THE EVOLUTIONARY STABILITY OF CROSS‐SEX,CROSS‐TRAIT GENETIC COVARIANCES

Although knowledge of the selective agents behind the evolution of sexual dimorphism has advanced considerably in recent years, we still lack a clear understanding of the evolutionary durability of cross‐sex genetic covariances that often constrain its evolution. We tested the relative stability of cross‐sex genetic covariances for a suite of homologous contact pheromones of the fruit fly Drosophila serrata, along a latitudinal gradient where these traits have diverged in mean. Using a Bayesian framework, which allowed us to account for uncertainty in all parameter estimates, we compared divergence in the total amount and orientation of genetic variance across populations, finding divergence in orientation but not total variance. We then statistically compared orientation divergence of within‐sex ( G ) to cross‐sex ( B ) covariance matrices. In line with a previous theoretical prediction, we find that the cross‐sex covariance matrix, B , is more variable than either within‐sex G matrix. Decomposition of B matrices into their symmetrical and nonsymmetrical components revealed that instability is linked to the degree of asymmetry. We also find that the degree of asymmetry correlates with latitude suggesting a role for spatially varying natural selection in shaping genetic constraints on the evolution of sexual dimorphism.     

Similarity in G matrix structure among natural populations of Arabidopsis lyrata

Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories; yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half‐sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display, and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape, and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.     

Cross‐sex genetic covariances limit the evolvability of wing‐shape within and among species of Drosophila

The independent evolution of males and females is potentially constrained by both sexes inheriting the same alleles from their parents. This genetic constraint can limit the evolvability of complex traits; however, there are few studies of multivariate evolution that incorporate cross‐sex genetic covariances in their predictions. Drosophila wing‐shape has emerged as a model high‐dimensional phenotype; wing‐shape is highly evolvable in contemporary populations, and yet perplexingly stable across phylogenetic timescales. Here, we show that cross‐sex covariances in Drosophila melanogaster, given by the B ‐matrix, may considerably bias wing‐shape evolution. Using random skewers, we show that B would constrain the response to antagonistic selection by 90%, on average, but would double the response to concordant selection. Both cross‐sex within‐trait and cross‐sex cross‐trait covariances determined the predicted response to antagonistic selection, but only cross‐sex within‐trait covariances facilitated the predicted response to concordant selection. Similar patterns were observed in the direction of extant sexual dimorphism in D. melanogaster, and in directions of most and least dimorphic variation across the Drosophila phylogeny. Our results highlight the importance of considering between‐sex genetic covariances when making predictions about evolution on both macro‐ and microevolutionary timescales, and may provide one more explanatory piece in the puzzle of stasis.     

Genetic covariances promote climatic adaptation in Australian Drosophila*

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance-covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population- and sex-specific G matrices for wing size and three climatic stress-resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex-specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.     

Structure and stability of genetic variance–covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three‐spined stickleback

The genetic variance–covariance matrix ( G ) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G ‐matrices is limited for two reasons. First, phenotypes are high‐dimensional, whereas traditional statistical methods are tuned to estimate and analyse low‐dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high‐dimensional G ‐matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half‐sib breeding design of three‐spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low‐temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability—as well as the similarity among G ‐matrices—may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G ‐matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G , they also illustrate that by enabling the estimation of large G ‐matrices, the BSFG method can improve predicted evolutionary responses to selection.     

Limited plasticity in the phenotypic variance‐covariance matrix for male advertisement calls in the black field cricket,Teleogryllus commodus

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent study, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance‐covariance matrix ( P ) stability are sparse, and largely focused on morphological traits. Here, we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild‐caught crickets from each of the populations and then a second subset after rearing crickets under common‐garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high‐ and low‐nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

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.     

Effects of the demographic transition on the genetic variances and covariances of human life‐history traits

The recent demographic transitions to lower mortality and fertility rates in most human societies have led to changes and even quick reversals in phenotypic selection pressures. This can only result in evolutionary change if the affected traits are heritable, but changes in environmental conditions may also lead to subsequent changes in the genetic variance and covariance (the G matrix) of traits. It currently remains unclear if there have been concomitant changes in the G matrix of life‐history traits following the demographic transition. Using 300 years of genealogical data from Finland, we found that four key life‐history traits were heritable both before and after the demographic transition. The estimated heritabilities allow a quantifiable genetic response to selection during both time periods, thus facilitating continued evolutionary change. Further, the G matrices remained largely stable but revealed a trend for an increased additive genetic variance and thus evolutionary potential of the population after the transition. Our results demonstrate the validity of predictions of evolutionary change in human populations even after the recent dramatic environmental change, and facilitate predictions of how our biology interacts with changing environments, with implications for global public health and demography.     

ACROSS‐ENVIRONMENT GENETIC CORRELATIONS AND THE FREQUENCY OF SELECTIVE ENVIRONMENTS SHAPE THE EVOLUTIONARY DYNAMICS OF GROWTH RATE IN IMPATIENS CAPENSIS

Trade‐offs can exist within and across environments, and constrain evolutionary trajectories. To examine the effects of competition and resource availability on trade‐offs, we grew individuals of recombinant inbred lines of Impatiens capensis in a factorial combination of five densities with two light environments (full light and neutral shade) and used a Bayesian logistic growth analysis to estimate intrinsic growth rates. To estimate across‐environment constraints, we developed a variance decomposition approach to principal components analysis, which accounted for sample size, model‐fitting, and within‐RIL variation prior to eigenanalysis. We detected negative across‐environment genetic covariances in intrinsic growth rates, although only under full‐light. To evaluate the potential importance of these covariances, we surveyed natural populations of I. capensis to measure the frequency of different density environments across space and time. We combined our empirical estimates of across‐environment genetic variance–covariance matrices and frequency of selective environments with hypothetical (yet realistic) selection gradients to project evolutionary responses in multiple density environments. Selection in common environments can lead to correlated responses to selection in rare environments that oppose and counteract direct selection in those rare environments. Our results highlight the importance of considering both the frequency of selective environments and the across‐environment genetic covariances in traits simultaneously.     

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. II COASTAL-INLAND DIVERGENCE IN THE GARTER SNAKE,THAMNOPHIS ELEGANS

The time-scale for the evolution of additive genetic variance-covariance matrices (G-matrices) is a crucial issue in evolutionary biology. If the evolution of G-matrices is slow enough, we can use standard multivariate equations to model drift and selection response on evolutionary time scales. We compared the G-matrices for meristic traits in two populations of gaiter snakes (Thamnophis elegans) with an apparent separation time of 2 million years. Despite considerable divergence in the meristic traits, foraging habits, and diet, these populations show conservation of structure in their G-matrices. Using Flury's hierarchial approach to matrix comparisons, we found that the populations have retained the principal components (eigenvectors) of their G-matrices, but their eigenvalues have diverged. In contrast, we were unable to reject the hypothesis of equal environmental matrices (E-matrices) for these populations. We propose that a conserved pattern of multivariate stabilizing selection may have contributed to conservation of G- and E-matrix structure during the divergence of these populations.     

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance–covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.     

Multilevel and sex‐specific selection on competitive traits in North American red squirrels

Individuals often interact more closely with some members of the population (e.g., offspring, siblings, or group members) than they do with other individuals. This structuring of interactions can lead to multilevel natural selection, where traits expressed at the group‐level influence fitness alongside individual‐level traits. Such multilevel selection can alter evolutionary trajectories, yet is rarely quantified in the wild, especially for species that do not interact in clearly demarcated groups. We quantified multilevel natural selection on two traits, postnatal growth rate and birth date, in a population of North American red squirrels (Tamiasciurus hudsonicus). The strongest level of selection was typically within‐acoustic social neighborhoods (within 130 m of the nest), where growing faster and being born earlier than nearby litters was key, while selection on growth rate was also apparent both within‐litters and within‐study areas. Higher population densities increased the strength of selection for earlier breeding, but did not influence selection on growth rates. Females experienced especially strong selection on growth rate at the within‐litter level, possibly linked to the biased bequeathal of the maternal territory to daughters. Our results demonstrate the importance of considering multilevel and sex‐specific selection in wild species, including those that are territorial and sexually monomorphic.     

Rapid genome‐wide evolution in Brassica rapa populations following drought revealed by sequencing of ancestral and descendant gene pools

There is increasing evidence that evolution can occur rapidly in response to selection. Recent advances in sequencing suggest the possibility of documenting genetic changes as they occur in populations, thus uncovering the genetic basis of evolution, particularly if samples are available from both before and after selection. Here, we had a unique opportunity to directly assess genetic changes in natural populations following an evolutionary response to a fluctuation in climate. We analysed genome‐wide differences between ancestors and descendants of natural populations of Brassica rapa plants from two locations that rapidly evolved changes in multiple phenotypic traits, including flowering time, following a multiyear late‐season drought in California. These ancestor‐descendant comparisons revealed evolutionary shifts in allele frequencies in many genes. Some genes showing evolutionary shifts have functions related to drought stress and flowering time, consistent with an adaptive response to selection. Loci differentiated between ancestors and descendants (F_ST outliers) were generally different from those showing signatures of selection based on site frequency spectrum analysis (Tajima's D), indicating that the loci that evolved in response to the recent drought and those under historical selection were generally distinct. Very few genes showed similar evolutionary responses between two geographically distinct populations, suggesting independent genetic trajectories of evolution yielding parallel phenotypic changes. The results show that selection can result in rapid genome‐wide evolutionary shifts in allele frequencies in natural populations, and highlight the usefulness of combining resurrection experiments in natural populations with genomics for studying the genetic basis of adaptive evolution.     

Evolutionary potential of morphological traits across different life‐history stages

Despite accumulating examples of selection acting on heritable traits in the wild, predicted evolutionary responses are often different from observed phenotypic trends. Various explanations have been suggested for these mismatches. These include within‐individual changes across lifespan that can create important variation in genetic architecture of traits and selection acting on them, but also potential problems with the methodological approach used to predict evolutionary responses of traits. Here, we used an 8‐year data set on tree swallow (Tachycineta bicolor) to first assess the effects of differences among three nestling life‐history stages on the genetic (co)variances of two morphological traits (body mass and primary feather length) and the selection acting on them over three generations. We then estimated the evolutionary potential of these traits by predicting their evolutionary responses using the breeder's equation and the secondary theorem of selection approaches. Our results showed variation in strength and direction of selection and slight changes in trait variance across ages. Predicted evolutionary responses differed importantly between both approaches for half of the trait–age combinations we studied, suggesting the presence of environmentally induced correlations between focal traits and fitness possibly biasing breeder's equation predictions. Our results emphasize that predictions of evolutionary potential for morphological traits are likely to be highly variable, both in strength and direction, depending on the life stage and method used, thus mitigating our capacity to predict adaptation and persistence of wild populations.     

THE GENOMIC ARCHITECTURE OF SEXUAL DIMORPHISM IN THE DIOECIOUS PLANT SILENE LATIFOLIA

Evaluating the genetic architecture of sexual dimorphism can aid our understanding of the extent to which shared genetic control of trait variation versus sex‐specific control impacts the evolutionary dynamics of phenotypic change within each sex. We performed a QTL analysis on Silene latifolia to evaluate the contribution of sex‐specific QTL to phenotypic variation in 46 traits, whether traits involved in trade‐offs had colocalized QTL, and whether the distribution of sex‐specific loci can explain differences between the sexes in their variance/covariance matrices. We used a backcross generation derived from two artificial‐selection lines. We found that sex‐specific QTL explained a significantly greater percent of the variation in sexually dimorphic traits than loci expressed in both sexes. Genetically correlated traits often had colocalized QTL, whose signs were in the expected direction. Lastly, traits with different genetic correlations within the sexes displayed a disproportionately high number of sex‐specific QTL, and more QTL co‐occurred in males than females, suggesting greater trait integration. These results show that sex differences in QTL patterns are congruent with theory on the resolution of sexual conflict and differences based on G ‐matrix results. They also suggest that trade‐offs and trait integration are likely to affect males more than females.     

Relaxation of herbivore‐mediated selection drives the evolution of genetic covariances between plant competitive and defense traits

Insect herbivores are important mediators of selection on traits that impact plant defense against herbivory and competitive ability. Although recent experiments demonstrate a central role for herbivory in driving rapid evolution of defense and competition‐mediating traits, whether and how herbivory shapes heritable variation in these traits remains poorly understood. Here, we evaluate the structure and evolutionary stability of the G matrix for plant metabolites that are involved in defense and allelopathy in the tall goldenrod, Solidago altissima. We show that G has evolutionarily diverged between experimentally replicated populations that evolved in the presence versus the absence of ambient herbivory, providing direct evidence for the evolution of G by natural selection. Specifically, evolution in an herbivore‐free habitat altered the orientation of G , revealing a negative genetic covariation between defense‐ and competition‐related metabolites that is typically masked in herbivore‐exposed populations. Our results may be explained by predictions of classical quantitative genetic theory, as well as the theory of acquisition‐allocation trade‐offs. The study provides compelling evidence that herbivory drives the evolution of plant genetic architecture.     

Environmental effects on the structure of the G‐matrix

Genetic correlations between traits determine the multivariate response to selection in the short term, and thereby play a causal role in evolutionary change. Although individual studies have documented environmentally induced changes in genetic correlations, the nature and extent of environmental effects on multivariate genetic architecture across species and environments remain largely uncharacterized. We reviewed the literature for estimates of the genetic variance–covariance ( G ) matrix in multiple environments, and compared differences in G between environments to the divergence in G between conspecific populations (measured in a common garden). We found that the predicted evolutionary trajectory differed as strongly between environments as it did between populations. Between‐environment differences in the underlying structure of G (total genetic variance and the relative magnitude and orientation of genetic correlations) were equal to or greater than between‐population differences. Neither environmental novelty, nor the difference in mean phenotype predicted these differences in G . Our results suggest that environmental effects on multivariate genetic architecture may be comparable to the divergence that accumulates over dozens or hundreds of generations between populations. We outline avenues of future research to address the limitations of existing data and characterize the extent to which lability in genetic correlations shapes evolution in changing environments.     

Genetic correlations and sex‐specific adaptation in changing environments

Females and males have conflicting evolutionary interests. Selection favors the evolution of different phenotypes within each sex, yet divergence between the sexes is constrained by the shared genetic basis of female and male traits. Current theory predicts that such “sexual antagonism” should be common: manifesting rapidly during the process of adaptation, and slow in its resolution. However, these predictions apply in temporally stable environments. Environmental change has been shown empirically to realign the direction of selection acting on shared traits and thereby alleviate signals of sexually antagonistic selection. Yet there remains no theory for how common sexual antagonism should be in changing environments. Here, we analyze models of sex‐specific evolutionary divergence under directional and cyclic environmental change, and consider the impact of genetic correlations on long‐run patterns of sex‐specific adaptation. We find that environmental change often aligns directional selection between the sexes, even when they have divergent phenotypic optima. Nevertheless, some forms of environmental change generate persistent sexually antagonistic selection that is difficult to resolve. Our results reinforce recent empirical observations that changing environmental conditions alleviate conflict between males and females. They also generate new predictions regarding the scope for sexually antagonistic selection and its resolution in changing environments.     

THE DETERMINATION OF GENETIC COVARIANCES AND PREDICTION OF EVOLUTIONARY TRAJECTORIES BASED ON A GENETIC CORRELATION MATRIX

There is much interest in measuring selection, quantifying evolutionary constraints, and predicting evolutionary trajectories in natural populations. For these studies, genetic (co)variances among fitness traits play a central role. We explore the conditions that determine the sign of genetic covariances and demonstrate a critical role of selection in shaping genetic covariances. In addition, we show that genetic covariance matrices rather than genetic correlation matrices should be characterized and studied in order to infer genetic basis of population differentiation and/or to predict evolutionary trajectories.