Polymorphism in a varied environment: how robust are the models?

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Abstract
SUMMARY: This paper shows that a number of models of the maintenance of polymorphism in a heterogeneous environment, including those of Levene and Dempster, can be derived from a simple assumption about the way in which the numbers and kinds of individuals emerging from a niche depend on the number of eggs laid in it. It is shown that for such models, unless selective advantages per locus are large, protected polymorphism requires that the relative niche sizes lie in a narrow range. This lack of robustness applies also to models of stable polymorphism proposed by Clarke and by Stewart & Levin. Excluding models relaying on habitat selection or restricted migration, the only models which may escape this criticism are diploid models with partial dominance with respect to fitness, such as one proposed by Gillespie, in which in all niches the fitness of heterozygotes is higher than the arithmetic mean of the homozygotes.