phylo3 - Ancestral Reconstruction & Selection Pressure...

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Unformatted text preview: Ancestral Reconstruction & Selection Pressure Christopher Lee December 3, 2009 Evolutionary Trees as Markov Chains Assume were given binary tree as a directed graph G with nodes u , and branch lengths t uv for each edge u v . Assume leaf-node u emits observation X u with likelihood p ( X u = x | u = x ) = 1 . No obs for internal nodes! How to perform HMM calculations on this tree? e.g. p ( X ) 1 Maximum Posterior Tree Find * that maximizes p ( , X ) . Algorithm? Computational complexity? 2 Viterbi on Binary Trees Recursion rule for maximizing p ( X ) ? How do we take into account priors? Match to intuitive ancestor inference rules? 3 Posterior for Ancestral States p ( u | X ) ? p ( X ) ? Really a question of how to split the tree. 4 Above-Below Algorithm Split tree into descendants X u of u and non-descendants X u . below: b ui = p ( X u | u = s i ) above: a ui = p ( X u , u = s i ) p ( u | X ) = p ( X u | u = s i ) p ( X u , u = s i ) p ( X ) 5 Below Probability Summation Probability of descendants X u of u : b ui = p ( X u | u = s i ) = j p ( v = s j | u = s i ) b vj ! k p ( w = s k | u = s i ) b wk !...
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This note was uploaded on 04/12/2010 for the course CHEM CHEM 260A taught by Professor Chrislee during the Spring '10 term at UCLA.

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phylo3 - Ancestral Reconstruction & Selection Pressure...

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