SOME NATURAL VIABILITY SYSTEMS FOR A MULTIALLELIC LOCUS: A THEORETICAL STUDY

Samuel Karlin ¹

¹ Department of Mathematics, Stanford University, Stanford, California 94305

The maintenance of genetic polymorphism under various natural structured viability regimes vs. general unrestricted fitness assignments are compared. The selection models considered include a generalized dominance fitness system, a generalized viability model based on allelic activity values, viability matrices based on multilocus activity levels, viability matrices defined by partitioned "resource" or "substrate" variables, and circulant-type viability matrices. A number of examples that support these formulations are discussed. Detailed results on the nature of the genotype frequency equilibrium configurations for the specified viability models are presented. An increased likelihood for a globally stable equilibrium is predicted for the more structured viability models.

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