Wright–Fisher model
The Wright–Fisher model is a discrete-generation stochastic model of genetic drift.
Binomial sampling
For a haploid population of size \(N\), if allele \(A\) has current frequency \(p_t\), then the number of copies in the next generation satisfies
\[X_{t+1}\sim\operatorname{Binomial}(N,p_t),\qquad p_{t+1}=\frac{X_{t+1}}{N}.\]Hence
\[E[p_{t+1}\mid p_t]=p_t,\qquad \operatorname{Var}(p_{t+1}\mid p_t)=\frac{p_t(1-p_t)}{N}.\]Extensions
Selection, mutation and migration can be incorporated by changing the sampling probability before the next generation is drawn.
Key idea. Wright–Fisher drift arises because each new generation is a random sample derived from the previous generation.