  A theoretical and experimental analysis is made of the effects of
self-adaptation in a simple evolving system. Specifically, we consider the
effects of coding the mutation and crossover probabilities of a genetic
algorithm evolving in certain model fitness landscapes. The resultant
genotype-phenotype mapping is degenerate, there being no direct selective
advantage for one probability versus another. We show that the action of
mutation and crossover breaks this degeneracy leading to an induced symmetry
breaking among the genotypic synonyms. We demonstrate that this induced
symmetry breaking allows the system to self-adapt in a time dependent
environment.
