N

which when multiplied by —- gives the e simpler equation

The terms in the numerator and denominator can be multiplied out to give an expression that is fairly complex (feel free to do the expansion if you are curious). However, if we again invoke the assumption that the migration rate is small and much, much less than the effective population size, then terms in the expansion of equation 4.60 containing m or powers of m can be ignored since they are very small (e.g. if m = 0.01 then 2m = 0.02 and m2 = 0.0001). This then leads to the approximation for the expected value of the fixation index

Substituting the full expressions for a, b, and c gives

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