Intraspecific competitive divergence and convergence under assortative mating

Ecologically driven sympatric speciation has received much attention recently. We investigate a multilocus model of a quantitative trait that is under frequency-dependent selection caused by intraspecific competition and acts as mating character for assortment. We identify the conditions that lead to the establishment of reproductively isolated clusters. This may be interpreted as evolutionary splitting or sympatric speciation. In our model, there are parameters that independently determine the strength of assortment, the costs for being choosy, and the strength of frequency-dependent natural selection. Sufficiently strong frequency dependence leads to disruptive selection on the phenotypes. The population consists of (sexual) haploid individuals. If frequency dependence is strong enough to induce disruptive selection and costs are absent or low, the result of evolution depends in a distinctive nonlinear way on the strength of assortment: under moderately strong assortment, less genetic variation is maintained than under weak or strong assortment, and sometimes there is none at all. Evolutionary splitting occurs only if frequency dependence and assortment are both strong enough and costs are low. Even then, the evolutionary outcome depends on the genetics and the initial conditions. The roles of the number of loci, of linkage, and of asymmetric selection are also explored.     

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.     

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.     

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.     

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.     

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.     

Linking intra‐ and interspecific assortative mating: Consequences for asymmetric sexual isolation

Assortative mating is of interest because of its role in speciation and the maintenance of species boundaries. However, we know little about how within‐species assortment is related to interspecific sexual isolation. Most previous studies of assortative mating have focused on a single trait in males and females, rather than utilizing multivariate trait information. Here, we investigate how intraspecific assortative mating relates to sexual isolation in two sympatric and congeneric damselfly species (genus Calopteryx). We connect intraspecific assortment to interspecific sexual isolation by combining field observations, mate preference experiments, and enforced copulation experiments. Using canonical correlation analysis, we demonstrate multivariate intraspecific assortment for body size and body shape. Males of the smaller species mate more frequently with heterospecific females than males of the larger species, which showed less attraction to small heterospecific females. Field experiments suggest that sexual isolation asymmetry is caused by male preferences for large heterospecific females, rather than by mechanical isolation due to interspecific size differences or female preferences for large males. Male preferences for large females and male–male competition for high quality females can therefore counteract sexual isolation. This sexual isolation asymmetry indicates that sexual selection currently opposes a species boundary.     

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.     

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.     

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.     

Incipient sympatric speciation in Midas cichlid fish from the youngest and one of the smallest crater lakes in Nicaragua due to differential use of the benthic and limnetic habitats?

Understanding how speciation can occur without geographic isolation remains a central objective in evolutionary biology. Generally, some form of disruptive selection and assortative mating are necessary for sympatric speciation to occur. Disruptive selection can arise from intraspecific competition for resources. If this competition leads to the differential use of habitats and variation in relevant traits is genetically determined, then assortative mating can be an automatic consequence (i.e., habitat isolation). In this study, we caught Midas cichlid fish from the limnetic (middle of the lake) and benthic (shore) habitats of Crater Lake Asososca Managua to test whether some of the necessary conditions for sympatric speciation due to intraspecific competition and habitat isolation are given. Lake As. Managua is very small (<900 m in diameter), extremely young (maximally 1245 years of age), and completely isolated. It is inhabited by, probably, only a single endemic species of Midas cichlids, Amphilophus tolteca. We found that fish from the limnetic habitat were more elongated than fish collected from the benthic habitat, as would be predicted from ecomorphological considerations. Stable isotope analyses confirmed that the former also exhibit a more limnetic lifestyle than the latter. Furthermore, split‐brood design experiments in the laboratory suggest that phenotypic plasticity is unlikely to explain much of the observed differences in body elongation that we observed in the field. Yet, neutral markers (microsatellites) did not reveal any genetic clustering in the population. Interestingly, demographic inferences based on RAD‐seq data suggest that the apparent lack of genetic differentiation at neutral markers could simply be due to a lack of time, as intraspecific competition may only have begun a few hundred generations ago.     

Refining the conditions for sympatric ecological speciation

Can speciation occur in a single population when different types of resources are available, in the absence of any geographical isolation, or any spatial or temporal variation in selection? The controversial topics of sympatric speciation and ecological speciation have already stimulated many theoretical studies, most of them agreeing on the fact that mechanisms generating disruptive selection, some level of assortment, and enough heterogeneity in the available resources, are critical for sympatric speciation to occur. Few studies, however, have combined the three factors and investigated their interactions. In this article, I analytically derive conditions for sympatric speciation in a general model where the distribution of resources can be uni‐ or bimodal, and where a parameter controls the range of resources that an individual can exploit. This approach bridges the gap between models of a unimodal continuum of resources and Levene‐type models with discrete resources. I then test these conditions against simulation results from a recently published article (Thibert‐Plante & Hendry, 2011, J. Evol. Biol. 24 : 2186–2196) and confirm that sympatric ecological speciation is favoured when (i) selection is disruptive (i.e. individuals with an intermediate trait are at a local fitness minimum), (ii) resources are differentiated enough and (iii) mating is assortative. I also discuss the role of mating preference functions and the need (or lack thereof) for bimodality in resource distributions for diversification.     

STRONG ASSORTATIVE MATING BY DIET,COLOR, SIZE,AND MORPHOLOGY BUT LIMITED PROGRESS TOWARD SYMPATRIC SPECIATION IN A CLASSIC EXAMPLE: CAMEROON CRATER LAKE CICHLIDS

Models predict that sympatric speciation depends on restrictive parameter ranges, such as sufficiently strong disruptive selection and assortative mating, but compelling examples in nature have rarely been used to test these predictions. I measured the strength of assortative mating within a species complex of Tilapia in Lake Ejagham, Cameroon, a celebrated example of incipient sympatric adaptive radiation. This species complex is in the earliest stages of speciation: morphological and ecological divergence are incomplete, species differ primarily in breeding coloration, and introgression is common. I captured 27 mated pairs in situ and measured the diet, color, size, and morphology of each individual. I found strong assortative mating by color, size, head depth, and dietary source of benthic or pelagic prey along two independent dimensions of assortment. Thus, Ejagham Tilapia showed strong assortative mating most conducive to sympatric speciation. Nonetheless, in contrast to a morphologically bimodal Sarotherodon cichlid species pair in the lake, Ejagham Tilapia show more limited progress toward speciation, likely due to insufficient strength of disruptive selection on morphology estimated in a previous study (γ = 0.16). This supports the predicted dependence of sympatric speciation on strong assortment and strong disruptive selection by examining a potentially stalled example in nature.     

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.     

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.     

Assortative mating by diet in a phenotypically unimodal but ecologically variable population of stickleback

Speciation with gene flow may be driven by a combination of positive assortative mating and disruptive selection, particularly if selection and assortative mating act on the same trait, eliminating recombination between ecotype and mating type. Phenotypically unimodal populations of threespine stickleback (Gasterosteus aculeatus) are commonly subject to disruptive selection due to competition for alternate prey. Here we present evidence that stickleback also exhibit assortative mating by diet. Among-individual diet variation leads to variation in stable isotopes, which reflect prey use. We find a significant correlation between the isotopes of males and eggs within their nests. Because egg isotopes are derived from females, this correlation reflects assortative mating between males and females by diet. In concert with disruptive selection, this assortative mating should facilitate divergence. However, the stickleback population remains phenotypically unimodal, highlighting the fact that assortative mating and disruptive selection do not guarantee evolutionary divergence and speciation.     

Quantitative traits and mode of speciation in Martinique anoles

We investigate extensive quantitative trait variation (dewlap hue, colour pattern, dorsum hue, body proportions and scalation) in the Martinique anole across eight transects representing nascent parapatric ecological speciation, nascent allopatric speciation and allopatric divergence without sufficient genetic structure to suggest speciation. Quantitative trait divergence can be extremely large between adjacent sets of populations, but with one exception that this is associated with difference in habitat rather than past allopatry. Nascent ecological speciation shows the greatest level of quantitative trait divergence across all character sets including those implicated in natural, as well as sexual selection. The sole example of nascent allopatric speciation is associated with fairly strong quantitative trait divergence among most character sets, but not the set most implicated in natural (rather than sexual) selection. The role of sexual selection in ecological speciation is discussed, both in terms of female choice with assortative mating and male–male competition with condition‐dependant sexual signals.     

Competitive environments induce shifts in host fidelity

Recent models support the idea of sympatric speciation as a result of the joint effects of disruptive selection and assortative mating. We present experimental data, testing models of speciation through frequency‐dependent selection. We show that under high competition on a mixture of resources/hosts, strains of the Seed beetle, Callosobruchus maculatus, change their host fidelity and evolve a more generalistic behaviour in resource utilization among females. The change in host fidelity did not result in disruptive selection and was not followed by assortative mating. This means that only one of three fundamental prerequisites for sympatric speciation evolved as a result of the frequency‐dependent selection. We conclude that for this process to work, a shift to a novel food resource as a result of selection must also lead to a loss of preference for the original resource such that individuals are only able to use either one of the two.     

Reinforcement and divergence under assortative mating

Traits that cause assortative mating such as the flowering time in plants and body size in animals can produce reproductive isolation between hybridizing populations. Can selection against unfit hybrids cause two populations to diverge in their mean values for these kinds of traits? Here I present a haploid analytical model of one population that receives gene flow from another. The partial pre-zygotic isolation between the two populations is caused by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by selection against genetic incompatibilities that can involve any form of selection on individual genes and gene combinations (epistasis). The analysis assumes that the introgression rate and selection coefficients are small. The results show that the assortment trait mean will not diverge from the immigrants unless there is direct selection on the trait favouring it to do so or there are genes of very large effect. The amount of divergence at equilibrium is determined by a balance between direct selection on the assortment trait and introgression from the other population. Additional selection against hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discussed in the light of these results.     

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.