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.     

THE MEASUREMENT OF SELECTION ON QUANTITATIVE TRAITS: BIASES DUE TO ENVIRONMENTAL COVARIANCES BETWEEN TRAITS AND FITNESS

The use of regression techniques for estimating the direction and magnitude of selection from measurements on phenotypes has become widespread in field studies. A potential problem with these techniques is that environmental correlations between fitness and the traits examined may produce biased estimates of selection gradients. This report demonstrates that the phenotypic covariance between fitness and a trait, used as an estimate of the selection differential in estimating selection gradients, has two components: a component induced by selection itself and a component due to the effect of environmental factors on fitness. The second component is shown to be responsible for biases in estimates of selection gradients. The use of regressions involving genotypic and breeding values instead of phenotypic values can yield estimates of selection gradients that are not biased by environmental covariances. Statistical methods for estimating the coefficients of such regressions, and for testing for biases in regressions involving phenotypic values, are described.     

COMPARING STRENGTHS OF DIRECTIONAL SELECTION: HOW STRONG IS STRONG?

The fundamental equation in evolutionary quantitative genetics, the Lande equation, describes the response to directional selection as a product of the additive genetic variance and the selection gradient of trait value on relative fitness. Comparisons of both genetic variances and selection gradients across traits or populations require standardization, as both are scale dependent. The Lande equation can be standardized in two ways. Standardizing by the variance of the selected trait yields the response in units of standard deviation as the product of the heritability and the variance-standardized selection gradient. This standardization conflates selection and variation because the phenotypic variance is a function of the genetic variance. Alternatively, one can standardize the Lande equation using the trait mean, yielding the proportional response to selection as the product of the squared coefficient of additive genetic variance and the mean-standardized selection gradient. Mean-standardized selection gradients are particularly useful for summarizing the strength of selection because the mean-standardized gradient for fitness itself is one, a convenient benchmark for strong selection. We review published estimates of directional selection in natural populations using mean-standardized selection gradients. Only 38 published studies provided all the necessary information for calculation of mean-standardized gradients. The median absolute value of multivariate mean-standardized gradients shows that selection is on average 54% as strong as selection on fitness. Correcting for the upward bias introduced by taking absolute values lowers the median to 31%, still very strong selection. Such large estimates clearly cannot be representative of selection on all traits. Some possible sources of overestimation of the strength of selection include confounding environmental and genotypic effects on fitness, the use of fitness components as proxies for fitness, and biases in publication or choice of traits to study.     

Testing for environmentally induced bias in phenotypic estimates of natural selection: theory and practice

Measuring natural selection has been a fundamental goal of evolutionary biology for more than a century, and techniques developed in the last 20 yr have provided relatively simple means for biologists to do so. Many of these techniques, however, share a common limitation: when applied to phenotypic data, environmentally induced covariances between traits and fitness can lead to biased estimates of selection and misleading predictions about evolutionary change. Utilizing estimates of breeding values instead of phenotypic data with these methods can eliminate environmentally induced bias, although this approach is more difficult to implement. Despite this potential limitation to phenotypic methods and the availability of a potential solution, little empirical evidence exists on the extent of environmentally induced bias in phenotypic estimates of selection. In this article, we present a method for detecting bias in phenotypic estimates of selection and demonstrate its use with three independent data sets. Nearly 25% of the phenotypic selection gradients estimated from our data are biased by environmental covariances. We find that bias caused by environmental covariances appears mainly to affect quantitative estimates of the strength of selection based on phenotypic data and that the magnitude of these biases is large. As our estimates of selection are based on data from spatially replicated field experiments, we suggest that our findings on the prevalence of bias caused by environmental covariances are likely to be conservative.     

MEASURING NATURAL SELECTION ON PHENOTYPIC PLASTICITY

To understand natural selection we need to integrate its measure across environments. We present a method for measuring phenotypic selection that combines the potential for both environmental variation and phenotypic plasticity. The method uses path analysis and a measure of selection that is analogous to selection on breeding values. For individuals growing in alternative environments, paths are created that represent potential changes in the environment. The probabilities for these changes are then multiplied by the path coefficients to calculate selection coefficients. Selection on plasticity is measured as the difference in selection within each environment. We illustrate these methods using data on selection in an experimental population of Arabidopsis thaliana. Individuals from 36 families were grown in one of four environments, a factorial combination of shaded/open and early/late shading. For final height of the inflorescence, there was positive selection in both the open and shaded environments and negative selection on plasticity of height. For bolting time, there was also positive selection in both environments, but no selection on plasticity. We show how to use this information to examine how selection would change with changes in environmental frequencies and their transition probabilities. These methods can be expanded to encompass continuous traits and continuous environments as well as other complexities of natural 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.     

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.     

Synthetic analyses of phenotypic selection in natural populations: lessons, limitations and future directions

There are now thousands of estimates of phenotypic selection in natural populations, resulting in multiple synthetic reviews of these data. Here we consider several major lessons and limitations emerging from these syntheses, and how they may guide future studies of selection in the wild. First, we review past analyses of the patterns of directional selection. We present new meta-analyses that confirm differences in the direction and magnitude of selection for different types of traits and fitness components. Second, we describe patterns of temporal and spatial variation in directional selection, and their implications for cumulative selection and directional evolution. Meta-analyses suggest that sampling error contributes importantly to observed temporal variation in selection, and indicate that evidence for frequent temporal changes in the direction of selection in natural populations is limited. Third, we review the apparent lack of evidence for widespread stabilizing selection, and discuss biological and methodological explanations for this pattern. Finally, we describe how sampling error, statistical biases, choice of traits, fitness measures and selection metrics, environmental covariance and other factors may limit the inferences we can draw from analyses of selection coefficients. Current standardized selection metrics based on simple parametric statistical models may be inadequate for understanding patterns of non-linear selection and complex fitness surfaces. We highlight three promising areas for expanding our understanding of selection in the wild: (1) field studies of stabilizing selection, selection on physiological and behavioral traits, and the ecological causes of selection; (2) new statistical models and methods that connect phenotypic variation to population demography and selection; and (3) availability of the underlying individual-level data sets from past and future selection studies, which will allow comprehensive modeling of selection and fitness variation within and across systems, rather than meta-analyses of standardized selection metrics.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

VISUALIZING MULTIVARIATE SELECTION

Recent developments in quantitative-genetic theory have shown that natural selection can be viewed as the multivariate relationship between fitness and phenotype. This relationship can be described by a multidimensional surface depicting fitness as a function of phenotypic traits. We examine the connection between this surface and the coefficients of phenotypic selection that can be estimated by multiple regression and show how the interpretation of multivariate selection can be facilitated through the use of the method of canonical analysis. The results from this analysis can be used to visualize the surface implied by a set of selection coefficients. Such a visualization provides a compact summary of selection coefficients, can aid in the comparison of selection surfaces, and can help generate testable hypotheses as to the adaptive significance of the traits under study. Further, we discuss traditional definitions of directional, stabilizing, and disruptive selection and conclude that selection may be more usefully classified into two general modes, directional and nonlinear selection, with stabilizing and disruptive selection as special cases of nonlinear selection.     

Using path analysis to measure natural selection

We expand current methods for calculating selection coefficients using path analysis and demonstrate how to analyse nonlinear selection. While this incorporation is a straightforward extension of current procedures, the rules for combining these traits to calculate selection coefficients can be complex. We demonstrate our method with an analysis of selection in an experimental population of Arabidopsis thaliana consisting of 289 individuals. Multiple regression analyses found positive directional selection and positive nonlinear selection only for inflorescence height. In contrast, the path analyses also revealed positive directional selection for number of rosette leaves and positive nonlinear selection for leaf number and time of inflorescence initiation. These changes in conclusions came about because indirect selection was converted into direct selection with the change in causal structure. Path analysis has great promise for improving our understanding of natural selection but must be used with caution since coefficient estimates depend on the assumed causal structure.     

Estimating selection on neonatal traits in red deer using elasticity path analysis

Van Tienderen recently published a method that links selection gradients between a phenotypic trait and multiple fitness components with the effects of these fitness components on the population growth rate (mean absolute fitness). The method allows selection to be simultaneously estimated across multiple fitness components in a population dynamic framework. In this paper we apply the method to a population of red deer living in the North Block of the Isle of Rum, Scotland. We show that (1) selection on birth date and birth weight can operate through multiple fitness components simultaneously; (2) our estimates of the response to selection are consistent with the observed change in trait values that we cannot explain with environmental and phenotypic covariates; (3) selection on both traits has fluctuated over the course of the study; (4) selection operates through different fitness components in different years; and (5) no environmental covariates correlate with selection because different fitness components respond to density and climatic variation in contrasting ways.     

MEASUREMENTS OF NATURAL SELECTION ON FLORAL TRAITS IN WILD RADISH (RAPHANUS RAPHANISTRUM). II. SELECTION THROUGH LIFETIME MALE AND TOTAL FITNESS

It has often been suggested that selection on floral traits in hermaphroditic plants should occur primarily through differences in male fitness. However, measurements of selection on floral traits through differences in lifetime male fitness have been lacking. We measured selection on a variety of wild radish floral traits using lifetime male fitness measures derived from genetic paternity analysis. These male fitness estimates were then combined with estimates of lifetime female fitness of the same plants to produce measurements of selection based on lifetime total fitness. Contrary to the prediction above, there was no strong evidence for selection on floral morphology through male fitness differences in any of the three years of the study, but there was strong selection for increased flower size through female fitness differences in one year. The main determinant of both male and female fitness in all years was flower number; this lead to moderately positive correlations between male and female fitness in all three years.     

Assortment and the analysis of natural selection on social traits

A central problem in evolutionary biology is to determine whether and how social interactions contribute to natural selection. A key method for phenotypic data is social selection analysis, in which fitness effects from social partners contribute to selection only when there is a correlation between the traits of individuals and their social partners (nonrandom phenotypic assortment). However, there are inconsistencies in the use of social selection that center around the measurement of phenotypic assortment. Here, we use data analysis and simulations to resolve these inconsistencies, showing that: (i) not all measures of assortment are suitable for social selection analysis; and (ii) the interpretation of assortment, and how to detect nonrandom assortment, will depend on the scale at which it is measured. We discuss links to kin selection theory and provide a practical guide for the social selection approach.     

Antagonistic multilevel selection on size and architecture in variable density settings

In some ecological settings, an individual's fitness depends on both its own phenotype (individual-level selection) as well as the phenotype of the individuals with which it interacts (group-level selection). Using contextual analysis to measure multilevel selection in experimental stands of Arabidopsis thaliana, we detected significant linear selection that reversed across individual versus group levels for two composite phenotypic traits, "size" and "elongation." In both cases, selection at the individual level acted to increase values of these traits, presumably due to their positive effect on resource acquisition. Group selection favored decreased values of the same traits. Nonlinear selection was weak but significant in several cases, including stabilizing selection on developmental rate; individuals with very rapid development likely had lower than average fitness due to their reduced resource level at reproduction, while very delayed reproduction may have resulted in lower fitness if prolonged competition for resources reduced overall environmental quality and fitness of all individuals in a group. Under this scenario, stabilizing selection on individual traits is evidence of selection at the group level. Significant density-dependent selection suggests that a threshold density must be reached before group selection acts. Below this threshold, selection at the individual level affects phenotypic evolution more strongly than group selection. A second experiment measured multilevel selection in progeny stands of the original experimental plants. Multilevel selection again acted antagonistically on a composite trait that included size and elongation as well as on an architectural trait, branch production. The magnitude of individual versus group selection was relatively similar in the progeny generation, and the observed balance of individual versus group selection across densities is generally consistent with the hypotheses that multilevel selection can contribute to phenotypic evolution and to important demographic phenomena, including soft selection and the "law of constant yield."     

LOGISTIC REGRESSION FOR EMPIRICAL STUDIES OF MULTIVARIATE SELECTION

Understanding the mechanics of adaptive evolution requires not only knowing the quantitative genetic bases of the traits of interest but also obtaining accurate measures of the strengths and modes of selection acting on these traits. Most recent empirical studies of multivariate selection have employed multiple linear regression to obtain estimates of the strength of selection. We reconsider the motivation for this approach, paying special attention to the effects of nonnormal traits and fitness measures. We apply an alternative statistical method, logistic regression, to estimate the strength of selection on multiple phenotypic traits. First, we argue that the logistic regression model is more suitable than linear regression for analyzing data from selection studies with dichotomous fitness outcomes. Subsequently, we show that estimates of selection obtained from the logistic regression analyses can be transformed easily to values that directly plug into equations describing adaptive microevolutionary change. Finally, we apply this methodology to two published datasets to demonstrate its utility. Because most statistical packages now provide options to conduct logistic regression analyses, we suggest that this approach should be widely adopted as an analytical tool for empirical studies of multivariate selection.     

Evolution in stressful environments II: adaptive value and costs of plasticity in response to low light in Sinapis arvensis

Plants possess a remarkable capacity to alter their phenotype in response to the highly heterogeneous light conditions they commonly encounter in natural environments. In the present study with the weedy annual plant Sinapis arvensis, we (a) tested for the adaptive value of phenotypic plasticity in morphological and life history traits in response to low light and (b) explored possible fitness costs of plasticity. Replicates of 31 half-sib families were grown individually in the greenhouse under full light and under low light (40% of ambient) imposed by neutral shade cloth. Low light resulted in a large increase in hypocotyl length and specific leaf area (SLA), a reduction in juvenile biomass and a delayed onset of flowering. Phenotypic selection analysis within each light environment revealed that selection favoured large SLA under low light, but not under high light, suggesting that the observed increase in SLA was adaptive. In contrast, plasticity in the other traits measured was maladaptive (i.e. in the opposite direction to that favoured by selection in the low light environment). We detected significant additive genetic variance in plasticity in most phenotypic traits and in fitness (number of seeds). Using genotypic selection gradient analysis, we found that families with high plasticity in SLA had a lower fitness than families with low plasticity, when the effect of SLA on fitness was statistically kept constant. This indicates that plasticity in SLA incurred a direct fitness cost. However, a cost of plasticity was only expressed under low light, but not under high light. Thus, models on the evolution of phenotypic plasticity will need to incorporate plasticity costs that vary in magnitude depending on environmental conditions.     

Measuring Natural Selection on Proportional Traits: Comparisons of Three Types of Selection Estimates for Resistance and Susceptibility to Herbivore Damage

To compare the strength of natural selection on different traits and in different species, evolutionary biologists typically estimate selection differentials and gradients in standardized units. Measuring selection differentials and gradients in standard deviation units or mean-standardized units facilitates such comparisons by converting estimates with potentially varied units to a common scale. In this note, I compare the performance of variance- and mean-standardized selection differentials and gradients for a unique and biologically important class of traits: proportional traits, that can only vary between zero and one, and their complements (1 minus the trait) using simple algebra and analysis of data from a field-study using morning glories. There is a systematic, mathematical relationship between unstandardized and variance-standardized selection gradients for proportional traits and their complements, but such a general relationship is lacking for mean-standardized gradients, potentially leading investigators to mistakenly conclude that a proportional change in a trait would have little effect on fitness. Despite this potential limitation, mean-standardized selection differentials and gradients represent a useful tool for studying natural selection on proportional traits, because by definition they measure how proportional changes in the mean of a trait lead to proportional changes in relative fitness.Co-ordinating editor: I. Olivieri     

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.     

Power and potential bias in field studies of natural selection

The advent of multiple regression analyses of natural selection has facilitated estimates of both the direct and indirect effects of selection on many traits in numerous organisms. However, low power in selection studies has possibly led to a bias in our assessment of the levels of selection shaping natural populations. Using calculations and simulations based on the statistical properties of selection coefficients, we find that power to detect total selection (the selection differential) depends on sample size and the strength of selection relative to the opportunity of selection. The power of detecting direct selection (selection gradients) is more complicated and depends on the relationship between the correlation of each trait and fitness and the pattern of correlation among traits. In a review of 298 previously published selection differentials, we find that most studies have had insufficient power to detect reported levels of selection acting on traits and that, in general, the power of detecting weak levels of selection is low given current study designs. We also find that potential publication bias could explain the trend that reported levels of direct selection tend to decrease as study sizes increase, suggesting that current views of the strength of selection may be inaccurate and biased upward. We suggest that studies should be designed so that selection is analyzed on at least several hundred individuals, the total opportunity of selection be considered along with the pattern of selection on individual traits, and nonsignificant results be actively reported combined with an estimate of power.