666.05 - Distribution of Mutations Biostatistics 666...

This preview shows pages 1–9. Sign up to view the full content.

Distribution of Mutations Biostatistics 666 Lecture 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 36

666.05 - Distribution of Mutations Biostatistics 666...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online