Monotonic change of the mean phenotype in two-locus models.

Abstract

It is shown that the mean phenotype monotonically approaches the optimum in a class of symmetric, two-locus, two-allele models with stabilizing selection. In this model, mean fitness does not change monotonically. Thus, Fisher's fundamental theorem does not hold, even though another quantity of evolutionary interest, the mean phenotype, can be shown to change monotonically. Using this quantity, it is proven that global stability results for this model.