Wright-Fisher Model

Wright-Fisher model is the canonical mathematical model of population genetics, developed independently by Sewall Wright and R.A. Fisher in the early 1930s. It describes how allele frequencies change from one generation to the next in an idealized population of constant size N, where each individual in the offspring generation is formed by randomly sampling two parents (with replacement) from the previous generation.

The model's simplifying assumptions — discrete generations, random mating, no selection, no mutation, no gene flow — make it analytically tractable but biologically unrealistic. Its value lies not in descriptive accuracy but in providing a null model against which real population dynamics can be measured. Deviations from Wright-Fisher predictions reveal the action of selection, drift, or non-random mating.

Under the Wright-Fisher model, the probability that an allele reaches fixation is equal to its initial frequency, and the expected time to fixation or loss scales with population size. The model is the foundation of coalescent theory and the diffusion approximation for allele frequency dynamics, which extend it to include selection and mutation.