Polyploid and multilocus extensions of the Wahlund inequality

Wahlundʹs inequality informally states that if a structured and an unstructured population have the same allele frequencies at a locus, the structured population contains more homozygotes. We show that this inequality holds generally for ploidy level P, that is, the structured population has more P-polyhomozygotes. Further, for M randomly chosen loci (M 2), the structured population is also expected to contain more M-multihomozygotes than an unstructured population with the same single-locus homozygosities. The extended inequalities suggest multilocus identity coefficients analogous to FST. Using microsatellite genotypes from human populations, we demonstrate that the multilocus Wahlund inequality can explain a positive bias in “identity-in-state excess”.