On the Evolution of Phenotypic Exploration Distributions

In nature, phenotypic variability is highly structured with respect to correlations between different phenotypic traits. In this paper we argue that this structuredness can be understood as the outcome of an adaptive process of phenotypic exploration distributions, similar to the adaptation of the search distribution in heuristic search schemes or Estimation-of-Distribution Algorithms. The key ingredient of this process is a non-trivial genotype-phenotype mapping: We rigorously define non-triviality, in which case neutral traits (as a generalization of strategy parameters) influence phenotype evolution by determining exploration distributions. Our main result is the description of the evolution of exploration distributions themselves in terms of an ordinary evolution equation. Accordingly, the “fitness” of an exploration distribution is proportional to its similarity (in the sense of the Kullback-Leibler divergence) to the fitness distribution over phenotype space. Hence, exploration distributions evolve such that dependencies and correlations between phenotypic variables in selection are naturally adopted by the way evolution explores phenotype space.