 where \(p_0\) is the initial frequency of the \(A_1\) allele in the population, i.e., before any migration has taken place. Since the expression \((1 - m)^t\) tends towards zero as \(t\) grows large, it follows that equilibrium will eventually be reached when \(p_t = p_m\), i.e., when the gene frequency of the migrants equals the gene frequency of the resident population.