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, ...) infer the phylogeny • A Simpler Question: Given data and a phylogeny , evaluate “how much change” is needed to fit data to tree

Parsimony General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events 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 A Human A T G A T ... A 0 changes A A Chimp A T G A T ... A A Gorilla A T G A G ... (of course A Rat A T G C G ... other, less parsimonious, A A Mouse A T G C T ... answers possible)

Parsimony General idea ~ Occam’s Razor: Given data where change is rare, prefer an explanation that requires few events T Human A T G A T ... T 0 changes T T Chimp A T G A T ... T T Gorilla A T G A G ... T Rat A T G C G ... T T 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 G Human A T G A T ... G 0 changes G G Chimp A T G A T ... G G Gorilla A T G A G ... G Rat A T G C G ... G 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 A Human A T G A T ... A 1 change A A Chimp A T G A T ... A A/C Gorilla A T G A G ... C Rat A T G C G ... C C 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 T Human A T G A T ... T 2 changes G/T T Chimp A T G A T ... G G/T Gorilla A T G A G ... G Rat A T G C G ... T G/T Mouse A T G C T ...

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

Sankoff & Rousseau, ‘75 P u (s) = best parsimony score of subtree rooted at node u , assuming u is labeled by character s 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 T T G G T

Sankoff-Rousseau Recurrence P u (s) = best parsimony score of subtree rooted at node u , assuming u is labeled by character s For Leaf u : For leaf u : � 0 if u is a leaf labeled s P u ( s ) = if u is a leaf not labeled s ∞ For Internal node u : For internal node u : � P u ( s ) = t ∈ { A,C,G,T } cost( s, t ) + P v ( t ) min v ∈ child ( u ) Time: O(alphabet 2 x tree size)

Sankoff & Rousseau, ‘75 P u (s) = best parsimony score of subtree rooted at node u , assuming u is labeled by character s internal node u : � P u ( s ) = t ∈ { A,C,G,T } cost( s, t ) + P v ( t ) min v ∈ child ( u ) s v t cost( s,t )+ P v (t) min A C v 1 G u T A C G T A C v 2 G A C G T A C G T T v 1 v 2 sum: P u (s) =

Sankoff & Rousseau, ‘75 P u (s) = best parsimony score of subtree rooted at node u , assuming u is labeled by character s internal node u : � P u ( s ) = t ∈ { A,C,G,T } cost( s, t ) + P v ( t ) min v ∈ child ( u ) s v t cost( s,t )+ P v (t) min 0 + ∞ A 1 + ∞ C v 1 1 1 + ∞ G u T 1 + 0 A C G T A 2 2 2 0 0 + ∞ A 1 + ∞ C v 2 1 1 + ∞ G A C G T A C G T ∞ ∞ ∞ 0 ∞ ∞ ∞ 0 T 1 + 0 v 1 v 2 sum: P u (s) = 2 T T

Sankoff & Rousseau, ‘75 P u (s) = best parsimony score of subtree rooted at node u , assuming u is labeled by character s A C G T Min = 2 (G or T) 4 4 2 2 A C G T 2 2 1 1 A C G T A C G T 2 2 2 0 2 2 1 1 A C G T A C G T A C G T A C G T A C G T ∞ ∞ ∞ 0 ∞ ∞ ∞ 0 ∞ ∞ 0 ∞ ∞ ∞ 0 ∞ ∞ ∞ ∞ 0 T T G G T

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.

Phylogenetic Footprinting See link to Tompa’s slides on course web page http://www.cs.washington.edu/homes/tompa/papers/ortho.ppt