Convergence of multilocus systems under weak epistasis or weak selection |
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Authors: | Thomas Nagylaki Josef Hofbauer Pavol Brunovský |
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Affiliation: | (1) Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, Illinois 60637-1573, USA, US;(2) Institute of Mathematics, University Vienna, Strudlhofgasse 4, A-1090 Wien, Austria, AT;(3) Institute of Applied Mathematics, Comenius University, Mlynska Dolina, 84215 Bratislava, Slovakia, XX |
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Abstract: | The convergence of multilocus systems under viability selection with constant fitnesses is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. It is proved that if epistasis or selection is sufficiently weak (and satisfies a certain nondegeneracy assumption whose genericity we establish), then there is always convergence to some equilibrium point. In particular, cycling cannot occur. The behavior of the mean fitness and some other aspects of the dynamics are also analyzed. Received: 15 November 1997 / Revised version: 25 May 1998 |
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Keywords: | : Selection Recombination Epistasis Convergence Chain recurrence Invariant manifold Quasi-linkage equilibrium |
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