A Moran process or Moran model is a simple stochastic process used in biology to describe finite populations. The process is named after Patrick Moran, who first proposed the model in 1958.[1] It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift and natural selection. The process can describe the probabilistic dynamics in a finite population of constant size N in which two alleles A and B are competing for dominance. The two alleles are considered to be true replicators (i.e. entities that make copies of themselves).
In each time step a random individual (which is of either type A or B) is chosen for reproduction and a random individual is chosen for death; thus ensuring that the population size remains constant. To model selection, one type has to have a higher fitness and is thus more likely to be chosen for reproduction. The same individual can be chosen for death and for reproduction in the same step.