A population of fruit flies contains two genetically determined kinds of individuals: white-eyed flies and red-eyed flies. Suppose that a scientist maintains the population at constant size NN by randomly choosing NN juvenile flies after reproduction to form the next generation. Eventually, because of the random sampling in each generation, by chance the population will contain only a single type of fly. This is called genetic drift. Suppose that the initial fraction of the population that are white-eyed is p0p0. An equation for the average number of generations required before all flies are white-eyed (given that this occurs instead of all flies being red-eyed) is

g=2N(1p0/p0)ln(1p0).

compute dg/dp0