G53BIO - Bioinformatics Phylogenetic Trees

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G53BIO - BioinformaticsPhylogenetic Trees

• Dr. Jaume Bacardit
• http//www.cs.nott.ac.uk/jqb/G53BIO

Examples from D.A.Krane M.L. Raymers
Fundamental Concepts of Bioinformatics and from
D.W. Mounts Bioinformatics Sequence and Genome
Analysis
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Outline

• Introduction and motivation
• Types of trees
• Algorithms to construct trees
• UPGMA
• Fitch-Margoliash
• Neighbour-Joining
• Sources of information

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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

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• 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

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• 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.

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Rooted trees
Unrooted trees
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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.

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Unweighted pair group method with arithmetic
meant (UPGMA)

• The oldest tree reconstructions method (1960)
• Requires a distance matrix, e.g.

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• E.G. dAB represents the distance between species
  A B, while dAC is the distance between taxa A
  C, etc
• UPGMA
• 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.
• Recalculate the distance matrix with the new
  group (AB) against C and D
• d(AB)C 0.5 (dACdBC)
• d(AB)D 0.5 (dADdBD)
• With the new distance matrix repeat 1 until all
  species have been grouped.

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EXAMPLE
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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

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Fitch-Margoliash Algorithm

• From the distance matrix find the closest pair,
  e.g., A B
• 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
• Use these values to calculate the distances a and
  b between A and the joining common node to B and
  the same for B.
• 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.
• Indentify the next pair of most closely related
  sequences and proceed as in step 1 to calculate
  the next set of branch length.
• When necessary substract extended branch lengths
  to calculate lengths of intermediate branches.
• Repeat the entire procedure starting with all
  possible pairs of sequences A and B, A and C, A
  and D, etc
• Calculate the predicted distances between each
  pair of sequences for each tree to find the tree
  that best fits the original data

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D
a
D and E are the closest sequences
c
A-C
b
E
a 4 b 6 c 29
Now lets recompute the complate distance matrix
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C
a
b is not just for that segment, it represents the
complete distance from the connecting node to the
leaves
C and DE are the closet sequences
c
A-B
b
DE
a 9 b 10 c 31
Now lets recompute the complate distance matrix
C
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31
A-B
5
4
D
6
E
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B
Now we are in thee trivial case of 3 sequences
b
b is not just for that segment, it represents the
complete distance from the connecting node to the
leaves
c
A
a
CDE
a 29.5 b 10 c 12
A
C
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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)
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5
4
12
D
B
6
E
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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

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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.

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• Decompose the star-like tree by combining pairs
  of sequences. Using the same example as before
  this gives

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• Each possible sequence pair is chosen and the sum
  of the branch lengths of the corresponding tree
  is calculated. For the example S_AB67.7,
  S_BC81, S_CD76, S_DE70 plus six other
  possibilities.
• Choose the one with the lowest sum, in this case
  S_AB.
• Once the choice is made calculate the brachn
  lengths a,b and the average distance from AB to
  CDE using FM method
• a d_AB (d_ACd_ADd_AE)/3
  (d_BCd_BDd_DE)/3/2
• (22 39.7 -41.7)/2
• 10
• b d_AB (d_BCd_BDd_BE)/3
  (d_ACd_ADd_AE)/3/2
• (22 41.7 39.7)/2
• 12

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• 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.

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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

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Tree of life constructed from all species for
which their complete genome has been sequenced
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Summary

• 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