Post on 20-Jun-2015
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Phylogeny UPGMA Neighbor Joining Method
Phylogeny
Understanding life through time, over long periods of past time, the connections between all groups of organisms
as understood by ancestor/descendant relationships,
Tree of life.
Phylogeny
Phylogeny
Rooted and Unrooted trees:
Phylogeny
Rooted and Unrooted trees:– Most phylogenetic methods produce unrooted trees,
because they detect differences between sequences, but have no means to orient residue changes relatively to time.
Phylogeny
Rooted and Unrooted trees:– Two means to root an unrooted tree :
The outgroup method : include in the analysis a group of sequences known a priori to be external to the group under study; the root is by necessity on the branch joining the outgroup to other sequences.
Make the molecular clock hypothesis : all lineages are supposed to have evolved with the same speed since divergence from their common ancestor. Root the tree at the midway point between the two most distant taxa in the tree, as determined by branch lengths. The root is at the equidistant point from all tree leaves.
Phylogeny
Rooted and Unrooted trees:– Two means to root an unrooted tree :
Phylogeny
Orthology / Paralogy:
Phylogeny
Species Tree and Gene Tree:
Evolutionary relationship between seven eukaryotes
E gene tree for Na+-K+ ion pump membrane protein family members
Phylogeny
Species Tree and Gene Tree:
Phylogeny
Additive Tree:A distance matrix corresponding to a tree is called additive,– THEOREM: D is additive if and only if:
For every four indices i,j,k,l, the maximum and median of the three pairwise sums are identical:
Dij+Dkl < Dik+Djl = Dil+Djk
UPGMA
Building Phylogenetic Trees by UPGMA:– Unweighted Pair – Group Method using arithmetic
Averages,– Assume constant mutation rate,– The two sequences with with the shortest
evolutionary distance between them are assumed to have been the last two diverge, and represented by the most racent internal node.
UPGMA
Building Phylogenetic Trees by UPGMA:– The distance between two clusters:
Assume we have N sequences, Cluster X has NX sequences, cluster Y has NY sequences,
dXY : the evlotionary distance between X and Y
YjXiij
YXXY d
NNd
,
1
UPGMA
Building Phylogenetic Trees by UPGMA:– When cluster X and Y are combined to make a new
cluster Z: No need to use sequence – sequence distances, Calculate the distance of each cluster (such as W) to the new
cluster Z
YX
YWYXWXZW NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
The distance matrix
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
A – D becomes a new cluster lets say V, We have to modify the distance matrix, What are the distances between:
– V and B,– V and C,– V and E,– V and F.
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
A – D becomes a new cluster lets say V, We have to modify the distance matrix, What are the distances between:
– V and B (Calculate),
611
6*16*1
DA
DBDABAVB NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
A – D becomes a new cluster lets say V, We have to modify the distance matrix, What are the distances between:
– V and C (Calculate),
811
8*18*1
DA
DCDACAVC NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
A – D becomes a new cluster lets say V, We have to modify the distance matrix, What are the distances between:
– V and E (Calculate),
211
2*12*1
DA
DEDAEAVE NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
A – D becomes a new cluster lets say V, We have to modify the distance matrix, What are the distances between:
– V and F (Calculate),
611
6*16*1
DA
DFDAFAVF NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
New matrix:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
Cluster according to min distance:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
V – E becomes a new cluster lets say W, We have to modify the distance matrix, What are the distances between:
– W and B,– W and C,– W and F.
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
V – E becomes a new cluster lets say W, We have to modify the distance matrix, What are the distances between:
– W and B (Calculate),
612
6*16*2
EV
EBEVBVWB NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
V – E becomes a new cluster lets say W, We have to modify the distance matrix, What are the distances between:
– W and C (Calculate),
812
8*18*2
EV
ECEVCVWC NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
V – E becomes a new cluster lets say W, We have to modify the distance matrix, What are the distances between:
– W and F (Calculate),
612
6*16*2
EV
EFEVFVWF NN
dNdNd
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
New matrix:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
Cluster according to min distance:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
F – B becomes a new cluster lets say X, We have to modify the distance matrix, What are the distance between:
– W and X.
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
What are the distance between: W and X (Calculate).
6)666666(*2*3
1
)(1
1
,
EFEBDFDBAFABXW
XjWiij
XWWX
ddddddNN
dNN
d
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
New matrix:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
Cluster according to min distance:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
X – W becomes a new cluster lets say Y, We have to modify the distance matrix, What are the distance between:
– Y and C.
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
What are the distance between: Y and C (Calculate).
8)88888(*1*5
1
)(1
1
,
FCBCECDCACCY
CjYiij
CYYC
dddddNN
dNN
d
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
New matrix:
UPGMA
Building Phylogenetic Trees by UPGMA:– Example:
Cluster according to min distance:
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Do not make the assumption of constant mutation
rate,– Assume that the distances are additive.
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– The distances dij:
32
31
21
bbd
bbd
bbd
BC
AC
AB
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– The branch lengths:
)(2
1
)(2
1
)(2
1
3
2
1
ABBCAC
ACBCAB
BCACAB
dddb
dddb
dddb
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– The distances between clusters are defined as
UPGMA:
YjXiij
YXXY d
NNd
,
1
YX
YWYXWXZW NN
dNdNd
Fitch-Margoliash Method:
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
D and E are the closest sequences
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
D and E are the closest sequences
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Name {A, B, C} as W,
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Distance between W and D:
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E33)184139(*1*3
1
)(1
1
,
CDBDADDW
DjWiij
DWWD
dddNN
dNN
d
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Distance between W and E:
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E35)204341(*1*3
1
)(1
1
,
CEBEAEEW
EjWiij
EWWE
dddNN
dNN
d
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Branches a, b and c:
29433
6410
4)351033(2
1)(
2
1
c
b
ddda WEDEWD
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Branches a, b and c:
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Update the distance matrix:
A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
A B C {D,E}
A 22 39 40
B 41 42
C 19
{D,E}
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
{D,E} and C are the closest sequences
A B C {D,E}
A 22 39 40
B 41 42
C 19
{D,E}
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Name {A, B} as W:
A B C {D,E}
A 22 39 40
B 41 42
C 19
{D,E}
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Distance between W and C:
40)4139(*1*2
1
)(1
1
,
BCACCW
CjWiij
CWWC
ddNN
dNN
d A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Distance between W and {D,E} (name {D,E} as X):
41)43414139(*2*2
1
)(1
1
,
BEBDAEADXW
XjWiij
XWWX
ddddNN
dNN
d A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Distance between C and {D,E} (name {D,E} as X):
19)2018(*2*1
1
)(1
1
,
CECDXC
XjCiij
XCCX
ddNN
dNN
d A B C D E
A 22 39 39 41
B 41 41 43
C 18 20
D 10
E
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Branches a, b and c:
31940
10919
9)411940(2
1)(
2
1
c
b
ddda WXCXWC
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Branches a, b and c:
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Update the distance matrix:
A B C {D,E}
A 22 39 40
B 41 42
C 19
{D,E}
A B {C,D,E}
A 22 39.5
B 41.5
{C,D,E}
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
Now we are in thee trivial case of 3 sequences (remember the previous example):
A B {C,D,E}
A 22 39.5
B 41.5
{C,D,E}
Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:– Another Example:
FINAL TREE:
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– The true tree will be that for which the total branch
length, S, is shortest,– Neighbors: a pair of nodes that are seperated by just
one other node,
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– Algorithm (Given a distance matrix):
Iterate Until 2 Nodes are left:– For each node find
– Choose pair (i, j) with smallest – Mege two nodes i and j with a new internal node Y, and
find branch lengths by
– Update the distance matrix using
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– Example:
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– Example:
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– Example:
The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:– Example:
References
M. Zvelebil, J. O. Baum, “Understanding Bioinformatics”, 2008, Garland Science
Andreas D. Baxevanis, B.F. Francis Ouellette, “Bioinformatics: A practical guide to the analysis of genes and proteins”, 2001, Wiley.
Barbara Resch, “Hidden Markov Models - A Tutorial for the Course Computational Intelligence”, 2010.