Distance Matrix Methods-Phylogentic Analysis-Lecture Slides, Slides of Phylogenetics

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Distance Matrix Methods

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Distance matrix

• A distance matrix is calculated from the sequence dataset
• Algorithms: Fitch-Margoliash, Neighbor-Joining or UPGMA in tree building
• Simple, finds only one tree
• Somewhat old-fashioned (OK if your alignment is good and evolutionary distances are short)

Iterative Pair-Wise Alignment

 Compute score for each pair of alignment

 Merge two string with the minimum distance

between them.

 Successively merge in a string with the smallest

distance from any of the strings already in MSA.

 Use spanning tree algorithm

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Iterative Pair-Wise Alignment

 Implementation:

 Represent strings as vertices of graph.

 Represent distance between vertices as edges

with weight corresponding to the distance

between them.

 Spanning Tree:

 A tree developed from a graph which connects

all the vertices and has no loop.

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S 1 = ATGC-T-C S 4 = ATGCATGC D ( S 1 , S 4 ) = 2

S 2 = ATG-A-GC S 4 = ATGCATGC D ( S 2 , S 4 ) = 2

S 2 = ATGAGC S 3 = TTCTG- D ( S 2 , S 3 ) = 4

S 3 = -TTC-TG- S 4 = ATGCATGC D ( S 3 , S 4 ) = 4

 Distance matrix D

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1 2 3 4

4

4 2

2 3 2

S

S

S

S

S S S S

• Step 2: Find the minimal spanning tree based on matrix D From the Graph.

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1

1 2 3 4

4

4 2

2 3 2

S

S

S

S

S S S S

UPGMA

 Abbreviation of “Unweighted Pair Group Method

with Arithmetic Mean”

 Originally developed for numeric taxonomy in

1958 by Sokal and Michener

 Simplest algorithm for tree construction, so it's fast!

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How to construct a tree with UPGMA?

 Prepare a distance matrix

 Repeat step 1 and step 2 until there are only two

clusters

 Step 1:

Cluster a pair of leaves (taxa) by shortest distance

 Step 2:

Recalculate a new average distance with the new

cluster and other taxa, and make a new distance

matrix

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3. Phylogenetic Tree Construction

example (UPGMA algorithm)

1. Pick smallest entry Dij
2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes

Dij Bear^ Raccoon^ Weasel^ Seal Bear - 0.26 0.34 0. Raccoon - 0.42 0. Weasel - 0. Seal -

Bear Raccoon 0.13 0.

UPMGA (Michener & Sokal 1957)

3. Phylogenetic Tree Construction

example (UPGMA algorithm)

Dij Bear^ Raccoon^ Weasel^ Seal Bear - 0.26 0.34 0. Raccoon - 0.42 0. Weasel - 0. Seal -

3. Compute new distances to the other species using arithmetic means

4. 365 2

5. 29 0. 44 2

2 0.^3420.^420.^38 ( )

( )

    

    

S BR SB^ SR

W BR WB WR

D D^ D

D D D

Bear Raccoon 0.13 0.

3. Phylogenetic Tree Construction

example (UPGMA algorithm)

Dij BR^ Weasel^ Seal

BR - 0.38 0. Weasel - 0. Seal -

3. Compute new distances to the other species using arithmetic means

4. 4 3

5. 34 0. 42 0. 44 ( ) 3 DW BRS  DWB  DWR ^ DWS    

Bear Raccoon Seal

0.1825 0.

3. Phylogenetic Tree Construction

example (UPGMA algorithm)

Dij BRS^ Weasel

BRS - 0. Weasel -

1. Pick smallest entry Dij.
2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes.
3. Done!

Bear Raccoon Seal Weasel 0.13 0. 0.2 0.