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.     

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.     

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. I. USING THE FLURY HIERARCHY

The comparison of additive genetic variance-covariance matrices (G-matrices) is an increasingly popular exercise in evolutionary biology because the evolution of the G-matrix is central to the issue of persistence of genetic constraints and to the use of dynamic models in an evolutionary time frame. The comparison of G-matrices is a nontrivial statistical problem because family structure induces nonindependence among the elements in each matrix. Past solutions to the problem of G-matrix comparison have dealt with this problem, with varying success, but have tested a single null hypothesis (matrix equality or matrix dissimilarity). Because matrices can differ in many ways, several hypotheses are of interest in matrix comparisons. Flury (1988) has provided an approach to matrix comparison in which a variety of hypotheses are tested, including the two extreme hypotheses prevalent in the evolutionary literature. The hypotheses are arranged in a hierarchy and involve comparisons of both the principal components (eigenvectors) and eigenvalues of the matrix. We adapt Flury's hierarchy of tests to the problem of comparing G-matrices by using randomization testing to account for nonindependence induced by family structure. Software has been developed for carrying out this analysis for both genetic and phenotypic data. The method is illustrated with a garter snake test case.     

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.     

Phenotypic variation and covariation indicate high evolvability of acoustic communication in crickets

Studying the genetic architecture of sexual traits provides insight into the rate and direction at which traits can respond to selection. Traits associated with few loci and limited genetic and phenotypic constraints tend to evolve at high rates typically observed for secondary sexual characters. Here, we examined the genetic architecture of song traits and female song preferences in the field crickets Gryllus rubens and Gryllus texensis. Song and preference data were collected from both species and interspecific F1 and F2 hybrids. We first analysed phenotypic variation to examine interspecific differentiation and trait distributions in parental and hybrid generations. Then, the relative contribution of additive and additive‐dominance variation was estimated. Finally, phenotypic variance–covariance ( P ) matrices were estimated to evaluate the multivariate phenotype available for selection. Song traits and preferences had unimodal trait distributions, and hybrid offspring were intermediate with respect to the parents. We uncovered additive and dominance variation in song traits and preferences. For two song traits, we found evidence for X‐linked inheritance. On the one hand, the observed genetic architecture does not suggest rapid divergence, although sex linkage may have allowed for somewhat higher evolutionary rates. On the other hand, P matrices revealed that multivariate variation in song traits aligned with major dimensions in song preferences, suggesting a strong selection response. We also found strong covariance between the main traits that are sexually selected and traits that are not directly selected by females, providing an explanation for the striking multivariate divergence in male calling songs despite limited divergence in female preferences.     

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.     

A TEST OF THE CONJECTURE THAT G‐MATRICES ARE MORE STABLE THAN B‐MATRICES

The G‐matrix occupies an important position in evolutionary biology both as a summary of the inheritance of quantitative traits and as an ingredient in predicting how those traits will respond to selection and drift. Consequently, the stability of G has an important bearing on the accuracy of predicted evolutionary trajectories. Furthermore, G should evolve in response to stable features of the adaptive landscape and their trajectories through time. Although the stability and evolution of G might be predicted from knowledge of selection in natural populations, most empirical comparisons of G‐matrices have been made in the absence of such a priori predictions. We present a theoretical argument that within‐sex G‐matrices should be more stable than between‐sex B‐matrices because they are more powerfully exposed to multivariate stabilizing selection. We tested this conjecture by comparing estimates of B‐ and within‐sex G‐matrices among three populations of the garter snake Thamnophis elegans. Matrix comparisons using Flury's hierarchical approach revealed that within‐sex G‐matrices had four principal components in common (full CPC), whereas B‐matrices had only a single principal component in common and eigenvalues that were more variable among populations. These results suggest that within‐sex G is more stable than B , as predicted by our theoretical argument.     

Sexual selection and population divergence II. Divergence in different sexual traits and signal modalities in field crickets (Teleogryllus oceanicus)

Sexual selection can target many different types of traits. However, the relative influence of different sexually selected traits during evolutionary divergence is poorly understood. We used the field cricket Teleogryllus oceanicus to quantify and compare how five traits from each of three sexual signal modalities and components diverge among allopatric populations: male advertisement song, cuticular hydrocarbon (CHC) profiles and forewing morphology. Population divergence was unexpectedly consistent: we estimated the among‐population (genetic) variance‐covariance matrix, D , for all 15 traits, and D_max explained nearly two‐thirds of its variation. CHC and wing traits were most tightly integrated, whereas song varied more independently. We modeled the dependence of among‐population trait divergence on genetic distance estimated from neutral markers to test for signatures of selection versus neutral divergence. For all three sexual trait types, phenotypic variation among populations was largely explained by a neutral model of divergence. Our findings illustrate how phenotypic integration across different types of sexual traits might impose constraints on the evolution of mating isolation and divergence via sexual selection.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF THE MAMMALIAN BACULUM BY SEXUAL SELECTION

Male genitalia exhibit a taxonomically widespread pattern of rapid and divergent evolution. Sexual selection is generally believed to be responsible for these patterns of evolutionary divergence, although empirical support for the sexual selection hypothesis comes mainly from studies of insects. Here we show that sexual selection is responsible for an evolutionary divergence in baculum morphology among populations of house mice Mus domesticus. We sourced mice from three isolated populations known to be subject to differing strengths of postcopulatory sexual selection and bred them under common‐garden conditions. Mice from populations with strong postcopulatory sexual selection had bacula that were relatively thicker compared with mice from populations with weak selection. We used experimental evolution to determine whether these patterns of divergence could be ascribed to postcopulatory sexual selection. After 27 generations of experimental evolution, populations of mice subjected to postcopulatory sexual selection evolved bacula that were relatively thicker than populations subjected to enforced monogamy. Our data thereby provide evidence that postcopulatory sexual selection underlies an evolutionary divergence in the mammalian baculum and supports the hypothesis that sexual selection plays a general role in the evolution of male genital morphology across evolutionary diverse taxonomic groups.     

Potential adaptive divergence between subspecies and populations of snapdragon plants inferred from QST–FST comparisons

Phenotypic divergence among natural populations can be explained by natural selection or by neutral processes such as drift. Many examples in the literature compare putatively neutral (F_ST) and quantitative genetic (Q_ST) differentiation in multiple populations to assess their evolutionary signature and identify candidate traits involved with local adaptation. Investigating these signatures in closely related or recently diversified species has the potential to shed light on the divergence processes acting at the interspecific level. Here, we conducted this comparison in two subspecies of snapdragon plants (eight populations of Antirrhinum majus pseudomajus and five populations of A. m. striatum) in a common garden experiment. We also tested whether altitude was involved with population phenotypic divergence. Our results identified candidate phenological and morphological traits involved with local adaptation. Most of these traits were identified in one subspecies but not the other. Phenotypic divergence increased with altitude for a few biomass‐related traits, but only in A. m. striatum. These traits therefore potentially reflect A. m. striatum adaptation to altitude. Our findings imply that adaptive processes potentially differ at the scale of A. majus subspecies.     

The evolution of hominoid cranial diversity: A quantitative genetic approach

Hominoid cranial evolution is characterized by substantial phenotypic diversity, yet the cause of this variability has rarely been explored. Quantitative genetic techniques for investigating evolutionary processes underlying morphological divergence are dependent on the availability of good ancestral models, a problem in hominoids where the fossil record is fragmentary and poorly understood. Here, we use a maximum likelihood approach based on a Brownian motion model of evolutionary change to estimate nested hypothetical ancestral forms from 15 extant hominoid taxa. These ancestors were then used to calculate rates of evolution along each branch of a phylogenetic tree using Lande's generalized genetic distance. Our results show that hominoid cranial evolution is characterized by strong stabilizing selection. Only two instances of directional selection were detected; the divergence of Homo from its last common ancestor with Pan, and the divergence of the lesser apes from their last common ancestor with the great apes. In these two cases, selection gradients reconstructed to identify the specific traits undergoing selection indicated that selection on basicranial flexion, cranial vault expansion, and facial retraction characterizes the divergence of Homo, whereas the divergence of the lesser apes was defined by selection on neurocranial size reduction.     

Morphometric differentiation across House Sparrow Passer domesticus populations in Finland in comparison with the neutral expectation for divergence

To understand the biology of organisms it is important to take into account the evolutionary forces that have acted on their constituent populations. Neutral genetic variation is often assumed to reflect variation in quantitative traits under selection, though with even low neutral divergence there can be substantial differentiation in quantitative genetic variation associated with locally adapted phenotypes. To study the relative roles of natural selection and genetic drift in shaping phenotypic variation, the levels of quantitative divergence based on phenotypes (P_ST) and neutral genetic divergence (F_ST) can be compared. Such a comparison was made between 10 populations of Finnish House Sparrows (n = 238 individuals) collected in 2009 across the whole country. Phenotypic variation in tarsus‐length, wing‐length, bill‐depth, bill‐length and body mass were considered and 13 polymorphic microsatellite loci were analysed to quantify neutral genetic variation. Calculations of P_ST were based on Markov‐Chain Monte Carlo Bayesian estimates of phenotypic variances across and within populations. The robustness of the conclusions of the P_ST–F_ST comparison was evaluated by varying the proportion of variation due to additive genetic effects within and across populations. Our results suggest that body mass is under directional selection, whereas the divergence in other traits does not differ from neutral expectations. These findings suggest candidate traits for considering gene‐based studies of local adaptation. The recognition of locally adapted populations may be of value in the conservation of this declining species.     

The potential influence of morphology on the evolutionary divergence of an acoustic signal

The evolution of acoustic behaviour and that of the morphological traits mediating its production are often coupled. Lack of variation in the underlying morphology of signalling traits has the potential to constrain signal evolution. This relationship is particularly likely in field crickets, where males produce acoustic advertisement signals to attract females by stridulating with specialized structures on their forewings. In this study, we characterize the size and geometric shape of the forewings of males from six allopatric populations of the black field cricket (Teleogryllus commodus) known to have divergent advertisement calls. We sample from each of these populations using both wild‐caught and common‐garden‐reared cohorts, allowing us to test for multivariate relationships between wing morphology and call structure. We show that the allometry of shape has diverged across populations. However, there was a surprisingly small amount of covariation between wing shape and call structure within populations. Given the importance of male size for sexual selection in crickets, the divergence we observe among populations has the potential to influence the evolution of advertisement calls in this species.     

Drift versus selection as drivers of phenotypic divergence at small spatial scales: The case of Belgjarskógur threespine stickleback

Divergence in phenotypic traits is facilitated by a combination of natural selection, phenotypic plasticity, gene flow, and genetic drift, whereby the role of drift is expected to be particularly important in small and isolated populations. Separating the components of phenotypic divergence is notoriously difficult, particularly for multivariate phenotypes. Here, we assessed phenotypic divergence of threespine stickleback (Gasterosteus aculeatus) across 19 semi‐interconnected ponds within a small geographic region (~7.5 km²) using comparisons of multivariate phenotypic divergence (PST), neutral genetic (FST), and environmental (EST) variation. We found phenotypic divergence across the ponds in a suite of functionally relevant phenotypic traits, including feeding, defense, and swimming traits, and body shape (geometric morphometric). Comparisons of PSTs with FSTs suggest that phenotypic divergence is predominantly driven by neutral processes or stabilizing selection, whereas phenotypic divergence in defensive traits is in accordance with divergent selection. Comparisons of population pairwise PSTs with ESTs suggest that phenotypic divergence in swimming traits is correlated with prey availability, whereas there were no clear associations between phenotypic divergence and environmental difference in the other phenotypic groups. Overall, our results suggest that phenotypic divergence of these small populations at small geographic scales is largely driven by neutral processes (gene flow, drift), although environmental determinants (natural selection or phenotypic plasticity) may play a role.     

Nutrients from salmon parents alter selection pressures on their offspring

Organisms can modify their surrounding environment, but whether these changes are large enough to feed back and alter their evolutionary trajectories is not well understood, particularly in wild populations. Here we show that nutrient pulses from decomposing Atlantic salmon (Salmo salar) parents alter selection pressures on their offspring with important consequences for their phenotypic and genetic diversity. We found a strong survival advantage to larger eggs and faster juvenile metabolic rates in streams lacking carcasses but not in streams containing this parental nutrient input. Differences in selection intensities led to significant phenotypic divergence in these two traits among stream types. Stronger selection in streams with low parental nutrient input also decreased the number of surviving families compared to streams with high parental nutrient levels. Observed effects of parent‐derived nutrients on selection pressures provide experimental evidence for key components of eco‐evolutionary feedbacks in wild populations.     

Correlated evolution of life-history with size at maturity in Daphnia pulicaria: patterns within and between populations

Explaining the repeated evolution of similar sets of traits under similar environmental conditions is an important issue in evolutionary biology. The extreme alternative classes of explanations for correlated suites of traits are optimal adaptation and genetic constraint resulting from pleiotropy. Adaptive explanations presume that individual traits are free to evolve to their local optima and that convergent evolution represents particularly adaptive combinations of traits. Alternatively, if pleiotropy is strong and difficult to break, strong selection on one or a few particularly important characters would be expected to result in consistent correlated evolution of associated traits. If pleiotropy is common, we predict that the pattern of divergence among populations will consistently reflect the within-population genetic architecture. To test the idea that the multivariate life-history phenotype is largely a byproduct of strong selection on body size, we imposed divergent artificial selection on size at maturity upon two populations of the cladoceran Daphnia pulicaria, chosen on the basis of their extreme divergence in body size. Overall, the trajectory of divergence between the two natural populations did not differ from that predicted by the genetic architecture within each population. However, the pattern of correlated responses suggested the presence of strong pleiotropic constraints only for adult body size and not for other life-history traits. One trait, offspring size, appears to have evolved in a way different from that expected from the within-population genetic architecture and may be under stabilizing selection.     

Comparison of Populations Based on Attribute Data,when Covariance Matrices are Unequal

Mahalanobis—like distance indices B² and G² of BALAKRISHNAN and SANGHVI (1968) are employed to compare multinomial populations of proportions in human data. Recently, BOWERING and MISRA (1982) employed these methods, with modifications, in a different field viz. to compare fish stocks, based on meristic characters. The method of BALAKRISHNAN and SANGHVI (1968), however, assumes equality of covariance matrices, which is doubtful with multinomial populations of proportions. In this paper a statistical method for comparing such populations (where covariance matrices are not equal) is presented. Also, a feature of the G² method of BALAKRISHNAN and SANGHVI (1968) is discussed, which makes its statistical status a little more clear.     

Global investigation of the co‐evolution of MIRNA genes and microRNA targets during soybean domestication

Although the selection of coding genes during plant domestication has been well studied, the evolution of MIRNA genes (MIRs) and the interaction between microRNAs (miRNAs) and their targets in this process are poorly understood. Here, we present a genome‐wide survey of the selection of MIRs and miRNA targets during soybean domestication and improvement. Our results suggest that, overall, MIRs have higher evolutionary rates than miRNA targets. Nonetheless, they do demonstrate certain similar evolutionary patterns during soybean domestication: MIRs and miRNA targets with high expression and duplication status, and with greater numbers of partners, exhibit lower nucleotide divergence than their counterparts without these characteristics, suggesting that expression level, duplication status, and miRNA–target interaction are essential for evolution of MIRs and miRNA targets. Further investigation revealed that miRNA–target pairs that are subjected to strong purifying selection have greater similarities than those that exhibited genetic diversity. Moreover, mediated by domestication and improvement, the similarities of a large number of miRNA–target pairs in cultivated soybean populations were increased compared to those in wild soybeans, whereas a small number of miRNA–target pairs exhibited decreased similarity, which may be associated with the adoption of particular domestication traits. Taken together, our results shed light on the co‐evolution of MIRs and miRNA targets during soybean domestication.     

Testing drivers of acoustic divergence in cicadas (Cicadidae: Tettigettalna)

Divergence in acoustic signals may have a crucial role in the speciation process of animals that rely on sound for intra-specific recognition and mate attraction. The acoustic adaptation hypothesis (AAH) postulates that signals should diverge according to the physical properties of the signalling environment. To be efficient, signals should maximize transmission and decrease degradation. To test which drivers of divergence exert the most influence in a speciose group of insects, we used a phylogenetic approach to the evolution of acoustic signals in the cicada genus Tettigettalna, investigating the relationship between acoustic traits (and their mode of evolution) and body size, climate and micro-/macro-habitat usage. Different traits showed different evolutionary paths. While acoustic divergence was generally independent of phylogenetic history, some temporal variables’ divergence was associated with genetic drift. We found support for ecological adaptation at the temporal but not the spectral level. Temporal patterns are correlated with micro- and macro-habitat usage and temperature stochasticity in ways that run against the AAH predictions, degrading signals more easily. These traits are likely to have evolved as an anti-predator strategy in conspicuous environments and low-density populations. Our results support a role of ecological selection, not excluding a likely role of sexual selection in the evolution of Tettigettalna calling songs, which should be further investigated in an integrative approach.