The adaptive dynamics of function-valued traits

This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments.     

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.     

Group-beneficial traits, frequency-dependent selection and genotypic diversity: an antibiotic resistance paradigm

The evolution of group-beneficial traits potentially allows the survival of 'cheaters' that would otherwise be unfit. Here we describe experimental work on group-beneficial traits and the consequences of frequency-dependent selection in the context of bacterial antibiotic resistance. We constructed a 'self-limited antibiotic resistant' (SLAR) strain of Escherichia coli in which a TEM-1 beta-lactamase was anchored to the inner membrane. In pairwise competition experiments between the SLAR strain and ampicillin-sensitive strains, only the SLAR strain survived in the presence of ampicillin. We also constructed a 'shared antibiotic resistant' (SAR) strain in which TEM-1 beta-lactamase protected both the SAR strain and nearby sensitive cells, thus acting as a model for a genetically defined group-beneficial trait. In pairwise competition experiments of the SAR strain against two different sensitive strains of E. coli, we found that the sensitive strains maintained themselves at frequencies of 5-12% in the presence of ampicillin. When the relative cost of the SAR strain was lowered, its equilibrial frequency rose. Sensitive strains also arose from pure cultures of the SAR strain. In these cases, too, the sensitive 'cheaters' were maintained in ampicillin at frequencies comparable to those observed in the previous competitions. These results suggest that traits which benefit other group members can permit survival of genotypes that otherwise would be eliminated by natural selection, and allow the maintenance of greater genetic variation upon which evolution can operate.     

Evolution of a mating preference for a dual‐utility trait used in intrasexual competition in genetically monogamous populations

The selection pressures by which mating preferences for ornamental traits can evolve in genetically monogamous mating systems remain understudied. Empirical evidence from several taxa supports the prevalence of dual‐utility traits, defined as traits used both as armaments in intersexual selection and ornaments in intrasexual selection, as well as the importance of intrasexual resource competition for the evolution of female ornamentation. Here, we study whether mating preferences for traits used in intrasexual resource competition can evolve under genetic monogamy. We find that a mating preference for a competitive trait can evolve and affect the evolution of the trait. The preference is more likely to persist when the fecundity benefit for mates of successful competitors is large and the aversion to unornamented potential mates is strong. The preference can persist for long periods or potentially permanently even when it incurs slight costs. Our results suggest that, when females use ornaments as signals in intrasexual resource competition, males can evolve mating preferences for those ornaments, illuminating both the evolution of female ornamentation and the evolution of male preferences for female ornaments in monogamous species.     

The evolution of resource specialization through frequency-dependent and frequency-independent mechanisms

Levins's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins's approach is that it explicitly excludes frequency-dependent selection. Frequency dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency dependence has not been studied in detail. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency independent or frequency dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levins's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized.     

Long-term evolution of polygenic traits under frequency-dependent intraspecific competition

We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical results (provided by Bürger [2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50, 355-396]; Schneider [2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52, 483-523]) on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a 'largest' element, an LTE which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large.     

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.     

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we numerically analyze the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with two alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, here we add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductively isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.     

The evolution of alternative mating strategies in variable environments

Summary We assessed the influence of phenotypic plasticity in age at maturity on the maintenance of alternative mating strategies in male Atlantic salmon,Salmo salar. We calculated the fitness,r, associated with the parr and the anadromous strategies, using age-specific survival data from the field and strategy-specific fertilization data from the laboratory. The fitness of each strategy depended largely on mate competition (numbers of parr per female, i.e. parr frequency) and on age at maturity. Fitness declined with increasing numbers of parr per female with equilibrium frequencies (at which the fitnesses of each strategy are equal) being within the range observed in the wild. Equilibrium parr frequencies declined with decreasing growth rate and increasing age at maturity. Within populations, the existence of multiple age-specific sets of fitness functions suggests that the fitnesses of alternative strategies are best represented as multidimensional surfaces. The points of intersection of these surfaces, whose boundaries encompass natural variation in age at maturity and mate competition, define an evolutionarily stable continuum (ESC) of strategy frequencies along which the fitnesses associated with each strategy are equal. We propose a simple model that incorporates polygenic thresholds of a largely environmentally-controlled trait (age at maturity) to provide a mechanism by which an ESC can be maintained within a population. An indirect test provides support for the prediction that growth-rate thresholds for parr maturation exist and are maintained by stabilizing selection. Evolutionarily stable continua, maintained by negative frequency-dependent selection on threshold traits, provide a theoretical basis for understanding how alternative life histories can evolve in variable environments.     

Inertia: the discrepancy between individual and common good in dispersal and prospecting behaviour

The group selection debate of the 1960s made it clear that evolution does not necessarily increase population performance. Individuals can be selected to have traits that diminish a common good and make population persistence difficult. At the extreme, the discrepancy between levels of selection is predicted to make traits evolve towards values at which a population can no longer persist (evolutionary suicide). Dispersal and prospecting are prime examples of traits that have a strong influence on population persistence under environmental and demographic stochasticity. Theory predicts that an ‘optimal’ dispersal strategy from a population point of view can differ considerably from that produced by individual‐level selection. Because dispersal is frequently risky or otherwise costly, individuals are often predicted to disperse less than would be ideal for population performance (persistence or size). We define this discrepancy as ‘inertia’ and examine current knowledge of its occurrence and effects on population dynamics in nature. We argue that inertia is potentially widespread but that a framework is currently lacking for predicting precisely the extent to which it has a real influence on population persistence. The opposite of inertia, ‘hypermobility’ (more dispersal by individuals than would maximize population performance) remains a possibility: it is known that highest dispersal rates do not lead to best expected population performance, and examples of such high dispersal evolving exist at least in the theoretical literature. We also show, by considering prospecting behaviour, that similar issues arise in species with advanced cognitive and learning abilities. Individual prospecting strategies and the information acquired during dispersal are known to influence the decisions and therefore the fate of individuals and, as a corollary, populations. Again, the willingness of individuals to sample environments might evolve to levels that are not optimal for populations. This conflict can take intriguing forms. For example, better cognitive abilities of individuals may not always lead to better population‐level performance. Simulation studies have found that ‘blind’ dispersal can lead to better connected metapopulations than cognitively more advanced habitat choice rules: the latter can lead to too many individuals sticking to nearby safe habitat. The study of the mismatch between individual and population fitness should not be a mere intellectual exercise. Population managers typically need to take a population‐level view of performance, which may necessitate human intervention if it differs from what is selected for. We conclude that our knowledge of inertia and hypermobility would advance faster if theoretical studies—without much additional effort—quantified the population consequences of the evolving traits and compared this with hypothetical (not selectively favoured) dispersal rules, and if empirical studies were similarly conducted with the differing levels of selection in mind.     

The capture of heritable variation for genetic quality through social competition

In theory, females of many species choose mates based on traits that are indicators of male genetic quality. A fundamental question in evolutionary biology is why genetic variation for such indicator traits persists despite strong persistent selection imposed by female preference, which is known as the lek paradox. One potential solution to the lek paradox suggests that the traits that are targets of mate choice should evolve condition-dependent expression and that condition should have a large genetic variance. Condition is expected to exhibit high genetic variance because it is affected by a large number of physiological processes and hence, condition-dependent traits should 'capture' variation contributed by a large number of loci. We suggest that a potentially important cause of variation in condition is competition for limited resources. Here, we discuss a pair of models to analyze the evolutionary genetics of traits affected by success in social competition for resources. We show that competition can contribute to genetic variation of 'competition-dependent' traits that have fundamentally different evolutionary properties than other sources of variation. Competition dependence can make traits honest indicators of genetic quality by revealing the relative competitive ability of males, can provide a component of heritable variation that does not contribute to trait evolution, and can help maintain heritable variation under directional selection. Here we provide a general introduction to the concept of competition dependence and briefly introduce two models to demonstrate the potential evolutionary consequences of competition-dependent trait expression.     

Insight into the genetic bases of climatic adaptation in experimentally evolving wheat populations

Experimental populations evolving under natural selection represent an interesting tool to study genetic bases of adaptation. Evolution of genes possibly involved in adaptive response can be followed together with the corresponding phenotypic traits. Using experimental populations of hexaploid wheat, we studied the evolution of flowering time, a major adaptive trait that synchronizes the initiation of reproduction and the occurrence of favourable environmental conditions. During 12 generations, three populations were grown in contrasted environments (Vervins North France, Le Moulon near Paris, Toulouse South France) under the influence of natural selection, drift, mutation and recombination. Evolution of diversity at the major gene VRN-1 involved in wheat vernalization response has been analysed jointly with earliness estimated in controlled conditions. Whatever the population, rapid phenotypic changes as well as parallel genotypic variations were observed in the first seven generations, probably as the result of selection acting on this major gene which explains 80% of the trait variation overall. Different allelic combinations at physically unlinked copies of VRN-1 located on distinct genomes (A, B and D) were selected between populations. As theoretically expected, due to population differentiation, a high level of genetic diversity was maintained overall in generation 12. Surprisingly, in two populations out of three, the emergence of new alleles by mutation or migration, coupled with temporal variable selection or frequency-dependent selection, allowed to maintain within-population diversity despite local genetic drift and natural selection. This result may plead for an evolutionary approach of wheat genetic resource conservation.     

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.     

ON THE EVOLUTION OF PHENOTYPIC PLASTICITY IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

A genetic model for the dynamics of a quantitative trait is analyzed in terms of gene frequencies, linkage disequilibria, and environmental effects on the trait. In a randomly mating population, at each generation progeny move to niches where they are subject to weak Gaussian selection on the trait, with different fitness levels in the different niches. Initially, the variability of the trait is due to additive loci with heterozygous homeostasis. The evolution of plasticity is then described in terms of the invasion of the population by genetic modifiers that may epistatically affect the trait, its optimum in each niche, the strengths of selection, and other parameters characteristic of the niches. We show that the evolution of trait means within niches depends on the overall evolution in the whole system, and in general, optimum phenotypic values are not attained. The reaction norm and genotype-environment interaction may evolve even if the only effects of the modifier are on individual rates of dispersal, or on fitness effects resulting from the different environments in the different niches; this evolution does not require that the modifier affect parameters that influence the values of the trait. It is conjectured that in the least frequently reached niches with low fitness levels, the deviations from the trait optima should be larger than those in more commonly experienced and less stringent niches. Our analysis makes explicit the different contribution of between- and within-niche effects on the evolutionary dynamics of phenotypic plasticity in heterogeneous environments.     

Evolution of the elaborate male intromittent organ of Xiphophorus fishes

Internally fertilizing animals show a remarkable diversity in male genital morphology that is associated with sexual selection, and these traits are thought to be evolving particularly rapidly. Male fish in some internally fertilizing species have “gonopodia,” highly modified anal fins that are putatively important for sexual selection. However, our understanding of the evolution of genital diversity remains incomplete. Contrary to the prediction that male genital traits evolve more rapidly than other traits, here we show that gonopodial traits and other nongonopodial traits exhibit similar evolutionary rates of trait change and also follow similar evolutionary models in an iconic genus of poeciliid fish (Xiphophorus spp.). Furthermore, we find that both mating and nonmating natural selection mechanisms are unlikely to be driving the diverse Xiphophorus gonopodial morphology. Putative holdfast features of the male genital organ do not appear to be influenced by water flow, a candidate selective force in aquatic habitats. Additionally, interspecific divergence in gonopodial morphology is not significantly higher between sympatric species, than between allopatric species, suggesting that male genitals have not undergone reproductive character displacement. Slower rates of evolution in gonopodial traits compared with a subset of putatively sexually selected nongenital traits suggest that different selection mechanisms may be acting on the different trait types. Further investigations of this elaborate trait are imperative to determine whether it is ultimately an important driver of speciation.     

An evolutionary tipping point in a changing environment

Populations can persist in directionally changing environments by evolving. Quantitative genetic theory aims to predict critical rates of environmental change beyond which populations go extinct. Here, we point out that all current predictions effectively assume the same specific fitness function. This function causes selection on the standing genetic variance of quantitative traits to become increasingly strong as mean trait values depart from their optima. Hence, there is no bound on the rate of evolution and persistence is determined by the critical rate of environmental change at which populations cease to grow. We then show that biologically reasonable changes to the underlying fitness function can impose a qualitatively different extinction threshold. In particular, inflection points caused by weakening selection create local extrema in the strength of selection and thus in the rate of evolution. These extrema can produce evolutionary tipping points, where long‐run population growth rates drop from positive to negative values without ever crossing zero. Generic early‐warning signs of tipping points are found to have little power to detect imminent extinction, and require hard‐to‐gather data. Furthermore, we show how evolutionary tipping points produce evolutionary hysteresis, creating extinction debts.     

Early diversification of sperm size in the evolutionary history of the old world leaf warblers (Phylloscopidae)

Sperm morphological traits are highly variable among species and are commonly thought to evolve by post‐copulatory sexual selection. However, little is known about the evolutionary dynamics of sperm morphology, and whether rates of evolutionary change are variable over time and among taxonomic groups. Here, we examine sperm morphology from 21 species of Old World leaf warblers (Phylloscopidae), a group of generally dull, sexually monochromatic birds, which are known to have high levels of extra‐pair paternity. We found that sperm length differs markedly across species, spanning about 40% of the range observed across a larger selection of passerine birds. Furthermore, we found strong support for an ‘early‐burst’ model of trait evolution, implying that the majority of divergence in sperm length has occurred early in the evolutionary history of this clade with subsequent evolutionary stasis. This large early divergence matches the early divergence reported in ecological traits (i.e. body size and feeding behaviour). Our findings demonstrate that rates of evolution in sperm morphology can change over time in passerine taxa, and that evolutionary stasis in sperm traits can occur even in species exhibiting characteristics consistent with moderate‐to‐high levels of sperm competition. It remains a major challenge to identify the selection mechanisms and possible constraints responsible for these variable rates of sperm evolution.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF INDIRECT GENETIC EFFECTS: CHANGES IN THE INTERACTION EFFECT COEFFICIENT,PSI (Ψ), DUE TO SEXUAL SELECTION

Indirect genetics effects (IGEs)—when the genotype of one individual affects the phenotypic expression of a trait in another—may alter evolutionary trajectories beyond that predicted by standard quantitative genetic theory as a consequence of genotypic evolution of the social environment. For IGEs to occur, the trait of interest must respond to one or more indicator traits in interacting conspecifics. In quantitative genetic models of IGEs, these responses (reaction norms) are termed interaction effect coefficients and are represented by the parameter psi (Ψ). The extent to which Ψ exhibits genetic variation within a population, and may therefore itself evolve, is unknown. Using an experimental evolution approach, we provide evidence for a genetic basis to the phenotypic response caused by IGEs on sexual display traits in Drosophila serrata. We show that evolution of the response is affected by sexual but not natural selection when flies adapt to a novel environment. Our results indicate a further mechanism by which IGEs can alter evolutionary trajectories—the evolution of interaction effects themselves.     

Evolutionary stability of coexistence due to the storage effect in a two-season model

The question of species coexistence has been central to ecology since its founding. Ever-present environmental variation may be one answer to that question. Previous models have demonstrated that species can exploit this variation to coexist with competitors by having different environmental responses (the storage effect). When traits governing species’ environmental response can evolve, however, coexistence is not assured. In this study, we use a continuous time, two-season model to determine the evolutionary outcome of competing species evolving in their seasonal performance trait. We extend the competitive exclusion principle to show that the storage effect can allow no more than N species to coexist on N discrete seasons with no relative nonlinearity. We find a broad region of parameter space where coexistence is evolutionarily stable. The size of this region depends on the period of fluctuations relative to the individual lifespan. Relatively long period fluctuations yield a large coexistence region, but as the period decreases, the region narrows and disappears asymptotically. Finally, we cast our adaptive dynamics technique in terms of Chesson’s concept of equalizing and stabilizing mechanisms to demonstrate that the breakdown in coexistence at short periods is due to loss of the stabilizing covariance between the environment and competition.