The variance rapidly approaches the value of about 1.16 as the number of lineages sampled, k, increases to large values. The finite maximum value of the variance and the fact that the variance in tree height for k = 2 lineages is 1.0 highlights the major impact of the coalescence time of the last pair of lineages on the overall height of a coalescence tree. Figure 3.27 illustrates the variance in the total height of genealogies by displaying the time to MRCA for 1000 replicate genealogies each starting with k = 6. The range of time to MRCA is large and the distribution has a very long tail representing a small proportion of genealogies that take a very long time for all coalescence events to occur.

Another useful measure is the total branch length of a coalescent genealogy of k lineages or Lk. The total branch length is the sum of the waiting times

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