A graphical approach to multi-locus match probability computation: revisiting the product rule

The genealogical relationships of individuals in a finite population can create statistical non-independence of alleles at unlinked loci. In this paper, we introduce a flexible graphical method for computing the probabilities that two individuals in a finite, randomly mating population have the same haplotype or genotype at several loci. This method allows us to generalize the analysis of Laurie and Weir [2003. Dependency effects in multi-locus match probabilities. Theor. Popul. Biol. 63, 207-219] to cases with more loci and other models of mating. We show that monogamy increases the probabilities of genotypic matches at unlinked loci and that the effect of monogamy increases with the number L of loci. We conjecture a sharp upper bound on the effect of monogamy for a given L.