Regression Analysis of Natural Selection: Statistical Inference and Biological Interpretation

Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.