Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation

Differential Stage-Specific Mortality as a Mechanism for Diversification

AbstractIndividual variability in mortality is widespread in nature. The general rule is that larger organisms have a greater chance of survival than smaller conspecifics. There is growing evidence that differential mortality between developmental stages has important consequences for the ecology and evolution of populations and communities. However, we know little about how it can influence diversification. Using an eco-evolutionary model of diversification that considers individual variability in mortality, I show that commonly observed differences in mortality between juveniles and adults can facilitate adaptive diversification. In particular, diversification is expected to be less restricted when mortality is more biased toward juveniles. Additionally, I find stage-specific differences in metabolic cost and foraging capacity to further facilitate diversification when adults are slightly superior competitors, due to either a lower metabolic cost or a higher foraging capacity, than juveniles. This is because by altering the population composition, differential stage-specific mortality and competitive ability can modulate the strength of intraspecific competition, which in turn determines the outcome of diversification. These results demonstrate the strong influence that ecological differences between developmental stages have on diversification and highlight the need for integrating developmental processes into diversification theory.

The succession of ecological divergence and reproductive isolation in adaptive radiations

Adaptive radiation is a major source of biodiversity but the way in which known components of ecological opportunity, ecological differentiation, and reproductive isolation underpin such biodiversity patterns remains elusive. Much is known about the evolution of ecological differentiation and reproductive isolation during single speciation events, but exactly how those processes scale up to complete adaptive radiations is less understood. Do we expect complete reproductive barriers between newly formed species before the ecological differentiation continues, or does proper species formation occur much later, long after the ecological diversification? Our goal is to improve our mechanistic understanding of adaptive radiations by analyzing an individual-based model that includes a suite of mechanisms that are known to contribute to biodiversity. The model includes variable biogeographic settings, ecological opportunities, and types of mate choice, which makes several different scenarios of an adaptive radiation possible. We find that evolving clades tend to exploit ecological opportunities early whereas reproductive barriers evolve later, demonstrating a decoupling of ecological differentiation and species formation. In many cases, we also find a long-term trend where assortative mating associated with ecological traits is replaced by sexual selection of neutral display traits as the primary mechanism for reproductive isolation. Our results propose that reticulate phylogenies are likely common and stem from initially low reproductive barriers, rather than the previously suggested idea of repeated hybridization events between well-separated species.

The impact of dormancy on evolutionary branching

In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

Resource Variation Within and Between Patches: Where Exploitation Competition, Local Adaptation, and Kin Selection Meet

AbstractIn patch- or habitat-structured populations, different processes can favor adaptive polymorphism at different scales. While spatial heterogeneity can generate spatially disruptive selection favoring variation between patches, local competition can lead to locally disruptive selection promoting variation within patches. So far, almost all theory has studied these two processes in isolation. Here, we use mathematical modeling to investigate how resource variation within and between habitats influences the evolution of variation in a consumer population where individuals compete in finite patches connected by dispersal. We find that locally and spatially disruptive selection typically act in concert, favoring polymorphism under a wider range of conditions than when in isolation. But when patches are small and dispersal between them is low, kin competition inhibits the emergence of polymorphism, especially when the latter is driven by local competition for resources. We further use our model to clarify what comparisons between trait and neutral genetic differentiation (Q ST / F ST comparisons) can tell about the nature of selection. Overall, our results help us understand the interaction between two major drivers of polymorphism: locally and spatially disruptive selection, and how this interaction is modulated by the unavoidable effects of kin selection under limited dispersal.

A geometric process of evolutionary game dynamics

Many evolutionary processes occur in phenotype spaces which are continuous. It is therefore of interest to explore how selection operates in continuous spaces. One approach is adaptive dynamics, which assumes that mutants are local. Here we study a different process which also allows non-local mutants. We assume that a resident population is challenged by an invader who uses a strategy chosen from a random distribution on the space of all strategies. We study the repeated donation game of direct reciprocity. We consider reactive strategies given by two probabilities, denoting respectively the probability to cooperate after the co-player has cooperated or defected. The strategy space is the unit square. We derive analytic formulae for the stationary distribution of evolutionary dynamics and for the average cooperation rate as function of the cost-to-benefit ratio. For positive reactive strategies, we prove that cooperation is more abundant than defection if the area of the cooperative region is greater than 1/2 which is equivalent to benefit, b, divided by cost, c, exceeding [Formula: see text]. We introduce the concept of strategies that are stable with probability one. We also study an extended process and discuss other games.

The molding of intraspecific trait variation by selection under ecological inheritance

Organisms continuously modify their environment, often impacting the fitness of future conspecifics due to ecological inheritance. When this inheritance is biased toward kin, selection favors modifications that increase the fitness of downstream individuals. How such selection shapes trait variation within populations remains poorly understood. Using mathematical modelling, we investigate the coevolution of multiple traits in a group-structured population when these traits affect the group environment, which is then bequeathed to future generations. We examine when such coevolution favors polymorphism as well as the resulting associations among traits. We find in particular that two traits become associated when one trait affects the environment while the other influences the likelihood that future kin experience this environment. To illustrate this, we model the coevolution of (a) the attack rate on a local renewable resource, which deteriorates environmental conditions, with (b) dispersal between groups, which reduces the likelihood that kin suffers from such deterioration. We show this often leads to the emergence of two highly differentiated morphs: one that readily disperses and depletes local resources, and another that maintains these resources and tends to remain philopatric. More broadly, we suggest that ecological inheritance can contribute to phenotypic diversity and lead to complex polymorphism.

Evolutionary game theory and the adaptive dynamics approach: adaptation where individuals interact

Evolutionary game theory and the adaptive dynamics approach have made invaluable contributions to understanding how gradual evolution leads to adaptation when individuals interact. Here, we review some of the basic tools that have come out of these contributions to model the evolution of quantitative traits in complex populations. We collect together mathematical expressions that describe directional and disruptive selection in class- and group-structured populations in terms of individual fitness, with the aims of bridging different models and interpreting selection. In particular, our review of disruptive selection suggests there are two main paths that can lead to diversity: (i) when individual fitness increases more than linearly with trait expression; (ii) when trait expression simultaneously increases the probability that an individual is in a certain context (e.g. a given age, sex, habitat, size or social environment) and fitness in that context. We provide various examples of these and more broadly argue that population structure lays the ground for the emergence of polymorphism with unique characteristics. Beyond this, we hope that the descriptions of selection we present here help see the tight links among fundamental branches of evolutionary biology, from life history to social evolution through evolutionary ecology, and thus favour further their integration. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

A kin-selection model of fairness in heterogeneous populations

Humans and other primates exhibit pro-social preferences for fairness. These preferences are thought to be reinforced by strong reciprocity, a policy that rewards fair actors and punishes unfair ones. Theories of fairness based on strong reciprocity have been criticized for overlooking the importance of individual differences in socially heterogeneous populations. Here, we explore the evolution of fairness in a heterogeneous population. We analyse the Ultimatum Game in cases where players' roles in the game are determined by their status. Importantly, our model allows for non-random pairing of players, and so we also explore the role played by kin selection in shaping fairness. Our kin-selection model shows that, when individuals condition their behaviour on their role in the game, fairness can be understood as either altruistic or spiteful. Altruistic fairness directs resources from less valuable members of a genetic lineage to more valuable members of the same lineage, whereas spiteful fairness keeps resources away from the competitors of the actor's high-value relatives. When individuals express fairness unconditionally it can be understood as altruistic or selfish. When it is altruistic, unconditional fairness again serves to direct resources to high-value members of genetic lineages. When it is selfish, unconditional fairness simply improves an individual's own standing. Overall, we expand kin-selection based explanations for fairness to include motivations other than spite. We show, therefore, that one need not invoke strong reciprocity to explain the advantage of fairness in heterogeneous populations.

The effectiveness of pseudomagic traits in promoting premating isolation

Upon the secondary contact of populations, speciation with gene flow is greatly facilitated when the same pleiotropic loci are both subject to divergent ecological selection and induce non-random mating, leading to loci with this fortuitous combination of functions being referred to as 'magic trait' loci. We use a population genetics model to examine whether 'pseudomagic trait' complexes, composed of physically linked loci fulfilling these two functions, are as efficient in promoting premating isolation as magic traits. We specifically measure the evolution of choosiness, which controls the strength of assortative mating. We show that, surprisingly, pseudomagic trait complexes, and to a lesser extent also physically unlinked loci, can lead to the evolution of considerably stronger assortative mating preferences than do magic traits, provided polymorphism at the involved loci is maintained. This is because assortative mating preferences are generally favoured when there is a risk of producing maladapted recombinants, as occurs with non-magic trait complexes but not with magic traits (since pleiotropy precludes recombination). Contrary to current belief, magic traits may not be the most effective genetic architecture for promoting strong premating isolation. Therefore, distinguishing between magic traits and pseudomagic trait complexes is important when inferring their role in premating isolation. This calls for further fine-scale genomic research on speciation genes.

Microbial warfare and the evolution of symbiosis

Cooperative symbionts enable their hosts to exploit a diversity of environments. A low genetic diversity (high relatedness) between the symbionts within a host is thought to favour cooperation by reducing conflict within the host. However, hosts will not be favoured to transmit their symbionts (or commensals) in costly ways that increase relatedness, unless this also provides an immediate fitness benefit to the host. We suggest that conditionally expressed costly competitive traits, such as antimicrobial warfare with bacteriocins, could provide a relatively universal reason for why hosts would gain an immediate benefit from increasing the relatedness between symbionts. We theoretically test this hypothesis with a simple illustrative model that examines whether hosts should manipulate relatedness, and an individual-based simulation, where host control evolves in a structured population. We find that hosts can be favoured to manipulate relatedness, to reduce conflict between commensals via this immediate reduction in warfare. Furthermore, this manipulation evolves to extremes of high or low vertical transmission and only in a narrow range is partly vertical transmission stable.

The evolution of manipulative cheating

A social cheat is typically assumed to be an individual that does not perform a cooperative behaviour, or performs less of it, but can still exploit the cooperative behaviour of others. However, empirical data suggests that cheating can be more subtle, involving evolutionary arms races over the ability to both exploit and resist exploitation. These complications have not been captured by evolutionary theory, which lags behind empirical studies in this area. We bridge this gap with a mixture of game-theoretical models and individual-based simulations, examining what conditions favour more elaborate patterns of cheating. We found that as well as adjusting their own behaviour, individuals can be selected to manipulate the behaviour of others, which we term 'manipulative cheating'. Further, we found that manipulative cheating can lead to dynamic oscillations (arms races), between selfishness, manipulation, and suppression of manipulation. Our results can help explain both variation in the level of cheating, and genetic variation in the extent to which individuals can be exploited by cheats.

The enrichment paradox in adaptive radiations: Emergence of predators hinders diversification in resource rich environments

Adaptive radiations are known for rapid niche diversification in response to ecological opportunity. While most resources usually exist prior to adaptive radiation, novel niches associated with novel resources can be created as a clade diversifies. For example, in African lake cichlid radiations some species prey upon other species of the clade (intraclade consumers). Using a trait-based eco-evolutionary model, we investigate the evolution of intraclade consumers in adaptive radiations and the effect of this novel trophic interaction on the diversification process of the radiating clade. We find that the evolutionary emergence of intraclade consumers halts the diversification processes of other ecomorphs as a result of increased top-down control of density. Because high productivity enables earlier evolution of intraclade consumers, highly productive environments come to harbour less species-rich radiations than comparable radiations in less productive environments. Our results reveal how macroevolutionary and community patterns can emerge from ecological and microevolutionary processes.

Transient Eco-Evolutionary Dynamics and the Window of Opportunity for Establishment of Immigrants

AbstractTo what extent does landscape genetic structure bear the signature of arrival order of lineages during population assembly? Rapid genetic adaptation of resident populations founded by early colonists to local conditions might prevent establishment of later-arriving lineages, resulting in an evolution-mediated priority effect. This might result in a limited window of opportunity for establishment during which the resident population did not have sufficient time yet to monopolize the patch through local adaptation. The length of this window of opportunity is expected to depend on the degree to which early colonists and immigrants are preadapted to local habitat conditions. We present an intraspecific competition model of the initial transient population and evolutionary dynamics that quantifies the window of opportunity for establishment for asexual species. The model explicitly addresses the long-lasting effects of evolution-mediated priority effects by tracking lineages through time. Our results show that the difference in initial preadaptation between early colonists and late immigrants and the speed of evolution codetermine the window of opportunity for establishment. Our results also suggest that local populations should often be dominated by descendants of just a few early colonist lineages and that landscape genetic structure should often reflect the legacy of colonization history.

Sexual dimorphism driven by intersexual resource competition: Why is it rare, and where to look for it?

Sexes often differ more obviously in secondary sexual characteristics than in traits that appear naturally selected, despite conceivable benefits to intersexual niche partitioning. Genetic constraints may play a role in limiting sex‐specific niche evolution; however, it is not clear why this limit should apply to naturally selected traits more than those under sexual selection; the latter routinely produces dimorphism. We ask whether ecological factors and/or features of the mating system limit dimorphism in resource use, or conversely, what conditions are the most permissible ones for sexual niche differences.

The scale of mating competition and spatial variation in resource availability can help predict sexually dimorphic niches or the lack thereof. We investigate why and when dimorphism might fail to evolve even if genetic covariation between the sexes posed no constraint.

Our analytical model incorporates the first aspect of spatial interactions (scale of mating competition). It is followed by simulations that explore broader conditions, including multiple resources with habitat heterogeneity, genetic correlations and non‐Gaussian resource‐use efficiency functions.

We recover earlier known conditions for favourable conditions for the evolution of niche partitioning between sexes, such as narrow individual niche and low degrees of genetic constraint. We also show spatial considerations to alter this picture. Sexual niche divergence occurs more readily when local mating groups are small and different resources occur reliably across habitats. Polygyny (medium‐sized or large mating groups) can diminish the prospects for dimorphism even if no genetic constraints are present. Habitat heterogeneity typically also disfavours niche dimorphism but can also lead to polymorphism within a sex, if it is beneficial to specialize to be very competitive in one habitat, even at a cost to performance in the other.

Sexual conflict is usually used to explain dimorphic traits or behaviours. Our models highlight that introducing conflict (achieved by switching from monogamy to polygamy) can also be responsible for sexual monomorphism. Under monogamy, males benefit from specializing to consume other resources than what feeds the female best. Polygyny makes males disregard this female benefit, and both sexes compete for the most profitable resource, leading to overlapping niches.

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation

"Magic traits," in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these "pseudomagic traits" can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.

Using mathematical modelling to investigate the adaptive divergence of whitefish in Fennoscandia

Modern speciation theory has greatly benefited from a variety of simple mathematical models focusing on the conditions and patterns of speciation and diversification in the presence of gene flow. Unfortunately the application of general theoretical concepts and tools to specific ecological systems remains a challenge. Here we apply modeling tools to better understand adaptive divergence of whitefish during the postglacial period in lakes of northern Fennoscandia. These lakes harbor up to three different morphs associated with the three major lake habitats: littoral, pelagic, and profundal. Using large-scale individual-based simulations, we aim to identify factors required for in situ emergence of the pelagic and profundal morphs in lakes initially colonized by the littoral morph. The importance of some of the factors we identify and study - sufficiently large levels of initial genetic variation, size- and habitat-specific mating, sufficiently large carrying capacity of the new niche - is already well recognized. In addition, our model also points to two other factors that have been largely disregarded in theoretical studies: fitness-dependent dispersal and strong predation in the ancestral niche coupled with the lack of it in the new niche(s). We use our theoretical results to speculate about the process of diversification of whitefish in Fennoscandia and to identify potentially profitable directions for future empirical research.

How Does Joint Evolution of Consumer Traits Affect Resource Specialization?

Consumers regularly experience trade-offs in their ability to find, handle, and digest different resources. Evolutionary ecologists recognized the significance of this observation for the evolution and maintenance of biological diversity long ago and continue to elaborate on the conditions under which to expect one or several specialists, generalists, or combinations thereof. Existing theory based on a single evolving trait predicts that specialization requires strong trade-offs such that generalists perform relatively poorly, while weak trade-offs favor a single generalist. Here, we show that this simple dichotomy does not hold true under joint evolution of two or more foraging traits. In this case, the boundary between trade-offs resulting in resource specialists and resource generalists is shifted toward weaker trade-off curvatures. In particular, weak trade-offs can result in evolutionary branching, leading to the evolution of two coexisting resource specialists, while the evolution of a single resource generalist requires particularly weak trade-offs. These findings are explained by performance benefits due to epistatic trait interactions enjoyed by phenotypes that are specialized in more than one trait for the same resource.

Why So Variable: Can Genetic Variance in Flowering Thresholds Be Maintained by Fluctuating Selection?

We use integral projection models (IPMs) and individual-based simulations to study the evolution of genetic variance in two monocarpic plant systems. Previous approaches combining IPMs with an adaptive dynamics-style invasion analysis predicted that genetic variability in the size threshold for flowering will not be maintained, which conflicts with empirical evidence. We ask whether this discrepancy can be resolved by making more realistic assumptions about the underlying genetic architecture, assuming a multilocus quantitative trait in an outcrossing diploid species. To do this, we embed the infinitesimal model of quantitative genetics into an IPM for a size-structured cosexual plant species. The resulting IPM describes the joint dynamics of individual size and breeding value of the evolving trait. We apply this general framework to the monocarpic perennials Oenothera glazioviana and Carlina vulgaris. The evolution of heritable variation in threshold size is explored in both individual-based models (IBMs) and IPMs, using a mutation rate modifier approach. In the Oenothera model, where the environment is constant, there is selection against producing genetically variable offspring. In the Carlina model, where the environment varies between years, genetically variable offspring provide a selective advantage, allowing the maintenance of genetic variability. The contrasting predictions of adaptive dynamics and quantitative genetics models for the same system suggest that fluctuating selection may be more effective at maintaining genetic variation than previously thought.

Joint evolution of dispersal propensity and site selection in structured metapopulation models

We propose a novel mathematical model for a metapopulation in which dispersal occurs on two levels: juvenile dispersal from the natal site is mandatory but it may take place either locally within the natal patch or globally between patches. Within each patch, individuals live in sites. Each site can be inhabited by at most one individual at a time and it may be of high or low quality. A disperser immigrates into a high-quality site whenever it obtains one, but it immigrates into a low-quality site only with a certain probability that depends on the time within the dispersal season. The vector of these low-quality-site-acceptance probabilities is the site-selection strategy of an individual. We derive a proxy for the invasion fitness in this model and study the joint evolution of long-distance-dispersal propensity and site-selection strategy. We focus on the way different ecological changes affect the evolutionary dynamics and study the interplay between global patch-to-patch dispersal and local site-selection. We show that ecological changes affect site-selection mainly via the severeness of competition for sites, which often leads to effects that may appear counterintuitive. Moreover, the metapopulation structure may result in extremely complex site-selection strategies and even in evolutionary cycles. The propensity for long-distance dispersal is mainly determined by the metapopulation-level ecological factors. It is, however, also strongly affected by the winter-survival of the site-holders within patches, which results in surprising non-monotonous effects in the evolution of site-selection due to interplay with long-distance dispersal. Altogether, our results give new additional support to the recent general conclusion that evolution of site-selection is often dominated by the indirect factors that take place via density-dependence, which means that evolutionary responses can rarely be predicted by intuition.

Synergy from reproductive division of labor and genetic complexity drive the evolution of sex

Computer experiments that mirror the evolutionary dynamics of sexual and asexual organisms as they occur in nature were used to test features proposed to explain the evolution of sexual recombination. Results show that this evolution is better described as a network of interactions between possible sexual forms, including diploidy, thelytoky, facultative sex, assortation, bisexuality, and division of labor between the sexes, rather than a simple transition from parthenogenesis to sexual recombination. Diploidy was shown to be fundamental for the evolution of sex; bisexual reproduction emerged only among anisogamic diploids with a synergistic division of reproductive labor; and facultative sex was more likely to evolve among haploids practicing assortative mating. Looking at the evolution of sex as a complex system through individual-based simulations explains better the diversity of sexual strategies known to exist in nature, compared to classical analytical models.

The evolution of site-selection strategy during dispersal

We propose a mathematical model that enables the evolutionary analysis of site-selection process of dispersing individuals that encounter sites of high or low quality. Since each site can be inhabited by at most one individual, all dispersers are not able to obtain a high-quality site. We study the evolutionary dynamics of the low-quality-site acceptance as a function of the time during the dispersal season using adaptive dynamics. We show that environmental changes affect the evolutionary dynamics in two ways: directly and indirectly via density-dependent factors. Direct evolutionary effects usually follow intuition, whereas indirect effects are often counter-intuitive and hence difficult to predict without mechanistic modeling. Therefore, the mechanistic derivation of the fitness function, with careful attention on density- and frequency dependence, is essential for predicting the consequences of environmental changes to site selection. For example, increasing fecundity in high-quality sites makes them more tempting for dispersers and hence the direct effect of this ecological change delays the acceptance of low-quality sites. However, increasing fecundity in high-quality sites also increases the population size, which makes the competition for sites more severe and thus, as an indirect effect, forces evolution to favor less picky individuals. Our results indicate that the indirect effects often dominate the intuitive effects, which emphasizes the need for mechanistic models of the immigration process.

Evolutionary Stability of Jointly Evolving Traits in Subdivided Populations

The evolutionary stability of quantitative traits depends on whether a population can resist invasion by any mutant. While uninvadability is well understood in well-mixed populations, it is much less so in subdivided populations when multiple traits evolve jointly. Here, we investigate whether a spatially subdivided population at a monomorphic equilibrium for multiple traits can withstand invasion by any mutant or is subject to diversifying selection. Our model also explores the correlations among traits arising from diversifying selection and how they depend on relatedness due to limited dispersal. We find that selection tends to favor a positive (negative) correlation between two traits when the selective effects of one trait on relatedness is positively (negatively) correlated to the indirect fitness effects of the other trait. We study the evolution of traits for which this matters: dispersal that decreases relatedness and helping that has positive indirect fitness effects. We find that when dispersal cost is low and the benefits of helping accelerate faster than its costs, selection leads to the coexistence of mobile defectors and sessile helpers. Otherwise, the population evolves to a monomorphic state with intermediate helping and dispersal. Overall, our results highlight the effects of population subdivision for evolutionary stability and correlations among traits.

Where Two Are Fighting, the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.

Adaptive dynamics of saturated polymorphisms

We study the joint adaptive dynamics of n scalar-valued strategies in ecosystems where n is the maximum number of coexisting strategies permitted by the (generalized) competitive exclusion principle. The adaptive dynamics of such saturated systems exhibits special characteristics, which we first demonstrate in a simple example of a host-pathogen-predator model. The main part of the paper characterizes the adaptive dynamics of saturated polymorphisms in general. In order to investigate convergence stability, we give a new sufficient condition for absolute stability of an arbitrary (not necessarily saturated) polymorphic singularity and show that saturated evolutionarily stable polymorphisms satisfy it. For the case [Formula: see text], we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.

Evolutionary branching in complex landscapes

Divergent adaptation to different environments can promote speciation, and it is thus important to consider spatial structure in models of speciation. Earlier theoretical work, however, has been limited to particularly simple types of spatial structure (linear environmental gradients and spatially discrete metapopulations), leaving unaddressed the effects of more realistic patterns of landscape heterogeneity, such as nonlinear gradients and spatially continuous patchiness. To elucidate the consequences of such complex landscapes, we adapt an established spatially explicit individual-based model of evolutionary branching. We show that branching is most probable at intermediate levels of various types of heterogeneity and that different types of heterogeneity have, to some extent, additive effects in promoting branching. In contrast to such additivity, we find a novel refugium effect in which refugia in hostile environments provide opportunities for colonization, thus increasing the probability of branching in patchy landscapes. Effects of patchiness depend on the scale of patches relative to dispersal. Providing a needed connection to empirical research on biodiversity and conservation policy, we introduce empirically accessible spatial environmental metrics that quantitatively predict a landscape's branching propensity.

Evolution of specialization under non-equilibrium population dynamics

We analyze the evolution of specialization in resource utilization in a mechanistically underpinned discrete-time model using the adaptive dynamics approach. We assume two nutritionally equivalent resources that in the absence of consumers grow sigmoidally towards a resource-specific carrying capacity. The consumers use resources according to the law of mass-action with rates involving trade-off. The resulting discrete-time model for the consumer population has over-compensatory dynamics. We illuminate the way non-equilibrium population dynamics affect the evolutionary dynamics of the resource consumption rates, and show that evolution to the trimorphic coexistence of a generalist and two specialists is possible due to asynchronous non-equilibrium population dynamics of the specialists. In addition, various forms of cyclic evolutionary dynamics are possible. Furthermore, evolutionary suicide may occur even without Allee effects and demographic stochasticity.

An evolutionary dynamics model adapted to eusocial insects

This study aims to better understand the evolutionary processes allowing species coexistence in eusocial insect communities. We develop a mathematical model that applies adaptive dynamics theory to the evolutionary dynamics of eusocial insects, focusing on the colony as the unit of selection. The model links long-term evolutionary processes to ecological interactions among colonies and seasonal worker production within the colony. Colony population dynamics is defined by both worker production and colony reproduction. Random mutations occur in strategies, and mutant colonies enter the community. The interactions of colonies at the ecological timescale drive the evolution of strategies at the evolutionary timescale by natural selection. This model is used to study two specific traits in ants: worker body size and the degree of collective foraging. For both traits, trade-offs in competitive ability and other fitness components allows to determine conditions in which selection becomes disruptive. Our results illustrate that asymmetric competition underpins diversity in ant communities.

Adaptive divergence in Darwin's race: how coevolution can generate trait diversity in a pollination system

Understanding how reciprocal selection shapes interacting species in Darwin's coevolutionary race is a captivating pursuit in evolutionary ecology. Coevolving traits can potentially display following three patterns: (1) geographical variation in matched traits, (2) bias in trait matching, and (3) bimodal distribution of a trait in certain populations. Based on the framework of adaptive dynamics, we present an evolutionary model for a coevolving pollination system involving the long-proboscid fly (Moegistorhynchus longirostris) and the long-tubed iris (Lapeirousia anceps). The model successfully demonstrates that Darwin's hypothesis can lead to all three patterns if costs are involved. Geographical variation in matched traits could be driven by geographical variation in environmental factors that affect the cost rate of trait escalation. Unequal benefits derived from the interaction by the fly and the flower could potentially cause the bias in trait matching of the system. Different cost rates to trait elongation incurred by the two species and weak assortative interactions in the coevolutionary race can drive divergent selection (i.e., an evolutionary branching) that leads to the bimodal distribution of traits. Overall, the model highlights the importance of assortative interactions and the balance of costs incurred by coevolving species as factors determining the eventual phenotypic outcome of coevolutionary interactions.

Selection against accumulating mutations in niche-preference genes can drive speciation

Our current understanding of sympatric speciation is that it occurs primarily through disruptive selection on ecological genes driven by competition, followed by reproductive isolation through reinforcement-like selection against inferior intermediates/heterozygotes. Our evolutionary model of selection on resource recognition and preference traits suggests a new mechanism for sympatric speciation. We find speciation can occur in three phases. First a polymorphism of functionally different phenotypes is established through evolution of specialization. On the gene level, regulatory functions have evolved in which some alleles are conditionally switched off (i.e. are silent). These alleles accumulate harmful mutations that potentially may be expressed in offspring through recombination. Second mating associated with resource preference invades because harmful mutations in parents are not expressed in the offspring when mating assortatively, thereby dividing the population into two pre-zygotically isolated resource-specialist lineages. Third, silent alleles that evolved in phase one now accumulate deleterious mutations over the following generations in a Bateson-Dobzhansky-Muller fashion, establishing a post-zygotic barrier to hybridization.

A METHODOLOGY FOR THE STOCHASTIC MODELING AND SIMULATION OF SYMPATRIC SPECIATION BY SEXUAL SELECTION

In the evolution literature, sympatric speciation is the origin of two, or more, species from a single local population. Many models have been developed to study the role of ecological competition and sexual selection in sympatric speciation.

In this paper we propose a methodology for systematically deriving efficient computational models to study speciation in populations evolving with overlapping generations. As a particular case, we consider sympatric speciation by sexual selection and we follow an individual based approach: a population is represented as a set of individuals that can mate and survive according to given probabilities.

We use our methodology to construct four different models for sympatric speciation, based on male traits and female preferences. These models differ in the genotypical representation of the individuals. Results of simulations in the different models are shown and discussed.

The study of the models show that sympatric speciation by sexual selection is unlikely, also with a favorable distribution of genotypes in the initial population.

What role does natural selection play in speciation?

If distinct biological species are to coexist in sympatry, they must be reproductively isolated and must exploit different limiting resources. A two-niche Levene model is analysed, in which habitat preference and survival depend on underlying additive traits. The population genetics of preference and viability are equivalent. However, there is a linear trade-off between the chances of settling in either niche, whereas viabilities may be constrained arbitrarily. With a convex trade-off, a sexual population evolves a single generalist genotype, whereas with a concave trade-off, disruptive selection favours maximal variance. A pure habitat preference evolves to global linkage equilibrium if mating occurs in a single pool, but remarkably, evolves to pairwise linkage equilibrium within niches if mating is within those niches--independent of the genetics. With a concave trade-off, the population shifts sharply between a unimodal distribution with high gene flow and a bimodal distribution with strong isolation, as the underlying genetic variance increases. However, these alternative states are only simultaneously stable for a narrow parameter range. A sharp threshold is only seen if survival in the 'wrong' niche is low; otherwise, strong isolation is impossible. Gene flow from divergent demes makes speciation much easier in parapatry than in sympatry.

Live where you thrive: joint evolution of habitat choice and local adaptation facilitates specialization and promotes diversity

We derive a comprehensive overview of specialization evolution based on analytical results and numerical illustrations. We study the separate and joint evolution of two critical facets of specialization-local adaptation and habitat choice-under different life cycles, modes of density regulation, variance-covariance structures, and trade-off strengths. A particular feature of our analysis is the investigation of arbitrary trade-off functions. We find that local-adaptation evolution qualitatively changes the outcome of habitat-choice evolution under a wide range of conditions. In addition, habitat-choice evolution qualitatively and invariably changes the outcomes of local-adaptation evolution whenever trade-offs are weak. Even weak trade-offs, which favor generalists when habitat choice is fixed, select for specialists once local adaptation and habitat choice are both allowed to evolve. Unless trapped by maladaptive genetic constraints, joint evolution of local adaptation and habitat choice in the models analyzed here thus always leads to specialists, independent of life cycle, density regulation, and trade-off strength, thus raising the bar for evolutionarily sound explanations of generalism. Whether a single specialist or two specialists evolve depends on the life cycle and the mode of density regulation. Finally, we explain why the gradual evolutionary emergence of coexisting specialists requires more restrictive conditions than does their evolutionarily stable maintenance.

Species invasion history influences community evolution in a tri-trophic food web model

Background

Recent experimental studies have demonstrated the importance of invasion history for evolutionary formation of community. However, only few theoretical studies on community evolution have focused on such views.

Methodology and Principal Findings

We used a tri-trophic food web model to analyze the coevolutionary effects of ecological invasions by a mutant and by a predator and/or resource species of a native consumer species community and found that ecological invasions can lead to various evolutionary histories. The invasion of a predator makes multiple evolutionary community histories possible, and the evolutionary history followed can determine both the invasion success of the predator into the native community and the fate of the community. A slight difference in the timing of an ecological invasion can lead to a greatly different fate. In addition, even greatly different community histories can converge as a result of environmental changes such as a predator trait shift or a productivity change. Furthermore, the changes to the evolutionary history may be irreversible.

Conclusions and Significance

Our modeling results suggest that the timing of ecological invasion of a species into a focal community can largely change the evolutionary consequences of the community. Our approach based on adaptive dynamics will be a useful tool to understand the effect of invasion history on evolutionary formation of community.

Maintenance of host variation in tolerance to pathogens and parasites

Tolerance and resistance provide hosts with two distinct defense strategies against parasitism. In resistance the hosts "fight" the parasite directly, whereas in tolerance the hosts fight the disease by ameliorating the damage that infection causes. There is increasing recognition that the two mechanisms may exhibit very different evolutionary behaviors. Although empirical work has often noted considerable variance in tolerance within hosts, theory has predicted the fixation of tolerance due to positive frequency dependence through a feedback with disease prevalence. Here we reconcile these findings through a series of dynamic game theoretical models. We emphasize that there is a crucial distinction between tolerance to the effects of disease-induced mortality and tolerance to the effect of the disease-induced reductions in fecundity. Only mortality tolerance has a positive effect on parasite fitness, whereas sterility tolerance is neutral and may therefore result in polymorphisms. The nature of the costs to defense and their relationship to trade-offs between resistance and tolerance are crucial in determining the likelihood of variation, whereas the co-evolution of the parasite will not affect diversity. Our findings stress that it is important to measure the effects of different mechanisms on characteristics that affect the epidemiology of the parasite to completely understand the evolutionary dynamics of defense.

Emergence and loss of assortative mating in sympatric speciation

We have studied an agent model which presents the emergence of sexual barriers through the onset of assortative mating, a condition that might lead to sympatric speciation. In the model, individuals are characterized by two traits, each determined by a single locus A or B. Heterozygotes on A are penalized by introducing an adaptive difference from homozygotes. Two niches are available. Each A homozygote is adapted to one of the niches. The second trait, called the marker trait has no bearing on the fitness. The model includes mating preferences, which are inherited from the mother and subject to random variations. A parameter controlling recombination probabilities of the two loci is also introduced. We study the phase diagram by means of simulations, in the space of parameters (adaptive difference, carrying capacity, recombination probability). Three phases are found, characterized by (i) assortative mating, (ii) extinction of one of the A alleles and (iii) Hardy-Weinberg like equilibrium. We also make perturbations of these phases to see how robust they are. Assortative mating can be gained or lost with changes that present hysteresis loops, showing the resulting equilibrium to have partial memory of the initial state and that the process of going from a polymorphic panmictic phase to a phase where assortative mating acts as sexual barrier can be described as a first-order transition.

Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.