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

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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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Unformatted text preview: Sketch out a genealogy for this sample. The E-M Algorithm 1. In a study of the ACE gene, an Alu insertion deletion (I/D) and a nearby C/T single nucleotide polymorphism were genotyped in randomly sampled individuals. The following genotypic counts are found: C/C C/T T/T I/I 25 I/D 40 10 D/D 15 10 a) Describe the E-M procedure for estimating two marker haplotype frequencies, including relevant equations. b) Use the E-M algorithm to estimate haplotype frequencies p IC , p IT , p DC and p DT for the two markers. c) Compare the likelihood of the observed counts assuming linkage equilibrium between markers and using the haplotype frequencies estimated by E-M. Comment on your result. d) Estimate D and for this marker pair. e) Is there evidence for ancestral recombination between the I/D polymorphism and the C/T mutation in this population? Would the I/D polymorphism be a suitable surrogate for the C/T SNP in an association study?...
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This note was uploaded on 12/26/2011 for the course BIO 666 taught by Professor Staff during the Fall '06 term at University of Michigan.

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

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