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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.

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