Algorithm Summary Method Input Output Neighbor Joining Distance - - PDF document

3/10/09 1

CSCI1950‐Z Computa3onal Methods for Biology Lecture 11

Ben Raphael March 2, 2009

hFp://cs.brown.edu/courses/csci1950‐z/

Algorithm Summary

Method Input Output Neighbor Joining Distance matrix D T, B UPGMA Distance matrix D T, B Sankoff’s & Fitch’s Alg. Characters, T A, B Perfect Phylogeny Characters A, B, T Felsenstein Characters, T, B A T = tree topology B = branch lengths A = ancestral states Distance based Probabilis3c (Likelihood) Parsimony Compa3bility

Heuris3c search methods used to find T, B in parsimony and likelihood.

3/10/09 2

Using Mul3ple Methods

• Reliance on purely one method or dataset for

phylogene3c analysis o_en provides incomplete picture.

• If different methods (parsimony, distance‐

based, etc.) applied to same/different datasets give same result, greater confidence that this is correct answer.

• Consensus or supertree methods can be used

to combine this evidence.

Phylogeny of Insects

Build phylogeny of winged and wingless s3ck insects Used data from: 18S ribosomal DNA (~1,900 base pairs (bp)) 28S rDNA (2,250 bp) Por3on of histone 3 (H3, 372 bp) Used mul3ple tree reconstruc3on techniques (Nature 2003)

3/10/09 3

Further Problems…

Contradictory answers some3mes not a fault of data, but from overly simplis3c assump3ons about evolu3onary process.

• No homoplasy: characters change state only
• nce.
• Independence of characters.
• Modeling muta3ons in DNA.
• Genes/genomes evolve only by single leFer

muta3ons.

Biology 101

3/10/09 4

Cell Division and Muta3on

Single nucleo3de change

Copy number Structural

Whole‐Genome Phylogeny

Finding same gene (descended from common ancestor) is non‐trivial.

3/10/09 5

Phylogeny of Insects

Build phylogeny of winged and wingless s3ck insects Used data from: 18S ribosomal DNA (~1,900 base pairs (bp)) 28S rDNA (2,250 bp) Por3on of histone 3 (H3, 372 bp) Used mul3ple tree reconstruc3on techniques (Nature 2003) These genes used because they are assumed to be highly conserved across large evolu3onary distances.

Outline

Whole Genome Phylogeny

• Gene Trees vs. Species Trees
• Reconciling Trees
• Genome Rearrangements

Genome sequencing is now rou3ne. Thus, data for these methods is increasingly available/ useful.

3/10/09 6

Gene Trees vs. Species Trees

These trees indicate different phylogene3c rela3onships. One of them is wrong???

Gene Clusters/Families

Gene duplica3on is a common mechanism for evolu3on of new gene

• func3on. (Ohno 1970)

3/10/09 7

Gene Trees and Species Trees

Evolu3on of gene family inside species tree. Duplica3ons and losses occur.

Gene Trees and Species Trees

Hypothe3cal duplica3ons explain discrepancy between gene and species trees.

3/10/09 8

Gene Trees and Species Trees

Duplica3ons are observed. Do not know which copies of gene descended from common ancestor.

Evolu3on of Gene Tree Inside Species Tree

Three events:

• 1. Specia3on
• 2. Loss
• 3. Duplica3on

3/10/09 9

Orthologs vs. Paralogs

Three events:

• 1. Specia3on

Orthologs: genes descended from a common ancestor.

• 2. Loss
• 3. Duplica3on

Paralogs: genes related by duplica3on.

Dis3nguishing orthologs from paralogs is difficult! Sequence similarity is not enough.

Gene‐Species Tree Reconcilia3on

Given: Rooted binary tree TG and rooted binary tree TS. Find: Embedding of TG in TS that minimizes number of duplica3ons (and losses). Embedded tree is called a reconciled tree (Goodman et al. 1979).

3/10/09 10

Reconcilia3on Example Reconcilia3on Example

3/10/09 11

Reconcilia3on Algorithm

Zmasek and Eddy (2001) M(g) := λG,T(g)

Run Time analysis

n = # leaves in TG Ini3aliza3on: O(n): number nodes of TS

O(n): label external nodes (using hash‐table)

Reconcilia3on Algorithm

O(n2) O(n) O(n log n)

O(n2) worst case. Using algorithms to compute LCA in O(1) 3me gives O(n) algorithm (Zhang 1997, Chen

• et. al 2001)

3/10/09 12

Gene Trees and Species Trees Extensions

• 1. Species tree TS unknown.

– Use minimum duplica3on/loss as objec3ve func3on to search tree space. – NP‐hard (Ma et al. 1998) – Heuris3c search (NNI, SPR, TBR, etc.)

• 2. Mul3ple gene trees TG1, TG2, …, TGN

Minimize: Where c(TGi, S) = # duplic./losses on reconciled tree for TGi.

N

• i=1

c(TGi, S)

3/10/09 13

Roo3ng By Duplica3on

1 duplica3on 3 duplica3ons

• Gene trees o_en

unrooted.

• Root determined using
• utgroup:

species known to be distantly related to all remaining.

• Duplica3ons can be used

to determine outgroup.

Roo3ng By Duplica3on

Tree of life: Three major branches: bacteria, archaea, eukaryotes. No outgroup!