ISOLATION BY DISTANCE IN EQUILIBRIUM AND NON-EQUILIBRIUM POPULATIONS

TLDR

Analytic theory shows that in populations with restricted dispersal, the relationship between gene flow (M̂) and geographic distance is simple and largely independent of mutation rate when it is small. The authors applied this isolation‑by‑distance analysis to two allozyme datasets from gulls and pocket gophers. Using the measure M∘ = (1/FST–1)/4 (or NST for sequence data), the authors found that gene flow can be estimated, and simulations indicate that isolation by distance is detectable with reasonable sample sizes and that non‑equilibrium patterns can sometimes be distinguished.

Abstract

It is shown that for allele frequency data a useful measure of the extent of gene flow between a pair of populations is M∘=(1/FST-1)/4, which is the estimated level of gene flow in an island model at equilibrium. For DNA sequence data, the same formula can be used if FST is replaced by NST . In a population with restricted dispersal, analytic theory shows that there is a simple relationship between M̂ and geographic distance in both equilibrium and non-equilibrium populations and that this relationship is approximately independent of mutation rate when the mutation rate is small. Simulation results show that with reasonable sample sizes, isolation by distance can indeed be detected and that, at least in some cases, non-equilibrium patterns can be distinguished. This approach to analyzing isolation by distance is used for two allozyme data sets, one from gulls and one from pocket gophers.