Differential Fertility in Population Genetics Models
Genetics, 51 (3):
411--424 (March 1965)DOI: 10.1093/genetics/51.3.411
Abstract
ALMOST all investigations of the changes in gene frequency caused by nat-
ural 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 addi-
tive fertility model gave the same equations as the usual models involving differ-
ential 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.