An analysis of Expected Population States in the Space of Population States: the Case Study of Three-Element Populations

In this paper, an analysis of phenotypic evolutionary search with proportional selection and Gaussian mutation is presented. Evolution is regarded in the space of population states where population is considered as a whole. This approach enables theoretical studies of expected states for small populations. In this paper, three-element populations are examined. The expected states of populations cannot be calculated explicitly due to overwhelming complexity. Therefore, they are approximated numerically. A study of the expected states dynamics and its dependence on several parameters is also provided. It appears that the population moves around, in a fitness landscape, as a compact cluster of individuals and quickly locates neighborhoods of optima.