Similarity in G matrix structure among natural populations of Arabidopsis lyrata

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing [Formula: see text] matrices

Theory predicts that the additive genetic covariance ([Formula: see text]) matrix determines a population's short-term (in)ability to respond to directional selection-evolvability in the Hansen-Houle sense-which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

Genetic architecture of multiple mutualisms and mating system in Turnera ulmifolia

Plants often associate with multiple arthropod mutualists. These partners provide important services to their hosts, but multiple interactions can constrain a plant's ability to respond to complex, multivariate selection. Here, we quantified patterns of genetic variance and covariance among rewards for pollination, biotic defence and seed dispersal mutualisms in multiple populations of Turnera ulmifolia to better understand how the genetic architecture of multiple mutualisms might influence their evolution. We phenotyped plants cultivated from 17 Jamaican populations for several mutualism and mating system-related traits. We then fit genetic variance-covariance (G) matrices for the island metapopulation and the five largest individual populations. At the metapopulation level, we observed significant positive genetic correlations among stigma-anther separation, floral nectar production and extrafloral nectar production. These correlations have the potential to significantly constrain or facilitate the evolution of multiple mutualisms in T. ulmifolia and suggest that pollination, seed dispersal and defence mutualisms do not evolve independently. In particular, we found that positive genetic correlations between floral and extrafloral nectar production may help explain their stable coexistence in the face of physiological trade-offs and negative interactions between pollinators and ant bodyguards. Locally, we found only small differences in G among our T. ulmifolia populations, suggesting that geographic variation in G may not shape the evolution of multiple mutualisms.

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

PREMISE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

A conserved genetic architecture among populations of the maize progenitor, teosinte, was radically altered by domestication

We investigated the genetic architecture of maize domestication using a quantitative genetics approach. With multiple populations of teosinte and maize, we also compared the genetic architecture among populations within maize and teosinte. We showed that genetic architecture among populations within teosinte or maize is generally conserved, in contrast to the radical differences between teosinte and maize. Our results suggest that while selection drove changes in essentially all traits between teosinte and maize, selection is far less important for explaining domestication trait differences among populations within teosinte or maize.

Very little is known about how domestication was constrained by the quantitative genetic architecture of crop progenitors and how quantitative genetic architecture was altered by domestication. Yang et al. [C. J. Yang et al., Proc. Natl. Acad. Sci. U.S.A. 116, 5643–5652 (2019)] drew multiple conclusions about how genetic architecture influenced and was altered by maize domestication based on one sympatric pair of teosinte and maize populations. To test the generality of their conclusions, we assayed the structure of genetic variances, genetic correlations among traits, strength of selection during domestication, and diversity in genetic architecture within teosinte and maize. Our results confirm that additive genetic variance is decreased, while dominance genetic variance is increased, during maize domestication. The genetic correlations are moderately conserved among traits between teosinte and maize, while the genetic variance–covariance matrices (G-matrices) of teosinte and maize are quite different, primarily due to changes in the submatrix for reproductive traits. The inferred long-term selection intensities during domestication were weak, and the neutral hypothesis was rejected for reproductive and environmental response traits, suggesting that they were targets of selection during domestication. The G-matrix of teosinte imposed considerable constraint on selection during the early domestication process, and constraint increased further along the domestication trajectory. Finally, we assayed variation among populations and observed that genetic architecture is generally conserved among populations within teosinte and maize but is radically different between teosinte and maize. While selection drove changes in essentially all traits between teosinte and maize, selection explains little of the difference in domestication traits among populations within teosinte or maize.

Introduced populations of ragweed show as much evolutionary potential as native populations

Invasive species are a global economic and ecological problem. They also offer an opportunity to understand evolutionary processes in a colonizing context. The impacts of evolutionary factors, such as genetic variation, on the invasion process are increasingly appreciated, but there remain gaps in the empirical literature. The adaptive potential of populations can be quantified using genetic variance-covariance matrices (G), which encapsulate the heritable genetic variance in a population. Here, we use a multivariate Bayesian approach to assess the adaptive potential of invasive populations of ragweed (Ambrosia artemisiifolia), a serious allergen and agricultural weed. We compared several aspects of genetic architecture and the structure of G matrices between three native and three introduced populations, based on phenotypic data collected in a field common garden experiment. We found moderate differences in the quantitative genetic architecture among populations, but we did not find that introduced populations suffer from a limited adaptive potential or increased genetic constraint compared with native populations. Ragweed has an annual life history, is an obligate outcrosser, and produces very large numbers of seeds and pollen grains. These characteristics, combined with the significant additive genetic variance documented here, suggest ragweed will be able to respond quickly to selection pressures in both its native and introduced ranges.

The genetic architecture of sexual dimorphism in the moss Ceratodon purpureus

A central problem in evolutionary biology is to identify the forces that maintain genetic variation for fitness in natural populations. Sexual antagonism, in which selection favours different variants in males and females, can slow the transit of a polymorphism through a population or can actively maintain fitness variation. The amount of sexually antagonistic variation to be expected depends in part on the genetic architecture of sexual dimorphism, about which we know relatively little. Here, we used a multivariate quantitative genetic approach to examine the genetic architecture of sexual dimorphism in a scent-based fertilization syndrome of the moss Ceratodon purpureus. We found sexual dimorphism in numerous traits, consistent with a history of sexually antagonistic selection. The cross-sex genetic correlations (rmf) were generally heterogeneous with many values indistinguishable from zero, which typically suggests that genetic constraints do not limit the response to sexually antagonistic selection. However, we detected no differentiation between the female- and male-specific trait (co)variance matrices (Gf and Gm, respectively), meaning the evolution of sexual dimorphism may be constrained. The cross-sex cross-trait covariance matrix B contained both symmetric and asymmetric elements, indicating that the response to sexually antagonistic or sexually concordant selection, and the constraint to sexual dimorphism, are highly dependent on the traits experiencing selection. The patterns of genetic variances and covariances among these fitness components is consistent with partly sex-specific genetic architectures having evolved in order to partially resolve multivariate genetic constraints (i.e. sexual conflict), enabling the sexes to evolve towards their sex-specific multivariate trait optima.

Towards a comparative approach to the structure of animal personality variation

Latent personality traits underpinning observed behavioral variation have been studied in a great many species. However, a lack of standardized behavioral assays, coupled to a common reliance on inferring personality from a single, observed, behavioral trait makes it difficult to determine if, when, and how conclusions can be directly compared across taxa. Here, we estimate the among-individual (co)variance structure (ID) for a set of four behaviors expressed in an open field trial, putatively indicative of boldness, in seven species of small freshwater fish. We show that the ID matrices differ in terms of the total amount of variation present, and crucially the orientation, and as a consequence, biological interpretation of the first eigenvector. Specifically, loading of observed traits on the main axis of variation in ID matched a priori expectations for a shy-bold continuum in only three of the seven cases. Nonetheless, when the "shape" of the matrices was compared in higher dimensions, there was a high level of similarity among species, and weak evidence of phylogenetic signal. Our study highlights the present difficulty of trying to compare empirical inferences about specific personality traits across studies. However, it also shows how multivariate data collection and analysis allows the structure of behavioral variation to be quantitatively compared across populations or species without reliance on ambiguous verbal labels. This suggests that the field may have much to gain from greater uptake of phylogenetically informed comparative approaches when seeking to test evolutionary hypotheses about the origin and maintenance of personality variation.

Antagonistic selection and pleiotropy constrain the evolution of plant chemical defenses

When pleiotropy is present, genetic correlations may constrain the evolution of ecologically important traits. We used a quantitative genetics approach to investigate constraints on the evolution of secondary metabolites in a wild mustard, Boechera stricta. Much of the genetic variation in chemical composition of glucosinolates in B. stricta is controlled by a single locus, BCMA1/3. In a large-scale common garden experiment under natural conditions, we quantified fitness and glucosinolate profile in two leaf types and in fruits. We estimated genetic variances and covariances (the G-matrix) and selection on chemical profile in each tissue. Chemical composition of defenses was strongly genetically correlated between tissues. We found antagonistic selection between defense composition in leaves and fruits: compounds that were favored in leaves were disadvantageous in fruits. The positive genetic correlations and antagonistic selection led to strong constraints on the evolution of defenses in leaves and fruits. In a hypothetical population with no genetic variation at BCMA1/3, we found no evidence for genetic constraints, indicating that pleiotropy affecting chemical profile in multiple tissues drives constraints on the evolution of secondary metabolites.

The G-matrix Simulator Family: Software for Research and Teaching

Genetic variation plays a fundamental role in all models of evolution. For phenotypes composed of multiple quantitative traits, genetic variation is best quantified as additive genetic variances and covariances, as these values determine the rate and trajectory of evolution. Additive genetic variances and covariances are often summarized conveniently in the G-matrix, which has additive genetic variances for each trait on the diagonal and additive genetic covariances as its off-diagonal elements. The evolution of the G-matrix is an interesting topic in its own right, because the processes that affect trait means also affect the distribution of standing genetic variation, which, in turn, feeds back to affect the rate of change of trait means. Theoretical studies of the G-matrix have profitably employed simulation-based models because the topic is often too complex to yield meaningful analytical results. Here, we present a series of G-matrix simulation software packages, which have emerged from about 15 years of research on this topic. These simulation models are useful for research and for building intuition regarding the evolution of the G-matrix under a wide variety of circumstances. A tutorial and source code also provide a foundation upon which future models can be built. These tools will be useful to students as well as researchers.

Local adaptation and ecological differentiation under selection, migration, and drift in Arabidopsis lyrata

How the balance between selection, migration, and drift influences the evolution of local adaptation has been under intense theoretical scrutiny. Yet, empirical studies that relate estimates of local adaptation to quantification of gene flow and effective population sizes have been rare. Here, we conducted a reciprocal transplant trial, a common garden trial, and a whole-genome-based demography analysis to examine these effects among Arabidopsis lyrata populations from two altitudinal gradients in Norway. Demography simulations indicated that populations within the two gradients are connected by gene flow (0.1 < 4Ne m < 11) and have small effective population sizes (Ne <  6000), suggesting that both migration and drift can counteract local selection. However, the three-year field experiments showed evidence of local adaptation at the level of hierarchical multiyear fitness, attesting to the strength of differential selection. In the lowland habitat, local superiority was associated with greater fecundity, while viability accounted for fitness differences in the alpine habitat. We also demonstrate that flowering time differentiation has contributed to adaptive divergence between these locally adapted populations. Our results show that despite the estimated potential of gene flow and drift to hinder differentiation, selection among these A. lyrata populations has resulted in local adaptation.

The genetic variance but not the genetic covariance of life-history traits changes towards the north in a time-constrained insect

Seasonal time constraints are usually stronger at higher than lower latitudes and can exert strong selection on life-history traits and the correlations among these traits. To predict the response of life-history traits to environmental change along a latitudinal gradient, information must be obtained about genetic variance in traits and also genetic correlation between traits, that is the genetic variance-covariance matrix, G. Here, we estimated G for key life-history traits in an obligate univoltine damselfly that faces seasonal time constraints. We exposed populations to simulated native temperatures and photoperiods and common garden environmental conditions in a laboratory set-up. Despite differences in genetic variance in these traits between populations (lower variance at northern latitudes), there was no evidence for latitude-specific covariance of the life-history traits. At simulated native conditions, all populations showed strong genetic and phenotypic correlations between traits that shaped growth and development. The variance-covariance matrix changed considerably when populations were exposed to common garden conditions compared with the simulated natural conditions, showing the importance of environmentally induced changes in multivariate genetic structure. Our results highlight the importance of estimating variance-covariance matrixes in environments that mimic selection pressures and not only trait variances or mean trait values in common garden conditions for understanding the trait evolution across populations and environments.

Conserved G-matrices of morphological and life-history traits among continental and island blue tit populations

The genetic variance-covariance matrix (G-matrix) summarizes the genetic architecture of multiple traits. It has a central role in the understanding of phenotypic divergence and the quantification of the evolutionary potential of populations. Laboratory experiments have shown that G-matrices can vary rapidly under divergent selective pressures. However, because of the demanding nature of G-matrix estimation and comparison in wild populations, the extent of its spatial variability remains largely unknown. In this study, we investigate spatial variation in G-matrices for morphological and life-history traits using long-term data sets from one continental and three island populations of blue tit (Cyanistes caeruleus) that have experienced contrasting population history and selective environment. We found no evidence for differences in G-matrices among populations. Interestingly, the phenotypic variance-covariance matrices (P) were divergent across populations, suggesting that using P as a substitute for G may be inadequate. These analyses also provide the first evidence in wild populations for additive genetic variation in the incubation period (that is, the period between last egg laid and hatching) in all four populations. Altogether, our results suggest that G-matrices may be stable across populations inhabiting contrasted environments, therefore challenging the results of previous simulation studies and laboratory experiments.