G53BIO

Bioinformatics
Phylogenetic Trees
Dr. Jaume Bacardit
http://www.cs.nott.ac.uk/~jqb/G53BIO
Examples from D.A.Krane & M.L. Raymer
’
s
“
Fundamental
Concepts of Bioinformatics
”
and from D.W.
Mount
’
s
“
Bioinformatics: Sequence and Genome Analysis
”
Outline
•
Introduction and motivation
•
Types of trees
•
Algorithms to construct trees
•
UPGMA
•
Fitch

Margoliash
•
Neighbour

Joining
•
Sources of information
Aims
•
Phylogeny has the goals of working out the relationships
among species, populations, individuals or genes (taxa in a
general sense)
•
The results of phylogenetic analysis are usually presented
as a collection of nodes and branches. That is, a tree
•
In such tree, taxa that are closely related in an evolutionary
sense appear close to each other, and taxa that are
distantly related are in different (far) branches of the trees
•
Phylogenetic trees are also important for multiple
sequence alignment
•
Various…
–
Types of tree exists
–
Sources of information to generate the trees
–
Ways to generate the trees
•
Trees are usually bifurcating but it is also possible to have multifurcating trees
•
Interpretation:
–
At some point in the past an ancestral population gave rise to more than 2
lineages or
–
Insufficient/erroneous data impedes the discrimination of the true nature
of the tree thus coalescing various branches into one multifurcating one.
•
Not only the topology of the trees convey information, also the relative sizes
of the branches:
–
Scaled trees:
branch length are proportional to the differences between
pairs of neighbouring nodes.
–
Additive trees:
these are scaled trees in which the physical length of the
branches connecting two nodes is an accurate representation of their
accumulated differences
–
Unscaled trees
: only convey kinship information
•
Phylogenetic Trees can be:
–
Rooted:
A single node is designated as root and it represents a common
ancestor with a unique path leading from it through evolutionary time to
any other node
–
Unrooted tree:
specifies only the nodes interrelations but says nothing
about the direction in which evolution occurred.
Roots can be artificially assigned to unrooted trees by means of an
outgroup.
An outgroup is a species that have unambiguously separated early from the other
species being considered
Example: comparing Humas and Gorilas, Baboons could be used as outgroups and
the root would be placed somewhere along the branch conecting Baboons to
the common ancestors for Humans and Gorilas.
Rooted trees
Unrooted trees
Number of Rooted VS Unrooted
Trees
NR = (2n

3)!/ 2^(n

2) * (n
–
2)!
NU = (2n
–
5)!/ 2^(n

3) * (n
–
3)!
But only one of these represents the true turn of events!
Most phylogenetic trees generated with molecular data are thus referred to as
inferred trees
.
Unweighted pair group method
with arithmetic meant (UPGMA)
•
The oldest tree reconstructions method (1960)
•
Requires a distance matrix, e.g.:
Species
A
B
C
B
dAB


C
dCA
dBC

D
dAD
dBD
dCD
•
E.G. dAB represents the distance between
species A & B, while dAC is the distance between
taxa A & C, etc
UPGMA:
1.
Cluster the two species with the smallest distance
putting then into a single group. Assume that in the
example dAB is the smallest, hence a new group (AB)
is created.
2.
Recalculate the distance matrix with the new group
(AB) against C and D:
1.
d(AB)C = 0.5 * (dAC+dBC)
2.
d(AB)D = 0.5 * (dAD+dBD)
3.
With the new distance matrix repeat 1 until all
species have been grouped.
EXAMPLE
Fitch

Margoliash Algorithm
Main idea:
•
Sequences are first combined into groups of three
and used to calculated branches
’
length.
•
Sequences are added progresively
•
Branch lengths are assumed to be additive
•
Then join all sequences in pair, assess their inferred
distances and calculate a percentage squared error
•
Repeat with different initialisation until finding a
good (small error) tree
Fitch

Margoliash Algorithm
1.
From the distance matrix find the closest pair, e.g., A & B
2.
Treat the rest of the sequences as a single composite sequence. Calculate the
average distance from A to all of the other sequences and B to all of the other
sequences
3.
Use these values to calculate the distances a and b between A and the joining
common node to B and the same for B.
4.
Take A and B as a single composite sequence AB, calculate the average
distances between AB and each of the other sequences, and make a new
distance table from these values.
5.
Indentify the next pair of most closely related sequences and proceed as in
step 1 to calculate the next set of branch length.
6.
When necessary substract extended branch lengths to calculate lengths of
intermediate branches.
7.
Repeat the entire procedure starting with all possible pairs of sequences A and
B, A and C, A and D, etc
8.
Calculate the predicted distances between each pair of sequences for each
tree to find the tree that best fits the original data
D and E are the closest sequences
D
E
A

C
b
a
c
A

C
D
E
A

C

32.6
34.6
D

10
E

a = 4
b = 6
c = 29
Now let
’
s recompute the complate distance matrix
A
B
C
DE
A

22
39
40
B

41
42
C

19
DE

C and DE are the closet sequences
C
A

B
b
a
c
AB
C
DE
AB

40
412
C

19
DE

a = 9
b = 10
c = 31
Now let
’
s recompute the complate distance matrix
DE
b is not just for that
segment, it represents
the complete distance
from the connecting
node to the leaves
C
A

B
5
9
31
D
E
4
6
A
B
C

E
A

22
39.5
D

41.5
E

Now we are in thee trivial case of 3 sequences
B
A
a
b
c
a = 29.5
b = 10
c = 12
CDE
b is not just for that
segment, it represents
the complete distance
from the connecting
node to the leaves
C
5
9
20
D
E
4
6
A
B
C

E
A

22
39.5
D

41.5
E

A
B
10
12
This time we got the perfect tree.
However, this is not always the case.
The algorithm should be repeated
with different initial pairings (who
are A and B) and then compare the
difference between the actual and
predicted distnaces (from summing
the length of the branches)
Neighbour Joining Algorithm
•
Similar to Fitch

Margoliash except that
sequences are paired based on the effect of
the pairing on the sum of the branch lengths
of the tree.
•
The general Neighbour Joining algorithm can
be downloaded from
ftp.virginia.edu/pub/fasta/GNJ
The Algorithm
1.
The distances between pair of objects are used
to calculate the sum of the branch length for a
tree that has no preferred pairing of sequences.
2.
Decompose the star

like tree by combining
pairs of sequences. Using the same example
as before this gives:
3.
Each possible sequence pair is chosen and the sum of the branch lengths of
the corresponding tree is calculated. For the example: S_AB=67.7, S_BC=81,
S_CD=76, S_DE=70 plus six other possibilities.
4.
Choose the one with the lowest sum, in this case S_AB.
5.
Once the choice is made calculate the brachn lengths a,b and the average
distance from AB to CDE using FM method:
1.
a = [d_AB + (d_AC+d_AD+d_AE)/3
–
(d_BC+d_BD+d_DE)/3]/2
= (22 + 39.7

41.7)/2
= 10
2.
b = [ d_AB +(d_BC+d_BD+d_BE)/3
–
(d_AC+d_AD+d_AE)/3]/2
= (22 + 41.7 +39.7)/2
= 12
6.
Like in Fitch

Margoliash method: A new
distance table with A and B forming a single
composite sequence is produced and the
algorithm is iterated from the beginning to
find the next sequence pair and the next
branch lengths.
Sources of information
•
So far, all methods shown computed the
distance matrix between species from a set of
aligned sequences (DNA or Protein)
•
There are many more sources of information
–
Complete genomes
–
Restriction sites
–
Non

coding DNA regions
Tree of life
constructed
from all species for
which their complete
genome has been
sequenced
•
There are several methods to compute phylogenetic
trees, and sources of information
•
Need to be familiar with several of them to appreciate
their differences
•
There are various guiding mechanisms to choose how
to build the trees based on likelihood functions and
information theory
•
Get familiar with
Phylip
package as it is a standard one
•
Other programs
exist
Summary
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