Population Division

F_ST

A difference in allele frequencies between populations can be quantified by "missing heterozygosity" with F_ST.

[math]F_{ST} = \frac{H_T-H_S}{H_T} = 1-\frac{H_S}{H_T}[/math]

Under an "infinite migration model" where each migrant comes from a new population (analagous to the Infinite Alleles Model where each mutation results in a new allele). At migration-drift equilibrium

[math]F_{ST} = \frac{1/(2N)}{1/(2N)+2m}[/math]

This is the rate of drift (1/(2N) the rate of pairwise coalescence within a population each generation), driving allele frequency differences between populations out of the total rate of drift and migration (2m the rate of migration when gene copies are considered in pairs to put it on the same scale as pairwise drift).

We can multiply the numerator and denominator by 2N.

[math]F_{ST} = \frac{1/(2N)}{1/(2N)+2m}\times\frac{2N}{2N} = \frac{1}{1+4Nm}[/math]

This can be rearranged to solve for Nm.

[math]\frac{\frac{1}{F_{ST}}-1}{4} = Nm[/math]