Mathematical Constraints on FST: Biallelic Markers in Arbitrarily Many Populations

FST is one of the most widely used statistics in population genetics; however, recent mathematical studies have identified constraints that challenge interpretations of FST as a measure with potential to range from 0 for genetically similar populations to 1 for divergent populations. The current study found that for fixed K, FST has a peculiar constraint as a function of M, with a maximum of 1 only if M = i/K, for integers i with ceiling(K/2) = i = K-1. For fixed M, as K grows large, the range of FST becomes the full closed or half-open unit interval. For fixed K, however, some M < (K-1)/K always exists at which the upper bound on FST lies below 2v2-2 &#8776; 0.8284. Coalescent simulations were used to show that under weak migration, FST depends strongly on M when K is small, but not when K is large. Finally, using data on human genetic variation, researchers used their results to explain the generally smaller FST values between pairs of continents relative to global FST values. Implications are discussed for the interpretation and use of FST. (Publisher abstract modified)