Mathematical frameworks for phenotypical selection and epistasis.
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.
Lyubich
Yuri
Y
Department of Mathematics, Technion, Haifa 32000, Israel. lyubich@techunix.technion.ac.il
Kirzhner
Valery
V
D000483:Alleles; D000818:Animals; D004843:Epistasis, Genetic; D019143:Evolution, Molecular; D005838:Genotype; D008957:Models, Genetic; D010641:Phenotype; D012641:Selection, Genetic