 This reasoning can be repeated in a natural way. Suppose that the two genes we pick do not coalesce in the immediately previous generation, i.e., they have different parents. Then, those two parents genes will themselves either derive from a single copy in the previous generation, or they will not. If so, then the two genes we have picked will coalesce two generations ago, i.e., derive from a single grandparent gene. The probability of this is \(\frac{1}{2N} \times (1 - \frac{1}{2N})\). By iterating this reasoning, we can work out the probability distribution that two randomly chosen gene copies in the current generation derive from a common ancestor t generations ago. This is given by: