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Building Phylogenies
Parsimony 1
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Methods
• Distance-based• Parsimony• Maximum likelihood
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Note
• Some of the following figures come from:– [S05] Swofford
http://www.csit.fsu.edu/~swofford/bioinformatics_spring05
– [F05] Felsenstein http://evolution.gs.washington.edu/gs541/2005/
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Parsimony methods
• Goal: Find the tree that allows evolution of the sequences with the fewest changes.
• This is called a most parsimonious (MP) tree
• Parsimony is implemented in PAUP* http://paup.csit.fsu.edu/
• Compatibility methods are closely related to parsimony: – Goal: Find tree that perfectly fits the most
characters.
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Evolutionary Steps
G A
A G
G
Steps can have weights
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Parsimony
a0111
ABCD
c0011
d0110
e0001
f1000
b0111
A B C D
f
a, b
dc
ed
Typically, each site is treated separately
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Some numbers
Number of unrooted trees on n 2 species:
Un = (2n5)(2n7)(2n9) . . . (3)(1),
Number of rooted trees on n 3 species:
Rn = (2n5) Un
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The number of rooted trees
[F05]
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Small versus Large Parsimony
• Parsimony score of a tree: The smallest (weighted) number of steps required by the tree
• (Large) Parsimony: Find the tree with the lowest parsimony score
• Small Parsimony: Given a tree, find its parsimony score
• Small parsimony is by far the easier problem. – Used to solve large parsimony
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A DNA data set
[F05]
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An example tree
[F05]
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Most parsimonious states for site 1
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Most parsimonious states for site 2
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Most parsimonious states for site 3
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Most parsimonious states for sites 4 and 5
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Most parsimonious states for site 6
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Evolutionary steps on tree
Only one choice of reconstruction at each site is shown9 steps in all
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Algorithms for Small Parsimony
• Fitch’s algorithm: – Based on set operations– Evolutionary steps have 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.
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Fitch’s Algorithm
• Each node v in tree has a set X(v)• If v is a leaf (tip), X(v) is the nucleotide
observed at v – if there is ambiguity, X(v) contains all
possible nucleotides at v
• If v is a node with descendants u and w, – Let Y X(u) X(w)– If Y make X(v) Y,– If Y make X(v) X(u)X(w) and count
one step.
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Fitch’s Algorithm: Example
[F05]
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Sankoff’s Algorithm
• Let cij be the cost of going from state i to state j.
• E.g., transitions (AG or CT) are more probable than transversions, so give lower weight to transitions
• Let Sv(k) be the smallest (weighted) number of steps needed to evolve the subtree at or above node v, given that node v is in state k.
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Sankoff’s Algorithm• If v is a leaf (tip)
• If v is a node with descendants u and w
• The minimum number of (weighted) steps is
otherwise
state have) could (or has node if0)(
kvkSv
jSc iSckS wkjj
ukii
v minmin
kSS rootk
min*
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Sankoff’s Algorithm: Example
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Sankoff’s Algorithm: Traceback
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Searching for an MP tree
• Exhaustive search (exact)• Branch-and-bound search (exact)• Heuristic search methods
– Stepwise addition– Branch swapping– Star decomposition
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Homology, orthology, and paralogy
• Homology: Similarity attributed to descent from a common ancestor.
• Orthologous sequences: Homologous sequences in different species that arose from a common ancestral gene during speciation; may or may not be responsible for a similar function.
• Paralogous sequences: Homologous sequences within a single species that arose by gene duplication.
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Orthology and Paralogy
http://www.ncbi.nlm.nih.gov/Education/BLASTinfo/Orthology.html