MULTILOCUS BEHAVIOR IN RANDOM ENVIRONMENTS I. RANDOM LEVENE MODELS

John Gillespie ¹ and Charles Langley ¹

¹ Environmental Mutagenesis Branch, National Institute of Environmental Health Sciences, P. O. Box 12233, Research Triangle Park, North Carolina 27709

In this paper the consequences of natural selection acting on several loci simultaneously in a spatially fluctuating environment are described. The fitnesses of the genotypes are assumed to be additive both within and between loci. The environment is assumed to be made up of a very large (effectively infinite) number of patches in which fitnesses are assigned at random. The resulting deterministic model is called a Random Levene Model and its properties are approximated by a system of differential equations. The main equilibrium properties are that (1) the linkage disequilibrium is zero and (2) the correlations in fitnesses between alleles at different loci are the principle determinants of the dynamic inter-locus interactions. Although there is no epistasis as conventionally defined, the equilibrium state at the two loci are highly interdependent, the governing principle being that two alleles at different loci whose fitness are negatively correlated across environments have a higher overall fitness due to the reduction in their variance in fitness through the negative correlation. When a large number of loci are considered, they naturally fall into correlation groupings which lead to an enhanced likelihood for polymorphism over that predicted by single-locus theory.

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