Parent—offspring correlation in fitness under fluctuating selection

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Abstract
Cyclical selection that does not result in gene fixation may maintain a parent-offspring (P-O) correlation in fitness that is, most of the time, not far below one-half. This tends to happen when the following conditions are fulfilled: (i) slow cycling in allele frequencies occurs at many loci independently; (ii) most alleles make only small differences to fitness; (iii) dominance in allelic fitness contribution is rare and overdominance rarer still. In contrast, drastic cyclical selection (dependent on large fitness differences without overdominance), because direction reverses so frequently, may give P-O correlations in fitness that are near zero or even negative. Also, if much fitness variance is maintained by heterozygote advantage, or is caused environmentally, the correlation is reduced in proportion to the ratio of relevant standard deviations. P-O correlation in fitness that is almost permanently positive may help to explain mate choice in sexually promiscuous species. The most likely source of the multiple independent cyclical systems of selection required is host-parasite relations. To cause evolution of mate choice, and the subsequent manifestations of sexual selection, intermediate rather than extremely long cycles are most effective. A chooser's achievement for the offspring depends on the fitness variance in the sex chosen; in extremely long cycles this variance is on average close to zero.

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