Sympatric speciation : a simulation model

Transcription

1 Bioli~qica~Jouma~ofthe Linnean Society, 11: 1JI-139. With 2 tigurrs March 1979 Sympatric speciation : a simulation model STUART L. PIMM Department of Biological Sciences, Texm Tech University, Lubbock, Texas 7949 U.S.A. Acrppted fir publication Januaty 1978 A model of mating and population growth dependent on competition that suggests circumstances under which syrnpatric speciation might occur is described. The model is similar to one in a companion paper by Rosenzweig in that a heterozygote genotype, involving a new allele, is first selected by virtue of its ability to exploit a new niche and is then eliminated through competition. The superior competitor, which eliminates the heterozygote, is the homozygote for the new allele. For this process to occur the heterozygote must be sufficiently fit to exploit and invade a new niche, but not so fit that a classical polymorphism results from heterozygous advantage. This process of speciation is inost likely to occur when there are vacant niches. When and where these might occur are discussed. KEY WORDS: - competition - model - simulation - sympatric speciation. CONTENTS Introduction The model Results Discussion Acknowledgements References INTRODUCTION The purpose of this paper is to outline a model of sympatric speciation which relies on changes in relative fitness associated with competition for resources. The ideas are similar, though derived independently, to those of a companion paper by Rosenzweig (1978) who reviews the pertinent literature. This paper provides a quantitative model to complement the general approach used by Rosennveig. To attain two species with genotypes AA and BB from a parent species (here assumed to be AA), one must first select for the heterozygote (AB) and, at some subsequent period, eliminate this genotype. The relative fitness of the heterozygote must be initially high and then be reduced to the point where it is disadvantageous for the two homozygote types to interbreed and produce it. It is /79/ /$2./ 1979TheLinneanSocietyofLondon

2 132 S. L. PIMM this change in the heterozygote s relative fitness that has led authors to reject sympatric speciation as a viable process (Mayr, 1963). Consider a population of n individuals in which there are n-1 AA genotypes and one AB genotype; the single B allele having arisen through mutation. Even in a mildly stochastic environment repeated mutations are required to ensure the persistence of the B allele in the population even if the AB genotype has superior fitness to the AA genotype (Fisher, 1958). This, however, is a requirement of any genetic change. Let the AA genotype be at its carrying capacity in the environment but let the new genotype, AB, exploit a set of resources somewhat different from those exploited by the AA genotype. The AB genotype will increase and, as it does, the homozygote BB will appear in increasing numbers. Finally, suppose the BB genotype exploits resources similar to those exploited by the AB genotype, but much more efficiently. As the number of BB genotypes increase the number of AB genotypes will decrease through competition with the BB s. The AB genotype starts with a high relative fitness but this is eroded by competition from the BB genotype. There now may be selection for reproductive isolation between the AA and BB genotypes. The model requires competition as a factor altering the relative fitness of the organisms. Many authors have argued that competition is an important process in structuring vertebrate communities (Brown, 1975; Cody, 1974; Lack, 197 1; Pianka, 1975; Wilbur, 1972). The model requires changes in the organisms fitness as density changes, an idea discussed by Fretwell & Lucas (197) and Fretwell (1972). The model is deterministic; it does not involve random changes nor drift. The events are not improbable and may involve considerable selective forces. The details of the simulation model are similar to those of King & Anderson (197 11, although age structure has not been incorporated. The three genotypes grow and compete according to a finite difference model considered to be the analogue of the logistic growth equation (May, 1974). Unlike the model of King & Anderson (197 11, the model is more general in regard to the magnitude of the competition between the different genotypes. The model requires the evolution of reproductive isolation between the two homozygous genotypes, but this is a requirement for any speciation model. It will be shown that reproductive isolation will confer greater relative fitness on the individuals. Some of the details are for convenience only. A finite difference growth model was used instead of differential equation models, because it is easier to interface with the section of the model involving matings. The problem of keeping track of offspring in a model with overlapping generations could best be solved by incorporating age structure in the manner of King & Anderson (197 11, but this would considerably complicate the model. A single locus model has been used because this is an approximation to the dynamics of various situations, such as chromosomal inversions, rather than to imply that single gene differences are sufficient for speciation. THE MODEL Suppose there are PAA, PAB, and PBB adult individuals of the three genotypes AA, AB, and BB, respectively and that the sex ratio is unity.

3 SYM PATRIC SPECIATI N 133 (A) Calculate the number of matings which take place assuming they are random. Let PTOT/Z=(PAA+ PAB + PBB)/P equal the number of males (or females) in the population. The number of matings which takes place is given below and will be called the matrix Mij (i, j = 1 to 3) thus: Male genotype AA AB BB PAA PAA PTOT PAA PAB PTOT PAA PBB PTOT AA- x- x--x-x-- x-x- PTOT PTOT 2 PTOT PTOT 2 PTOT PTOT 2 & I AB PAB PAA PTOT PAB PAB PTOT PAB PBB PTOT x-- X- x-- x-xm T PTOT 2 PTOT PTOT 2 PTOT PTOT 2 OJ x- PBB PAA PTOT PBB PAB PTOT PBB PBB PTOT x-- X- x-- x-x- 2 PTOT PTOT 2 PTOT PTOT 2 (B) Calculate the number of offspring produced by these matings. (a) Calculate the potential number of offspring produced from the matrix of matings described above. The various numbers are given by: Where, for example, MZ9 is the number of matings between a female of genotype AB and a male of genotype BB, and YAA the relative number of young produced of genotype AA. The actual number of offspring produced must be corrected for the birth rates per mating and the survival of the offspring. If YAA, for example, were the actual number of genotype AA offspring, this would imply that each mating produced only one young. (b) Calculate the growth of the populations produced. Consider the finite difference analogue of the familiar logistic equation (May, 1974), which is N, + 1 = N, + N,. r. (1 -N,/K), (2) where Nt+l and N, are the populations sizes at time periods t+ 1 and t, r is the intrinsic rate of increase, and K is the carrying capacity of the population. The positive terms represent the births in the population and the negative terms and density dependent mortalities. This model must be extended to incorportate the differences in the numbers of the three genotypes and the fact that the three genotypes have different inhibitory effects upon each other. The

4 134 S. L. PIMM model used is (l-(aii. YAA + A12. YAB + A13. YBB)) PAA=YAA+YAA.r. KAA (l-(a21. YAA + A22. YAB + A23. YBB)) PAB = YAB + YAB. r. KAB (3) PBB = YBB + YBB. (l-(a31. YAA + A32. YAB + A33. YBB)) r. KBB The elements of matrix A are the intra- and inter-genotype competition coefficients, r is the intrinsic rate of increase (assumed the same for all genotypes for simplicity), and KAA, KAB, and KBB are the carrying capacities of the three genotypes. The terms Aii are always unity and the off-diagonal terms will generally be less than unity and will reflect, in part, the degree to which the particular pair of genotypes share resources. The existence of the matrix A permits modelling of situations where the resources of the three genotypes are not identical. With the new values for the numbers of the adult genotypes the calculations return to stage A above. The model is simply a three species competition model using finite difference equations with additional coupling between the three species to allow for the fact that the model involves genotypes which, unlike species, can interbreed. RESULTS I described above a very general model of a population consisting of three genotypes which grow subject to intra- and inter-genotype competition. The behaviours of such a model are quite diverse. I have chosen three situations which exhibit several characteristics relevant to the discussion of sympatric speciation. The results are shown in Fig. 1, and the parameter values associated with the runs are presented in Table 1. Case 1 (Fig. 1 A,B). In this example, the BB genotype has a carrying capacity of 5 compared with carrying capacities of 1 for the AA genotype and 5 for the AB genotype. Note that the AB genotype is a less effective organism, judged on its carrying capacity.there is little competition between the AB and AA genotypes (permitting AB genotypes to initially increase), no competition between the two homozygous genotypes, but considerable competition between the AB and BB genotypes. BB is a better competitor and severely inhibits the growth of the heterozygote. The precise results from this example depend on the value of the intrinsic rate of increase (r), but they are qualitatively similar to each other with a balanced polymorphism involving an equilibrium density of the BB genotype much less than its potential of 5. Case 2 (not shown). In this example, there is considerable competition between the three genotypes and inter-genotype competition is high; the carrying capacities remain unchanged. The increased competition prevents the heterozygote from increasing and the B allele is lost. This is analogous to the blocking gap of Rosenzweig (1978). Care 3 (Fig. 1 C,D). In this example, the heterozygote has an advantage over either homozygote (KAA= 1, KAB=5, KBB=5), and the competition between the three genotypes is the same as case one. The exact equilibrium values

5 SYMPATRIC SPECIATION 135 depend on the intrinsic rate of increase, but in each case a balanced polymorphism results. The oscillatory behaviour about equilibrium when r= 1.5 is to be expected from finite difference models (May, 1974). DISCUSSION How might any of these cases lead to a speciation event? For two populations to be considered biological species, they must be incapable of effectively interbreeding. In allopatric speciation models this is effected, at least initially, by geographical isolation. One must ask why, how and when reproductive isolation might develop. These three questions will be answered in turn. (a) Why might reproductive isolation occur? Case one above contains an unusual feature. The genotype BB equilibrates at a level of less than four percent of its possible carrying capacity, yet is subject to a small amount of intergenotypic competition from the AB genotype and none from the AA genotype. The overall fitness of the BB genotype is composed of two components : that due to the process of competition (both intra- and inter-genotype) and that due to Table 1. Parameter values for cases shown in Fig. 1 or described in the text Matrix A in equations (3) ettect of KAA KAB KB B AA AB BB e ; AA e C t AB.1 1.o.8 BB n Case 1: Fig. IA;r=1.5andB;r=.5 effect of KAA KAB KBB AA AB BB e f AA e AB.5 1.o.8 Case 2: Not Shown-see text n BB effect of KAA KAB KB B AA AB BB e Case3: Fig. 1 C;r= 1.5andD;r=.5 ; AA e ; AB.1 1.O.8 n BB

6 S. L. PIMM 2o4 1 AB i 1 BB. o o G 1 l c 4- C F I D f E 3- Gene ro t io n Figure I. Two sets of simulations with parameter values described in Table 1 (A and B, Case 1 ; C and D Case 3). 5C 4C u).- A 3C u) C.- c - a 8" 2oc 1 il Generations Figure 2. Two sets of simulations with parameter values described in Table I, case 1 (A). Dashed lines indicate an increase of 1% per generation and solid lines indicate an increase of 5% per generation of the BB genotype which inbreed. In both cases inbreeding starts at the tenth generation.

7 SYM PATRIC SPECIATION 137 the subsequent survival of its offspring. At the equilibrium levels found in case one, competitive fitness is high, and the BB genotypes survive with little mortality. However on reaching maturity, their random choice of mates is dominated by the more numerous AA genotypes. The product of these matings are AB genotypes, which are competitively of low fitness. It is the poor choice of mates that negates the high competitive fitness of the BB genotypes. Under these circumstances, the advantage to BB individuals of mating only with other BB individuals in considerable. The B allele has a potential equilibrium of 1 (2 x 5); the A allele, if the AA genotypes inbreed, a potential equilibrium of 2 (2 x 1). At the equilibrium under random mating, the B allele numbers a few percent of its potential of 1, but the A allele numbers greater than 2 due to the presence of a large number of heterozygotes. There is therefore no advantage to the AA individuals to inbreed. Under these circumstances the evolution of reproductive isolation of the BB genotypes will be selected once an adaption allowing preferential mating arises. An alternative evolutionary sequence is the evolution of modifiers which effect a change in the heterozygote so that it has the phenotype of one of the homozygotes. Under these circumstances the heterozygote will not be under a competitive disadvantage and reproductive isolation might not be expected. The evolution of dominance is known to have happened in certain situations (e.g. domestic fowl, Fisher (1958). (b) How might reproductive isolation occur? BB individuals, which inbreed, have a selective advantage in not producing the competitively inferior AB genotype. A postmating isolation mechanism conferring some kind of inviability on the AB genotype is selectively similar to those offspring being competitively inviable. Clearly for a preproductive isolation mechanism to be selected it must be premating. The evolution of such a premating isolation mechanism has two possible consequences. If it evolves rapidly (and experimental evidence suggests that this is a possibility (Thoday 8c Gibson, , then the heterozygotes will be quickly eliminated by competition from the BB genotype and AA will become effectively inbred by dint of BB s effective choice of mates. This situation is shown in Fig. 2A. The example has identical parameter values to case one; except that after ten generations there arises a mutation which confers reproductive isolation on a percentage of the BB individuals. This percentage increases at 1% per generation. However, despite the large selective advantage to BB individuals that inbreed, it is possible that reproductive isolation may evolve slowly. Figure 2B shows this possibility. The percentage of inbreeding BB genotypes increases at 5% per generation. The AB genotypes are lost through competition and subsequently the AA genotypes are also lost. The reason is that the AA genotypes now have inappropriate choices of mate, the BB genotypes which outbreed. As the numbers of AA decrease, it becomes increasingly probable that they will mate with the still large population of outbreeding BB individuals to produce heterozygotes of low fitness. Under these circumstances the AA individuals must also inbreed or be lost. (c) When might the processes described above occur? A possible answer is to be found in comparing case one with cases two and three. In case one,

8 138 S. L. PIMM reproductive isolation will be selected if it arises. The heterozygote initially increases because of its relatively higher fitness, but in the presence of the more highly competitive genotype BB it would be expected to be eliminated. In case two, the heterozygote never achieves a fitness high enough to permit it to increase. In case three, as in case one, there is a balanced polymorphism and little overlap between the three genotypes. However, reproductive isolation between the homozygotes is improbable because the heterozygotes have a high fitness. The results suggest that there must be little competition between the two homozygote genotypes, but strong competition between the new homozygote (BB) and the heterozygote. One expects this process to occur when there is a vacant niche available to the new homozygote; it is not likely to occur in communities saturated with species. In geological time there have been periods of mass extinctions (at the end of the Cretaceous for reptiles, in the Pleistocene for large mammals), which might have been followed by periods of extensive sympatric speciation as surviving species began to fill vacant niches. Early colonists on volcanic islands are another possibility and the example of the cichlid fishes in Lake Nabugabo described by Greenwood ( 1965) seems to require this kind of an explanation. This process of sympatric speciation requires a heterozygote to be selected for and then eliminated. This is possible due to the dynamic nature of fitness, an idea usually neglected by opponents of sympatric speciation models. The model discussed is deterministic, does not rely on improbable events and is driven by selective forces which could be considerable. The parameter values and form of the model described here are in widespread use in the literature on competition and many authors have argued the importance of competition in shaping the structure of animal communities. This does not mean the process has occurred, but it does suggest that it cannot be ignored. ACKNOWLEDGEMENTS I would like to thank Edward Broadhead, Brent Davis, James Hallett and Michael Rosenzweig for many helpful comments, the members of several population biology classes who suffered the model in its formative stages and the Texas Tech University Computer Center for computer time. REFERENCES BROWN, J. H., Geographical ecology of desert rodents. In M. L. Cody & J. M. Diamond, (Eds), Ecoloe and Evolution of Communities: Harvard: Belknap Press. CODY, M. L., Competition and the Structure OJBird Communities. Princeton: Princeton University Press. FISHER, R. A., Genetical rheoryofnaturalselection, rev. ed. New York: Dover. FRETWELL, S. D., Populationr in a Seasonal Environment. Princeton: Princeton University Press. FRETWELL, S. L. & LUCAS, H. L., Jr., 197. On territorial behavior and other factors influencing habitat distribution in birds. I. Theoretical development. Acta Biotheoretica, 19: GREENWOOD, P. H., The cichlid fishes of Lake Nabugabo, Uganda. Bulletin ofthe British Museum of Natural Histoy, 12: KING, C. E. & ANDERSON, W. W., Age-specific selection 11. The interaction of r and k during population growth. American Naturalist, 15: LACK, D. L., Ecological Isolation in Birds. Oxford: Blackwell Scientific. MAY, R.M., Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science, 186: MAYR, E., Animal Species and Evolution. Harvard: Belknap Press.

9 SYMPATRIC SPECIATION 139 PIANKA, E. R., Niche relations of desert lizards. In M. L. Cody & J. M. Diamond (Eds), Ecology and Evolution ofcornmunities: Harvard: Belknap Press. ROSENZWEIG, M. L., Competitive speciation. BiologicdJoumd Linnean Society, 1: THODAY. J. M. &GIBSON, J. B., Isolation by disruptive selection. Nature, 193: WILBUR, H. M., Competition, predation and the structure of the Ambystoma-Rana syluatica community. Ecolou, 53: 3-2 I.