Coalescent genealogies and population bottlenecks

Let's examine the distribution of coalescence times in a population that experiences a bottleneck to see how genealogical branching patterns are affected. The situation in Fig. 3.28 is analogous to that in section 3.3 where a population starts out with 100 individuals, is reduced to 10 individuals for one generation, and then returns to a size of 100 individuals in the third generation (see Fig. 3.16). For a bottleneck of 100-10-100 over three generations, equations 3.85 and 3.86 can be used to determine the probability of coalescence events. A 100-10-100 population is equivalent to a population of 25 that is constant in size. Therefore, the average probability of two randomly sampled gene copies not finding their common ancestor over the three generations spanning the bottleneck is:

giving a chance of coalescence of 1 - PnC = 1 -0.9418 = 0.0582. This probability is equivalent to for three generations of 100-10-100 or

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