Phenotypic selection analysis and confounding environmental variables

When environmental variation contributes to relationships between traits and fitness, it can confound analyses of phenotypic selection and, ultimately, bias predictions of adaptive evolution. To date, discussions of how to combat this problem emphasise complex statistical analyses aimed at estimating the genetic basis of the relationship between traits and fitness (e.g., the secondary theorem of selection). This article presents a path analysis-based description of the environmental confounding problem, which clarifies the issue and motivates simpler analyses as potential solutions. We show how standard selection analyses can be expanded to explicitly include environmental variables that may confound trait-fitness relationships, potentially leading to dramatically improved predictions of the evolutionary response to selection relative to classical phenotype-based estimates. We provide both univariate and multivariate treatments of the decomposition of the selection differential into components that may cause evolution via direct and indirect selection and components representing evolutionarily inert, environmentally-induced covariance. The multivariate treatment also yields expressions for the decomposition of the selection differential based on extended selection gradients, which may be of wide general interest beyond the environmental problem. Our approach to the environmental confounding problem makes more plausible demands on data than previous, more involved, quantitative genetic approaches, and addresses the issue of environmental confounding in a more biologically informative way. ### Competing Interest Statement The authors have declared no competing interest.