Drift 2

5The mean of a binomial random variable with parameters n (= 2N) and p = 2Np, Var =2NpqLet p' = X/2N, so E[p'] = E[X]/2N = 2Np/2N = pVar(p') = Var[X]/4N 2 = pq/2NSee JHG Equation B.12 for derivationDefine N e as the size of an ideal Wright-Fisher population with Var(p') = pq/2N, calledthe "variance effective size"In words, N e is the size of an ideal W-F population that undergoes an equivalent amountof genetic drift as the real population in question.- Two special cases of N e1. Fluctuating population size (N not constant)1/N e = (1/N 1 + 1/N 2 +...1/N t )N e = the "harmonic" meane.g., N 1 = 1000, N 2 = 10, N 3 = 1000, N e = 29.4, (arithmetic mean N = 670)2. Unequal sex ratio (i.e., in a dioecious species)N e = 4N m N f /(N f + N m )e.g., N m =10, N f = 100, Ne = 36.4III. Mutation and DriftDrift removes variation, mutation puts it back in. Now we'll see what happens when weviolate the second H-W assumption, i.e., no mutation.III.A. Rate of change of allele frequency under mutation alone- Let A1 → A2 = u- Let A2 → A1 = vSo, p' = p(1-u) + (1-p)vIn words, the frequency of the A1 allele in the next generation is the frequency in thecurrent generation (p) multiplied by the probability an A1 allele does not mutate (1-u)