Luonan Chen

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Phylogenetic Prediction and Evolutionary Tree
Chaper-6

• Luonan Chen

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Methods

• Phenetic Approach Clustering approach,
  Fitch-Margoliash method, Neighbor-joining method
• -- based on similarity
• Cladistic Approach maximum parsimony and maxmum
  likelihood approaches
• -- based on genealogy
• -- Cladistic approaches are superior to
  clustering techniques but require more CPU time

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Distance Matrix (Phenetic approach depends on
distance matrix)

• DNA
• -- Hamming distance, e.g. D2 for agbc and agta
• -- Levenshtein distance (edit distance) minimal
  number to change one string into the other by
  deletion, insertion or substitution. E.g. D3 for
  ag-tcc and cgctca
• Protein
• -- PAM matrix, BLOSUM matrix

Similarity measure of the number of sequence
positions that match in an alignment. Distance
the number of positions that are different and
that must be changed to
convert
one sequence into the other.
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Amino Acid Distances

• Distances between amino acid sequences are a bit
  more complicated to calculate.
• Some amino acids can replace one another with
  relatively little effect on the structure and
  function of the final protein while other
  replacements can be functionally devastating.
• From the standpoint of the genetic code, some
  amino acid changes can be made by a single DNA
  mutation while others require two or even three
  changes in the DNA sequence.
• In practice, what has been done is to calculate
  tables of frequencies of all amino acid
  replacements within families of related protein
  sequences in the databanks i.e. PAM and BLOSSUM

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The PAM 250 scoring matrix
A R N D C Q E G H I L K
M F P S T W Y V A 2
R -2 6 N 0 0 2
D 0 -1 2 4
C -2 -4 4 -5 4 Q 0 1 1 2 -5
4 E 0 -1 1 3 -5 2 4
G 1 -3 0 1 -3 -1 0 5 H -1
2 2 1 -3 3 1 -2 6 I -1 -2 -2
-2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4
-6 -2 -3 -4 -2 2 6 K -1 3 1 0
-5 1 0 -2 0 -2 -3 5 M -1 0 -2
-3 -5 -1 -2 -3 -2 2 4 0 6 F -4
-4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9
P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5
6 S 1 0 1 0 0 -1 0 1 -1 -1
-3 0 -2 -3 1 3 T 1 -1 0 0 -2
-1 0 0 -1 0 -2 0 -1 -2 0 1 3
W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2
-5 17 Y -3 -4 -2 -4 0 -4 -4 -5 0
-1 -1 -4 -2 7 -5 -3 -3 0 10 V 0
-2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0
-6 -2 4 Dayhoff, M, Schwartz, RM, Orcutt, BC
(1978) A model of evolutionary change in
proteins. in Atlas of Protein Sequence and
Structure, vol 5, sup. 3, pp 345-352. M. Dayhoff
ed., National Biomedical Research Foundation,
Silver Spring, MD.
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Phenetic Methods

• Computer algorithms based on the phenetic model
  rely on Distance Methods to build of trees from
  sequence data.
• Phenetic methods count each base of sequence
  difference equally, so a single event that
  creates a large change in sequence
  (insertion/deletion or recombination) will move
  two sequences far apart on the final tree.
• Phenetic approaches generally lead to faster
  algorithms and they often have nicer statistical
  properties for molecular data.
• The phenetic approach is popular with molecular
  evolutionists because it relies heavily on
  objective character data (such as sequences) and
  it requires relatively few assumptions.

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Clustering Algorithms

• Clustering algorithms use distances to calculate
  phylogenetic trees. These trees are based solely
  on the relative numbers of similarities and
  differences between a set of sequences.
• Start with a matrix of pairwise distances
• Cluster methods construct a tree by linking the
  least distant pairs of taxa, followed by
  successively more distant taxa.

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UPGMA

• The simplest of the distance methods is the UPGMA
  (Unweighted Pair Group Method using Arithmetic
  averages)
• Minimize the total edge length of tree.
• Many multiple alignment programs such as PILEUP
  use a variant of UPGMA to create a dendrogram of
  DNA sequences which is then used to guide the
  multiple alignment algorithm.

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Clustering Method (UPGMA)(Molecular clock
hypothesis uniform rate of mutation in the tree
branches)
Other distance matrix (PAM) can be used
average distance
Improvement Choosing outgroup
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Fitch-Margoliash (FM) Algorithm-I
(Minimize total edge length at each step)
Distance Table for 5-sequence

• 1. The most closely related sequences are D and
  E. A new Table is made with the remaining
  sequences combined.
• 2. The average distances from D and E to ABC are
  calculated.

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Fitch-Margoliash Algorithm-II
average

• 3. Distance D--E de DABC dm, EABC em,
  (mg(c2fab)/2)
• Then d4 e6
• 4. D and E are treaded as a single DE. A new
  Table is calculated by the average distances
  between A,B,C and DE
• 5. The next most closely related sequences are C
  with DE. We have new Table. Similarly, we have
  c9, and n10, (ng (ef)/2)
• 6.In the same way, we finally, a10, b12, g5
  and f20. Then we have the tree.

How about starting with A and B ?
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Neighbor Joining

• The Neighbor Joining method is the most popular
  way to build trees from distance measurements
• (Saitou and Nei 1987, Mol. Biol. Evol. 4406)
• Neighbor Joining corrects the UPGMA method for
  its (frequently invalid) assumption that the same
  rate of evolution applies to each branch of a
  tree.
• The distance matrix is adjusted for differences
  in the rate of evolution of each taxon (branch).
• Neighbor Joining has given the best results in
  simulation studies and it is the most
  computationally efficient of the distance
  algorithms (N. Saitou and T. Imanishi, Mol.
  Biol. Evol. 6514 (1989)

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Neighbor-joining Method (No
requirement for molecular clock hypothesis)

• The algorithm is the same as FM method except the
  choice of pair
• The choice of pair is based on minimal sum of the
  branch lengths of the tree
• lt Algorithm gt
• Step-1 Star-like connection S0abcde78.5
• Step-2 Comparing the distances of all pairs, and
  choosing one pair with minimal overall lengths.
  SAB67.7, SBC81,SCE76,SED70. Choose AB pair.
• Step-3 As Steps 2 and 3 of FM method,
  calculating average distance from AB to CDE, we
  have a10, b12.
• Step-4 As FM method, calculate a new Table with
  A and B forming a single pair.
• Continue the computation to find the next
  pair until finished.

Overall length when AB joining
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Cladistic Methods

• For character data about the physical traits of
  organisms (such as morphology of organs etc.)
  and for deeper levels of taxonomy, the cladistic
  approach is almost certainly superior.
• Cladistic methods are often difficult to
  implement with molecular data because all of the
  assumptions are generally not satisfied.

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Cladistic methods

• Cladistic methods are based on the assumption
  that a set of sequences evolved from a common
  ancestor by a process of mutation and selection
  without mixing (hybridization or other horizontal
  gene transfers).
• These methods work best if a specific tree, or at
  least an ancestral sequence, is already known so
  that comparisons can be made between a finite
  number of alternate trees rather than calculating
  all possible trees for a given set of sequences.

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Parsimony

• Parsimony is the most popular method for
  reconstructing ancestral relationships.
• Parsimony allows the use of all known
  evolutionary information in building a tree
• In contrast, distance methods compress all of the
  differences between pairs of sequences into a
  single number

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Building Trees with Parsimony

• Parsimony involves evaluating all possible trees
  and giving each a score based on the number of
  evolutionary changes that are needed to explain
  the observed data.
• The best tree is the one that requires the fewest
  base changes for all sequences to derive from a
  common ancestor.

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Cladistic Method Maximum Parsimony Method (
minimizing overall number of evolutionary changes
(mutations) )
Sequences ATCT, ATGG, TCCA, TTCA
Optimal Solution
4 mutations
7 mutations
Problem varying rates of evolution Note gaps
are treated as a fifth base
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Maximum Likelihood

• The method of Maximum Likelihood attempts to
  reconstruct a phylogeny using an explicit model
  of evolution.
• This method works best when it is used to test
  (or improve) an existing tree.
• Even with simple models of evolutionary change,
  the computational task is enormous, making this
  the slowest of all phylogenetic methods.

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Assumptions for Maximum Likelihood

• The frequencies of DNA transitions (Clt-gtT,Alt-gtG)
  and transversions (C or Tlt-gtA or G).
• The assumptions for protein sequence changes are
  taken from the PAM matrix - and are quite likely
  to be violated in real data.
• Since each nucleotide site evolves independently,
  the tree is calculated separately for each site.
  The product of the likelihood's for each site
  provides the overall likelihood of the observed
  data.

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Improving Efficiency by Compression

• S1 ACGTTTGGGGCCCCTTT
• S2 ACGTTTGGGGCCCCTTT
• S3 ACGTTTGGGGCCCCTTT
• S4 ACGCTCGGGGCCCCTTT

Data Compression

• S1 A C G T T
• S2 A C G T T
• S3 A C G T T
• S4 A C G C T
• 1, 5,5,2,4

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Conclusions

• Given the huge variety of methods for computing
  phylogenies, how can the biologist determine what
  is the best method for analyzing a given data
  set?
• Published papers that address phylogenetic issues
  generally make use of several different
  algorithms and data sets in order to support
  their conclusions.
• In some cases different methods of analysis can
  work synergistically
• Neighbor Joining methods generally produce just
  one tree, which can help to validate a tree built
  with the parsimony or maximum likelihood method
• Using several alternate methods can give an
  indication of the robustness of a given
  conclusion.