SLIDE 1
Parsimony and Phylogenetic Footprinting
Phylogenies
(aka Evolutionary Trees)
“Nothing in biology makes sense, except in the light of evolution”
- - Dobzhansky
CSE 527 Lecture 10 Parsimony and Phylogenetic Footprinting - - PowerPoint PPT Presentation
CSE 527 Lecture 10 Parsimony and Phylogenetic Footprinting - - PowerPoint PPT Presentation
CSE 527 Lecture 10 Parsimony and Phylogenetic Footprinting Phylogenies (aka Evolutionary Trees) Nothing in biology makes sense, except in the light of evolution -- Dobzhansky A Complex Question: Given data (sequences, anatomy,
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SLIDE 3
- A Complex Question:
Given data (sequences, anatomy, ...) infer the phylogeny
- A Simpler Question:
Given data and a phylogeny, evaluate “how much change” is needed to fit data to tree
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ...
Parsimony
General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ... General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
Parsimony
A A A A A A A A A
0 changes (of course
- ther, less
parsimonious, answers possible)
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ... General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
Parsimony
T T T T T T T T T
0 changes
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ... General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
Parsimony
G G G G G G G G G
0 changes
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ... General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
Parsimony
A C A/C A A A A C C
1 change
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Human A T G A T ... Chimp A T G A T ... Gorilla A T G A G ... Rat A T G C G ... Mouse A T G C T ... General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events
Parsimony
T G/T G/T G/T T T G T G
2 changes
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Counting Events Parsimoniously
- Lesson of example – no unique
reconstruction
- But there is a unique minimum number, of
course
- How to find it?
- Early solutions 1965-75
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G G T T T
A C G T A C G T A C G T A C G T A C G T A C G T A C G T A C G T A C G T
Sankoff & Rousseau, ‘75
Pu(s) = best parsimony score of subtree rooted at node u, assuming u is labeled by character s
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For leaf u: Pu(s) = if u is a leaf labeled s ∞ if u is a leaf not labeled s For internal node u: Pu(s) =
- v∈child(u)
min
t∈{A,C,G,T } cost(s, t) + Pv(t)
Sankoff-Rousseau Recurrence
For Leaf u: For Internal node u: Time: O(alphabet2 x tree size) Pu(s) = best parsimony score of subtree rooted at node u, assuming u is labeled by character s
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A C G T A C G T
Sankoff & Rousseau, ‘75
Pu(s) = best parsimony score of subtree rooted at node u, assuming u is labeled by character s
A C G T
internal node u: Pu(s) =
- v∈child(u)
min
t∈{A,C,G,T } cost(s, t) + Pv(t)
u v1 v2
s v t
cost(s,t)+Pv(t) min
v1
A C G T
v2
A C G T sum: Pu(s) =
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T T
A C G T A C G T
Sankoff & Rousseau, ‘75
Pu(s) = best parsimony score of subtree rooted at node u, assuming u is labeled by character s ∞ ∞ ∞ 0 ∞ ∞ ∞ 0
A C G T
2 2 2 0
internal node u: Pu(s) =
- v∈child(u)
min
t∈{A,C,G,T } cost(s, t) + Pv(t)
u v1 v2
s v t
cost(s,t)+Pv(t) min A
v1
A 0 + ∞ 1 C 1 + ∞ G 1 + ∞ T 1 + 0
v2
A 0 + ∞ 1 C 1 + ∞ G 1 + ∞ T 1 + 0 sum: Pu(s) = 2
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G G T T T
A C G T A C G T A C G T A C G T A C G T A C G T A C G T A C G T A C G T
Sankoff & Rousseau, ‘75
Pu(s) = best parsimony score of subtree rooted at node u, assuming u is labeled by character s ∞ ∞ ∞ 0 ∞ ∞ ∞ 0 ∞ ∞ 0 ∞ ∞ ∞ 0 ∞ ∞ ∞ ∞ 0 2 2 2 0 2 2 1 1 2 2 1 1 4 4 2 2 Min = 2 (G or T)
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Parsimony – Generalities
- Parsimony is not necessarily the best way to
evaluate a phylogeny (maximum likelihood generally preferred)
- But it is a natural approach, & fast.
- Finding the best tree: a much harder problem
- Much is known about these problems;
Inferring Phylogenies by Joe Felsenstein
is a great resource.
SLIDE 17
Phylogenetic Footprinting
See link to Tompa’s slides on course web page
http://www.cs.washington.edu/homes/tompa/papers/ortho.ppt