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Convergence of multilocus systems under weak epistasis or weak selection. (English) Zbl 0981.92019
Summary: 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.

MSC:
92D15 Problems related to evolution
37N25 Dynamical systems in biology
92D10 Genetics and epigenetics
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