Geographical patterns of adaptation within a species' range: interactions between drift and gene flow

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.     

The adaptive value of epigenetic mutation: Limited in large but high in small peripheral populations

The fate of populations during range expansions, invasions and environmental changes is largely influenced by their ability to adapt to peripheral habitats. Recent models demonstrate that stable epigenetic modifications of gene expression that occur more frequently than genetic mutations can both help and hinder adaptation in panmictic populations. However, these models do not consider interactions between epimutations and evolutionary forces in peripheral populations. Here, we use mainland–island mathematical models and simulations to explore how the faster rate of epigenetic mutation compared to genetic mutations interacts with migration, selection and genetic drift to affect adaptation in peripheral populations. Our model focuses on cases where epigenetic marks are stably inherited. In a large peripheral population, where the effect of genetic drift is negligible, our analyses suggest that epimutations with random fitness impacts that occur at rates as high as 10^–3 increase local adaptation when migration is strong enough to overwhelm divergent selection. When migration is weak relative to selection and epimutations with random fitness impacts decrease adaptation, we find epigenetic modifications must be highly adaptively biased to enhance adaptation. Finally, in small peripheral populations, where genetic drift is strong, epimutations contribute to adaptation under a wider range of evolutionary conditions. Overall, our results suggest that epimutations can change outcomes of adaptation in peripheral populations, which has implications for understanding conservation and range expansions and contractions, especially of small populations.     

Local adaptation and ecological differentiation under selection,migration, and drift in Arabidopsis lyrata*

How the balance between selection, migration, and drift influences the evolution of local adaptation has been under intense theoretical scrutiny. Yet, empirical studies that relate estimates of local adaptation to quantification of gene flow and effective population sizes have been rare. Here, we conducted a reciprocal transplant trial, a common garden trial, and a whole‐genome‐based demography analysis to examine these effects among Arabidopsis lyrata populations from two altitudinal gradients in Norway. Demography simulations indicated that populations within the two gradients are connected by gene flow (0.1 < 4N_em < 11) and have small effective population sizes (N_e < 6000), suggesting that both migration and drift can counteract local selection. However, the three‐year field experiments showed evidence of local adaptation at the level of hierarchical multiyear fitness, attesting to the strength of differential selection. In the lowland habitat, local superiority was associated with greater fecundity, while viability accounted for fitness differences in the alpine habitat. We also demonstrate that flowering time differentiation has contributed to adaptive divergence between these locally adapted populations. Our results show that despite the estimated potential of gene flow and drift to hinder differentiation, selection among these A. lyrata populations has resulted in local adaptation.     

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 effect of mating system on invasiveness: some genetic load may be advantageous when invading new environments

The role of adaptation in determining invasion success has been acknowledged recently, notably through the accumulation of case studies of rapid evolution during bioinvasions. Despite this growing body of empirical evidence, there is still a need to develop the theoretical background of invasions with adaptation. Specifically, the impact of mating system on the dynamics of adaptation during invasion of a new environment remains only partially understood. Here, we analyze a simulation demo-genetic model of bioinvasion accounting for partial asexuality rates. We simulate two levels of recurrent immigration from a source population at mutation–drift–selection equilibrium to a new empty environment with a different adaptive landscape (black-hole sink). Adaptation relies on a quantitative trait coded explicitly by 10 loci under mutation, selection and genetic drift. Using this model, we confirm previous results on the positive effects on invasiveness of migration, mutation and similarity of local phenotypic optima. We further show how the invasion dynamics of the introduced population is affected by the rate of asexuality. Purely asexual species have lower invasion success in terms of probability and time to invasion than species with other mating systems. Among species with mixed mating systems, the greatest invasiveness is observed for species with high asexual rates. We suggest that this pattern is due to inflated genetic variance in the source population through the Hill-Robertson effect (i.e., clonal interference). An interesting consequence is that species with the highest genetic load in their source environment have greatest invasiveness in the new environment.     

Evolution of migration under kin selection and local adaptation

We present here a stochastic two-locus, two-habitat model for the evolution of migration with local adaptation and kin selection. One locus determines the migration rate while the other causes local adaptation. We show that the opposing forces of kin competition and local adaptation can lead to the existence of one or two convergence stable migration rates, notably depending on the recombination rate between the two loci. We show that linkage between migration and local adaptation loci has two antagonist effects: when linkage is tight, cost of local adaptation increases, leading to smaller equilibrium migration rates. However, when linkage is tighter, the population structure at the migration locus tends to be very high because of the indirect selection, and thus equilibrium migration rates increases. This result, qualitatively different from results obtained with other models of migration evolution, indicates that ignoring drift or the detail of the genetic architecture may lead to incorrect conclusions.     

Free fitness that always increases in evolution

I here introduce a free fitness function in population biology, which monotonically increases with time and takes its maximum at the evolutionary equilibrium. By suitably defining an "index" for each state, the free fitness is expressed as the average index plus an entropy term. In many cases, the index has a biologically clear meaning, such as the logarithmic population mean fitness. The technique is applicable to any Markov process model (either continuous or discrete) with a positive steady state. I discuss four examples from various branches of population biology: (1) one-locus-two-allele system of population genetics with mutation, selection, and random genetic drift; (2) evolutionary dynamics of quantitative characters; (3) a molecular evolution model; and (4) an ecological succession model. Introducing free fitness clarifies the balance between systematic forces (e.g. natural selection or successional trend toward the climax) and disturbing processes (e.g. random drift).     

The genomic footprint of climate adaptation in Chironomus riparius

The gradual heterogeneity of climatic factors poses varying selection pressures across geographic distances that leave signatures of clinal variation in the genome. Separating signatures of clinal adaptation from signatures of other evolutionary forces, such as demographic processes, genetic drift and adaptation, to nonclinal conditions of the immediate local environment is a major challenge. Here, we examine climate adaptation in five natural populations of the harlequin fly Chironomus riparius sampled along a climatic gradient across Europe. Our study integrates experimental data, individual genome resequencing, Pool‐Seq data and population genetic modelling. Common‐garden experiments revealed significantly different population growth rates at test temperatures corresponding to the population origin along the climate gradient, suggesting thermal adaptation on the phenotypic level. Based on a population genomic analysis, we derived empirical estimates of historical demography and migration. We used an F_ST outlier approach to infer positive selection across the climate gradient, in combination with an environmental association analysis. In total, we identified 162 candidate genes as genomic basis of climate adaptation. Enriched functions among these candidate genes involved the apoptotic process and molecular response to heat, as well as functions identified in studies of climate adaptation in other insects. Our results show that local climate conditions impose strong selection pressures and lead to genomic adaptation despite strong gene flow. Moreover, these results imply that selection to different climatic conditions seems to converge on a functional level, at least between different insect species.     

The resolution of sexual antagonism by gene duplication

Disruptive selection between males and females can generate sexual antagonism, where alleles improving fitness in one sex reduce fitness in the other. This type of genetic conflict arises because males and females carry nearly identical sets of genes: opposing selection, followed by genetic mixing during reproduction, generates a population genetic "tug-of-war" that constrains adaptation in either sex. Recent verbal models suggest that gene duplication and sex-specific cooption of paralogs might resolve sexual antagonism and facilitate evolutionary divergence between the sexes. However, this intuitive proximal solution for sexual dimorphism potentially belies a complex interaction between mutation, genetic drift, and positive selection during duplicate fixation and sex-specific paralog differentiation. The interaction of these processes--within the explicit context of duplication and sexual antagonism--has yet to be formally described by population genetics theory. Here, we develop and analyze models of gene duplication and sex-specific differentiation between paralogs. We show that sexual antagonism can favor the fixation and maintenance of gene duplicates, eventually leading to the evolution of sexually dimorphic genetic architectures for male and female traits. The timescale for these evolutionary transitions is sensitive to a suite of genetic and demographic variables, including allelic dominance, recombination, sex linkage, and population size. Interestingly, we find that female-beneficial duplicates preferentially accumulate on the X chromosome, whereas male-beneficial duplicates are biased toward autosomes, independent of the dominance parameters of sexually antagonistic alleles. Although this result differs from previous models of sexual antagonism, it is consistent with several findings from the empirical genomics literature.     

The magnitude of local adaptation under genotype‐dependent dispersal

Dispersal moves individuals from patches where their immediate ancestors were successful to sites where their genotypes are untested. As a result, dispersal generally reduces fitness, a phenomenon known as “migration load.” The strength of migration load depends on the pattern of dispersal and can be dramatically lessened or reversed when individuals move preferentially toward patches conferring higher fitness. Evolutionary ecologists have long modeled nonrandom dispersal, focusing primarily on its effects on population density over space, the maintenance of genetic variation, and reproductive isolation. Here, we build upon previous work by calculating how the extent of local adaptation and the migration load are affected when individuals differ in their dispersal rate in a genotype‐dependent manner that alters their match to their environment. Examining a one‐locus, two‐patch model, we show that local adaptation occurs through a combination of natural selection and adaptive dispersal. For a substantial portion of parameter space, adaptive dispersal can be the predominant force generating local adaptation. Furthermore, genetic load may be largely averted with adaptive dispersal whenever individuals move before selective deaths occur. Thus, to understand the mechanisms driving local adaptation, biologists must account for the extent and nature of nonrandom, genotype‐dependent dispersal, and the potential for adaptation via spatial sorting of genotypes.     

The geometry and genetics of hybridization

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher's geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the “composite effects.” Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.     

ON THE EVOLUTION OF MIGRATION IN HETEROGENEOUS ENVIRONMENTS

Populations often experience variable conditions, both in time and space. Here we develop a novel theoretical framework to study the evolution of migration under the influence of spatially and temporally variable selection and genetic drift. First, we examine when polymorphism is maintained at a locus under heterogeneous selection, as a function of the pattern of spatial heterogeneity and the migration rate. In a second step, we study how levels of migration evolve under the joint action of kin competition and local adaptation at a polymorphic locus. This analysis reveals the existence of evolutionary bistability, whereby a low or a high migration rate may evolve depending on the initial conditions. Last, we relax several assumptions regarding selection heterogeneity commonly made in previous studies and explore the consequences of more complex spatial and temporal patterns of variability in selection on the evolution of migration. We found that small modifications in the pattern of environmental heterogeneity may have dramatic effects on the evolution of migration. This work highlights the importance of considering more general scenarios of environmental heterogeneity when studying the evolution of life‐history traits in ecologically complex settings.     

Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

Experimental evolution: Assortative mating and sexual selection,independent of local adaptation,lead to reproductive isolation in the nematode Caenorhabditis remanei

Using experimental evolution, we investigated the contributions of ecological divergence, sexual selection, and genetic drift to the evolution of reproductive isolation in Caenorhabditis remanei. The nematodes were reared on two different environments for 100 generations. They were assayed for fitness on both environments after 30, 64, and 100 generations, and hybrid fitness were analyzed after 64 and 100 generations. Mating propensity within and between populations was also analyzed. The design allowed us to determine whether local adaptation was synchronous with pre‐ and postzygotic reproductive isolation. Prezygotic isolation evolved quickly but was unconnected with adaptation to the divergent environments. Instead, prezygotic isolation was driven by mate preferences favoring individuals from the same replicate population. A bottleneck treatment, meant to enhance the opportunity for genetic drift, had no effect on prezygotic isolation. Postzygotic isolation occurred in crosses where at least one population had a large fitness advantage in its “home” environment. Taken together, our results suggest that prezygotic isolation did not depend on drift or adaptation to divergent environments, but instead resulted from differences in sexual interactions within individual replicates. Furthermore, our results suggest that postzygotic isolation can occur between populations even when only one population has greater fitness in its home environment.     

Population Genetic Studies Revealed Local Adaptation in a High Gene-Flow Marine Fish,the Small Yellow Croaker (Larimichthys polyactis)

The genetic differentiation of many marine fish species is low. Yet local adaptation may be common in marine fish species as the vast and changing marine environment provides more chances for natural selection. Here, we used anonymous as well as known protein gene linked microsatellites and mitochondrial DNA to detect the population structure of the small yellow croaker (Larimichthys polyactis) in the Northwest Pacific marginal seas. Among these loci, we detected at least two microsatellites, anonymous H16 and HSP27 to be clearly under diversifying selection in outlier tests. Sequence cloning and analysis revealed that H16 was located in the intron of BAHCC1 gene. Landscape genetic analysis showed that H16 mutations were significantly associated with temperature, which further supported the diversifying selection at this locus. These marker types presented different patterns of population structure: (i) mitochondrial DNA phylogeny showed no evidence of genetic divergence and demonstrated only one glacial linage; (ii) population differentiation using putatively neutral microsatellites presented a pattern of high gene flow in the L. polyactis. In addition, several genetic barriers were identified; (iii) the population differentiation pattern revealed by loci under diversifying selection was rather different from that revealed by putatively neutral loci. The results above suggest local adaptation in the small yellow croaker. In summary, population genetic studies based on different marker types disentangle the effects of demographic history, migration, genetic drift and local adaptation on population structure and also provide valuable new insights for the design of management strategies in L. polyactis.     

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated (“pulled”) waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.     

The probability of parallel genetic evolution from standing genetic variation

Parallel evolution is often assumed to result from repeated adaptation to novel, yet ecologically similar, environments. Here, we develop and analyse a mathematical model that predicts the probability of parallel genetic evolution from standing genetic variation as a function of the strength of phenotypic selection and constraints imposed by genetic architecture. Our results show that the probability of parallel genetic evolution increases with the strength of natural selection and effective population size and is particularly likely to occur for genes with large phenotypic effects. Building on these results, we develop a Bayesian framework for estimating the strength of parallel phenotypic selection from genetic data. Using extensive individual‐based simulations, we show that our estimator is robust across a wide range of genetic and evolutionary scenarios and provides a useful tool for rigorously testing the hypothesis that parallel genetic evolution is the result of adaptive evolution. An important result that emerges from our analyses is that existing studies of parallel genetic evolution frequently rely on data that is insufficient for distinguishing between adaptive evolution and neutral evolution driven by random genetic drift. Overcoming this challenge will require sampling more populations and the inclusion of larger numbers of loci.     

Cultural transmission of fitness: genes take the fast lane

Classical population genetics describes how the fate of an allele is driven by four forces: mutation, migration, selection and drift. However, these are sometimes insufficient to explain how the observed allele frequency changes and, therefore, another factor must be invoked: cultural transmission of fitness (CTF). CTF is the non-genetic transmission of any kind of behaviour that affects reproductive success. There are several clearly documented examples of CTF, and theoretical studies have shown that it affects effective population size, linkage disequilibrium and coalescent times. It is therefore a factor that must be taken into account to explain the structure of genetic diversity. In this article, we will present documented cases of how CTF affects the genetic diversity of populations and yields dramatic changes in allele frequencies.     

Drivers of population genetic differentiation in the wild: isolation by dispersal limitation,isolation by adaptation and isolation by colonization

Empirical population genetic studies have been dominated by a neutralist view, according to which gene flow and drift are the main forces driving population genetic structure in nature. The neutralist view in essence describes a process of isolation by dispersal limitation (IBDL) that generally leads to a pattern of isolation by distance (IBD). Recently, however, conceptual frameworks have been put forward that view local genetic adaptation as an important driver of population genetic structure. Isolation by adaptation (IBA) and monopolization (M) posit that gene flow among natural populations is reduced as a consequence of local genetic adaptation. IBA stresses that effective gene flow is reduced among habitats that show dissimilar ecological characteristics, leading to a pattern of isolation by environment. In monopolization, local genetic adaptation of initial colonizing genotypes results in a reduction in gene flow that fosters the persistence of founder effects. Here, we relate these different processes driving landscape genetic structure to patterns of IBD and isolation by environment (IBE). We propose a method to detect whether IBDL, IBA and M shape genetic differentiation in natural landscapes by studying patterns of variation at neutral and non‐neutral markers as well as at ecologically relevant traits. Finally, we reinterpret a representative number of studies from the recent literature by associating patterns to processes and identify patterns associated with local genetic adaptation to be as common as IBDL in structuring regional genetic variation of populations in the wild. Our results point to the importance of quantifying environmental gradients and incorporating ecology in the analysis of population genetics.