  The Wright-Fisher process with selection is an important tool in population
genetics theory. Traditional analysis of this process relies on the diffusion
approximation. The diffusion approximation is usually studied in a partial
differential equations framework. In this paper, I introduce a path integral
formalism to study the Wright-Fisher process with selection and use that
formalism to obtain a simple perturbation series to approximate the transition
density. The perturbation series can be understood in terms of Feynman
diagrams, which have a simple probabilistic interpretation in terms of
selective events. The perturbation series proves to be an accurate
approximation of the transition density for weak selection and is shown to be
arbitrarily accurate for any selection coefficient.
