How to quantify (the response to) sexual selection on traits

Natural selection operates via fitness components like mating success, fecundity, and longevity, which can be understood as intermediaries in the causal process linking traits to fitness. In particular, sexual selection occurs when traits influence mating or fertilization success, which, in turn, influences fitness. We show how to quantify both these steps in a single path analysis, leading to better estimates of the strength of sexual selection. Our model controls for confounding variables, such as body size or condition, when estimating the relationship between mating and reproductive success. Correspondingly, we define the Bateman gradient and the Jones index using partial rather than simple regressions, which better captures how they are commonly interpreted. The model can be applied both to purely phenotypic data and to quantitative genetic parameters estimated using information on relatedness. The phenotypic approach breaks down selection differentials into a sexually selected and a “remainder” component. The quantitative genetic approach decomposes the estimated evolutionary response to selection analogously. We apply our method to analyze sexual selection in male dusky pipefish, Syngnathus floridae, and in two simulated datasets. We highlight conceptual and statistical limitations of previous path‐based approaches, which can lead to substantial misestimation of sexual selection.     

SELECTION AND EVOLUTION OF CAUSALLY COVARYING TRAITS

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait‐fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining “extended” selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.     

Variation,selection and evolution of function-valued traits

We describe an emerging framework for understanding variation, selection and evolution of phenotypic traits that are mathematical functions. We use one specific empirical example – thermal performance curves (TPCs) for growth rates of caterpillars – to demonstrate how models for function-valued traits are natural extensions of more familiar, multivariate models for correlated, quantitative traits. We emphasize three main points. First, because function-valued traits are continuous functions, there are important constraints on their patterns of variation that are not captured by multivariate models. Phenotypic and genetic variation in function-valued traits can be quantified in terms of variance-covariance functions and their associated eigenfunctions: we illustrate how these are estimated as well as their biological interpretations for TPCs. Second, selection on a function-valued trait is itself a function, defined in terms of selection gradient functions. For TPCs, the selection gradient describes how the relationship between an organism's performance and its fitness varies as a function of its temperature. We show how the form of the selection gradient function for TPCs relates to the frequency distribution of environmental states (caterpillar temperatures) during selection. Third, we can predict evolutionary responses of function-valued traits in terms of the genetic variance-covariance and the selection gradient functions. We illustrate how non-linear evolutionary responses of TPCs may occur even when the mean phenotype and the selection gradient are themselves linear functions of temperature. Finally, we discuss some of the methodological and empirical challenges for future studies of the evolution of function-valued traits.     

Does natural selection promote population divergence? A comparative analysis of population structure using amplified fragment length polymorphism markers and quantitative traits

Divergent natural selection is considered an important force in plant evolution leading to phenotypic differentiation between populations exploiting different environments. Extending an earlier greenhouse study of population differentiation in the selfing annual plant Senecio vulgaris, we estimated the degree of population divergence in several quantitative traits related to growth and life history and compared these estimates with those based on presumably neutral molecular markers (amplified fragment length polymorphisms; AFLPs). This approach allowed us to disentangle the effects of divergent selection from that of other evolutionary forces (e.g. genetic drift). Five populations were examined from each of two habitat types (ruderal and agricultural habitats). We found a high proportion of total genetic variance to be among populations, both for AFLP markers (phiST = 0.49) and for quantitative traits (range of QST: 0.26-0.77). There was a strong correlation between molecular and quantitative genetic differentiation between pairs of populations (Mantel's r = 0.59). However, estimates of population differentiation in several quantitative traits exceeded the neutral expectation (estimated from AFLP data), suggesting that divergent selection contributed to phenotypic differentiation, especially between populations from ruderal and agricultural habitats. Estimates of within-population variation in AFLP markers and quantitative genetic were poorly correlated, indicating that molecular marker data may be of limited value to predict the evolutionary potential of populations of S. vulgaris.     

A general model of the relation between phenotypic selection and genetic response

The phenotypic view of selection assumes that genetic responses can be predicted from selective forces and heritability — or in the classical quantitative genetic equation: R = h²S. However, data on selection in bird populations show that often no selection responses is found, despite consistent selective forces on phenotypes and significant heritable variation. Such discrepancies may arise due to the assumption that selection only acts on observed phenotypes. We derive a general selection equation that takes into account the possibility that some relevant (internal or external) traits are not measured. This equation shows that the classic equation applies if selection directly acts on the measured, phenotypic traits. This is not the case when, for instance, there are unknown internal genetic trade-offs, or unknown common environmental factors affecting both trait and fitness. In such cases, any relationship between phenotypic selection and genetic response is possible. Fortunately, the classical model can be tested by comparing phenotypic and genetic covariances between traits and fitness; an indication that important internal or external traits are missing can thus be obtained. Such an analysis was indeed found in the literature; for selection on fledging weight in Great Tits it yielded valuable extra information.     

driftsel: an R package for detecting signals of natural selection in quantitative traits

Approaches and tools to differentiate between natural selection and genetic drift as causes of population differentiation are of frequent demand in evolutionary biology. Based on the approach of Ovaskainen et al. (2011), we have developed an R package (driftsel ) that can be used to differentiate between stabilizing selection, diversifying selection and random genetic drift as causes of population differentiation in quantitative traits when neutral marker and quantitative genetic data are available. Apart from illustrating the use of this method and the interpretation of results using simulated data, we apply the package on data from three‐spined sticklebacks (Gasterosteus aculeatus) to highlight its virtues. driftsel can also be used to perform usual quantitative genetic analyses in common‐garden study designs.     

Predicting evolutionary responses to selection on polyandry in the wild: additive genetic covariances with female extra-pair reproduction

The evolutionary forces that underlie polyandry, including extra-pair reproduction (EPR) by socially monogamous females, remain unclear. Selection on EPR and resulting evolution have rarely been explicitly estimated or predicted in wild populations, and evolutionary predictions are vulnerable to bias due to environmental covariances and correlated selection through unmeasured traits. However, evolutionary responses to (correlated) selection on any trait can be directly predicted as additive genetic covariances (cov_A) with appropriate components of relative fitness. I used comprehensive life-history, paternity and pedigree data from song sparrows (Melospiza melodia) to estimate cov_A between a female''s liability to produce extra-pair offspring and two specific fitness components: relative annual reproductive success (ARS) and survival to recruitment. All three traits showed non-zero additive genetic variance. Estimates of cov_A were positive, predicting evolution towards increased EPR, but 95% credible intervals overlapped zero. There was therefore no conclusive prediction of evolutionary change in EPR due to (correlated) selection through female ARS or recruitment. Negative environmental covariance between EPR and ARS would have impeded evolutionary prediction from phenotypic selection differentials. These analyses demonstrate an explicit quantitative genetic approach to predicting evolutionary responses to components of (correlated) selection on EPR that should be unbiased by environmental covariances and unmeasured traits.     

Multiple-Trait Genomic Selection Methods Increase Genetic Value Prediction Accuracy

Genetic correlations between quantitative traits measured in many breeding programs are pervasive. These correlations indicate that measurements of one trait carry information on other traits. Current single-trait (univariate) genomic selection does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e., GBLUP, BayesA, and BayesCπ) were presented and compared to univariate models using simulated and real quantitative traits controlled by different genetic architectures. We also extended BayesA with fixed hyperparameters to a full hierarchical model that estimated hyperparameters and BayesCπ to impute missing phenotypes. We found that optimal marker-effect variance priors depended on the genetic architecture of the trait so that estimating them was beneficial. We showed that the prediction accuracy for a low-heritability trait could be significantly increased by multivariate genomic selection when a correlated high-heritability trait was available. Further, multiple-trait genomic selection had higher prediction accuracy than single-trait genomic selection when phenotypes are not available on all individuals and traits. Additional factors affecting the performance of multiple-trait genomic selection were explored.     

EXPERIMENTAL EVIDENCE FOR THE EVOLUTION OF INDIRECT GENETIC EFFECTS: CHANGES IN THE INTERACTION EFFECT COEFFICIENT,PSI (Ψ), DUE TO SEXUAL SELECTION

Indirect genetics effects (IGEs)—when the genotype of one individual affects the phenotypic expression of a trait in another—may alter evolutionary trajectories beyond that predicted by standard quantitative genetic theory as a consequence of genotypic evolution of the social environment. For IGEs to occur, the trait of interest must respond to one or more indicator traits in interacting conspecifics. In quantitative genetic models of IGEs, these responses (reaction norms) are termed interaction effect coefficients and are represented by the parameter psi (Ψ). The extent to which Ψ exhibits genetic variation within a population, and may therefore itself evolve, is unknown. Using an experimental evolution approach, we provide evidence for a genetic basis to the phenotypic response caused by IGEs on sexual display traits in Drosophila serrata. We show that evolution of the response is affected by sexual but not natural selection when flies adapt to a novel environment. Our results indicate a further mechanism by which IGEs can alter evolutionary trajectories—the evolution of interaction effects themselves.     

On the assignment of fitness to parents and offspring: whose fitness is it and when does it matter?

There has been a long‐standing conceptual debate over the legitimacy of assigning components of offspring fitness to parents for purposes of evolutionary analysis. The benefits and risks inherent in assigning fitness of offspring to parents have been given primarily as verbal arguments and no explicit theoretical analyses have examined quantitatively how the assignment of fitness can affect evolutionary inferences. Using a simple quantitative genetic model, we contrast the conclusions drawn about how selection acts on a maternal character when components of offspring fitness (such as early survival) are assigned to parents vs. when they are assigned directly to the individual offspring. We find that there are potential shortcomings of both possible assignments of fitness. In general, whenever there is a genetic correlation between the parental and direct effects on offspring fitness, assigning components of offspring fitness to parents yields incorrect dynamical equations and may even lead to incorrect conclusions about the direction of evolution. Assignment of offspring fitness to parents may also produce incorrect estimates of selection whenever environmental variation contributes to variance of the maternal trait. Whereas assignment of offspring fitness to the offspring avoids these potential problems, it introduces the possible problem of missing components of kin selection provided by the mother, which may not be detected in selection analyses. There are also certain conditions where either model can be appropriate because assignment of offspring fitness to parents may yield the same dynamical equations as assigning offspring fitness directly to offspring. We discuss these implications of the alternative assignments of fitness for modelling, selection analysis and experimentation in evolutionary biology.     

Quantitative genetic versions of Hamilton's rule with empirical applications

Hamilton''s theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton''s perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton''s rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton''s rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton''s rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution.     

Rapid changes in genetic architecture of behavioural syndromes following colonization of a novel environment

Behavioural syndromes, that is correlated behaviours, may be a result from adaptive correlational selection, but in a new environmental setting, the trait correlation might act as an evolutionary constraint. However, knowledge about the quantitative genetic basis of behavioural syndromes, and the stability and evolvability of genetic correlations under different ecological conditions, is limited. We investigated the quantitative genetic basis of correlated behaviours in the freshwater isopod Asellus aquaticus. In some Swedish lakes, A. aquaticus has recently colonized a novel habitat and diverged into two ecotypes, presumably due to habitat‐specific selection from predation. Using a common garden approach and animal model analyses, we estimated quantitative genetic parameters for behavioural traits and compared the genetic architecture between the ecotypes. We report that the genetic covariance structure of the behavioural traits has been altered in the novel ecotype, demonstrating divergence in behavioural correlations. Thus, our study confirms that genetic correlations behind behaviours can change rapidly in response to novel selective environments.     

Natural selection, evolvability and bias due to environmental covariance in the field in an annual plant

Estimates of the form and magnitude of natural selection based on phenotypic relationships between traits and fitness measures can be biased when environmental factors influence both relative fitness and phenotypic trait values. I quantified genetic variances and covariances, and estimated linear and quadratic selection coefficients, for seven traits of an annual plant grown in the field. For replicates of 50 paternal half-sib families, coefficients of selection were calculated both for individual phenotypic values of the traits and for half-sib family mean values. The potential for evolutionary response was supported by significant heritability and phenotypic directional selection for several traits but contradicted by the absence of significant genetic variation for fitness estimates and evidence of bias in phenotypic selection coefficients due to environmental covariance for at least two of the traits analysed. Only studies of a much wider range of organisms and traits will reveal the frequency and extent of such bias.     

Stabilizing selection and adaptive evolution in a combination of two traits in an arctic ungulate

Stabilizing selection is thought to be common in wild populations and act as one of the main evolutionary mechanisms, which constrain phenotypic variation. When multiple traits interact to create a combined phenotype, correlational selection may be an important process driving adaptive evolution. Here, we report on phenotypic selection and evolutionary changes in two natal traits in a semidomestic population of reindeer (Rangifer tarandus) in northern Finland. The population has been closely monitored since 1969, and detailed data have been collected on individuals since they were born. Over the length of the study period (1969–2015), we found directional and stabilizing selection toward a combination of earlier birth date and heavier birth mass with an intermediate optimum along the major axis of the selection surface. In addition, we demonstrate significant changes in mean traits toward earlier birth date and heavier birth mass, with corresponding genetic changes in breeding values during the study period. Our results demonstrate evolutionary changes in a combination of two traits, which agree closely with estimated patterns of phenotypic selection. Knowledge of the selective surface for combinations of genetically correlated traits are vital to predict how population mean phenotypes and fitness are affected when environments change.     

Opposite responses to selection and where to find them

We generally expect traits to evolve in the same direction as selection. However, many organisms possess traits that appear to be costly for individuals, while plant and animal breeding experiments reveal that selection may lead to no response or even negative responses to selection. We formalize both of these instances as cases of “opposite responses to selection.” Using quantitative genetic models for the response to selection, we outline when opposite responses to selection should be expected. These typically occur when social selection opposes direct selection, when individuals interact with others less related to them than a random member of the population, and if the genetic covariance between direct and indirect effects is negative. We discuss the likelihood of each of these occurring in nature and therefore summarize how frequent opposite responses to selection are likely to be. This links several evolutionary phenomena within a single framework.     

Evolutionary dynamics of a sexual ornament in the house sparrow (Passer domesticus): the role of indirect selection within and between sexes

The relative contribution of sexual and natural selection to evolution of sexual ornaments has rarely been quantified under natural conditions. In this study we used a long-term dataset of house sparrows in which parents and offspring were matched genetically to estimate the within- and across-sex genetic basis for variation and covariation among morphological traits. By applying two-sex multivariate "animal models" to estimate genetic parameters, we estimated evolutionary changes in a male sexual ornament, badge size, from the contribution of direct and indirect selection on correlated traits within males and females, after accounting for overlapping generations and age-structure. Indirect natural selection on genetically correlated traits in males and females was the major force causing evolutionary change in the male ornament. Thus, natural selection on female morphology may cause indirect evolutionary changes in male ornaments. We observed however no directional phenotypic change in the ornament size of one-year-old males during the study period. On the other hand, changes were recorded in other morphological characters of both sexes. Our analyses of evolutionary dynamics in sexual characters require application of appropriate two-sex models to account for how selection on correlated traits in both sexes affects the evolutionary outcome of sexual selection.     

ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION

Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian‐MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson–Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses.     

PHENOTYPIC SELECTION IN AN ARTIFICIAL POPULATION OF IMPATIENS PALLIDA: THE IMPORTANCE OF THE INVISIBLE FRACTION

Multiple-regression techniques for measuring phenotypic selection have been used in a large number of recent field studies. One benefit of this technique is its ability to discern the direct action of selection on traits by removing effects of correlated traits. However, covariation among traits expressed at different stages in an organism's life history is often poorly estimated because individuals that die before reaching adulthood cannot be measured as adults. Accurate estimates of trait covariances are necessary for the correct interpretation of the direct action of selection on a trait. If phenotypic characters expressed at different life-history stages are of interest, and mortality occurs between stages, the components of the selection model will be biased by not including those individuals that died (the “invisible fraction”).     

Evolutionary potential of a widespread clonal grass under changing climate

Adaptive responses are probably the most effective long‐term responses of populations to climate change, but they require sufficient evolutionary potential upon which selection can act. This requires high genetic variance for the traits under selection and low antagonizing genetic covariances between the different traits. Evolutionary potential estimates are still scarce for long‐lived, clonal plants, although these species are predicted to dominate the landscape with climate change. We studied the evolutionary potential of a perennial grass, Festuca rubra, in western Norway, in two controlled environments corresponding to extreme environments in natural populations: cold–dry and warm–wet, the latter being consistent with the climatic predictions for the country. We estimated genetic variances, covariances, selection gradients and response to selection for a wide range of growth, resource acquisition and physiological traits, and compared their estimates between the environments. We showed that the evolutionary potential of F. rubra is high in both environments, and genetic covariances define one main direction along which selection can act with relatively few constraints to selection. The observed response to selection at present is not sufficient to produce genotypes adapted to the predicted climate change under a simple, space for time substitution model. However, the current populations contain genotypes which are pre‐adapted to the new climate, especially for growth and resource acquisition traits. Overall, these results suggest that the present populations of the long‐lived clonal plant may have sufficient evolutionary potential to withstand long‐term climate changes through adaptive responses.     

Evolution of quantitative traits in the wild: mind the ecology

Recent advances in the quantitative genetics of traits in wild animal populations have created new interest in whether natural selection, and genetic response to it, can be detected within long-term ecological studies. However, such studies have re-emphasized the fact that ecological heterogeneity can confound our ability to infer selection on genetic variation and detect a population''s response to selection by conventional quantitative genetics approaches. Here, I highlight three manifestations of this issue: counter gradient variation, environmentally induced covariance between traits and the correlated effects of a fluctuating environment. These effects are symptomatic of the oversimplifications and strong assumptions of the breeder''s equation when it is applied to natural populations. In addition, methods to assay genetic change in quantitative traits have overestimated the precision with which change can be measured. In the future, a more conservative approach to inferring quantitative genetic response to selection, or genomic approaches allowing the estimation of selection intensity and responses to selection at known quantitative trait loci, will provide a more precise view of evolution in ecological time.