Convergence to Equilibrium in a Polylocus Polyallele Population with Additive Selection

he article considers an infinite panmix autosomal population with discrete nonoverlapping generations that is haploid on the gamete level and diploid on the zygote level. In the population there is additive selection with respect to any number of autosomal loci with any number of alleles at each locus; there are no mutations. It is shown that if the fitnesses at each locus are positive, then the population tends to equilibrium regardless of its initial state. This had been established earlier only for two diallele loci with preference of heterozygotes at each one [S. Karlin and M. W. Feldman, J. Appl. Probab., 1970, no. 7, pp. 262–271].