Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics |
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| Authors: | K. J. Brown S. S. Lin A. Tertikas |
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| Affiliation: | (1) Department of Mathematics, Heriot-Watt University, EH14 4AS Riccarton, Edinburgh, UK;(2) Department of Applied Mathematics, National Chiao Tung University, Hsin-Chu, Taiwan 300, Republic of China |
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| Abstract: | We discuss a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. It is shown that if A1 is at an overall disadvantage to A2 and the rate of gene flow is sufficiently large than A1 must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A1 and A2 can coexist no matter how great the rate of gene flow. |
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| Keywords: | Population genetics Bifurcation theory Indefinite weight functions Sub- and supersolutions |
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