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where time is in continuous units of multiples of 2N. Thus, the average height in continuous time of a coalescent tree starts at 2(1 - V2) = 1 for a pair of lineages and approaches 2 as k grows very large. In time units of 2N generations, the average tree height starts at 2N and increases to 4N as k grows. The average total waiting time for all lineages to coalesce is heavily influenced by the average waiting time for the last pair of lineages to coalesce. Stated another way, average waiting times are shorter when k is larger and increase as lineages coalesce and k gets smaller. This result makes sense since there are fewer and fewer independent pairs of lineages that k(k -1)

can coalesce as k decreases (think of —2— as k decreases to 2).

The variance in the height of a coalescent tree is the sum of the variances in the coalescence time for each set of coalescent events since all coalescent events are independent:

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