Convergence to equilibrium in a genetic model with differential viability between the sexes. (English) Zbl 0634.92008

Selgrade, James F.; Ziehe, Martin

J. Math. Biol. 25, 477-490 (1987).

Authors’ abstract: A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.

Reviewer: R.Bürger

MSC:

92D10

Genetics and epigenetics

Keywords:

convergence to equilibrium; differential viability; strongly monotone; transition equations; stable manifold; sexually asymmetrical viability selection; single locus, diallelic selection model; viability differences; ratios of allele frequencies; 2-dimensional difference equation; strong monotonicity; genotypic structure; equilibrium structure

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