The evolutionary genetics of adaptation: a simulation study

It is now clear that the genetic basis of adaptation does not resemble that assumed by the infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I consider recent theoretical attempts to predict the genetic architecture of adaptation from first principles. In particular, I review the history of work on Fisher's geometric model of adaptation, including recent studies which suggest that adaptation should be characterized by exponential distributions of gene effects. I also present the results of new simulation studies that test the robustness of this finding. I explore the effects of changes in the distribution of mutational effects (absolute versus relative) as well as in the nature of the character studied (total phenotypic effect versus single characters). The results show that adaptation towards a fixed optimum is generally characterized by an exponential effects trend.     

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.     

FISHER'S GEOMETRIC MODEL WITH A MOVING OPTIMUM

Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive‐walk approximation,” which is checked against individual‐based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.     

FISHER'S MODEL AND THE GENOMICS OF ADAPTATION: RESTRICTED PLEIOTROPY,HETEROGENOUS MUTATION,AND PARALLEL EVOLUTION

Genetic theories of adaptation generally overlook the genes in which beneficial substitutions occur, and the likely variation in their mutational effects. We investigate the consequences of heterogeneous mutational effects among loci on the genetics of adaptation. We use a generalization of Fisher's geometrical model, which assumes multivariate Gaussian stabilizing selection on multiple characters. In our model, mutation has a distinct variance–covariance matrix of phenotypic effects for each locus. Consequently, the distribution of selection coefficients s varies across loci. We assume each locus can only affect a limited number of independent linear combinations of phenotypic traits (restricted pleiotropy), which differ among loci, an effect we term “orientation heterogeneity.” Restricted pleiotropy can sharply reduce the overall proportion of beneficial mutations. Orientation heterogeneity has little impact on the shape of the genomic distribution, but can substantially increase the probability of parallel evolution (the repeated fixation of beneficial mutations at the same gene in independent populations), which is highest with low pleiotropy. We also consider variation in the degree of pleiotropy and in the mean s across loci. The latter impacts the genomic distribution of s, but has a much milder effect on parallel evolution. We discuss these results in the light of evolution experiments.     

Stabilizing selection,mutational bias,and the evolution of sex*

Stabilizing selection around a fixed phenotypic optimum is expected to disfavor sexual reproduction, since asexually reproducing organisms can maintain a higher fitness at equilibrium, while sex disrupts combinations of compensatory mutations. This conclusion rests on the assumption that mutational effects on phenotypic traits are unbiased, that is, mutation does not tend to push phenotypes in any particular direction. In this article, we consider a model of stabilizing selection acting on an arbitrary number of polygenic traits coded by bialellic loci, and show that mutational bias may greatly reduce the mean fitness of asexual populations compared with sexual ones in regimes where mutations have weak to moderate fitness effects. Indeed, mutation and drift tend to push the population mean phenotype away from the optimum, this effect being enhanced by the low effective population size of asexual populations. In a second part, we present results from individual‐based simulations showing that positive rates of sex are favored when mutational bias is present, while the population evolves toward complete asexuality in the absence of bias. We also present analytical (QLE) approximations for the selective forces acting on sex in terms of the effect of sex on the mean and variance in fitness among offspring.     

The distribution of beneficial and fixed mutation fitness effects close to an optimum

The distribution of the selection coefficients of beneficial mutations is pivotal to the study of the adaptive process, both at the organismal level (theories of adaptation) and at the gene level (molecular evolution). A now famous result of extreme value theory states that this distribution is an exponential, at least when considering a well-adapted wild type. However, this prediction could be inaccurate under selection for an optimum (because fitness effect distributions have a finite right tail in this case). In this article, we derive the distribution of beneficial mutation effects under a general model of stabilizing selection, with arbitrary selective and mutational covariance between a finite set of traits. We assume a well-adapted wild type, thus taking advantage of the robustness of tail behaviors, as in extreme value theory. We show that, under these general conditions, both beneficial mutation effects and fixed effects (mutations escaping drift loss) are beta distributed. In both cases, the parameters have explicit biological meaning and are empirically measurable; their variation through time can also be predicted. We retrieve the classic exponential distribution as a subcase of the beta when there are a moderate to large number of weakly correlated traits under selection. In this case too, we provide an explicit biological interpretation of the parameters of the distribution. We show by simulations that these conclusions are fairly robust to a lower adaptation of the wild type and discuss the relevance of our findings in the context of adaptation theories and experimental evolution.     

GENETIC REGULATORY NETWORK MOTIFS CONSTRAIN ADAPTATION THROUGH CURVATURE IN THE LANDSCAPE OF MUTATIONAL (CO)VARIANCE

Systems biology is accumulating a wealth of understanding about the structure of genetic regulatory networks, leading to a more complete picture of the complex genotype–phenotype relationship. However, models of multivariate phenotypic evolution based on quantitative genetics have largely not incorporated a network‐based view of genetic variation. Here we model a set of two‐node, two‐phenotype genetic network motifs, covering a full range of regulatory interactions. We find that network interactions result in different patterns of mutational (co)variance at the phenotypic level (the M ‐matrix), not only across network motifs but also across phenotypic space within single motifs. This effect is due almost entirely to mutational input of additive genetic (co)variance. Variation in M has the effect of stretching and bending phenotypic space with respect to evolvability, analogous to the curvature of space–time under general relativity, and similar mathematical tools may apply in each case. We explored the consequences of curvature in mutational variation by simulating adaptation under divergent selection with gene flow. Both standing genetic variation (the G ‐matrix) and rate of adaptation are constrained by M , so that G and adaptive trajectories are curved across phenotypic space. Under weak selection the phenotypic mean at migration‐selection balance also depends on M .     

NICHE DIMENSIONALITY AND THE GENETICS OF ECOLOGICAL SPECIATION

Niche dimensionality is suggested to be a key determinant of ecological speciation (“multifarious selection” hypothesis), but genetic aspects of this process have not been investigated theoretically. We use Fisher's geometrical model to study how niche dimensionality influences the mean fitness of hybrids formed upon secondary contact between populations adapting in allopatry. Gaussian selection for an optimum generates two forms of reproductive isolation (RI): an extrinsic component due to maladaptation of the mean phenotype, and an intrinsic variance load resulting from what we term transgressive incompatibilities between mutations fixed in different populations. We show that after adaptation to a new environment, RI increases with (1) the mean initial maladaptation of diverging population, and (2) niche dimensionality, which increases the phenotypic variability of fixed mutations. Under mutation selection drift equilibrium in a constant environment, RI accumulates steadily with time, at a rate that also increases with niche dimensionality. A similar pattern can be produced by successive shifts in the optimum phenotype. Niche dimensionality thus has an effect per se on postzygotic isolation, beyond putative indirect effects (stronger selection, more genes). Our mechanism is consistent with empirical evidence about transgressive segregation in crosses between divergent populations, and with patterns of accumulation of RI with time in many taxa.     

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.     

The distribution of fitness effects among beneficial mutations

We know little about the distribution of fitness effects among new beneficial mutations, a problem that partly reflects the rarity of these changes. Surprisingly, though, population genetic theory allows us to predict what this distribution should look like under fairly general assumptions. Using extreme value theory, I derive this distribution and show that it has two unexpected properties. First, the distribution of beneficial fitness effects at a gene is exponential. Second, the distribution of beneficial effects at a gene has the same mean regardless of the fitness of the present wild-type allele. Adaptation from new mutations is thus characterized by a kind of invariance: natural selection chooses from the same spectrum of beneficial effects at a locus independent of the fitness rank of the present wild type. I show that these findings are reasonably robust to deviations from several assumptions. I further show that one can back calculate the mean size of new beneficial mutations from the observed mean size of fixed beneficial mutations.     

ADAPTIVE GENETIC VARIATION IN GROWTH AND DEVELOPMENT OF TADPOLES OF THE HYBRIDOGENETIC RANA ESCULENTA COMPLEX

The distribution and proportion of the sexual species Rana lessonae to the hemiclonal hybrid R. esculenta among natural habitats suggests that these anurans may differ in adaptive abilities. I used a half-sib design to partition phenotypic and quantitative genetic variation in tadpole responses at two food levels into causal variance components. Rana lessonae displays strong phenotypic variation across food levels. Growth rate is strictly determined by environmental factors and includes weak maternal effects. Larval period and body size at metamorphosis both contain moderate levels of additive genetic variance. The sire x food interactions and the lack of environmental correlations indicate that adaptive phenotypic plasticity is present in both of these traits. In contrast, R. esculenta displays less phenotypic variation across food levels, especially for larval period. Variation in body size at metamorphosis is underlain by genetic variation as shown by high levels of additive genetic variance, yet growth rate and larval period are not. Significant environmental correlations between larval period at high food level and growth, larval period, and body size at low food, indicate phenotypic plasticity is absent. A positive phenotypic correlation between body size at metamorphosis and larval period for R. lessonae at both food levels suggests a trade-off between growing large and metamorphosing quickly to escape predation or pond drying. The lack of a similar correlation for R. esculenta at the high food level suggests it may be less constrained. Different levels of adaptive genetic variation among larval traits suggest that the sexual species and the hybridogenetic hemiclone differ in their abilities to cope with temporally and spatially heterogeneous environments.     

THE LOCI OF REPEATED EVOLUTION: A CATALOG OF GENETIC HOTSPOTS OF PHENOTYPIC VARIATION

What is the nature of the genetic changes underlying phenotypic evolution? We have catalogued 1008 alleles described in the literature that cause phenotypic differences among animals, plants, and yeasts. Surprisingly, evolution of similar traits in distinct lineages often involves mutations in the same gene (“gene reuse”). This compilation yields three important qualitative implications about repeated evolution. First, the apparent evolution of similar traits by gene reuse can be traced back to two alternatives, either several independent causative mutations or a single original mutational event followed by sorting processes. Second, hotspots of evolution—defined as the repeated occurrence of de novo mutations at orthologous loci and causing similar phenotypic variation—are omnipresent in the literature with more than 100 examples covering various levels of analysis, including numerous gain‐of‐function events. Finally, several alleles of large effect have been shown to result from the aggregation of multiple small‐effect mutations at the same hotspot locus, thus reconciling micromutationist theories of adaptation with the empirical observation of large‐effect variants. Although data heterogeneity and experimental biases prevented us from extracting quantitative trends, our synthesis highlights the existence of genetic paths of least resistance leading to viable evolutionary change.     

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.     

GENETIC ARCHITECTURE FOR THE ADAPTIVE ORIGIN OF ANNUAL WILD RICE, ORYZA NIVARA

The wild progenitors of cultivated rice, Oryza nivara and Oryza rufipogon , provide an experimental system for characterizing the genetic basis of adaptation. The evolution of annual O. nivara from a perennial ancestor resembling its sister species, O. rufipogon , was associated with an ecological shift from persistently wet to seasonally dry habitats. Here we report a quantitative trait locus (QTL) analysis of phenotypic differentiation in life history, mating system, and flowering time between O. nivara and O. rufipogon . The exponential distribution of effect sizes of QTL fits the prediction of a recently proposed population genetic model of adaptation. More than 80% of QTL alleles of O. nivara acted in the same direction of phenotypic evolution, suggesting that they were fixed under directional selection. The loss of photoperiod sensitivity, which might be essential to the survival of the ancestral populations of O. nivara in the new environment, was controlled by QTL of relatively large effect. Mating system evolution from cross- to self-fertilization through the modification of panicle and floral morphology was controlled by QTL of small-to-moderate effect. The lack of segregation of the recessive annual habit in the F₂ mapping populations suggested that the evolution of annual from perennial life form had a complex genetic basis. The study captured the genetic architecture for the adaptive origin of O. nivara and provides a foundation for rigorous experimental tests of population genetic theories of adaptation.     

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.     

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721–3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual’s overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.     

The genetics of adaptation: the roles of pleiotropy, stabilizing selection and drift in shaping the distribution of bidirectional fixed mutational effects

Pleiotropy allows for the deterministic fixation of bidirectional mutations: mutations with effects both in the direction of selection and opposite to selection for the same character. Mutations with deleterious effects on some characters can fix because of beneficial effects on other characters. This study analytically quantifies the expected frequency of mutations that fix with negative and positive effects on a character and the average size of a fixed effect on a character when a mutation pleiotropically affects from very few to many characters. The analysis allows for mutational distributions that vary in shape and provides a framework that would allow for varying the frequency at which mutations arise with deleterious and positive effects on characters. The results show that a large fraction of fixed mutations will have deleterious pleiotropic effects even when mutation affects as little as two characters and only directional selection is occurring, and, not surprisingly, as the degree of pleiotropy increases the frequency of fixed deleterious effects increases. As a point of comparison, we show how stabilizing selection and random genetic drift affect the bidirectional distribution of fixed mutational effects. The results are then applied to QTL studies that seek to find loci that contribute to phenotypic differences between populations or species. It is shown that QTL studies are biased against detecting chromosome regions that have deleterious pleiotropic effects on characters.     

DISCOVERING EXCEPTIONAL DIVERSIFICATIONS AT CONTINENTAL SCALES: THE CASE OF THE ENDEMIC FAMILIES OF NEOTROPICAL SUBOSCINE PASSERINES

The study of continental adaptive radiations has lagged behind research on their island counterparts in part because the mere identification of adaptive radiations is more challenging at continental scales. Here, I demonstrate a new method based on simulations for discovering clades that show exceptionally high phenotypic diversity. The method does not require a phylogeny but accounts for differences in age and species richness among clades and incorporates effects of the phylogenetic structure of data. In addition, I developed a new multivariate measure of phenotypic diversity, which has the advantage over other measures of disparity in that it takes covariation into account. I applied these methods to a clade of endemic Neotropical suboscine passerines, within which the family Furnariidae has been considered an adaptive radiation. I found that the families Thamnophilidae, Furnariidae, and Dendrocolaptidae have experienced a higher rate of cladogenesis than have other clades. Although Thamnophilidae is exceptionally diverse in body size, only Furnariidae and Dendrocolaptidae are exceptionally diverse in shape. The combination of high rates of cladogenesis and high morphometric diversity in traits related to feeding and locomotion suggest that the clade Furnariidae‐Dendrocolaptidae represent an authentic continental adaptive radiation.     

Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales

We tested the ability of six quantitative genetic models to explain the evolution of phenotypic means using an extensive database compiled by Gingerich. Our approach differs from past efforts in that we use explicit models of evolutionary process, with parameters estimated from contemporary populations, to analyze a large sample of divergence data on many different timescales. We show that one quantitative genetic model yields a good fit to data on phenotypic divergence across timescales ranging from a few generations to 10 million generations. The key feature of this model is a fitness optimum that moves within fixed limits. Conversely, a model of neutral evolution, models with a stationary optimum that undergoes Brownian or white noise motion, a model with a moving optimum, and a peak shift model all fail to account for the data on most or all timescales. We discuss our results within the framework of Simpson's concept of adaptive landscapes and zones. Our analysis suggests that the underlying process causing phenotypic stasis is adaptation to an optimum that moves within an adaptive zone with stable boundaries. We discuss the implication of our results for comparative studies and phylogeny inference based on phenotypic characters.