Selection in populations with overlapping generations. I. The use of Malthusian parameters in population genetics.

Abstract The concept of the Malthusian parameter of a genotype is discussed, and an expression derived for it in terms of the age-specific mortality and fecundity functions of the genotype in question. It is shown that certain assumptions which are often made in using Malthusian parameters are not generally applicable and may sometimes lead to inaccurate results. In particular, Fisher's Fundamental Theorem of natural selection is not exact, even in the form in which he originally put it forward. Expressions for equilibrium gamete frequencies in the one and two locus situations are derived, and it is shown that they are analogous to the discrete generation equations if fitnesses are defined appropriately. They differ, however from the results using Malthusian parameters with the usual simplifying assumptions.