Bridging developmental and statistical approaches to variation and evolution.

Phenotypic variation is the raw material for evolutionary diversification and adaptation. However, a critical gap remains in evolutionary theory between developmental and statistical representations of phenotypic variation, limiting our ability to understand and predict evolutionary change. In this paper, we close this gap by establishing a formal bridge between developmental and statistical accounts of phenotypic variation. Representing development as a dynamical system, we derive explicit relationships between perturbations to developmental systems and quantitative-genetic parameters. Through this framework, we obtain two important results. First, we show that the full developmental trajectory contains information that can improve the estimation of statistical parameters relevant to evolution. Second, we explain how different sources of variation-genetic, environmental, and stochastic-shape the distribution of phenotypic variation. This reveals conditions under which covariance matrices are expected to align, offering a developmental explanation for statistical patterns of phenotypic variation at both micro- and macroevolutionary scales. These findings advance our understanding of how developmental processes structure phenotypic variation, shape evolutionary dynamics, and influence evolvability.