1-35: may. Via-U: ‘. I re: IL: .53 7! any 1... Linux! i This is to certify that the thesis entitled Analytical Paleontology: Patterns of Taxonomic Extinction presented by Jean Lower Yomker has been accepted towards fulfillment of the requirements for _Ph‘_D_._ degree in MY— Major professor Date 7401/. H; M7; J 0-7639 ABSTRACT ANALYTICAL PALBONTODOGY: PATTERNS OF TAXONOMIC EXTINCTION By Jean Lower Younker A simulation model was designed to investigate the re- lationship between taxonomic duration and extinction probability. In this model, a group of mutually interacting species are non- itored through space and tine. The space is a fitness space in which there exists an optimun fitness position. Position of a species relative to the fitness optimum controls its reproductive success and thereby determines its potential for survival under the forces of selection. Change in the position of the fitness optimum alters the relative fitness of a particular species location, and a species occupying a low fitness position for an extended time undergoes extinction. Speciation occurs when area becomes available through extinction at the same time a prob- abilistic isolation event occurs. Output from the model was expressed in life-table format, and taxonomic survivorship curves were drawn. Different boundary conditions, representing different biological constraints, were used so that factors producing systematic alteration in taxonoaic survivorship data could be identified. Specific factors considered Jean Lower Younker were: 1) availability of living area; 2) intensity of selection; 3) resource instability; and 4) methodological treatment of living and extinct taxa. The principle conclusions of this analysis are: l) A simple Darwinian-Mendelian evolutionary model can produce linear taxonomic survivorship curves under conditions of dynamic evolutionary change; stable non-dynamic conditions tend to produce concave or convex survivorship curves. 2) External time-related factors can modify taxonomic duration patterns; analysis of age-related patterns requires removal of temporal effects. 3) Inclusion of living taxa in the life- table compilation for extinct taxa can substantially alter the survivorship curves. 4) Inclusion of deterministic as well as stochastic components in the model, and removal of taxonomic restraints on lineage shape and size produced cladograms which are not the result of preconceived notions of phylogenesis. 5) Without taxonomic restraints, the general cladogram shape produced by the simulation appears reasonable when compared to clades for living and fossil organisms. ANALYTICAL PALEONTOLOGY: ‘ PATTERNS OF TAXONOMIC EXTINCTION By Jean Lower Younker A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geology 1976 ACKNOWLEDGMENTS I extend my appreciation and thanks to the following people: Dr. R. Anstey, Dr. D. Sibley, Dr. A. Holman, Dr. B. H. Weinberg, and Dr. T. A. Vogel. ii TABLE OF CONTENTS LIST OF TABLES ......................... ....... ............... iv LIST OF FIGURES ......................... ............. ......... v INTRODUCTION.. ............. ..................... ......... .....l PREVIOUS STUDIES..............................................7 DEVELOPMENT OF THE EVOLUTIONARY mDEL. . . . . . General Description of the Model........................12 Components of the Model.................................18 0.0.0... ..... 00.0.12 0.0.00.0000000000018 Establishing Species Centers.... Reproduction.................... Genetic Variability of Species.. Movement of Fitness Optimum. ..... . ...... ...........26 Selection..........................................28 Extinction.........................................33 Speciation.........................................34 000......00000000022 ......OOOOOOOOOOOOZS APPLICATION AND DISCUSSION...................................37 OPERATION OF THE MDDEL......................... ........... ...44 Operator Controlled Parameters................ ...... ....44 List of Variables ..... ... ..... . .......... ....... ...... ..47 METHODS OF SURVIVORSHIP ANALYSIS.............................49 Tests for Linearity.....................................SS ANALYSIS OF SIMULATION RESULTS............. ........... .......60 Effect of Competition Intensity.........................60 Effect of Resource Instability..........................68 Effects of Changes in Area68 Survivorship Curves for Living and Extinct Taxa.........75 Results of Linearity Tests..............................78 AREAS FORFWMR smy...............OOOOOOOOOOOOOOOO......082 APPENDIX A ...... . .......... . ................................. 85 APPENDIX B ..... ..... ............... ... ....................... 94 LIST OF REFERENCES... ..... . ................................. 111 iii Table LIST OF TABLES Class numbering scheme and corresponding binary designations.... ..... ...... ......... ..21 Allele permutations for classes 1 - 27... .......... ....24 Life-table for survivorship data plotted on Figure 4...... ........... .... ............. 53 Sample calculation of total lives test.. ............... 58 iv Figure l. 10. ll. 12. LIST OF FIGURES General organization of computer model............ .......... 17 Class positions relative to species center (Class l4).......20 Three general types of survivorship curves: I. Convex II. Concave III. Linear ..... ....51 General survivorship curve for data in Table 3.. ............ S4 Survivorship curves fer varying levels of competition- selection..................... ...... . ..... ....61 Temporal pattern of extinction for high(DSURV s .008) and low(DSURV I .001) competition...... ....... 66 Clades l - 5: Representative clades for low- competition conditions Clades 6 -10: Representative clades for intense- competition conditions.............. ....... ...67 Survivorship curves fer conditions of increasing(l) and decreasing(II) area (resources) ........... 70 Temporal extinction patterns fer taxa plotted on survivorship curves in Figure 8...............72 Glades l - 5: Representative clades for conditions of increasing area Glades 6 ~10: Representative clades for conditions of decreasing area............................73 Diversity variation in 17 reptilian clades (From Raup, et. a1., 1973)... ................. 74 Survivorship curves for pooled, living, and extinct samples........ ...... .. ............. . ......... 77 INTRODUCTION The spectrum of paleontological research encompasses both the systematic analysis of fossil organisms, and an attempt to extract from this systematic analysis, the fundamental principles of phylogenesis and evolution. Identification of meaningful macroevolutionary parameters requires careful analysis of data sources and their potential biases. Characterizations of macroevolution have been based on measurements of faunal diversity, both temporal and spatia1(Raup, 1972; Schopf, 1974; Stehli, 1969; and Valentine, 1971, 1973b), and extinction rates(Boucot, 1975; Simpson, 1953; and Van Valen, 1973). The controversies which surround these areas of information have generated much recent literature(reviews by Valentine, 1973; Van Valen, 1973). Analysis of the fossil record has not produced unequivocal solutions to all of these problems. As an alternative to direct analysis of data from the fossil record, it is possible to design computer simulation models to assist in the investigation of evolutionary processes. This approach can be uniquely effective in paleontology because evolutionary processes operate on a time scale which often makes experimental or analytical problem-solving techniques impractical. Complex genetic and evolutionary systems can be simulated in mathematical terms, conforming to the accepted models of evolutionary processes and operating at a chosen level of com- plexity. Assumptions used to construct a simulation model determine the degree of correspondence between the model and the simulated system. Because boundary conditions are known, comparison of results produced by the model under different biological constraints provides an effective method for quantitative evaluation of complex systems. Although the fossil record provides the only source for documentation of large-scale organic evolution, it has contri- buted little to our understanding of evolutionary mechanisms (Raup and Stanley, 1971). A recent trend toward a nomothetic paleontology(Raup and Gould, 1974) is based on the conviction that it is possible to extract evolutionary principles from the fessil record. Within this framework, the direct analysis of empirical fossil data is the first step, preceded of course, by sound taxonomic studies. The next step involves testing general evolutionary models by comparing predictions of the models with observations from the fossil record. This link is often difficult to make, and simplification by means of simulation techniques can be extremely helpful for establishing the connection between general evolutionary models and the empirical fossil record. In this study, a group of mutually interacting species are monitored through space and time. Each species is symbolically represented by a variable number of genotype- phenotype classes, and each class contains a variable number of individuals. The space occupied by the species can be considered to be a fitness space in which there exists an optimum fitness position. The position of a species, relative to the fitness optimum controls its reproductive success, and thereby determines its potential for survival under the forces of selection. Species are considered to be in competition with each other, because change in the position of the fitness optimum alters the relative fitness of a species location in space. Species occupying a low fitness position for an extended time period are reduced below a critical number of individuals by selection, and undergo extinction. Probability of speciation is controlled by the density of species in fitness space and the genetic variability within the species. The inherent genetic variability is assumed to provide the raw material for evolutionary change(Bonner, 1974). This variability may or may not be reflected in phenotypic variability. This model was designed to examine several specific paleontological problems, related to patterns and rates of taxonomic extinction. Extinction of taxa (and replacement) is responsible for temporal change in diversity. 0f the various possible methods that characterize extinction rates and allow analysis of the factors influencing them, an effective approach is that of Van Valen(1973). His method involved the use of survivorship curves, plots showing the proportion of taxa surviving fer various time durations. A logarithmic ordinate was used so that when the taxonomic extinction rate is constant, a straight line results. After analysis of 25,000 taxa of plants and animals from the fossil record, van Valen concluded that the survivorship curves were essentially linear, with varying slapes reflecting differences in extinction rates. A linear taxonomic survivorship curve indicates extinction probability is constant throughout the duration of the taxon under investigation. Several authors have recently commented on this question and suggested possible explanations for the linearity or departure from linearity of taxonomic survivorship curves fer extinct taxa. Raup(l975) reviewed the problem and isolated biases inherent in data treatment. He also suggested linearity tests which could be used to make the data statistically reliable. Sepkoski(197S) presented stratigraphic biases, potentially affecting the shape of survivorship curves. He pointed out that because time intervals representing taxonomic durations are estimates, systematic biases could cause non-linear survivorship curves to appear linear. Incomplete sampling was also shown to con- tribute to this systematic error. Data produced by the simulation model developed for this study was plotted as survivorship curves. Different boundary conditions, representing different assumed biological constraints, were considered so that factors responsible fer changes in the survivorship curves could be identified. The Specific factors under consideration as potential modifiers of extinction rates, and therefbre responsible for irregularities in taxonomic survivorship curves were: 1) availability of living area; 2) intensity of selection; 3) temporal changes in genetic variability; 4) resource instability; and S) a procedural factor involving the effect of including data for living taxa in the data pool fer extinct taxa. In this paper, previous studies utilizing simulation models for investigation of biological-paleontologica1 problems are reviewed. The basic characteristics of the simulation model used in this study are discussed and specific output from the model is compared to data for living and extinct organisms. The degree of correspondence between output from the model and data from living and extinct organisms is dependent upon the range of boundary conditions imposed. When the boundary con- straints are biologically reasonable, operation of the model produces results not unlike those produced by nature. This aspect of simulation modeling is very useful, allowing extreme conditions in nature to be studied. In this particular case, conditions of very high interspecific competition or resource instability as well as very low competition and constant resource conditions can be simulated. The principal conclusions of this analysis are: l) A simple Mendelian-Darwinian evolutionary model can produce linear taxonomic survivorship curves; 2) Taxonomic survivorship curves systematically depart from linearity as competition between taxa is reduced; and 3) Inclusion of living taxa in the analysis of extinct groups alters the survivorship curves in a predictable manner. Resource instability has not, within the context of this model, produced significant alteration of extinction rates. In addition, the effects of temporal changes in genetic variability are not resolvable under the current mode of operation of the model. This is an artifact of model design, and will be a topic for additional investigation. A model such as this one can provide insight into the operation of evolutionary processes and establish the reason- ableness of alternative hypotheses. If an accepted evolutionary hypothesis is not supported by the model, the alternatives are: l) The model does not adequately simulate the system; 2) Geologic time factors are affecting the results; 3) The original data was incorrectly collected or interpreted; or 4) The evolutionary hypothesis should be reevaluated. PREVIOUS STUDIES The fossil record has contributed little to our under- standing of basic evolutionary mechanisms(Raup, 1971). It does, however, provide the only source for documentation of large- scale organic evolution. Retrieval of information from the fossil record requires accurate taxonomic studies, transforming the raw data to a ferm which is useable in quantitative studies of diversity, and in analysis of evolution and extinction rates. Simulation of evolutionary patterns by computer provides an alternative approach to the direct analysis of empirical data from the fossil record. Computer models can be used to simulate evolutionary mechanisms at the genotypic level or to investigate the Operation of large-scale evolutionary processes. Fraser(1959) develoPed a model simulating the variability in a polygenic system in which the phenotype was controlled by several genes and different assortments of genes produced similar phenotypes. A situation then occurs where genetic variability is high, but phenotypic variability is low. Fraser concluded that selection could favor low phenotypic variability without modification of genetic variability. Another early study by Crosby(1963) involved genetic anomalies in the primrose population in England. Differences in the movement of pollinating insects in the area, influenced by the spatial distribution of insect habitats, were thought to produce differences in interbreeding. By making assumptions about the behavior of pollinating insects, a simulation model was developed which produced genetic distributions very similar to those identified in the wild primrose population. A comprehensive evolutionary model was developed by Papentin(1973). His main goal was to identify the specific model which would produce maximum rates of adaptation. A system containing three arrays was considered: genotype, phenotype, and environment; and feur operators: selection, mutation, recombination, and alteration. Evolutionary processes were represented by actions of the operators on the arrays. Population fitness increased with the number of generations, and evolutionary rates increased with variance of fitness and selection pressure. Rates of evolution increased with the number of genotypes con- sidered, but decreased with the number of loci. Free recombi- nation was shown to be optimal, and for a given system, there was an optimal mutation rate. Epistatic gene effects tended to decrease evolutionary rates. Maximum rates of adaptation were obtained by large, haploid sexual populations under strong selection pressure, and exhibiting a low degree of epistatic gene interactions. Papentin concluded that the exact design of an evolutionary model must be a function of the type of problem under investigation, and the level of generality must also be chosen to fit the specific problem. Raup and Gou1d(1974) and Raup, et. al.(1973) used com- puter models to investigate aspects of macroevolutionary processes. Their major concern has been with the causes of morphological order in evolutionary trees. They point out that much evolutionary interpretation has been based on an assumption of directional causes in macroevolution, a direct outgrowth of the observation of "order" in the fossil record. Using random decisions to determine whether a lineage undergoes diversification, extinction, or is allowed to persist unchanged, their simulation studies have shown that directional selection forces may not be required to produce morphologic trends, character correlations, convergence, and related changes. Totally stochastic systems were shown to replicate many of the evolutionary patterns observed in the fossil record. Other quantitative studies have addressed the question of rates of extinction and speciation. Using publications such as The Fossil Record(1969) and the Treatise on Invertebrate Paleontology, Van Valen(1973) compiled life tables (taxonomic durations) for 25,000 taxa and indicated that his data support a constant extinction rate within a given subgroup of a homogeneous higher taxon. He pointed out in a reply to criticism by Hallam(1976) that he did not argue that extinction probability was independent of age, but that the mean probability of ex- tinction was constant over a long period of time. Van Valen offered a possible explanation for constancy of extinction 10 rates in which he suggested that a successful adaptation by one species has a net negative effect on all other species, and causes the overall species environment to deteriorate at a stochastically constant rate. If the positive and negative effects are on the average, equal, then the average intensity of selection and rate of adaptive evolution would be constant through time. Both Sepkoski(l975) and Raup(l975) investigated aspects of this model via simulation studies. Sepkoski concluded that less than 25% of the survivorship curves presented by Van Valen support the conclusion of constant extinction rates. Raup questioned the survivorship analysis techniques, and proposed methodological changes and statistical tests for linearity. Some deviation from linearity, according to Raup, may be due to monographic effects (i.e. artifacts of the literature) related to the taxonomy of supraspecific taxa. The Fraser model(1959) was an attempt to deal with selection at the phenotype level which does not necessarily produce modifications in the genotype. Papentin(l973) modeled genetic changes during adaptation and investigated factors controlling rates of adaptation. The Raup-Gould model(l974) operated at the morphological level, generating phylogenetic trees that were then compared to evolutionary trees for a variety of organisms, derived from the fossil record. The model developed for this study simulates the basic components of evolution: reproduction, natural selection, extinction, 11 and speciation. Patterns of diversification are displayed by generating cladograms for simulation data. Data is also ex- tracted in the form of taxonomic durations and plotted as taxonomic survivorship curves. Characteristic survivorship trends are identified and related to Specific boundary conditions. By analogy, similar factors affecting survivorship of fossil and living taxa can be recognized. This model is specifically designed to identify trends which could be produced by directed (non-random) aspects of evolutionary processes. These directed causes, together with the non-directed(random) processes isolated by Raup and Gould, should provide a more complete understanding of macro-evolutionary processes and products. DEVELOPBENT OF THE EVOLUTIONARY ADDEL General Description of the Model Darwinian evolution is a process which acts at the phenotypic level(Lewontin, 1974) and is capable of producing changes in the phenotype distribution of a population. The change in phenotype is not directly related to genotype change. Because of dominance effects, recombination, extranuclear inheritance, pleiotropy, and canalization, modification at the genotype level may be out-ofephase with phenotype change in response to selection. For investigation of patterns of diversification and morphologic change during macroevolution, the genetic system should be modeled at a level of complexity analogous to the information content of the fossil record. Simpson's work on evolutionary patterns(l953) is based on the assumption that large-scale phenotypic change observed in the fossil record is a true reflection of evolutionary change. This assumption is reasonable, based on the quality of resolution of the fossil record. Choice of an approach for modeling evolutionary processes was based on several considerations. According to Crosby(1973), there are two methods for modeling genetic systems: 1) algebraic- utilizing mathematical techniques from population genetics; and 2) creation of model organisms- inducing them to behave 12 13 in a way analogous to the behavior of real organisms. Arrays of these organisms represent the model population. The second alternative was chosen for this study because the complexity of theoretical genetics would be difficult to reduce to the level of generality appropriate for this study. The simulation developed for this study is based on a simple Darwinian-Mendelian evolutionary model. The initial species population is generated and placed in three-dimensional fitness space. Each species occupies a fixed volume of fitness space, and coordinates of species positions can be specified. A position of maximum adaptive fitness is also specified. The Euclidean distance from a species to this maximum fitness position is used to determine the fitness of a species during a given generation, and ultimately to establish its survival potential as it competes for resources with other species. This general model of resource competition resembles the Red Queen Hypothesis, proposed by Van Valen(197l; 1973). He visualized species occupying an adaptive landscape in resource space. Total resources are fixed, and a depression in the landscape in one location necessitates a compensatory increase in elevation in another area. This suggests that a successful adaptive response by one species produces a net negative effect on all other species. Species occupying the landscape attempt to maximize their share of the resources, and the fitness of a species is proportional to the amount of resources it 14 controls. This resource control is the feature which is optimized by natural selection, according to the basic Red Queen Hypothesis. Resource space-fitness space in the model is not a static feature but undergoes change each generation, not in total quantity of resources but in distribution of resources. Change in resource distribution was used to represent environmental variability, which causes the relative fitness of species to change. This dynamic feature of the resource space was designed to allow either minor or major shifts, so that concomitant effects on species populations can be monitored. A species which continues to successfully control its resources gains individuals; likewise, a species which loses control of resources decreases in total number of individuals. If the loss of fitness (resources) is severe enough, the species becomes extinct as the total number of individuals falls to zero. The total number of species occupying resource space varies about an equilibrium value, determined within the simulation. The application of biological-ecological equilibrium models in paleontology is part of the nomothetic trend, lauded by Raup et. al.(l973). This strategy allows the complexity of events in the real world to be adequately simulated by models using relatively few generating factors, according to Raup et. al. The probability of speciation during 15 a given generation is determined by the overall density of species in fitness space, and the internal variability of the individual species. Mayr(l963) suggested that speciation occurs when internal genetic variability becomes available to a species at a time of increasing (or unexploited) resources. Several mechanisms for releasing this variability are proposed, but for purposes of this model, the species with high genetic variability in a generation where resources are available has the highest probability of speciation. When a new species is formed, it is given a fixed quantity of resources (a number of individuals + a position in fitness space), and then must compete to maintain or gain more resources during the ensuing generations. Each species undergoes reproduction once per generation. New individuals are produced from the parent population by randomly choosing two parents and combining their characteristics into one offspring individual. This part of the model is designed so that four times as many offspring are produced as survive under conditions of average species fitness. This allows selection to reduce the population size each generation, based on the relative fitness of all species and the survival value for individuals within the species. Offspring replace the parents in the population, a method which accelerates the generation-to-generation change in the simulated population. This general reproduction model is similar to one suggested 16 by Fraser and Burnell(l970). It produces a change in the character and number of individuals in a species based on its competitive success in the previous generation. The total number of individuals in resource space is governed by an equilibrium value which controls the survival value of the fittest species. This survival value fluctuates so that it reaches a maximum when the total population size is increasing, and a minimum when the population size is decreasing. A highly generalized flow chart for the computer model is shown in Figure l, and a more detailed flow chart is included as Appendix A. The remainder of this section discusses each component of the simulation in detail, developing the conceptual and mathematical framework for the computer model. 17 Input: Dimensions and characteristics of fitness space and species populations; selection intensity; variability in distribution of resources l Locate species in fitness space *1 Reproduction: parents replaced by offspring 1 Change distribution of resources in fitness space 4 Establish survival value of species positions } T - GENERATIONS , YES Test for extinction tertore ages of extinct taxa N0 N0 1 ‘ ilTest for speciation] YES Locate new species NO T-Generations completed YES Cumulation of durations for simulated taxa of durations for extinct and Output cumulative frequencies extant taxa Figure 1. General organization of simulation model. 18 Components of the Model Establishing Species Centers The original species are placed in a three-dimensional fitness space. Coordinates defining the species centers are determined by the use of random numbers, generated by an internal library function. These numbers are then adjusted so they fall between zero and the dimensions of the fitness space into which the species are placed. This adjustment does not destroy the randomness of initial species position because it is accomplished by making the same modification in all location coordinates. The procedure is as follows: Rl - RANF(-l) IR1 I R1 * (DSPACE - 3) + 2 X(I) - 1R1 * XUNIT ...........Y(1) & 2(1) where RANF is an internal library function which generates a random number falling between 0 and l DSPACE is the dimension(x, Y, and Z directions) of fitness space XUNIT is the unit of distance in the X direction (equal to YUNIT G ZUNIT) A three-dimensional coordinate space was used to represent resource-fitness space, mainly for ease of data treatment and visualization. After the second species center is located, the Euclidean distance between each species pair is calculated and compared to a minimum distance. This comparison is necessary 19 to solve computational problems occurring if species centers fall too close to each other. If the centers are too close, the program returns and randomly chooses new X, Y, and Z coordinates for the species center. Rather than locate all individuals constituting a species population in the same position in fitness space, each species center is surrounded by 26 genotype-phenotype locations which are termed classes. After the coordinates of a species center are calculated, the coordinates of the class positions are fixed as shown in Figure 2. Each class has a X—Y—Z coordinate as well as a "genotype" which specifies the position of the class relative to the species center and to the other classes. Table 1 displays the class numbering scheme with the class designations expressed in 3 x 3 x 3 coordinate space and the corresponding binary (diploid) genotype for the position of the class relative to an arbitrarily defined origin (Class 1 I 00 00 00). Each species can be considered a cluster of individuals in fixed positions relative to the species center, and occupying a region of fitness space. Of the 27 class positions, seven are assigned individuals for the first iteration of the model. The seven classes initially occupied were chosen for reasons explained later in the paper. Eight additional classes are "open" and can be assigned offspring during reproduction. The remaining twelve classes are "closed" classes, simulating the "closed genetic system" as visualized 20 /6 “5 /24 9 wI'BE—""i"“27 ‘ 2: ‘ J’" 12!) I l I" 5 ----- :l‘élr" ""23 { 8 '73.. “1.35.“, ......... l, x .. : /' ..-4' '3 /2‘2 [,7" '6 25 Y” Figure 2. Class positions relative to species center (Class 14). 21 Table 1- Class numbering scheme and corresponding binary designations crass x-v-z BINARY noun COORDINATES (GBNOTYPE) 1 1 1 1 oo oo oo 2 1 1 2 oo oo 10 3 1 1 3 oo oo 11 4 1 2 1 oo 10 oo 5 1 2 2 oo 10 1o 6 1 3 3 oo 10 11 7 1 3 1 00 11.00 s 1 3 2 oo 11 1o 9 1 3 3 oo 11 11 10 2 1 1 10 oo oo 11 2 1 2 10 oo 10 12 2 1 3 10 oo 11 13 2 2 1 1o 10 oo 14 2 2 2 10 10 1o 15 2 2 3 1o 10 11 16 2 3 1 10 11 oo 17 2 3 2 10 11 10 13 2 3 3 1o 11 11 19 3 1 1 11 oo oo 20 3 1 2 11 oo 10 21 3 1 3 11 oo 11 22 3 2f1 11 10 oo 23 3 2 2 11 10 1o 24 3 2 3 11 1o 11 25 3 3 1 11 11 oo 26 332 111110 27 3 3 3 11 11 11 22 by Carson(l975). These classes may become viable following major reorganization of the internal species makeup(Carson's flush- crash cycle), or when there are major changes in the environment. After species and class coordinates are calculated and stored, the original species population enters the main program and proceeds through the first reproductive generation. Reproduction This section is designed to simulate a form of sexual reproduction where the offspring replace the parents in the population. This could be considered sampling without replace- ment, because classes of the species available for reproduction in the following generation do not include the parents from the previous generation. The potential parent classes for the first generation are those initially assigned individuals. After one generation, additional parent classes become available whenever the offspring fall into the "open" classes. Two parents are chosen at random from the occupied classes. Each class (1 - 27) has a genotype designation (Table l). Genotypes of the parents are used to assign the offspring to one of the 27 classes as shown in the following example: Parent 1 is randomly selected and belongs to class 7. The binary designation for class 7 is 99 ll 99, By analogy with simple Mendelian genetics, this parent can be considered a triple homozygote with each pair of digits corresponding to a gene locus. No further analysis is necessary for this parent because the haploid genotype is fixed; it must 23 contain one allele from each loci, and therefore will have a designation of 0_l_ 0. Parent 2 is randomly selected and belongs to class 14. This is the completely heterozygous class with genotype 10 19.12: In this case, the allele provided by eaEh'locus is not fixed, but can be either 1 or 0. The resulting haploid genotype can be any one of the following combinations. lv-‘IOIH IHIHIH Ionoh- luv-4o “one“: Ion—1c l°l° lop- 11-41- Random numbers are again utilized for purposes of selecting the haploid genotype to be contributed by parent 2. For each of the allelic pairs, one of the two positions is chosen at random, and the three positions chosen are the genotype for the "gamete" provided by parent 2. If, for example, l_ _O_ 2 were the genotype produced by parent 2, combination with the 9.1.9. genotype of parent 1 produces an off- spring with genotype 12 10 29 Referring to Table 1, this offspring can be assigned to class 13, which has an internal position of 2 2 1 in the species array (also refer to Figure 2). The order of the alleles at each of the three positions in the genotype is not considered. Because of this factor, the probabilities of offspring falling into classes are unequal. As mentioned in the first section, not all classes are viable at any one time, nor are the viable classes necessarily occupied. The choice of viable and nonviable classes was based on the unequal probabilities. Table 2 demonstrates the reason for the higher probability of the "occupied" and "open" classes. As shown by Figure 2 and Table 2, the classes which were initially assigned individuals are the classes allowing the greatest 24 Table 2 , Allele permutations for classes 1 - 27 CLASS BINARY PERMUTATIONS CLASS BINARY PERMUTATIONS 1 OO 00 00 14 01 10 01 01 01 10 2 00 OO 01 10 01 01 00 00 10 01 01 01 3 00 00 ll 15 10 10 11 10 01 11 4 OO 10 00 01 10 11 00 01 00 01 01 11 S 00 10 10 16 10 11 00 00 01 01 Ol 11 00 00 01 10 00 10 01 17 10 11 10 01 11 10 6 00 10 11 01 11 01 00 01 11 10 11 01 7 00 11 00 18 10 11 11 01 11 11 8 00 11 10 00 11 01 19 ll 00 00 9 00 11 ll 20 11 00 10 11 00 01 10 10 00 00 01 00 00 21 11 00 11 11 10 OO 10 22 11 10 ll 01 00 01 11 01 00 Ol 00 10 10 00 01 23 11 10 10 11 01 10 12 10 00 11 11 01 01 01 00 11 11 10 01 13 10 10 00 24 11 10 11 01 10 00 ll 01 11 10 01 00 Ol 01 00 25 ll 11 00 14 10 10 10 26 ll 11 10 01 10 10 11 11 01 10 01 10 10 10 01 27 11 11 11 25 number of permutations in the alleles (5, ll, l3, 14, 15, 17, 23). They are also the classes in the center of each face of the three-dimensional cube, and class 14, the body-centered position. The Open classes represent the next level of permutation (4, 6, 7, 10, 12, 16, 18, 22, 24), each having two allelic arrange- ments for a specific position. The closed classes are the re- maining classes (1, 2, 3, 7, 8, 9, 20, 21, 25, 26, 27), and are located on the edges of the species block. Eight of these classes can be obtained by only one allelic combination, and thus are very low probability occurrences. Since order of the alleles within each pair is not considered, the number of different ways a genotype can be produced determines the prob- ability of occurence of that offspring during reproduction. Genetic Variability of Species Several aspects of genetic variability and its origin were considered when this section of the model was designed. Three distinct problems were addressed: 1) What is the relation- ship between phenotype and genotype? 2) How does the "closed" system of genetic variability(Carson, 1968; Mayr, 1963) partic- ipate in evolutionary change? and 3) How does environmental stability affect genetic variability(Ayala, et. a1, 1975; Bretsky and Lorenz, 1969; Schopf, 1976)? In the present mode of operation of the model, the phenotype and genotype were assumed to be directly related. 26 Modification in the genotype (except for order of alleles- i.e.- l Q_and 9_l_are the same genotype) produces a corre- sponding change in phenotype. This is not unreasonable be- cause many authors (Anstey and Pachut,in press; Hawkins, 1964; and Raup and Michelson, 1965) have shown that large-scale mor- phological characters may be under the control of simple genetic systems. In addition, as suggested earlier in this section, the clarity of genetic data preserved in the fossil record limits the degree of complexity which a simulation model should contain. Without the assumption of a direct link between genotype and phenotype, simulation models become more complex and the results are therefore, more difficult to interpret. Two distinct components must be added to a model for simulation of the more complex system: 1) a method for more than one genotype to produce the same phenotype; and 2) a method allowing one genotype to produce more than one phenotype. These specific components are not included in the present model. They can be incorporated for a second phase of operation which requires the foundation established by the basic model. Movement of Fitness Optimum The fitness optimum is a position in X-Y-Z coordinate space which can be moved relative to the species locations. This section of the program was written to accomodate either 27 random or directional movement of the fitness optimum position. If movement is random, changes in the coordinates of the optimum position are determined by selection of new values from a Gaussian distribution (refer to Subroutine NORMAL in Appendix B). The old fitness optimum coordinates are used as means of the Gaussian distributions of possible values, assuring the most probable change in position is a small one. Larger coordinate changes are possible but have lower statistical probabilities. The standard deviation of the distribution is set independently for each coordinate direction and can be varied through time. Move- ment of the optimum fitness position is analogous to environ- mental instability, because each species becomes either more or less suited at his given location as a result of the change in position of optimum fitness. New distances are calculated each generation after the optimum has shifted, and relative survival rates are calculated. The following Fortran statement calculates the distance from the I£h_species to the fitness optimum - (ENVX, ENVY, ENVZ): DIST(I) I SQRT((X(I) - ENVX)**2 + (Y(I) - ENVY)**2 + (2(1) - ENVZ**2))/DVAR Distances were standardized by dividing the true Euclidean distance by DVAR, a number reflecting the internal species variability. This modification is based on the assumption that species with higher genetic variability should be given an advantage in their 28 struggle for control of fitness space(Mayr, 1963). This pro- cedure was designed so that units used to measure distances in fitness space are not constant, but depend upon the species internal genetic makeup. Directed movement of the fitness optimum can also be simulated. Coordinates of the fitness optimum position can be incremented by a chosen distance in fitness space. Following are the statements designed for this purpose: ENVX I ENVX + XSEL ENVY I ENVY + YSEL ENVZ I ENVZ + ZSEL Where ENVX, ENVY, ENVZ are the X-Y-Z coordinates of the fitness optimum position XSEL, YSEL, ZSEL are the directed changes for the X-Y-Z, coordinate directions By including options such as the one discussed above, the simulation model is made more general, and can be run with a greater variety of boundary conditions. Selection Selection is the primary cause of changes in gene fre- quencies(Mayr, 1963) and presumably one of the major factors in macroevolution. This section of the program was designed to accomodate either random or directed selection. The nature of the selection process is a function of the movement of the 29 Optimum fitness position. The movement is not necessarily equal in all three coordinate directions under deterministic change, and movement direction and magnitude are totally stochastic in the random movement option, as discussed above. Coordinates of the Species centers are ordered by a sub- routine called SORT, which places them in a decreasing sequential list. This list, containing the species centers in order of increasing distance from the fitness optimum, is used to establish a fitness value for each species position. This is accomplished by assigning a maximum value to the species located nearest the fitness optimum position. The fitness space can be envisioned as a three-dimensional adaptive landscape in resource space. The species fitness is directly proportional to the amount of resource space it controls, and resource space is an adaptive factor which is a function of distance from the fitness optimum. The assumption is made that as a species becomes better adapted (occupies a position closer to the fitness optimum), it is able to control a greater amount of resource Space. Fitness of the species nearest the position of the optimum is arbitrarily set at the maximum allowable value. Each species position is then given a fitness determined by its distance relative to the position of the fittest species. Although Euclidean distances are calculated, the internal variability of the species is considered in the calculation so that a species with higher variability is given a competitive advantage in 30 terms of survival and reproduction in the next generation. The following set of statements demonstrate the procedure for deter- mining the relative survival value of a species position: FITSP I AVSUR + (CSPEC - l)*DSURV where FITSP is survival value of species located nearest the fitness Optimum AVSUR is survival value fer the mean species position CSPEC is 8*(NSPEC) where NSPEC I I species present DSURV is the Survival increment; this I controls intensity of species competition Determination of AVSUR AVSUR is used to maintain an equilibrium 0 of individuals NHIGH I 1.25*NTOTAL NLOW I .75'NTOTAL SUMN I SUMN + NIND(I) IF(SM.LT.NLOW)GO TO 1 IF(SUMN.GT.NHIGH)GO TO 2 l AVSUR I AVSUR + .01 2 AVSUR I AVSUR - .01 where NHIGH and NLOW represent the upper and lower limits on I individuals SUMN is the number of individuals AVSUR is the survival value for the average species; it is used to determine the relative survival of all other species 31 NTOTAL is the total number of individuals allowed; it is dependent on AREA, a variable reflecting fitness space available and species density The survival value for each Species position relative to FITSP is determined as follows: SURV(I) I FITSP - (K*DSURV) where K is the position of a particular species relative to FITSP DSURV is the survival increment The number of individuals in a species is determined from the survival value. These individuals are not randomly distributed across the classes but are allocated according to the survival value of each class, determined in a way analogous to the pro- cedure described above. Distances from each class within a species to the fitness optimum position are calculated. The classes are then placed in order of increasing distance by sub- routine SORT. After selection has acted, the total number of individuals belonging in a Species is known, but their class distribution must be calculated. The fellowing procedure was used to determine the number in each class after selection: x * a + (X-.01)b + (x-.02)c ..... I N1ND(I) NIND(I) is known after selection and represents the number of individuals in the species 32 Solving the above equation for X gives NIND(I) + (.Olb + .02c + .03d . . .) (a + b + c + d + . . .) The value of X can be used to determine the number in each class of species I. 'The .01 value is the class survival increment, analogous to DSURV at the species level. The number Of individuals in the Jth_class of Species I_is determined as fellows: SPECIES(I,J) I 4*OCCUP(J)*(X-POSIT(J)-l)*.01) where SPECIES(I,J) refers to the Jth_class of the Ith_species 4'OCCUP(J) refers to an assumption that fOur times as many individuals are produced as survive, giving the average species a .25 survival rate POSIT is the position of the Jth class in the ordered sequence containing all occupied classes of species I .01 is the increment used to determine class position The selection section is designed so that survival values of individual Species are dependent upon position relative to other Species, and not absolute distance from the fitness optimum. This is based on the assumption that relative fitness and com- petition, rather than absolute fitness controls the probability of survival of a species. Within a species, classes in positions 33 closest to the fitness optimum gain individuals at the expense of classes located further away. Extinction Foin et. al.(l975) established three distinct evolutionary problems related to extinction: 1) How does the probability of extinction vary through time? 2) How does the probability of extinction change with taxonomic age? 3) How does the probability of extinction vary within one taxonomic group? In this Study, the number of individuals in a species varies through time as the fitness of the Species changes due to movement of the optimum fitness position. There iS no specific set of operations for simulation of extinction. As an alternative to modeling exI tinction as a probabilistic event, the model was designed so that extinction occurs when the number of individuals in a species falls below a critical number. The total number of Species present is then reduced, and the species density correspondingly decreases. Because this increases the probabil- ity of Speciation, a balance exists between speciation and extinction. A very low probability event could move the fitness optimum a considerable distance, causing Species located near the old position to lose many individuals in the ensuing gener- ations. This might appear as a "mass extinction" in the output. The probability distributions for all three types of extinction can be calculated fer the species in the simulation. Type (2) 34 is the extinction probability which Van Valen(1973) has dealt with. The Statements controlling extinction are as fellow: IF(NIND(I).LE.MINNO)GO TO 100 100 NIND(I) - o where NIND is the variable containing the number of individuals in species I MINNO sets the minimum I of individuals necessary for species persistence statement 100 assigns "0" individuals to species I_ Speciation Populations are given the opportunity to Speciate during each generation. Speciation probability is a function of species density in fitness space and the internal variability of the species, arranged in a two-step hierarchial probabilistic sequence. The following set of statements summarize the Speciation procedure: NICSAT I NSPECP/AREA R3 . RANF(-l) IF(NICSAT — R3) 3L_ - O or + ; NO SPECIATION J: PISOL . AVEVAR(I) MAXVAR R4 + RANF(-l) IF(R4 - PISOL) [3;] J r 01‘" NO SPECIATION SPECIATION 3S NICSAT is a variable which changes as extinction removes species and speciation adds species. It represents a density function which depends on an operator selected value for AREA, the variable specifying the saturation number of species, and the value of NSPECP, the number of Species currently inhabiting fitness space. R3 and R4 are random numbers, generated by the internal library function RANF. R3 is compared to NICSAT, and as shown in the statements above, a negative value fer this comparison signifies the first step in speciation has been com- pleted. This step can be considered analgous to the opening Of an ecological niche through extinction, migration, or environ- mental change. Calculation of the PISOL(probability of isolation) value is analogous to asking the question whether the genetic variability necessary for reproductive isolation to develop is available. Mayr(l963) suggested that most of the divergence necessary fOr reproductive isolation occurs as the result of the utilization of genetic variants already present as polymorphs in the population. Speciation is not dependent upon the appearance Of novel new mutations, but rather on exposure of inherent genetic variability, according to Mayr's thesis. For this reason, the PISOL value was determined by taking the ratio of internal variability Of Species I (AVEVAR) to the maximum genetic varia- bility found in any species in the population (MAXVAR). Then the PISOL value is compared to a second random number (R4), and a negative result in this probabilistic event produces successful 36 isolation. These two events, occurring in concert are sufficient to produce speciation. The new Species center is assigned co- ordinates in fitness Space within a fixed distance of the parent species. New Species are given a number of individuals equal to 40% of the number in the parent species. Class coordinates are assigned and the Species is available to undergo reproduction and selection in the next iteration of the model. APPLICATION AND DISCUSSION When Simulation models are developed, certain aSpects of the system under investigation must be deemphasized while other aspects are considered. Loss of information in this manner is a "cost" of model building(Levins, 1966). Levins suggests there are three general types of costs: 1) degree of generality; 2) degree of realism; and 3) degree of precision. These factors should be considered in the model design, with acceptable operating levels chosen for the Specific problem. The general procedure followed when using a simulation model is to run the computer program with a range Of’known values or known distributions fer the parameters under operator control. Boundary conditions can then be established for which the model produces results not unlike the real world. After these boundary conditions are identified, analogous factors responsible fOr natural variation can be extracted and analyzed. Because many systems do not permit experimental analysis fer reasons of slow rates Of change, system complexity, or unknown boundary conditions, the simulation approach may be the only procedure for Obtaining information on the nature of the system. The "costs" of model building should be explicitly defined during development Of the model. The fellowing discussion 37 38 analyzes some of the costs required for construction of the model used in this study. 1. Degree of Generality: It is particularly important to choose the appropriate level of generality when designing a model. This requires care- ful analysis of the purpose of the model, prior to model develop- ment. A primary concern must be that the system is not mis- represented due to loss of infermation. At the same time, if the design is too complex, the advantages of Simulation are lost because the model will be as difficult to understand as the natural system. The complexity of a model of evolutionary processes can vary from duplication of molecular evolution at the chromosome level(Papentin, 1973) to studies of evolutionary patterns in the fessil record(Raup et. a1., 1973). The level of generality of the model does not determine its validity or accuracy. The validity is directly related to the validity of the underlying assumptions. The accuracy is a measure of the model's ability to replicate the "real world" at the chosen level of generality. This model was designed to monitor evolution at the population level. Although the model could be used for asexually reproducing organisms, the current mode of operation is based on sexual reproduction. The reproduction section describes the nature of this part of the model. The Offspring genotypes are 39 a function of the parent genotypes, chosen randomly from occupied genotype classes, and a second random decision when alleles are chosen from heterozygous loci. This is a reasonable model for sexual reproduction, but does not incorporate chromosomal muta- tions, nor spontaneous allelic mutations. Since the purpose of the model was not specifically aimed at monitoring change in genetic composition at the chromosome level, these omissions are considered acceptable "costs" of the modeling process. An un- known "cost" must also be included: the validity of the under- lying Darwinian Evolutionary process. As previously outlined, the conceptual model fer selection involves species competition for control of resources. The species are located in a three-dimensional Space which also contains a position, specified as the fitness optimum. Species located nearest the Optimum position are given a reproductive advantage, relative to more distant species. This reproductive advantage is realized in the total number of Offspring produced, and in the specific classes occupied by those offspring. Within each Species, the individual classes vary in fitness, and selec- tion assures the classes in the best fitness position are favored during reproduction. When an Offspring falls into a class which is nonviable, it is rejected and new parents are chosen. In a natural system, selection is generally not this harsh, except in the case of lethal variants. The analogy between control of resource Space 40 and position of the Species relative to the fitness Optimum position reflects a model design which, although generalized, includes the principal components of Darwinian natural selection. Speciation and extinction are two other components of the model which require attention. Speciation may occur in response to several different conditions in the natural system. Allopatric Speciation is thought to occur when peripheral populations are geographically isolated and undergo adaptive change in an environ- ment different from the parent SpecieS(Eldredge and Gould, 1972). With phyletic speciation, the pOpulation undergoes a change in gene frequencies due to unidirectional change in the environment. A third type of speciation may occur when a population passes through severe changes in Size due to varying selection inten- sities. According to Carson(l975), this speciation mode explains the formation of new species which are not adaptively different from the parent Species. It is probable that all three models describe a Speciation mode that occurs in nature, either independently or in combination with the others. In this model, the probability of Speciation for a Species is determined at the end of each generation. This probability takes into account the number of extinctions occurring (an index Of resource availability), a probabilistic isolation event based on a random decision, and the inherent genetic variability. A species with high genetic variability in a generation (iteration) where unutilized or unexploited resources 41 are available has the highest probability of undergoing Speciation. Because the "geographic" position of the species determines both its variability (developed over a number of generations), and the portion of fitness Space controlled by the Species (resources), this corresponds most closely to the aIIOpatric Speciation model. However, it could be argued that at this level of generality, phyletic speciation is also a reasonable model. No Special consideration was given to changes in genetic variability during the Speciation event. If Mayr(1963) is correct in believing that major genetic reorganization occurs during speciation, this model does not correctly simulate the speciation event. Extinction takes place when the number of individuals in a Species falls below a preset minimum number. This occurs when a species loses control of its resources by remaining in an un- favored position in fitness Space fer a number of generations. Extinction is modeled as another part of the evolutionary process of a species pOpulation, rather than an event requiring exotic explanations and mechanisms. 11. Degree Of Realism It is difficult to evaluate this model on a scale Of absolute realism because the natural processes Simulated by the various sections are complex and in some cases, not well understood. The simulation was designed to consider conflicting 42 models or interpretations where possible. The "degree of realism" is a measure of how well the model utilizes the current under- standing of natural evolutionary processes, because only if the model produces results, comparable to the "real world" can its value be determined. Although the degree of realism of a model is not directly related to the level of generality, it Often becomes more difficult to be realistic in all aspects as the model is made more general. The reproduction section is the most realistic fer its level Of generality. It effectively produces a population of OffSpring, genetically distinct from the parent population. However, because it relies totally on recombination for inducing genetic change in the population, it is unrealistic in its omission of spontaneous gene mutations as the ultimate source of new genetic material. The allOpatric model of speciation was fellowed because it is the most widely accepted in the literature. Allopatric speciation, according to Eldridge and Gou1d(1972), occurs in isolated peripheral populations where selection pressures are more intense or different from those pressures acting on the main body of the Species. In these "fringe" conditions, pheno- types which are less successful in the central range of the species may thrive and become highly successful. Eventually they may become competitively equal or better fit than the parent population and replace them. This type of speciation does not 43 require the occurrence of a new and favorable mutant at a time when selection allows the new gene to become established in the population. Rather, as suggested by Mayr(1963), it relies on the genetic variability inherent in the population, and perhaps brought to expression by differences in the regulatory processes that control morphogenesis. 111. Degree of Precision A simulation model can be designed to operate with high precision but precision does not imply accuracy. Accuracy can only be evaluated by determining the reasonableness of predic- tions based on the model, or by comparison of data generated by the model to similar results produced by natural systems. If the simulation does not produce reasonable results, several explanations are possible: 1) the system was incorrectly modeled; 2) boundary conditions were inaccurate; 3) original information was incorrect. OPERATION OF THE MODEL In the evolutionary model designed for this study, certain parameters are assigned values at the beginning of the program; some vary about fixed or variable mean values; and others are assigned values within the body of the program, contingent upon a Specific event or series of events.- The fOllowing section discusses the parameters which are directly or indirectly under operator control, and therefOre the parameters which are used to establish realistic boundary conditions for operation of the model. Operator Controlled Parameters 1) Intensity of Species COmpetition A parameter called DSURV allows the increment of survival to be set by the Operator. With small survival increments, the difference in species survival as a function Of position is re- duced. This represents a situation where species competition for resources is low (abundant resource supply - low population density) giving all Species approximately the same survival potential. 2) Variability of Fitness Optimum Position The fitness Optimum position can be controlled directly or indirectly by the operator. Direct control is possible through 44 45 the parameter DIRECT. This parameter can be used to produce unidirectional change in the coordinates of the fitness position, simulating long-term changes in environmental conditions or resource availability. Indirect control is provided by the NORMAL subroutine, attached tO the main computer'program. By choosing to use this option rather than the DIRECT procedure described above, the fit- ness position is allowed to vary in a random fashion about the coordinates of the optimum fitness location in the previous generation. Different Standard deviation values for the Gaussian distribution can be specified, causing the degree of fluctuation in the fitness position to vary. Because the actual coordinates are chosen from the Gaussian distribution about the previous mean, the most probable change in position of the fitness Optimum is a small one, with large changes occurring less frequently. 3) Area Available fer Occupation The variable, DAREA is used to choose one of three possible area effects: a) area constant; b) area increasing; and c) area decreasing. The increment of area increase or decrease can be specified allowing simulation of loss or influx of resources. With increasing area, the total space available for occupation increases. This allows an increase in the equilibrium number of species by decreasing the DSURV value, the number determining the intensity of competition. When DSURV decreases, more species are able to successfully remain above the extinction level, 46 bringing about a higher Species density and a lower probability of speciation. When the available area is occupied, the DSURV value increases. This increases competition between Species and tends to drive more of them to extinction. 4) Number of Generations The number of iterations is under operator control and is limited by financial restrictions rather than Specific biological constraints. If the program was not run long enough for trends or variations about trends to become apparent, the number of generations could have a strong effect on the results. Sepkoski(l975) addressed a Similar problem with regard to the information content of the fossil record. He concluded that systematic biases are produced when stratigraphic resolution is not good enough to reveal anomalous patterns of taxonomic duration. Simulation studies suggested that taxonomic durations must be long relative to the stratigraphic interval used to measure durations if non-linear survivorship curves are to be recognized. Similar problems must be considered when computer models are used to simulate long periods of time. It must be recognized that exact origin and extinction times are known in the simulation, whereas fer fossil taxa of Short duration, loss of infermation may produce systematic changes in the Observed survivorship. 47 Additional Parameters Initially set by Operator The remainder of the variables to be discussed are less important in their overall effect on the operation Of the model. For this reason they are presented in list format with a brief statement. The complete computer listing can be found in Appendix II. LIST OF VARIABLES AVSUR - AVSUR sets the initial mean survival at a specified number which later varies with the number of species present. CLDIST - This is the value used to keep a minimum separation between species centers. DSPACE - DSPACE establishes the dimensions of fitness space. ICLAS(I,J,K) - This subscripted variable identifies the po- sition of each of the 27 classes in the 3 x 3 matrix occupied by members of a Species. IRANF - This value defines the starting point fer the random number generator in the random number table. IX, JX, IY, JY, 12, J2 - These values contain the genotypes fer each of the 27 classes (either 1 or O in each position). MINNO - The value provided for this number sets the minimum number of individuals allowed fer Species persistence. NAREA and DAREA - These variables are used to call for con- stant or changing AREA, and to establish the increment Of area increase or decrease. NINDPS - This value sets the number of individuals per species fer the initial reproduction run. NSPEC - This value sets the initial number of species. 48 SPECIE(I,J) - This subscripted variable contains the class designations for the J classes of species I - con- sisting of occupied classes, open classes, and lethal (closed) classes. VXI and VX2 - These values are used to vary the effect that genetic variability has on probability of speciation. XUNIT, YUNIT, and ZUNIT - The values for these parameters specify the units in the X, Y, 3 Z coordinate directions. For identification of other variables calculated within the program, refer to the documented program listing in Appendix B. METHODS OF SURVIVORSHIP ANALYSIS A complete picture of the mortality of a population can be Obtained by construction of a life table. Several types of life tables have been used fer a systematic approach to survivor- ship analysis(Odum, 1971). In general laboratory usage, the number of individuals surviving at specific time intervals (day, month, year) are monitored fer a generation. A life table is then prepared consisting of several columns: 1 - the number X of individuals surviving after a Specific time interval; dx - the number of individuals dying during successive time intervals; qx - death or mortality rate during successive intervals; and ex - the life expectancy at the end of each interval. Curves plotted from life-table data can be used to determine the statistical properties of a population. Survivorship curves have also been applied to the study of fossil lineages(Van Valen, 1973). When survivorship curves are used fer analysis of taxonomic durations and extinction rates, stratigraphic ranges constitute the raw data. If the data is fer extinct taxa, the information required is the time interval between origination and extinction. In living taxa, the time span between origin of the taxon and the Recent is used. Time-dependent biases in range data must be considered, as outlined 49 50 by Raup(l975). He also pointed out that systematic changes in the total number of coexisting taxa lowers the reliability of the survivorship trends. An equilibrium number of taxa is main- tained in the model so that only minor random fluctuations occur. For paleontological data, assuming the world ecosystem has been saturated Since middle Paleozoic(Raup, 1972), this source of error is not likely to substantially bias the large-scale trends observed in survivorship fer fessil taxa. To construct a survivorship curve, data from column 11‘ (number of survivors) is plotted on the vertical coordinate axis and duration of the taxa is plotted on the horizontal coordinate axis. The lx value can be converted to a logarithm as suggested by Van Valen(1973), so that a straight line on the survivorship plot indicates a constant extinction rate for the group under consideration. Three general types of survivorship curves are possible (Figure 3): 1. Highly convex - characteristic of a group in which extinction rate was low until near the end of its stratigraphic range; 11. Highly concave - resulting from a survival pattern where extinctions were prominent in an early or immature stage of the group; and III. Intermediate patterns, representing conditions where age-specific survival is nearly constant. If age-specific extinction rates are constant through- out the history of the group, the result will be a straight line on the semi-logarithmic plot. A stair-step or sigmoidal a? 3: 3.: I: wé- ‘9 r: gs 25 9 IOKI¢ '01 51 P : 1 s _: INARAHTCU' Figure 3. Three general types of survivorship curves: 1. Convex II. Concave III. Linear 52 survivorship curve indicates the extinction rate differs at successive stages in the phylogenetic history of the group. All of the factors affecting speciation and extinction combine to produce the phylogeny of a taxonomic group. When survivorship analysis is applied to fessil populations, the fossil record must be interpreted as a record of normal mortality (raw data will be placed in the dx column in the life table), or a census-type record representing mass mortality of a stable population (raw data will be placed in 1x column). The Strati- graphic ranges fbr extinct taxa are dx values, as are the durations of extinct taxa in this study. To obtain the 1x values, the dx values must be cumulated as Shown in the example in Table 3. Figure 4 is the survivorship curve fer the data in Table 3. To calculate the rate of extinction fer an approximately linear curve, the formula for determining the decay constant of an exponential decay series can be used. It is expressed in sur- vivorship terms (see Raup, 1975) as follows: -Xt St I 80 e where S I the number of survivors at beginning of time period St I number Of survivors after t time units '%.I rate of extinctions per unit time 53 Table 3 , Life-table for survivorship data plotted on Figure 4 DURATION dx 1x 1 30 179 2 19 149 3 14 130 4 14 116 s 19 102 6 12 83 7 17 71 3 9 54 9 6 45 1o 9 39 11 5 3o 12 3 25 13 s 22 14 2 17 1s 1 15 16 6 14 19 3 8 20 2 s 21 1 3 23 1 2 32 1 1 NUMBER OF MXA (Cumulative Frequency) zoo .. 54 -O --0- ALL - X — X - EXTINCT b‘ 0 I00 41- \d 0‘ "1° 1\ so A» 2:5" “‘31 a as $1, “Iqrv é;\ \ 1 Q 1 1 1 p 1 1 | 1 a \ \ \ \ q \ \ \ \ \ \ \ .L 1 4 10 20 SO 40 DURATION Figure 4. General survivorship curve for data in Table 3. $5 The extinction rate can also be computed from the sur- vivorship curve as fellows: )\. 1nSO _ lnS t t or )\a log10 So - loglo St t loglo e For the example above, assuming approximate linearity: )1: 111179 - 1110 I .130 40 Tests for Linearity Van Valen(1973) did not use statistical procedures to test the linearity of his survivorship curves. He pointed out that because of the nature of the data, statistical significance or non-significance of the curves was not the important factor. He admitted that real sources of irregularity exist including sampling errors, but claimed that sample size and magnitude of the irregularities determined the significance Of departures from linearity. In several examples, departure from linearity was shown to be the result of insufficient time since origin of the group. Raup(1975), while critically reviewing Van Valen's work, agreed that uncertainties in the data and small sample size rendered statistical testing Of debatable value but also pointed 56 out that visual inspection of survivorship curves was not accept- able when important evolutionary questions were being considered. Because survivorship curves are cumulative frequency plots, points determining the nature of the distribution are not in- dependent of each other. Unless a cumulative curve is highly concave or convex, it will tend to appear linear, and a statis- tical test sensitive to subtle departures from linearity would be very useful. One of the most effective methods fer statistical testing of exponential curves is the Total Lives Method of Epstein(l960a, b). This method makes use of the basic properties of Poisson processes, and was originally designed fer use in determining changes in probability of failure of industrial equipment with age. If metal fatigue causes increasing probability Of failure with age, a convex survivorship curve results. If fatigue does not produce an increasing likelihood of failure, the survivorship curves will appear linear. The null hypothesis in the Total Lives Test is that the underlying distribution iS exponential with constant mean life. Too many early failures (extinctions); too few failures in the early part of the distribution; or a change in failure rate during the test can be detected. The vocabulary and general procedure fer performing the test is given in Raup(l975) and can be summarized as fellows: 57 "total life" I sum of durations of all taxa in the group before the taxon under con- sideration became extinct Consider 100 taxa - 5 of the taxa lived 20 gener- ations, and 5 more became extinct after 30 gener- ations. Total Life calculation at the first extinction would be - (100 taxa) x 20 generations I 2000 For the second extinction event - 2000 +(95 taxa x 10 generations) I 2950 .......etc. In general: If there are r taxa in all, with durations d1 , d2 °""dr' total lives are calculated by T1=rdl T2 = d1 + (r - 1)d2 Tr I dl + d2 + ...... + d The sum of the first (r I 1) total lives is normally distributed if the survivorship is linear(Epstein, 1960 b). The mean of the normal distribution is given by (r - l)Tr / 2 and standard deviation by ((r - l)/ 12)3 x Tr; The test for linearity of survivorship is perfOrmed by comparing the theoretical range of values in the mean total life acceptable at a chosen level of significance to the calculated sum of the total lives. If 2. Ti falls within the allowable range, the hypothesis of linear survivorship is accepted. Table 4 shows an example of this calculation, using the data from the example in the previous 58 Table 4. Sample calculation of total lives test SUM or DURATION TOTAL LIVES TOTAL LIVES vcrl "r303 1 179 + 1(0) 179 30(179) verso -149) 2 179 + 149(1) 323 19(323) vorso -763) 3 323 + 130(1) 453 14(453) V(T64 -¢77) 4 453 + 116(1) 574 14(574) V0r73 -796) s 774 + 102(1) 676 19(676) ver97 '1103) 6 676 + 33(1) 759 12(759) V(7109 ‘T1253 7 759 + 71(1) 330 17(330) V‘7126 -1134) 3 330 + 54(1) 334 9(334) V(T -1- ) 9 334 + 45(1) 929 6(929) V(T}i§ -1%:g) 10 929 + 39(1) 968 9(968) vcr150 -1154) 11 963 + 30(1) 993 5(993) V(¢ -T ) 12 993 O 25(1) 1023 3(1023) ver155 - 57) 13 1023 4 22(1) 1045 5(1045) vcrlss - 62) 14 1045 + 17(1) 1062 2(1062) V(7163) 16‘ 15 1062 + 15(1) 1077 1(1077) ver165 -r ) 16 1077 + 14(1) 1091 6(1091) vcrlfig -7171) 19 1091 + 3(3) 1115 3(1115) vet};5 “T176) 20 1115 + 5(1) 1120 2(1120) 21 1120 + 3(1) 1123 1(1123) V(71;;) 23 1123 + 2(2) 1127 1(1127) V(¢i79) 32 1127 + 1(9) 1136 1(1136) 2.. 116353 Under assumption of exponentiality, the 178 total lives VTi, i I 1, 2 ..... 178 should be unifbrmly distributed in (0, V(T178). Theoretical mean fOr zfizg'vcri) - 173/2 (V71) . 178/2(1136) -101104 Standard Deviation I 178/2(VT1) I 3.85 * 1136 I 4374 The 95% acceptance interval for hypothesis Of underlying exponential distribution is given by: 101104 : l.96(4374) . 101104 t 3575 Acceptance interval I 92529 to 109679 Observed sum is 116358; This number is outside the acceptance interval. Therefore, null hypothesis must be rejected at the .05 I'- level. 59 section. Because of the nature of the Tetal Lives Test, a variety of curves can fall within the 95% confidence limit. Calculation of the sum of durations allows a large deviation in one time unit to be cancelled by a small contribution from another time frame, SO that the sum of total lives is not affected. Epstein also included tests for determining the type of deviation respon- sible fer a nonlinear result. There is a test for abnormally early failure; a test fer long first failure; a test fOr mean life fluctuation; and a test fer abnormally long periods with no failure. These tests will prove useful in analysis of specific fossil lineages which Show systematic deviation from linearity. Similiarly, taxonomic patterns produced by the Simulation model can effectively be analyzed using these procedures. . I I I. l .l‘ .. Illa-II ANALYSIS OF SIMULATION RESULTS The following sections summarize the principal categories of output produced by the simulation model. A detailed listing of the computer program is included in Appendix B. Units on parameters in different runs of the program are arbitrary, and actual values fer the parameters are significant only when compared to values for other runs. Starting points for the random number generator were varied in repeated runs under the same boundary conditions so that effects of this change could be monitored. For all of the data used to illustrate systematic results of parameter changes, a minimum of five (5) separate runs were made to verify the results were repeatable. Precision remained high in the duplicate runs, except as noted, and no problems were apparent from this source. Effect of Competition Intensity Operator induced changes in intensity of competition produce systematic changes in the survivorship curves. Three survivorship curves produced by runs with DSURV equal to .001 fer I, .005 fer II, and .008 for III are shown in Figure 5. All other parameters were held constant for these runs. DSURV is the variable which designates the survival value for an 60 61 x DSURV X __-_- .001 °\ x‘ -o—o- .005 ...... 3.3, \ ‘1 °. X 1 ’1 X \ \ 2‘ \ X “_-\~— x \ A \ \\ >. \ <2 x\ \\ fie X \ 1-= \ 1L2 OIL “ \ x.- 10'1- \o \ 11.1.5 1“ \ g2 X0 ‘ :3 m I 1 1 2E 1 1 \ 5 1 ° . 1. 1 ’1‘ 1 \ O 1 ' 1 1 1 \ \ X‘ ‘ 1 \ 1 1 \ 1 1 x O \ \ 1 \ \ 1 \\ \ | \ \ l I A A- \au\l\ ‘ a . r ...- , 10 20 30 4O DURATION Figure 5. Survivorship curves for varying levels of competition - selection. 62 increment of fitness space. When DSURV is set at .001, the difference in survival potential fer two consecutive species positions is small, compared to a DSURV value of .008. A larger value for DSURV produces a situation where Species position, relative to the fimness optimum is more important, analogous to conditions of increased competition. Because position relative to the fitness optimum ultimately controls the fate of a group, the DSURV variable is one of the most important parameters in the program. Change in the shape of the survivorship curve from convex(l) to curves II and III, with increased S10pes and more nearly constant age-Specific extinction rates results from several factors. In curve I (DSURV I .001), intensity of competition was low and individuals surviving five generations had a high probability of surviving 20 generations. Extinction and Speciation events were rare, resulting in a relatively Stable population. After a taxon persisted for 25 generations, the extinction rate - probability of extinction increased rapidly as Shown by the very Steep slope for durations of 25 through 40 generations. This increase in slope occurred because under relatively Stable fit- ness conditions, the total population grew Old as a unit. In this particular case, age and time are almost coincident, and the age axis can be thought of as a time axis. After approximately 20 generations had passed, competition had finally reduced the number of individuals in the less favored groups to the 63 point where extinctions began to occur. Whenever species density is reduced by extinction, speciation probability increases. As new species appeared, some of their locations in fitness space placed them in more favorable survival positions. This tended to increase competition and cause the extinction of some of the longer-lived groups. The other survivorship curves in Figure 5 illustrate conditions of higher extinction rates throughout the entire run. DSURV values of .005 and .008 produce more intense com- petition between species, and speciation and extinction are common events. The tendency toward constant survivorship ob- served in curves II and III occurs because there is no waiting period for competition to reduce the number of individuals in the less favored species to the extinction level. Competition is high enough to reduce numbers rapidly, and many groups are near extinction levels after surviving only a few generations. As soon as extinction occurs, probability of speciation increases and a static equilibrium is established. The trend toward in- creasing concavity with increasing competition suggests that species with durations greater than some minimum duration (where the curve becomes sub-parallel to the duration axis) have an increased probability of avoiding extinction, whereas those with shorter taxonomic durations have a higher probability of ex- tinction. Because studies of taxonomic survivorship remove the 64 temporal effects and concentrate on age-related evolutionary processes, it is important to note that indirectly, temporal processes still influence survivorship patterns in specific cases. We would normally look to intrinsic age-related factors for explanation of survivorship trends, but this additional source of information must be considered, together with biases inherent in sampling the fossil record. If the patterns shown in Figure 5 have general application to fossil and living taxa, it is possible that unstable taxonomic groups undergoing changes in survival potential tend to produce taxonomic survivorship curves with higher slopes and more nearly constant mean rates of extinction. Stable groups tend to exhibit non-linear survivorship curves because new taxa have a higher probability of successfully claiming their share of the resources. This is shown by the flat-topped upper portion of the survivor- ship curve observed under stable conditions. If the time axis were used instead of duration, the flat portion of the curve would represent a period of static conditions during which ex- tinctions were low-frequency events, followed by a time of more frequent extinctions as competition effects reached levels necessary to produce dynamic population conditions. It is apparent that a simple change in one input variable produces widely different results. Because these changes are reasonable, an indirect check on the Operation of the simulation model is provided. 6S Survivorship curves show changing survivorship with taxonomic age but do not give a temporal picture, except in the situation where time and taxonomic age happen to correspond. To better represent changes through time, Figure 6 is a plot of the per-cent of total extinctions occurring in eight consecutive five-generation time periods. The approximate constancy of the extinction rate through time for the high competition situation can be contrasted with the extreme variability in the extinction] time for the low competition boundary conditions. Cladograms can also be plotted to show the temporal development of taxonomic groups. Figure 7 is a series of cladograms, with numbers 1 - 5 produced under conditions of low competition(.001), and numbers 6 - 10 produced under high competition(.008). Several general observations can be made. The low-competition conditions produce no activity for over half of the run, and then only very con- servative diversification occurs. In the high-competition situation, diversification and extinction occured after only a few generations. Then one very successful group became dominant for the remainder of the run. The high-competition conditions allowed one well-positioned group to gain control of the resources (fitness space) early in the run, and all further diversification and extinction occured within this monophyletic group. 66 -O- DSURV ' .OOI ~x- DSURV ' .008 o I \ I \ I \ I \ “z” I \ 2 ’ b 5 I \ z , I \ F: ’ ‘ >< I .. , ,2: I a! 0" 1"] \ ’x I, I \\ / no 2': go is 30 TIME Figure 6. Temporal pattern of extinction for high(DSURV - .008) and low(DSURV - .001) competition. .mcoMumvcou newuwueasoqumcoucm you mommau o>Mumucumouoo¢ "o— n o mmowumucomouno¢ "m I H mmcwumucomomao¢ "cu . e mmnmumucomomno¢ ”m u u mmo ARE THE COORDINATES OF THE SPECIES CENTER FOR SPECIES l, STOX, vax, ETC. ARE THE COORDINATES AND STANDARD CEVIATIOU FOR THE POSITION 0F THE FITNESS OPTIMUM. THEY Ant USFD TO GEIERATE THE NORMAL CURVE WHICH IS USED To RANUOHLT DAODUCE 4E: FITNESS OPTIMUM POSITIONS. YSTL, YsgL, {SFL ARE THE VALUES USED FOR DIRccTEO MOVEMENT OI THE FITNESS DPTINUE POSITION. SINULATING DIREG'IONAL MOVEMENT OF THE ENVIRONMENTIPITNESS OPTIMUM). ARFA, OAREI. AND NAREA ARE USED To CONTROL THC SPECIES DENSITY. DEAD 181. IRANF.MINNOIDSURV.AREA.DAREAINAREA RiAD 1fi2, CIRECT,STox.ENVX,STDY.ENVY.SIDE.£sz REAC 103. NSPEC.DSPACE.XUNIT.YU~IT.2UNITICLOIST HEAD 1940 XSELIYSELIZSEL READ 1P5, thu.vx1,vx2 READ 1060 (SPECIE(10J)0J'1027I ‘VSUR'.25 AIIDPSBBU CO 1 IIZINSPLC 00 1 J31027 SPECIE(XIJ)=SPECIE‘1OJ) 00 2 IFIINSPEC CONTINUE 94 >>)))>>)>>>)’>>>)),>>>)>>>)>>>)>>’>>,’>)>’>’))’>D, ‘Ofl%hflwfififlflflthhrl Io¢m~A0\ranauuoe K 8 pa ROOQOODONF uremicn:xrcwlvn: NOO\OULU~“ c000! C Co... Cooo| 000. c009! Coco! Co... OA’ cel't COO... 95 PPDCRAH PEPRD IIHPUT.DUTPOT.TAPEDI-IHPUT.TAPEDI-oUTPuTI RE‘D 197A (!X(‘)OJX("A!Y(I,CJY‘I)0!!“’0Ji(l,o"1027’ RE‘O 193. II‘ICLAS(IlJoKivKiioS’.Jl103’o‘lloS’ RANDOM NUHBER GENERATOR FOLLOHSo CALL RANSET (FLOAT(IPAHFII Do 3 HH.1.NSPEC VINOIMHIIBB CANONIHH)I75 ASPECPsAg CONTINUE COORDINATES FOR SPchES CENTERS. AND DISTANCE BETWEEN EACH PAIR OF SPECIES ARE CALCULATED In THE FDLLOHIHC STATEMENTS, COORDINATES or SPECIES ARE LOCATED BETWEEN A AND DSPACE. DIS IS THE DISTANCE PETHch EACH SPECIES PAIR. CO 6 I'1.NSPEC AGEIIIBI. CONTINUE p1agAuVIv1) RZIRANFI-l) 93=RANPI-1I IaiuRIOInSPACE-SIAZ IRZIRZOIOSPACE-3)+2 IR38930(OSPACE-3)02 X(1)81R1oxtNIT YIIIaIRZOYUNIT ZIIIPIR3PEbNIT IF'II.ED.1) CD To 6 «HAX'I-l DO 5 J31.JHAX DIS-«(XIII-X(J))-020(YIIT~YIJ))O'20I!I|)-!(JI)002)-0.5 DIS LESS THAN CLDIST '- SPECIES IS NOT ‘LLOHED IN THIS POSITION. RELOCATE THIS SPECIES. IF (015.570CL0187) GO TO 5 60 TO 4 CONTINUE CONTINUE DO 16 I=1oNSPEC J'0 00 9 1‘3103 00 8 JJ'103 DO 7 KK'103 JIJ+1 PDLLOHIHC STATEMENTS CALCULATE COORDINATEI'PDR 27 CLASSESL THESE CLASS POSITIONS ARE FIXED AFTER SPECIES CENT!" ’>)1DIMDIDDJDID’IDJD’IDIP’IDDP’IDI'D}.)VDIbfiVDID’dblhfilbfiHblb)EDI-’WDJD,WDIP)I>,PD 96 PROGRAM REPRO IINPUT.OUTPUT.TAPEOO-INPUT.TAPEOIIOUTPUII C.... HAs BEEN LOCATED. A 191 c A 192 CORXII.JIc¢xIII-XUNITIoIII-1I-XUNIT A 106 CORY!an’lIYIII-YUNIT)¢(JJ~1"VUNIV A 194 0092‘I.JI:I2¢I).!UNIT).IKK-1"10NII A 199 7 CONTINUE' A 199 o CONTINUE A IN? 9 CONTINUE A 19a 10 CONTINUE A 199 C A 11C COCO. l" LOOP ‘s T“: GENER‘YlON LOOP ‘ 1‘1 C A 112 00 86 IHa1.NGEN A 113 FR‘NT 1390 I" A 1!! C A 115 C...I JH LOOP TAKES SPEcIEs THROUGH REPRODUCTION AND CANALIIATION A 116 C A I DO 37 JHIIINSPEC A {is If (NIND(JPII 37.37.11 A 119 11 CONTINUE A 129 COUNT-O. A 121 Klfl A 122 OO 13 J'1o27 A 125 OLOSPCTJH.JI-SPECIEIJH.JI A 124 IE ISPECIEIJH.JII 13.13.12 A 125 12 K'K’i A 126 PARIKIxSPECIEIJH.JI A 127 CLASSIKTIJ A 12C SPECIEIJM.J).z A 129 13 CONTINUE * 19° C A 141 c.,., THE POLLDUINC sTATEHENTs ARE THE CANAleATION PORTION OF THE A 132 3.... PROCRAP, USED ONLY IN THE sEcONo HODE OF OPERATION IHOOE III. A 135 6.... HHCU A SPECIES IS HITHIN A FIXED DISTANCE of THE FITNESS A 114 C.... OPTIMUM FOR A pRESET ”ORDER OF 1TERATION5. THE NUMBER OF CLASS A 193 c.... AVAILARLE FOR OCCUPATION IS DECREASEO. THIS IS AN ATTEHPT To A 1S6 C.... 5!"ULATE THE DEVELOPHENT or SPECIALIEED rORHSIPHENO AND GENOI- A 1O? c.... AND SUCCESTS THAT STABLE RESOURCE CONDITIoNs HAv PRODUCE A A 138 6.... DECREASE IR GEAETIC VARIABILITY AS PRoPosED BY BRETSKY A 199 Coco! ‘ND LOQENT2(1970)I A 130 C..., THE DUESTION AS To THE NATuRE 0F TH: LINK BETHEEN PHENOIYPE A 131 c.... AND GENOTYPE HUST RE AnDREser. IF THE LINK Is ASSUHEO To BE A 132 C.... DIRECT. THEN CHANCES AT THE PHENO TPE LEVEL IN RESPONSE TO A 126 C.... SELECTION PRESSURE HILL HAVE IHHEDIATE EFFECTS AT THE CENOTTPE A 14¢ 6.... LEVEL. IT IS POSSIBLE. HOHEVER. THAT TH; HDRE COMMON A 135 C.... SITUATION Is THAT ALTHOUGH PNENOTYPIC VARIADILITV A 136 c.... DECREASES. THE CENETIC vARIARILITT IS HAINTAINED DUE TO THE A 137 C.... DEVELOPMENT OF CANALIEED TRAITS AND CHARACTER coMPLEXES. A 138 C.... A THIRD ALTERNATIVE Is SUGGESTED 8T VALENTINE AND AVALA<1975T. A 139 C.... THEY PROPOSE THAT A SPECIES IN STABLE RESOURCE CONDITlous IS A 1:. Con... Co... 14 15 16 17 18 19 2O 21 CC... c0090 Co... C.... 00'! c0000 97 PROGRAM REPRO IINPUT.OUTPUT.TAPEoC-INPUT.TAPEA1-OUTPUTI MORE LIKELY TO EXHIBIT HICH VARIADILITT DUE TO MANY HAYS TO MAKE A SUCCESSFUL LIVInG. TOTAL DATA IS IncoNCLUSIvE. IF (CANONIJHIoLTo75I GO T0 20 IF (CANONIJHI.EO.7OI CD To 14 IE (CAFONIJH).EO.77I CD To 15 IF (CANONIUHI.EO.7OI Go To 16 IF (CANONIJH).E0.79) GO TO 17 IE ICANONTUHI.EC.OOI CD To 18 IE (CANONTJHI.EC.O1I CO TO 19 Go To PC OLOSPCIJH.1I"1 oLnSPCIJHI2TII-1 OLOSPCIJN.7Iu-1 OLOSPCIJMI21I'-1 Go TO 20 OLDSPCIJH.19I=-1 OLOSPCIJH.9Iu-1 OLDSPCIJH025I'-1 OLDSPCIJfloa’U-1 CO-TO 20 OLDSPCIJM.2I"1 OLOSPCIJM.26)P-1 OLDSPCIJM.RI--1 OLDSPCIJH'20)I.1 Co To PC , OLOSPCIJH.4)n-1 OLOSPCIJHIZZIao1 OLDSPCIJHIGII'l OLDSPCIJH.24II-1 ’GO T0 ?0 OLDSPCIJHolflI'II OLUSPCIJHA18)8-1 OLUSPCIJM012)'-1 OLDSPCIJ"016)"1 GO TO 70 CLDSPCIJH013I3-1 OLDSPCIJ"0151'-1 CONTINUE CONTINUE PDTEITIAL PARENT CLASSES ARE ISOLATED. IE GENDTYPE AND PHENOTva HERE NOT DIRECTLY RELATED. ALL CLASSES COULD ACT AS PARENTS. THIS HOULD ALLON HIGHLY CANALIEEO 8P£CIES TO UTILIz; THEIR INHERE~T VARIARILITT AS HAVRI1963T SUGGESIS THEY ARE ABLE TO DO. THO PARENTS ARE CNoSEN FOR REPR00UCTION DO 24 Nlloz RQIRAN'Iil’ ’fi”””"D”’)))’DD’>D)),)’,’D”’),,,,’D’D,’>>>>D 22 CO.;‘ CRIS. C Co... C 23 2‘ C...’ 6000'. COCOS 60.0. C...‘ COCO. C C.... Co... Co...- Coco! CCCII Co... CC... COCOA C 98 PROGRAH REPRo IINPUT.OUTPUT.TAPEOO'INPUT.TAPEOI'OUTPUII IRANo-RQCININDIJNI-1I01 SUHae, KIM NIKOi SUMIPARIKIOSUH HHEN IRAND Is LESS THAN SUH. PREVIOUS CLASS CONTAINS THE INDIVIDUAL PARIK). IF (IRRND-SUN) 23.23.22 FOLLOHING STATEHENT IOENTIFIES PARENt AS BEING FROM CLASS K. PARENTINICCLASSIKI CONTINUE IIIBU JJJIH KKK-fl THE-SO LOOP COMBINES PARENT GENOTVPES RANDONLV To PRODUCE THE OFFSPRING GENOTYPE. 00 34 H.102 PARENTINI IS THE CLASS TO HHICH PARENT N RELONCS. INT-pARENTINI NT RUNS FROM 1'27 XIIJO E1CO ARE READ IN AND ARE IN: CLASS NOTATIONS FOR CLASSES 1 ' 27A X1!IXIINT) X2=JXIINTI Y18I¥IINTI Y2=JYIINTI 21=I?IINTI PZIJEIINT) IE Ix AND JX ARE THE SAME VALUE. GENL x I5 GIVEN THIS VALUE. SIHULATING THE HOHOZYCOUS STATE. IF Ix AND Jx ARE UNEDUAL. A RANDOH NUHBER Is CHOSEN. IE THE RANOOH NUHUER IS LESS THAN .5. THE X; VALUE IS ASSIGNED To GENE x. If THE RANOOH NUHDER IS GREATER THAN .5. THE X2 VALUE 18 ASSIGNED TO GENE X. LIKENISE EOR GENES Y AND 2. If (X1.EO.X2) GO TO 26 RXIR‘NF(¢1’ )2>lbfiflbIhfilhivfilD)HDI>,3b)R>IDIP)JD)WD)D,IDIP’ID)DDID)DDID,IFID)D)ID)DfiltiDID)ID 291 2u2 293 209 2C: 296 297 298 229 21c 211 212 215 214 215 216 217 21C 219 22C 221 222 226 224 225 226 227 228 229 290 2&1 2S2 293 244 2S5 399 297 268 239 240 231 232 241 244 235 246 240 259 22C 25 26 27 28 29 39 31 32 33 C Co... C C C.... Cg... Co... C 34 C C...{ 00.. Co... C 99 PROGRAh REPRD IINPHT.OUTPUT.TAPEODAINPUT.TAPESIsOUTPU!I IF (RX.GY,,5) 60 JD 25 GENEX'Xl GO TO 27 CEMEXIXZ GO To 27 GEUEXOXi CONTINUE IF (Y1.ED.Y2) GO ID 29 RX.R‘~F‘I1’ IF IPX.GY..5) 60 To 23 GENEYSY1 GO TO 30 GEUEYOYZ GO TO 30 GEHEYIY1 CONTINUE IF (21.E0.223 60 T0 32 RXSR‘NF(O1’ IV'IRX.GT..5I 00 To 31 GENEilll GO TO 33 GENEEIZZ GO TO 33 GE1E7I21 CONTINUE VALUES FOR GENE x. GENE V. AND GENE 2 HAVE BEEN ODTAINRD. GEJXINI=GENEX DENYINI=CENEV cEHZINT=cENEz PREVIOUS THREE STATEMENTS STORE GENOTVPES OE PARENTINI. FOLLDHINC STATEMENTS SUH GENDTYPE VALUES FOR EACH COORDINATE SO THAT CLASS IDENTIEICATION Is POSSIBLE. III=III*GENXINI JJJIJJJ*GENYIN) KKK-KKK45ENZIN) CDVTINUE III-11191 JJJIJJJ01 KKK-KKK41 OFFSPGIICLASIIIIAJJJ,KKK) IF OFFSPRIKG Is NON-VIADLE. MEANING IT DELDNGS ID A CLASS ASSIGNED A -1. PROGRAM RETURNS '0 STATEMENT 40 AND GENERATES THD NEH PARENTS . ‘7 (OLOSPCCJHIOFFSPG77 21035-35 DID’IDfilbfilD’lb>lbDl>>JD,Ibblbfidblb)lb’3.’JN>I>>ID’ID’ID)JD)JD)ID’WDDJD>ID, 292 2v: 2y2 223 2V9 225 2go 2?? 29a 229 39D 39 C C.... C 900'! C 36 37 C Co... C.... 00'. CO... C...‘ C C COCOS COCO. C 38 39 C Coo... C...‘ C 49 100 PROGRAM REPRD IINPuT.DUTPUT.TAPEbo-INPUT.TAPE61IOUTPUII CONTINUE COUNTICOUNIO1 SPECIEIJH.0FF5PGI'SPECIEIJH.0FFSPG’01 PREVIOUS STATEHENT SUNS NUMBER IN OFFSPRING CLASS I? (COUNT.LT.NIND(JHII GO TO 21 RETURN TO BEGINNING OF REPRODUCTION FDR SPECIES 2. DO 36 381.27 IF IDLDSPCIJN.JI.ED.41) SPECIEIJN.JI'-1 COVTINUE CouTIUUE Ir (DIRficT.LT.2) CD TO 33 THE NORMAL SURROUTINE IS USED TO MOVE THE FITNESS OPTIMUM. THE COORDINATES OF THE PREVIOUS FITNESS POSITION ARE USED RS VEAN VALUES. AND STANDARo oEvnATloNS ARE READ IN. THE MOVEMENT or THE FITNESS POSITION HILL 9: PROBABILISTIC. NITH THE MOST PROBABLE HOVE A SHALL ONE FROM THE PREVIOUS POSITION. CALL NORMAL (ENVXo5TO‘3EX1) CALL NORMAL IENVV.STOV.EV1I C‘LL NORMAL IENV2.ST02.E21I GO TO 39 FOLLOHINC STATEMENTS ALLDH DIRECTIONAL NOVENENT or FITNESS DPTIRUN POSITION. ENVX!!NVX¢XSEL ENVY=E1VY¢YSEL ENV785NVFOISEL [XiaENVX EY1=CNVV EE1=ENV2 CONTINUE PRINT 11D. EX1.EY1.E21 ENVXIEX1 ENVY=EV1 ENV28E21 K30 FDLLDNING LOOP cALDULATES AVERAGE AND NAXIHuH VARIANCE PDR SPECIES roR USE IN CALCULATINC SPECIATION PRoRADILITV. MAXVARSO 00 45 3'10NSPEC IF (NIND(I)) 45.45.40 KIKO1 ’””DDD,”D,’)>D),),))DD)D)))>’)DD)))”>,)’DD,)" 391 392 393 3g4 30: 396 397 398 399 319 311 312 313 314 315 316 31) 310 319 32¢ 321 322 323 324 325 326 323 329 33C 331 332 333 334 33: 333 333 339 353 41 42 43 44 C...,' Co... Co... 45 CO... CD... 101 PROGRAM REPRD IINPHT.OUTPUT.TAPEOD-INPUT.TAPE61-OUTPUTI SPEcTKI-I J80 5X88 SY'B 52-0 SUHXZOD SUMYzlP SUHizsn DO 42 J'1027 IF ISPECIEII.JI) 42.41.41 Sx.SPECIE(I.JIODDRXII.J).SX SY'SFECIEIIIJ7.CORYII.J7OSY $2=SP£CIE(I.JIOCDR2(I.J)032 CONTINuE XBARISXININOII) YRARISV/NINDII) zaARPSP/NINDII) 00 44 J81327 IF (SPECIEII.J77 44043043 anchDRXII.JI-XBAR YDEVICGRVII.JI-YBAR zu:v-CDR2.I.J,-29AR SUNXasXDEVOXOEV'SPFCIEII.JT°SU"32 suwvzgvoEV4VDEV-SPECIEII.JIoSUNVZ SU422=20EVOZDEVGSPECIEII.JI‘SUH22 CONTINUE ‘ VARanUHXZIININDIII'gI VARY=SUNY2IININOIII-1) vAnztsuHBZIININDIII-1I SDXSSQRTIVARXI SOY-SDRTIVARV) sPEssuRTIVARz) AVEVARII)sISonsoyosnles DVARaI14VX14AV£VARIIIocvsz FDLLoNING STATEHENT CALCULATES DISTANCE REIHEEN SPECIES CEnTER AND FITNESS OPTIMUM. DISTANcE IS STANDARDIEED FOR INTERNAL SPECIES VARIADILITV aY oIVIDING DV THE AVERAGE VARIANCE. DIST(KISSDRTI(XIII-ENVX)0020IYIII-ENVYI'OzoIZIII-ENVEIO'2I/DVA R DISTSIRI'DIST(KI IF IAVEVARIII.CT.NAXVARI NAXVAR-AVEVARII) CONTINUE SORT IS A SUBROUTINE “RICH ORDERS THE DIST(K) FOR SPECIES PRESENT FROM CLOSEST TO FURTHEST FROM THE FITNESS OPTIMUM. CALL SORT INSPECP.DISTI DO 49 KIg.N3PECP ’JD)JD,ID’IDFID,ID)ID’ID>I>>,>,IDDW>)DDILDID)ID’ID))IDID’IDDID>I>)ID’I>))D) 3:1 3:2 4?4 3:4 3:5 3:3 3;" 3:8 3?9 49' C..’..‘ Co... C 46 47 Cogo. 09.. D... 48 49 c990. c4490 Co... COCO. c499| c9900 c4900 59 51 52 Coco]. Co... C 53 102 PRDCpAH nEPnD IINPUT.DuyPur.EAPEGCIINPut.TAPE61IOUTPUT’ DO 46 KK'1.NSPECP Ir THE FDLLONINC STATEHEnT IS TRUE. TRE KK VALUE IDENTIFIES THE PDSITIDN or THE HTH SPECIES IN THE SEDULNCE. IF (DISTSIKI.E0.DISTIKKII 60 T0 47 CONTINUE POSITINI'KK LlaSPECIK) POSITIK) IS THE POSITION or SPEcIES RELATIVE To THE FITNESS DPTIHuM, IF THIS VALUE IS LESS THAN 19. CANON VALUE IS INCREMENTED. IF IPDSITIRI~1DI 48.49.49 GANDHIL1T'GANONIL1I41 PRINT 111. SPEcIKI.CANONIL1I Go Tn 49 CDNTINOE EOLLOHING STATEMENTS KEEP EOUILIDRIUM NuMDER Or INDIVIDUALS 8V SETTING UPPER AND LONER LIMITS 0N THE NUMBER ALLDNED. THE CUTBACK OR INCREASE IS NOT IMMEDIATE SINcE THE CONTROL IS SET So THAT HHEN THE NUMaER FALLS TOO L0H. THE SURVIVAL PERCENTAGE OF THE AVERAGE FITNESS POSITION IS INcREASED. THIS KEEPS THE NUMRER or INDIVIDUALS NITMIN A RANGE OF THE CHOSEN NDHDER. 00 SR K'loNSPECP L1ISPECIK) NINDSIL1TSRINDIL1I CONTINUE NTOTALSAREAONIUDPS NHIGH:1,25'NTOTRL NLOH..75.NTDTAL RT.” TINT-NSPEcP/2 INTINSPECP/2 IF (INT [0 TINT) 0° TO 51 Go To 52 CSPECSNSPECP/Z GO TO 53 CSPECINSPECP/2‘1 FDLLDN NG STATEHENTS DETERHINE FITNESS Of SPEO.ES ASSUHING AVERAGE EITNESS IS 25 PERCENT. FITSP-AVSUR.ICSPEC'IIIOSURV NTcNTOI PRINT 112. IH.RVSUR >D))’),’>.D))’)D,)D)fi,’,fiDD),)’,D”,,>D)D,),))’,), 491 492 493 494 495 493 497 49a ‘99 41! 411 412 413 414 415 416 417 416 419 4;: 421 422 423 424 425 426 427 429 429 439 431 432 433 494 439 436 437 433 439 44C 441 452 443 444 455 436 447 450 499 499 c.... 6.... 54 Co... C....' 55 COOO. CC... 56 57 98 59 Co... C.... COOOQ 60 103 PRocRAM REPRo IINPUT.DUTPUT.TAPEGOIINPDT.TAP561-DUTPU!’ DO 54 KOUNT'1ONSPECP KOKOUNT-l NEXT STATEMENT ESTABLISNES SURVIVAL VALUE OF EACH SPECICS POSITION RELATIVE TO FITSP, THE BEST ADAPTED SPECIES. NK-SPECIKDUNT) SURVIKOUNTIOFITSP-(KODSURV) CONTINUE SUMN-3.5 NDIC'D TRIS LOOP CALCULATES THE NUMBER OF INDIVIDUALS IN EACH SPECIES PASEO ON PERCENT SURVIVAL FOR THEIR POSITION. DD 55 K41.NSPECP L1=SPECIKT LZIPOSITIKI HINoIL1I=SURVTL2144ONINDSIL1I SUMNSSUHNoNINDILII IE IVINDIL1T.OT.NDIGI NaIG.NINoIL1I CONTINUE ' FOLLOWING STATEMENTS INCRENENT PERCENT SURVIVAL BASED ON NUMBER 07 INDIVIDUALS PRESENT. IF INT.EO.2) GO TO 58 IF (SUHN.LT.KLONI GO TO 56 IF ISUHN.GT.NHICHI GO TO 57 GO TO 58 AVSUR-AVSUR*.01 GO TO 53 AVSURsAVSUR'.D1 GO TO 53 CONTINUE PRINT 113. NSPEcp PRINT 114, SUMN no 59 H81.hSPECP L1=SPECIKI LZSPJSITIKI PRINT 115O L1.NIND(L11.SURV(L27 CONTINUE CLASS LEVEL SELECTION PDLLONS --- CLASSES HITHIN SPECIES ARE NON ASSIGNED HENDERS BASED ON RELATIVE DISTANCE FRCN FITNESS DPTINUN. DO 69 IO1.NSPEC IF (NIND(I)) 69.69.60 K30 ’>>§§)’D’>>”D,’>>D>’D)>””DD’>)FD)‘>)’))”’)DDD)) 421 491 492 495 396 491 495 499 S99 61 C c...‘ COOVD 62 C 6.... CO... C 63 C C...O Co... 64 69 66 C GOOD.- CO... C 67 C CQQO. COOO‘ C 104 PROGRAM REPRo IINPUT.OUTPUT.TAPE6DIINPUT.TAPE61800TPUI’ DD 62 3-1.27 IF (SPECIEIIOJII 62061061 KCKO1 . OCCUPIKI RECORDS NUHBER OF INDIVIDUALS IN CLASS K. CLASSIK) CONTAINS TNE CLASSES NHIGH ARE OCCUPIED. CLASSIKIIJ OCCUPIKIISPECIEII.JI SPECIEIIOJI'R CONTINUE Do 63 IIPIOK K1-CLASSIIII CALCULATE DISTANCE PROH EACH CLASS T0 ENVIRONMENTAL OPTIMUM POSITION. DISHSIIII-SDRIIICDRXII.N1IoENVXI0024ICoRVII.K1I-ENVV19'20ICD R2II.K1I-ENV2I'02I OISTHSIIIISDISHSIIII CoNTINUE CLASSES ORDERED FROM CLOSEST TO FURTHEST FROM FITNESS OPIINUN BY SORT. 'CALL SORT TH.DISHSI DO 66 II=1.K 00 64 III'IOK IF (DISTNSIIII.EO.DISNS(III)I 60 To 65 CONTINUE POSTIIII'III CO‘ITINUE SUN.” SUHZCO. rDLLOHING STATEHENTS CALCULATE NUMBER IN EACH CLASS AFTER SELECTION. Do 37 II=1.H SUHSSUH*OCCUPIIIIO4 suwz.SUM2.IPDST(III-110.01OOCCUPTIII°4 CoNTINUE CONST IS THE VALUE NHICN ASSICNS CORRECT NUMBER OF INDIVIDUALS TO EACH CLASS. CONSTRININOIIIOSUN27/SUN 50".”. SUNZ'O. DO 60 II'1OK :91 >92 >93 >94 >99 :96 by? :99 ’99 S19 511 :12 :13 :14 91: >13 51? 519 519 929 S21 S22 :23 :24 925 >26 :27 >29 :29 :39 :91 932 :33 >34 :3: 593 :37 >30 >39 :49 S41 :32 >33 :34 >45 :56 b4? 513 :39 SOD C CO... C 68 69 C CO... CO... COCO. COOP. ngo! Co... C 7a 71 C COOOI CO401 COOP! C 72 C CO... C 73 C Co... Co... COO'I C 74 105 PROGRAM REPRo IINPUT.ouTPUT.TAPEoooINPUT.TAPEOIaoUTPUII JIICLASSIII) SPECIETI.J1T-4'DCCUPIIIIOIcONST-TPDSTIIII-1IO.D1I SUM coNTAINs THE "UMBER or INDIVIDUALS IN SPECIEII.JI. SUHOSPECIEII.J1IOSUH SUM2OISPECIEII.J1I-OLDSPCII.J1’I'P2OSUN2 CONTINUE NINDIII'SUp DSPEC(I)'SUH2 CONTINUE NEXTCsH Do 71 I91,NSPECP L1-SPECIII FOLLUHING STATEMENT CONFARES THE NU"BEH 0F INDIVIDUALS 1U SPECIES TO A PRESET NINIHUN. IF THE NUMBER OF INDIVIDUALS IS SHALLER. EXTINCTION OCCURS. EXTINCTION Is NOT PROBABILISTIC IN THE FINAL STEP. BUT THE SPECIES HA5 VARIED PROBABILISTICALLY. AND THIS CONTROLS THE NUMBER OF INDIVIDUALS. IF (NIND(L1I-MINNOI 70.70.71 PRINT 116. L1.AGEIL1) NEXTC‘MEXTCP1 HINOILIIOD CONTINUE PRINT 117. IM.NEXTC FOLLOHINC IS THE SPECIATION PART OF THE MODEL. NAREA NEGATIVE INDICATES NEH AREA IS AVAILABLE FOR SPECIES COLONIZATION. OR THAT RESOURCES ARE INCREASING. IF INAREAI 72.73.73 AREASAREAODAREA NICSAT RFFLECTS THE SPECIES DENSITY. NICSATINSPECP/AREA ROUNT=3 DO 82 I'1.“SPEC IF (NINDIII.LE.2R) CD To 82 R3=RANFI-1) IF INICSATPR3) 74.82.82 PISOL IS THE FINAL THRESHOLD FOR SPECIATION - SPECIES HITH HIGHER RELATIVE VARIAOILITV ARE GIVEN HIGHER PROBABILITIES FOR SPECIATION. PISOL'AVEVARIII/NAXVAR fi))’)D’>)>)>D>D)’>))),fib)’D)”’>>D>>D’D)>))>>>>>D) >91 >92 >92 :93 :97 598 599 399 7’ COO... 0.... CD... CD... 76 77 78 C.... 79 DH 61 106 PROGRAM REPRO IINPUT.OUTPUT.TAPEOO-INPUT.TAPEO1-OUTPUTT R4IRANFI'1I IF IR4.PISDLI 75.82.82 KoUNTIRoUNTS1 NCNSPECOKDUNT RSSRANFI'lI R6ORANFI-17 R78RANFI'1I HER SPECIES CENTER IS LOCATED. XINIIXIIIPRSOtzoCLDISTI VIHIOYIIIOR6OI2OCLDIST) EINIIEIIT‘R7OI2OCLOISTI 46E("7'3O CANDNIM,P7S. PRINT 11BO IOH NEH SPECIES ARE GIVEN A NUMBER OF INDIVIDUALS EOUAL TO 49 PERCENT OF THE NUHDER IN PARENT SPECIES. NIND(H)O.4DONINDIII JOO COORDINATES DF CLASSES IN NEH SPECIES ARE ASSIGNED. DD 78 II-1.3 DO 77 33-1.3 DD 73 KK-1.3 JIJ+1 GORXIM.JI-TXIHT-XUNITIoIII-IonUNIT coRVIH.JI.IVIMI-VUNITI.I33-1T-VUNIT CONTINUE CONTINUE CONTINUE SUHGO ASSIGNMENT or OPEN AND CLOSED CLASSES FOR NEH SPECIES FOLLONS. RENO 1190 (SPECIEIMOJ’OJ'13277 PACKSPACE 39 BACHSPACE 69 389 NIDsVINDIHI DD 61 NI1.NIO J'J'l IF (JOGT0277 J'1 IF (SPECIEIN.JII 79.BI.BD SPECIEIN.JIOSPECIEIN.JIo1 ConflnuE IP)IDDP)I>DPDIPDHDIP,ID)P,I>DPDIDDP)I>’P)ID)P,IDID’IDIP>I>,P!1>’V’)>IDfiV’IP)-DID)I’ 391 312 °.§ O13 319 62B 321 322 323 624 625 .23 327 323 329 399 331 35¢ 82 C 0.... 83 B4 85 c o C.... COOP. C 86 C . COOOI COCO. CQQO. C 87 BO 59 99 91 92 107 PROGRAM REPRo IINPuT.oUTPUT.TAPEODIINPuT.TAPE61-oUTPUTI CONTINUE PRINT 126. IN.KOUNT NSPEC IS INCRENENTEO AS NEN SPECIEs ARE IODED. IF (KOUNT.CT.RI NSPEC'H COUNTSO DO 85 I'1.NSPEC IF (“IIDIIII °4084033 CONTINUE ACEIIIIAGEIIIP1 GO TO 85 COUNT-CoUNTO1 CONTINUE NUMBER OF EXTINCT SPECIES ARE TABULATED 4ND SUBTRACTEO FRO" NSPEC TO GIVE NSPEC? -- THE NUMBER OF SPECIES PRESENT. LSPECPINSPEC'COUNT CONTINUE THE FOLLONING STATEMENTS TABULATE THE NUMBER OF EXTINCT AND EXTANT SPECIES. AND THEIR DURATIONS SO THAT SURVIVORSHIP CURVES CAN BE ORAHN. PRINT 121 . DD 89 II1.NSPEC IF (NIND(I)) 87.87.88 PRINT 116. I.AGEIII CD To 99 PRINT 122. I.AGE(II CONTINUE PRINT 123 NCENRNCEN41 DD 93 J=1.NGEN CTNIJI=M.O EXTSPEC:G.H RIOAGEIU.O DO 92 I=1.NSPEC IF (NINDIII.EO.DI GO TO 91 60 T0 92 FXTSPECPFXTSPECPl IF IAGEIII.CT.BIGAGEI RICAGEaAGEIII JIAGEII) CTNIJIPCTNIJIO1 CONTINUE CUHFRQPO.2 DO 93 JP1.OIGAGE CUHFRQSCUNFROPCTNIJ) SPECRaEXTSPEC-CUMFRD )>)'DIDDPD2>’P’lb)%>lb)lbIP>)>)P)ID)PDJD)I>JD)-DJDFP)IDFP)ID)H>)P’P,O>'P>3D)P)I>)P) 3:1 322 3:3 324 335 3:3 3:7 399 399 338 399 691 392 693 694 695 696 697 693 699 7!. 108 PROGRAH REPRO IINPUT.OUTPUT.TAPE60'INPUT.TAPE61IOUTPUII PRINT 124, J.SPEcR.J.CTN(J) A 791 93 CONTINUE A I92 PRINT 125 A 793 DD 94 381.NGEN A 794 94 CTNIJIIU.O A 799 RIGAGE-g.g A 796 Do 95 I81.NsPEC A 797 IF (AGEIII.GT.DIGACEI OIGAGE-AGEIII A 798 J=AGEIII A 799 CTNI31.CTNIJI.1 A 712 95 CONTINUE A 711 CU”F"°‘9'" A 712 00 96 J81.RIGAGE A I13 CUHFRO=CUMFRDOCTNIJI A 714 SPECRanspEC-CUMFRO A 712 PRINT 124. J.SPECR.J.CTNIJT A 713 96 CONTINUE A 717 PRINT 126 A I18 00 97 JO1,NGEN A 719 97 ,CINIJ):0.0 A 722 BIGACE:9.g A 721 Do 99 I'IINSPEC A 122 IF (NINDIII.GT.D. GO TO 93 A 723 GO TO 99 A 724 93 IF (ACEII).CT.BICAGEI BICACEOAGEIII A 725 JIACEIII A I26 CTnIJI-CTNIJI01 A 727 99 CONTINUE A 723 CUMFRD=D.R A 729 00 1.36 J31.RIGAGE A 7.30 CUHFROSCUHFROOCTN(JI A 731 SPECR.HSPECP-CUMFRO A 732 PRInT 124. 3.5PECR.J.CTNIJI A 793 103 CONTINUE A 734 A 735 121 FORMAT (I5.IS.3FO.3.I5) A 733 122 FORMAT (7FO.1) A 737 163 FORMAT (7X.I7.5F7.2I A 738 134 FORMAT (3F7.27 A 739 125 FORMAT (13.2F6.1I A 742 126 FORMAT I16F5.a/11F5.HI A 731 127 FORMAT I49I2/4812/4OI2/40I2/2I2) A I32 123 FORMAT (26I3/I3) A 733 129 FONHAT I1R-.35RTHIS IS THE BEGINNING OF GENERATION.IST A 744 113 FORMAT I1Hp,4HEX1s,F7.2.4HEY1:.F7.2,6H £21.,r7.21 . 755 111 FORN‘T (1N-.7HSPECIES.F7.2.45H Is TN FAVOREO posITION ANo HAS CANo A 733 1‘3 VOLUE '0'7021 A ’27 1.2 FORMAT (.HO,12H GENERATION.I4.45H AVERAGE SURVIVAL RATE FOR ALL A 798 1 SPECIES -.F7.2) A 799 113 FORMAT I1HC.1DX.31HTHE NUMBER oF SPECIES PRESENT I.I4I A I?! 109 PROGRAM REPRo IINPUT.OUTPUT7TAP560-INPuT.TAPE61I0UTPU!’ 114 FORMAT I1Ma.10x.42HrHE NuHRER OF INDIVIDUALS IN SPECIE SPACE-777.0 1) 115 FORMAT (1H-,36HTHE NUMBER OF INDIVIDUALS IN SPECIES.14.39H AFTER 1 SELECTION AND REPRoDUCTION-715.29H SURVIVAL PERCENT 31*7.27 116 F0"”AT I1HR.IOX.7HSPECIES.IA.3R IS.F7.2.25H UNI 5 OLD AND IS EXTIN 1CTI 117 FORMAT (1Rp,1ax,49HTOTAL NUMBER OF EXTINCT SPEclES DURING GENERATI 10N31403H c.14) 118 FORMAT (1H0.10X.16HPAR£NT SPECIES c.14720H DAUGHTER SPECIE§ -.IA) 119 FORMAT I16F5.O/11F5.9) 120 FORMAT I1MO,10X,39RTHE NUMBER OF NEH SPECIES IN GENERATION,I4.1H-, 115) 121 ronMAT (1H1.32HRAH DATA FOR SURVIVORSHIP CURVES) 122 FORMAT I1HR.10X.7HSPECIESoI473H ISAF7o2724H UNITS OLD AND I? EXTAN 1T) ‘ 123 FoRMAT I1H1.1ox.52HTHE FoLLOHluG AuALYSlS lNcLuOEs onLY EXTINOT SP 1ECIES 124 FORMA I1HR.1BX.9HOURATION:.I4.29H SPEcIES REMAINING-.Fs.o.27u N 1UHn£R or SPECIES LASTING.14.13H GENERATIONS-.F7 o’ 129 FoRnAT (IR-.43HTHE FntL guluc AN A LYsIS INC 0055 AL Lt SPECIES) 126 FORMAT (1H1.51HTHE F0 L RING ANALYSIS INC Uocs 0N Y LIVING SPECIES 1) END )FD)’)>)’>,>)>’D)>)>D>) 7:1 7:2 7:3 7?4 7:5 156 7:7 [)8 7:9 771 772 773. C 110 Coco! SUPPROGaAH NORMAL I: USED To CIOQCE "RAHE'ERS 7"" I c...q NORHAL DISTRIBUTION RHIcu RA: srchFIco RFAR AND 5000. SYINO‘RO D‘V""°~. C Coco.‘ Cogof C 1 5 Q 5 SURROUTINE NORMAL (£X.3IDX.X) SU"IJ. 00 1 I'1712 RUIRANF(-1) SUM-SUNORO CONTINUE X'STOXOISUN-6.IIOEX RETURN END SUBROUTIVE SORT (N.X) DI"ENSIOV XIZQg) TNYEGER BOTOHA HICHleN REAL XAT FORTRAN SUBPROGRAH FOR ORDERING SPECIES AND cLASSES FRO" FITNESS oPTIHUH. BOTOHaN-i SHICHI1 ' 00 5 I'1ABOTOH IF (XIII-X‘I‘ll) 303:2 TIXIII ‘ XI1)'X(%01I XII'II' SRICHRI CONTINUE IF (SHICH-i) 4.50‘ QOTOHOSHICH-i GO TO 1 RETURN END OOOOOOOOOOOOOOOGOGOOO O H . .ODNOUOONH uniwm anon. 134- ODVOU‘AUNN LIST OF REFERENCES LIST OF REFERENCES Anstey, R. L., and Pachut, J. F., 1976, Morphogenetic field dynamics in the development and evolution of Paleozoic bryozoans: In review. Ayala, F. J., Valentine, J. N., Hedgecock, D., and Barr, L. 6., 1975, Deep-sea asteroids: high genetic variability in a stable environment: Evolution, v. 29, p. 203-212. Bonner, J. T., 1974, On development - the biology of form: Harvard University Press, Cambridge, Massachusetts, 282 p. Boucot, A. J., 1975, Evolution and extinction rate controls: Elsevier Scientific Co., New York, N. Y., 426 p. Bretsky, P. N., and Lorenz, D. N., 1969, Adaptive response to environmental stability: unifying concept in paleoecology: Proc. N. Amer. Paleontology Conv., Part E., p. 522-550. Brues, A. N., 1964, The cost of evolution vs. the cost of not evolving: Evolution, v. 18, p. 379-383. Carson, H. L., 1968, The population flush and its genetic conse- quences: In R. C. Lewontin, ed., Population biology and evolution, Syracuse Univ. Press, Syracuse, N. Y., 205 p. Carson, H. L., 1975, The genetics of speciation at the diploid level: The American Naturalist, v. 109, no. 965, p. 83-92. Crosby, J. L., 1963, Evolution by computer: New Scientist, no. 327, p. 415-417. Crosby, J. L., 1973, Computer simulation in genetics: New York, N. Y., John Riley 6 Sons, 477 p. Eldredge, N., and Gould, S. J., 1972, Punctuated equilibria: an alternative to phyletic gradualism: In Schopf, T.J.M., ed., Models in paleobiology: San Francisco, Freeman, Cooper, and Co., p. 82-115. Epstein, B., 1960a, Test for the validity of the assumption that the underlying distribution of life is exponential: Part I: Technometrics, v. 2, no. 1, p. 83-101. 111 112 Epstein, 8., 1960b, Test for the validity of the assumption that the underlying distribution of life is exponential: Part II: Technometrics, v. 2, no. 2, p. 167-183. Foin, T. C., Valentine, J. N., and Ayala, F. J., 1975, Extinction of taxa and Van Valen's law: Nature, v. 257, p. 514-515. Fossil Record, The: see Harland, et. al.(1967). Fraser, A. S., 1957, Simulation of genetic systems by automatic digital computers I. Introduction: Aust. J. Biol. Sci., v. 10, p. 484-491. Fraser, A. S., 1960, Simulation of genetic systems by automatic digital computers VI. Epistasis: Aust. J. Biol. Sci., v. 13, p. 150-162. Fraser, A. S., and Burnell, 0., 1970, Computer models in genetics: New York, N. Y., McGraw-Hill Co. 206 p. Hallam, A., 1976, The Red Queen dethroned: Nature, v. 259, p. 12-13. Harland, N. 8., Smith, A. G., and Wilcock, 8., 1967, The fessil record: Geol. Soc. London, London, 828 p. Hawkins, 0., 1964, On chance and choice: Reviews of Modern Physics, p. 510-517. Kitts, D. 8., 1974, Stochastic models of phylogeny and the evolution of diversity: A discussion: Jour. Geology, v. 83, p. 125-126. Levins, R., 1966, The strategy of model building in population biology: American Scientist, v. 54, p. 421-431. Lewontin, R. C., 1974, The genetic basis of evolutionary change: New York, N. Y., Columbia University Press, 346 p. Mayr, E., 1963, Animal species and evolution: Cambridge, Mass., Belknap Press of Harvard University Press, 797 p. Mayr, E., 1970, Populations, species and evolution: Cambridge, Mass., Belknap Press of Harvard University Press, 453 p. Naylor, T. H., 1966, Computer Simulation Techniques: Wiley and Sons, New York, N. Y., 352 p. Odum, E. P., 1971, Fundamentals of ecology, 33d_ed.: Philadelphia, Pa., N. 8. Saunders Co., 574 p. 113 Papentin, F., 1973, A Darwinian evolutionary system I. Definition and basic properties: J. Theor. 8101., v. 39, p. 397-514. Raup, D. M. 1972, Taxonomic diversity during the Phanerozoic: Science, v. 177, p. 1065-1071. Raup, D. M. 1975, Taxonomic survivorship curves and Van Valen's Law: Paleobiology, v. 1, p. 82-96. Raup, D. N., and Stanley, 8., 1971, Principles of paleontology: Freeman, New York, N. Y., 388 p. Raup, D. H., and Gould, S. J., 1974, Stochastic simulation and evolution of morphology - towards a nomothetic paleontology: Syst. 2001., v. 23, p. 305-322. Raup, D. N., Gould, S. J., Schopf, T. J. H., and Simberloff, D. 5., 1973, Stochastic models of phylogeny and the evolution of diversity: J. Geol., v. 81, p. 525-542. Schopf, T. J. N., 1974, Permo-Triassic Extinctions: relation to sea-floor spreading: J. Geol., v. 82, p. 129-143. Schopf, T. J. N., 1976, Environmental versus genetic causes of morphologic variability in bryozoan colonies from the deep sea: Paleobiology, v. 2, p. 156-165. Sepkoski, J. J., Jr., 1975, Stratigraphic biases in the analysis of taxonomic survivorship: Paleobiology, v. 1, p. 343-355. Simpson, G. C., 1953, The major features of evolution: Columbia University Press, New York, N. Y., 434 p. Stanley, S. N., 1975, Clades versus clones in evolution: why do we still have sex?: Science, v. 190, p. 382-383. Stehli, F. 6., Douglas, R. G., and Newell, N. 0., 1969, Generation and maintenance of gradients in taxonomic diversity: Science, v. 164, p. 947-949. Valentine, J. N., 1971, Plate tectonics and shallow marine diversity and endemicity, an actualistic model: Syst. 2001., v. 20, p. 253-264. Valentine, J. N., 1973a, Evolutionary paleoecology of the marine biosphere: Prentice-Hall, Inc., New Jersey, 511 p. Valentine, J. N., 1973b, Phanerozoic taxonomic diversity: a test of alternative models: Science, v. 180, p. 1078-1079. 114 Valentine, J. N., and Moores, E. M., 1974, Global tectonics and the fossil record: J. Geology, v. 80, p. 167-184. Van Valen, L., 1973, A new evolutionary law: Evolutionary Theory, v. 1, p. 1-30. Van Valen, L., 1974a, Molecular evolution as predicted by natural selection: J. Mol. Evol., v. 3, p. 89-101. Van Valen, L., 1974b, Two modes of evolution: Nature, v. 252, p. 298-300. Van Valen, L., 1975, Reply to Foin, Valentine, 8 Ayala: Nature, v. 257, p. 515-516. Walker, T. M., and Cotterman, N. N., 1968, An introduction to computer science and algorithmic processes: Boston, Mass., Allyn and Bacon, 563 p. IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII ImmmumuIIIIIIIII“MIMIH 3 129