Moran process
stochastic process used in biology to describe finite populations
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. 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.
Neutral drift
Neutral drift is the idea that a neutral mutation can spread throughout a population, so that eventually the original allele is lost.
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