Evolution of migration in a periodically changing environment

The ability to migrate can evolve in response to various forces. In particular, when selection is heterogeneous in space but constant in time, local adaptation induces a fitness cost on immigrants and selects against migration. The evolutionary outcome, however, is less clear when selection also varies temporally. Here, we present a two-locus model analyzing the effects of spatial and temporal variability in selection on the evolution of migration. The first locus is under temporally varying selection (various periodic functions are considered, but a general nonparametric framework is used), and the second locus is a modifier controlling migration ability. First, we study the dynamics of local adaptation and derive the migration rate that maximizes local adaptation as a function of the speed and geometry of the fluctuations in the environment. Second, we derive an analytical expression for the evolutionarily stable migration rate. When there is no cost of migration, we show that higher migration rates are favored when selection changes fast. When migration is costly, however, the evolutionarily stable migration rate is maximal for an intermediate speed of the variation of selection. This model may help in understanding the evolution of migration in a broad range of scenarios and, in particular, in host-parasite systems, where selection is thought to vary quickly in both space and time.     

Evolution in heterogeneous environments: between soft and hard selection

Since their first formulations about half a century ago, the soft and hard selection models have become classical frameworks to study selection in subdivided populations. These models differ in the timing of density regulation and represent two extreme types of selection: density- and frequency-dependent selection (soft) and density- and frequency-independent selection (hard). Yet only few attempts have been made so far to model intermediate scenarios. Here, we design a model where migration may happen twice during the life cycle: before density regulation with probability d(J) (juvenile migration) and after density regulation with probability d(A) (adult migration). In the first step, we analyze the conditions for the coexistence of two specialists. We find that coexistence is possible under a large range of selection types, even when environmental heterogeneity is low. Then, we investigate the different possible outcomes obtained through gradual evolution. We show that polymorphism is more likely to evolve when the trade-off is weak, environmental heterogeneity is high, migration is low, and in particular when juvenile migration is low relative to adult migration, because the timing of migration affects the magnitude of frequency-dependent selection relative to gene flow. This model may provide a more general theoretical framework to experimentally study evolution in heterogeneous environments.     

When can refuges mediate the genetic effects of fire regimes? A simulation study of the effects of topography and weather on neutral and adaptive genetic diversity in fire‐prone landscapes

Understanding how landscape heterogeneity mediates the effects of fire on biodiversity is increasingly important under global changes in fire regimes. We used a simulation experiment to investigate how fire regimes interact with topography and weather to shape neutral and selection‐driven genetic diversity under alternative dispersal scenarios, and to explore the conditions under which microrefuges can maintain genetic diversity of populations exposed to recurrent fire. Spatial heterogeneity in simulated fire frequency occurred in topographically complex landscapes, with fire refuges and fire‐prone “hotspots” apparent. Interannual weather variability reduced the effect of topography on fire patterns, with refuges less apparent under high weather variability. Neutral genetic diversity was correlated with long‐term fire frequency under spatially heterogeneous fire regimes, being higher in fire refuges than fire‐prone areas, except under high dispersal or low fire severity (low mortality). This generated different spatial genetic structures in fire‐prone and fire‐refuge components of the landscape, despite similar dispersal. In contrast, genetic diversity was only associated with time since the most recent fire in flat landscapes without predictable refuges and hotspots. Genetic effects of selection driven by fire‐related conditions depended on selection pressure, migration distance and spatial heterogeneity in fire regimes. Allele frequencies at a locus conferring higher fitness under successional environmental conditions followed a pattern of “temporal adaptation” to contemporary conditions under strong selection pressure and high migration. However, selected allele frequencies were correlated with spatial variation in long‐term mean fire frequency (relating to environmental predictability) under weak dispersal, low selection pressure and strong spatial heterogeneity in fire regimes.     

The evolution of recombination in a heterogeneous environment

Most models describing the evolution of recombination have focused on the case of a single population, implicitly assuming that all individuals are equally likely to mate and that spatial heterogeneity in selection is absent. In these models, the evolution of recombination is driven by linkage disequilibria generated either by epistatic selection or drift. Models based on epistatic selection show that recombination can be favored if epistasis is negative and weak compared to directional selection and if the recombination modifier locus is tightly linked to the selected loci. In this article, we examine the joint effects of spatial heterogeneity in selection and epistasis on the evolution of recombination. In a model with two patches, each subject to different selection regimes, we consider the cases of mutation-selection and migration-selection balance as well as the spread of beneficial alleles. We find that including spatial heterogeneity extends the range of epistasis over which recombination can be favored. Indeed, recombination can be favored without epistasis, with negative and even with positive epistasis depending on environmental circumstances. The selection pressure acting on recombination-modifier loci is often much stronger with spatial heterogeneity, and even loosely linked modifiers and free linkage may evolve. In each case, predicting whether recombination is favored requires knowledge of both the type of environmental heterogeneity and epistasis, as none of these factors alone is sufficient to predict the outcome.     

Molecular mechanisms of dominance evolution in Müllerian mimicry

Natural selection acting on dominance between adaptive alleles at polymorphic loci can be sufficiently strong for dominance to evolve. However, the molecular mechanisms underlying such evolution are generally unknown. Here, using Müllerian mimicry as a case‐study for adaptive morphological variation, we present a theoretical analysis of the invasion of dominance modifiers altering gene expression through different molecular mechanisms. Toxic species involved in Müllerian mimicry exhibit warning coloration, and converge morphologically with other toxic species of the local community, due to positive frequency‐dependent selection acting on these colorations. Polymorphism in warning coloration may be maintained by migration–selection balance with fine scale spatial heterogeneity. We modeled a dominance modifier locus altering the expression of the warning coloration locus, targeting one or several alleles, acting in cis or trans, and either enhancing or repressing expression. We confirmed that dominance could evolve when balanced polymorphism was maintained at the color locus. Dominance evolution could result from modifiers enhancing one allele specifically, irrespective of their linkage with the targeted locus. Nonspecific enhancers could also persist in populations, at frequencies tightly depending on their linkage with the targeted locus. Altogether, our results identify which mechanisms of expression alteration could lead to dominance evolution in polymorphic mimicry.     

Bet‐hedging as a complex interaction among developmental instability,environmental heterogeneity,dispersal, and life‐history strategy

One potential evolutionary response to environmental heterogeneity is the production of randomly variable offspring through developmental instability, a type of bet‐hedging. I used an individual‐based, genetically explicit model to examine the evolution of developmental instability. The model considered both temporal and spatial heterogeneity alone and in combination, the effect of migration pattern (stepping stone vs. island), and life‐history strategy. I confirmed that temporal heterogeneity alone requires a threshold amount of variation to select for a substantial amount of developmental instability. For spatial heterogeneity only, the response to selection on developmental instability depended on the life‐history strategy and the form and pattern of dispersal with the greatest response for island migration when selection occurred before dispersal. Both spatial and temporal variation alone select for similar amounts of instability, but in combination resulted in substantially more instability than either alone. Local adaptation traded off against bet‐hedging, but not in a simple linear fashion. I found higher‐order interactions between life‐history patterns, dispersal rates, dispersal patterns, and environmental heterogeneity that are not explainable by simple intuition. We need additional modeling efforts to understand these interactions and empirical tests that explicitly account for all of these factors.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Evolution of mutation rates in bacteria

Evolutionary success of bacteria relies on the constant fine-tuning of their mutation rates, which optimizes their adaptability to constantly changing environmental conditions. When adaptation is limited by the mutation supply rate, under some conditions, natural selection favours increased mutation rates by acting on allelic variation of the genetic systems that control fidelity of DNA replication and repair. Mutator alleles are carried to high frequency through hitchhiking with the adaptive mutations they generate. However, when fitness gain no longer counterbalances the fitness loss due to continuous generation of deleterious mutations, natural selection favours reduction of mutation rates. Selection and counter-selection of high mutation rates depends on many factors: the number of mutations required for adaptation, the strength of mutator alleles, bacterial population size, competition with other strains, migration, and spatial and temporal environmental heterogeneity. Such modulations of mutation rates may also play a role in the evolution of antibiotic resistance.     

Competition and the Effect of Spatial Resource Heterogeneity on Evolutionary Diversification

A model is presented to explore how the form of selection arising from competition for resources is affected by spatial resource heterogeneity. The model consists of a single species occupying two patches connected by migration, where the two patches can differ in the type of resources that they contain. The main goal is to determine the conditions under which competition for resources results in disruptive selection (i.e., selection favoring a polymorphism) since it is this form of selection that will give rise to the evolutionary diversification of resource exploitation strategies. In particular, comparing the conditions giving rise to disruptive selection when the two patches are identical to the conditions when they contain different resources reveals the effect of spatial resource heterogeneity. Results show that when the patches are identical, the conditions giving rise to disruptive selection are identical to those that give rise to character displacement in previous models. When the patches are different, the conditions giving rise to disruptive selection can be either more or less stringent depending upon demographic parameters such as the intrinsic rate of increase and the migration rate. Surprisingly, spatial resource heterogeneity can actually make forms of evolutionary diversification such as character displacement less likely. It is also found that results are dependent on how the resource exploitation strategies and the spatial resource heterogeneity affect the population dynamics. One robust conclusion however, is that spatial resource heterogeneity always has a disruptive effect when the migration rate between patches is low.     

The factors that favor adaptive habitat construction versus non‐adaptive environmental conditioning

Adaptive habitat construction is a process by which individuals alter their environment so as to increase their (inclusive) fitness. Such alterations are a subset of the myriad ways that individuals condition their environment. We present an individual‐based model of habitat construction to explore what factors might favor selection when the benefits of environmental alterations are shared by individuals of the same species. Our results confirm the predictions of inclusive fitness and group selection theory and expectations based on previous models that construction will be more favored when its benefits are more likely to be directed to self or near kin. We found that temporal variation had no effect on the evolution of construction. For spatial heterogeneity, construction was disfavored when the spatial pattern of movement did not match the spatial pattern of environmental heterogeneity, especially when there was spatial heterogeneity in the optimal amount of construction. Under those conditions, very strong selection was necessary to favor genetic differentiation of construction propensity among demes. We put forth a constitutive theory for the evolution of adaptive habitat construction that unifies our model with previous verbal and quantitative models into a formal conceptual framework.     

The genetics of phenotypic plasticity. XII. Temporal and spatial heterogeneity

To understand empirical patterns of phenotypic plasticity, we need to explore the complexities of environmental heterogeneity and how it interacts with cue reliability. I consider both temporal and spatial variation separately and in combination, the timing of temporal variation relative to development, the timing of movement relative to selection, and two different patterns of movement: stepping‐stone and island. Among‐generation temporal heterogeneity favors plasticity, while within‐generation heterogeneity can result in cue unreliability. In general, spatial variation more strongly favors plasticity than temporal variation, and island migration more strongly favors plasticity than stepping‐stone migration. Negative correlations among environments between the time of development and selection can result in seemingly maladaptive reaction norms. The effects of higher dispersal rates depend on the life history stage when dispersal occurs and the pattern of environmental heterogeneity. Thus, patterns of environmental heterogeneity can be complex and can interact in unforeseen ways to affect cue reliability. Proper interpretation of patterns of trait plasticity requires consideration of the ecology and biology of the organism. More information on actual cue reliability and the ecological and developmental context of trait plasticity is needed.     

MALADAPTATION AS A SOURCE OF SENESCENCE IN HABITATS VARIABLE IN SPACE AND TIME

In this study, we use a quantitative genetics model of structured populations to investigate the evolution of senescence in a variable environment. Adaptation to local environments depends on phenotypic traits whose optimal values vary with age and with environmental conditions. We study different scenarios of environmental heterogeneity, where the environment changes abruptly, gradually, or cyclically with time and where the environment is heterogeneous in space with different populations connected by migration. The strength of selection decreases with age, which predicts slower adaptation of traits expressed late in the life cycle, potentially generating stronger senescence in habitats where selection changes in space or in time. This prediction is however complicated by the fact that the genetic variance also increases with age. Using numerical calculations, we found that the rate of senescence is generally increased when the environment varies. In particular, migration between different habitats is a source of senescence in heterogeneous landscapes. We also show that the rate of senescence can vary transiently when the population is not at equilibrium, with possible implications for experimental evolution and the study of invasive species. Our results highlight the need to study age‐specific adaptation, as a changing environment can have a different impact on different age classes.     

GENETIC VARIATION AND THE EVOLUTION OF EPIGENETIC REGULATION

Epigenetic variation has been observed in a range of organisms, leading to questions of the adaptive significance of this variation. In this study, we present a model to explore the ecological and genetic conditions that select for epigenetic regulation. We find that the rate of temporal environmental change is a key factor controlling the features of this evolution. When the environment fluctuates rapidly between states with different phenotypic optima, epigenetic regulation may evolve but we expect to observe low transgenerational inheritance of epigenetic states, whereas when this fluctuation occurs over longer time scales, regulation may evolve to generate epigenetic states that are inherited faithfully for many generations. In all cases, the underlying genetic variation at the epigenetically regulated locus is a crucial factor determining the range of conditions that allow for evolution of epigenetic mechanisms.     

The evolution of resistance to a parasite is determined by resources

Given the ubiquity of parasites, it is critical to understand the evolution of defense against them. Using a selection experiment performed across a broad range of host resources, I examine how resistance and associated costs depend on resource availability. Higher resistance to a natural viral pathogen evolves in a host when there are more resources, and this directly suggests a resource-dependent cost of the evolution of resistance. Resistance is traded off with host growth rate, and the costs are stronger under poor resource environments, although adaptation to poor environments reduces these costs. The level of resistance and the costs that are paid for this resistance depend on both the selection environment and the environment in which hosts are assayed, implying that different resistance mechanisms may evolve in different environments. More broadly, the results emphasize that environmental heterogeneity in time and space may underpin variation in immune diversity.     

Experimental evolution across different thermal regimes yields genetic divergence in recombination fraction but no divergence in temperature associated plastic recombination

Phenotypic plasticity is pervasive in nature. One mechanism underlying the evolution and maintenance of such plasticity is environmental heterogeneity. Indeed, theory indicates that both spatial and temporal variation in the environment should favor the evolution of phenotypic plasticity under a variety of conditions. Cyclical environmental conditions have also been shown to yield evolved increases in recombination frequency. Here, we use a panel of replicated experimental evolution populations of D. melanogaster to test whether variable environments favor enhanced plasticity in recombination rate and/or increased recombination rate in response to temperature. In contrast to expectation, we find no evidence for either enhanced plasticity in recombination or increased rates of recombination in the variable environment lines. Our data confirm a role of temperature in mediating recombination fraction in D. melanogaster, and indicate that recombination is genetically and plastically depressed under lower temperatures. Our data further suggest that the genetic architectures underlying plastic recombination and population‐level variation in recombination rate are likely to be distinct.     

The role of migration in the evolution of phenotypic switching

Stochastic switching is an example of phenotypic bet hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here, we explore the interaction of temporal and spatial change in determining the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.     

Spatial heterogeneity in the strength of selection against deleterious alleles and the mutation load

According to current estimates of genomic deleterious mutation rates (which are often of the order 0.1-1) the mutation load (defined as a reduction in the average fitness of a population due to the presence of deleterious alleles) may be important in many populations. In this paper, I use multilocus simulations to explore the effect of spatial heterogeneity in the strength of selection against deleterious alleles on the mutation load (for example, it has been suggested that stressful environments may increase the strength of selection). These simulations show contrasted results: in some situations, spatial heterogeneity may greatly reduce the mutation load, due to the fact that migrants coming from demes under stronger selection carry relatively few deleterious alleles, and benefit from a strong advantage within demes under weaker selection (where individuals carry many more deleterious alleles); in other situations, however, deleterious alleles accumulate within demes under stronger selection, due to migration pressure from demes under weaker selection, leading to fitness erosion within those demes. This second situation is more frequent when the productivity of the different demes is proportional to their mean fitness. The effect of spatial heterogeneity is greatly reduced, however, when the response to environmental differences is inconsistent across loci.     

The effects of the mating system on the evolution of migration in a spatially heterogeneous population

Summary Verbal explanations for the evolution of migration and dispersal often invoke inbreeding depression as an important force. Experimental work on plant populations indicates that while inbreeding depression may favor increased migration rates, adaptation to local environments may reduce the advantage to migrants. We formalize and test this hypothesis using a two-locus genetic model that incorporates lowered fitness in offspring produced by self-fertilization, and habitat differentiation. We also use the model to address questions about the general theory of genetic modifiers and the modifier reduction principle. We find that even under conditions when migration would increase the mean fitness of a population, migration may not be favored. This result is due to the associations that develop between genotypes at a locus subject to overdominant selection and at a neutral locus controlling the migration rate. Thus, it appears that, in this model, the forces of local adaptation, which favor a reduction in the migration rate, overwhelm those of inbreeding depression, which may favor dispersal.     

The evolution of preference strength under sensory bias: a role for indirect selection?

Evidence suggests that female preferences may sometimes arise through sensory bias, and that males may subsequently evolve traits that increase their conspicuousness to females. Here, we ask whether indirect selection, arising through genetic associations (linkage disequilibrium) during the sexual selection that sensory bias imposes, can itself influence the evolution of preference strength. Specifically, we use population genetic models to consider whether or not modifiers of preference strength can spread under different ecological conditions when female mate choice is driven by sensory bias. We focus on male traits that make a male more conspicuous in certain habitats-and thus both more visible to predators and more attractive to females-and examine modifiers of the strength of preference for conspicuous males. We first solve for the rate of spread of a modifier that strengthens preference within an environmentally uniform population; we illustrate that this spread will be extremely slow. Second, we used a series of simulations to consider the role of habitat structure and movement on the evolution of a modifier of preference strength, using male color polymorphisms as a case study. We find that in most cases, indirect selection does not allow the evolution of stronger or weaker preferences for sensory bias. Only in a "two-island" model, where there is restricted migration between different patches that favor different male phenotypes, did we find that preference strength could evolve. The role of indirect selection in the evolution of sensory bias is of particular interest because of ongoing speculation regarding the role of sensory bias in the evolution of reproductive isolation.     

Divergent outcomes of reinforcement speciation: the relative importance of assortative mating and migration modification

Most studies of reinforcement speciation focus on the evolution of assortative mating, but R. A. Fisher argued that migration modification is likely to be a common alternative mechanism. Despite previous models showing that assortative mating and migration modification may both be involved in reinforcement, no one has determined their relative evolutionary importance. This is surprising because understanding the biological conditions favoring these mechanisms may explain why certain pairs of species exhibit abutting, nonoverlapping geographical ranges with habitat fidelity while other pairs coexist in sympatry with sexual isolation. In this article, we explicitly model the evolution of both mechanisms simultaneously. First, we explore how these mechanisms differ in their evolutionary dynamics. Second, we ask how they affect each other's evolution and whether the interaction alters their relative importance in reinforcement. Our results reveal that assortative mating may evolve faster and under a broader range of biological conditions than migration modification. However, direct evolutionary interactions favor migration modification when populations experience strong divergent selection. Depending on the nature of postmating isolation, these mechanisms may either interfere with each other's evolution or coevolve in the same system. These results illustrate the importance of studying multiple mechanisms of speciation simultaneously in future speciation models.