BCB%20444/544

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BCB 444/544

• Lecture 31
• Phylogenetics Character-Based Methods
• 31_Nov05

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Required Reading (before lecture)

• Fri Oct 30 - Lecture 30
• Phylogenetic Distance-Based Methods
• Chp 11 - pp 142 169
• Mon Nov 5 - Lecture 31
• Phylogenetics Parsimony and ML
• Chp 11 - pp 142 169
• Wed Nov 7 - Lecture 32
• Machine Learning
• Fri Nov 9 - Lecture 33
• Functional and Comparative Genomics
• Chp 17 and Chp 18

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Assignments Announcements

• Mon Oct 29 - HW5
• HW5 Hands-on exercises with
  phylogenetics
• and tree-building software
• Due Mon Nov 5 (not Fri Nov 1 as previously
  posted)

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BCB 544 Only New Homework Assignment

• 544 Extra2
• Due vPART 1 - ASAP
• PART 2 - meeting prior to 5 PM Fri Nov 2
• Part 1 - Brief outline of Project, email to Drena
  Michael
• after response/approval, then
• Part 2 - More detailed outline of project
• Read a few papers and summarize status of
  problem
• Schedule meeting with Drena Michael to
  discuss ideas

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Seminars this Week

• BCB List of URLs for Seminars related to
  Bioinformatics
• http//www.bcb.iastate.edu/seminars/index.html
• Nov 7 Wed - BBMB Seminar 410 in 1414 MBB
• Sharon Roth Dent MD Anderson Cancer Center
• Role of chromatin and chromatin modifying
  proteins in regulating gene expression
• Nov 8 Thurs - BBMB Seminar 410 in 1414 MBB
• Jianzhi George Zhang U. Michigan
• Evolution of new functions for proteins
• Nov 9 Fri - BCB Faculty Seminar 210 in 102
  SciI
• Amy Andreotti ISU
• Something about NMR

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Chp 11 Phylogenetic Tree Construction Methods
and Programs

• SECTION IV MOLECULAR PHYLOGENETICS
• Xiong Chp 11 Phylogenetic Tree Construction
  Methods and Programs
• Distance-Based Methods
• Character-Based Methods
• Phylogenetic Tree Evaluation
• Phylogenetic Programs

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Tree Construction

• Two main categories of tree building methods
• Distance-based
• Overall similarity between sequences
• Character-based
• Consider the entire MSA

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Summary of Distance-Based Methods

• Clustering-based methods
• Computationally very fast and can handle large
  datasets that other methods cannot
• Not guaranteed to find the best tree
• Optimality-based methods
• Better overall accuracies
• Computationally slow
• All distance-based methods lose all sequence
  information and cannot infer the most likely
  state at an internal node

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Character-Based Methods

• Based directly on the sequence characters in the
  MSA rather than overall distances
• Count mutational events accumulated on sequences
• Evolutionary dynamics of each character can be
  studied and ancestral sequences inferred
• Two popular approaches
• Parsimony
• Maximum Likelihood (ML)

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Parsimony

• Parsimony is based on Occams Razor the
  simplest explanation is most likely correct
• Goal Find the tree that allows evolution of the
  sequences with the fewest changes

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Parsimony

• Parsimony score of a tree The smallest
  (weighted) number of steps required by the tree
• Two parsimony problems
• Large Parsimony problem Find the tree with the
  lowest parsimony score
• Small Parsimony problem Given a tree, find its
  parsimony score
• Use the small parsimony problem to solve the
  large parsimony problem

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Algorithms for Small Parsimony

• Fitchs algorithm
• Based on set operations
• Evolutionary steps have the same weight
• Sankoffs algorithm
• Based on dynamic programming
• Allows steps to have different weights
• Both algorithms compute the minimum (weighted)
  number of steps a tree requires at a given site

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Fitchs Algorithm Example
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Sankoffs Algorithm

• Allows for different weights for different
  evolutionary steps
• Transitions (A lt-gt G or C lt-gt T) are more
  probable than transversions, so give a lower
  weight to transitions

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Sankoffs Algorithm Example
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Sankoffs Algorithm Traceback
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Searching for a Most Parsimonious Tree

• Solving the large parsimony problem requires
  searching all possible trees (or does it?)
• Exhaustive search (exact)
• Branch-and-Bound (exact)
• Heuristic search methods (not exact)

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Exhaustive Search

• Build the only possible unrooted tree for three
  taxa (can be randomly chosen)
• Try all possible places to add the fourth taxon
  and score each tree
• Try all places to add the fifth taxon to the
  trees and score again

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Why Finding a True Tree is Difficult
Number of rooted trees

• The number of possible trees grows exponentially
  with the number of species (or sequences)
• Nr (2n -3)!/2(n-2)(n-2)!
• Nu (2n -5)!/2(n-3)(n-3)!
• To find the best tree, you must explore all
  possibilities (or must you?)

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Adding the Fourth Taxon
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Adding the Fifth Taxon
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(No Transcript)
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Branch and Bound

• Similar to exhaustive search except that we
  maintain the score of best tree obtained so far
• If score of current tree exceeds the current best
  score, backtrack and take next available path
• Main idea The parsimony score of a tree can
  only increase as we add another taxa

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Branch and Bound

• When a tip of the search tree is reached the tree
  is either optimal (and retained) or suboptimal
  (and rejected)
• When all paths leading from the initial 3 taxon
  tree have been explored, the algorithm
  terminates, and all most parsimonious trees will
  have been identified

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Branch and Bound
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Branch and Bound

• One way to find a reasonable lower bound quickly
• Use UPGMA or NJ to build a complete tree
• Calculate the parsimony score of this tree and
  use it as a lower bound in our search

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Heuristic Search

• Shortcuts have been designed to reduce the search
  space
• Idea Build a tree quickly (by NJ or some other
  fast method) and rearrange parts of it to explore
  some of the possible trees
• Branch swapping
• Nearest neighbor interchange
• Subtree pruning and regrafting
• Tree bisection and reconnection

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Nearest-Neighbor Interchange
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Subtree Pruning and Regrafting
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Tree Bisection and Reconnection
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Stepwise Addition Another Heuristic

• A greedy method
• Start with 3 taxon tree
• Add one taxon at a time
• Keep only the best tree found so far
• No guarantee of optimality, but may provide a
  good starting point for a search

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Maximum Likelihood Method

• ML is based on a Markov model of evolution
• Observed The species labeling the leaves
• Hidden The ancestral states
• Transition probabilities The mutation
  probabilities
• Assumptions
• Only mutations are allowed
• Sites are independent

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Models of Evolution at a Site

• Transition probability matrix
• M mij, i,j A,C,T,G
• Where
• mij Prob(i -gt j mutation in 1 time unit)
• Branches may have different lengths

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The Probability of an Assignment
T
G
T
A
G
C
T
Probability mTG mGA mGG mTT mTC mTT
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Ancestral Reconstruction Most Likely Assignment
X
Y
Z
A
G
C
T
L maxX,Y,Z mXY mYA mYG mXZ mZC mZT
Compute using Viterbi algorithm
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Likelihood of a Tree
X
Y
Z
A
G
C
T
L ??X,Y,Z mXY mYA mYG mXZ mZC mZT
Compute using forward algorithm
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Maximum Likelihood Comments

• ML is robust
• ML converges to the correct answer as more data
  is added
• Can put in a Bayesian statistical framework to
  obtain a distribution of possible phylogenies
• ML can be slow

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Phylogenetic Tree Evaluation

• Bootstrapping
• Jackknifing
• Bayesian Simulation
• Statistical difference tests (are two trees
  significantly different?)
• Kishino-Hasegawa Test (paired t-test)
• Shimodaira-Hasegawa Test (?2 test)

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Bootstrapping

• A bootstrap sample is obtained by sampling sites
  randomly with replacement
• Obtain a data matrix with same number of taxa and
  number of characters as original one
• Construct trees for samples
• For each branch in original tree, compute
  fraction of bootstrap samples in which that
  branch appears
• Assigns a bootstrap support value to each branch
• Idea If a grouping has a lot of support, it
  will be supported by at least some positions in
  most of the bootstrap samples

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Bootstrapping Comments

• Bootstrapping doesnt really assess the accuracy
  of a tree, only indicates the consistency of the
  data
• To get reliable statistics, bootstrapping needs
  to be done on your tree 500 1000 times, this is
  a big problem if your tree took a few days to
  construct

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Jackknifing

• Another resampling technique
• Randomly delete half of the sites in the dataset
• Construct new tree with this smaller dataset, see
  how often taxa are grouped
• Advantage sites arent duplicated
• Disadvantage again really only measuring
  consistency of the data

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Bayesian Simulation

• Using a Bayesian ML method to produce a tree
  automatically calculates the probability of many
  trees during the search
• Most trees sampled in the Bayesian ML search are
  near an optimal tree

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Phylogenetic Programs

• Huge list at
• http//evolution.genetics.washington.edu/phylip/so
  ftware.html
• PAUP - one of the most popular programs,
  commercial, Mac and Unix only, nice user
  interface
• PHYLIP free, multiplatform, a bit difficult to
  use but web servers make it easier
• WebPhylip another interface for PHYLIP online

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Phylogenetic Programs

• TREE-PUZZLE uses a heuristic to allow ML on
  large datasets, also available as a web server
• PHYML web based, uses genetic algorithm
• MrBayes Bayesian program, fast and can handle
  large datasets, multiplatform download
• BAMBE web based Bayesian program

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Final Comments on Phylogenetics

• No method is perfect
• Different methods make very different assumptions
• If multiple methods using different assumptions
  come up with similar results, we should trust the
  results more than any single method