Pointed out the previous section mutation breaks this symmetry
140 FRONTIERS OF EVOLUTIONARY COMPUTATION
In the limit
(or in more general circumstances when the strengths of operators other than reproductive selection
0)
The key element behind effective fitness, irrespective of its mathematical definition, is that population flows in the presence of operators other than pure reproductive selection are much more readily understood in terms of it. In fact, to go further, even in the case of pure reproductive selection, if one performs any sort of coarse graining and considers schemata rather than strings, then population flow is more readily understood in terms of an effective fitness landscape rather than the reproductive one. As an example, for the evolution of a particular order-1 schema in a population of N-bit strings it is more natural to consider the time dependent one-dimensional landscape associated with the schema than the collective dynamics of the
string types that go up to make the 1-schema. The job of evolution at the end of the day is to produce fit offspring which in their turn produce fit offspring which in their turn... It is no use having an individual with high reproductive fitness that is associated with a high probability to mutate to a very low fitness individual.
dependent). In this model mutation breaks the genotype-phenotype symmetry among the non-needle strings in such a way that those strings that are closer in Hamming distance to the needle have more reproductive success. Once again, this cannot be understood in terms of the fitness landscape as it is flat for the non-needle strings. The analog of equation (7.5) for non-needle strings shows us however that the effective fitness of strings that are close to the needle is higher than that of distant strings. Effective fitness in this sense is a direct measure of the strength of the breaking of the genotype-phenotype symmetry and hence offers both a qualitative and quantitative framework within which phenomena such as GP bloat and evolutionary robustness may be understood.
UNDERSTANDING GENETIC DYNAMICS:
WHAT ARE THE RIGHT EFFECTIVE DEGREES OF FREEDOM?
