T

where 0 = 4Ne|. (This requires the assumptions that the time of lineage divergence T is a random variable with a geometric distribution as in a genealogical branching model, and that Ne is large and | is small.) As shown in Math box 8.1, this new version of the dispersion index can be re-written as

If we assume that there is no ancestral polymorphism or that T = 0 in Fig. 8.17, then 0 is zero and R(t) is identical to what is expected under the Poisson process molecular clock dictated by divergence only.

The major conclusion is that the two-process version of R(t) is expected to be greater than one when there is any ancestral polymorphism even when DNA changes follow a constant molecular clock. Stated another way, ancestral polymorphism increases the variance in the number of substitutions seen for pairs of sequences evolving under a constant rate compared with a pure divergence process. Unfortunately, the index of dispersion in equation 8.43 seems impossible

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