Convergence of multilocus systems under weak epistasis or weak selection

The convergence of multilocus systems under viability selection with consta nt 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 no ndegeneracy 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 a re also analyzed.