1. Phylogenetic Analysis
Introduction to bioinformatics
Stinus Lindgreen
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 ( )

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. The result is only as good as the alignment
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

11. Interpretation Know your model Know the assumptions of the 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
Don’t make hasty conclusions!
Does your tree contradict common sense?
Then it’s 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 we’ll 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 don’t 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!

17. PhyloWin Another free program Simple, not many possibilities
But you can make bootstrapping

18. Getting the software Install BioEdit, PHYLIP, PhyloWin and NJplot
Links on the wiki

19. 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

20. 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?
Clustal’s guide tree: Not correct phylogeny
What parameters are used?
Solve ambiguities, remove near-identical sequences
Gappy regions, identical sequences can bias the result

21. 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

22. Nucleotide models Create 4×4 matrix Either fixed cost Or rate matrices
Character state
Or rate matrices
Probabilities
Used for different kinds of tree estimations
Include site specific information
Third codon position more variable

23. 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 - 2 1

24. Nucleotide model 2 Simple substitution rate matrix
Assume same rates AB and BA
Assume all mutations equally likely: Rate α
The Jukes-Cantor model A C G T
-3α α

25. Nucleotide model 3 More advanced rate matrix
Include transitions/tranversions
Rates α1 and α2
The Kimura 2-parameter model A C G T
-(α2+α1) α2 α1

26. Amino acid models A 20×20 substitution matrix The BLOSUM matrices
Fixed cost matrices
Or the PAM matrices
Rate matrices
Described last week

27. 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

28. Problems with trees The number of possible trees grows exponentially
For 15 taxa: 2.13·1014 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

29. 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

30. 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

31. 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

32. UPGMA illustrated Find two closest: A and D Create a new group [A+D]
Update distances: A B C D E - 8 3 2 5 6 7
A+D B C E - 7 5 4 6
Repeat for all sequences
Next time: Connect [A+D] with E

33. Trying UPGMA
Go to the wiki and do the UPGMA exercise

34. 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

35. 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

36. 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

37. Trying NJ
Go to the wiki and do the NJ exercise

38. Character methods Use the data (the actual characters)
All information at hand
More advanced, slower, but also more accurate
Maximum Parsimony (MP)
Occam’s razor: Simplest explanation
Maximum Likelihood (ML)
Advanced statistical method
Most probable tree given the data and the model

39. 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

40. MP illustrated
A C G G C
{A,C} {G}
{A,C,G}
{C}

41. MP illustrated
A C G G C
{A,C} {G}
{A,C,G}
{C} X X
Cost: 2 changes

42. MP illustrated
A C G G C
C G C
CA
CG

43. 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

44. 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 C C A
A A C G A
L=P +P +P +…

45. 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

46. MP and ML exercise
Go to the wiki and do the MP and ML exercises

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

48. 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

49. 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?

50. 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 don’t put too much faith in it

51. 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

52. 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)

53. 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 #:
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 - 1 5 8 7 4 A B C D

54. Bootstrap example Sample 2: A B C D - 2 4 7 5 3 A B C D
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 - 2 4 7 5 3 A B C D

55. Bootstrap example Sample 3: A B C D - 3 4 7 6 A B C D
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 - 3 4 7 6 A B C D

56. 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

57. Bootstrapping exercise
Do the bootstrapping exercise on the wiki

58. 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 