Analogy to inbreeding

You may have noticed some similarities between drift and inbreeding. Specifically, both processes lead to a loss of heterozygosity and an increase in homozygosity. This analogy leads to a useful heuristic for helping us to understand the dynamics of genetic drift.

Remember our old friend $f$, the inbreeding coefficient? I'm going to re-introduce you to it in the form of the population inbreeding coefficient, the probability that two alleles chosen at random from a population are identical by descent. We're going to study how the population inbreeding coefficient changes from one generation to the next as a result of reproduction in a finite population.¹²

$$\begin{eqnarray*} f_{t+1} &=& \mbox{Prob. ibd from preceding generation} \\ ... ...en.}) \\ &=& \frac{1}{2N} + \left(1 - \frac{1}{2N}\right)f_t \end{eqnarray*}$$

or, in general,

$$f_{t+1} = 1 - \left(1 - \frac{1}{2N}\right)^t(1-f_0) \quad .$$