A mathematical synthesis of genetics, development, and evolution

Abstract

Mathematically integrating genetics, development, and evolution is a longstanding challenge. A prevalent approach is quantitative genetics underpinned by the infinitesimal model, which considers a simplification of development, where phenotypes are described as the sum of many independent gene contributions. While this approach enjoys predictive success under controlled conditions, it is of interest to relax the model to consider more realistic development. Here I develop general mathematical theory that integrates sexual, discrete, multilocus genetics, developmental dynamics, and evolution. This yields an exact method to describe the evolutionary dynamics of allele frequencies and linkage disequilibria in multilocus systems and the associated evolutionary dynamics of mean phenotypes constructed via arbitrarily complex developmental dynamics. The theory shows that development affects evolution under realistic genetics by shaping the fitness landscape of allele frequencies and linkage disequilibria and by constraining adaptation to an admissible evolutionary manifold where mean phenotypes and phenotype (co-)variances can be developed. I derive a first-order approximation of this exact method, which yields equations in gradient form describing change in allele frequency, linkage disequilibria, and mean phenotypes as constrained, sometimes-adaptive topographies. Both the exact and approximated equations describe long-term phenotypic and genetic evolution. I provide worked examples to illustrate the methods. The theory obtained can be interpreted as an extension of population genetics, with some similarities with quantitative genetics under the infinitesimal model but with fundamental differences. The theory may improve prediction accuracy and shed light on empirical observations that have been paradoxical under previous theory, but appear less paradoxical in this theory.