1. #31 - Phylogenetics Character-Based Methods
BCB 444/544
11/05/07
Lecture 31
Phylogenetics – Character-Based Methods
#31_Nov05
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

2. Required Reading (before lecture)
#31 - Phylogenetics Character-Based Methods
Required Reading (before lecture)
11/05/07
Fri Oct 30 - Lecture 30
Phylogenetic – Distance-Based Methods
Chp 11 - pp 142 – 169
Mon Nov 5 - Lecture 31
Phylogenetics – Parsimony and ML
Wed Nov 7 - Lecture 32
Machine Learning
Fri Nov 9 - Lecture 33
Functional and Comparative Genomics
Chp 17 and Chp 18
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

3. Assignments & Announcements
#31 - Phylogenetics Character-Based Methods
Assignments & Announcements
11/05/07
Mon Oct 29 - HW#5
HW#5 = Hands-on exercises with phylogenetics
and tree-building software
Due: Mon Nov 5 (not Fri Nov 1 as previously posted)
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

4. BCB 544 Only: New Homework Assignment
#31 - Phylogenetics Character-Based Methods
11/05/07
BCB 544 Only: New Homework Assignment
544 Extra#2
Due: √PART 1 - ASAP
PART 2 - meeting prior to 5 PM Fri Nov 2
Part 1 - Brief outline of Project, 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

5. #31 - Phylogenetics Character-Based Methods
11/05/07
Seminars this Week
BCB List of URLs for Seminars related to Bioinformatics:
Nov 7 Wed - BBMB Seminar 4:10 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 4:10 in 1414 MBB
Jianzhi George Zhang U. Michigan
Evolution of new functions for proteins
Nov 9 Fri - BCB Faculty Seminar 2:10 in 102 SciI
Amy Andreotti ISU
Something about NMR
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

6. Chp 11 – Phylogenetic Tree Construction Methods and Programs
#31 - Phylogenetics Character-Based Methods
11/05/07
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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods
BCB 444/544 Fall 07 Dobbs

7. Two main categories of tree building methods Distance-based
Tree Construction
Two main categories of tree building methods
Distance-based
Overall similarity between sequences
Character-based
Consider the entire MSA
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

8. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

9. 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)
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

10. Parsimony
Parsimony is based on Occam’s Razor – the simplest explanation is most likely correct
Goal: Find the tree that allows evolution of the sequences with the fewest changes
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

11. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

12. Algorithms for Small Parsimony
Fitch’s algorithm:
Based on set operations
Evolutionary steps have the same weight
Sankoff’s 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

13. Fitch’s Algorithm Example
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

14. Allows for different weights for different evolutionary steps
Sankoff’s Algorithm
Allows for different weights for different evolutionary steps
Transitions (A <-> G or C <-> T) are more probable than transversions, so give a lower weight to transitions
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

15. Sankoff’s Algorithm Example
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

16. Sankoff’s Algorithm Traceback
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

17. 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)
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

18. Try all possible places to add the fourth taxon and score each tree
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 …
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

19. 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?)
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

20. Adding the Fourth Taxon
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

21. Adding the Fifth Taxon
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

22. BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

23. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

24. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

25. Branch and Bound
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

26. One way to find a reasonable lower bound quickly:
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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

27. Shortcuts have been designed to reduce the search space
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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

28. Nearest-Neighbor Interchange
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

29. Subtree Pruning and Regrafting
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

30. Tree Bisection and Reconnection
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

31. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

32. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

33. Models of Evolution at a Site
Transition probability matrix:
M = [mij], i,j {A,C,T,G}
Where
mij = Prob(i -> j mutation in 1 time unit)
Branches may have different lengths
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

34. The Probability of an AssignmentC T
Probability = mTG · mGA · mGG · mTT · mTC · mTT
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

35. Ancestral Reconstruction: Most Likely AssignmentX Y Z A G C T
L* = maxX,Y,Z {mXY · mYA · mYG · mXZ · mZC · mZT}
Compute using Viterbi algorithm
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

36. L* = X,Y,Z {mXY · mYA · mYG · mXZ · mZC · mZT}
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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

37. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

38. Phylogenetic Tree Evaluation
Bootstrapping
Jackknifing
Bayesian Simulation
Statistical difference tests (are two trees significantly different?)
Kishino-Hasegawa Test (paired t-test)
Shimodaira-Hasegawa Test (χ2 test)
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

39. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

40. Bootstrapping Comments
Bootstrapping doesn’t 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

41. Another resampling technique
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 aren’t duplicated
Disadvantage – again really only measuring consistency of the data
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

42. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

43. Phylogenetic Programs
Huge list at:
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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

44. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods

45. 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
BCB 444/544 F07 ISU Terribilini #31- Phylogenetics - Character-Based Methods