DIFFERENTIAL FERTILITY IN POPULATION GENETICS MODELS

Abstract

ALMOST all investigations of the changes in gene frequency caused by natural selection are based upon the assumption that selection operates through differential survival of the zygote from birth to maturity. It is, no doubt, generally assumed that selection through differential fertility would in most situations give similar qualitative results. There have, however, been very few specific analyses of population genetic models involving fertility differentials. PENROSE (1949) showed that, with random mating and one locus with two alleles, a simple additive fertility model gave the same equations as the usual models involving differential survival to maturity. Evidence for fertility differences associated with the hemoglobin sickle-cell trait (see review by RUCKNAGEL and NEEL 1961) , has revived interest in models which specifically take account of both differential survival and fertility. Completely general models involving fertility and survival parameters which may be functions of the genotype frequencies (as for example, in the case of Rh incompatible matings) , and survival parameters which may be functions of the mating type (as in the case of competition within families or familial selection (HALDANE 1924) are analytically intractable. We shall assume random mating, constant fertilities, and viabilities, which latter are the same for all mating types. Then, granted certain restrictions on the fertilities, it will be shown that there is a close correspondence between fertility and viability models. The solutions of some special cases of the models are examined in detail. Formulation of Random Mating Model with T m Alleles at a Single Locus