Maximum Parsimony

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Maximum Parsimony

• Character-based
• vs Distance-based

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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

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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
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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

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Possible Trees
Sequence W A C G C G T T G G G Sequence X A C
G C G T T G G G Sequence Y A C G C A A T G A A
Sequence Z A C A C A G G G A A
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Sequence W A C G C G T T G G G Sequence X A C
G C G T T G G G Sequence Y A C G C A A T G A A
Sequence Z A C A C A G G G A A
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Some Possible Evolutionary Paths
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All Possible Evolutionary Paths
of Possible Paths / OTU / Position (Number
of States)(Number of Nodes) (Number of
States)(Number of OTU -1) 43 64
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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)

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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 i if i gets
  residue X

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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

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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

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Evaluate Parsimony Score for The Whole Sequence

• Score is evaluated at each position
  independently.
• Then scores are summed over all positions.

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Step 2. Pick the Tree

• With the lowest total parsimony score

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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)
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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
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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
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Calculate Parsimony Score
1
3
3
4 1 - G 2 - C 3 - T 4 - A
2
4
3
3
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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
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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
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Maximum Parsimony
4 1 - G 2 - A 3 - A 4 - G
A
G
G
A
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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
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Maximum Parsimony
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Pro and Con

• Guaranteed to find the most parsimonious tree
• Misleading when rates of mutation in the
  different branches differ

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Number of Possible Trees
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Searching for the Optimal Tree

• Exhaustive Search
• Very intensive
• Branch and Bound
• A compromise
• Heuristic
• Fast
• Usually starts with NJ

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How to evaluate confidence/uncertainty of a tree?

• Bootstrap methods

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