The following problem arises in the context of a paper on population genetics (Kimura 1962, p. 717). I have posted it here because its solution should demand only straightforward applications of tools from analysis and algebra. However, I cannot figure it out. 1. The problem statement, all variables and given/known data Let z = 4 N s [1 - 2 N v x (1 - x)] G(x) = e^-∫z dx u(p) = [∫G(x)dx (from x = 0 to p)] / [∫G(x)dx (from x = 0 to 1)] Assume that v << 1, and 2Nv << 1. Assume further that Ns is large, but (8 N^2 s v) is very small. We have u = 2s - v. My question is: how is this obtained? 2. The attempt at a solution One first multiplies z out, getting z = 4Ns - 8N^2 v s x (1 - x) Then one can plug this into the expression for G(x) G(x) = e^-∫z dx At this point, I have tried to take 8N^2 v s -> 0, and so we are left with the expression G(x) = e^-∫4Ns dx However, I do not know if it is justified to do this now, and this may be where I go wrong. Nevertheless, if we do this, we can simply integrate ∫4Ns dx = 4Nsx, and so G(x) = e^-4Nsx. Then we plug this expression into the u(p) expression, but this does not yield the correct solution. I would be very grateful for any advice.