Theme preservation and the evolution of representation

In his thesis Toussaint calls for a "general project to develop theories on adaptation processes that account for the adaptation of representations". The theory developed in this paper is a contribution to this project. We first define the simple concept of a genotypic theme and define what it means for mutation operators to be theme preserving and theme altering. We use the idea of theme preservation to develop the concept of subrepresentation. Then we develop a theory that illuminates the behavior of a mutation-only fitness proportional evolutionary algorithm in which mutation preserves genotypic themes with high probability. Our theory shows that such evolutionary algorithms implicitly implement what we call subrepresentation evolving multithreaded evolution, i.e. such EAs conduct second-order search over a predetermined set of representations and exploit promising representations for first order evolutionary search. We illuminate subrepresentaiton evolving multithreaded evolution by comparing and contrasting it with the behavior of island model EAs. Our theory is immediately useful in understanding the significance of the low probability with which theme altering type 2 mutations are applied to genotypes of the evolutionary systems in Toussaint's thesis.