Testing for spatially divergent selection: comparing QST to FST.

Q(ST) is a standardized measure of the genetic differentiation of a quantitative trait among populations. The distribution of Q(ST)'s for neutral traits can be predicted from the F(ST) for neutral marker loci. To test for the neutral differentiation of a quantitative trait among populations, it is necessary to ask whether the Q(ST) of that trait is in the tail of the probability distribution of neutral traits. This neutral distribution can be estimated using the Lewontin-Krakauer distribution and the F(ST) from a relatively small number of marker loci. We develop a simulation method to test whether the Q(ST) of a given trait is consistent with the null hypothesis of selective neutrality over space. The method is most powerful with small mean F(ST), strong selection, and a large number (>10) of measured populations. The power and type I error rate of the new method are far superior to the traditional method of comparing Q(ST) and F(ST).