Theoretical distributions

The distribution of the time to the most recent common ancestor, in units of \(2N_e\) generations. For a sample of \(n\) haploid lineages, the distribution is \(n - 2\) convolutions of exponential random variables. See Wakeley [2008], page 77, for details.

The distribution of the total time on a non-recombining tree, in units of \(2N_e\) generations. The plot is based on Equation 3.34 from Wakeley [2008], page 78.

The distribution of the number of polymorphic mutations (“segregating sites”) on a tree under the infinitely-many sites model. The formula plotted is from Tavaré [1984], which can be found on page 94 of Wakeley [2008].

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Theoretical expectations

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Mutation frequencies under selection (interactive Python)