666.05 - Distribution of Mutations Biostatistics 666...

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Distribution of Mutations Biostatistics 666 Lecture 5
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Last Lecture: Introduction to the Coalescent z Coalescent approach Proceed backwards through time. Genealogy of a sample of sequences. z Infinite sites model All mutations distinguishable. No reverse mutation.
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Some key ideas … z Probability of coalescence events z Length of genealogy and its branches z Expected number of mutations z Parameter θ which combines population size and mutation rate
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Building Blocks… z Probability of sampling distinct ancestors for n sequences z Coalescence time t is approximately exponentially distributed N n N i n P n i = = 2 1 1 ) ( 1 1
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Some Key Results… z Coalescence Time (population size units) z Total Length (population size units) = = 1 1 2 ) ( n i tot i T E = 2 / 1 ) ( j T E j
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Some More Key Results … z Expected Number of Polymorphisms = = = = = = = = 1 1 1 1 1 1 1 1 / 1 / 1 2 ) ( sample haploid an For / 1 / 1 4 ) ( sample diploid a For n i n i n i n i i i N S E i i N S E θ µ
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Inferences about θ z Could be estimated from S Divide by expected length of genealogy z Could then be used to: Estimate N, if mutation rate µ is known Estimate µ , if population size N is known = = 1 1 / 1 ˆ n i i S θ
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Alternative Estimator for θ z Count pairwise differences between sequences z Compute average number of differences ∑∑ =+ = = n i n i j ij S n 11 1 2 ~ θ
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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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666.05 - Distribution of Mutations Biostatistics 666...

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