month. The average selection intensity (SI), generation interval (CI) and inbreeding resulting from the stochastic simulation were later used in deterministic models and are summarized in Table 2. Table 2. Parameters averaged from the 5 replicates of each simulated MOET population that were used in the deterministic equations. pepulation Selection Intensity Generation Interval Inbreeding male female male female MOET 1 1.8485 1.488 2.83 3.64 22.5% MOET 2 1.6865 1.400 3.25 3.45 4.8% MOET 3 1.6865 1.400 3.25 3.75 3.9% Deterministic models Genetic responses. A summary of the alternative deterministic equations of RRE and GFM used in this study is given in Table 3. 47 Table 3. Description of modified Rendel and Robertson's equations (RRE) and Gene Flow Models (GFM). Models description Unmodified: Rendel & Robertson Equation (RRE) ignoring inbreeding and Gene Flow Model (GFM) linkage disequilibrium Modified: RRE(F) modified for inbreeding GFM(F) only RRE(LD) modified for linkage GFM(LD) disequilibrium only RRE(F,LD) modified for both inbreeding GFM(F,LD) and linkage disequilibrium (l) Rendel and Robertson's equation (RRE). By the selection index theory, Rendel and Robertson's equation (1950) is commonly denoted as: AG/year - EGi/ELi where AG/year is annual genetic gain; G1 is genetic superiority of the 1th 1th pathway; L1 is generation interval of the pathway; and i-l,2 with 1 being from bull to produce bull and cow and 2 being from cow to produce bull and cow. For simplification of model calculations, the genetic superiority of the bull was computed based only on pedigree information traced back two generations . For the dam, her first lactation record was also included in addition to the pedigree information. The genetic superiority of the ith pathway is: Gi - 811 x (ITI)1 x 08 [1] 48 where 811 is selection intensity of the ith pathway; (rTI)i is accuracy of the ith path, or correlation between estimated and true breeding values; 08 is additive genetic standard deviation. To compute rTI' the selection index equation for true breeding value, g, was set as: I - b'x [2] where b is a vector of index weights; x is a vector of phenotypic values adjusted for all fixed effects that were assumed to be of known magnitude. The relatives' information in index equation [1] were dam, dam's full-sib, dam's half-sib, sire's full-sib of females, sire's half-sib of females, and paternal grandam. This index has a similar structure as the one outlined in the paper given by Wooliams and Smith (1988) except indicator traits were not included. The index weights were obtained as b-P'IG, where P is the phenotypic covariance matrix of x; G is covariances between x and g. Then, the accuracy, rTI’ was computed as: rTI - J(b'PB$ Us (2) Gene Flow Model (GFM). The gene flow model (GFM) gives a more exact estimation of selection responses than RRE because it accounts for earlier fluctuation of selection responses. The main principle of GFM is to use a recurrence relationship employing the transition probability matrix method developed by Hill (1976). The GFM in matrix notation was: ”i(t)'TP(“i(t-1)+s(i)) [3] where “i(t) is a vector of genetic means of animals at age i at time (t); Tp is the transition probability matrix that specifies the 49 proportion of genes in the animals at time (t) coming from selected animals at age 1 at time (t—l); ”i(t-l) is a vector of genetic means of animals at age 1 at time (t-l), i.e., ”i(t) and ”i(t—l) are a recurrence relationship to each other in time t and (t-l) ; 8(1) is a vector of genetic selection differential of selected animals at age 1. The unit for age used in GFM was a month in the study. A detail description of [3] is: :gml(t): :0...0 pm 0...0:0...0 pfm 0...0: ::3m1(t-l): : 0 :: gm2t ' ' Em C- I .( )l | I -i llamgIt-Bl |.|l I I I I I 0 -I ll - I Is 111 l I I l .l 11 I 13” | . | I oI -I II - I I II Igmk(t)| I 0I 0I II8m1(t-1)I I 0 II I """ I ' I """""""" I """""""" I II """" I + |"'|| I8f1(t)l IO 0 me 0 0|0 0 Pff 0 0I I18f1(t-1)I I 0 II I8f2(t)l I I -I IISf2(t-1)| I II :-:: : -:::° HI: . SI. I l I o I I .I || i 18” I . I I -| -I II - I I - II Ika(t)I I 0I 0I IIka(t-1)| I 0 II b Taking the first row of equation [4] as illustration: 8m1(t) ' Pmm(8mi(t-1)+smi)+Ptm(8fi(t-1)+S£i) where 5m1(t) is average genetic mean of males at age 1 mo at time (t); pmm and pfm are proportion of genes in male progeny transmitted from selected males and females, respectively; smi and sfi are genetic superiority of the selected male and female parents at age 1, with genetic means of gmi and gfi' respectively. In the subscripts for pmm' me’ pfm’ and pff in the transition probability matrix, mm, mf, fm, and ff denote, respectively, male to male, male to female, female to male, and female to female pathways of gene transmission. 50 The genetic responses estimated by equation [4] were obtained by restricting smi of [4] in right-hand-side to zero for the initial time period corresponding to their generation intervals of the three MOET populations. The restriction was due to the use of sires from base populations, where all sire were unselected and these unselected sires were used at least for one generation (i.e., selection superiority-0) in initial MOET application to the populations. (3) Modified RRE and GFM to account for inbreeding Reduction of genetic variance due to inbreeding is directly proportional to the level of inbreeding according to the function: ”i(t) " (1‘Ft)03(0) where Ft is an average inbreeding coefficient in the population at time t; and ”i(t) and 06(0) are genetic variances at time t and in base generation, respectively. The simulated populations, MOETl, MOET2, and MOET3, resulted in 22.5%, 4.8%, and 3.9% inbreedings, respectively, after 12 years, which were assumed to follow a linear trend. In computing genetic changes, 08 of RRE in [1] and smi and sfi of GFM in [4] were adjusted according to annually reduced variances due to F. (4) Modified RRE and GFM to account for linkage disequilibrium. Selection of parental generation induces a reduction in genetic variance in next generation. This reduction in variance is known as linkage disequilibrium or Bulmer effect (1971). The theory derives from a simple regression equation by regressing progeny (y) on both parents (P1 and P2): 51 y - a + b(P1 + P2) + e where a is intercept; b is regression weight; and e is error. Taking the variance (V), V(e) is (1-.5(h2)2)V(y), where V(y) is a total phenotypic variance. After selection in parents, then the variance in progeny generation becomes: V(y*) - b2V(P1) + b2V(P2) + V(e) - 2b21v2dV(y) [51 where V(y*) is a new variance after selection in parental generation. The second term in the right-hand-side of equation [5], .5(h2)2dV(y) is the amount of reduction in variance in progeny generation due to parental selection, where d can be expressed as: d - iv-v