Analysis of Finite Population Evolution Models Using a Moment Closure Approximation

Evolutionary dynamics is traditionally considered under either an infinite population or a finite population assumptions. The stochastic effects due to sampling of finite population system play important role in evolution and have been analyzed since 1930s. Here, we connect the infinite and finite population cases using moment closure approximation. We develop a moment closure scheme for the Wright–Fisher model, connecting it with the discrete time Eigen model. Numerical simulations show that our method efficiently solves problems of evolutionary dynamics such as allele fixation. We apply the same method to the finite population version of the Crow–Kimura model and derive the finite population corrections to the mean fitness of population for the single peak fitness case. The result that is supported by numerical simulations is that these corrections diverge near the error threshold point.