ab 10 phylo - biotec · by michael schroeder, biotec 21 unrooted and rooted trees rooted tree with...
TRANSCRIPT
Michael Schroeder Biotechnology CenterTU 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
opentreeoflife.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