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Selection gradients, the opportunity for selection, and the coefficient of determination.

ABSTRACT: Abstract We derive the relationship between R(2) (the coefficient of determination), selection gradients, and the opportunity for selection for univariate and multivariate cases. Our main result is to show that the portion of the opportunity for selection that is caused by variation for any trait is equal to the product of its selection gradient and its selection differential. This relationship is a corollary of the first and second fundamental theorems of natural selection, and it permits one to investigate the portions of the total opportunity for selection that are involved in directional selection, stabilizing (and diversifying) selection, and correlational selection, which is important to morphological integration. It also allows one to determine the fraction of fitness variation not explained by variation in measured phenotypes and therefore attributable to random (or, at least, unknown) influences. We apply our methods to a human data set to show how sex-specific mating success as a component of fitness variance can be decoupled from that owing to prereproductive mortality. By quantifying linear sources of sexual selection and quadratic sources of sexual selection, we illustrate that the former is stronger in males, while the latter is stronger in females.

SUBMITTER: Moorad JA

PROVIDER: S-EPMC3620722 | biostudies-literature | 2013 Mar

REPOSITORIES: biostudies-literature

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Selection gradients, the opportunity for selection, and the coefficient of determination.

Moorad Jacob A JA Wade Michael J MJ

The American naturalist 20130128 3

Abstract We derive the relationship between R(2) (the coefficient of determination), selection gradients, and the opportunity for selection for univariate and multivariate cases. Our main result is to show that the portion of the opportunity for selection that is caused by variation for any trait is equal to the product of its selection gradient and its selection differential. This relationship is a corollary of the first and second fundamental theorems of natural selection, and it permits one t ...[more]

PMID: 23448880

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Project description:Natural selection can only occur if individuals differ in fitness. For this reason, the variance in relative fitness has been equated with the 'opportunity for selection' ( I ), which has a long, albeit somewhat controversial, history. In this paper we discuss the use/misuse of I and related metrics in evolutionary ecology. The opportunity is only realised if some fraction of I is caused by trait variation. Thus, I>0 does not imply that selection is occurring, as sometimes erroneously assumed, because all fitness variation could be independent of phenotype. The selection intensity on any given trait cannot exceed I , but this upper limit will never be reached because (a) stochastic factors always affect fitness, and (b) there might be multiple traits under selection. The expected magnitude of the stochastic component of I is negatively correlated with mean fitness. Uncertainty in realised I is also larger when mean fitness or population/sample size are low. Variation in I across time or space thus can be dominated (or solely driven) by variation in the strength of demographic stochasticity. We illustrate these points using simulations and empirical data from a population study on great tits Parus major. Our analysis shows that the scope for fecundity selection in the great tits is substantially higher when using annual number of recruits as the fitness measure, rather than fledglings or eggs, even after adjusting for the dependence of I on mean fitness. This suggests nonrandom survival of juveniles across families between life stages. Indeed, previous work on this population has shown that offspring recruitment is often nonrandom with respect to clutch size and laying date of parents, for example. We conclude that one cannot make direct inferences about selection based on fitness data alone. However, examining variation in ∆IF (the opportunity for fecundity selection adjusted for mean fitness) across life stages, years or environments can offer clues as to when/where fecundity selection might be strongest, which can be useful for research planning and experimental design.

Dataset Information

Selection gradients, the opportunity for selection, and the coefficient of determination.

Publications

Selection gradients, the opportunity for selection, and the coefficient of determination.

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