 The simplest approach to coalescence uses the Wright-Fisher model, expounded above. Recall that this model involves a diploid population of fixed size \(N\), in which selection is absent, mating is random, and generations are non-overlapping. Each new generation is formed by randomly sampling \(2N\) of the gametes produced by the previous generation. To illustrate coalescence, suppose that we pick two gene copies at random from the current population. There are then two possibilities: either both derive from a single copy in the preceding generation, or they do not. These two events occur with probabilities \(\frac{1}{2N}\) and \((1 - \frac{1}{2N})\) respectively. To see this, note that the first gene we pick must have some parent or other in the previous generation; so the probability that the two genes we pick derive from a single copy in the previous generation is simply the probability that the second gene has the same parent as the first; since there are \(2N\) possible parents, this equals \(\frac{1}{2N}\). So the alternative possibility, that the two genes do not coalesce in the previous generation, has the complementary probability of \((1 - \frac{1}{2N})\).