EVOLUTION OF DOMINANCE UNDER FREQUENCY-DEPENDENT INTRASPECIFIC COMPETITION IN AN ASSORTATIVELY MATING POPULATION

We study the evolution of higher levels of dominance as a response to negative frequency-dependent selection. In contrast to previous studies, we focus on the effect of assortative mating on the evolution of dominance under frequency-dependent intraspecific competition. We analyze a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under a mixture of frequency-independent stabilizing selection, density-dependent selection, and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The second (modifier) locus determines the degree of dominance at the trait level. Additionally, the population mates assortatively with respect to similarities in the ecological trait. Our analysis shows that the parameter region in which dominance can be established decreases if small levels of assortment are introduced. In addition, the degree of dominance that can be established also decreases. In contrast, if assortment is intermediate, sexual selection for extreme types can be established, which leads to evolution of higher levels of dominance than under random mating. For modifiers with large effects, intermediate levels of assortative mating are most favorable for the evolution of dominance. For large modifiers, the speed of fixation can even be higher for intermediate levels of assortative mating than for random mating.     

Sexual dimorphism and adaptive speciation: two sides of the same ecological coin

Models of adaptive speciation are typically concerned with demonstrating that it is possible for ecologically driven disruptive selection to lead to the evolution of assortative mating and hence speciation. However, disruptive selection could also lead to other forms of evolutionary diversification, including ecological sexual dimorphisms. Using a model of frequency-dependent intraspecific competition, we show analytically that adaptive speciation and dimorphism require identical ecological conditions. Numerical simulations of individual-based models show that a single ecological model can produce either evolutionary outcome, depending on the genetic independence of male and female traits and the potential strength of assortative mating. Speciation is inhibited when the genetic basis of male and female ecological traits allows the sexes to diverge substantially. This is because sexual dimorphism, which can evolve quickly, can eliminate the frequency-dependent disruptive selection that would have provided the impetus for speciation. Conversely, populations with strong assortative mating based on ecological traits are less likely to evolve a sexual dimorphism because females cannot simultaneously prefer males more similar to themselves while still allowing the males to diverge. This conflict between speciation and dimorphism can be circumvented in two ways. First, we find a novel form of speciation via negative assortative mating, leading to two dimorphic daughter species. Second, if assortative mating is based on a neutral marker trait, trophic dimorphism and speciation by positive assortative mating can occur simultaneously. We conclude that while adaptive speciation and ecological sexual dimorphism may occur simultaneously, allowing for sexual dimorphism restricts the likelihood of adaptive speciation. Thus, it is important to recognize that disruptive selection due to frequency-dependent interactions can lead to more than one form of adaptive splitting.     

Revisiting santa rosalia to unfold a degeneracy of classic models of speciation

Abstract Many classic models of speciation incorporate assortative mating based on mating groups, such as plants with different flowering times, and they investigate whether an ecological trait under disruptive natural selection becomes genetically associated with the selectively neutral mating trait. It is well known that this genetic association is potently destroyed by recombination. In this note, we point out a more fundamental difficulty: if a "knife-edge" symmetry assumption of previous models is violated, then the mating trait is no longer neutral and sexual selection eliminates the polymorphism in the mating locus. This result strengthens the growing consensus that magic traits are the more likely route to nonallopatric speciation. We expand the model assuming also ecological selection on the mating trait and investigate the conditions for natural selection to overcome sexual selection and maintain mating polymorphism; we find that the combination of natural and sexual selection can cause also bistability of allele frequencies.     

Modelling sympatric speciation by means of biologically plausible mechanistic processes as exemplified by threespine stickleback species pairs

We investigate the plausibility of sympatric speciation through a modelling study. We built up a series of models with increasing complexity while focussing on questioning the realism of model assumptions by checking them critically against a particular biological system, namely the sympatric benthic and limnetic species of threespine stickleback in British Columbia, Canada. These are morphologically adapted to their feeding habits: each performs better in its respective habitat than do hybrids with intermediate morphology. Ecological character displacement through disruptive selection and competition, and reinforcement through mating preferences may have caused their divergence. Our model assumptions include continuous morphological trait(s) instead of a dimorphic trait, and mating preferences based on the same trait(s) as selected for in food competition. Initially, morphology is intermediate. We apply disruptive selection against intermediates, frequency-dependent resource competition, and one of two alternative mating preference mechanisms. Firstly, preference is based on similarity where mating preference may result from “imprinting” on conspecifics encountered in their preferred foraging habitat. Here, speciation occurs easily—ecological hybrid inferiority is not necessary. Hybrid inferiority reinforces the stringency of assortative mating. Secondly, individual preferences exist for different trait values. Here, speciation occurs when linkage disequilibrium between trait and preference develops, and some hybrid inferiority is required. Finally, if the morphology subject to disruptive selection, frequency-dependent competition, and mate choice, is coded for by two loci, linkage disequilibrium between the two loci is required for speciation. Speciation and reinforcement of stringency of choosiness are possible in this case too, but rarely. Results demonstrate the contingency of speciation, with the same starting point not necessarily producing the same outcome. The study resulted in flagging issues where models often lack in biological realism and issues where more empirical studies could inform on whether assumptions are likely valid.     

Does competitive divergence occur if assortative mating is costly?

Most models of sympatric speciation have assumed that assortative mating has no costs. A few studies, however, have shown that the costs for being choosy can prevent such speciation. Here, we investigate the role of the strength of assortment and of the costs for being choosy for a simple genetic model of a single ('magic') trait that mediates both intraspecific competition for a continuum of resources and assortative mating, which is induced by choosy females who preferentially mate with males of similar phenotype. Choosiness may be costly if it is difficult to find a mating partner. Such magic trait models are considered to be most conducive of sympatric speciation. We consider a sexually reproducing population of haploid individuals that is density regulated. The trait is determined by a single locus with multiple alleles. The strength of stabilizing selection (caused by a unimodal resource distribution), the strength of competition, the degree of assortment and the costs for being choosy are independent parameters. We investigate analytically and numerically how these parameters determine the equilibrium and stability structure. In particular, we identify conditions under which no polymorphism at all is maintained as well as conditions under which strong competitive divergence occurs, or the population even splits into two reproductively isolated classes of highly diverse phenotypes. If costs are absent or moderate, genetic variability tends to be minimized at intermediate strengths of assortment, and reproductively isolated classes of phenotypes are a likely result of evolution only for intermediate or strong competition and for very strong assortment. The likelihood of divergence depends relatively weakly on the costs as long as they are not high. With high costs, however, increasingly strong assortment rapidly depletes all genetic variation, and strong competitive divergence is prevented.     

Evolution of assortative mating in a population expressing dominance

In this article, we study the influence of dominance on the evolution of assortative mating. We perform a population-genetic analysis of a two-locus two-allele model. We consider a quantitative trait that is under a mixture of frequency-independent stabilizing selection and density- and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The trait is determined by a single (ecological) locus and expresses intermediate dominance. The second (modifier) locus determines the degree of assortative mating, which is expressed in females only. Assortative mating is based on similarities in the quantitative trait ('magic trait' model). Analytical conditions for the invasion of assortment modifiers are derived in the limit of weak selection and weak assortment. For the full model, extensive numerical iterations are performed to study the global dynamics. This allows us to gain a better understanding of the interaction of the different selective forces. Remarkably, depending on the size of modifier effects, dominance can have different effects on the evolution of assortment. We show that dominance hinders the evolution of assortment if modifier effects are small, but promotes it if modifier effects are large. These findings differ from those in previous work based on adaptive dynamics.     

Assortative mating counteracts the evolution of dispersal polymorphisms

Polymorphic dispersal strategies are found in many plant and animal species. An important question is how the genetic variation underlying such polymorphisms is maintained. Numerous mechanisms have been discussed, including kin competition or frequency-dependent selection. In the context of sympatric speciation events, genetic and phenotypic variation is often assumed to be preserved by assortative mating. Thus, recently, this has been advocated as a possible mechanism leading to the evolution of dispersal polymorphisms. Here, we examine the role of assortative mating for the evolution of trade-off-driven dispersal polymorphisms by modeling univoltine insect species in a metapopulation. We show that assortative mating does not favor the evolution of polymorphisms. On the contrary, assortative mating favors the evolution of an intermediate dispersal type and a uni-modal distribution of traits within populations. As an alternative, mechanism dominance may explain the occurrence of two discrete morphs.     

Adaptive speciation when assortative mating is based on female preference for male marker traits

Adaptive speciation occurs when frequency-dependent ecological interactions generate conditions of disruptive selection to which lineage splitting is an adaptive response. Under such selective conditions, evolution of assortative mating mechanisms enables the break-up of the ancestral lineage into diverging and reproductively isolated descendent species. Extending previous studies, I investigate models of adaptive speciation due to the evolution of indirect assortative mating that is based on three different mating traits: the degree of assortativity, a female preference trait and a male marker trait. For speciation to occur, linkage disequilibria between different mating traits, e.g. between female preference and male marker traits, as well as between mating traits and the ecological trait, must evolve. This can lead to novel speciation scenarios, e.g. when reproductive isolation is generated by a splitting in the degree of assortativeness, with one of the emerging lineages mating assortatively, and the other one disassortatively. I investigate the effects of variation in various model parameters on the likelihood of speciation, as well as robustness of speciation to introducing costs of assortative mating. Even though in the models presented speciation requires the genetic potential for strong assortment as well as rather restrictive ecological conditions, the results show that adaptive speciation due to the evolution of assortative mating when mate choice is based on separate female preference and male marker traits is a theoretically plausible evolutionary scenario.     

Frequency-dependent selection and the evolution of assortative mating

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a "one-allele" model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to "reinforcement") regardless of the form of natural selection.     

An analytically tractable model for competitive speciation

Several recent models have shown that frequency-dependent disruptive selection created by intraspecific competition can lead to the evolution of assortative mating and, thus, to competitive sympatric speciation. However, since most of these results rely on limited numerical analyses, their generality has been debated. Here, we consider one of the standard models (the so-called Roughgarden model) with a simplified genetics where the selected trait is determined by a single diallelic locus. This model is sufficiently complex to maintain key properties of the general multilocus case but simple enough to allow for comprehensive analytical treatment by means of invasion fitness arguments. Depending on (1) the strength and (2) the shape of stabilizing selection, (3) the strength and (4) the shape of pairwise competition, (5) the shape of the mating function, and (6) whether assortative mating leads to sexual selection, we find five different evolutionary regimes. In one of these regimes, complete reproductive isolation can evolve through arbitrarily small steps in the strength of assortative mating. Our approach provides a mechanistic understanding of several phenomena that have been found in previous models. The results demonstrate how even in a simple model, the evolutionary outcome depends in a complex way on ecological and genetic parameters.     

The effects of sexual selection on trait divergence in a peripheral population with gene flow

The unique aspects of speciation and divergence in peripheral populations have long sparked much research. Unidirectional migration, received by some peripheral populations, can hinder the evolution of distinct differences from their founding populations. Here, we explore the effects that sexual selection, long hypothesized to drive the divergence of distinct traits used in mate choice, can play in the evolution of such traits in a partially isolated peripheral population. Using population genetic continent‐island models, we show that with phenotype matching, sexual selection increases the frequency of an island‐specific mating trait only when female preferences are of intermediate strength. We identify regions of preference strength for which sexual selection can instead cause an island‐specific trait to be lost, even when it would have otherwise been maintained at migration‐selection balance. When there are instead separate preference and trait loci, we find that sexual selection can lead to low trait frequencies or trait loss when female preferences are weak to intermediate, but that sexual selection can increase trait frequencies when preferences are strong. We also show that novel preference strengths almost universally cannot increase, under either mating mechanism, precluding the evolution of premating isolation in peripheral populations at the early stages of species divergence.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Inheritance of female mating preference in a sympatric sibling species pair of Lake Victoria cichlids: implications for speciation

Female mate choice has often been proposed to play an important role in cases of rapid speciation, in particular in the explosively evolved haplochromine cichlid species flocks of the Great Lakes of East Africa. Little, if anything, is known in cichlid radiations about the heritability of female mating preferences. Entirely sympatric distribution, large ecological overlap and conspicuous differences in male nuptial coloration, and female preferences for these, make the sister species Pundamilia pundamilia and P. nyererei from Lake Victoria an ideally suited species pair to test assumptions on the genetics of mating preferences made in models of sympatric speciation. Female mate choice is necessary and sufficient to maintain reproductive isolation between these species, and it is perhaps not unlikely therefore, that female mate choice has been important during speciation. A prerequisite for this, which had remained untested in African cichlid fish, is that variation in female mating preferences is heritable. We investigated mating preferences of females of these sister species and their hybrids to test this assumption of most sympatric speciation models, and to further test the assumption of some models of sympatric speciation by sexual selection that female preference is a single-gene trait. We find that the differences in female mating preferences between the sister species are heritable, possibly with quite high heritabilities, and that few but probably more than one genetic loci contribute to this behavioural speciation trait with no apparent dominance. We discuss these results in the light of speciation models and the debate about the explosive radiation of cichlid fishes in Lake Victoria.     

A quantitative genetic competition model for sympatric speciation

I use multilocus genetics to describe assortative mating in a competition model. The intensity of competition between individuals is influenced by a quantitative character whose value is determined additively by alleles from many loci. With assortative mating based on this character, frequency- and density-dependent competition can subdivide a population with an initially unimodal character distribution. The character distribution becomes bimodal, and the subpopulations corresponding to the two modes are reproductively separated because mating is assortative. This happens if the resource distribution is unimodal, i.e. even if selection due to phenotypic carrying capacities is not disruptive. The results suggest that sympatric speciation due to frequency-dependent selection can occur in quite general ecological scenarios if mating is assortative. I also discuss the evolution of assortative mating. Since it induces bimodal phenotype distributions, assortative mating leads to a better match of the resources if their distribution is also bimodal. Moreover, in a population with a bimodal phenotype distribution, the average strength of frequency-dependent competition is lower than in a unimodal population. Therefore, assortative mating permits higher equilibrium densities than random mating even if the resource distribution is unimodal. Thus, even though it may lead to a less efficient resource use, assortative mating is favoured over random mating because it reduces frequency-dependent effects of competition.     

Male-male competition and speciation: aggression bias towards differently coloured rivals varies between stages of speciation in a Lake Victoria cichlid species complex

Sympatric speciation driven by sexual selection by female mate choice on a male trait is a much debated topic. The process is problematic because of the lack of negative frequency-dependent selection that can facilitate the invasion of a novel colour phenotype and stabilize trait polymorphism. It has recently been proposed that male-male competition for mating territories can generate frequency-dependent selection on male colouration. Rare male cichlid fish would enjoy a fitness advantage if territorial defenders bias aggression towards male cichlid fish of their own colour. We used blue (ancestral type) and red phenotypes of the Lake Victoria cichlid species complex Pundamilia. We tested the aggression bias of wild-caught territorial blue male cichlid fish from five separate populations for blue vs. red rival male cichlid fish using simulated intruder choice tests. The different populations vary in the frequency of red male cichlid fish, and in the degree of reproductive isolation between red and blue, reflecting different stages of speciation. Blue male cichlid fish from a population that lack red phenotypes biased aggression towards blue stimulus male cichlid fish. The same was found in two populations where blue and red are reproductively isolated sister species. This aggression bias may facilitate the invasion of a novel colour phenotype and species coexistence. Blue male cichlid fish from two populations where red and blue are hybridizing incipient species biased aggression towards red stimulus male cichlid fish. Thus, after a successful invasion of red, aggression bias alone is not likely to generate frequency dependence required to stabilize the coexistence of phenotypes. The findings show that aggression bias varies between stages of speciation, but is not enough to stabilize the process of speciation.     

The effect of Wolbachia versus genetic incompatibilities on reinforcement and speciation

Wolbachia is a widespread group of intracellular bacteria commonly found in arthropods. In many insect species, Wolbachia induce a cytoplasmic mating incompatibility (CI). If different Wolbachia infections occur in the same host species, bidirectional CI is often induced. Bidirectional CI acts as a postzygotic isolation mechanism if parapatric host populations are infected with different Wolbachia strains. Therefore, it has been suggested that Wolbachia could promote speciation in their hosts. In this article we investigate theoretically whether Wolbachia-induced bidirectional CI selects for premating isolation and therefore reinforces genetic divergence between parapatric host populations. To achieve this we combined models for Wolbachia dynamics with a well-studied reinforcement model. This new model allows us to compare the effect of bidirectional CI on the evolution of female mating preferences with a situation in which postzygotic isolation is caused by nuclear genetic incompatibilities (NI). We distinguish between nuclear incompatibilities caused by two loci with epistatic interactions, and a single locus with incompatibility among heterozygotes in the diploid phase. Our main findings are: (1) bidirectional CI and single locus NI select for premating isolation with a higher speed and for a wider parameter range than epistatic NI; (2) under certain parameter values, runaway sexual selection leads to the increase of an introduced female preference allele and fixation of its preferred male trait allele in both populations, whereas under others it leads to divergence in the two populations in preference and trait alleles; and (3) bidirectional CI and single locus NI can stably persist up to migration rates that are two times higher than seen for epistatic NI. The latter finding is important because the speed with which mutants at the preference locus spread increases exponentially with the migration rate. In summary, our results show that bidirectional CI selects for rapid premating isolation and so generally support the view that Wolbachia can promote speciation in their hosts.     

Limits to the evolution of assortative mating by female choice under restricted gene flow

The evolution of assortative mating is a key component of the process of speciation with gene flow. Several recent theoretical studies have pointed out, however, that sexual selection which can result from assortative mating may cause it to plateau at an intermediate level; this is primarily owing to search costs of individuals with extreme phenotypes and to assortative preferences developed by individuals with intermediate phenotypes. I explore the limitations of assortative mating further by analysing a simple model in which these factors have been removed. Specifically, I use a haploid two-population model to ask whether the existence of assortative mating is sufficient to drive the further evolution of assortative mating. I find that a weakening in the effective strength of sexual selection with strong assortment leads to the existence of both a peak level of trait differentiation and the evolution of an intermediate level of assortative mating that will cause that peak. This result is robust to the inclusion of local adaptation and different genetic architecture of the trait. The results imply the existence of fundamental limits to the evolution of assortment via sexual selection in this situation, with which other factors, such as search costs, may interact.     

The conditions for speciation through intraspecific competition

Abstract It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency‐dependent selection caused by a balance of intraspecific competition and frequency‐independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment sometimes none at all. In addition to the strength of frequency‐dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.