Quasi equilibrium approximations of the fixation index under neutrality: The finite and infinite island models

The fixation index FST and the coefficient of gene differentiation GST are analyzed for the finite island model under short time spans, ignoring mutations. Dividing the reproduction cycle into the three steps-gamete formation, fertilization, and migration-we develop a new approach for computing quasi equilibrium formulas for FST (and GST). Our formulas generalize earlier ones and reveal that the equilibrium value of FST is influenced not only by the migration rate and local effective population size, Ne, but also by the local census size N, particularly so when the migration rate is high. The order of migration and fertilization is found to have a smaller effect on FST. A major advantage compared to previous approaches is that stochastic allele frequency of migrants is easily accommodated, thereby avoiding underestimation of FST for large migration rates.