Evolutionary constraints in high-dimensional trait sets

A mathematical framework for evo-devo dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

Rapid evolution of a family-diagnostic trait: artificial selection and correlated responses in wild radish, Raphanus raphanistrum

The mechanisms underlying trait conservation over long evolutionary time scales are poorly known. These mechanisms fall into the two broad and nonmutually exclusive categories of constraint and selection. A variety of factors have been hypothesized to constrain trait evolution. Alternatively, selection can maintain similar trait values across many species if the causes of selection are also relatively conserved, while many sources of constraint may be overcome over longer periods of evolutionary divergence. An example of deep trait conservation is tetradynamy in the large family Brassicaceae, where the four medial stamens are longer than the two lateral stamens. Previous work has found selection to maintain this difference in lengths, which we call anther separation, in wild radish, Raphanus raphanistrum. Here, we test the constraint hypothesis using five generations of artificial selection to reduce anther separation in wild radish. We found a rapid linear response to this selection, with no evidence for depletion of genetic variation and correlated responses to this selection in only four of 15 other traits, suggesting a lack of strong constraint. Taken together, available evidence suggests that tetradynamy is likely to be conserved due to selection, but the function of this trait remains unclear.

Selection and the direction of phenotypic evolution

Predicting adaptive phenotypic evolution depends on invariable selection gradients and on the stability of the genetic covariances between the component traits of the multivariate phenotype. We describe the evolution of six traits of locomotion behavior and body size in the nematode Caenorhabditis elegans for 50 generations of adaptation to a novel environment. We show that the direction of adaptive multivariate phenotypic evolution can be predicted from the ancestral selection differentials, particularly when the traits were measured in the new environment. Interestingly, the evolution of individual traits does not always occur in the direction of selection, nor are trait responses to selection always homogeneous among replicate populations. These observations are explained because the phenotypic dimension with most of the ancestral standing genetic variation only partially aligns with the phenotypic dimension under directional selection. These findings validate selection theory and suggest that the direction of multivariate adaptive phenotypic evolution is predictable for tens of generations.

Using inbreeding to test the contribution of non-additive genetic effects to additive genetic variance: a case study in Drosophila serrata

Additive genetic variance, V_A, is the key parameter for predicting adaptive and neutral phenotypic evolution. Changes in demography (e.g. increased close-relative inbreeding) can alter V_A, but how they do so depends on the (typically unknown) gene action and allele frequencies across many loci. For example, V_A increases proportionally with the inbreeding coefficient when allelic effects are additive, but smaller (or larger) increases can occur when allele frequencies are unequal at causal loci with dominance effects. Here, we describe an experimental approach to assess the potential for dominance effects to deflate V_A under inbreeding. Applying a powerful paired pedigree design in Drosophila serrata, we measured 11 wing traits on half-sibling families bred via either random or sibling mating, differing only in homozygosity (not allele frequency). Despite close inbreeding and substantial power to detect small V_A, we detected no deviation from the expected additive effect of inbreeding on genetic (co)variances. Our results suggest the average dominance coefficient is very small relative to the additive effect, or that allele frequencies are relatively equal at loci affecting wing traits. We outline the further opportunities for this paired pedigree approach to reveal the characteristics of V_A, providing insight into historical selection and future evolutionary potential.

Dimensionality and Modularity of Adaptive Variation: Divergence in Threespine Stickleback from Diverse Environments

AbstractPopulations are subjected to diverse environmental conditions that affect fitness and induce evolutionary or plastic responses, resulting in phenotypic divergence. Some authors contend that such divergence is concentrated along a single major axis of trait covariance even if that axis does not lead populations directly toward a fitness optimum. Other authors argue that divergence can occur readily along many phenotype axes at the same time. We use populations of threespine stickleback (Gasterosteus aculeatus) from 14 lakes with contrasting ecological conditions to find some resolution along the continuum between these two extremes. Unlike many previous studies, we included several functional suites of traits (defensive, swimming, trophic) potentially subject to different sources of selection. We find that populations exhibit dimensionality of divergence that is high enough to preclude a history of constraint along a single axis-both for divergence in multivariate mean trait values and for the structure of trait covariances. Dimensionality varied among trait suites and were strongly influenced by the inclusion of specific traits, and integration of trait suites varied between populations. We leverage this variation into new insights about the process of divergence and suggest that similar analyses could increase understanding of other adaptive radiations.

Pleiotropy Structures Plant Height and Seed Weight Scaling in Barley despite Long History of Domestication and Breeding Selection

Size scaling describes the relative growth rates of different body parts of an organism following a positive correlation. Domestication and crop breeding often target the scaling traits in the opposite directions. The genetic mechanism of the size scaling influencing the pattern of size scaling remains unexplored. Here, we revisited a diverse barley (Hordeum vulgare L.) panel with genome-wide single-nucleotide polymorphisms (SNPs) profile and the measurement of their plant height and seed weight to explore the possible genetic mechanisms that may lead to a correlation of the two traits and the influence of domestication and breeding selection on the size scaling. Plant height and seed weight are heritable and remain positively correlated in domesticated barley regardless of growth type and habit. Genomic structural equation modeling systematically evaluated the pleiotropic effect of individual SNP on the plant height and seed weight within a trait correlation network. We discovered seventeen novel SNPs (quantitative trait locus) conferring pleiotropic effect on plant height and seed weight, involving genes with function in diverse traits related to plant growth and development. Linkage disequilibrium decay analysis revealed that a considerable proportion of genetic markers associated with either plant height or seed weight are closely linked in the chromosome. We conclude that pleiotropy and genetic linkage likely form the genetic bases of plant height and seed weight scaling in barley. Our findings contribute to understanding the heritability and genetic basis of size scaling and open a new venue for seeking the underlying mechanism of allometric scaling in plants.

Evolvability and constraint in the evolution of three-dimensional flower morphology

PREMISE

Flower phenotypes evolve to attract pollinators and to ensure efficient pollen transfer to and from the bodies of pollinators or, in self-compatible bisexual flowers, between anthers and stigmas. If functionally interacting traits are genetically correlated, response to selection may be subject to genetic constraints. Genetic constraints can be assessed by quantifying standing genetic variation in (multivariate) phenotypic traits and by asking how much the available variation is reduced under specific assumptions about phenotypic selection on functionally interacting and genetically correlated traits.

METHODS

We evaluated multivariate evolvability and potential genetic constraints underlying the evolution of the three-dimensional structure of Dalechampia blossoms. First, we used data from a greenhouse crossing design to estimate the G matrix for traits representing the relative positions of male and female sexual organs (anthers and stigmas) and used the G matrix to ask how genetic variation is distributed in multivariate space. To assess the evolutionary importance of genetic constraints, we related standing genetic variation across phenotypic space to evolutionary divergence of population and species in the same phenotypic directions.

RESULTS

Evolvabilities varied substantially across phenotype space, suggesting that certain traits or trait combinations may be subject to strong genetic constraint. Traits involved functionally in flower-pollinator fit and autonomous selfing exhibited considerable independent evolutionary potential, but population and species divergence tended to occur in phenotypic directions associated with greater-than-average evolvability.

CONCLUSIONS

These results are consistent with the hypothesis that genetic constraints can hamper joint trait evolution towards optimum flower-pollinator fit and optimum self-pollination rates.

Phylogenetic conservation of behavioural variation and behavioural syndromes

Individuals frequently differ consistently from one another in their average behaviours (i.e. 'animal personality') and in correlated suites of consistent behavioural responses (i.e. 'behavioural syndromes'). However, understanding the evolutionary basis of this (co)variation has lagged behind demonstrations of its presence. This lag partially stems from comparative methods rarely being used in the field. Consequently, much of the research on animal personality has relied on 'adaptive stories' focused on single species and populations. Here, we used a comparative approach to examine the role of phylogeny in shaping patterns of average behaviours, behavioural variation and behavioural correlations. In comparing the behaviours and behavioural variation for five species of Gryllid crickets, we found that phylogeny shaped average behaviours and behavioural (co)variation. Despite differences among species, behavioural responses and variation were most similar among more closely related species. These results suggest that phylogenetic constraints play an important role in the expression of animal personalities and behavioural syndromes and emphasize the importance of examining evolutionary explanations within a comparative framework.

The contribution of mutation and selection to multivariate quantitative genetic variance in an outbred population of Drosophila serrata

Genetic variance is not equal for all multivariate combinations of traits. This inequality, in which some combinations of traits have abundant genetic variation while others have very little, biases the rate and direction of multivariate phenotypic evolution. However, we still understand little about what causes genetic variance to differ among trait combinations. Here, we investigate the relative roles of mutation and selection in determining the genetic variance of multivariate phenotypes. We accumulated mutations in an outbred population of Drosophila serrata and analyzed wing shape and size traits for over 35,000 flies to simultaneously estimate the additive genetic and additive mutational (co)variances. This experimental design allowed us to gain insight into the phenotypic effects of mutation as they arise and come under selection in naturally outbred populations. Multivariate phenotypes associated with more (less) genetic variance were also associated with more (less) mutational variance, suggesting that differences in mutational input contribute to differences in genetic variance. However, mutational correlations between traits were stronger than genetic correlations, and most mutational variance was associated with only one multivariate trait combination, while genetic variance was relatively more equal across multivariate traits. Therefore, selection is implicated in breaking down trait covariance and resulting in a different pattern of genetic variance among multivariate combinations of traits than that predicted by mutation and drift. Overall, while low mutational input might slow evolution of some multivariate phenotypes, stabilizing selection appears to reduce the strength of evolutionary bias introduced by pleiotropic mutation.

Quantitative assessment of observed versus predicted responses to selection

Although artificial-selection experiments seem well suited to testing our ability to predict evolution, the correspondence between predicted and observed responses is often ambiguous due to the lack of uncertainty estimates. We present equations for assessing prediction error in direct and indirect responses to selection that integrate uncertainty in genetic parameters used for prediction and sampling effects during selection. Using these, we analyzed a selection experiment on floral traits replicated in two taxa of the Dalechampia scandens (Euphorbiaceae) species complex for which G-matrices were obtained from a diallel breeding design. After four episodes of bidirectional selection, direct and indirect responses remained within wide prediction intervals, but appeared different from the predictions. Combined analyses with structural-equation models confirmed that responses were asymmetrical and lower than predicted in both species. We show that genetic drift is likely to be a dominant source of uncertainty in typically-dimensioned selection experiments in plants and a major obstacle to predicting short-term evolutionary trajectories.

Correlational selection in the age of genomics

Ecologists and evolutionary biologists are well aware that natural and sexual selection do not operate on traits in isolation, but instead act on combinations of traits. This long-recognized and pervasive phenomenon is known as multivariate selection, or-in the particular case where it favours correlations between interacting traits-correlational selection. Despite broad acknowledgement of correlational selection, the relevant theory has often been overlooked in genomic research. Here, we discuss theory and empirical findings from ecological, quantitative genetic and genomic research, linking key insights from different fields. Correlational selection can operate on both discrete trait combinations and quantitative characters, with profound implications for genomic architecture, linkage, pleiotropy, evolvability, modularity, phenotypic integration and phenotypic plasticity. We synthesize current knowledge and discuss promising research approaches that will enable us to understand how correlational selection shapes genomic architecture, thereby linking quantitative genetic approaches with emerging genomic methods. We suggest that research on correlational selection has great potential to integrate multiple fields in evolutionary biology, including developmental and functional biology, ecology, quantitative genetics, phenotypic polymorphisms, hybrid zones and speciation processes.

Structure of the G-matrix in relation to phenotypic contributions to fitness

Classical theory in population genetics includes derivation of the stationary distribution of allele frequencies under balance between selection, genetic drift, and mutation. Here we investigate the simplest generalization of these single locus models to quantitative genetics with many loci, assuming simple additive effects on a set of phenotypes and a linear approximation to the fitness function. Genetic effects and pleiotropy are simulated by a prescribed stochastic model. Our goal is to analyze the structure of the G-matrix at stasis when the model is not very close to being neutral. The smallest eigenvalue of the G-matrix is practically zero by Fisher's fundamental theorem for natural selection and the fitness function is approximately a linear function of the corresponding eigenvector. Evolution of genetic trade-offs is closely linked to the fitness function. If a single locus never codes for more than two traits, then additive genetic covariance between two phenotype components always has the opposite sign of the product of their coefficients in the fitness function under no mutation, a pattern that is likely to occur frequently also in more complex models. In our major examples only 1-2 percent of the loci are over-dominant for fitness, but they still account for practically all dominance variance in fitness as well as all contributions to the G-matrix. These analyses show that the structure of the G-matrix reveals important information about the contribution of different traits to fitness.

Why call it developmental bias when it is just development?

The concept of developmental constraints has been central to understand the role of development in morphological evolution. Developmental constraints are classically defined as biases imposed by development on the distribution of morphological variation.

This opinion article argues that the concepts of developmental constraints and developmental biases do not accurately represent the role of development in evolution. The concept of developmental constraints was coined to oppose the view that natural selection is all-capable and to highlight the importance of development for understanding evolution. In the modern synthesis, natural selection was seen as the main factor determining the direction of morphological evolution. For that to be the case, morphological variation needs to be isotropic (i.e. equally possible in all directions). The proponents of the developmental constraint concept argued that development makes that some morphological variation is more likely than other (i.e. variation is not isotropic), and that, thus, development constraints evolution by precluding natural selection from being all-capable.

This article adds to the idea that development is not compatible with the isotropic expectation by arguing that, in fact, it could not be otherwise: there is no actual reason to expect that development could lead to isotropic morphological variation. It is then argued that, since the isotropic expectation is untenable, the role of development in evolution should not be understood as a departure from such an expectation. The role of development in evolution should be described in an exclusively positive way, as the process determining which directions of morphological variation are possible, instead of negatively, as a process precluding the existence of morphological variation we have no actual reason to expect.

This article discusses that this change of perspective is not a mere question of semantics: it leads to a different interpretation of the studies on developmental constraints and to a different research program in evolution and development. This program does not ask whether development constrains evolution. Instead it asks questions such as, for example, how different types of development lead to different types of morphological variation and, together with natural selection, determine the directions in which different lineages evolve.

Why does allometry evolve so slowly?

Morphological allometry is striking due to its evolutionary conservatism, making it an example of a certain sort of evolutionary stasis. Organisms that vary in size, whether for developmental, environmental, or evolutionary reasons, adopt shapes that are predictable from that size alone. There are two major hypotheses to explain this. It may be that natural selection strongly favors each allometric pattern, or that organisms lack the development and genetic capacity to produce variant shapes for selection to act on. Using a high-throughput system for measuring the size and shape of Drosophila wings, we documented an allometric pattern that has been virtually unchanged for 40 million years. We performed an artificial selection experiment on the static allometric slope within one species. In just 26 generations, we were able to increase the slope from 1.1 to 1.4, and decrease it to 0.8. Once artificial selection was suspended, the slope rapidly evolved back to a value near the initial static slope. This result decisively rules out the hypothesis that allometry is preserved due to a lack of genetic variation, and provides evidence that natural selection acts to maintain allometric relationships. On the other hand, it seems implausible that selection on allometry in the wing alone could be sufficiently strong to maintain static allometries over millions of years. This suggests that a potential explanation for stasis is selection on a potentially large number of pleiotropic effects. This seems likely in the case of allometry, as the sizes of all parts of the body may be altered when the allometric slope of one body part is changed. Unfortunately, hypotheses about pleiotropy have been very difficult to test. We lay out an approach to begin the systematic study of pleiotropic effects using genetic manipulations and high-throughput phenotyping.

EIGENVALUE DISTRIBUTIONS OF VARIANCE COMPONENTS ESTIMATORS IN HIGH-DIMENSIONAL RANDOM EFFECTS MODELS

We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well-approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedure. Our proof uses operator-valued free probability theory, and we establish a general asymptotic freeness result for families of rectangular orthogonally-invariant random matrices, which is of independent interest. Our work is motivated in part by the estimation of components of covariance between multiple phenotypic traits in quantitative genetics, and we specialize our results to common experimental designs that arise in this application.

Causes of maladaptation

Evolutionary biologists tend to approach the study of the natural world within a framework of adaptation, inspired perhaps by the power of natural selection to produce fitness advantages that drive population persistence and biological diversity. In contrast, evolution has rarely been studied through the lens of adaptation's complement, maladaptation. This contrast is surprising because maladaptation is a prevalent feature of evolution: population trait values are rarely distributed optimally; local populations often have lower fitness than imported ones; populations decline; and local and global extinctions are common. Yet we lack a general framework for understanding maladaptation; for instance in terms of distribution, severity, and dynamics. Similar uncertainties apply to the causes of maladaptation. We suggest that incorporating maladaptation-based perspectives into evolutionary biology would facilitate better understanding of the natural world. Approaches within a maladaptation framework might be especially profitable in applied evolution contexts - where reductions in fitness are common. Toward advancing a more balanced study of evolution, here we present a conceptual framework describing causes of maladaptation. As the introductory article for a Special Feature on maladaptation, we also summarize the studies in this Issue, highlighting the causes of maladaptation in each study. We hope that our framework and the papers in this Special Issue will help catalyze the study of maladaptation in applied evolution, supporting greater understanding of evolutionary dynamics in our rapidly changing world.

Hormonal pleiotropy and the evolution of allocation trade-offs

Recent empirical evidence suggests that trade-off relationships can evolve, challenging the classical image of their high entrenchment. For energy reliant traits, this relationship should depend on the endocrine system that regulates resource allocation. Here, we model changes in this system by mutating the expression and conformation of its constitutive hormones and receptors. We show that the shape of trade-offs can indeed evolve in this model through the combined action of genetic drift and selection, such that their evolutionarily expected curvature and length depend on context. In particular, the shape of a trade-off should depend on the cost associated with resource storage, itself depending on the traded resource and on the ecological context. Despite this convergence at the phenotypic level, we show that a variety of physiological mechanisms may evolve in similar simulations, suggesting redundancy at the genetic level. This model should provide a useful framework to interpret and unify the overly complex observations of evolutionary endocrinology and evolutionary ecology.

Is the sky the limit? On the expansion threshold of a species' range

More than 100 years after Grigg's influential analysis of species' borders, the causes of limits to species' ranges still represent a puzzle that has never been understood with clarity. The topic has become especially important recently as many scientists have become interested in the potential for species' ranges to shift in response to climate change-and yet nearly all of those studies fail to recognise or incorporate evolutionary genetics in a way that relates to theoretical developments. I show that range margins can be understood based on just two measurable parameters: (i) the fitness cost of dispersal-a measure of environmental heterogeneity-and (ii) the strength of genetic drift, which reduces genetic diversity. Together, these two parameters define an 'expansion threshold': adaptation fails when genetic drift reduces genetic diversity below that required for adaptation to a heterogeneous environment. When the key parameters drop below this expansion threshold locally, a sharp range margin forms. When they drop below this threshold throughout the species' range, adaptation collapses everywhere, resulting in either extinction or formation of a fragmented metapopulation. Because the effects of dispersal differ fundamentally with dimension, the second parameter-the strength of genetic drift-is qualitatively different compared to a linear habitat. In two-dimensional habitats, genetic drift becomes effectively independent of selection. It decreases with 'neighbourhood size'-the number of individuals accessible by dispersal within one generation. Moreover, in contrast to earlier predictions, which neglected evolution of genetic variance and/or stochasticity in two dimensions, dispersal into small marginal populations aids adaptation. This is because the reduction of both genetic and demographic stochasticity has a stronger effect than the cost of dispersal through increased maladaptation. The expansion threshold thus provides a novel, theoretically justified, and testable prediction for formation of the range margin and collapse of the species' range.

Genetic constraints on adaptation: a theoretical primer for the genomics era

Genetic constraints are features of inheritance systems that slow or prohibit adaptation. Several population genetic mechanisms of constraint have received sustained attention within the field since they were first articulated in the early 20th century. This attention is now reflected in a rich, and still growing, theoretical literature on the genetic limits to adaptive change. In turn, empirical research on constraints has seen a rapid expansion over the last two decades in response to changing interests of evolutionary biologists, along with new technologies, expanding data sets, and creative analytical approaches that blend mathematical modeling with genomics. Indeed, one of the most notable and exciting features of recent progress in genetic constraints is the close connection between theoretical and empirical research. In this review, we discuss five major population genetic contexts of genetic constraint: genetic dominance, pleiotropy, fitness trade-offs between types of individuals of a population, sign epistasis, and genetic linkage between loci. For each, we outline historical antecedents of the theory, specific contexts where constraints manifest, and their quantitative consequences for adaptation. From each of these theoretical foundations, we discuss recent empirical approaches for identifying and characterizing genetic constraints, each grounded and motivated by this theory, and outline promising areas for future work.

How does mutation affect the distribution of phenotypes?

The potential for mutational processes to influence patterns of neutral or adaptive phenotypic evolution is not well understood. If mutations are directionally biased, shifting trait means in a particular direction, or if mutation generates more variance in some directions of multivariate trait space than others, mutation itself might be a source of bias in phenotypic evolution. Here, we use mutagenesis to investigate the affect of mutation on trait mean and (co)variances in zebrafish, Danio rerio. Mutation altered the relationship between age and both prolonged swimming speed and body shape. These observations suggest that mutational effects on ontogeny or aging have the potential to generate variance across the phenome. Mutations had a far greater effect in males than females, although whether this is a reflection of sex-specific ontogeny or aging remains to be determined. In males, mutations generated positive covariance between swimming speed, size, and body shape suggesting the potential for mutation to affect the evolutionary covariation of these traits. Overall, our observations suggest that mutation does not generate equal variance in all directions of phenotypic space or in each sex, and that pervasive variation in ontogeny or aging within a cohort could affect the variation available to evolution.

Artificial Selection to Increase the Phenotypic Variance in gmax Fails

Stabilizing selection is important in evolutionary theories of the maintenance of genetic variance and has been invoked as the key process determining macroevolutionary patterns of trait evolution. However, manipulative evidence for the extent of stabilizing selection, particularly on multivariate traits, is lacking. We used artificial disruptive selection in Drosophila serrata as a tool to determine the relative strength of stabilizing selection experienced by multivariate trait combinations with contrasting levels of genetic and mutational variance. Contrary to expectation, when disruptive selection was applied to the major axis of standing genetic variance, g_max, we observed a significant and repeatable decrease in its phenotypic variance. In contrast, the multivariate trait combination predicted to be under strong stabilizing selection showed a significant and repeatable increase in its phenotypic variance. Correlated responses were observed in all selection treatments, and viability selection operating on extreme phenotypes of traits genetically correlated with those directly selected on limited our ability to increase their phenotypic range. Our manipulation revealed that multivariate trait combinations were subject to stabilizing selection; however, we did not observe a direct relationship between the strength of stabilizing selection and the levels of standing genetic variance in multivariate trait combinations. Contrasting patterns of allele frequencies underlying traits with high versus low levels of standing genetic variance may be implicated in determining the response to artificial selection in multivariate trait combinations.

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix.

Heritable Micro-environmental Variance Covaries with Fitness in an Outbred Population of Drosophila serrata

The genetic basis of stochastic variation within a defined environment, and the consequences of such micro-environmental variance for fitness are poorly understood . Using a multigenerational breeding design in Drosophila serrata, we demonstrated that the micro-environmental variance in a set of morphological wing traits in a randomly mating population had significant additive genetic variance in most single wing traits. Although heritability was generally low (<1%), coefficients of additive genetic variance were of a magnitude typical of other morphological traits, indicating that the micro-environmental variance is an evolvable trait. Multivariate analyses demonstrated that the micro-environmental variance in wings was genetically correlated among single traits, indicating that common mechanisms of environmental buffering exist for this functionally related set of traits. In addition, through the dominance genetic covariance between the major axes of micro-environmental variance and fitness, we demonstrated that micro-environmental variance shares a genetic basis with fitness, and that the pattern of selection is suggestive of variance-reducing selection acting on micro-environmental variance.

Trait Correlations in the Genomics Era

Thinking about the evolutionary causes and consequences of trait correlations has been dominated by quantitative genetics theory that is focused on hypothetical loci. Since this theory was initially developed, technology has enabled the identification of specific genetic variants that contribute to trait correlations. Here, we review studies of the genetic basis of trait correlations to ask: What has this new information taught us? We find that causal variants can be pleiotropic and/or linked in different ways, indicating that pleiotropy and linkage are not alternative genetic mechanisms. Further, many trait correlations have a polygenic basis, suggesting that both pleiotropy and linkage likely contribute. We discuss implications of these findings for the evolutionary causes and consequences of trait correlations.

Simultaneous Estimation of Additive and Mutational Genetic Variance in an Outbred Population of Drosophila serrata

How new mutations contribute to genetic variation is a key question in biology. Although the evolutionary fate of an allele is largely determined by its heterozygous effect, most estimates of mutational variance and mutational effects derive from highly inbred lines, where new mutations are present in homozygous form. In an attempt to overcome this limitation, middle-class neighborhood (MCN) experiments have been used to assess the fitness effect of new mutations in heterozygous form. However, because MCN populations harbor substantial standing genetic variance, estimates of mutational variance have not typically been available from such experiments. Here we employ a modification of the animal model to analyze data from 22 generations of Drosophila serrata bred in an MCN design. Mutational heritability, measured for eight cuticular hydrocarbons, 10 wing-shape traits, and wing size in this outbred genetic background, ranged from 0.0006 to 0.006 (with one exception), a similar range to that reported from studies employing inbred lines. Simultaneously partitioning the additive and mutational variance in the same outbred population allowed us to quantitatively test the ability of mutation-selection balance models to explain the observed levels of additive and mutational genetic variance. The Gaussian allelic approximation and house-of-cards models, which assume real stabilizing selection on single traits, both overestimated the genetic variance maintained at equilibrium, but the house-of-cards model was a closer fit to the data. This analytical approach has the potential to be broadly applied, expanding our understanding of the dynamics of genetic variance in natural populations.

Selection on bristle length has the ability to drive the evolution of male abdominal appendages in the sepsid fly Themira biloba

Many exaggerated and novel traits are strongly influenced by sexual selection. Although sexual selection is a powerful evolutionary force, underlying genetic interactions can constrain evolutionary outcomes. The relative strength of selection vs. constraint has been a matter of debate for the evolution of male abdominal appendages in sepsid flies. These abdominal appendages are involved in courtship and mating, but their function has not been directly tested. We performed mate choice experiments to determine whether sexual selection acts on abdominal appendages in the sepsid Themira biloba. We tested whether appendage bristle length influenced successful insemination by surgically trimming the bristles. Females paired with males that had shortened bristles laid only unfertilized eggs, indicating that long bristles are necessary for successful insemination. We also tested whether the evolution of bristle length was constrained by phenotypic correlations with other traits. Analyses of phenotypic covariation indicated that bristle length was highly correlated with other abdominal appendage traits, but was not correlated with abdominal sternite size. Thus, abdominal appendages are not exaggerated traits like many sexual ornaments, but vary independently from body size. At the same time, strong correlations between bristle length and appendage length suggest that selection on bristle length is likely to result in a correlated increase in appendage length. Bristle length is under sexual selection in T. biloba and has the potential to evolve independently from abdomen size.

Genetic variation, simplicity, and evolutionary constraints for function-valued traits

Understanding the patterns of genetic variation and constraint for continuous reaction norms, growth trajectories, and other function-valued traits is challenging. We describe and illustrate a recent analytical method, simple basis analysis (SBA), that uses the genetic variance-covariance (G) matrix to identify "simple" directions of genetic variation and genetic constraints that have straightforward biological interpretations. We discuss the parallels between the eigenvectors (principal components) identified by principal components analysis (PCA) and the simple basis (SB) vectors identified by SBA. We apply these methods to estimated G matrices obtained from 10 studies of thermal performance curves and growth curves. Our results suggest that variation in overall size across all ages represented most of the genetic variance in growth curves. In contrast, variation in overall performance across all temperatures represented less than one-third of the genetic variance in thermal performance curves in all cases, and genetic trade-offs between performance at higher versus lower temperatures were often important. The analyses also identify potential genetic constraints on patterns of early and later growth in growth curves. We suggest that SBA can be a useful complement or alternative to PCA for identifying biologically interpretable directions of genetic variation and constraint in function-valued traits.

Dominance genetic variance for traits under directional selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait-fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.

Female mate choice predicts paternity success in the absence of additive genetic variance for other female paternity bias mechanisms in Drosophila serrata

After choosing a first mate, polyandrous females have access to a range of opportunities to bias paternity, such as repeating matings with the preferred male, facilitating fertilization from the best sperm or differentially investing in offspring according to their sire. Female ability to bias paternity after a first mating has been demonstrated in a few species, but unambiguous evidence remains limited by the access to complex behaviours, sperm storage organs and fertilization processes within females. Even when found at the phenotypic level, the potential evolution of any mechanism allowing females to bias paternity other than mate choice remains little explored. Using a large population of pedigreed females, we developed a simple test to determine whether there is additive genetic variation in female ability to bias paternity after a first, chosen, mating. We applied this method in the highly polyandrous Drosophila serrata, giving females the opportunity to successively mate with two males ad libitum. We found that despite high levels of polyandry (females mated more than once per day), the first mate choice was a significant predictor of male total reproductive success. Importantly, there was no detectable genetic variance in female ability to bias paternity beyond mate choice. Therefore, whether or not females can bias paternity before or after copulation, their role on the evolution of sexual male traits is likely to be limited to their first mate choice in D. serrata.