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.     

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.     

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.     

Social selection acts on behavior and body mass but does not contribute to the total selection differential in eastern chipmunks

Through social interactions, phenotypes of conspecifics can affect an individual's fitness, resulting in social selection. Social selection is assumed to represent a strong and dynamic evolutionary force that can act with or in opposition to natural selection. Few studies, however, have estimated social selection and its contribution to total selection in the wild. We estimated natural and social selection gradients on exploration, docility, and body mass, and their contribution to selection differentials, in a wild eastern chipmunk population (Tamias striatus). We applied trait-based multiple regression models derived from classical phenotypic selection analyses, which allowed us to include several social partners (i.e., neighbors). We detected social selection gradients on female docility and male body mass, indicating that female with docile neighbors and males with large neighbors had lower fitness. In both sexes, social selection gradients varied with the season. However, we found no phenotypic assortment or disassortment for the studied traits. Social selection gradients, therefore, did not contribute to total selection differentials, and natural selection alone could drive phenotypic changes. Evaluating the factors that drive the evolution of the covariance between interacting phenotypes is necessary to understand the role of social selection as an evolutionary force.     

Quantifying selection on standard metabolic rate and body mass in Drosophila melanogaster

Standard metabolic rate (SMR), defined as the minimal energy expenditure required for self‐maintenance, is a key physiological trait. Few studies have estimated its relationship with fitness, most notably in insects. This is presumably due to the difficulty of measuring SMR in a large number of very small individuals. Using high‐throughput flow‐through respirometry and a Drosophila melanogaster laboratory population adapted to a life cycle that facilitates fitness measures, we quantified SMR, body mass, and fitness in 515 female and 522 male adults. We used a novel multivariate approach to estimate linear and nonlinear selection differentials and gradients from the variance‐covariance matrix of fitness, SMR, and body mass, allowing traits specific covariates to be accommodated within a single model. In males, linear selection differentials for mass and SMR were positive and individually significant. Selection gradients were also positive but, despite substantial sample sizes, were nonsignificant due to increased uncertainty given strong SMR‐mass collinearity. In females, only nonlinear selection was detected and it appeared to act primarily on body size, although the individual gradients were again nonsignificant. Selection did not differ significantly between sexes although differences in the fitness surfaces suggest sex‐specific selection as an important topic for further study.     

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.     

GENETIC CONSTRAINTS ON ADAPTATION TO A CHANGING ENVIRONMENT

Genetic correlations between traits can constrain responses to natural selection. To what extent such correlations limit adaptation depends on patterns of directional selection. I derive the expected rate of adaptation (or evolvability) under randomly changing selection gradients. When directional selection gradients have an arbitrary covariance matrix, the average rate of adaptation depends on genetic correlations between traits, contrary to the isotropic case investigated in previous studies. Adaptation may be faster on average with more genetic correlation between traits, if these traits are selected to change jointly more often than the average pair of traits. However, natural selection maximizes the long‐term fitness of a population, not necessarily its rate of adaptation. I therefore derive the average lag load caused by deviations of the mean phenotype from an optimum, under several forms of environmental changes typically experienced by natural populations, both stochastic and deterministic. Simple formulas are produced for how the G matrix affects long‐term fitness in these contexts, and I discuss how their parameters can be estimated empirically.     

UNIFICATION OF REGRESSION‐BASED METHODS FOR THE ANALYSIS OF NATURAL SELECTION

Regression analyses are central to characterization of the form and strength of natural selection in nature. Two common analyses that are currently used to characterize selection are (1) least squares–based approximation of the individual relative fitness surface for the purpose of obtaining quantitatively useful selection gradients, and (2) spline‐based estimation of (absolute) fitness functions to obtain flexible inference of the shape of functions by which fitness and phenotype are related. These two sets of methodologies are often implemented in parallel to provide complementary inferences of the form of natural selection. We unify these two analyses, providing a method whereby selection gradients can be obtained for a given observed distribution of phenotype and characterization of a function relating phenotype to fitness. The method allows quantitatively useful selection gradients to be obtained from analyses of selection that adequately model nonnormal distributions of fitness, and provides unification of the two previously separate regression‐based fitness analyses. We demonstrate the method by calculating directional and quadratic selection gradients associated with a smooth regression‐based generalized additive model of the relationship between neonatal survival and the phenotypic traits of gestation length and birth mass in humans.     

Measuring natural and sexual selection on breeding values of male display traits in Drosophila serrata

Fundamental to many theories of sexual selection is the expectation that sexual traits, which males use in an attempt to increase mating success, confer costs as well as benefits to individual males. Although evolution of exaggerated male traits is predicted to be halted, by costs applied by natural selection, there is a lack of empirical work devoted to quantitatively establishing whether natural selection opposes sexual selection generated by the preferences of females. In this study, we quantified natural and sexual selection gradients on breeding values for cuticular hydrocarbon (CHC) components of male contact pheromones in Drosophila serrata. As male sexual traits may often be environmentally condition dependent, breeding values were used in the selection analysis to remove the possibility of environmental correlations between the measured trait and fitness biasing estimates of selection. The direction of natural selection was found to oppose sexual selection on a subset of CHCs examined. Opposing natural and sexual selection suggests that further evolution of the male pheromone may in part be limited by costs associated with attractive male CHC blends.     

Phenotypic selection in natural populations: what limits directional selection?

Studies of phenotypic selection document directional selection in many natural populations. What factors reduce total directional selection and the cumulative evolutionary responses to selection? We combine two data sets for phenotypic selection, representing more than 4,600 distinct estimates of selection from 143 studies, to evaluate the potential roles of fitness trade-offs, indirect (correlated) selection, temporally varying selection, and stabilizing selection for reducing net directional selection and cumulative responses to selection. We detected little evidence that trade-offs among different fitness components reduced total directional selection in most study systems. Comparisons of selection gradients and selection differentials suggest that correlated selection frequently reduced total selection on size but not on other types of traits. The direction of selection on a trait often changes over time in many temporally replicated studies, but these fluctuations have limited impact in reducing cumulative directional selection in most study systems. Analyses of quadratic selection gradients indicated stabilizing selection on body size in at least some studies but provided little evidence that stabilizing selection is more common than disruptive selection for most traits or study systems. Our analyses provide little evidence that fitness trade-offs, correlated selection, or stabilizing selection strongly constrains the directional selection reported for most quantitative traits.     

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.     

Spatiotemporal fluctuations in natural selection acting on the gall‐parasitic aphid Tetraneura sorini

The measurement of the selection gradient is crucial for understanding the magnitude of selection acting directly on a trait and predicting the evolutionary trajectory of that trait. This study evaluated the selection gradient acting on the morphology of the gall‐parasitic aphid Tetraneura sorini during the galling process and compared the strength among populations. Gall formers (first instars) frequently fight with conspecifics or heterospecifics for usurping incipient galls using their well‐developed hind legs. First instars that successfully acquired galls were found within galls, whereas those that failed were found dead on leaf surfaces. Selection gradients were estimated using logistic stepwise regression and partial least square (PLS) regression. Calculated selection differentials indicated that first instars that secured galls were larger in body size than failed individuals through all populations. However, selection gradients on weapon traits varied largely among populations or among years in the same population. We confirmed microevolutionary changes in the relationship between traits, which accorded with the expectation from changes in the selection gradients. When gall formers were transferred onto developing buds individually, individuals that successfully induced galls had smaller body size than failed individuals. Available evidence suggests that the selection gradient on body size becomes higher with an increasing proportion of T. sorini in the Tetraneura species community. Thus, we concluded that more intense fighting with conspecifics leads to stronger selective pressure on body size, but that selective pressure for each trait is variable depending on differences in the tactics and species composition among populations.     

MULTIYEAR STUDY OF MULTIVARIATE LINEAR AND NONLINEAR PHENOTYPIC SELECTION ON FLORAL TRAITS OF HUMMINGBIRD-POLLINATED SILENE VIRGINICA

Pollination syndromes suggest that convergent evolution of floral traits and trait combinations reflects similar selection pressures. Accordingly, a pattern of selection on floral traits is expected to be consistent with increasing the attraction and pollen transfer of the important pollinator. We measured individual variation in six floral traits and yearly and lifetime total plant seed and fruit production of 758 plants across nine years of study in natural populations of Ruby-Throated Hummingbird-pollinated Silene virginica. The type, strength, and direction of selection gradients were observed by year, and for two cohorts selection was estimated through lifetime maternal fitness. Positive directional selection was detected on floral display height in all years of study and stigma exsertion in all years but one. Significant quadratic and correlational selection gradients were rare. However, a canonical analysis of the gamma matrix indicated nonlinear selection was common; if significant curvature was detected it was convex with one exception. Our analyses demonstrated selection favored trait combinations and the integration of floral features of attraction and pollen transfer efficiency that were consistent with the hummingbird pollination syndrome.     

Natural selection on gall size: variable contributions of individual host plants to population-wide patterns

Studies that provide estimates of the form and magnitude of selection on herbivore traits at the level of individual plants in natural populations represent a vital step in understanding the interaction of selection and gene flow among host-affiliated insect populations when individual plants equate to differing selective regimes. We analyzed phenotypic selection on the trait gall size for a host-specific gall former at both the individual host plant and population level (across host plants) in each of two years. Linear and nonlinear selection and the fitness function relating gall size to the probability of survivorship in the absence of natural enemies were estimated for each level and year. Selection imposed by the host plant was observed in 19 of the 22 subpopulations monitored. At the population level, linear and nonlinear selection were evident each year. However, population-level estimates masked the significant heterogeneity in the form and direction of selection evident among plants each year. Heterogeneity among gall-former subpopulations is emphasized by our findings that selection varied from directional to stabilizing among plants and the majority of selection gradients estimated for individual plants did not fall within the 95% CIs of the population-level estimates.     

Selection on floral traits through male fertility in a natural plant population

Most studies on selection in plants estimate female fitness components and neglect male mating success, although the latter might also be fundamental to understand adaptive evolution. Information from molecular genetic markers can be used to assess determinants of male mating success through parentage analyses. We estimated paternal selection gradients on floral traits in a large natural population of the herb Mimulus guttatus using a paternity probability model and maximum likelihood methods. This analysis revealed more significant selection gradients than a previous analysis based on regression of estimated male fertilities on floral traits. There were differences between results of univariate and multivariate analyses most likely due to the underlying covariance structure of the traits. Multivariate analysis, which corrects for the covariance structure of the traits, indicated that male mating success declined with distance from and depended on the direction to the mother plants. Moreover, there was directional selection for plants with fewer open flowers which have smaller corollas, a smaller anther–stigma separation, more red dots on the corolla and a larger fluctuating asymmetry therein. For most of these traits, however, there was also stabilizing selection indicating that there are intermediate optima for these traits. The large number of significant selection gradients in this study shows that even in relatively large natural populations where not all males can be sampled, it is possible to detect significant paternal selection gradients, and that such studies can give us valuable information required to better understand adaptive plant evolution. Second affiliation for Mark Van Kleunen is temporary until February 2007.     

A meta‐analysis of the agents of selection on floral traits

Floral traits are hypothesized to evolve primarily in response to selection by pollinators. However, selection can also be mediated by other environmental factors. To understand the relative importance of pollinator‐mediated selection and its variation among trait and pollinator types, we analyzed directional selection gradients on floral traits from experiments that manipulated the environment to identify agents of selection. Pollinator‐mediated selection was stronger than selection by other biotic factors (e.g., herbivores), but similar in strength to selection by abiotic factors (e.g., soil water), providing partial support for the hypothesis that floral traits evolve primarily in response to pollinators. Pollinator‐mediated selection was stronger on pollination efficiency traits than on other trait types, as expected if efficiency traits affect fitness via interactions with pollinators, but other trait types also affect fitness via other environmental factors. In addition to varying among trait types, pollinator‐mediated selection varied among pollinator taxa: selection was stronger when bees, long‐tongued flies, or birds were the primary visitors than when the primary visitors were Lepidoptera or multiple animal taxa. Finally, reducing pollinator access to flowers had a relatively small effect on selection on floral traits, suggesting that anthropogenic declines in pollinator populations would initially have modest effects on floral evolution.     

Selection against late emergence and small offspring in Atlantic salmon (Salmo salar)

Timing of breeding and offspring size are maternal traits that may influence offspring competitive ability, dispersal, foraging, and vulnerability to predation and climatic conditions. To quantify the extent to which these maternal traits may ultimately affect an organism's fitness, we undertook laboratory and field experiments with Atlantic salmon (Salmo salar). To control for confounding effects caused by correlated traits, manipulations of the timing of fertilization combined with intraclutch comparisons were used. In the wild, a total of 1462 juveniles were marked at emergence from gravel nests. Recapture rates suggest that up to 83.5% mortality occurred during the first four months after emergence from the gravel nests, with the majority (67.5%) occurring during the initial period ending 17 days after median emergence. Moreover, the mortality was selective during this initial period, resulting in a significant phenotypic shift toward an earlier date of and an increased length at emergence. However, no significant selection differentials were detected thereafter, indicating that the critical episode of selection had occurred at emergence. Furthermore, standardized selection gradients indicated that selection was more intense on date of than on body size at emergence. Timing of emergence had additional consequences in terms of juvenile body size. Late-emerging juveniles were smaller than early-emerging ones at subsequent samplings, both in the wild and in parallel experiments conducted in seminatural stream channels, and this may affect success at subsequent size-selective episodes, such as winter mortality and reproduction. Finally, our findings also suggest that egg size had fitness consequences independent of the effects of emergence time that directly affected body size at emergence and, in turn, survival and size at later life stages. The causality of the maternal effects observed in the present study supports the hypothesis that selection on juvenile traits may play an important role in the evolution of maternal traits in natural populations.     

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.     

Climate drives among‐year variation in natural selection on flowering time

To predict long‐term responses to climate change, we need to understand how changes in temperature and precipitation elicit both immediate phenotypic responses and changes in natural selection. We used 22 years of data for the perennial herb Lathyrus vernus to examine how climate influences flowering phenology and phenotypic selection on phenology. Plants flowered earlier in springs with higher temperatures and higher precipitation. Early flowering was associated with a higher fitness in nearly all years, but selection for early flowering was significantly stronger in springs with higher temperatures and lower precipitation. Climate influenced selection through trait distributions, mean fitness and trait?fitness relationships, the latter accounting for most of the among‐year variation in selection. Our results show that climate both induces phenotypic responses and alters natural selection, and that the change in the optimal phenotype might be either weaker, as for spring temperature, or stronger, as for precipitation, than the optimal response.     

Pollinators cause stronger selection than herbivores on floral traits in Lobelia cardinalis (Lobeliaceae)

Measures of selection on floral traits in flowering plants are often motivated by the assumption that pollinators cause selection. Flowering plants experience selection from other sources, including herbivores, which may enhance or oppose selection by pollinators. Surprisingly, few studies have examined selection from multiple sources on the same traits. We quantified pollinator-mediated selection on six floral traits of Lobelia cardinalis by comparing selection in naturally and supplementally (hand-) pollinated plants. Directional, quadratic and correlational selection gradients as well as total directional and quadratic selection differentials were examined. We used path analysis to examine how three herbivores--slugs, weevils and caterpillars--affected the relationship between floral traits and fitness. We detected stronger total selection on four traits and correlational selection (γ(ij)) on three trait combinations in the natural pollination treatment, indicating that pollinators caused selection on these traits. Weak but statistically significant selection was caused by weevil larvae on stem diameter and anther-nectary distance, and by slugs on median-flower date. In this study, pollinators imposed stronger selection than herbivores on floral traits in L. cardinalis. In general, the degree of pollen limitation and rate of herbivory are expected to influence the relative strength of selection caused by pollinators or herbivores.