1. Phylogenetic reconstruction

2. Types of data used in phylogenetic inference:
Distance-based methods: Transform the sequence data into pairwise distances, and use the matrix during tree building.
A B C D E
Species A
Species B
Species C
Species D
Species E
Character-based methods: Use the aligned characters directly.
Taxa Characters
Species A ATGGCTATTCTTATAGTACG
Species B ATCGCTAGTCTTATATTACA
Species C TTCACTAGACCTGTGGTCCA
Species D TTGACCAGACCTGTGGTCCG
Species E TTGACCAGTTCTCTAGTTCG
Example 1:
Uncorrected
“p” distance
(=observed percent
sequence difference)
Example 2: Kimura 2-parameter distance
(estimate of the true number of substitutions between taxa)

3. Tree-Building Methods
Distance
UPGMA, NJ, FM, ME
Character
Maximum Parsimony
Maximum Likelihood

4. Distance Methods Measure distance (dissimilarity) Methods
UPGMA (Unweighted Pair Group Method with Arithmetic Mean)
NJ (Neighbor joining)
ME (Minimal Evolution)

5. UPGMA: Distance measure
Clustering: All leaves are assigned to a cluster, which then are iteratively merged according to their distance.
The distance between two clusters i and j can be defined as:
Number of mismatches in gap free alignment

6. UPGMA: Replacing Node k replaces nodes i and j with their union:
(1)
The new distances between the new node k and all other clusters l are computed according to:
(2)

7. UPGMA: Algorithm Initialization: Iteration Termination
Assign each sequence i to its own cluster Ci .
Define one leaf of T for each sequence, and place at height zero.
Iteration
Determine the two clusters i, j for which di,j is minimal.
Define a new cluster k by Ck = Ci U Cj, and define dkl for all l by (2).
Define a node k with daughter nodes i and j, and place it at height di,j/2.
Add k to the current clusters and remove i.
Termination
When only two clusters i, j remain, place the root at height di,j/2.

8. UPGMA example: Step 1 Alignment -> distance
Example: observed percent sequence difference A B C D E F G - 63 94 79
111 96 47 67 20 83
100 23 58 89
106 62
107 92 43 16
102
Distance matrix:
DNA/RNA overview

9. Step 2: distance -> cladeB C D E F G - 63 94 79
111 96 47 67 23 83
100 20 58 89
106 62
107 92 43 16
102
DNA/RNA overview

10. Step 3: merge D and G A B C D E F G - 63 94 79 111 96 47 67 23 83 10020 58 89
106 62
107 92 43 16
102 A B C E F DG - 63 94 79 67 23 83 20 58 89 62
109 45 98
104
DNA/RNA overview

11. Step 4 A B C E F DG - 63 94 79 67 23 83 20 58 89 62
109 45 98
104
DNA/RNA overview

12. Step 5 AF B C E DG - 61 92 79 65 23 62 107 94 45 98 A B C E F DG - 6367 23 83 20 58 89 62
109 45 98
104
DNA/RNA overview

13. Step 6 AF B C E DG - 61 92 79 65 23 62
107 94 45 98
DNA/RNA overview

14. Step 7 AF BE C DG - 63 92 71
107 96 45
DNA/RNA overview

15. Step 8 AF BE C DG - 63 92 71
107 96 45
DNA/RNA overview

16. Step 9 AF BE
CDG - 63
102 88
DNA/RNA overview

17. Step 10 AF BE
CDG - 63
102 88
DNA/RNA overview A F

18. UPGMA: distance -> phylogeny
AFBE
CDG - 94 A F A F
DNA/RNA overview
Root

19. Additivity A C a c e
Neighbors B b d D
Fourpoint condition

20. Neighbor-joining (N-J)
Starts with a star-like tree
Neighbors are sequentially merged, if they minimize the total length of branches B B C C A A D F F E D E
Find 1 and 2 that give minimum Q

21. Clustering methods (UPGMA & N-J)
Optimality criterion: NONE. The algorithm itself builds
‘the’ tree.
UPGMA: rootet tree
N-J: unrootet tree
Advantages:
Can be used on indirectly-measured distances (immunological, hybridization).
Distances can be ‘corrected’ for unseen events.
The fastest of the methods available.
Can therefore analyze very large datasets quickly (needed for HIV, etc.).
Can be used for some types of rate and date analysis.
Disadvantages:
Similarity and relationship are not necessarily the same thing, so clustering by
similarity does not necessarily give an evolutionary tree.
Cannot be used for character analysis!
Have no explicit optimization criteria, so one cannot even know if the program
worked properly to find the correct tree for the method.

22. Minimum evolution (ME) methods
Optimality criterion: The tree with the shortest overall tree length
is chosen as the best tree.
Advantages:
Can be used on indirectly-measured distances (immunological, hybridization).
Distances can be ‘corrected’ for unseen events.
Usually faster than character-based methods.
Can be used for some rate analyses.
Has an objective function (as compared to clustering methods).
Disadvantages:
Information lost when characters transformed to distances.
Cannot be used for character analysis.
Slower than clustering methods.

23. Character Methods Maximum Parsimony Maximum Likelihood
minimal changes to produce data
Maximum Likelihood

24. Parsimony methods:
Optimality criterion: The ‘most-parsimonious’ tree is the one that
requires the fewest number of evolutionary events (e.g., nucleotide
substitutions, amino acid replacements) to explain the sequences.
Occam’s razor: “Of two competing theories or explanations, all other things being equal, the simpler one is to be preferred.” (William of Occam, )
Advantages:
Are simple, intuitive, and logical (many possible by ‘pencil-and-paper’).
Can be used on molecular and non-molecular (e.g., morphological) data.
Can tease apart types of similarity (shared-derived, shared-ancestral, homoplasy)
Can be used for character (can infer the exact substitutions) and rate analysis.
Can be used to infer the sequences of the extinct (hypothetical) ancestors.
Disadvantages:
Are simple, intuitive, and logical (derived from “Medieval logic”, not statistics!)
Can become positively misleading in the “Felsenstein Zone”:

25. Parsimony Comparison # changes 1-2 1 1-3 2 1-4 2-3 2-4 3-4 1 CCCAGG
2 CCCAAG
3 CCCAAA
4 CCCAAC
Comparison
# changes
1-2 1
1-3 2
1-4
2-3
2-4
3-4
1,2 can be sister taxa
AND
3,4 can be sister taxa
Infer ancestor of 1,2 and 3,4

26. Parsimony CCCAGG CCCAAG-> CCCAAG CCCAAA-> CCCAAA CCCAAC
3 changes

27. Calculate # changes | tree
a acgtatgga
b acgggtgca
g aacggtgga
d aactgtgca
a: c
g: a
a: c
g: a
a: c
g: a
b: c
d: a
d: a
b: c
b: c
d: a
Total tree length: 7
Total tree length: ?
Total tree length: ?

28. Calculate # changes | tree
a acgtatgga
b acgggtgca
g aacggtgga
d aactgtgca
a: c
g: a
a: c
g: a
a: c
g: a
b: c
d: a
d: a
b: c
b: c
d: a
Total tree length: 7
Total tree length: 8
Total tree length: 8

29. Maximum likelihood (ML) methods
Optimality criterion: ML methods evaluate phylogenetic hypotheses
in terms of the probability that a proposed model of the evolutionary
process and the proposed unrooted tree would give rise to the
observed data. The tree found to have the highest ML value is
considered to be the preferred tree.
Advantages:
Are inherently statistical and evolutionary model-based.
Usually the most ‘consistent’ of the methods available.
Can be used for character (can infer the exact substitutions) and rate analysis.
Can be used to infer the sequences of the extinct (hypothetical) ancestors.
Can help account for branch-length effects in unbalanced trees.
Can be applied to nucleotide or amino acid sequences, and other types of data.
Disadvantages:
Are not as simple and intuitive as many other methods.
Are computationally very intense (Iimits number of taxa and length of sequence).
Like parsimony, can be fooled by high levels of homoplasy.
Violations of the assumed model can lead to incorrect trees.

30. Using models Example: Jukes-Cantor , if i≠j , if i=j
Observed differences A G C T
, if i=j
, if i≠j
Actual changes
pt : proportion of different nucleotides

31. Maximum likelihood
Given two trees, the one with the higher likelihood, i.e. the one with the higher conditional probability of observing the data, is the better

32. 30 nucleotides from yh-globin genes of two primates on a one-edge tree
* *
Gorilla GAAGTCCTTGAGAAATAAACTGCACACTGG
Orangutan GGACTCCTTGAGAAATAAACTGCACACTGG
There are two differences and 28 similarities at
at=
lnL=
lnL

33. Likelihoods of a more interesting tree
Data for one site is shown on the tree
Edge lengths are defined as di=3(at)i
Computational root is chosen arbitrarily (homogenous models) at an internal node (arrow)
u is the state at the root node, v at the other internal node A C d1 d3 d5 d4 d2 A T u
Maximize L with respect to d’s

34. Confidence assesment
Bootstrap

35. Bootstrap Original analysis, e.g. MP, ML, NJ.
Aus
Beus
Ceus
Deus
Original analysis, e.g. MP, ML, NJ.
Original data set with n characters.
Draw n characters randomly with re-placement.
Repeat m
times.
m pseudo-replicates, each with n characters.
Aus
Beus
Ceus
Deus
Repeat original analysis on each of the pseudo-replicate data sets.
Aus
Beus
Ceus
Deus
75%
Evaluate the results from the m analyses.

36. Pros and cons of some methods
Pair-wise, algorithmic approach
+ Fast
+ Models can be used when transforming to distances
- Information is lost when transforming to pair-wise distances
- One will get a tree, but no measure of goodness to compare with other hypotheses
Parsimony
+ Philosophically appealing
- Models can not be used
- Can be computationally slow
Maximum likelihood
+ Model based
- Model based
- Computationally veeeeery slow

37. Computation
For large data sets (many taxa) exact solutions for any method employing an optimality criterion (parsimony, maximum likelihood, minimum evolution) are not possible
=> Use Neghbor-Joining

38. What can go wrong? Reality
A tree may be a poor model of the real history
Information has been lost by subsequent evolutionary changes
“Species” vs. “gene” trees

39. What is wrong with this tree?
Canis
Mus
Gadus
100
100

40. The expected tree…
Gene duplication
“Species” tree
“Gene” trees

41. Two copies (paralogs) present in the genomes
Orthologous
Orthologous
Canis
Mus
Gadus
Paralogous
Two copies (paralogs) present in the genomes

42. What we have studied…
Canis
Gadus
Mus

43. HIV Genome Diversity Error prone (RT) replication
High rate of replication
1010 virions/day
In vivo selection pressure

44. HIV tree
ENV
AIDS 1996, 10:S13
GAG
Recombinants!

45. To conclude– Trash in, trash out : Alignment crucial
Try several methods, for consistency
Beware of paraloges
Choos outgroup wisly: related sequence of more ancient origin than ”ingroup”
If recombinations possible: each site has its own tree.