Exact analysis of selection and recombination for two and three loci

Deterministic equations are derived describing the evolution of gene frequencies for two and three loci with binary alleles. Even ONEMAX function leads to nonlinear di erence equations. An exact expression for the realized heritability is derived. It is shown with simple tness functions that recombination may fail to lead the population to the optimum. The challenge of population genetics and genetic algorithm research remains to find approximate solutions to the exact equations. Our approximation for the ONEMAX function, based on the assumption of binomial distributed tness values, reasonably predicts the evolution of the average fitness