Phylogenetic Analysis

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Phylogenetic Analysis

• Greek phylon race
• genetic -- birth

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Phylogenetic Analysis

• The evolutionary relationship among a set of
  species is called a Phylogeny, represented by a
  phylogenetic tree.
• Infer phylogenetic tree (Reconstruction) from
  observation of the existing organisms
• Then morphological characters
• Now molecular sequences!
• Zuckerkandl Pauling 1962

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Relationship to MSA

• Multiple alignment of sequences should take
  account of their evolutionary relationship. (Some
  multiple alignment algorithms do use a guide
  tree)
• Alignment and tree-building can proceed
  simultaneously

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Phylogeny of

• Orthologues divergence from a common ancestor,
  speciation
• -- in different species
• Paralogues divergence from gene duplication
• -- within same species/organism

Speciation
1A
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Elements of a Tree

• Leaves/Nodes sequences
• Taxa (singular taxon) outer leaves
• Edges edge lengths correspond to evolutionary
  time periods
• Roots

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Molecular Clock Theory
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Molecular Clock Theory I(Zukerkandl Pauling,
early 1960s)

• For any given protein, accepted mutations in the
  amino acid sequence for the protein occur at
  constant rate
• Implication
• of accepted mutations proportional to length of
  time interval
• All proteins/species observed today have the same
  molecular age
• Works well for closely related species

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Molecular Clock Theory II

• Rate of accepted mutations maybe different for
  different proteins (depending on their tolerance
  for mutations)
• Different parts of a protein may evolve at
  different rates

Counting mutations
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Distance-based Methods

• We assume that the distance between each pair
  of sequences is proportional to the evolutionary
  time between them.

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How to Collect Distance Data

• Lab methods mix single strands of DNA from
  different species, measure how tightly they
  associate.
• Sequence analysis methods estimate number of
  mutations based on sequence comparisons

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Fill Out A Distance Matrix
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Ultrametric Distance Matrices

• D is an ultrametric distance matrix, if and only
  if
• for every three indices i, j and k there is a tie
  for the maximum of D(i,j), D(i,k) and D(j,k).
  That is, the maximum is not unique.

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Test if the data is ultrametric
Mol. Clock Theory I is valid for this group of
seq.s
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Ultrametric

• not-ultrametric

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Constant mutation rate
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When MCT. 1 fails

• The distance matrix is no longer ultrametric

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When distance is additive
Inferring an inner node
k
j
m
i
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Neighbor Joining

• Can we use this fact to construct trees?
• Infer inner nodes
• Gradually strip off leaves (outer nodes)

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Finding Neighboring Leaves

• Let
• where
• Theorem if D(i,j) is minimal (among all pairs of
  leaves), then i and j are neighbors in the tree

g
j
i
h
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Neighbor Joining

• Set L to contain all leaves
• Iteration
• Choose i,j such that D(i,j) is minimal
  (neighbors)
• Create new node k, and set
• remove i,j from L, and add k
• Terminatewhen L 2, connect two remaining
  nodes

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NJ will construct the correct tree (if additive)