In population genetics an idealised population or a Fisher — Wright population is a population whose members can mate and reproduce with any other member of the other gender, and where random genetic drift does not occur. Population genetics is the study of the distribution of and change in allele frequencies under the influence of the five evolutionary forces: natural selection, genetic drift, mutation, migration and nonrandom mating. ... A pair of lions copulating in the Maasai Mara, Kenya. ... Reproduction is the creation of one thing as a copy of, product of, or replacement for a similar thing, e. ... Genetic drift is a mechanism of evolution that acts in concert with natural selection to change the characteristics of species over time. ...

Deviation from the idealised population results in the effective population size. The effective population size (Ne) is defined as the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration (Sewall Wright). ...

It is sometimes called the Fisher — Wright population after Ronald Fisher and Sewall Wright. Is the most popular stochastic model for reproduction in population genetics is the Wright-Fisher model. Sir Ronald Fisher Sir Ronald Aylmer Fisher, FRS (February 17, 1890 – July 29, 1962) was an evolutionary biologist, geneticist and statistician. ... Sewall Green Wright (December 21, 1889 - March 3, 1988) was one of the primary founders of population genetics which led to the modern evolutionary synthesis. ...

Wright-Fisher has many of the same assumptions as Hardy-Weinberg Equilibrium, with the important exception of finite population size N (after all, it is the effects of sampling gametes in a finite population that we are interested in modeling). The really crucial assumptions are:

1. finite and constant N,
2. random mating with respect to the gene being studied, and
3. non-overlapping generations.

This is enough to generate the basic reproductive model, but here, being interested in the stochastic fate of a neutral variant, we will further assume neutrality (no selective differences between alleles) and no additional mutation during the sojourn of our variant. This gives us a complete description of the forces acting on alleles across generations, and we can now derive some simple (but as it turns out, quite powerful) results. Of particular interest is the probability of fixation of a mutant, the replacement of one allelic type with another on a population scale. Independent fixation events along separate lineages form the basic evidence for phylogenetic reconstruction of the relationships of those lineages.

First, note that because allelic variants are neutral, it makes no difference to the fate of individuals (and thus the descent of their alleles) how the alleles are distributed among individuals. We can consider a haploid model then, as equivalent to a diploid model and in general, no matter what the ploidy level, consider the``individuals" in the model to be gametes, without regard to their arrangement in the organisms themselves. Because most organisms of biological study are diploidgif, we will keep that convention, but the only effect in this case is that our population size is 2N gametes, rather than N. The remaining necessary specifications to the model are as follows:

1. 2 alleles, A1 and A2
2. let X(t)=number of A2 alleles at time t
3. let p(i,j)=Probability(X(t+1)=j|X(t)=i)

 In the Wright-Fisher model, we imagine that gametes are chosen randomly each generation from an effectively infinite gamete pool reflecting the parental allele frequencies. Then the sampling is binomial, and 

p(i,j)={2N choose j} (i/2N)^j (1- i/2N)^{2N-j}

 Recall that one of the implications of Hardy-Weinberg was that under random mating and absent any directional perturbing forces such as mutation and selection, genetic systems will be at a stable equilibrium.