Convergence to equilibrium in a genetic model with differential viability between the sexes |
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| Authors: | James F. Selgrade Martin Ziehe |
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| Affiliation: | (1) Mathematics Department, North Carolina State University, 27695 Raleigh, NC, USA;(2) Genetics Department, North Carolina State University, 27695 Raleigh, NC, USA;(3) Present address: Abteilung für Forstgenetik und Forstpflanzenzüchtung der Universität Göttingen, Büsgenweg 2, D-3400 Göttingen, FRG |
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| 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.Partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, USASupported by a grant from the Max Kade Foundation, New York, USA |
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| Keywords: | Differential viability Strongly monotone Transition equations Equilibrium Stable manifold |
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