Patterns of quantitative genetic variation in multiple dimensions

Assessing multivariate constraints to evolution across ten long-term avian studies

Background

In a rapidly changing world, it is of fundamental importance to understand processes constraining or facilitating adaptation through microevolution. As different traits of an organism covary, genetic correlations are expected to affect evolutionary trajectories. However, only limited empirical data are available.

Methodology/Principal Findings

We investigate the extent to which multivariate constraints affect the rate of adaptation, focusing on four morphological traits often shown to harbour large amounts of genetic variance and considered to be subject to limited evolutionary constraints. Our data set includes unique long-term data for seven bird species and a total of 10 populations. We estimate population-specific matrices of genetic correlations and multivariate selection coefficients to predict evolutionary responses to selection. Using Bayesian methods that facilitate the propagation of errors in estimates, we compare (1) the rate of adaptation based on predicted response to selection when including genetic correlations with predictions from models where these genetic correlations were set to zero and (2) the multivariate evolvability in the direction of current selection to the average evolvability in random directions of the phenotypic space. We show that genetic correlations on average decrease the predicted rate of adaptation by 28%. Multivariate evolvability in the direction of current selection was systematically lower than average evolvability in random directions of space. These significant reductions in the rate of adaptation and reduced evolvability were due to a general nonalignment of selection and genetic variance, notably orthogonality of directional selection with the size axis along which most (60%) of the genetic variance is found.

Conclusions

These results suggest that genetic correlations can impose significant constraints on the evolution of avian morphology in wild populations. This could have important impacts on evolutionary dynamics and hence population persistence in the face of rapid environmental change.

The nature and extent of mutational pleiotropy in gene expression of male Drosophila serrata

The nature and extent of mutational pleiotropy remain largely unknown, despite the central role that pleiotropy plays in many areas of biology, including human disease, agricultural production, and evolution. Here, we investigate the variation in 11,604 gene expression traits among 41 mutation accumulation (MA) lines of Drosophila serrata. We first confirmed that these expression phenotypes were heritable, detecting genetic variation in 96% of them in an outbred, natural population of D. serrata. Among the MA lines, 3385 (29%) of expression traits were variable, with a mean mutational heritability of 0.0005. In most traits, variation was generated by mutations of relatively small phenotypic effect; putative mutations with effects of greater than one phenotypic standard deviation were observed for only 8% of traits. With most (71%) traits unaffected by any mutation, our data provide no support for universal pleiotropy. We further characterized mutational pleiotropy in the 3385 variable traits, using sets of 5, randomly assigned, traits. Covariance among traits chosen at random with respect to their biological function is expected only if pleiotropy is extensive. Taking an analytical approach in which the variance unique to each trait in the random 5-trait sets was partitioned from variance shared among traits, we detected significant (at 5% false discovery rate) mutational covariance in 21% of sets. This frequency of statistically supported covariance implied that at least some mutations must pleiotropically affect a substantial number of traits (>70; 0.6% of all measured traits).

Multi-trait assessment of early-in-life female, male and genomic measures for use in genetic selection to improve female reproductive performance of Brahman cattle

Early-in-life female and male measures with potential to be practical genetic indicators were chosen from earlier analyses and examined together with genomic measures for multi-trait use to improve female reproduction of Brahman cattle. Combinations of measures were evaluated on the genetic gains expected from selection of sires and dams for each of age at puberty (AGECL, i.e. first observation of a corpus luteum), lactation anoestrous interval in 3-year-old cows (LAI), and lifetime annual weaning rate (LAWR, i.e. the weaning rate of cows based on the number of annual matings they experienced over six possible matings). Selection was on an index of comparable records for each combination. Selection intensities were less than theoretically possible but assumed a concerted selection effort was able to be made across the Brahman breed. The results suggested that substantial genetic gains could be possible but need to be confirmed in other data. The estimated increase in LAWR in 10 years, for combinations without or with genomic measures, ranged from 8 to 12 calves weaned per 100 cows from selection of sires, and from 12 to 15 calves weaned per 100 cows from selection of sires and dams. Corresponding reductions in LAI were 60–103 days or 94–136 days, and those for AGECL were 95–125 or 141–176 days, respectively. Coat score (a measure of the sleekness or wooliness of the coat) and hip height in females, and preputial eversion and liveweight in males, were measures that may warrant wider recording for Brahman female reproduction genetic evaluation. Pregnancy-test outcomes from Matings 1 and 2 also should be recorded. Percentage normal sperm may be important to record for reducing LAI and scrotal size and serum insulin-like growth factor-I concentration in heifers at 18 months for reducing AGECL. Use of a genomic estimated breeding value (EBV) in combination with other measures added to genetic gains, especially at genomic EBV accuracies of 40%. Accuracies of genomic EBVs needed to approach 60% for the genomic EBV to be the most important contributor to gains in the combinations of measures studied.

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.

Space, time and complexity in plant dispersal ecology

Dispersal of pollen and seeds are essential functions of plant species, with far-reaching demographic, ecological and evolutionary consequences. Interest in plant dispersal has increased with concerns about the persistence of populations and species under global change. We argue here that advances in plant dispersal ecology research will be determined by our ability to surmount challenges of spatiotemporal scales and heterogeneities and ecosystem complexity. Based on this framework, we propose a selected set of research questions, for which we suggest some specific objectives and methodological approaches. Reviewed topics include multiple vector contributions to plant dispersal, landscape-dependent dispersal patterns, long-distance dispersal events, spatiotemporal variation in dispersal, and the consequences of dispersal for plant communities, populations under climate change, and anthropogenic landscapes.

Evolutionary inevitability of sexual antagonism

Sexual antagonism, whereby mutations are favourable in one sex and disfavourable in the other, is common in natural populations, yet the root causes of sexual antagonism are rarely considered in evolutionary theories of adaptation. Here, we explore the evolutionary consequences of sex-differential selection and genotype-by-sex interactions for adaptation in species with separate sexes. We show that sexual antagonism emerges naturally from sex differences in the direction of selection on phenotypes expressed by both sexes or from sex-by-genotype interactions affecting the expression of such phenotypes. Moreover, modest sex differences in selection or genotype-by-sex effects profoundly influence the long-term evolutionary trajectories of populations with separate sexes, as these conditions trigger the evolution of strong sexual antagonism as a by-product of adaptively driven evolutionary change. The theory demonstrates that sexual antagonism is an inescapable by-product of adaptation in species with separate sexes, whether or not selection favours evolutionary divergence between males and females.

Evolutionary constraints and the maintenance of individual specialization throughout succession

Constraints on life-history traits, with their close links to fitness, are widely invoked as limits to niche expansion at most organizational levels. Theoretically, such constraints can maintain individual specialization by preventing adaptation to all niches available, but empirical evidence of them remains elusive for natural populations. This problem may be compounded by a tendency to seek constraints involving multiple traits, neglecting their added potential to manifest in trait expression across environments (i.e., within reaction norms). By replicating genotypes of a colonial marine invertebrate across successional stages in its local community, and taking a holistic approach to the analysis of ensuing reaction norms for fitness, we show the potential for individual specialization to be maintained by genetic constraints associated with these norms, which limit the potential for fitness at one successional stage to improve without loss of fitness at others. Our study provides new insight into the evolutionary maintenance of individual specialization in natural populations and reinforces the importance of reaction norms for studying this phenomenon.

Genetic regulatory network motifs constrain adaptation through curvature in the landscape of mutational (co)variance

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

Can invasions occur without change? A comparison of G-matrices and selection in the peach-potato aphid, Myzus persicae

Most evolutionary research on biological invasions has focused on changes seen between the native and invaded range for a particular species. However, it is likely that species that live in human-modified habitats in their native range might have evolved specific adaptations to those environments, which increase the likelihood of establishment and spread in similar human-altered environments. From a quantitative genetic perspective, this hypothesis suggests that both native and introduced populations should reside at or near the same adaptive peak. Therefore, we should observe no overall changes in the G (genetic variance-covariance) matrices between native and introduced ranges, and stabilizing selection on fitness-related traits in all populations. We tested these predictions comparing three populations of the worldwide pest Myzus persicae from the Middle East (native range) and the UK and Chile (separately introduced ranges). In general, our results provide mixed support for this idea, but further comparisons of other species are needed. In particular, we found that there has been some limited evolution in the studied traits, with the Middle East population differing from the UK and Chilean populations. This was reflected in the structure of the G-matrices, in which Chile differed from both UK and Middle East populations. Furthermore, the amount of genetic variation was massively reduced in Chile in comparison with UK and Middle East populations. Finally, we found no detectable selection on any trait in the three populations, but clones from the introduced ranges started to reproduce later, were smaller, had smaller offspring, and had lower reproductive fitness than clones from the native range.

Key questions in the genetics and genomics of eco-evolutionary dynamics

Increasing acceptance that evolution can be 'rapid' (or 'contemporary') has generated growing interest in the consequences for ecology. The genetics and genomics of these 'eco-evolutionary dynamics' will be--to a large extent--the genetics and genomics of organismal phenotypes. In the hope of stimulating research in this area, I review empirical data from natural populations and draw the following conclusions. (1) Considerable additive genetic variance is present for most traits in most populations. (2) Trait correlations do not consistently oppose selection. (3) Adaptive differences between populations often involve dominance and epistasis. (4) Most adaptation is the result of genes of small-to-modest effect, although (5) some genes certainly have larger effects than the others. (6) Adaptation by independent lineages to similar environments is mostly driven by different alleles/genes. (7) Adaptation to new environments is mostly driven by standing genetic variation, although new mutations can be important in some instances. (8) Adaptation is driven by both structural and regulatory genetic variation, with recent studies emphasizing the latter. (9) The ecological effects of organisms, considered as extended phenotypes, are often heritable. Overall, the study of eco-evolutionary dynamics will benefit from perspectives and approaches that emphasize standing genetic variation in many genes of small-to-modest effect acting across multiple traits and that analyze overall adaptation or 'fitness'. In addition, increasing attention should be paid to dominance, epistasis and regulatory variation.

Pleiotropy of FRIGIDA enhances the potential for multivariate adaptation

An evolutionary response to selection requires genetic variation; however, even if it exists, then the genetic details of the variation can constrain adaptation. In the simplest case, unlinked loci and uncorrelated phenotypes respond directly to multivariate selection and permit unrestricted paths to adaptive peaks. By contrast, 'antagonistic' pleiotropic loci may constrain adaptation by affecting variation of many traits and limiting the direction of trait correlations to vectors that are not favoured by selection. However, certain pleiotropic configurations may improve the conditions for adaptive evolution. Here, we present evidence that the Arabidopsis thaliana gene FRI (FRIGIDA) exhibits 'adaptive' pleiotropy, producing trait correlations along an axis that results in two adaptive strategies. Derived, low expression FRI alleles confer a 'drought escape' strategy owing to fast growth, low water use efficiency and early flowering. By contrast, a dehydration avoidance strategy is conferred by the ancestral phenotype of late flowering, slow growth and efficient water use during photosynthesis. The dehydration avoidant phenotype was recovered when genotypes with null FRI alleles were transformed with functional alleles. Our findings indicate that the well-documented effects of FRI on phenology result from differences in physiology, not only a simple developmental switch.

Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism's entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse - affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.

The quantitative genetic architecture of the bold-shy continuum in zebrafish, Danio rerio

In studies of consistent individual differences (personality) along the bold-shy continuum, a pattern of behavioral correlations frequently emerges: individuals towards the bold end of the continuum are more likely to utilize risky habitat, approach potential predators, and feed under risky conditions. Here, we address the hypothesis that observed phenotypic correlations among component behaviors of the bold-shy continuum are a result of underlying genetic correlations (quantitative genetic architecture). We used a replicated three-generation pedigree of zebrafish (Danio rerio) to study three putative components of the bold-shy continuum: horizontal position, swim level, and feeding latency. We detected significant narrow-sense heritabilities as well as significant genetic and phenotypic correlations among all three behaviors, such that fish selected for swimming at the front of the tank swam closer to the observer, swam higher in the water column, and fed more quickly than fish selected for swimming at the back of the tank. Further, the lines varied in their initial open field behavior (swim level and activity level). The quantitative genetic architecture of the bold-shy continuum indicates that the multivariate behavioral phenotype characteristic of a “bold” personality type may be a result of correlated evolution via underlying genetic correlations.

Natural variation and genetic constraints on drought tolerance

Drought is a central abiotic stress for both natural plant populations and agricultural crops. Substantial natural genetic variation in drought resistance traits has been identified in plant populations, crop species, and laboratory model systems. In particular, studies in Arabidopsis thaliana have discovered variation in a number of key physiological traits involved in plant-water relations that may underlie evolved drought stress responses among accessions. Despite this abundant variation, we still know little about the complex genetic architecture of drought tolerance or its role in constraining evolution. Unfortunately, few natural allelic variants have been cloned for drought related traits--progress cloning QTL, the use of RNA-sequencing methods for evaluating gene expression responses to soil drying, and improved methodology for exploring complex multivariate data all hold promise for moving the field forward. In particular, a better understanding of the molecular nature of pleiotropic gene action and the genetics of phenotypic plasticity will give insight into local adaptation in plants and provide new avenues for improving crops.

Rapid and unpredictable changes of the G-matrix in a natural bird population over 25 years

Knowledge of the genetic variances and covariances of traits (the G-matrix) is fundamental for the understanding of evolutionary dynamics of populations. Despite its essential importance in evolutionary studies, empirical tests of the temporal stability of the G-matrix in natural populations are few. We used a 25-year-long individual-based field study on almost 7000 breeding attempts of the collared flycatcher (Ficedula albicollis) to estimate the stability of the G-matrix over time. Using animal models to estimate G for several time periods, we show that the structure of the time-specific G-matrices changed significantly over time. The temporal changes in the G-matrix were unpredictable, and the structure at one time period was not indicative of the structure at the next time period. Moreover, we show that the changes in the time-specific G-matrices were not related to changes in mean trait values or due to genetic drift. Selection, differences in acquisition/allocation patterns or environment-dependent allelic effects are therefore likely explanations for the patterns observed, probably in combination. Our result cautions against assuming constancy of the G-matrix and indicates that even short-term evolutionary predictions in natural populations can be very challenging.

Phenotypic covariance at species' borders

Background

Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species’ borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes.

Results

Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species.

Conclusions

Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species’ borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future.

Quantitative genetic divergence and standing genetic (co)variance in thermal reaction norms along latitude

Although the potential to adapt to warmer climate is constrained by genetic trade-offs, our understanding of how selection and mutation shape genetic (co)variances in thermal reaction norms is poor. Using 71 isofemale lines of the fly Sepsis punctum, originating from northern, central, and southern European climates, we tested for divergence in juvenile development rate across latitude at five experimental temperatures. To investigate effects of evolutionary history in different climates on standing genetic variation in reaction norms, we further compared genetic (co)variances between regions. Flies were reared on either high or low food resources to explore the role of energy acquisition in determining genetic trade-offs between different temperatures. Although the latter had only weak effects on the strength and sign of genetic correlations, genetic architecture differed significantly between climatic regions, implying that evolution of reaction norms proceeds via different trajectories at high latitude versus low latitude in this system. Accordingly, regional genetic architecture was correlated to region-specific differentiation. Moreover, hot development temperatures were associated with low genetic variance and stronger genetic correlations compared to cooler temperatures. We discuss the evolutionary potential of thermal reaction norms in light of their underlying genetic architectures, evolutionary histories, and the materialization of trade-offs in natural environments.

Evolutionary rescue by beneficial mutations in environments that change in space and time

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the 'effective selection coefficient', whose value is an average that gives most weight to a mutant's fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation's maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.

Separating intrinsic and environmental contributions to growth and their population consequences

Among-individual heterogeneity in growth is a commonly observed phenomenon that has clear consequences for population and community dynamics yet has proved difficult to quantify in practice. In particular, observed among-individual variation in growth can be difficult to link to any given mechanism. Here, we develop a Bayesian state-space framework for modeling growth that bridges the complexity of bioenergetic models and the statistical simplicity of phenomenological growth models. The model allows for intrinsic individual variation in traits, a shared environment, process stochasticity, and measurement error. We apply the model to two populations of steelhead trout (Oncorhynchus mykiss) grown under common but temporally varying food conditions. Models allowing for individual variation match available data better than models that assume a single shared trait for all individuals. Estimated individual variation translated into a roughly twofold range in realized growth rates within populations. Comparisons between populations showed strong differences in trait means, trait variability, and responses to a shared environment. Together, individual- and population-level variation have substantial implications for variation in size and growth rates among and within populations. State-dependent life-history models predict that this variation can lead to differences in individual life-history expression, lifetime reproductive output, and population life-history diversity.

Interspecific divergence of transcription networks along lines of genetic variance in Drosophila: dimensionality, evolvability, and constraint

Change in gene expression is a major facilitator of phenotypic evolution. Understanding the evolutionary potential of gene expression requires taking into account complex systems of regulatory networks, the structure of which could potentially bias evolutionary trajectories. We analyzed the evolutionary potential and divergence of multigene expression in three well-characterized signaling pathways in Drosophila, the mitogen-activated protein kinase (MapK), the Toll, and the insulin receptor/Foxo (InR/Foxo or InR/TOR) pathways in a multivariate quantitative genetic framework. Gene expression data from a natural population of D. melanogaster were used to estimate the genetic variance-covariance matrices (G) for each network. Although most genes within each pathway exhibited significant genetic variance, the number of independent dimensions of multivariate genetic variance was fewer than the number of genes analyzed. However, for expression, the reduction in dimensionality was not as large as seen for other trait types such as morphology. We then tested whether gene expression divergence between D. melanogaster and an additional six species of the Drosophila genus was biased along the major axes of standing variation observed in D. melanogaster. In many cases, divergence was restricted to directions of phenotypic space harboring above average levels of genetic variance in D. melanogaster, indicating that genetic covariances between genes within pathways have biased interspecific divergence. We tested whether co-expression of genes in both sexes has also biased the pattern of divergence. Including cross-sex genetic covariances increased the degree to which divergence was biased along major axes of genetic variance, suggesting that the co-expression of genes in males and females can generate further constraints on divergence across the Drosophila phylogeny. In contrast to patterns seen for morphological traits in vertebrates, transcriptional constraints do not appear to break down as divergence time between species increases, instead they persist over tens of millions of years of divergence.

Multivariate analysis of adaptive capacity for upper thermal limits in Drosophila simulans

Thermal tolerance is an important factor influencing the distribution of ectotherms, but our understanding of the ability of species to evolve different thermal limits is limited. Based on univariate measures of adaptive capacity, it has recently been suggested that species may have limited evolutionary potential to extend their upper thermal limits under ramping temperature conditions that better reflect heat stress in nature. To test these findings more broadly, we used a paternal half-sibling breeding design to estimate the multivariate evolutionary potential for upper thermal limits in Drosophila simulans. We assessed heat tolerance using static (basal and hardened) and ramping assays. Our analyses revealed significant evolutionary potential for all three measures of heat tolerance. Additive genetic variances were significantly different from zero for all three traits. Our G matrix analysis revealed that all three traits would contribute to a response to selection for increased heat tolerance. Significant additive genetic covariances and additive genetic correlations between static basal and hardened heat-knockdown time, marginally nonsignificant between static basal and ramping heat-knockdown time, indicate that direct and correlated responses to selection for increased upper thermal limits are possible. Thus, combinations of all three traits will contribute to the evolution of upper thermal limits in response to selection imposed by a warming climate. Reliance on univariate estimates of evolutionary potential may not provide accurate insight into the ability of organisms to evolve upper thermal limits in nature.

Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance-covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.

Quantifying multivariate plasticity: genetic variation in resource acquisition drives plasticity in resource allocation to components of life history

Acquisition and allocation of resources are central to life-history theory. However, empirical work typically focuses only on allocation despite the fact that relationships between fitness components may be governed by differences in the ability of individuals to acquire resources across environments. Here, we outline a statistical framework to partition the genetic basis of multivariate plasticity into independent axes of genetic variation, and quantify for the first time, the extent to which specific traits drive multitrait genotype-environment interactions. Our framework generalises to analyses of plasticity, growth and ageing. We apply this approach to a unique, large-scale, multivariate study of acquisition, allocation and plasticity in the life history of the cricket, Gryllus firmus. We demonstrate that resource acquisition and allocation are genetically correlated, and that plasticity in trade-offs between allocation to components of fitness is 90% dependent on genetic variance for total resource acquisition. These results suggest that genotype-environment effects for resource acquisition can maintain variation in life-history components that are typically observed in the wild.

Evolution in a changing environment

We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with "specialist" individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents "generalist" individuals not affected by environmental changes. The rest of the landscape is occupied by "maladapted" individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change.

Joint allelic effects on fitness and metric traits

Theoretical explanations of empirically observed standing genetic variation, mutation, and selection suggest that many alleles must jointly affect fitness and metric traits. However, there are few direct demonstrations of the nature and extent of these pleiotropic associations. We implemented a mutation accumulation (MA) divergence experimental design in Drosophila serrata to segregate genetic variants for fitness and metric traits. By exploiting naturally occurring MA line extinctions as a measure of line-level total fitness, manipulating sexual selection, and measuring productivity we were able to demonstrate genetic covariance between fitness and standard metric traits, wing size, and shape. Larger size was associated with lower total fitness and male sexual fitness, but higher productivity. Multivariate wing shape traits, capturing major axes of wing shape variation among MA lines, evolved only in the absence of sexual selection, and to the greatest extent in lines that went extinct, indicating that mutations contributing wing shape variation also typically had deleterious effects on both total fitness and male sexual fitness. This pleiotropic covariance of metric traits with fitness will drive their evolution, and generate the appearance of selection on the metric traits even in the absence of a direct contribution to fitness.

The many faces of pleiotropy

Pleiotropy is the well-established phenomenon of a single gene affecting multiple traits. It has long played a central role in theoretical, experimental, and clinical research in genetics, development, molecular biology, evolution, and medicine. In recent years, genomic techniques have brought data to bear on fundamental questions about the nature and extent of pleiotropy. However, these efforts are plagued by conceptual difficulties derived from disparate meanings and interpretations of pleiotropy. Here, we describe distinct uses of the pleiotropy concept and explain the pitfalls associated with applying empirical data to them. We conclude that, for any question about the nature or extent of pleiotropy, the appropriate answer is always 'What do you mean?'.

The B-matrix harbors significant and sex-specific constraints on the evolution of multicharacter sexual dimorphism

The extent to which sexual dimorphism can evolve within a population depends on an interaction between sexually divergent selection and constraints imposed by a genetic architecture that is shared between males and females. The degree of constraint within a population is normally inferred from the intersexual genetic correlation, r(mf) . However, such bivariate correlations ignore the potential constraining effect of genetic covariances between other sexually coexpressed traits. Using the fruit fly Drosophila serrata, a species that exhibits mutual mate preference for blends of homologous contact pheromones, we tested the impact of between-sex between-trait genetic covariances using an extended version of the genetic variance-covariance matrix, G, that includes Lande's (1980) between-sex covariance matrix, B. We find that including B greatly reduces the degree to which male and female traits are predicted to diverge in the face of divergent phenotypic selection. However, the degree to which B alters the response to selection differs between the sexes. The overall rate of male trait evolution is predicted to decline, but its direction remains relatively unchanged, whereas the opposite is found for females. We emphasize the importance of considering the B-matrix in microevolutionary studies of constraint on the evolution of sexual dimorphism.

Genetic constraints on adaptation to a changing environment

Genetic correlations between traits can constrain responses to natural selection. To what extent such correlations limit adaptation depends on patterns of directional selection. I derive the expected rate of adaptation (or evolvability) under randomly changing selection gradients. When directional selection gradients have an arbitrary covariance matrix, the average rate of adaptation depends on genetic correlations between traits, contrary to the isotropic case investigated in previous studies. Adaptation may be faster on average with more genetic correlation between traits, if these traits are selected to change jointly more often than the average pair of traits. However, natural selection maximizes the long-term fitness of a population, not necessarily its rate of adaptation. I therefore derive the average lag load caused by deviations of the mean phenotype from an optimum, under several forms of environmental changes typically experienced by natural populations, both stochastic and deterministic. Simple formulas are produced for how the G matrix affects long-term fitness in these contexts, and I discuss how their parameters can be estimated empirically.

Genetics and evolution of function-valued traits: understanding environmentally responsive phenotypes

Many central questions in ecology and evolutionary biology require characterizing phenotypes that change with time and environmental conditions. Such traits are inherently functions, and new 'function-valued' methods use the order, spacing, and functional nature of the data typically ignored by traditional univariate and multivariate analyses. These rapidly developing methods account for the continuous change in traits of interest in response to other variables, and are superior to traditional summary-based analyses for growth trajectories, morphological shapes, and environmentally sensitive phenotypes. Here, we explain how function-valued methods make flexible use of data and lead to new biological insights. These approaches frequently offer enhanced statistical power, a natural basis of interpretation, and are applicable to many existing data sets. We also illustrate applications of function-valued methods to address ecological, evolutionary, and behavioral hypotheses, and highlight future directions.

Diversifying and correlational selection on behavior toward conspecific and heterospecific competitors in brook stickleback (Culaea inconstans)

Behaviors toward heterospecifics and conspecifics may be correlated because of shared mechanisms of expression in both social contexts (nonadaptive covariation) or because correlational selection favors adaptive covariation. We evaluated these hypotheses by comparing behavior toward conspecifics and heterospecifics in brook stickleback (Culaea inconstans) from three populations sympatric with and three allopatric from a competitor, the ninespine stickleback (Pungitius pungitius). Behavioral traits were classified into three multivariate components: overt aggression, sociability, and activity. The correlation of behavior between social contexts for both overt aggression and activity varied among populations in a way unrelated to sympatry with ninespine stickleback, while mean aggression was reduced in sympatry. Correlations in allopatric populations suggest that overt aggression and activity may genetically covary between social contexts for nonadaptive reasons. Sociability was rarely correlated in allopatry but was consistently correlated in sympatry despite reduced mean sociability, suggesting that correlational selection may favor a sociability syndrome in brook stickleback when they coexist with ninespine stickleback. Thus, interspecific competition may impose diversifying selection on behavior among populations, although the causes of correlated behavior toward conspecifics and heterospecifics and whether it can evolve in one social context independent of the other may depend on the type of behavior.

Population synchrony decreases with richness and increases with environmental fluctuations in an experimental metacommunity

Fluctuations of local but connected populations may show correlation or synchrony whenever they experience significant dispersal or correlated environmental biotic and abiotic variability. Synchrony may be an important variable in multispecies systems, but its nature and implications have not been explicitly examined. Because the number of locally coexisting species (richness) affects the population variability of community members, we manipulated richness under different regimes of environmental fluctuation (EF). We predicted that the temporal synchrony of populations in a species should decline with increasing richness of the metacommunity they live in. Additionally, we predicted that specialist species that are sensitive to a specific environmental factor would show higher synchronization when EF increases. We thus created experimental communities with varied richness, EF, and species specialization to examine the synchronizing effects of these factors on three aquatic invertebrate species. We created four levels of richness and three levels of EF by manipulating the salinity of the culture media. Monocultures exhibited higher population synchrony than metacommunities of 2-4 species. Furthermore, we found that species responded differently to EF treatments: high EF enhanced population synchrony for the specialist and intermediate species, but not for the generalist species. Our findings emphasize that the magnitude of EF and species richness both contribute to determine population synchrony, and importantly, our results suggest that biotic diversity may actually stabilize metacommunities by disrupting synchrony.

How much can the orientation of G's eigenvectors tell us about genetic constraints?

A key goal in evolutionary quantitative genetics is to understand how evolutionary trajectories are constrained by pleiotropic coupling among multiple traits. Because studying pleiotropic constraints directly at the molecular genetic level remains very difficult, several analytical approaches attempt to draw conclusions about constraints by relating the orientation of the eigenvectors of the traits' (co)variance matrix to vectors of multivariate selection. On the basis of explicit models of genetic architecture, I here argue that the value of such approaches is greatly overestimated. The reason is that eigenvector orientation can be highly unstable and lack a biologically meaningful relationship with the underlying traits' genetic architecture. Genetic constraints are more profitably explored through experimental approaches avoiding the mathematical abstraction inherent in eigenanalysis.

Evolutionary optimum for male sexual traits characterized using the multivariate Robertson-Price Identity

Phenotypes tend to remain relatively constant in natural populations, suggesting a limit to trait evolution. Although stationary phenotypes suggest stabilizing selection, directional selection is more commonly reported. However, selection on phenotypes will have no evolutionary consequence if the traits do not genetically covary with fitness, a covariance known as the Robertson-Price Identity. The nature of this genetic covariance determines if phenotypes will evolve directionally or whether they reside at an evolutionary optimum. Here, we show how a set of traits can be shown to be under net stabilizing selection through an application of the multivariate Robertson-Price Identity. We characterize how a suite of male sexual displays genetically covaries with fitness in a population of Drosophila serrata. Despite strong directional sexual selection on these phenotypes directly and significant genetic variance in them, little genetic covariance was detected with overall fitness. Instead, genetic analysis of trait deviations showed substantial stabilizing selection on the genetic variance of these traits with respect to overall fitness, indicating that they reside at an evolutionary optimum. In the presence of widespread pleiotropy, stabilizing selection on focal traits will arise through the net effects of selection on other, often unmeasured, traits and will tend to be stronger on trait combinations than single traits. Such selection may be difficult to detect in phenotypic analyses if the environmental covariance between the traits and fitness obscures the underlying genetic associations. The genetic analysis of trait deviations provides a way of detecting the missing stabilizing selection inferred by recent metaanalyses.

Reduced genetic variance among high fitness individuals: inferring stabilizing selection on male sexual displays in Drosophila serrata

Directional selection is prevalent in nature, yet phenotypes tend to remain relatively constant, suggesting a limit to trait evolution. However, the genetic basis of this limit is unresolved. Given widespread pleiotropy, opposing selection on a trait may arise from the effects of the underlying alleles on other traits under selection, generating net stabilizing selection on trait genetic variance. These pleiotropic costs of trait exaggeration may arise through any number of other traits, making them hard to detect in phenotypic analyses. Stabilizing selection can be inferred, however, if genetic variance is greater among low- compared to high-fitness individuals. We extend a recently suggested approach to provide a direct test of a difference in genetic variance for a suite of cuticular hydrocarbons (CHCs) in Drosophila serrata. Despite strong directional sexual selection on these traits, genetic variance differed between high- and low-fitness individuals and was greater among the low-fitness males for seven of eight CHCs, significantly more than expected by chance. Univariate tests of a difference in genetic variance were nonsignificant but likely have low power. Our results suggest that further CHC exaggeration in D. serrata in response to sexual selection is limited by pleiotropic costs mediated through other traits.

There is more than one way to skin a G matrix

Because of its importance in directing evolutionary trajectories, there has been considerable interest in comparing variation among genetic variance-covariance (G) matrices. Numerous statistical approaches have been suggested but no general analysis of the relationship among these methods has previously been published. In this study, we used data from a half-sib experiment and simulations to explore the results of applying eight tests (T method, modified Mantel test, Bartlett's test, Flury hierarchy, jackknife-manova, jackknife-eigenvalue test, random skewers, selection skewers). Whereas a randomization approach produced acceptable estimates, those from a bootstrap were typically unacceptable and we recommend randomization as the preferred method. All methods except the jackknife-eigenvalue test gave similar results although a fine-scale analysis suggested that the former group can be subdivided into two or possibly three groups, hierarchical tests, skewers and the rest (jackknife-manova, modified Mantel, T method, probably Bartlett's). An advantage of the jackknife methods is that they permit tests of association with other factors, such as in this case, temperature and sex. We recommend applying all the tests described in this article, with the exception of the T method, and provide R functions for this purpose.

Coevolution in multidimensional trait space favours escape from parasites and pathogens

Almost all species are subject to continuous attack by parasites and pathogens. Because parasites and pathogens tend to have shorter generation times and often experience stronger selection due to interaction than their victims do, it is frequently argued that they should evolve more rapidly and thus maintain an advantage in the evolutionary race between defence and counter-defence. This prediction generates an apparent paradox: how do victim species survive and even thrive in the face of a continuous onslaught of more rapidly evolving enemies? One potential explanation is that defence is physiologically, mechanically or behaviourally easier than attack, so that evolution is less constrained for victims than for parasites or pathogens. Another possible explanation is that parasites and pathogens have enemies themselves and that victim species persist because parasites and pathogens are regulated from the top down and thus generally have only modest demographic impacts on victim populations. Here we explore a third possibility: that victim species are not as evolutionarily impotent as conventional wisdom holds, but instead have unique evolutionary advantages that help to level the playing field. We use quantitative genetic analysis and individual-based simulations to show that victims can achieve such an advantage when coevolution involves multiple traits in both the host and the parasite.

Pervasive genetic integration directs the evolution of human skull shape

It has long been unclear whether the different derived cranial traits of modern humans evolved independently in response to separate selection pressures or whether they resulted from the inherent morphological integration throughout the skull. In a novel approach to this issue, we combine evolutionary quantitative genetics and geometric morphometrics to analyze genetic and phenotypic integration in human skull shape. We measured human skulls in the ossuary of Hallstatt (Austria), which offer a unique opportunity because they are associated with genealogical data. Our results indicate pronounced covariation of traits throughout the skull. Separate simulations of selection for localized shape changes corresponding to some of the principal derived characters of modern human skulls produced outcomes that were similar to each other and involved a joint response in all of these traits. The data for both genetic and phenotypic shape variation were not consistent with the hypothesis that the face, cranial base, and cranial vault are completely independent modules but relatively strongly integrated structures. These results indicate pervasive integration in the human skull and suggest a reinterpretation of the selective scenario for human evolution where the origin of any one of the derived characters may have facilitated the evolution of the others.

Independent axes of genetic variation and parallel evolutionary divergence of opercle bone shape in threespine stickleback

Evolution of similar phenotypes in independent populations is often taken as evidence of adaptation to the same fitness optimum. However, the genetic architecture of traits might cause evolution to proceed more often toward particular phenotypes, and less often toward others, independently of the adaptive value of the traits. Freshwater populations of Alaskan threespine stickleback have repeatedly evolved the same distinctive opercle shape after divergence from an oceanic ancestor. Here we demonstrate that this pattern of parallel evolution is widespread, distinguishing oceanic and freshwater populations across the Pacific Coast of North America and Iceland. We test whether this parallel evolution reflects genetic bias by estimating the additive genetic variance-covariance matrix (G) of opercle shape in an Alaskan oceanic (putative ancestral) population. We find significant additive genetic variance for opercle shape and that G has the potential to be biasing, because of the existence of regions of phenotypic space with low additive genetic variation. However, evolution did not occur along major eigenvectors of G, rather it occurred repeatedly in the same directions of high evolvability. We conclude that the parallel opercle evolution is most likely due to selection during adaptation to freshwater habitats, rather than due to biasing effects of opercle genetic architecture.

Effects of sex and age on genotype x environment interaction for beef cattle body weight studied using reaction norm models

The interest in the effect of genotype × environment interaction is increasing because animal breeding programs have become geographically broader. Climate changes in the next decades are also expected to challenge the present breeding goals, increasing the importance of environmental sensitivity. The aim of this work was to analyze genotype × environment interaction effect on cattle BW using the environmental sensitivity predicted by random regression reaction norm models, including sex and age effects as additional dimensions in the study. Genetic parameters were estimated for adjusted BW of Brazilian Nelore cattle at different ages (120, 210, 365, and 450 d), using linear polynomials for random regression analysis. The analyses with sex as a fixed effect (total analyses) were compared with those with sex-separated progenies (male and female progeny analyses, respectively). (Co)variance components were estimated and breeding values calculated EPD. The results showed important differences in reaction norm model genetic parameter estimates according to different age and sex analyses. The results confirmed the presence of an important genotype × environment × sex × age interaction for Nelore cattle BW. The patterns in these results lead to a revision of the importance of sexual and developmental factors on plasticity and adaptation concepts.

Quantitative genetics of migration syndromes: a study of two barn swallow populations

Migration is a complex trait although little is known about genetic correlations between traits involved in such migration syndromes. To assess the migratory responses to climate change, we need information on genetic constraints on evolutionary potential of arrival dates in migratory birds. Using two long-term data sets on barn swallows Hirundo rustica (from Spain and Denmark), we show for the first time in wild populations that spring arrival dates are phenotypically and genetically correlated with morphological and life history traits. In the Danish population, length of outermost tail feathers and wing length were negatively genetically correlated with arrival date. In the Spanish population, we found a negative genetic correlation between arrival date and time elapsed between arrival date and laying date, constraining response to selection that favours both early arrival and shorter delays. This results in a decreased rate of adaptation, not because of constraints on arrival date, but constraints on delay before breeding, that is, a trait that can be equally important in the context of climate change.