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666.Prob04

# 666.Prob04 - Sketch out a genealogy for this sample The E-M...

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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 -5 and the mutation rate is μ = 10 -5 per 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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