# Bridging developmental and statistical approaches to variation and evolution

## TL;DR

This paper connects how traits develop in organisms with how they evolve in populations, improving predictions about evolutionary change.

## Contribution

The paper introduces a framework linking developmental processes to statistical models of phenotypic variation in evolution.

## Key findings

- Developmental trajectories improve estimates of evolutionary statistical parameters.
- Genetic, environmental, and stochastic factors shape phenotypic variation distributions.
- Conditions for covariance matrix alignment are explained through developmental processes.

## Abstract

Evolution depends on variation, but the developmental processes that generate this variation have often been overlooked in evolutionary biology, which traditionally emphasizes statistical descriptions at the population level. Here, we present a framework that formally links these statistical descriptions to the underlying processes that generate phenotypic variation. We show that this link allows us to improve estimates of key evolutionary quantities and can help clarify empirical patterns that are surprising when analyzed from a purely population-level perspective. This work shows that the integration of population and developmental-level understandings of variation not only advances theoretical insight but also enables the construction of concrete mathematical tools to better understand and predict evolutionary change, an increasingly urgent goal amid rapid environmental change.

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.