Estimates and bounds on the rate and extent of allele frequency change

Two approximations are provided to the frequency of an autosomal allele after any number of generations of selection and, conversely, to the number of generations required for any given frequency change. These estimates are accurate over a wide range of selection coefficients and initial conditions, and have the added advantage of providing strict upper and lower bounds to the true values under quite general conditions. The approach employed here, of finding exact solutions to approximating difference equations, could easily be applied to models with migration, mutation, etc. and, indeed, to any non-linear difference equation. In such applications, it offers several advantages over traditional methods from approximation theory.