A mathematical framework for evo-devo dynamics

Abstract

AbstractNatural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five elementary components generate all equations including those describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of gene expression, phenotype, environment, and mutational covariation. This shows that genetic and phenotypic evolution must be followed simultaneously to yield a well-defined description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in geno-phenotype space. Genetic constraints in geno-phenotype space are necessarily absolute because the degrees of freedom of genetic covariation are necessarily limited by genetic space. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where “total genetic selection” vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of gene-expression space. Development thus modulates necessarily absolute genetic constraints, and hence it affects evolutionary equilibria, the admissible evolutionary path, and which equilibria are admissible. Our framework provides an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.