A population with nonoverlapping generations n = 0, 1, 2, 3, ... , and with  genes (or "individuals") at time n forms a Markov chain under the following assumptions. The introduction of an individual possessing an allele with a selective advantage corresponds to .
In the context of population dynamics, a group of individuals with non-overlapping generations (n = 0, 1, 2, 3, ...) and a fixed number of genes or individuals at each time point can be modeled as a Markov chain. The arrival of an individual carrying a beneficial allele is comparable to .