Selective sweep at a quantitative trait locus in the presence of background genetic variation

We model selection at a locus affecting a quantitative trait (QTL) in the presence of genetic variance due to other loci. The dynamics at the QTL are related to the initial genotypic value and to the background genetic variance of the trait, assuming that background genetic values are normally distributed, under three different forms of selection on the trait. Approximate dynamics are derived under the assumption of small mutation effect. For similar strengths of selection on the trait (i.e, gradient of directional selection beta) the way background variation affects the dynamics at the QTL critically depends on the shape of the fitness function. It generally causes the strength of selection on the QTL to decrease with time. The resulting neutral heterozygosity pattern resembles that of a selective sweep with a constant selection coefficient corresponding to the early conditions. The signature of selection may also be blurred by mutation and recombination in the later part of the sweep. We also study the race between the QTL and its genetic background toward a new optimum and find the conditions for a complete sweep. Overall, our results suggest that phenotypic traits exhibiting clear-cut molecular signatures of selection may represent a biased subset of all adaptive traits.     

Evolutionary Distributions and Competition by Way of Reaction-Diffusion and by Way of Convolution

Evolution by natural selection is the most ubiquitous and well understood process of evolution. We say distribution instead of the distribution of the density of populations of phenotypes across the values of their adaptive traits. A phenotype refers to an organism that exhibits a set of values of adaptive traits. An adaptive trait is a trait that a phenotype exhibits where the trait is subject to natural selection. Natural selection is a process by which populations of different phenotypes decline at different rates. An evolutionary distribution (ED) encapsulates the dynamics of evolution by natural selection. The main results are: (i) ED are derived by way of PDE of reaction-diffusion type and by way of integro-differential equations. The latter capture mutations through convolution of a kernel with the rate of growth of a population. The kernel controls the size and rate of mutations. (ii) The numerical solution of a logistic-like ED driven by competition corresponds to a bounded traveling wave solution of population models based on the logistic. (iii) Competition leads to increase in diversity of phenotypes on a single ED. Diversity refers to change in the number of local maxima (minima) within the bounds of values of adaptive traits. (iv) The principle of competitive exclusion in the context of evolution depends, smoothly, on the size and rate of mutations. (v) We identify the sensitivity—with respect to survival—of phenotypes to changes in values of adaptive traits to be an important parameter: increase in the value of this parameter results in decrease in evolutionary-based diversity. (vi) Stable ED corresponds to Evolutionary Stable Strategy; the latter refers to the outcome of a game of evolution.     

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.     

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.     

Trait adaptation promotes species coexistence in diverse predator and prey communities

Species can adjust their traits in response to selection which may strongly influence species coexistence. Nevertheless, current theory mainly assumes distinct and time‐invariant trait values. We examined the combined effects of the range and the speed of trait adaptation on species coexistence using an innovative multispecies predator–prey model. It allows for temporal trait changes of all predator and prey species and thus simultaneous coadaptation within and among trophic levels. We show that very small or slow trait adaptation did not facilitate coexistence because the stabilizing niche differences were not sufficient to offset the fitness differences. In contrast, sufficiently large and fast trait adaptation jointly promoted stable or neutrally stable species coexistence. Continuous trait adjustments in response to selection enabled a temporally variable convergence and divergence of species traits; that is, species became temporally more similar (neutral theory) or dissimilar (niche theory) depending on the selection pressure, resulting over time in a balance between niche differences stabilizing coexistence and fitness differences promoting competitive exclusion. Furthermore, coadaptation allowed prey and predator species to cluster into different functional groups. This equalized the fitness of similar species while maintaining sufficient niche differences among functionally different species delaying or preventing competitive exclusion. In contrast to previous studies, the emergent feedback between biomass and trait dynamics enabled supersaturated coexistence for a broad range of potential trait adaptation and parameters. We conclude that accounting for trait adaptation may explain stable and supersaturated species coexistence for a broad range of environmental conditions in natural systems when the absence of such adaptive changes would preclude it. Small trait changes, coincident with those that may occur within many natural populations, greatly enlarged the number of coexisting species.     

The adaptive dynamics of niche constructing traits in spatially subdivided populations: evolving posthumous extended phenotypes

Niche construction, by which organisms modify the environment in which they live, has been proposed to affect the evolution of many phenotypic traits. But what about the evolution of a niche constructing trait itself, whose expression changes the pattern of natural selection to which the trait is exposed in subsequent generations? This article provides an inclusive fitness analysis of selection on niche constructing phenotypes, which can affect their environment from local to global scales in arbitrarily spatially subdivided populations. The model shows that phenotypic effects of genes extending far beyond the life span of the actor can be affected by natural selection, provided they modify the fitness of those individuals living in the future that are likely to have inherited the niche construction lineage of the actor. Present benefits of behaviors are thus traded off against future indirect costs. The future costs will generally result from a complicated interplay of phenotypic effects, population demography and environmental dynamics. To illustrate these points, I derive the adaptive dynamics of a trait involved in the consumption of an abiotic resource, where resource abundance in future generations feeds back to the evolutionary dynamics of the trait.     

Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Functionally diverse communities can adjust their species composition to altered environmental conditions, which may influence food web dynamics. Trait-based aggregate models cope with this complexity by ignoring details about species identities and focusing on their functional characteristics (traits). They describe the temporal changes of the aggregate properties of entire communities, including their total biomasses, mean trait values, and trait variances. The applicability of aggregate models depends on the validity of their underlying assumptions that trait distributions are normal and exhibit small variances. We investigated to what extent this can be expected to work by comparing an innovative model that accounts for the full trait distributions of predator and prey communities to a corresponding aggregate model. We used a food web structure with well-established trade-offs among traits promoting mutual adjustments between prey edibility and predator selectivity in response to selection. We altered the shape of the trade-offs to compare the outcome of the two models under different selection regimes, leading to trait distributions increasingly deviating from normality. Their biomass and trait dynamics agreed very well for stabilizing selection and reasonably well for directional selection, under which different trait values are favored at different times. However, for disruptive selection, the results of the aggregate model strongly deviated from the full trait distribution model that showed bimodal trait distributions with large variances. Hence, the outcome of aggregate models is reliable under ideal conditions but has to be questioned when confronted with more complex selection regimes and trait distributions, which are commonly observed in nature.     

Adaptive evolution of reproductive and vegetative traits driven by breeding systems

The evolution of inflorescence size, a key trait in reproductive success, was studied in the genus Acer under a perspective of adaptive evolution. Breeding systems, hypothesized to indicate different levels of mating competition, were considered as the selective scenarios defining different optima of inflorescence size. Larger inflorescences, which increase male fitness by generating larger floral displays, were hypothesized to be selected under scenarios with higher competition with unisexuals. An identical approach was used to test if the same selective regimes could be driving the evolution of leaf size, a vegetative trait that was found to be correlated with inflorescence size. A Brownian motion model of inflorescence/leaf-size evolution (which cannot distinguish between changes caused by pure drift processes and changes caused by natural selection in rapidly and randomly changing environments) was compared with several adaptive Ornstein-Uhlenbeck (OU) models, which can quantify the effects of both stochasticity and natural selection. The best-fitting model for inflorescence/leaf-size evolution was an OU model with three optima that increased with the level of mating competition. Both traits evolved under the same selective regimes and in the same direction, confirming a pattern of correlated evolution. These results show that a selective regime hypothetically related to the evolution of a reproductive trait can also explain the evolution of a vegetative trait.     

The adaptive dynamics of altruism in spatially heterogeneous populations

Abstract.— We study the spatial adaptive dynamics of a continuous trait that measures individual investment in altruism. Our study is based on an ecological model of a spatially heterogeneous population from which we derive an appropriate measure of fitness. The analysis of this fitness measure uncovers three different selective processes controlling the evolution of altruism: the direct physiological cost, the indirect genetic benefits of cooperative interactions, and the indirect genetic costs of competition for space. In our model, habitat structure and a continuous life cycle makes the cost of competing for space with relatives negligible. Our study yields a classification of adaptive patterns of altruism according to the shape of the costs of altruism (with decelerating, linear, or accelerating dependence on the investment in altruism). The invasion of altruism occurs readily in species with accelerating costs, but large mutations are critical for altruism to evolve in selfish species with decelerating costs. Strict selfishness is maintained by natural selection only under very restricted conditions. In species with rapidly accelerating costs, adaptation leads to an evolutionarily stable rate of investment in altruism that decreases smoothly with the level of mobility. A rather different adaptive pattern emerges in species with slowly accelerating costs: high altruism evolves at low mobility, whereas a quasi-selfish state is promoted in more mobile species. The high adaptive level of altruism can be predicted solely from habitat connectedness and physiological parameters that characterize the pattern of cost. We also show that environmental changes that cause increased mobility in those highly altruistic species can beget selection-driven self-extinction, which may contribute to the rarity of social species.     

The effects of intraspecific competition and stabilizing selection on a polygenic trait

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.     

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.     

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal,with an application to socially synergistic traits

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance–covariances between traits that experience frequency‐dependent selection. Assuming a multivariate‐normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within‐individuals depends on the fitness effects of such associations between‐individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within‐individuals is costly but synergistically beneficial between‐individuals. As dispersal becomes limited and relatedness increases, associations between‐traits between‐individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.     

Adaptive melanin response of the soil fungus Aspergillus niger to UV radiation stress at "Evolution Canyon", Mount Carmel, Israel

Background

Adaptation is an evolutionary process in which traits in a population are tailored by natural selection to better meet the challenges presented by the local environment. The major discussion relating to natural selection concerns the portraying of the cause and effect relationship between a presumably adaptive trait and selection agents generating it. Therefore, it is necessary to identify trait(s) that evolve in direct response to selection, enhancing the organism''s fitness. “Evolution Canyon” (EC) in Israel mirrors a microcosmic evolutionary system across life and is ideal to study natural selection and local adaptation under sharply, microclimatically divergent environments. The south-facing, tropical, sunny and xeric “African” slope (AS) receives 200%–800% higher solar radiation than the north-facing, temperate, shady and mesic “European” slope (ES), 200 meters apart. Thus, solar ultraviolet radiation (UVR) is a major selection agent in EC influencing the organism-environment interaction. Melanin is a trait postulated to have evolved for UV-screening in microorganisms. Here we investigate the cause and effect relationship between differential UVR on the opposing slopes of EC and the conidial melanin concentration of the filamentous soil fungus Aspergillus niger. We test the working hypothesis that the AS strains exhibit higher melanin content than strains from the ES resulting in higher UV resistance.

Methodology/Principal Findings

We measured conidial melanin concentration of 80 strains from the EC using a spectrophotometer. The results indicated that mean conidial melanin concentration of AS strains were threefold higher than ES strains and the former resisted UVA irradiation better than the latter. Comparisons of melanin in the conidia of A. niger strains from sunny and shady microniches on the predominantly sunny AS and predominantly shady ES indicated that shady conditions on the AS have no influence on the selection on melanin; in contrast, the sunny strains from the ES displayed higher melanin concentrations.

Conclusions/Significance

We conclude that melanin in A. niger is an adaptive trait against UVR generated by natural selection.     

FORAGING TRAIT (CO)VARIANCES IN STICKLEBACK EVOLVE DETERMINISTICALLY AND DO NOT PREDICT TRAJECTORIES OF ADAPTIVE DIVERSIFICATION

How does natural selection shape the structure of variance and covariance among multiple traits, and how do (co)variances influence trajectories of adaptive diversification? We investigate these pivotal but open questions by comparing phenotypic (co)variances among multiple morphological traits across 18 derived lake‐dwelling populations of threespine stickleback, and their marine ancestor. Divergence in (co)variance structure among populations is striking and primarily attributable to shifts in the variance of a single key foraging trait (gill raker length). We then relate this divergence to an ecological selection proxy, to population divergence in trait means, and to the magnitude of sexual dimorphism within populations. This allows us to infer that evolution in (co)variances is linked to variation among habitats in the strength of resource‐mediated disruptive selection. We further find that adaptive diversification in trait means among populations has primarily involved shifts in gill raker length. The direction of evolutionary trajectories is unrelated to the major axes of ancestral trait (co)variance. Our study demonstrates that natural selection drives both means and (co)variances deterministically in stickleback, and strongly challenges the view that the (co)variance structure biases the direction of adaptive diversification predictably even over moderate time spans.     

Multi-species evolutionary dynamics

Dynamical attainability of an evolutionarily stable strategy (ESS) through the process of mutations and natural selection has mostly been addressed through the use of the continuously stable strategy (CSS) concept for species evolutionary games in which strategies are drawn from a continuum, and by the adaptive trait dynamics method. We address the issue of dynamical attainability of an ESS in coevolving species through the use of the concept of an ESNIS. It is shown that the definition of an ESNIS coalition for coevolving species is not in general equivalent to other definitions for CSS given in the literature. We show under some additional conditions that, in a dynamic system which involves the strategies of a dimorphic ESNIS coalition and at most two strategies that are not members of ESNIS coalition, the ESNIS coalition will emerge as the winner. In addition an ESNIS will be approached because of the invasion structure of strategies in its neighborhood. This proves that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS. The theory developed is applied to a class of coevolutionary game models with Lotka–Volterra type interactions and we show that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the ESS coalition is also an ESNIS coalition.Co-ordinating editor: Metz     

GENETIC ARCHITECTURE OF SKELETAL EVOLUTION IN EUROPEAN LAKE AND STREAM STICKLEBACK

Advances in genomic techniques are greatly facilitating the study of molecular signatures of selection in diverging natural populations. Connecting these signatures to phenotypes under selection remains challenging, but benefits from dissections of the genetic architecture of adaptive divergence. We here perform quantitative trait locus (QTL) mapping using 488 F₂ individuals and 2011 single nucleotide polymorphisms (SNPs) to explore the genetic architecture of skeletal divergence in a lake‐stream stickleback system from Central Europe. We find QTLs for gill raker, snout, and head length, vertebral number, and the extent of lateral plating (plate number and height). Although two large‐effect loci emerge, QTL effect sizes are generally small. Examining the neighborhood of the QTL‐linked SNPs identifies several genes involved in bone formation, which emerge as strong candidate genes for skeletal evolution. Finally, we use SNP data from the natural source populations to demonstrate that some SNPs linked to QTLs in our cross also exhibit striking allele frequency differences in the wild, suggesting a causal role of these QTLs in adaptive population divergence. Our study paves the way for comparative analyses across other (lake‐stream) stickleback populations, and for functional investigations of the candidate genes.     

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

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

Genome-Wide Association Analysis of Adaptation Using Environmentally Predicted Traits

Current methods for studying the genetic basis of adaptation evaluate genetic associations with ecologically relevant traits or single environmental variables, under the implicit assumption that natural selection imposes correlations between phenotypes, environments and genotypes. In practice, observed trait and environmental data are manifestations of unknown selective forces and are only indirectly associated with adaptive genetic variation. In theory, improved estimation of these forces could enable more powerful detection of loci under selection. Here we present an approach in which we approximate adaptive variation by modeling phenotypes as a function of the environment and using the predicted trait in multivariate and univariate genome-wide association analysis (GWAS). Based on computer simulations and published flowering time data from the model plant Arabidopsis thaliana, we find that environmentally predicted traits lead to higher recovery of functional loci in multivariate GWAS and are more strongly correlated to allele frequencies at adaptive loci than individual environmental variables. Our results provide an example of the use of environmental data to obtain independent and meaningful information on adaptive genetic variation.     

Selection on floral and carbon uptake traits of Lobelia siphilitica is similar in females and hermaphrodites

Sexual dimorphism is common in plants and animals. Although this dimorphism is often assumed to be adaptive, natural selection has rarely been measured on sexually dimorphic traits of plants. We measured phenotypic selection via seed set on two floral and four carbon uptake traits of female and hermaphrodite Lobelia siphilitica. Because females can reproduce only via seeds, which are costlier than pollen, we predicted that females with smaller flowers and enhanced carbon uptake would have higher fitness, resulting in either sex morph-specific directional selection or stabilizing selection for different optimal trait values in females and hermaphrodites. We found that directional selection on one carbon uptake trait differed between females and hermaphrodites. We did not detect significant stabilizing selection on traits of either sex morph. Our results provide little support for the hypothesis that sexual dimorphism in gynodioecious plants evolved in response to sex morph-specific selection.     

Tests of adaptation: functional studies of pollen removal and estimates of natural selection on anther position in wild radish

Background

There are a number of difficulties associated with the study of adaptation. One is a lack of variation in the trait, which is common in adaptations because past selection has removed unfit variants. This lack of variation makes it difficult to determine the relationship between trait variation and fitness. Another difficulty is proving causation in this trait–fitness relationship, because a correlated trait might be the actual adaptation. These difficulties can be ameliorated at least partially by combining studies of natural variation with studies of experimentally manipulated traits and traits whose variance has been augmented by artificial selection.

Scope

We review here a number of our studies on the adaptive value of two aspects of anther position in wild radish (Raphanus raphanistrum, Brassicaceae): anther exsertion, i.e. the degree to which anthers protrude from the mouth of the corolla tube, and anther height dimorphism, i.e. the difference in lengths of the filaments between the two short and four long stamens. We have used both functional analyses, in which the response variable is pollen removal, and measurements of selection, in which the response variable is lifetime male fitness estimated by molecular genetic paternity analyses. In these studies we use both the natural variation in populations as well as manipulated variation, the latter through both stamen removal and artificial selection, to re-create the ancestral trait conditions.

Conclusions

Our work provides convincing evidence that intermediate anther exsertion values are adaptive, and that this is probably an adaptation to a subset of the pollinator fauna, small bees. The picture for anther height dimorphism is much less clear, as the weight of current evidence suggests that current values of this trait might actually be maladaptive; however, if this is true it is difficult to understand how the dimorphism is maintained across the family Brassicaceae.Key words: Wild radish, Raphanus raphanistrum, adaptation, natural selection, anther position, pollination, pollen removal