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Evolutionary Ecology 1996, 10, 187-205 Conditions for sympatric speciation: a diploid model incorporating habitat fidelity and non-habitat assortative mating P A U L A. J O H N S O N 1., F. C. H O P P E N S T E A D T 2, J A M E S J. S M I T H 3 and G U Y L. BUSH 4 1NSF Center for Microbial Ecology, Michigan State University, East Lansing, MI 48824, USA 2Department of Mathematics, Department of Statistics and Probability and NSF Center for Microbial Ecology, Michigan State University, East Lansing, MI 48824, USA 3Department of Zoology and NSF Center for Microbial Ecology, Michigan State University, East Lansing, MI 48824, USA 4Department of Entomology, Department of Zoology and NSF Center for Microbial Ecology, Michigan Stale University, East Lansing, M1 48824, USA Summary Three types of genes have been proposed to promote sympatric speciation: habitat preference genes, assortative mating genes and habitat-based fitness genes. Previous computer models have analysed these genes separately or in pairs. In this paper we describe a multilocus model in which genes of all three types are considered simultaneously. Our computer simulations show that speciation occurs in complete sympatry under a broad range of conditions. The process includes an initial diversification phase during which a slight amount of divergence occurs, a quasi-equilibrium phase of stasis during which little or no detectable divergence occurs and a completion phase during which divergence is dramatic and gene flow between diverging habitat morphs is rapidly eliminated. Habitat preference genes and habitat-specific fitness genes become associated when assortative mating occurs due to habitat preference, but interbreeding between individuals adapted to different habitats occurs unless habitat preference is almost error free. However, 'nonhabitat assortative mating', when coupled with habitat preference can eliminate this interbreeding. Even when several loci contribute to the probability of expression of non-habitat assortative mating and the contributions of individual loci are small, gene flow between diverging portions of the population can terminate within less than 1000 generations. Keywords: speciation, habitat-sympatric divergence, divergent selection, habitat preference, assortative mating, linkage disequilibrium, penetrance Introduction A number of biologists, including Mayr (1963), Futuyma and Mayer (1980), Paterson (1981) and Futuyma (1986), pointed out limitations for sympatric divergence between co-adapting portions of a population. These limitations support the idea that speciation under sympatric conditions may be insignificant and rare events in nature. The claims of these biologists are supported by models (e.g. Felsenstein, 1981) which demonstrate that a major obstacle to sympatric speciation is the homogenizing effect of recombination (see Rice, 1987). By continually combining genes of two portions of a population adapting to different habitats, recombination can oppose natural selection in 'choosing' adaptive genes and gene combinations within each habitat. * Present address: Swedish University of Agricultural Sciences, Department of Plant Breeding Research, Box 7003, S750 07 Uppsala, Sweden. 0269-7653 © 1996 Chapman & Hall 188 Johnson A number of other biologists such as Bush (1975), White (1978), Kondrashov and Mina (1986), Bush and Howard (1986), Rice (1987) and Tauber and Tauber (1989) presented arguments suggesting that sympatric speciation in some animal groups may not be rare because in these groups the homogenizing effect of recombination can be reduced or circumvented. Rosenzweig (1978), Slatkin (1982), Rice (1984) and Diehl and Bush (1989), for example, developed models that support these arguments. Laboratory studies by Rice and Salt (1990) suggested that sympatric speciation may indeed have a role in nature and observations appear to confirm this: sympatric sister species (or races) exist for several organisms, such as parasitic insect species in the genus Megarhyssa (Heatwole and Davis, 1965), fruit flies in the genus Rhagoletis (Bush, 1969; Feder et al., 1989), fig wasps in the family Agaonidae (Murray, 1990), human-commensal flour beetles of the genus Tribolium (Wade et al., 1994) and the Enchenopa binotata complex of six treehopper species (Wood and Guttman, 1983). Also, endemic speciation occurs in isolated areas such as the Galapagos Islands (Lack, 1947; Grant, 1986), the Seychelles in the Indian Ocean (R'Kha et al., 1991) and the Juan Fernandez Islands near Chile (Crawford et al., 1992). Kondrashov and Mina (1986) and Tauber and Tauber (1989) compared theoretical investigations of sympaWic speciation with data collected from naturally occurring populations of insects, fish and molluscs. They concluded that sympatric speciation may be an important component in evolutionary diversification for certain taxa, especially those subject to disruptive selection. Bush (1992) argued that non-allopatric speciation (i.e. without geographical isolation) may be common among small animals such as insects, mites and nematodes. In these taxa, mating often occurs within a preferred habitat. If an alternative habitat becomes available to a population, individuals may select the new or original habitat based on genetically controlled habitat preference. Since mating is restricted to different habitats (habitat-based mating), two habitat races can arise. The objective of this paper is to determine, in theory, whether a diploid population having alternative habitats can develop sufficient linkage disequilibrium to speciate sympatrically. To approach this problem, we developed a model that incorporates the biological attributes likely to promote sympatric speciation and then used computer simulations of the model to analyse speciation under conditions of complete sympatry. Our model differs from previous models by taking into account both habitat-based and non-habitat-based (e.g. ethological) factors contributing to assortative mating. Non-habitat-mating and habitat-mating sympatric divergence Divergence between populations or portions of a population is sympatric when the probability of mating between two individuals depends only on their genotypes (Kondrashov and Mina, 1986). Sympatric divergence that leads to speciation involves two components (Maynard Smith, 1966). First, diversification of portions of an ancestral population, followed by the evolution of reproductive isolation between those portions. Barton and Charlesworth (1984) described the first component as the splitting of an ancestral population into populations located at different equilibria under selection. Hutchinson (1968) explains how different types of regions within niche space affect speciation processes. Integrating Hutchinson's (1968) ideas with the concepts of adaptive landscapes and intraspecific competition, Rosenzweig (1978) described, with a biological model, how certain regions of niche space can allow divergence under sympatric conditions and how divergence can result in sympatric speciation. These regions of niche space contain 'islands' separated by disruptive gaps. Conditions for sympatric speciation 189 For a population, these islands represent adaptively discrete habitats that individuals can select. If each individual in the population mates and places its progeny within its selected habitat, then mating is 'habitat-based' and the divergence that develops will be called habitat-mating sympatric divergence (HMSD). Sympatric divergence that might develop when mating is not habitat-based will be called non-habitat-mating sympatric divergence (NMSD). Note that HMSD is consistent with pure sympatry only if individuals of the population do not 'remember' the habitat in which they were born (A.S. Kondrashov, personal communication). This requires absence of conditioning, i.e. an individual's habitat choice is not altered by the habitat in which it was born. Levene (1953) and Maynard Smith (1962, 1966) broadly outlined the dynamics for NMSD using models with single loci both for fitness and for non-habitat assortative mating. Later, Gibbons (1979) analysed an NMSD model in which non-habitat assortative mating alleles are associated through linkage or pleiotropy with fitness alleles involved in intraspecific competition for a resource that varies over a spectrum. Along similar lines, Kondrashov (1983a, 1983b, 1986) studied the effects on NMSD of multiple loci pleiotropically controlling fitness and non-habitat assortative mating. Finally, besides fitness and non-habitat assortative mating, Seger (1985) included genetically controlled niche preference in an NMSD model. In NMSD, intraspecific competition drives divergence unassisted by habitat-based mating, whereas in HMSD, habitat assortative mating assists intraspecific competition. Although HMSD is in a sense just an elaboration of NMSD (see Levene, 1953, pp. 332-3), the difference in dynamics between these two types of sympatric divergence is considerable. Selection is disruptive for NMSD, but in HMSD, because habitat-based mating partitions individuals into separate mating pools which correspond to different habitats, selection is divergent (Pimental et al., 1967; Soans et al., 1974; Bush, 1982; Shaw and Platenkamp, 1993). In addition, habitat assortative mating cannot occur in NMSD because habitat-based mating is required, but it can occur during HMSD (Maynard Smith, 1962, 1965) if genes control habitat preference. Bush (1969, 1975), Tauber and Tauber (1977), Rice (1984), Diehi and Bush (1989) and De Meeus et al. (1993) analysed biological and mathematical models to explore the dynamics of HMSD when habitat assortative mating is unassisted by non-habitat assortative mating, while Dickinson and Antonovics (1973), Felsenstein (1981) and Fialkowski (1988, 1992) analysed HMSD models in which non-habitat assortative mating is unassisted by habitat assortative mating, i.e. only intraspecific competition drives divergence. In our simulations, we analyse the dynamics of HMSD when habitat assortative mating and non-habitat assortative mating complement one another to facilitate speciation. A basic two-habitat model for HMSD The model is patterned after a population of phytophagous insects in an area where there are two alternative host plants (habitats). A set of genes (hab genes) controls genotype-dependent migration in the form of habitat preference and individuals mate and place their offspring in the selected habitat. Habitat assortative mating develops because individuals are genetically predisposed to select a given host plant and thus have a high probability of mating with an individual with similar host preference. This mode of habitat or host-dependent mate recognition, which satisfies the characterizing requirements for HMSD, is common in many phytophagous and parasitic insects, mites and nematodes. Another set of genes (fit genes) controls habitat-specific survival by enabling individuals to utilize more effectively one host plant or the other. Individuals that select the host plant for which they are best adapted have a selective advantage, so association of habitat preference alleles and fitness alleles is favoured. If this association develops, a selective advantage occurs for individuals 190 Johnson who not only select the 'correct' host plant, but who also mate homogamously. Thus, a third set of genes (asm genes) for controlling non-habitat assortative mating operates to reduce interbreeding between individuals adapted to different habitats who happen to be in the same habitat due to less than absolute genetic control of habitat selection. The principle simulations of the model discussed in this paper involve either one or two fitness loci (fit loci), two habitat preference loci (hab loci), and two non-habitat assortative mating loci (asm loci). The hab, fit and asm loci are not linked and each locus has two alleles. Selection (s) acts directly on fit loci and indirectly on hab and asm loci. Generations are discrete and nonoverlapping, and soft selection occurs independently in each of the two habitats so that density is regulated independently in each. This allows simultaneous variation at fit and hab loci (Rausher, 1984). Habitat-specific selection and fitness Selection is directional in each habitat because at each fit locus, one allele contributes to fitness only in the original habitat and the other allele only in the new habitat. Therefore selection is also habitat specific and divergent. Let k be the number of fit loci and s be a selection factor. If an individual in a given habitat carries b homozygous fit loci with both alleles contributing to fitness in that habitat and c heterozygousfit loci, where (b + c) = k, its fitness value is (1 + ps) b (1 + Os)c if the loci interact multiplicatively and 1 + s (pb + 0c) if the loci interact additively. The ratio of p/0 is a measure of the fitness of heterozygotes relative to homozygotes. Underdominance occurs for p/0 > 2, while overdominance occurs for p/0 < 2. In our model, as in the model of Diem and Bush (1989), p = 2 and 0 = 1. Since underdominance is then minimal for the metapopulation, there is no direct selection against individuals that are heterozygous atilt loci. Results of simulations by Fialkowski (1988, 1992) suggest that p/0 --- 2 is a necessary condition for sympatric speciation and that the rate of speciation increases (to a point) as p/0 increases beyond 2 due to selection against heterozygotes. Migration The probability that an individual will live within its 'correct' habitat (i.e. where it is most fit) and place its young there is controlled by hab alleles. We denote this probability by g and call it the 'hab penetrance' of the individual because it is the probability that an individual will express its expected phenotype, based on its genotype, by selecting its preferred habitat. At each hab locus there are two alleles: one confers preference for the original habitat and the other for the new habitat. The model assumes that hab loci interact additively to determine the rate Ph~ of production of a 'pathway product'. Hab penetrance g, which is a function of Ph~b, is scaled so that penetrance is complete (g = 1.0) for an individual if ehab ~ 1.0. Individuals with complete hab penetrance are certain to express their habitat preference by selecting their genetically preferred habitat. Only homozygous loci confer preference for a habitat, because for simplicity we assume that alleles at heterozygous loci cancel each others effect. Let Lh~b denote the contribution by each homozygous hab locus to Phab" Contributions of hab loci to penetrance are additive if ehab < 1.0 for the individual and then g = Phab" If Phab< 1.0, then g = 1 regardless of the nature of interaction between the hab loci. If Phab = 0, the individual randomly selects a habitat and g = 0. If m is the number of hab loci, Phag is at most mLha b (i.e. max Phab = mLhab). We assume that max Phab can be less than sufficient for complete penetrance (Phab< 1.0 for all individuals in the population) or more than sufficient (Phab> 1.0 for some individuals). If max Phab is more than sufficient, individuals with Phab> 1.0 have an extra pathway product termed 'penetrance excess'. This extra pathway product increases the probability that offspring of such an 191 Conditions for sympatric speciation Table 1. Computed migration probabilities as proportions of individuals leaving or staying in a habitat for each habitat-preference genotype Habitat Reside in Prefer Proportion that stay for mating Proportion that migrate for mating Original Original New New Original New Original New g+ 0.5 0.5 g+ 0.5 g+ g+ 0.5 0.5 (l-g) (l-g) (l-g) 0.5 (l-g) (l-g) 0.05 (l-g) 0.5 (l-g) (l-g) Each genotype has an associated penetrance g, which determines the probability that an individual will either leave or stay in a given habitat for mating based on its genotype. The factor 0.5 reflects the fact that genotype-independentmigration for all individuals is maximized and that divergenceis truly sympatric. After Diehl and Bush (1989). individual will have complete penetrance, despite the effects of recombination. We call a population 'saturated' with respect to hab penetrance if individuals of at least one pair of genotypes prefer different habitats and have ehab ~- 1.0 SO that they always select their preferred habitat (g = 1o0). In our simulation models, a population is saturated when max Phab>- 1.0. Table 1 shows how migration probabilities are computed. The probability that an individual for whom g = 0 will migrate to a new habitat is used as a measure of genotype-independent migration. Since divergence is truly sympatric in our simulations, this probability is the maximum, 0.5 (see Table 1). In our model, Lhab is the same for all hab loci. Therefore, if b homozygous loci confer preference for one of the habitats and d for the other and if b is greater than d, then Phab ~" (b - d)Lha b. The preferred habitat for an individual is that for which most of the hab loci confer preference. Non-habitat assortative mating In our model, all three types of loci (hab, fit and asm) contribute to the pattern of mating. Positive habitat assortative mating evolves indirectly as a correlated character of hab loci because mating occurs only within a preferred habitat and mate choice is associated with habitat preference. However, habitat assortative mating also occurs as a correlated character of fit loci in response to habitat-specific divergent selection: each generation, within each habitat, natural selection increases the proportion of individuals adapted to that habitat, thereby increasing the probability within each habitat that the most fit individuals will mate with one another. Asm loci control traits not specifically associated with either habitat (e.g. pheromone synthesis) and non-habitat assortative mating occurs as an outcome of differences between individuals in these traits. There are three non-habitat assortative mating phenotypes: A, B and C and individuals of each phenotype mate at random with one another. Each asm locus is diallelic, with one allele favouring phenotype A and the other favouring phenotype B. Let r be the number of asm loci (therefore 2r is the number of asm alleles) and -q denote the number of asm alleles that favour phenotype A. If qq > r for an individual, then asm penetrance, p, is the probability that the individual will express phenotype A by mating homogamously, that is, by mating with other such individuals. Conversely, 1 - p is the probability that this individual will express phenotype C by mating at random with other individuals of phenotype C. If an individual has "q < r, the individual has a probability p that it will express phenotype B, with 1-p again the probability of expressing phenotype C. If "q = r, the individual has phenotype C. Johnson 192 Let easm (an analogue to Phab) be the rate of production of a pathway product for determining asm penetrance p (an analogue to hab penetrance g). asm penetrance p is complete for any individual in which Pasta >- 1.0, which means that such individuals mate homogamously with certainty. We assume that p is independent of the relative frequencies of the alleles favouring phenotypes A and B. The value o f p for an individual is computed in the same manner as hab penetrance g, with each asm locus contributing additively and equally an a m o u n t Las m to the rate Pasta" We scale p so that penetrance is complete (p = 1.0) for an individual if easm ~ 1.0. The concept of penetrance excess with respect to asm loci is analogous to that described for hab loci. We call a population saturated with respect to asm penetrance if individuals of at least one pair of genotypes, X and Y, for example, have complete penetrance (Pa~m> -- 1.0 and p = 1). Therefore, individuals of these genotypes always mate homogamously with individuals of their same phenotype. As the proportion of individuals of phenotype C decreases, interbreeding between the two subpopulations adapting to different habitats decreases. In cases in which phenotype C is eliminated, all heterozygotes are eliminated and speciation is completed. Thus, the proportion of individuals of phenotype C is a useful measure of the amount of interbreeding between the two diverging portions of the population. Life-cycle dynamics of the model The model can be described mathematically as follows. Let u denote the total number of hab, fit and asm loci and Gj the jth gamete, where j = 1, 2, 3 . . . . . 2u-l, 2u. Let q and Q denote the frequency of an arbitrary genotype (G~, Gj) in the original and new habitat, respectively. At generation n, just after migration, q = x~j(") and Q = Xu("). (Lower and upper case letters represent the original and new sympatric habitats, respectively.) We now follow the frequencies q and Q of (G i, Gj) through one life cycle. After reproduction, which marks the beginning of generation n + 1, q has changed to Yij(n+l) and Q to y/j(n+l), where E v(n) v(n) D Akl Ak'I' ,t klk,l,ij, y!.~+l) = klk'v tj (1) E "~kl'(n)x(n,/eklk'l'iT klk'l'iy' Yij(n+ 1) is obtained with an analogous equation. Pktk,l,ij,l is the probability that an individual of genotype kl and an individual of genotype k T mate and produce an offspring of genotype ij. Selection follows, changing q to zi/'+ 1) and Q to Z/j(~+ 1), where 7!.m+l) = -'J V(.n+l) (1 + Jq sq) E y}~,+l)(l + si~,) (2) iT Zij(n+ 1) is obtained with an analogous equation. Here s~i is the selection coefficient for genotype ij. After selection, migration occurs, changing q to xij(~+ 1) and Q to Xij('+ 1) where (1 + hij) 7 (.n+l) "Jr"Hi.~//; +1) x(n+l) _~_ U -'J E [(1 + hiT) -`"+1) ~itjt +n/~,zi~,,n+l)] (3) iT Xij(n 4-1) is obtained with an analogous equation. Here h 0 denotes the probability that an individual of genotype ij in the original habitat will migrate to the new habitat and Hij denotes the Conditions f o r sympatric speciation 193 probability that an individual of genotype ij in the new habitat will migrate to the original habitat (see Table 1). The next generation n + 2 now proceeds, etc. Methods Simulations were run using various combinations of fit, asm and hab loci. The majority of the results presented were obtained using one fit locus, two hab loci and two asm loci. Simulations using more loci tended to be computationally prohibitive. Each simulation begins with identical populations in an original and a new habitat. All hab, fit and asm loci are in Hardy-Weinberg equilibrium (i.e. within-locus equilibrium) and linkage equilibrium (i.e. between-locus equilibrium). Recombination is free. Each locus contains a low-frequency allele for promoting adaptation to the new habitat. In all simulations, initial relative frequencies for alleles of the three types of loci are hab ° = f i t ° = asm a = 0.99 and hab" = f i t ~ = asm b = 0.01 in each habitat, where the super-script (°)signifies the original habitat and superscript (") the new habitat. Superscripts (a) and (b) are used for the asm alleles because they are unassociated with either habitat. The only things different in the system initially are the habitats. Pair-wise linkage disequilibria were calculated for each subpopulation (within-population equilibrium) and the metapopulation (total linkage disequilibrium). Between-population linkage disequilibria were calculated using the Wahlund distribution of disequilibrium for two subpoputations. Since the ancestral population diverges into two portions utilizing different habitats in our models, total disequilibrium (Otot) between pairs of loci is a combination of the following. (1) The Wahlund disequilibrium (Obet) , which occurs when differences in allele frequencies at two loci co-vary between the diverging portions of the population (Smouse and Neel, 1977). (2) The disequilibrium within each of the diverging portions Dorig and Onew. Nei and Li (1973) showed that at total disequilibrium Dtot = D b e t -k-(Oorig +D,ew)/2. The Wahlund disequilibrium is unaffected by the homogenizing effects of recombination. Speciation sensu stricto (Templeton, 1989) occurs in our simulations when gene flow terminates and the diverging populations form two completely isolated gene pools, each adapted to a different habitat (Kondrashov, 1986). We recognize that speciation is completed when two portions of a diverging population become committed to different evolutionary pathways and does not require the complete elimination of all gene flow. However, accurate determination of the time and conditions for this bifurcation in simulations is not yet possible. Other criteria for completion of speciation must therefore be used. In all simulations, we determined the number of generations required for speciation. When alleles at each locus were within 1/100 of the frequencies they were approaching asymptotically, we considered speciation sensu stricto to have occurred, since linkage disequilibria between asm loci and fit loci was essentially completed, with virtually no gene flow between the two sibling species. In nature, under similar circumstances of approach to fixation, random drift completes the process. Results Simulations with at least one type o f locus absent To confirm results of earlier models and analyses pertaining to sympatric speciation, initial simulations were carried out using various combinations o f fit, asm and hab loci, but not all three together. With regard to HMSD models, we confirmed (1) the establishment of polymorphism by 194 Johnson divergent selection when onlyfit loci are involved (Levene, 1953; Maynard Smith, 1966; Diehl and Bush, 1989), (2) the joint action of genotype-dependent and genotype-independent population regulation when only hab loci are involved (Nagylaki and Moody, 1980; Moody, 1981) and (3) the establishment of polymorphism and of linkage disequilibrium between hab loci and fit loci when habitat assortative mating occurs as a result of habitat preference and only fit and hab loci are segregating (Diehl and Bush, 1989). We also confirmed the results of Felsenstein (1981) and Diehl and Bush (1989) that if nonhabitat assortative mating and adaptation to different habitats are not accompanied by habitat preference, then no linkage disequilibrium develops between a s m loci and fit loci irrespective of selection factor s and a s m penetrance, if the fitness loci interact additively. However, if there are at least two fit loci that interact multiplicatively, then very strong selection and non-habitat assortative mating can generate some linkage disequilibrium between fit and a s m loci. But as Felsenstein (1981) pointed out, such cases are unrealistic. Finally, we also corroborated data showing that higher numbers of loci weaken the effectiveness of individual loci to reduce speciation time. This was true for all three types of traits. With NMSD models, Kondrashov (1986) obtained similar results. S i m u l a t i o n s w i t h all three types o f loci p r e s e n t Figure 1 illustrates speciation times over a range of values for gene penetrances Lasm and Lha b when there is a single fit locus (s = 0.1) and a s m and hab penetrance are each controlled by two loci. When speciation is completed, between-population pairwise linkage disequilibrium is maximum for all pair combinations of the three types of loci. Speciation occurs when Las ~ >-- 0.5 and gha b > 0 (see Figs 1 and 2). Simulations were not run for values of Lha b < 0.2 because the time required for Generations 4,000 4,000 3,000 3,000 2,000 !,000 ,000 to Speciation Generations to Speciation 1,00( I S=0.1 ~netrance sm Gene 0.8 Figure 1. Generations to speciation as a function of both hab gene penetrance (Lhab) and asm gene penetrance (L,sm).Lha b varies in the range 0.2-0.8 and Lasm in the range 0.5-0.8. The selection factor s is set at 0.1. Computer rounding of values creates a slight asymmetry in the first generation that determines the fit allele with which the asm a (or asm b) allele becomes associated. When the rare asm allele asm b becomes associated with the frequent fit° alleles favouring fitness in the original habitat (light bars), time to speciation is slightly greater than when the rare asm b allele becomes associated with the rare fit" alleles for fitness in the new habitat (dark bars). 195 Conditions for sympatric speciation 4,000 - l 3,000 Generations to Speciation s=0.1 L ~ b = 0.7 2,000 1,000 0 0.45 I I 0.475 I " - ~ saturation (asm) 0.5 gene penetrance 0.525 0.55 L asm Figure 2. An illustration of the nature of the asm penetrance threshold for the occurence of speciation. The population is saturated with respect to hab penetrance (Lh~b = 0.7 ~ 0.5), S = 0.1 and La,m varies from 0.45 to 0.55. Generations to speciation are shown as a function of asm gene penetrance. With Lasm = 0.5, the population is also saturated with respect to asm penetrance and speciation occurs rapidly (approximately 1000 generations). As Las,, drops below the threshold of 0.5 so that the population is no longer saturated with respect to asm penetrance, the time to speciation increases sharply towards infinity. the process became computationally prohibitive. The number of generations to speciation ranged from less than 1000 when Zas m ~---0.5 and Lha b = 0.8 to more than 3000 when Zas m > 0.5 and Zha b = 0.2. Our results illustrate the role of habitat preference in facilitating sympatric speciation. Observe that if the population is saturated with respect both a s m and hab penetrance (Lasm >I 0.5,Lh~b I> 0.5), speciation occurs within approximately 1000 generations if s = 0.1 (see Fig. 1) and the sister species confine themselves to the habitat in which they are specifically adapted. Now consider the minimal condition for linkage disequilibrium to develop if there are no hab loci to facilitate the speciation process via habitat preference. Instead of just one f i t locus, there must be at least two that interact multiplicatively. If L,s m = 0.5 and s = 0.1, we obtain a speciation time of approximately 10 500 generations instead of 1000. Besides this 10-fold increase in speciation time, the resulting sympatric sister species migrate randomly between the two habitats. Correspondingly, within- and not between-population linkage disequilibrium becomes maximum. Enough simulations beyond those shown in Fig. i were run to construct a depiction (Fig. 3) of speciation times over the entire range of Lasm and Lhab values. We observe the following: (1) sympatric speciation occurs in our HMSD model only if the population is saturated with respect to a s m penetrance, (2) given that speciation does occur, Lh~ b determines the time required and (3) speciation is achieved in the shortest time when the population is saturated with respect to both hab and a s m penetrance (i.e. the 'complete habitat-fidelity' region where Las m and Lhab are ~ 0.5). ~n this region of complete habitat-fidelity (Fig. 3), gene flow between the sympatric sister species that emerge is impossible because homogamous mating and preference for the habitat in which an individual is adapted become errorless due to the elimination by natural selection of individuals with less than complete a s m and hab penetrance. The 'incomplete habitat-fidelity' region in Fig. 3 corresponds with cases when the population is only saturated with respect to a s m penetrance. Then speciation occurs because interbreeding between individuals of the two divergent portions of the population is terminated, even though some individuals of the sister species migrate between habitats due to incomplete h a b penetrance. 196 Johnson Although speciation is completed, individuals of the species adapted specifically to one of the habitats can sometimes be found in the other 'wrong' habitat (Fig. 4). The percentage of such individuals increases linearly as Lhab decreases. At Lhab = 0, this value becomes 50% and individuals of the sympatric sister species migrate at random between habitats. However, by the time the speciation process has reached the advanced stage of speciation, there is a fitness penalty against individuals that select the wrong habitat. Not only are they homozygous for the wrong fitness allele in that habitat, but they must mate with other such individuals since f i t and a s m alleles are completely associated. Offspring of these matings will also be maximally unfit, except those offspring that select the other 'correct' habitat to which they are adapted. Hence, the proportion of individuals of the sister species found in their respective 'wrong habitats' will in theory diminish and eventually disappear due to the selective advantage of mutations that increase habitat preference penetrance. This intrinsic process of increase in habitat fidelity can be facilitated by mutant f i t loci that introduce habitat preference pleiotropically or mutant hab loci linked to f i t loci ('hitchhiking'). When there are ten loci contributing to a s m penetrance, saturation results when gene penetrance Lasm = 0.1 and when there are 20 such loci, Lasm = 0.05 is sufficient for saturation; similarly for hab penetrance. This suggests that when enough hab and a s m loci are involved in HMSD, speciation can occur for a population almost regardless of how small the additive contributions of individual loci to penetrance may be. In theory, the complete habitat-fidelity region could expand (see Fig. 3) until the 'incomplete habitat-fidelity' region and the 'no speciation' region disappear. O0 20,000 20,000 15,000 15,000 10,000 Generations to Speciation Generations 10,00( to Speciation ,000 5,00 s=0.1 trance GE [] [] [] complete namtat-rme.ty incomplete habitat-fidelity no speciation 1.0 1.0 complete gene penetrance Figure 3. Delineation of three distinct forms of HMSD as a function of Zhab and La+m. Simulations were run with two hab loci, two asm loci and onefit locus (s = 0.1). Speciation is most rapid when both asm and hab penetrance are saturated, In this 'complete habitat-fidelity' region, both asm and hab penetrance become saturated. In the 'incomplete habitat-fidelity' region, speciation occurs even though only asm penetrance is saturated. Speciation does not occur when/_,asm< 0.5, i.e. when asm penetrance is not saturated. This is the 'non-occurence of speciation' region and bars are not shown. Conditions for sympatric speciation 197 Additional fitness loci Figure 5 shows the speciation times for conditions identical to those represented in Fig. 1, excepL for s, which is reduced by half, from 0.10 to 0.05. We observe that this approximately doubles the time to speciation. In the opposite direction, doubling the selection factor s for a single fit locus (0.05-0.10), which doubles the fitness of homozygous individuals, decreases speciation time by approximately half. On the other hand, the addition of a second fit locus with the same selection factor s as the first, which also doubles the fitness of homozygous individuals, decreases the time to speciation by less than one-third (Fig. 6) when s is > 0.05. This demonstrates the weakened effect of selection when the number of loci contributing to fitness increases. The weakening becomes greater as the additive contributions of each locus to fitness increases: when s is 0.50 (10-fold higher than 0.10), including a second locus reduces speciation time by less than one-sixth (Fig. 6). Having two fit loci interact multiplicatively reduced time to speciation only slightly and can be less effective than an additive interaction at values of s less than 0.05. When s was set above 0.2, increasing the additive or multiplicative contribution per fit locus did not significantly reduce speciation time. Migration of Sister Species Adapted to New Habitat O t... o o. 0 0.2 0.4 0.6 0.8 1 Gene Penetrance L hab Figure 4. The percent of individuals that migrate to the wrong habitat, where they are at a fitness disadvantage, is shown as a function of Lhab. This occurs for simulations that fall in the 'incomplete habitatfidelity' region of Fig. 3 where Lhab < 0.5. In these cases, some individuals of both new sister species disperse across the two habitats after speciation has occured. This figure only shows dispersal for the species specifically adapted to the new habitat. 198 Johnson 4,000 4,000 3,000 3,000 Generations 2,00C to Speciation 2,000 Generations to Speciation ,000 1,00, S = 0.05 ~netmnce Genq tsm Figure 5. Generations to speciation as a function of both hab gene penetrance (Lhab) and asm gene penetrance (L,~m)when the selection factor s = 0.05. As in Fig. 1, Lhab varies in the range 0.2-0.8 and Las,~ in the range 0.5-0.8. The light and dark shading of the bars is explained in the legend to Fig. 1. Development of linkage disequilibrium To illustrate basic features of HMSD divergence, the trajectory for development of pair-wise linkage disequilibrium between fit loci and asm loci was examined (Fig. 7). In the specific case used (Fig. 6, arrow), speciation occurred within approximately 850 generations. During a relatively short initial phase of population diversification, the rare hab allele rapidly becomes common and habitat preference initiates a reduction in gene flow between habitats within less than 50 generations. Soon after, the rare fit allele increases in frequency and some linkage disequilibrium develops between all loci. Within less than 200 generations, within-population linkage disequilibrium between the two asm loci reaches 0.099 or 40% of maximum, although the frequency of the rare asm allele has increased very little. However, the amount of disequilibrium between asm loci and fit loci is minuscule. A quasi-equilibrium is reached within less than 500 generations, which begins a period of stasis before the rare asm alleles begin to exhibit a noticeably rapid increase in frequency across habitats (the beginning of the speciation phase). During the period of stasis, the highest between-habitat linkage disequilibrium (0.038, 15% of maximum) occurs between the two hab loci and the next highest (0.0084, 3% of maximum), between hab loci andfit loci. In the absence of asm loci, this would be the final equilibrium state, as in the models analysed by Diehl and Bush (1989). The last component and phase of the speciation process, completion of speciation by reproductive isolation, is a short dramatic process (approximately 100 generations). Linkage disequilibrium suddenly increases to maximum for all pairs of loci. Interbreeding between individuals adapted to different habitats rapidly diminishes to zero as all intermediate forms disappear, resulting in the elimination of gene flow between the two diverging co-adapted subpopulations. Kondrashov (1986) observed a similar phenomenon for sympatric speciation in some of his NMSD models, namely, a prolonged initial stage of speciation when polymorphisms are developing, followed by a stage of rapid elimination of intermediate individuals (Kondrashov and Mina, 1986). 199 Conditions for sympatric speciation Although within-habitat linkage disequilibrium between fit and asm loci is predominant initially over between-population linkage disequilibrium, eventually a sudden shift to the latter occurs. This happens because the population is saturated with respect to both hab and asm penetrance (the complete habitat-fidelity region in Fig. 3). Should the population be only saturated with respect to asm penetrance (the incomplete habitat-fidelity region), some of the within-habitat disequilibrium would have been retained throughout the speciation process and each sympatric sister species would utilize both habitats to some extent (see Fig. 4). In summary, for populations that are saturated with respect to asm penetrance, the process of sympatric speciation via HMSD includes (1) an initial diversification phase during which a slight amount of divergence occurs, (2) a quasi-equilibrium phase of stasis, which can be long and during which little or no detectable divergence occurs and (3) a completion phase during which divergence is dramatic and gene flow between diverging habitat races is rapidly eliminated. Discussion This study expands earlier HMSD models by incorporating all three basic types of loci that facilitate sympatric divergence: habitat-based fitness (fit) loci, habitat preference (hab) loci and assortative mating (asm) loci. We found that each type of locus facilitates the effectiveness of the other two types so that the three types operate together to promote HMSD. Sympatric speciation is then theoretically quite plausible. If any one of the three types of loci is absent, then speciation 2,500 2,000 N u m b e r of Fitness Loci t w o (multiplicative interaction) o t w o (additive interaction) \ W C .9o 1,ooo 500 , 0 0 I 0.1 i I 0.2 , I , 0.3 I 0.4 , I , 0.5 Selection Factor s Figure 6. Generations to speciation as a ftmction of the selection factor s. In these simulations, there are two asm loci and two hab loci with L~s,, = Lh~b = 0.6. The contribution s of each fit allele to total fitness is the same, so when two fit loci interact additively, total fitness is doubled for homozygous individuals. The arrow is a reference mark for Figure 7. 200 Johnson completion (speciation in progress) stasis (no speciation) sister species (speciation completed) I ~ 1 Maximum 025 ® E ..~ e" L .10 o n , m O" P_ r~ 500 600 700 800 900 1000 Generations Figure 7. The development of a pair-wise linkage disequilibrium between fit and asm loci. In this simulation (see arrow in Fig. 6), there are two fit loci interacting additively, two hab loci and two asm loci (s = 0.1, Lasm = Lh~b = 0.6). Linkage disequilibrium increases suddenly to the maximum (0.25) from values difficult to detect, within less than 100 generations. becomes less likely and requires special genetic conditions such as underdominance or divergent selection on habitat preference (Rice, 1984). Diehl and Bush (1989) analysed a three-locus haploid HMSD model where variation at two unlinked loci affects fitness and a third locus influences host preference (no non-habitat assortative mating occurs). Although considerable progress towards speciation can occur in this model, sympatric speciation (sensu stricto) is possible only if habitat preference is error free, in which case habitat preference alone is sufficient for reproductive isolation. The role o f habitat preference Kondrashov (1983a,-b, 1986) showed with NMSD models that once reproductive isolation is virtually estabfished, then linkage disequilibrium between asm loci and fit loci can increase and complete the speciation process by eliminating interbreeding within a population between divergent morphs adapting to different niches or habitats. This occurs even when the intensity of disruptive selection is less than 10% and without involvement of hab loci. His results suggest that once linkage disequilibrium between asm loci and fit loci has developed sufficiently during HMSD, then NMSD is sufficient to bring about speciatlon. Habitat-based mating and niche or habitat preference become unnecessary. Conditions for sympatric speciation 201 This observation suggests that the role of habitat preference in sympatric speciation via HMSD is to initiate the process and allow development of disequilibrium between asm loci and fit loci to proceed until a threshold value is reached at which a self-sustaining momentum results in rapid completion. The execution of the role of habitat preference in HMSD can be explained as follows. Even if only hab loci are segregating, those loci rapidly proceed to polymorphism and reduce gene flow between habitats in the process (Diehl and Bush, 1989). Due to habitat preference, within each habitat the relative frequency of individuals that are homozygous for preferring that habitat increases relative to those that are homozygous for preferring the other habitat. Consequently, individuals that are heterozygous for habitat preference decrease in frequency across habitats due strictly to density-dependent selection and recombination at hab loci. This strengthens habitat assortative mating and facilitates the development of linkage disequilibrium between hab and fit alleles. Such linkage disequilibrium promotes linkage disequilibrium between asm and fit alleles and vice versa. The result is mutual enhancement of all combinations of pair-wise linkage disequilibria for the three types of loci. Liberman and Feldman (1989) showed that mutations that introduce additional hab loci which increase the level of hab penetrance can become established due to a selective advantage so that habitat preference can indeed perform the role of initiating the speciation process. They studied a model involving a multiple-allele modifier of migration rate between two habitats and found that although the modifier locus and a fit locus may achieve linkage equilibrium in each of the habitats (Hardy - Weinberg equilibrium), the equilibrium is externally unstable to alleles that reduce migration rates. The role of non-habitat assortative mating The role of non-habitat assortative mating in HMSD is apparent, namely, to reduce interbreeding between the diverging portions of a population that occurs when individuals of both portions are', found in the same habitat. As mentioned above, the selective advantage of non-habitat assortatiw~ mating during HMSD is increased whenfit and hab loci become associated. The diverging portions of the population can develop different mate recognition systems (e.g. pheromones, courtship behaviours, displays, etc.). If the population is saturated with respect to asm penetrance, the outcome is completion of speciation even though migration between habitats may still occur. Within a 'homogamy pool,' individuals are certain to mate only among themselves because the genotypes within the pool have complete asm penetrance. A metapopulation is saturated with respect to asm penetrance if it contains at least two homogamy pools. Due to recombination, some of the offspring of individuals with less than complete penetrance and therefore in neither homogamy pool, can have complete penetrance and therefore fall within one or the other homogamy pool. The set of genotypes within such a pool therefore constitutes an 'absorbing state', in that all descendents of an individual having one of those genotypes remain in that pool. If there are no homgamy pools, there is no means of eliminating interbreeding between individuals adapted to different habitats unless habitat prefererence is error free. The critical role of homogamy pools in sympatric speciation (sensu stricto) is confirmed by Kondrashov's (1983a,b, 1986) models. A population that is saturated with respect to asm penetrance can include individuals (or genotypes) with penetrance excess. The probability of the offspring of such an individual having complete penetrance is enhanced, since both homozygous and heterozygous offspring can yield the phenotype of a parent that has penetrance excess. A relationship between penetrance excess .and dominance is suggested by Haldane (1930) who proposed that the evolution of dominance can be achieved by the strengthening of the wild type allele, so that optimal rates of enzyme production can be attained even in the heterozygote. Sved and Mayo (1970) called such genes 'haplo- 202 Johnson sufficient'. Selection pressure and consequent evolution leading to some 'extra' pathway product, as suggested by Haldane (1970), seems plausible, unless one can think of a biological limitation on the capacity of metabolic pathways to produce more product than is sufficient to ensure the occurrence of a particular behaviour (or other phenotype). Even though there may be some physiological cost in producing 'extra' product, such cost must be weighed against the advantage of being able to pass the benefit of optimal rates of enzyme production to offspring who otherwise, due to a recombination event, are burdened by less than optimal rates. Behavioural characters, whose expression is often contingent on circumstances other than physiological, may be particularly amenable to penetrance excess. Natural populations of similar species existing in the same area but that do not interbreed due to differences in mate recognition systems controlled by more than one gene can theoretically be viewed as a metapopulation that is saturated with respect to a s m penetrance. The intermediate forms happen to have been largely eliminated in these cases. Such populations are not uncommon. The closely related sulfur butterflies Colias eurytheme and Colias philidiee are an example of this. These species occur together in most of North America but are sexually isolated under most natural conditions due to female response to species-specific visual and pheromonal signals (Taylor, 1972; Grula and Taylor, 1979). Non-habitat assortative mating models By including at least two a s m loci in our simulations, we take into account cases of non-habitat assortative mating (e.g. Grula and Taylor, 1979; Roelofs et al., 1987) in which one set of a s m loci is needed for variation in the display characters of one sex (for example, pheromone composition), and another set is needed for variation in preference by the other sex (for example, increased attraction for a specific pheromone composition). When a mutant a s m allele first occurs in a population, it will be heterozygous for the individual carrying the mutant. In our model, these mutant individuals are of phenotype C, so they easily find mates since that portion of the population continues to be large until the speciation process nears completion. But if the initial frequency of the rare a s m allele is too low, as may be the case in our simulation models (frequency = 0.01), the problem arises for individuals with nearly complete a s m penetrance and homozygous a s m loci. Those individuals may occur so infrequently as to seldom encounter one another, yet they are assumed to mate homogamously in our model. As a consequence, our model applies to HMSD when the a s m alleles have become frequent enough so that individuals with homozygous a s m loci and complete penetrance can be quite certain of finding mates. Although our model is a basic HMSD model in that it takes into account all three types of loci, it does not take into account mating success. It assumes that each generation all individuals succeed in mating and with one partner only. A more general HMSD model is needed that takes into account not only frequency-dependent mating success, but also mating success that is genotype dependent and habitat dependent (regardless of frequency dependence). Mating success is expected to be genotype dependent if changes in the genome by mutation can improve the probability of an individual finding mates and accomplishing successful courtships. It can also be habitat dependent, in particular under the conditions of HMSD. Genotype- and habitat-dependent mating success may particularly apply to species in which males compete for the number of females they inseminate. If mating success is habitat and genotype dependent for a population undergoing HMSD, natural selection will favour traits that increase habitat-specific mating success. Since habitat-specific homogamy occurs as a correlated trait, a s m alleles can reach the frequency at which our model applies, independent of natural selection on habitat-specific survival traits. Once HMSD is well Conditions for sympatric speciation 203 under way, the frequency dependence of asm penetrance can lead to a 'runaway' process that enhances the dramatic increase in linkage disequilibrium demonstrated in our model. Conclusions Under sympatric conditions and biologically reasonable intensities of selection and penetrance for habitat preference and non-habitat assortative mating, genetically controlled habitat preference can promote linkage disequilibrium between asm loci and fit loci in diploid populations. After a period of 'incubation', maximum linkage disequilibrium between all loci (completely correlated traits) can develop quickly and complete the speciation process. No further interbreeding (gene flow) is possible between the habitat-specific sister populations because linkage disequilibrium between fit loci and asm loci is complete. 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