Quantifying the causal pathways contributing to natural selection.

The consequences of natural selection can be understood from a purely statistical perspective. In contrast, an explicitly causal approach is required to understand why trait values covary with fitness. In particular, key evolutionary constructs, such as sexual selection, fecundity selection, and so on, are best understood as selection via particular fitness components. To formalize and operationalize these concepts, we must disentangle the various causal pathways contributing to selection. Such decompositions are currently only known for linear models, where they are sometimes referred to as "Wright's rules." Here, we provide a general framework, based on path analysis, for partitioning selection among its contributing causal pathways. We show how the extended selection gradient-which represents selection arising from a trait's causal effects on fitness-can be decomposed into path-specific selection gradients, which correspond to distinct causal mechanisms of selection. This framework allows for nonlinear effects and nonadditive interactions among variables, which may be estimated using standard statistical methods (e.g., generalized linear [mixed] models or generalized additive models). We thus provide a generalization of Wright's path rules that accommodates the nonlinear and nonadditive mechanisms by which natural selection commonly arises.