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Time to most recent common ancestor in units of 2Ne generations

Figure 3.27 The distribution of times to a MRCA (or genealogy heights) for 1000 replicate genealogies starting with six lineages (k = 6). The distribution of total coalescence times has a large variance because the range of times is large and also asymmetric with a long tail of a few genealogies that take a very long time to reach the MRCA. The genealogies shown above the distribution are those for the tenth, fiftieth, and ninetieth percentile times to MRCA. In this example Ne = 1000.

Time to most recent common ancestor in units of 2Ne generations

Figure 3.27 The distribution of times to a MRCA (or genealogy heights) for 1000 replicate genealogies starting with six lineages (k = 6). The distribution of total coalescence times has a large variance because the range of times is large and also asymmetric with a long tail of a few genealogies that take a very long time to reach the MRCA. The genealogies shown above the distribution are those for the tenth, fiftieth, and ninetieth percentile times to MRCA. In this example Ne = 1000.

represented along each lineage in the tree. If the branches represented a system of roadways, then the sum of the distances traversed when driving over each segment of road once would be analogous to the total branch length. For example, if a pair of lineages has a waiting time x until coalescence, then the total waiting time is x + x = 2x. The average total branch length of a genealogical tree is then just twice the sum of the average waiting times (using continuous time) for each coalescence event:

of two. The expected total branch length starts at two, increasing with greater k and never reaching a maximum. However, the expected total branch length of a genealogy grows more and more slowly as k increases since the expected time to coalescence decreases with increasing k.

This section defines how coalescent theory describes the probabilistic events associated with lineage branching for a single population. This basic model can be extended to include the influence of numerous population genetic processes on coalescence. Later sections and chapters will explore how changes in population size (the next section), subdivided populations that experience gene flow (Chapter 4), mutation (Chapter 5), and natural selection (Chapter 7) influence patterns of coalescence. The application of coalescent theory to DNA sequence data, including examples based on empirical data, will be covered in Chapter 8.

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