The rate of polygenic mutation

Evolvability predicts macroevolution under fluctuating selection

Heritable variation is a prerequisite for evolutionary change, but the relevance of genetic constraints on macroevolutionary timescales is debated. By using two datasets on fossil and contemporary taxa, we show that evolutionary divergence among populations, and to a lesser extent among species, increases with microevolutionary evolvability. We evaluate and reject several hypotheses to explain this relationship and propose that an effect of evolvability on population and species divergence can be explained by the influence of genetic constraints on the ability of populations to track rapid, stationary environmental fluctuations.

Moderating the neutralist-selectionist debate: exactly which propositions are we debating, and which arguments are valid?

Half a century after its foundation, the neutral theory of molecular evolution continues to attract controversy. The debate has been hampered by the coexistence of different interpretations of the core proposition of the neutral theory, the 'neutral mutation-random drift' hypothesis. In this review, we trace the origins of these ambiguities and suggest potential solutions. We highlight the difference between the original, the revised and the nearly neutral hypothesis, and re-emphasise that none of them equates to the null hypothesis of strict neutrality. We distinguish the neutral hypothesis of protein evolution, the main focus of the ongoing debate, from the neutral hypotheses of genomic and functional DNA evolution, which for many species are generally accepted. We advocate a further distinction between a narrow and an extended neutral hypothesis (of which the latter posits that random non-conservative amino acid substitutions can cause non-ecological phenotypic divergence), and we discuss the implications for evolutionary biology beyond the domain of molecular evolution. We furthermore point out that the debate has widened from its initial focus on point mutations, and also concerns the fitness effects of large-scale mutations, which can alter the dosage of genes and regulatory sequences. We evaluate the validity of neutralist and selectionist arguments and find that the tested predictions, apart from being sensitive to violation of underlying assumptions, are often derived from the null hypothesis of strict neutrality, or equally consistent with the opposing selectionist hypothesis, except when assuming molecular panselectionism. Our review aims to facilitate a constructive neutralist-selectionist debate, and thereby to contribute to answering a key question of evolutionary biology: what proportions of amino acid and nucleotide substitutions and polymorphisms are adaptive?

Causes of variability in estimates of mutational variance from mutation accumulation experiments

Characteristics of the new phenotypic variation introduced via mutation have broad implications in evolutionary and medical genetics. Standardized estimates of this mutational variance, V_M, span 2 orders of magnitude, but the causes of this remain poorly resolved. We investigated estimate heterogeneity using 2 approaches. First, meta-analyses of ∼150 estimates of standardized V_M from 37 mutation accumulation studies did not support a difference among taxa (which differ in mutation rate) but provided equivocal support for differences among trait types (life history vs morphology, predicted to differ in mutation rate). Notably, several experimental factors were confounded with taxon and trait, and further empirical data are required to resolve their influences. Second, we analyzed morphological data from an experiment in Drosophila serrata to determine the potential for unintentional heterogeneity among environments in which phenotypes were measured (i.e. among laboratories or time points) or transient segregation of mutations within mutation accumulation lines to affect standardized V_M. Approximating the size of an average mutation accumulation experiment, variability among repeated estimates of (accumulated) mutational variance was comparable to variation among published estimates of standardized V_M. This heterogeneity was (partially) attributable to unintended environmental variation or within line segregation of mutations only for wing size, not wing shape traits. We conclude that sampling error contributed substantial variation within this experiment, and infer that it will also contribute substantially to differences among published estimates. We suggest a logistically permissive approach to improve the precision of estimates, and consequently our understanding of the dynamics of mutational variance of quantitative traits.

General statistical model shows that macroevolutionary patterns and processes are consistent with Darwinian gradualism

Macroevolution posed difficulties for Darwin and later theorists because species’ phenotypes frequently change abruptly, or experience long periods of stasis, both counter to the theory of incremental change or gradualism. We introduce a statistical model that accommodates this uneven evolutionary landscape by estimating two kinds of historical change: directional changes that shift the mean phenotype along the branches of a phylogenetic tree, and evolvability changes that alter a clade’s ability to explore its trait-space. In mammals, we find that both processes make substantial independent contributions to explaining macroevolution, and are rarely linked. ‘Watershed’ moments of increased evolvability greatly outnumber reductions in evolutionary potentials, and large or abrupt phenotypic shifts are explicable statistically as biased random walks, allowing macroevolutionary theory to engage with the language and concepts of gradualist microevolution. Our findings recast macroevolutionary phenomena, illustrating the necessity of accounting for a variety of evolutionary processes simultaneously.

‘Macroevolution posed difficulties for Darwin and later theorists because species frequently change abruptly, or experience long periods of stasis, both counter to the theory of incremental change or gradualism. Here, the authors propose a macroevolutionary statistical model that accommodates this uneven evolutionary landscape, and shows how even abrupt macroevolutionary changes are compatible with gradualist microevolutionary processes.’

Genetics of quantitative traits with dominance under stabilizing and directional selection in partially selfing species

Recurrent self-fertilization is thought to lead to reduced adaptive potential by decreasing the genetic diversity of populations, thus leading selfing lineages down an evolutionary "blind alley." Although well supported theoretically, empirical support for reduced adaptability in selfing species is limited. One limitation of classical theoretical models is that they assume pure additivity of the fitness-related traits that are under stabilizing selection, despite ample evidence that quantitative traits are subject to dominance. Here, we relax this assumption and explore the effect of dominance on a fitness-related trait under stabilizing selection for populations that differ in selfing rates. By decomposing the genetic variance into additional components specific to inbred populations, we show that dominance components can explain a substantial part of the genetic variance of inbred populations. We also show that ignoring these components leads to an upward bias in the predicted response to selection. Finally, we show that when considering the effect of dominance, the short-term evolutionary potential of populations remains comparable across the entire gradient in outcrossing rates, and genetic associations can even make selfing populations more evolvable on the longer term, reconciling theoretical, and empirical results.

Assortative mating can help adaptation of flowering time to a changing climate: Insights from a polygenic model

Several empirical studies report fast evolutionary changes in flowering time in response to contemporary climate change. Flowering time is a polygenic trait under assortative mating, since flowering time of mates must overlap. Here, we test whether assortative mating, compared with random mating, can help better track a changing climate. For each mating pattern, our individual‐based model simulates a population evolving in a climate characterized by stabilizing selection around an optimal flowering time, which can change directionally and/or fluctuate. We also derive new analytical predictions from a quantitative genetics model for the expected genetic variance at equilibrium, and its components, the lag of the population to the optimum and the population mean fitness. We compare these predictions between assortative and random mating, and to our simulation results. Assortative mating, compared with random mating, has antagonistic effects on genetic variance: it generates positive associations among similar allelic effects, which inflates the genetic variance, but it decreases genetic polymorphism, which depresses the genetic variance. In a stationary environment with substantial stabilizing selection, assortative mating affects little the genetic variance compared with random mating. In a changing climate, assortative mating however increases genetic variance compared to random mating, which diminishes the lag of the population to the optimum, and in most scenarios translates into a fitness advantage relative to random mating. The magnitude of this fitness advantage depends on the extent to which genetic variance limits adaptation, being larger for faster environmental changes and weaker stabilizing selection.

Bayesian inference of natural selection from spatiotemporal phenotypic data

Spatiotemporal variations of natural selection may influence the evolution of various features of organisms such as local adaptation or specialisation. This article develops a method for inferring how selection varies between locations and between generations from phenotypic data. It is assumed that generations are non-overlapping and that individuals reproduce by selfing or asexually. A quantitative genetics model taking account of the effects of stabilising natural selection, the environment and mutation on phenotypic means and variances is developed. Explicit results on the evolution of populations are derived and used to develop a Bayesian inference method. The latter is applied to simulated data and to data from a wheat participatory plant breeding programme. It has some ability to infer evolutionary parameters, but estimates may be sensitive to prior distributions, for example when phenotypic time series are short and when environmental effects are large. In such cases, sensitivity to prior distributions may be reported or more data may be collected.

Polygenic Adaptation to an Environmental Shift: Temporal Dynamics of Variation Under Gaussian Stabilizing Selection and Additive Effects on a Single Trait

Predictions about the effect of natural selection on patterns of linked neutral variation are largely based on models involving the rapid fixation of unconditionally beneficial mutations. However, when phenotypes adapt to a new optimum trait value, the strength of selection on individual mutations decreases as the population adapts. Here, I use explicit forward simulations of a single trait with additive-effect mutations adapting to an "optimum shift." Detectable "hitchhiking" patterns are only apparent if (i) the optimum shifts are large with respect to equilibrium variation for the trait, (ii) mutation rates to large-effect mutations are low, and (iii) large-effect mutations rapidly increase in frequency and eventually reach fixation, which typically occurs after the population reaches the new optimum. For the parameters simulated here, partial sweeps do not appreciably affect patterns of linked variation, even when the mutations are strongly selected. The contribution of new mutations vs. standing variation to fixation depends on the mutation rate affecting trait values. Given the fixation of a strongly selected variant, patterns of hitchhiking are similar on average for the two classes of sweeps because sweeps from standing variation involving large-effect mutations are rare when the optimum shifts. The distribution of effect sizes of new mutations has little effect on the time to reach the new optimum, but reducing the mutational variance increases the magnitude of hitchhiking patterns. In general, populations reach the new optimum prior to the completion of any sweeps, and the times to fixation are longer for this model than for standard models of directional selection. The long fixation times are due to a combination of declining selection pressures during adaptation and the possibility of interference among weakly selected sites for traits with high mutation rates.

The Impact of Genomic and Traditional Selection on the Contribution of Mutational Variance to Long-Term Selection Response and Genetic Variance

De novo mutations (DNM) create new genetic variance and are an important driver for long-term selection response. We hypothesized that genomic selection exploits mutational variance less than traditional selection methods such as mass selection or selection on pedigree-based breeding values, because DNM in selection candidates are not captured when the selection candidates' own phenotype is not used in genomic selection, DNM are not on SNP chips and DNM are not in linkage disequilibrium with the SNP on the chip. We tested this hypothesis with Monte Carlo simulation. From whole-genome sequence data, a subset of ∼300,000 variants was used that served as putative markers, quantitative trait loci or DNM. We simulated 20 generations with truncation selection based on breeding values from genomic best linear unbiased prediction without (GBLUP_no_OP) or with own phenotype (GBLUP_OP), pedigree-based BLUP without (BLUP_no_OP) or with own phenotype (BLUP_OP), or directly on phenotype. GBLUP_OP was the best strategy in exploiting mutational variance, while GBLUP_no_OP and BLUP_no_OP were the worst in exploiting mutational variance. The crucial element is that GBLUP_no_OP and BLUP_no_OP puts no selection pressure on DNM in selection candidates. Genetic variance decreased faster with GBLUP_no_OP and GBLUP_OP than with BLUP_no_OP, BLUP_OP or mass selection. The distribution of mutational effects, mutational variance, number of DNM per individual and nonadditivity had a large impact on mutational selection response and mutational genetic variance, but not on ranking of selection strategies. We advocate that more sustainable genomic selection strategies are required to optimize long-term selection response and to maintain genetic diversity.

Empirical measures of mutational effects define neutral models of regulatory evolution in Saccharomyces cerevisiae

Understanding how phenotypes evolve requires disentangling the effects of mutation generating new variation from the effects of selection filtering it. Tests for selection frequently assume that mutation introduces phenotypic variation symmetrically around the population mean, yet few studies have tested this assumption by deeply sampling the distributions of mutational effects for particular traits. Here, we examine distributions of mutational effects for gene expression in the budding yeast Saccharomyces cerevisiae by measuring the effects of thousands of point mutations introduced randomly throughout the genome. We find that the distributions of mutational effects differ for the 10 genes surveyed and are inconsistent with normality. For example, all 10 distributions of mutational effects included more mutations with large effects than expected for normally distributed phenotypes. In addition, some genes also showed asymmetries in their distribution of mutational effects, with new mutations more likely to increase than decrease the gene's expression or vice versa. Neutral models of regulatory evolution that take these empirically determined distributions into account suggest that neutral processes may explain more expression variation within natural populations than currently appreciated.

Massive variation of short tandem repeats with functional consequences across strains of Arabidopsis thaliana

Short tandem repeat (STR) mutations may comprise more than half of the mutations in eukaryotic coding DNA, yet STR variation is rarely examined as a contributor to complex traits. We assessed this contribution across a collection of 96 strains of Arabidopsis thaliana, genotyping 2046 STR loci each, using highly parallel STR sequencing with molecular inversion probes. We found that 95% of examined STRs are polymorphic, with a median of six alleles per STR across these strains. STR expansions (large copy number increases) are found in most strains, several of which have evident functional effects. These include three of six intronic STR expansions we found to be associated with intron retention. Coding STRs were depleted of variation relative to noncoding STRs, and we detected a total of 56 coding STRs (11%) showing low variation consistent with the action of purifying selection. In contrast, some STRs show hypervariable patterns consistent with diversifying selection. Finally, we detected 133 novel STR-phenotype associations under stringent criteria, most of which could not be detected with SNPs alone, and validated some with follow-up experiments. Our results support the conclusion that STRs constitute a large, unascertained reservoir of functionally relevant genomic variation.

Using geometric morphometric visualizations of directional selection gradients to investigate morphological differentiation

Researchers studying extant and extinct taxa are often interested in identifying the evolutionary processes that have lead to the morphological differences among the taxa. Ideally, one could distinguish the influences of neutral evolutionary processes (genetic drift, mutation) from natural selection, and in situations for which selection is implicated, identify the targets of selection. The directional selection gradient is an effective tool for investigating evolutionary process, because it can relate form (size and shape) differences between taxa to the variation and covariation found within taxa. However, although most modern morphometric analyses use the tools of geometric morphometrics (GM) to analyze landmark data, to date, selection gradients have mainly been calculated from linear measurements. To address this methodological gap, here we present a GM approach for visualizing and comparing between-taxon selection gradients with each other, associated difference vectors, and "selection" gradients from neutral simulations. To exemplify our approach, we use a dataset of 347 three-dimensional landmarks and semilandmarks recorded on the crania of 260 primate specimens (112 humans, 67 common chimpanzees, 36 bonobos, 45 gorillas). Results on this example dataset show how incorporating geometric information can provide important insights into the evolution of the human braincase, and serve to demonstrate the utility of our approach for understanding morphological evolution.

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.

MUTATION, SELECTION, AND THE MAINTENANCE OF LIFE-HISTORY VARIATION IN A NATURAL POPULATION

In an effort to provide insight into the role of mutation in the maintenance of genetic variance for life-history traits, we accumulated spontaneous mutations in 10 sets of clonal replicates of Daphnia pulex for approximately 30 generations and compared the variance generated by mutation with the standing level of variation in the wild population. Mutations for quantitative traits appear to arise at a fairly high rate in this species, on the order of at least 0.6 per character per generation, but have relatively small heterozygous effects, changing the phenotype by less than 2.5% of the mean. The mean persistence time of a new mutation affecting life-history/body-size traits is approximately 40 generations in the natural population, which requires an average selection coefficient against new mutations of approximately 3% in the heterozygous state. These data are consistent with the idea that the vast majority of standing genetic variance for life-history characters may be largely a consequence of the recurrent introduction of transient cohorts of mutations that are at least conditionally deleterious and raise issues about the meaning of conventional measures of standing levels of variation for fitness-related traits.

STABILIZING SELECTION AND THE COMPARATIVE ANALYSIS OF ADAPTATION

Comparative studies tend to differ from optimality and functionality studies in how they treat adaptation. While the comparative approach focuses on the origin and change of traits, optimality studies assume that adaptations are maintained at an optimum by stabilizing selection. This paper presents a model of adaptive evolution on a macroevolutionary time scale that includes the maintenance of traits at adaptive optima by stabilizing selection as the dominant evolutionary force. Interspecific variation is treated as variation in the position of adaptive optima. The model illustrates how phylogenetic constraints not only lead to correlations between phylogenetically related species, but also to imperfect adaptations. From this model, a statistical comparative method is derived that can be used to estimate the effect of a selective factor on adaptive optima in a way that would be consistent with an optimality study of adaptation to this factor. The method is illustrated with an analysis of dental evolution in fossil horses. The use of comparative methods to study evolutionary trends is also discussed.

POLYGENIC MUTATION IN DROSOPHILA MELANOGASTER: ESTIMATES FROM DIVERGENCE AMONG INBRED STRAINS

A highly inbred line of Drosophila melanogaster was subdivided into 25 replicate sublines, which were independently maintained for 100 generations with 10 pairs of unselected flies per generation. The polygenic mutation rate (V_M ) for two quantitative traits, abdominal and sternopleural bristle number, was estimated from divergence among sublines at 10 generation intervals from generations 30-100, and from response of each line to divergent selection after more than 65 generations of mutation accumulation. Estimates of V_M averaged over males and females both from divergence among lines and from response to selection within lines were 3.3 × 10^-3 V_E for abdominal bristles and 1.5 × 10^-3 V_E for sternopleural bristles, where V_E is the environmental variance. The actual rate of production of mutations affecting these traits may be considerably higher if the traits are under stabilizing selection, and if mutations affecting bristle number have deleterious effects on fitness. There was a substantial component of variance for sex × mutant effect interaction and the sublines evolved highly significant mutational variation in sex dimorphism of abdominal bristle number. Pleiotropic effects on sex dimorphism may be a general property of mutations at loci determining bristle number.

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. I. RATE TESTS FOR RANDOM CHANGE VERSUS SELECTION IN DIFFERENTIATION OF LIVING SPECIES

The possible roles of random genetic change and natural selection in bryozoan speciation were analyzed using quantitative genetic methods on breeding data for traits of skeletal morphology in two closely related species of the cheilostome Stylopoma. The hypothesis that morphologic differences between the species are caused entirely by mutation and genetic drift could not be rejected for reasonable rates of mutation maintained for as few as 10³ to 10⁴ generations. Divergence times this short or shorter are consistent with the abrupt appearances of many invertebrate species in the fossil record, commonly followed by millions of years of morphologic stasis. To produce these differences over 10³ generations or fewer, directional selection acting alone would require unrealistically high levels of minimum selective mortality throughout divergence. Thus, selection is unnecessary to explain the divergence of these species, except as a means of accelerating the effects of random genetic change on shorter time scales (directional selection), or decelerating them over longer ones (stabilizing selection). These results are consistent with a variety of models of phenotypic evolution involving random shifts between multiple adaptive peaks. Similar results were obtained by substituting trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance in place of the values based on breeding data. Quantitative genetic analysis of speciation in fossil bryozoan lineages is thus justified.

PHYLOGENETIC HYPOTHESES UNDER THE ASSUMPTION OF NEUTRAL QUANTITATIVE-GENETIC VARIATION

There are many situations in which the only available characters for reconstructing phylogenies are morphological. Those traits that are subject only to the forces of mutation and random genetic drift can be used to obtain unbiased estimates of phylogenetic relationships. However, the accurate recovery of a phylogeny from information on neutral characters requires the procurement of data for a large number of independent traits, individuals, and populations. Phylogenetic trees fit to data from more than five species will almost always contain topological errors, even with very large data sets. The population-genetic consequences of the neutral model are reviewed, and some statistical methods for testing whether the diversification of a phylogeny is compatible with such a model are outlined. The theory is then applied to a very large data set on cranial morphology in modern man. The results are consistent with the hypothesis that interracial differences in human skull dimensions are a simple consequence of random drift and mutation.

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a "canalization limit" is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e ). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m . From this result it is concluded that characters with typical mutational variances of about 10^-3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.

THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, V^G in finite populations under weak stabilizing selection for triallelic loci and for an infinite "rare alleles" model. These are compared to results for neutral characters, to the "Gaussian allelic" model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in V^G. While it is easier to maintain absolute V^G when alleles interact to yield dominance or overdominance for fitness, less additivity also makes V^G more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and V^G. This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed V^G. The dependence of V^G on N could be used to test the adequacy of mutation-selection balance models.

MUTATIONAL CONTRIBUTIONS TO GENETIC VARIANCE-COVARIANCE MATRICES: AN EXPERIMENTAL APPROACH USING INDUCED MUTATIONS IN ARABIDOPSIS THALIANA

Genetic potential for evolutionary change and covariational constraints are typically summarized as the genetic variance-covariance matrix G, and there is currently debate over the extent to which G remains effectively constant during the course of adaptive evolution. However, G provides only a temporally restricted view of constraints that ignores possible biases in how new mutations affect multivariate phenotypes. We used chemical mutagenesis to study the effect of mutations as summarized by the mutational covariance matrix, M, in Arabidopsis thaliana. By introducing mutations into three isogenic strains of A. thaliana, we were able to quantify M directly as the genetic variance-covariance matrix of mutagenized lines. Induced mutations generally did not alter the means of the six morphology and life-history traits we measured, but they did affect the levels of available genetic variation and the covariances among traits. However, these effects were not consistent among the three isogenic lines; that is, there were significant differences among the lines in both the number of mutations produced by ethyl-methane-sulfonate treatment and the M matrices they induced. The evolutionary implications of the dependence of M on the number of mutations, the particular genetic background, and the mutagenic sampling of loci in the genome are discussed in light of commonly applied models of multivariate evolution and the potential for the genetic architecture itself to change in ways that facilitate the coordinated evolution of complex phenotypes.

Adaptive Genetic Robustness of Escherichia coli Metabolic Fluxes

Genetic robustness refers to phenotypic invariance in the face of mutation and is a common characteristic of life, but its evolutionary origin is highly controversial. Genetic robustness could be an intrinsic property of biological systems, a result of direct natural selection, or a byproduct of selection for environmental robustness. To differentiate among these hypotheses, we analyze the metabolic network of Escherichia coli and comparable functional random networks. Treating the flux of each reaction as a trait and computationally predicting trait values upon mutations or environmental shifts, we discover that 1) genetic robustness is greater for the actual network than the random networks, 2) the genetic robustness of a trait increases with trait importance and this correlation is stronger in the actual network than in the random networks, and 3) the above result holds even after the control of environmental robustness. These findings demonstrate an adaptive origin of genetic robustness, consistent with the theoretical prediction that, under certain conditions, direct selection is sufficiently powerful to promote genetic robustness in cellular organisms.

Gene Expression Evolves under a House-of-Cards Model of Stabilizing Selection

Divergence in gene regulation is hypothesized to underlie much of phenotypic evolution, but the role of natural selection in shaping the molecular phenotype of gene expression continues to be debated. To resolve the mode of gene expression, evolution requires accessible theoretical predictions for the effect of selection over long timescales. Evolutionary quantitative genetic models of phenotypic evolution can provide such predictions, yet those predictions depend on the underlying hypotheses about the distributions of mutational and selective effects that are notoriously difficult to disentangle. Here, we draw on diverse genomic data sets including expression profiles of natural genetic variation and mutation accumulation lines, empirical estimates of genomic mutation rates, and inferences of genetic architecture to differentiate contrasting hypotheses for the roles of stabilizing selection and mutation in shaping natural expression variation. Our analysis suggests that gene expression evolves in a domain of phenotype space well fit by the House-of-Cards (HC) model. Although the strength of selection inferred is sensitive to the number of loci controlling gene expression, the model is not. The consistency of these results across evolutionary time from budding yeast through fruit fly implies that this model is general and that mutational effects on gene expression are relatively large. Empirical estimates of the genetic architecture of gene expression traits imply that selection provides modest constraints on gene expression levels for most genes, but that the potential for regulatory evolution is high. Our prediction using data from laboratory environments should encourage the collection of additional data sets allowing for more nuanced parameterizations of HC models for gene expression.

Maintenance of Quantitative Genetic Variance Under Partial Self-Fertilization, with Implications for Evolution of Selfing

We analyze two models of the maintenance of quantitative genetic variance in a mixed-mating system of self-fertilization and outcrossing. In both models purely additive genetic variance is maintained by mutation and recombination under stabilizing selection on the phenotype of one or more quantitative characters. The Gaussian allele model (GAM) involves a finite number of unlinked loci in an infinitely large population, with a normal distribution of allelic effects at each locus within lineages selfed for τ consecutive generations since their last outcross. The infinitesimal model for partial selfing (IMS) involves an infinite number of loci in a large but finite population, with a normal distribution of breeding values in lineages of selfing age τ. In both models a stable equilibrium genetic variance exists, the outcrossed equilibrium, nearly equal to that under random mating, for all selfing rates, r, up to critical value, [Formula: see text], the purging threshold, which approximately equals the mean fitness under random mating relative to that under complete selfing. In the GAM a second stable equilibrium, the purged equilibrium, exists for any positive selfing rate, with genetic variance less than or equal to that under pure selfing; as r increases above [Formula: see text] the outcrossed equilibrium collapses sharply to the purged equilibrium genetic variance. In the IMS a single stable equilibrium genetic variance exists at each selfing rate; as r increases above [Formula: see text] the equilibrium genetic variance drops sharply and then declines gradually to that maintained under complete selfing. The implications for evolution of selfing rates, and for adaptive evolution and persistence of predominantly selfing species, provide a theoretical basis for the classical view of Stebbins that predominant selfing constitutes an "evolutionary dead end."

Bayesian analysis of additive epistasis arising from new mutations in mice

The continuous uploading of polygenic additive mutational variability has been reported in several studies in laboratory species with an inbred genetic background. These studies have focused on the direct contribution of new mutations without considering the possibility of epistatic effects derived from the interaction of new mutations with pre-existing polymorphisms. In this work we focused on this main topic and analysed the statistical and biological relevance of the epistatic variance for 9 week body weight in two populations of inbred mice. We developed a new linear mixed model parameterization where founder-related additive genetic variability, additive mutational variability and the interaction terms between both sources of variation were accounted for under a Bayesian design and without requiring the inversion of a matrix of epistatic genetic covariances. The analyses focused on a six-generations data set from C57BL/6J mice (n = 3736) and a five-generations data set from C57BL/6J(hg/hg) mice (n = 2843). The deviance information criterion (DIC) clearly favoured the model accounting for epistatic variability with reductions larger than 50 DIC units in both populations. Modal estimates for founder related, mutational and epistatic heritabilities were 0·068, 0·011 and 0·095 in C57BL/6J and 0·060, 0·010 and 0·113 in C57BL/6J(hg/hg), ruling out any doubt about the biological relevance of epistasis originating from new mutations in mice. These results contribute new insights on the relevance of epistasis in the genetic architecture of mammals and serve as an important component of an additional source of genetic heterogeneity for inbred strains of laboratory mice.

Rapid evolution of quantitative traits: theoretical perspectives

An increasing number of studies demonstrate phenotypic and genetic changes in natural populations that are subject to climate change, and there is hope that some of these changes will contribute to avoiding species extinctions ('evolutionary rescue'). Here, we review theoretical models of rapid evolution in quantitative traits that can shed light on the potential for adaptation to a changing climate. Our focus is on quantitative-genetic models with selection for a moving phenotypic optimum. We point out that there is no one-to-one relationship between the rate of adaptation and population survival, because the former depends on relative fitness and the latter on absolute fitness. Nevertheless, previous estimates that sustainable rates of genetically based change usually do not exceed 0.1 haldanes (i.e., phenotypic standard deviations per generation) are probably correct. Survival can be greatly facilitated by phenotypic plasticity, and heritable variation in plasticity can further speed up genetic evolution. Multivariate selection and genetic correlations are frequently assumed to constrain adaptation, but this is not necessarily the case and depends on the geometric relationship between the fitness landscape and the structure of genetic variation. Similar conclusions hold for adaptation to shifting spatial gradients. Recent models of adaptation in multispecies communities indicate that the potential for rapid evolution is strongly influenced by interspecific competition.

Histone variant HTZ1 shows extensive epistasis with, but does not increase robustness to, new mutations

Biological systems produce phenotypes that appear to be robust to perturbation by mutations and environmental variation. Prior studies identified genes that, when impaired, reveal previously cryptic genetic variation. This result is typically interpreted as evidence that the disrupted gene normally increases robustness to mutations, as such robustness would allow cryptic variants to accumulate. However, revelation of cryptic genetic variation is not necessarily evidence that a mutationally robust state has been made less robust. Demonstrating a difference in robustness requires comparing the ability of each state (with the gene perturbed or intact) to suppress the effects of new mutations. Previous studies used strains in which the existing genetic variation had been filtered by selection. Here, we use mutation accumulation (MA) lines that have experienced minimal selection, to test the ability of histone H2A.Z (HTZ1) to increase robustness to mutations in the yeast Saccharomyces cerevisiae. HTZ1, a regulator of chromatin structure and gene expression, represents a class of genes implicated in mutational robustness. It had previously been shown to increase robustness of yeast cell morphology to fluctuations in the external or internal microenvironment. We measured morphological variation within and among 79 MA lines with and without HTZ1. Analysis of within-line variation confirms that HTZ1 increases microenvironmental robustness. Analysis of between-line variation shows the morphological effects of eliminating HTZ1 to be highly dependent on the line, which implies that HTZ1 interacts with mutations that have accumulated in the lines. However, lines without HTZ1 are, as a group, not more phenotypically diverse than lines with HTZ1 present. The presence of HTZ1, therefore, does not confer greater robustness to mutations than its absence. Our results provide experimental evidence that revelation of cryptic genetic variation cannot be assumed to be caused by loss of robustness, and therefore force reevaluation of prior claims based on that assumption.

Short communication: Accounting for new mutations in genomic prediction models

Genomic evaluation models so far do not allow for accounting of newly generated genetic variation due to mutation. The main target of this research was to extend current genomic BLUP models with mutational relationships (model AM), and compare them against standard genomic BLUP models (model A) by analyzing simulated data. Model performance and precision of the predicted breeding values were evaluated under different population structures and heritabilities. The deviance information criterion (DIC) clearly favored the mutational relationship model under large heritabilities or populations with moderate-to-deep pedigrees contributing phenotypic data (i.e., differences equal or larger than 10 DIC units); this model provided slightly higher correlation coefficients between simulated and predicted genomic breeding values. On the other hand, null DIC differences, or even relevant advantages for the standard genomic BLUP model, were reported under small heritabilities and shallow pedigrees, although precision of the genomic breeding values did not differ across models at a significant level. This method allows for slightly more accurate genomic predictions and handling of newly created variation; moreover, this approach does not require additional genotyping or phenotyping efforts, but a more accurate handing of available data.

Evaluating alternative strategies for minimizing unintended fitness consequences of cultured individuals on wild populations

Artificial propagation strategies often incur selection in captivity that leads to traits that are maladaptive in the wild. For propagation programs focused on production rather than demographic contribution to wild populations, effects on wild populations can occur through unintentional escapement or the need to release individuals into natural environments for part of their life cycle. In this case, 2 alternative management strategies might reduce unintended fitness consequences on natural populations: (1) reduce selection in captivity as much as possible to reduce fitness load (keep them similar), or (2) breed a separate population to reduce captive-wild interactions as much as possible (make them different). We quantitatively evaluate these 2 strategies with a coupled demographic-genetic model based on Pacific salmon hatcheries that incorporates a variety of relevant processes and dynamics: selection in the hatchery relative to the wild, assortative mating based on the trait under selection, and different life cycle arrangements in terms of hatchery release, density dependence, natural selection, and reproduction. Model results indicate that, if natural selection only occurs between reproduction and captive release, the similar strategy performs better. However, if natural selection occurs between captive release and reproduction, the different and similar strategies present viable alternatives to reducing unintended fitness consequences because of the greater opportunity to purge maladaptive individuals. In this case, the appropriate approach depends on the feasibility of each strategy and the demographic goal (e.g., increasing natural abundance, or ensuring that a high proportion of natural spawners are naturally produced). In addition, the fitness effects of hatchery release are much greater if hatchery release occurs before (vs. after) density-dependent interactions. Given the logistical challenges to achieving both the similar and different strategies, evaluation of not just the preferred strategy but also the consequences of failing to achieve the desired target is critical.

Properties of spontaneous mutational variance and covariance for wing size and shape in Drosophila melanogaster

We estimated mutational variance-covariance matrices, M, for wing shape and size in two genotypes of Drosophila melanogaster after 192 generations of mutation accumulation. We characterized 21 potentially independent aspects of wing shape and size using geometric morphometrics, and analyzed the data using a likelihood-based factor-analytic approach. We implement a previously unused analysis that describes those directions with the greatest difference in evolvability between pairs of matrices. There are significant mutational effects on 19 of 21 possible aspects of wing form, consistent with the high dimensionality of standing genetic variation for wing shape previously identified in D. melanogaster. Mutations have partially recessive effects, consistent with average dominance around 0.25. Sex-specific matrices are relatively similar, although male-specific matrices are slightly larger, as expected due to dosage compensation on the X chromosome. Genotype-specific matrices are quite different. Matrices may differ both because of sampling error based on small samples of mutations with large phenotypic effects, and because of the mutational properties of the genotypes. Genotypic differences are likely to be involved, as the two genotypes have different molecular mutation rates and properties.