Density-dependent Limitation Research Articles

Selection in populations with overlapping generations VI. Rates of change of gene frequency and population growth rate

Two methods (Methods 1 and 2) are used to derive approximate equations describing the rates of change of gene frequency and population growth rate in an age-structured population which is not subject to density-dependent limitation of numbers. Method 2 gives equations which are closely related to Fisher's Malthusian parameter equations, and are good approximations even with quite strong selection (30% selection coefficients) in the case of a single autosomal locus. When there is strong heterotic selection, however, Method 2 gives a bad fit to the population's behaviour in the neighbourhood of equilibrium, but a good fit elsewhere. Method 1 gives a good fit near equilibrium, but a bad fit when gene frequencies change rapidly. With strong heterotic selection, therefore, no single set of selection parameters is adequate, but in other single locus cases, the genotypic intrinsic rates of increases may be used, except when selection is very intense. In multilocus situations it is shown that further specializing assumptions have to be made for this to be true. The asymptotic states of populations under various selection regimes are determined for the case of a single locus with two alleles, when the direction of selective differences remains constant throughout the life-span of an individual.