Estimating the Form of Natural Selection on a Quantitative Trait

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Abstract
The fitness function f relates fitness of individuals to the quantitative trait under natural selection. The function is useful in predicting fitness differences among individuals and in revealing whether an optimum is present within the range of phenotypes in the population. It may also be thought of as describing the ecological environment in terms of the trait. Quadratic regression will approximate the fitness function from data (e.g., Lande and Arnold, 1983), but the method does not reliably indicate features of f such as the presence of modes (stabilizing selection) or dips (disruptive selection). I employ an alternative procedure requiring no a priori model for the function. The method is useful in two ways: it provides a nonparametric estimate of f, of interest by itself, and it can be used to suggest an appropriate parametric model. I also discuss measures of selection intensity based on the fitness function. Analysis of six data sets yields a variety of forms of f and provides new insights for some familiar cases. Low amounts of variation and a low density of data points near the tails of many phenotype distributions emerge as limitations to gaining information on fitness functions. An experimental approach in which the distribution of a quantitative trait is broadened through manipulation would minimize these problems.