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

The fixation index F S T and the coefficient of gene differentiation G S T 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 F S T (and G S T ). Our formulas generalize earlier ones and reveal that the equilibrium value of F S T is influenced not only by the migration rate and local effective population size, N e , 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 F S T . A major advantage compared to previous approaches is that stochastic allele frequency of migrants is easily accommodated, thereby avoiding underestimation of F S T for large migration rates.