Building Phylogenies Parsimony 1. Methods Distance-based Parsimony Maximum likelihood.

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Presentation transcript:

Building Phylogenies Parsimony 1

Methods Distance-based Parsimony Maximum likelihood

Note Some of the following figures come from: –[S05] Swofford formatics_spring05 formatics_spring05 –[F05] Felsenstein 1/2005/ 1/2005/

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* Compatibility methods are closely related to parsimony: –Goal: Find tree that perfectly fits the most characters.

Evolutionary Steps G  A A G G Steps can have weights

Parsimony a0111a0111 ABCDABCD c0011c0011 d0110d0110 e0001e0001 f1000f1000 b0111b0111 ABC D f a, b d c ed Typically, each site is treated separately

Some numbers Number of unrooted trees on n  2 species: U n = (2n  5)(2n  7)(2n  9)... (3)(1), Number of rooted trees on n  3 species: R n = (2n  5) U n

The number of rooted trees [F05]

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

A DNA data set [F05]

An example tree [F05]

Most parsimonious states for site 1

Most parsimonious states for site 2

Most parsimonious states for site 3

Most parsimonious states for sites 4 and 5

Most parsimonious states for site 6

Evolutionary steps on tree Only one choice of reconstruction at each site is shown 9 steps in all

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.

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.

Fitch’s Algorithm: Example [F05]

Sankoff’s Algorithm Let c ij be the cost of going from state i to state j. E.g., transitions (A  G or C  T) are more probable than transversions, so give lower weight to transitions Let S v (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.

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

Sankoff’s Algorithm: Example

Sankoff’s Algorithm: Traceback

Searching for an MP tree Exhaustive search (exact) Branch-and-bound search (exact) Heuristic search methods –Stepwise addition –Branch swapping –Star decomposition

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.

Orthology and Paralogy