Phylogenetic tree Michael Schroeder Biotechnology Center TU - - PowerPoint PPT Presentation

Michael Schroeder

Biotechnology Center TU Dresden

Phylogenetic tree

Phylogenetic trees

• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining

Origin of mitochondria in eucaryotes?

Sequence comparison (Blast) of 601 mitochondrial yeast genes to bacteria and archaea

Origin of mitochondria in eucaryotes?

Sequence comparison (Blast) of 601 mitochondrial yeast genes to bacteria and archaea

Bacteria

Horiike et al. Nat Cell Biol. 2001. Adapted from Campbell and Heyer. Discovering genomics, proteomics, bioinformatics.

Archaea

Darwin‘s Tree of Life

5

Tree of Life with 2.3 Mio Species

• pentreeoflife.org

6

Phylogeny

§ Taxonomists classify and group organisms § Aristoteles, De Partibus Animalium

§ …discuss each separate species – man, lion, ox,… § or … deal first with the attributes which they have in common…

Schools of Taxonomists

§ Goal: create taxonomy § Approach: § Phenotype § Phylogeny § 3 schools: § Phenotype only § Evolutionary Taxonomists: Phenotype (+ Phylogeny) § Cladists: Phylogeny (+Phenotype)

Westnile virus in New York

When did homo sapiens leave Africa?

§ Recent-Africa Hypothesis: hundred(s) thousand years § Multi-regional Hypothesis: million(s) years

§ 53 humans § Outgroup chimpanzee

Clustal W: over 50 000 citations

Thompson, NAR, 1994

ClustalW uses phylogenetic trees as guide trees for multiple sequence alignment

Phylogenetic trees

• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining

Topixgallery.com

Bifurcating Trees

A B C D

Edge or Branch Ancestral node (root) Internal node (hypothetical ancestor) Terminal node (leave) Genes, Proteins, Populations, Species,... Bifurcating = two decendants

Unrooted and Rooted Trees

The principal uses of these numbers will be ... to frighten taxonomists.

Unrooted and Rooted Trees

A B C A C B B C A B C A

A B C D A B C D A B C D

A B C D A C B D B C A D C A B D D A B c A D B C A D B C B D A C C B A D D B A C A B C D B A C D C D A B D C A B A C B D

Unrooted and Rooted Trees

By Michael Schroeder, Biotec 20

Unrooted and Rooted Trees

8.200.794.532.637.891.559.375 unrooted trees for 20 leaves!

To get a feeling: 8.200.794.532.637.891.559.375 ms is 20 times longer than the universe exists

Felsenstein, 1978

By Michael Schroeder, Biotec 21

Unrooted and Rooted Trees

Rooted tree with m leaves has m-1 internal nodes and 2m-2 edges Unrooted tree with m leaves has m-2 internal nodes and 2m-3 edges Let Tunroot (m) be the number of unrooted trees with m leaves Given an unrooted tree with m leaves, an extra leaf can be added to any of the 2m-3 edges to make a tree with m+1 leaves Tunroot(m+1)=(2m-3) Tunroot(m) This is satisfied by Tunroot (m)=(2m-5)!! Double factorial = Factorial leaving out every other number

Felsenstein, 1978

Consequence: Algorithms that generate all trees, judge them, and pick the best cannot work, as there are too many trees. Alternatives: Hierarchical clustering and Neighbour joining

Phylogenetic trees

• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining

Hierarchical clustering

§ Input: Pairwise distances between sequences § Output: A tree of clusters of sequences

A B C D E A 2 6 10 9 B 5 9 8 C 4 5 D 3 E A B C D E

A B C D E A 2 6 10 9 B 5 9 8 C 4 5 D 3 E

(A,B)

C D E (A,B) 5 9 8 C 4 5 D 3 E A B

Hierarchical clustering

(A,B)

C (D,E) (A,B) 5 8 C 4 (D,E)

(A,B)

C D E (A,B) 5 9 8 C 4 5 D 3 E A B D E A B

Hierarchical clustering

(A,B)

C (D,E) (A,B) 5 8 C 4 (D,E) A B C D E

(A,B)

(C,(D,E)) (A,B) 5 (C,(D,E)) A B D E

Hierarchical clustering

((A,B),(C,(D,E)))

((A,B),(C,(D,E))) A B C D E

(A,B)

(C,(D,E)) (A,B) 5 (C,(D,E)) A B C D E

Hierarchical clustering

const m number of original sequences var U a set of current trees, initially, one tree for each original sequence. D The distance between the trees in U begin U = the set of one tree (each of one node) for each original sequence. while |U| >1 do (u,v) = the roots of two trees in U with the least distance in D Make a new tree with root w and with u and v as children Calculate the length of the edges (v, w) and (u, w) for each root x of the trees in U-{u, v} do D(x, w) = calculate the distance between x and the new node (w) end U = (U - {u,v} ) ∪ {w} update U end end

Algorithm

Hierarchical Clustering

Distance to the new cluster w = (u,v)

§ Single linkage:

§ D(x,w) = min { D(x,u), D(x,v) } § Example: Distance (A,B) to C is 1

§ Complete linkage:

§ D(x,w) = max { D(x,u), D(x,v) } § Example: Distance (A,B) is C is 2

§ Average linkage (WPGMA) (weighted pair group method with arithmetic mean)):

§ D(x,w) = ( D(x,u) + D(x,v) ) / 2 § Example: Distance (A,B) to C is 1.5

§ More general (UPGMA)

(unweighted pair group method using arithmetic mean):

§ D(x,w) = ( mu D(x,u) + mv D(x,v) ) / (mu + mv ) § mu is the number of nodes in the subtreee u

By Michael Schroeder, Biotec 30

Question: What’s the difference between UPGMA and WPGMA? Note: “weighted” because u and v may have different number of nodes, hences they are weighted.

C 1 B 2 1 A C B A

Are WPGMA and UPGMA the same?

§ Subtree D has 1000 nodes (mD =1000) § Subtree E has 1 node (mE =1) § Distance (D,E) to F is

§ ( 2 + 98)/ 2 = 50 for WPGMA § (1000*2 + 1*98)/(1000+1) = 2.09 for UPGMA

F 98 E 2 1 D F E D

UPGMA

Unweighted pair group method using arithmetic mean

A B C D E A 3 7 8 10 B 6 8 7 C 4 5 D 6 E

(A,B)

C D E (A,B) 6.5 8 8.5 C 4 5 D 6 E

(A,B)

(C,D) E (A,B) 7.25 8.5 (C,D) 5.5 E

(A,B)

(C,D),E) (A,B) 7.67 (C,D),E)

UPGMA: (2*7.25+1*8.5) / 3 = 7.67 WPGMA: (7.25+8.5) / 2 = 7.825

Does linkage method change trees?

By Michael Schroeder, Biotec 33

A

B C D A 1 2 5 B 4 5 C 3 D

A B C D A B C D

Summary

§ Applications of phylogenetic trees § Clustal W

§ Hierarchical clustering § Linkage methods