Biostatistics 666 Problem Set 3 Due February 8, 2006 Modeling Events in the Coalescent 1.Consider the genealogy of a set of three sequences from a population of N = 2500 diploid individuals. Assume that the recombination rate per sequence per generation is r= 10-5and the mutation rate is μ = 10-5per sequence per generation. When we move backwards in time by one generation, what is the probability of… a)… a coalescence event? b)… a mutation occurring? c)… a recombination event occuring? d)… one of these three events occuring? In addition, calculate the following quantities … e)Number of generations do you expect to pass before a), b) or c) occurs? f)When one of these events occurs, what is the probability that it is a recombination? Finally, … g)Assume that the following events occur in order as we trace the ancestry of the three sequences: mutation (event closest to the present), coalescence, recombination, mutation, coalescence, coalescence (most distant event).
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