N

Bringing these two probabilities together into an equation like 3.62 gives the probability that k lineages experience a single coalescent event t generations ago:

Since this probability also follows an exponential

distribution (e ^ 2 A2N1), the average time to coalescence for k lineages in a population of 2N is 2N

kk—1). For example, if k = 3 and 2N = 10, the aver-2

age time to coalescence is 31/3 generations. This is one-third of the average waiting time for two lineages since each of the three unique pairs of lineages (1-2, 1-3, and 2-3) can independently experience coalescence. Figure 3.26 shows the average coalescence times for six lineages based on this same logic. The general pattern is that coalescence times decrease when more lineages are present since there are a larger number of lineage pairs that can independently coalesce.

0.3 or 0.6N Present time

0 0

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