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Figure 3.25 Six independent realizations of the coalescent tree for six lineages. All six trees are drawn to the same scale. Each genealogy exhibits coalescent events between random pairs of lineages. The differences in the height of the trees is due to random variation in waiting times. Because of this random variation, average times to coalescence for a given number of lineages are only approached in a large sample of independent trees. Because genealogies are drawn sideways here, tree "heights" are actually width, from left to right.

where k is less than or equal to the total number of lineages sampled from a population of 2N. To see the problem in detail, let's consider the case of k = 3 lineages. When no coalescence events occur, one lineage finds its ancestor among any of the 2N individuals in the previous generation. That means the next lineage must find its ancestor among 2N - 1 individuals in the previous generation and the final lineage must find its ancestor among 2N - 2 possible parents. Thus the probability of non-coalescence is k-1 n x=0

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