Linkage disequilibrium in a finite population that is partially selfing

The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size N(e) = (1-(1/2)S)N and the effective recombination value r(e) = (1-S)r/(1-(1/2)S), where S is the proportion of selfing, are substituted for the population size and the recombination value. Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1-(1/2)S and the recombination value by a factor (1-S)/(1-(1/2)S).