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.     

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.     

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.     

Reducing environmental bias when measuring natural selection

Abstract.— Crucial to understanding the process of natural selection is characterizing phenotypic selection. Measures of phenotypic selection can be biased by environmental variation among individuals that causes a spurious correlation between a trait and fitness. One solution is analyzing genotypic data, rather than phenotypic data. Genotypic data, however, are difficult to gather, can be gathered from few species, and typically have low statistical power. Environmental correlations may act through traits other than through fitness itself. A path analytic framework, which includes measures of such traits, may reduce environmental bias in estimates of selection coefficients. We tested the efficacy of path analysis to reduce bias by re-analyzing three experiments where both phenotypic and genotypic data were available. All three consisted of plant species (Impatiens capensis, Arabidopsis thaliana , and Raphanus sativus) grown in experimental plots or the greenhouse. We found that selection coefficients estimated by path analysis using phenotypic data were highly correlated with those based on genotypic data with little systematic bias in estimating the strength of selection. Although not a panacea, using path analysis can substantially reduce environmental biases in estimates of selection coefficients. Such confidence in phenotypic selection estimates is critical for progress in the study of natural selection.     

Comparative methods with sampling error and within-species variation: contrasts revisited and revised

Comparative methods analyses have usually assumed that the species phenotypes are the true means for those species. In most analyses, the actual values used are means of samples of modest size. The covariances of contrasts then involve both the covariance of evolutionary changes and a fraction of the within-species phenotypic covariance, the fraction depending on the sample size for that species. Ives et al. have shown how to analyze data in this case when the within-species phenotypic covariances are known. The present model allows them to be unknown and to be estimated from the data. A multivariate normal statistical model is used for multiple characters in samples of finite size from species related by a known phylogeny, under the usual Brownian motion model of change and with equal within-species phenotypic covariances. Contrasts in each character can be obtained both between individuals within a species and between species. Each contrast can be taken for all of the characters. These sets of contrasts, each the same contrast taken for different characters, are independent. The within-set covariances are unequal and depend on the unknown true covariance matrices. An expectation-maximization algorithm is derived for making a reduced maximum likelihood estimate of the covariances of evolutionary change and the within-species phenotypic covariances. It is available in the Contrast program of the PHYLIP package. Computer simulations show that the covariances are biased when the finiteness of sample size is not taken into account and that using the present model corrects the bias. Sampling variation reduces the power of inference of covariation in evolution of different characters. An extension of this method to incorporate estimates of additive genetic covariances from a simple genetic experiment is also discussed.     

Reducing bias in the measurement of selection

Selection on quantitative characters is commonly mesured in natural populations using regression techniques based on phenotypic covariances between traits and fitness. However, such methods do not give an accutate view of the causal relationship between the phenotype and fitness if enviornmental factors also contribute to covariances between traits and fitness. A recently developed method for estimating selection eliminates the problem of bias resulting from enviormental covariances. This underappreciated method represents a significant addition to the toolbox of evolutionary ecologist.     

Using time series analysis to characterize evolutionary and plastic responses to environmental change: a case study of a shift toward earlier migration date in sockeye salmon

Environmental change can shift the phenotype of an organism through either evolutionary or nongenetic processes. Despite abundant evidence of phenotypic change in response to recent climate change, we typically lack sufficient genetic data to identify the role of evolution. We present a method of using phenotypic data to characterize the hypothesized role of natural selection and environmentally driven phenotypic shifts (plasticity). We modeled historical selection and environmental predictors of interannual variation in mean population phenotype using a multivariate state-space model framework. Through model comparisons, we assessed the extent to which an estimated selection differential explained observed variation better than environmental factors alone. We applied the method to a 60-year trend toward earlier migration in Columbia River sockeye salmon Oncorhynchus nerka, producing estimates of annual selection differentials, average realized heritability, and relative cumulative effects of selection and plasticity. We found that an evolutionary response to thermal selection was capable of explaining up to two-thirds of the phenotypic trend. Adaptive plastic responses to June river flow explain most of the remainder. This method is applicable to other populations with time series data if selection differentials are available or can be reconstructed. This method thus augments our toolbox for predicting responses to environmental change.     

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.     

Animal learning as a source of developmental bias

As a form of adaptive plasticity that allows organisms to shift their phenotype toward the optimum, learning is inherently a source of developmental bias. Learning may be of particular significance to the evolutionary biology community because it allows animals to generate adaptively biased novel behavior tuned to the environment and, through social learning, to propagate behavioral traits to other individuals, also in an adaptively biased manner. We describe several types of developmental bias manifest in learning, including an adaptive bias, historical bias, origination bias, and transmission bias, stressing that these can influence evolutionary dynamics through generating nonrandom phenotypic variation and/or nonrandom environmental states. Theoretical models and empirical data have established that learning can impose direction on adaptive evolution, affect evolutionary rates (both speeding up and slowing down responses to selection under different conditions) and outcomes, influence the probability of populations reaching global optimum, and affect evolvability. Learning is characterized by highly specific, path‐dependent interactions with the (social and physical) environment, often resulting in new phenotypic outcomes. Consequently, learning regularly introduces novelty into phenotype space. These considerations imply that learning may commonly generate plasticity first evolution.     

Genetic analysis of life-history constraint and evolution in a wild ungulate population

Trade-offs among life-history traits are central to evolutionary theory. In quantitative genetic terms, trade-offs may be manifested as negative genetic covariances relative to the direction of selection on phenotypic traits. Although the expression and selection of ecologically important phenotypic variation are fundamentally multivariate phenomena, the in situ quantification of genetic covariances is challenging. Even for life-history traits, where well-developed theory exists with which to relate phenotypic variation to fitness variation, little evidence exists from in situ studies that negative genetic covariances are an important aspect of the genetic architecture of life-history traits. In fact, the majority of reported estimates of genetic covariances among life-history traits are positive. Here we apply theory of the genetics and selection of life histories in organisms with complex life cycles to provide a framework for quantifying the contribution of multivariate genetically based relationships among traits to evolutionary constraint. We use a Bayesian framework to link pedigree-based inference of the genetic basis of variation in life-history traits to evolutionary demography theory regarding how life histories are selected. Our results suggest that genetic covariances may be acting to constrain the evolution of female life-history traits in a wild population of red deer Cervus elaphus: genetic covariances are estimated to reduce the rate of adaptation by about 40%, relative to predicted evolutionary change in the absence of genetic covariances. Furthermore, multivariate phenotypic (rather than genetic) relationships among female life-history traits do not reveal this constraint.     

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 stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.     

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.     

Evolutionary importance of parental care performance,food resources,and direct and indirect genetic effects in a burying beetle

Indirect genetic effects (IGE) of parental care performance and the direct–indirect covariance contribute substantially to total heritability in domesticated and laboratory mammals. For animals from natural populations empirical estimates of IGE are sparse. Thus, despite recent models relating IGE to evolution, evolutionary interpretations of IGE are limited. To address this deficit, we used a reciprocal cross‐fostering breeding design to estimate environmental influences, direct and indirect genetic effects, and direct–indirect genetic covariances in the burying beetle Nicrophorus pustulatus to determine the evolutionary importance of IGE arising from variation in parental care performance. Carrion size positively affected adult mass and time on carrion, but had no effect on total development time. Males were slightly larger than females. For both mass and development, independent of these environmental influences, direct and indirect genetic effects were of moderate magnitude. Total genetic effects explained 36–50% of the phenotypic variance in mass and size and 27–37% of phenotypic variance in development time. Direct–indirect genetic covariances were zero or close to zero. Thus, for both mass and development time, the response to natural selection arising from environmental variation may be accelerated by the presence of IGE in N. pustulatus. The generality of this pattern and the evolutionary significance of IGE arising from parental care awaits further study of natural populations.     

Lifetime selection on heritable life-history traits in a natural population of red squirrels

Abstract Despite their importance in evolutionary biology, heritability and the strength of natural selection have rarely been estimated in wild populations of iteroparous species or have usually been limited to one particular event during an organism's lifetime. Using an animal-model restricted maximum likelihood and phenotypic selection models, we estimated quantitative genetic parameters and the strength of lifetime selection on parturition date and litter size at birth in a natural population of North American red squirrels, Tamiasciurus hudsonicus. Litter size at birth and parturition date had low heritabilities ( h² = 0.15 and 0.16, respectively). We considered potential effects of temporal environmental covariances between phenotypes and fitness and of spatial environmental heterogeneity in estimates of selection. Selection favored early breeders and females that produced litter sizes close to the population average. Stabilizing selection on litter size at birth may occur because of a trade-off between number of offspring produced per litter and offspring survival or a trade-off between a female's fecundity and her future reproductive success and survival.     

Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N<38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.     

Estimating the variation,autocorrelation, and environmental sensitivity of phenotypic selection

Despite considerable interest in temporal and spatial variation of phenotypic selection, very few methods allow quantifying this variation while correctly accounting for the error variance of each individual estimate. Furthermore, the available methods do not estimate the autocorrelation of phenotypic selection, which is a major determinant of eco‐evolutionary dynamics in changing environments. We introduce a new method for measuring variable phenotypic selection using random regression. We rely on model selection to assess the support for stabilizing selection, and for a moving optimum that may include a trend plus (possibly autocorrelated) fluctuations. The environmental sensitivity of selection also can be estimated by including an environmental covariate. After testing our method on extensive simulations, we apply it to breeding time in a great tit population in the Netherlands. Our analysis finds support for an optimum that is well predicted by spring temperature, and occurs about 33 days before a peak in food biomass, consistent with what is known from the biology of this species. We also detect autocorrelated fluctuations in the optimum, beyond those caused by temperature and the food peak. Because our approach directly estimates parameters that appear in theoretical models, it should be particularly useful for predicting eco‐evolutionary responses to environmental change.     

The influence of environmentally induced heterogeneity on age-specific genetic variance for mortality rates

Using parametric models that describe the increase in mortality rates with age, we demonstrate that environmentally induced heterogeneity among genetically identical individuals is sufficient to generate biased estimates of age-specific genetic variance. Although the magnitude of the bias may change with age, one general trend emerges: the true genetic variance at the oldest ages is likely to be dramatically underestimated. Our results are robust to different manifestations of heterogeneity and suggest that such a bias is a general feature of these models. We note that age-dependent estimates of genetic variance for characters that are correlated with mortality (either genetically or environmentally) can be expected to be similarly affected. The results are independent of sample size and suggest that the bias may be more widespread in the literature than is currently appreciated. Our results are discussed with reference to existing data on mortality variance in Drosophila melanogaster.     

Evolutionary potential of morphological traits across different life‐history stages

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

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.