ON AN EXTREMUM PRINCIPLE IN THE GENETIC THEORY OF NATURAL-SELECTION

Natural selection causes gene frequency changes in a large population leading to genetic evolution over evolutionary time scales. Such gene frequency changes, however, involve an optimizing principle. According to Kimura, such changes, over a short interval of time, occur in a ma nner such that the increase in population fitness is maximum for a giv en distance between parent and daughter generation gene frequencies. B ut according to Ewens, of all gene frequency changes, including those that lead to the same partial increase in mean fitness as the natural selection gene frequency changes, the natural selection values minimiz e the generalized distance measure between parent and daughter generat ion gene frequency values. These two optimality principles happen to b e mirror images of each other. However, the optimality principles are restricted to the case where the increase in mean fitness is to the fi rst order in natural selection gene frequency changes. I show in this paper that, instead of linear approximation to the increase in mean fi tness, the treatment can be fairly general, and the exact increase in mean fitness can be considered so as to include the dominance effects of the genes.