Wright-Fisher Models, Approximations, and Minimum Increments of Evolution

Wright-Fisher models [1] are idealized models for genetic drift, the process by which the the population frequency of an allele varies with time stochastically, and, in particular, may disappear from the population entirely, or may fix in 100% of the population. Wright-Fisher models can be applied to the dynamics of neutral (or nearly neutral) mutations – the vastly dominating case, as emphasized by Kimura [2] – or to the case of alleles that have a fitness advantage or disadvantage, as parameterized by a selection coefficient s. Wright-Fisher models make three idealized assumptions: [3] (1) Generations are taken to be discrete, so that the population evolves by a discrete-step Markov process. (2) The population size is taken to be fixed, so that alleles compete only against other alleles and not against an external environment. (3) Random mating is assumed. None of these assumptions hold in any real population. Nevertheless, Wright-Fisher has proved to be a useful intuitive guide in real cases, and also a foundation on which more complicated population models can build. [4]