THE POPULATION GENETICS OF ADAPTATION: THE DISTRIBUTION OF FACTORS FIXED DURING ADAPTIVE EVOLUTION

We know very little about the genetic basis of adaptation. Indeed, we can make no theoretical predictions, however heuristic, about the distribution of phenotypic effects among factors fixed during adaptation nor about the expected “size” of the largest factor fixed. Study of this problem requires taking into account that populations gradually approach a phenotypic optimum during adaptation via the stepwise substitution of favorable mutations. Using Fisher's geometric model of adaptation, I analyze this approach to the optimum, and derive an approximate solution to the size distribution of factors fixed during adaptation. I further generalize these results to allow the input of any distribution of mutational effects. The distribution of factors fixed during adaptation assumes a pleasingly simple, exponential form. This result is remarkably insensitive to changes in the fitness function and in the distribution of mutational effects. An exponential trend among factors fixed appears to be a general property of adaptation toward a fixed optimum.     

The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation

Recent models of adaptation at the DNA sequence level assume that the fitness effects of new mutations show certain statistical properties. In particular, these models assume that the distribution of fitness effects among new mutations is in the domain of attraction of the so-called Gumbel-type extreme value distribution. This assumption has not, however, been justified on any biological or theoretical grounds. In this note, I study random mutation in one of the simplest models of mutation and adaptation-Fisher's geometric model. I show that random mutation in this model yields a distribution of mutational effects that belongs to the Gumbel type. I also show that the distribution of fitness effects among rare beneficial mutations in Fisher's model is asymptotically exponential. I confirm these analytic findings with exact computer simulations. These results provide some support for the use of Gumbel-type extreme value theory in studies of adaptation and point to a surprising connection between recent phenotypic- and sequence-based models of adaptation: in both, the distribution of fitness effects among rare beneficial mutations is approximately exponential.     

Adaptation and the cost of complexity

Abstract.— Adaptation is characterized by the movement of a population toward a many-character optimum, movement that results in an increase in fitness. Here I calculate the rate at which fitness increases during adaptation and describe the curve giving fitness versus time as a population approaches an optimum in Fisher's model of adaptation. The results identify several factors affecting the speed of adaptation. One of the most important is organismal complexity—complex organisms adapt more slowly than simple ones when using mutations of the same phenotypic size. Thus, as Fisher foresaw, organisms pay a kind of cost of complexity. However, the magnitude of this cost is considerably larger than Fisher's analysis suggested. Indeed the rate of adaptation declines at least as fast as n^-1 , where n is the number of independent characters or dimensions comprising an organism. The present results also suggest that one can define an effective number of dimensions characterizing an adapting species.     

The population genetics of adaptation on correlated fitness landscapes: the block model

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.     

The genetic theory of adaptation: a brief history

Theoretical studies of adaptation have exploded over the past decade. This work has been inspired by recent, surprising findings in the experimental study of adaptation. For example, morphological evolution sometimes involves a modest number of genetic changes, with some individual changes having a large effect on the phenotype or fitness. Here I survey the history of adaptation theory, focusing on the rise and fall of various views over the past century and the reasons for the slow development of a mature theory of adaptation. I also discuss the challenges that face contemporary theories of adaptation.     

The Impact of Population Demography and Selection on the Genetic Architecture of Complex Traits

Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequency, and effect sizes of mutations that contribute risk to complex traits. Because researchers are performing exome sequencing studies aimed at uncovering the role of low-frequency variants in the risk of complex traits, this topic is of critical importance. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynonymous variants segregating in the population, but does not affect the genetic load relative to a population that did not expand. Under a model where a mutation''s effect on a trait is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand. Further, when using a single-marker test, for a given false-positive rate and sample size, recent population growth decreases the expected number of significant associations with the trait relative to the number detected in a population that did not expand. However, in a model where there is no correlation between a mutation''s effect on fitness and the effect on the trait, common variants account for much of the additive genetic variance, regardless of demography. Moreover, here demography does not affect the number of significant associations detected. These findings suggest recent population history may be an important factor influencing the power of association tests and in accounting for the missing heritability of certain complex traits.     

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.     

Alleles versus mutations: Understanding the evolution of genetic architecture requires a molecular perspective on allelic origins

Perspectives on the role of large‐effect quantitative trait loci (QTL) in the evolution of complex traits have shifted back and forth over the past few decades. Different sets of studies have produced contradictory insights on the evolution of genetic architecture. I argue that much of the confusion results from a failure to distinguish mutational and allelic effects, a limitation of using the Fisherian model of adaptive evolution as the lens through which the evolution of adaptive variation is examined. A molecular‐based perspective reveals that allelic differences can involve the cumulative effects of many mutations plus intragenic recombination, a model that is supported by extensive empirical evidence. I discuss how different selection regimes could produce very different architectures of allelic effects under a molecular‐based model, which may explain conflicting insights on genetic architecture from studies of variation within populations versus between divergently selected populations. I address shortcomings of genome‐wide association study (GWAS) practices in light of more suitable models of allelic evolution, and suggest alternate GWAS strategies to generate more valid inferences about genetic architecture. Finally, I discuss how adopting more suitable models of allelic evolution could help redirect research on complex trait evolution toward addressing more meaningful questions in evolutionary biology.     

Little effect of HSP90 inhibition on the quantitative wing traits variation in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

Drosophila wings have been a model system to study the effect of HSP90 on quantitative trait variation. The effect of HSP90 inhibition on environmental buffering of wing morphology varies among studies while the genetic buffering effect of it was examined in only one study and was not detected. Variable results so far might show that the genetic background influences the environmental and genetic buffering effect of HSP90. In the previous studies, the number of the genetic backgrounds used is limited. To examine the effect of HSP90 inhibition with a larger number of genetic backgrounds than the previous studies, 20 wild-type strains of Drosophila melanogaster were used in this study. Here I investigated the effect of HSP90 inhibition on the environmental buffering of wing shape and size by assessing within-individual and among-individual variations, and as a result, I found little or very weak effects on environmental and genetic buffering. The current results suggest that the role of HSP90 as a global regulator of environmental and genetic buffering is limited at least in quantitative traits.     

The population genetics of adaptation: the adaptation of DNA sequences

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.     

Genetics, development and evolution of adaptive pigmentation in vertebrates

The study of pigmentation has played an important role in the intersection of evolution, genetics, and developmental biology. Pigmentation's utility as a visible phenotypic marker has resulted in over 100 years of intense study of coat color mutations in laboratory mice, thereby creating an impressive list of candidate genes and an understanding of the developmental mechanisms responsible for the phenotypic effects. Variation in color and pigment patterning has also served as the focus of many classic studies of naturally occurring phenotypic variation in a wide variety of vertebrates, providing some of the most compelling cases for parallel and convergent evolution. Thus, the pigmentation model system holds much promise for understanding the nature of adaptation by linking genetic changes to variation in fitness-related traits. Here, I first discuss the historical role of pigmentation in genetics, development and evolutionary biology. I then discuss recent empirically based studies in vertebrates, which rely on these historical foundations to make connections between genotype and phenotype for ecologically important pigmentation traits. These studies provide insight into the evolutionary process by uncovering the genetic basis of adaptive traits and addressing such long-standing questions in evolutionary biology as (1) are adaptive changes predominantly caused by mutations in regulatory regions or coding regions? (2) is adaptation driven by the fixation of dominant mutations? and (3) to what extent are parallel phenotypic changes caused by similar genetic changes? It is clear that coloration has much to teach us about the molecular basis of organismal diversity, adaptation and the evolutionary process.     

Limits to the evolution of assortative mating by female choice under restricted gene flow

The evolution of assortative mating is a key component of the process of speciation with gene flow. Several recent theoretical studies have pointed out, however, that sexual selection which can result from assortative mating may cause it to plateau at an intermediate level; this is primarily owing to search costs of individuals with extreme phenotypes and to assortative preferences developed by individuals with intermediate phenotypes. I explore the limitations of assortative mating further by analysing a simple model in which these factors have been removed. Specifically, I use a haploid two-population model to ask whether the existence of assortative mating is sufficient to drive the further evolution of assortative mating. I find that a weakening in the effective strength of sexual selection with strong assortment leads to the existence of both a peak level of trait differentiation and the evolution of an intermediate level of assortative mating that will cause that peak. This result is robust to the inclusion of local adaptation and different genetic architecture of the trait. The results imply the existence of fundamental limits to the evolution of assortment via sexual selection in this situation, with which other factors, such as search costs, may interact.     

Patterns of quantitative genetic variation in multiple dimensions

A fundamental question for both evolutionary biologists and breeders is the extent to which genetic correlations limit the ability of populations to respond to selection. Here I view this topic from three perspectives. First, I propose several nondimensional statistics to quantify the genetic variation present in a suite of traits and to describe the extent to which correlations limit their selection response. A review of five data sets suggests that the total variation differs substantially between populations. In all cases analyzed, however, the “effective number of dimensions” is less than two: more than half of the total genetic variation is explained by a single combination of traits. Second, I consider how patterns of variation affect the average evolutionary response to selection in a random direction. When genetic variation lies in a small number of dimensions but there are a large number of traits under selection, then the average selection response will be reduced substantially from its potential maximum. Third, I discuss how a low genetic correlation between male fitness and female fitness limits the ability of populations to adapt. Data from two recent studies of natural populations suggest this correlation can diminish or even erase any genetic benefit to mate choice. Together these results suggest that adaptation (in natural populations) and genetic improvement (in domesticated populations) may often be as much constrained by patterns of genetic correlation as by the overall amount of genetic variation.     

The relationship between the pleiotropic phenotypic effects of a mutation fixed by selection

A pleiotropic model of mutation is presented that allows for correlations between the effects of a new mutation and for the distribution of mutational effects to vary from being leptokurtic to normally distributed. Using this model I quantify how selection transforms the correlation between the effects of a new (random) mutation into the correlation between the effects of a mutation that is fixed by selection and contributes to an adaptation. Results suggest that under most conditions the correlation between the effects of a fixed mutation is less than the correlation between the effects of a new mutation. I also generalize previous results that quantified the expected size of a fixed mutation's effect on a character given an observed effect of that mutation on another character. In agreement with previous results, work here suggests that as the observed effect becomes large and beneficial the expected effect on another character approaches the expected effect of a new (random) mutation given the observed effect. Lastly, these theoretical results are related to recent empirical work that found beneficial mutations had a positive correlation in their pleiotropic effects.     

Genetic adaptation to captivity in species conservation programs

As wild environments are often inhospitable, many species have to be captive-bred to save them from extinction. In captivity, species adapt genetically to the captive environment and these genetic adaptations are overwhelmingly deleterious when populations are returned to wild environments. I review empirical evidence on (i) the genetic basis of adaptive changes in captivity, (ii) factors affecting the extent of genetic adaptation to captivity, and (iii) means for minimizing its deleterious impacts. Genetic adaptation to captivity is primarily due to rare alleles that in the wild were deleterious and partially recessive. The extent of adaptation to captivity depends upon selection intensity, genetic diversity, effective population size and number of generation in captivity, as predicted by quantitative genetic theory. Minimizing generations in captivity provides a highly effective means for minimizing genetic adaptation to captivity, but is not a practical option for most animal species. Population fragmentation and crossing replicate captive populations provide practical means for minimizing the deleterious effects of genetic adaptation to captivity upon populations reintroduced into the wild. Surprisingly, equalization of family sizes reduces the rate of genetic adaptation, but not the deleterious impacts upon reintroduced populations. Genetic adaptation to captivity is expected to have major effects on reintroduction success for species that have spent many generations in captivity. This issue deserves a much higher priority than it is currently receiving.     

Cross-action of extracellular stress adaptation factors in microorganisms]

The capacity of microorganisms from different taxa to adapt to stress conditions with the help of extracellular factors exhibiting similar mechanisms of action was demonstrated. The action of adaptation factors synthesized by the enteric bacterium Escherichia coli, the soil bacterium Bacillus subtilis, and the yeast Candida utilis was characterized in biological tests. It was demonstrated that the factor of accelerated adaptation to new media (FAANM) and the growth-rate-reducing factor (factor X(II)), which decreases the rate of exponential culture growth, were synthesized by all microorganisms tested. Antilysin (factor X(I)), which accelerates cell adaptation to N-ethylmaleimide, was not produced by C. utilis.     

PERSPECTIVE: MODELS OF SPECIATION: WHAT HAVE WE LEARNED IN 40 YEARS?

Theoretical studies of speciation have been dominated by numerical simulations aiming to demonstrate that speciation in a certain scenario may occur. What is needed now is a shift in focus to identifying more general rules and patterns in the dynamics of speciation. The crucial step in achieving this goal is the development of simple and general dynamical models that can be studied not only numerically but analytically as well. I review some of the existing analytical results on speciation. I first show why the classical theories of speciation by peak shifts across adaptive valleys driven by random genetic drift run into trouble (and into what kind of trouble). Then I describe the Bateson-Dobzhansky-Muller (BDM) model of speciation that does not require overcoming selection. I describe exactly how the probability of speciation, the average waiting time to speciation, and the average duration of speciation depend on the mutation and migration rates, population size, and selection for local adaptation. The BDM model postulates a rather specific genetic architecture of reproductive isolation. I then show exactly why the genetic architecture required by the BDM model should be common in general. Next I consider the multilocus generalizations of the BDM model again concentrating on the qualitative characteristics of speciation such as the average waiting time to speciation and the average duration of speciation. Finally, I consider two models of sympatric speciation in which the conditions for sympatric speciation were found analytically. A number of important conclusions have emerged from analytical studies. Unless the population size is small and the adaptive valley is shallow, the waiting time to a stochastic transition between the adaptive peaks is extremely long. However, if transition does happen, it is very quick. Speciation can occur by mutation and random drift alone with no contribution from selection as different populations accumulate incompatible genes. The importance of mutations and drift in speciation is augmented by the general structure of adaptive landscapes. Speciation can be understood as the divergence along nearly neutral networks and holey adaptive landscapes (driven by mutation, drift, and selection for adaptation to a local biotic and/or abiotic environment) accompanied by the accumulation of reproductive isolation as a by-product. The waiting time to speciation driven by mutation and drift is typically very long. Selection for local adaptation (either acting directly on the loci underlying reproductive isolation via their pleiotropic effects or acting indirectly via establishing a genetic barrier to gene flow) can significantly decrease the waiting time to speciation. In the parapatric case the average actual duration of speciation is much shorter than the average waiting time to speciation. Speciation is expected to be triggered by changes in the environment. Once genetic changes underlying speciation start, they go to completion very rapidly. Sympatric speciation is possible if disruptive selection and/or assortativeness in mating are strong enough. Sympatric speciation is promoted if costs of being choosy are small (or absent) and if linkage between the loci experiencing disruptive selection and those controlling assortative mating is strong.     

The effects of migration and drift on local adaptation to a heterogeneous environment

Local adaptation experiments are widely used to quantify the levels of adaptation within a heterogeneous environment. However, theoretical studies generally focus on the probability of fixation of alleles or the mean fitness of populations, rather than local adaptation as it is commonly measured experimentally or in field studies. Here, we develop mathematical models and use them to generate analytical predictions for the level of local adaptation as a function of selection, migration and genetic drift. First, we contrast mean fitness and local adaptation measures and show that the latter can be expressed in a simple and general way as a function of the spatial covariance between population mean phenotype and local environmental conditions. Second, we develop several approximations of a population genetics model to show that the system exhibits different behaviours depending on the rate of migration. The main insights are the following: with intermediate migration, both genetic drift and migration decrease local adaptation; with low migration, drift decreases local adaptation but migration speeds up adaptation; with high migration, genetic drift has no effect on local adaptation. Third, we extend this analysis to cases where the trait under selection is continuous using classical quantitative genetics theory. Finally, we discuss these results in the light of recent experimental work on local adaptation.     

The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa

Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.     

How to be early flowering: an evolutionary perspective

In wild and cultivated annual plant species, flowering time is an important life-history trait that coordinates the life cycle with local environmental conditions. Extensive studies on the genetic basis of flowering time in the model species Arabidopsis thaliana have revealed a complex genetic network that can detect environmental and internal signals. Based on this knowledge and on known pleiotropic effects associated with flowering time genes, we suggest that a natural shift towards an early-flowering life cycle might involve only particular functional regions in a limited number of genes. Our predictions are supported by genetic theories of adaptation and by recent data about genes associated with natural variation. We analyse the extent to which these predictions can also apply to crop species.