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By Queen Mary, Westfield College, Robert C. Griffiths, R. L. Dorit, H. Akashi and W. Gilbert


3. Write p(m, n) for the probability that a sample of size m sequences from the population has the same common ancestor as a subsample of n of the m sequences, given that the n sequences exhibit no variability. Standard arguments show that the p(m, n) satisfy the recursion (m(m- 1)+2NpLn)p(m, n) =n(n- 1 + 2N,u)p(m- 1, n- 1) + [m(m- 1)- n(n- 1)]p(m- 1, n), with initial conditions p(m, 1) = 1 if m = 1 and 0 otherwise, and p(n, n) = 1. We evaluated limm_p(m, 38) numerically. 4. Variable population size was modeled as follows: the population was of constant size N, = otNO until Z years ago, when it began exponential growth to it

Year: 2010
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