Phylogenetic Analysis

1
Phylogenetic Analysis

• Introduction to bioinformatics
• Stinus Lindgreen
• stinus_at_binf.ku.dk
• Bioinformatics Centre, University of Copenhagen

2
Outline of the lecture

• What is a phylogeny?
• Why and how to interpret them
• Programs PHYLIP, PAUP and BioEdit
• Building a tree 1 Multiple alignment
• Building a tree 2 The model
• Building a tree 3 Construction
• Building a tree 4 Evaluation

3

• Nothing in Biology Makes Sense Except in the
  Light of Evolution
• Theodosius Dobzhansky (1900-1975)

4
Phylogeny

• Phylogenetic inference predicts a tree based on
  characters (of some sort)
• Some variation needed
• Group together similar species/genes
• Connect to most common ancestor
• Unrooted tree Just show connections
• Rooted tree Direction of evolution
• Branch lengths can show divergence

5
Before sequences

• Phylogenetic trees show evolutionary
  relationships
• Existed longer than sequencing methods
• Previously based on morphological characters
• Still partly today at least for checking
• Mainly based on biological sequences
• DNA or protein
• Base phylogeny on mutations

6
Morphological tree
7
Modern tree

• A A G C
  G

X
X
8
Some pitfalls

• Determining phylogeny is important for
  understanding biology
• But also a very difficult problem
• Beware of incorrect trees
• Important to understand models and methods
• The programs are helpful tools
• The result is only as good as the alignment

9
Assumptions

• Basic concepts of evolutionary theory
• Relation to common ancestor
• Phylogenetics represented by bifurcating tree
• Mutations occur over evolutionary time
• Necessary to make phylogenetic inference possible

10
Tree of Life
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Interpretation

• Know your model
• Both evolutionary and for tree construction
• Know the assumptions of the model
• Evolution independent? Identical between sites?
  The same for all sequences?
• Are the sequences correct?
• And are they representative?
• And are they homologous?
• Is the multiple alignment correct?
• What you get out is no better than what you put in

12
Some biological pitfalls

• Dont make hasty conclusions!
• Does your tree contradict common sense?
• Then its probably wrong!
• Differentiate between the homologs
• Orthologs
• Speciation, common ancestor, similar function
• Paralogs
• Gene duplication, within 1 organism, differing
  functions
• Xenologs
• Horizontal gene transfer hard to tell, similar
  function

13
Software

• Today well look at the programs before the
  methods
• Some programs for phylogenetic analysis
• A multiple alignment program
• Clustal, T-Coffee, MAFFT, Muscle
• A phylogenetic program
• Phylip, PAUP, MacClade, BioEdit
• Visualizing the tree
• TreeView, NJplot

14
PAUP

• Commercial package
• Apparently good
• Many different methods and analysis methods
• But since we dont own a copy
• Similarly MacClade only works on Macintosh

15
PHYLIP

• Free package
• Many programs
• Both distance and character based
• Bootstrapping possible
• But
• It can be a little difficult
• No graphical user interface
• And you will need to run many programs

16
BioEdit

• Has phylogeny methods built in
• Can call Phylip routines
• No need for you to learn the command line
• But no bootstrapping (as far as I know)
• Point and click
• Select the sequences in the alignment
• Choose the wanted phylogeny
• Voila!

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PhyloWin

• Another free program
• Simple, not many possibilities
• But you can make bootstrapping

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Getting the software

• Install BioEdit, PHYLIP, PhyloWin and NJplot
• Links on the wiki

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Constructing a tree

• To make a phylogenetic tree, four steps are
  needed
• Perform multiple alignment
• Choose your model
• Build the tree
• Evaluate the quality
• A brief note
• Ideally Parallel alignment and phylogenetic
  inference
• Very difficult but it has been pursued

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1) The multiple alignment

• Already discussed
• Some notes
• Recall that MA programs are not exact
• Some manual editing often necessary
• Consider the algorithm used
• Does it consider the phylogeny of the data?
• Clustals guide tree Not correct phylogeny
• What parameters are used?
• Solve ambiguities, remove near-identical
  sequences
• Gappy regions, identical sequences can bias the
  result

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2) The model

• The model describes the data
• Evolutionary events
• Overall mutability
• Evolutionary model?
• Crucial both for alignment and tree building
• Are you looking at nucleotides or amino acids?
• Where do we get most information?
• Know the basis for the chosen model

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Nucleotide models

• Create 44 matrix
• Either fixed cost
• Character state
• Or rate matrices
• Probabilities
• Used for different kinds of tree estimations
• Include site specific information
• Third codon position more variable

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Nucleotide model 1

• Fixed cost for transitions and transversion
• E.g. transversions are twice as costly as
  transitions
• For a tree Count the number of
• transitions/transversions
• Calculate cost
• Tends to minimize number of
• transversion
• Cluster transitions

A C G T
A - 2 1 2
C 2 - 2 1
G 1 2 - 2
T 2 1 2 -
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Nucleotide model 2

• Simple substitution rate matrix
• Assume same rates A?B and B?A
• Assume all mutations equally likely Rate a
• The Jukes-Cantor model

A C G T
A -3a a a a
C a -3a a a
G a a -3a a
T a a a -3a
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Nucleotide model 3

• More advanced rate matrix
• Include transitions/tranversions
• Rates a1 and a2
• The Kimura 2-parameter model

A C G T
A -(a2a1) a2 a1 a2
C a2 -(a2a1) a2 a1
G a1 a2 -(a2a1) a2
T a2 a1 a2 -(a2a1)
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Amino acid models

• A 2020 substitution matrix
• The BLOSUM matrices
• Fixed cost matrices
• Or the PAM matrices
• Rate matrices
• Described last week

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3) Building the tree

• We have the sequences, the alignment and the
  model
• Find the best tree
• What is the best tree?
• Two main strategies
• Distance based
• Look at dissimilarities (distances)
• Character based
• Look at the data

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Problems with trees

• The number of possible trees grows exponentially
• For 15 taxa 2.131014 possibilities
• How to search?
• Branch and Bound
• Branch swapping
• Rooting the tree
• Not a simple problem
• All the following methods produce unrooted trees
• Use an outgroup
• Midpoint of longest branch

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Distance methods

• Some sequences more similar than others
• Closely related sequences should be close in the
  tree
• Abstract view on the data
• Loss of information is usually a bad sign
• Only use the distances between sequences
• Recall Clustal
• All methods start with a distance matrix

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Distance methods

• Can we get the correct answer?
• Yes, if all mutation events were present
• But After one mutation, the site is saturated
• Additional mutations do not give additional info
• A B C Distance 2
• A C Distance 1
• And mutations back will fool the method
• A B A Distance 2
• A A Distance 0

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UPGMA

• Unweighted Pair Group Method with Arithmetic Mean
• Unweighted The distances are used as they are
• Pair Find the two closest elements
• Group Put them together in a new group
• Arithmetic Mean Gives distances from the new
  group
• Correct tree assuming a molecular clock
• Evolutionary divergence time can be found from
  mutations
• Mutation rates are constant

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UPGMA illustrated

• Find two closest A and D
• Create a new group AD
• Update distances

A B C D E
A - 8 3 2 5
B - - 5 6 6
C - - - 7 5
D - - - - 3
E - - - - -
AD B C E
AD - 7 5 4
B - - 5 6
C - - - 5
E - - - -

• Repeat for all sequences
• Next time Connect AD with E

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Trying UPGMA

• Go to the wiki and do the UPGMA exercise

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Neighbour joining

• A little like UPGMA
• Difference NJ does not assume a molecular clock
• But it assumes an additive tree
• Distance between two leaves is the sum of the
  edges
• Find the closest pair that is most apart from the
  rest of the tree
• Connect pair and update distances
• A little advanced Take the overall distance to
  the rest of the tree into account
• Corrects for varying mutation
• Fast and can give good results

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Fitch-Margoliash

• FM method
• We have the pairwise distances
• Each branch in the tree has a length
• The length of all paths can be found
• Optimize tree by moving internal nodes around
• The best fit minimizes the overall error
• The minimum squared deviation

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Minimum Evolution

• The ME method
• Find the shortest tree
• Count number of changes
• Similar to FM but only looks at branches
• FM

B
ME
B
A
A
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Trying NJ

• Go to the wiki and do the NJ exercise

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Character methods

• Use the data (the actual characters)
• All information at hand
• More advanced, slower, but also more accurate
• Maximum Parsimony (MP)
• Occams razor Simplest explanation
• Maximum Likelihood (ML)
• Advanced statistical method
• Most probable tree given the data and the model

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Maximum parsimony

• How does evolution work?
• Assumption Path of least resistance
• True evolution gives rise to fewest changes
• The tree we want
• Describe the given sequences by fewest changes
• The ancestral nodes must be as similar as
  possible
• Predict a tree
• Count the number of changes needed

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MP illustrated

• A C G G C
• A,C G
• A,C,G
• C

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MP illustrated

• A C G G C
• A,C G
• A,C,G
• C

X
X
Cost 2 changes
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MP illustrated

• A C G G C
• C G
• C
• C

C?A
C?G
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Maximum Likelihood

• Given the data, predict the most probable model
• Can optimize both tree and substitution model
• We know the sequences
• What is the most likely substitution rates?
• Estimate from the alignment (and the phylogeny)
• And what is the most likely tree?
• Estimate from alignment and substitution rates
• Computationally heavy and rather slow
• Normally good results

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Maximum Likelihood

• General practice Optimize model then tree
• Calculate probability for each alignment column
• Combine to probability for entire alignment
• Averages over low and high probability sites
• Likelihood of column given tree

A A C A A
A A C C A
A A C G A
LP
P
P

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Maximum likelihood

• Then repeat this for all possible tree topologies
• And all possible assignments to internal nodes
• And then choose the combination that gives the
  highest probability
• Clearly very difficult

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MP and ML exercise

• Go to the wiki and do the MP and ML exercises

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Summary of methods
Distance Character based
Clustering UPGMA Neighbour Joining
Optimality criterion Least Squares Minimum evolution Maximum parsimony Maximum likelihood (Bayesian statistics)
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The differences

• Sometimes the differences can seem minimal
• They affect the tree but the same result is
  possible
• UPGMA and NJ
• Minimize the overall length of the tree
• Maximum parsimony
• Finds tree with fewest changes
• Maximum likelihood
• Maximizes the probability of the tree given the
  data

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4) Evaluating trees

• How good is the predicted tree?
• Some sequence variation needed
• Is the signal strong enough?
• There are so many possible trees
• Are there many trees similar to the prediction?
• Which one to choose?
• Is the tree robust?
• Does it change much when e.g. removing a sequence?

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Randomization

• Is it possible that tree is just random?
• Permute the columns of the alignment
• i.e. shuffle the characters in a column
• Build a new tree
• Is it (partly) identical?
• If the tree is just as likely to be random, then
  dont put too much faith in it

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Bootstrapping

• The story of Baron von Münchausen
• He pulled himself out of a swamp by his
  bootstraps
• The idea Evaluate the quality of the result
  using the same data all over again
• Make a large number of new datasets
• Create phylogenetic tree
• Observe the number of times clades are made

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Bootstrapping

• The datasets should be similar
• Thereby The trees are comparable
• Alignments of same size (length and sequences)
• Non-parametric Sample with replacement
• Choose a random column and add new alignment
• Parametric Simulate new datasets
• Use model that look like your data
• Characteristics are preserved (unlike
  randomization)

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Bootstrap example

• Non-parametric bootstrapping
• We have an alignment
• A A G G C U C C A A A
• B A G G U U C G A A A
• C A G C C C C G A A A
• D A U U U C C G A A C
• 0 1 2 0 3 0 1 2 0 1
• Sample columns
• A G G G U U U C A A A
• B G G G U U U G A A A
• C G C C C C C G A A A
• D U U U C C C G A A C

A B C D
A - - - -
B 1 - - -
C 5 5 - -
D 8 7 4 -
A B C D
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Bootstrap example

• Sample 2
• A A U U C C C C A A A
• B A U U C C G G A A A
• C A C C C C G G A A A
• D A C C C C G G C C C

A B C D
A - - - -
B 2 - - -
C 4 2 - -
D 7 5 3 -
A B C D
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Bootstrap example

• Sample 3
• A A C C C A A G G C C
• B A C C G A A G G U U
• C A C C G A A C C C C
• D A C C G C C U U U U

A B C D
A - - - -
B 3 - - -
C 3 4 - -
D 7 4 6 -
A B C D
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Bootstrap example

• Calculate consensus tree
• Can be done on many ways
• Put the bootstrap number at each branch point
• The proportions of times this branch is observed
• Of course, more than three samples needed

A B C D
1.0
0.66
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Bootstrapping exercise

• Do the bootstrapping exercise on the wiki

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Summary

• What is phylogenetic inference?
• What can a phylogenetic tree be used for?
• Be aware of the multiple alignment
• The different models
• Tree building methods NJ, UPGMA, ML and MP
• Evaluating trees Bootstrapping
• Programs Phylip, PAUP,PhyloWin and BioEdit
• Next time Gene finding (with Anders Krogh)
• Then RNA structure prediction with me again ?