Mathematical frameworks for phenotypical selection and epistasis |
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Authors: | Lyubich Yuri Kirzhner Valery |
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Affiliation: | Department of Mathematics, Technion, Haifa 32000, Israel. lyubich@techunix.technion.ac.il |
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Abstract: | A mathematical approach to interactions between genotypes and phenotypes in a multilocus multiallele population is developed. No a priori information on a fitness function is required. In particular, some structural definitions of epistasis and the position effect are given in terms of a decomposition of phenotypical structures. On this base a distance to the additive non-epistasis is introduced and an explicit formula for it is obtained. A class of phenotypical structures including multilocus dominance is described in terms of directed graphs. The evolutionary equations are adjusted to a fitness function compatible with a phenotypical structure. Some results on the finiteness of the equilibria set are presented. |
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