Error estimate for the diffusion approximation of the Wright--Fisher model

The Wright--Fisher model and its approximating diffusion model are compared in terms of the expected value of a smooth but arbitrary function of nth-generation gene frequency. In the absence of selection, this expectation is shown to differ in the two models by at most a linear combination (with coefficients depending only on the derivatives of the smooth function involved) of the maximum mutation rate and the reciprocal of the population size.