AB 10 phylo - Biotec · By Michael Schroeder, Biotec 21 Unrooted and Rooted Trees Rooted tree with...
Transcript of AB 10 phylo - Biotec · By Michael Schroeder, Biotec 21 Unrooted and Rooted Trees Rooted tree with...
![Page 1: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/1.jpg)
Michael Schroeder Biotechnology CenterTU Dresden
Phylogenetic tree
![Page 2: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/2.jpg)
Phylogenetic trees
• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining
![Page 3: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/3.jpg)
Origin of mitochondria in eucaryotes? Sequence comparison (Blast) of 601 mitochondrial yeast genes
to bacteria and archaea
![Page 4: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/4.jpg)
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
![Page 5: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/5.jpg)
Darwin‘s Tree of Life
5
![Page 6: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/6.jpg)
Tree of Life with 2.3 Mio Species
opentreeoflife.org 6
![Page 7: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/7.jpg)
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…
![Page 8: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/8.jpg)
Schools of Taxonomists
§ Goal: create taxonomy § Approach:
§ Phenotype § Phylogeny
§ 3 schools:
§ Phenotype only § Evolutionary Taxonomists:
Phenotype (+ Phylogeny) § Cladists:
Phylogeny (+Phenotype)
![Page 9: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/9.jpg)
Westnile virus in New York
![Page 10: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/10.jpg)
When did homo sapiens leave Africa?
§ Recent-Africa Hypothesis: hundred(s) thousand years § Multi-regional Hypothesis: million(s) years
![Page 11: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/11.jpg)
§ 53 humans § Outgroup
chimpanzee
![Page 12: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/12.jpg)
Clustal W: over 50 000 citations
![Page 13: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/13.jpg)
Thompson, NAR, 1994
ClustalW uses phylogenetic trees as guide trees for multiple sequence alignment
![Page 14: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/14.jpg)
Phylogenetic trees
• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining
![Page 15: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/15.jpg)
Topixgallery.com
![Page 16: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/16.jpg)
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
![Page 17: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/17.jpg)
Unrooted and Rooted Trees
The principal uses of these numbers will be ... to frighten taxonomists.
![Page 18: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/18.jpg)
Unrooted and Rooted Trees
A B C
A C B
B C A
B
C
A
![Page 19: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/19.jpg)
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
![Page 20: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/20.jpg)
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
![Page 21: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/21.jpg)
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
![Page 22: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/22.jpg)
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
![Page 23: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/23.jpg)
Phylogenetic trees
• Motivation
• Rooted and unrooted trees
• Rooted trees: Hierarchical clustering
• Drawing trees
• Unrooted trees: Neighbour joining
![Page 24: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/24.jpg)
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
![Page 25: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/25.jpg)
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
![Page 26: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/26.jpg)
(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
![Page 27: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/27.jpg)
(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
![Page 28: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/28.jpg)
((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
![Page 29: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/29.jpg)
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
![Page 30: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/30.jpg)
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
![Page 31: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/31.jpg)
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
![Page 32: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/32.jpg)
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
![Page 33: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/33.jpg)
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
![Page 34: AB 10 phylo - Biotec · 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](https://reader035.fdocuments.in/reader035/viewer/2022070718/5ede4245ad6a402d66699499/html5/thumbnails/34.jpg)
Summary § Applications of phylogenetic trees § Clustal W
§ Hierarchical clustering § Linkage methods