Evolutionary principles for polynomial models of frequency-dependent selection

A one-locus two-allele deterministic model of frequency-dependent selection is analyzed, where genotypic fitness [w(i)(q)] are assumed to be nth-degree polynomial functional of allele frequency (q). The model encompasses many modes of selection, including intraspecies competitive interaction, brood selection, meiotic drive, cyclical selection, and mixed models. Allelic frequencies converge monotonically to locally stable equilibria provided that [dw(i)(q)/dq] is not large. There exists a function T(q) that is nondecreasing and locally maximized at locally stable equilibria. The rate of change of T(q) per generation is approximately equal to the additive genetic variance in fitness. T(q) is a simple function of the average effect of an allelic substitution and is closely related to Wright's 'fitness function'. These results define 'evolutionary landscapes' for some complex selection processes and enlarge the scope of the classical methods embodied in Wright's 'mean fitness principle' and 'Fisher's 'fundamental theorem'.