Maximum Parsimony

1. Maximum Parsimony Character-based vs Distance-based

2. Character-based Trees • NO explicit measure of distance • Parsimony is widely used on character-based trees • Trees constructed on the basis of change of characters (or traits) • Explains the observed sequences with a minimum number of substitutions • Best for small sets of sequences with high similarity

3. Simple Example • Suppose we have five species, such that three have ‘C’ and two ‘T’ at a specified position • Minimal tree has one evolutionary change: C T C T C C C T T  C

4. 2 steps to Maximum Parsimony • Parsimony: for each possible tree topology, calculate parsimonious cost (involve filling in the inner nodes such that there is minimum # substitutions) • Maximum: pick the tree whose cost is the least

5. W W W X Y Z Y X X Z Z Y Possible Trees Sequence W:A C G C GT TG G GSequence X:A C G C GT TG G GSequence Y:A C G C A ATGA ASequence Z:A C A C A G G GA A

6. T T A G T A T G T G T A Sequence W:A C G C GT TG G GSequence X:A C G C GT TG G GSequence Y:A C G C A ATGA ASequence Z:A C A C A G G GA A

7. T T T T T T T T A A A A G G G G T T A G T T A T C A G A G T A G Some Possible Evolutionary Paths

8. T T A G ATGC ATGC ATGC All Possible Evolutionary Paths # of Possible Paths / OTU / Position: (Number of States)(Number of Nodes) = (Number of States)(Number of OTU -1) = 43 = 64

9. Step1. Given a Tree • How do we compute the Parsimony score? 1 for substitution, 0 no. • Weighted Parsimony • Each change of character a to b is weighted by the score c(a,b)

10. T T A G ATGC ATGC ATGC Calculate Parsimony Scores • From leaves to the root S(r, X) = cost of whole tree. r: root S(i, X) = cost of tree rooted at node iif igets residue X

11. Calculate Pars. Score Iteration: • if node k has children i and j, then S(k,X) = minY1(S(i,Y1)+c(X,Y1)) + minY2(S(j,Y2)+c(X,Y2)) Termination: • cost of tree is minxS(r,X) where r is the root

12. Calculate Parsimony Scores Initialization: • For each outer leaf i, for all X, • If X is given by the sequence, S(i,X) = 0  only possibility • Otherwise, S(i,X) =   impossible

13. T T A G ATGC ATGC ATGC

14. Evaluate Parsimony Score for The Whole Sequence • Score is evaluated at each position independently. • Then scores are summed over all positions.

15. Step 2. Pick the Tree • With the lowest total parsimony score

16. A Worked Example 1 2 3 4 5 6 7 8 9 10 Species 1 - A G G G T A A C T G Species 2 - A C G A T T A T T A Species 3 - A T A A T T G T C T Species 4 - A A T G T T G T C G How many possible unrooted trees? (tree topologies)

17. How Many Possible Trees? 1 2 3 4 5 6 7 8 9 10 Species 1 - A G G G T A A C T G Species 2 - A C G A T T A T T A Species 3 - A T A A T T G T C T Species 4 - A A T G T T G T C G

18. 0 0 0 Compute Pars. Score for Each 1 2 3 4 5 6 7 8 9 10 1 - A G G G T A A C T G 2 - A C G A T T A T T A 3 - A T A A T T G T C T 4 - A A T G T T G T C G

19. G T C A G C T A G T A C Calculate Parsimony Score 1 3 3 4 1 - G 2 - C 3 - T 4 - A 2 4 3 3

20. 0 3 0 3 0 3 Maximum Parsimony 1 2 3 4 5 6 7 8 9 10 1 - A G G G T A A C T G 2 - A C G A T T A T T A 3 - A T A A T T G T C T 4 - A A T G T T G T C G

21. 0 3 2 0 3 2 0 3 2 Maximum Parsimony 1 2 3 4 5 6 7 8 9 10 1 - A G G G T A A C T G 2 - A C G A T T A T T A 3 - A T A A T T G T C T 4 - A A T G T T G T C C

22. G A 2 A G G A 2 A G 1 Maximum Parsimony 4 1 - G 2 - A 3 - A 4 - G A G A G

23. 0 3 2 2 0 3 2 2 0 3 2 1 Maximum Parsimony 1 2 3 4 5 6 7 8 9 10 1 - A G G G T A A C T G 2 - A C G A T T A T T A 3 - A T A A T T G T C T 4 - A A T G T T G T C G

24. 0 3 2 2 0 1 1 1 1 2 13 0 3 2 2 0 1 2 1 2 2 15 0 3 2 1 0 1 2 1 2 2 14 Maximum Parsimony

25. Pro and Con • Guaranteed to find the most parsimonious tree • Misleading when rates of mutation in the different branches differ

26. Number of Possible Trees

27. Searching for the Optimal Tree • Exhaustive Search • Very intensive • Branch and Bound • A compromise • Heuristic • Fast • Usually starts with NJ

28. How to evaluate confidence/uncertainty of a tree? Bootstrap methods