1. Phylogenetic reconstruction

2. What is phylogenetic analysis and why should we perform it?
Phylogenetic analysis has two major components:
1. Phylogeny inference or “tree building”
2. Character and rate analysis
1. Phylogeny inference or “tree building” —
the inference of the branching orders, and ultimately the evolutionary relationships, between “taxa” (entities such as genes, populations, species, etc.)
2. Character and rate analysis —
using phylogenies as analytical frameworks
for rigorous understanding of the evolution of
various traits or conditions of interest.

3. Common Phylogenetic Tree Terminology
Edges A
TAXA (genes,
populations,
species, etc.)
used to infer
the phylogeny B C D E
Vertex or Nodes

4. Common Phylogenetic Tree Terminology
Terminal Nodes (Leaves)
Branches, Lineages
or Clades A
Represent the
TAXA (genes,
populations,
species, etc.)
used to infer
the phylogeny B C D
Ancestral Node
or ROOT of
the Tree E
Internal Nodes or
Divergence Points (represent hypothetical ancestors of the taxa)

5. Phylogenetic trees diagram the evolutionary
relationships between the taxa
Taxon A
Taxon B
Taxon C
Taxon E
Taxon D
No meaning to the
spacing or to order
- no scale (for ‘cladograms’),
- proportional to genetic distance or amount of change (for ‘phylograms’ or ‘additive trees’),
- proportional to time (for ‘ultrametric trees’ or true evolutionary trees).
These say that B and C are more closely related to each other than either is to A,
and that A, B, and C form a clade that is a sister group to the clade composed of
D and E. If the tree has a time scale, then D and E are the most closely related.
((A,(B,C)),(D,E)) = The above phylogeny as nested parentheses

6. A few examples of what can be inferred from phylogenetic trees built from DNA or protein sequence data:
Which species are the closest living relatives of modern humans?
Did the infamous Florida Dentist infect his patients with HIV?
What were the origins of specific transposable elements?
Plus countless others…..

7. Using Phylogeny to Understand Gene Duplication and Loss
A gene tree.
The gene tree superimposed on a species tree, allowing identification of the duplication and loss events.

8. Speciation
Ancestor a
Speciation a a
Species I
Species II
Orthologes

9. Gene duplication
Ancestor
Duplication a b
Mutations a b
Paraloges

10. Gene duplication & speciation
Ancestor
Duplication a b
Mutations
Paraloges a b
Speciation a b a b
Species I
Orthologes
Species II

11. Gene Phylogeny Species I a Orthologes a Species II a Species I b
Paraloges b
Species II b

12. Which species are the closest living relatives of modern humans?
Gorillas
Chimpanzees
Chimpanzees
Bonobos
Bonobos
Gorillas
Orangutans
Orangutans
Humans
Mitochondrial DNA and most nuclear DNA-encoded genes, show that bonobos and chimpanzees are related more closely to humans than either are to gorillas.
The pre-molecular view was that the great apes (chimpanzees, gorillas and orangutans) formed a clade separate from humans, and that humans diverged from the apes at least MYA. 14
15-30
MYA
MYA
Mitochondrial DNA and most nuclear DNA-encoded genes,
The pre-molecular view

13. Did the Florida Dentist infect his patients with HIV?
Phylogenetic tree
of HIV sequences
from the DENTIST,
his Patients, & Local
HIV-infected People:
Patient C
Patient A
Patient G
Yes:
The HIV sequences from
these patients fall within
the clade of HIV sequences found in the dentist.
Patient B
Patient E
Patient A
DENTIST
Local control 2
Local control 3 No
Patient F
Local control 9
Local control 35
Local control 3 No
Patient D
From Ou et al. (1992) and Page & Holmes (1998)

14. A few examples of what can be learned from character analysis using phylogenies as analytical frameworks:
When did specific episodes of positive Darwinian selection occur during evolutionary history?
What was the most likely geographical location of the common ancestor of the African apes and humans?
Plus countless others…..

15. Phylogenetic Resources
NCBI Taxonomy Browser
“Tree of Life”
TreeBase

16. Tree of Life

17. Completely unresolved bifurcating phylogeny
The goal of phylogeny inference is to resolve the
branching orders of lineages in evolutionary trees:
Completely unresolved
or "star" phylogeny
Partially resolved
phylogeny
Fully resolved,
bifurcating phylogeny A B C E D
Polytomy or multifurcation
A bifurcation

18. There are three possible unrooted trees for four taxa (A, B, C, D)
Phylogenetic tree building (or inference) methods are aimed at discovering which of the possible unrooted trees is "correct".
We would like this to be the “true” biological tree — that is, one that accurately represents the evolutionary history of the taxa.
However, we must settle for discovering the computationally correct or optimal tree for the phylogenetic method of choice
Which one is correct?

19. The number of unrooted trees increases in a greater than exponential manner with number of taxa
(2N - 5)!! = # unrooted trees for N taxa

20. Inferring evolutionary relationships between the taxa requires rooting the tree:C
Root D
Unrooted tree A B C D
Root
Note that in this rooted tree, taxon A is no more closely related to taxon B than it is to C or D.
Rooted tree B
To root a tree mentally, imagine that the tree is made of string. Grab the string at the root and tug on it until the ends of the string (the taxa) fall opposite the root:

21. Now, try it again with the root at another position:B C
Root
Unrooted tree D A A B B C D
Rooted tree
Note that in this rooted tree, taxon A is most closely related to taxon B, and together they are equally distantly related to taxa C and D.
Root

22. An unrooted, four-taxon tree theoretically can be rooted in five different places to produce five different rooted trees
Rooted tree 1b A B C D 2 A
Rooted tree 1d C D A B 4 C
Rooted tree 1a B A C D 1
The unrooted tree 1:
Rooted tree 1e D C A B 5
Rooted tree 1c A B C D 3 B D
These trees show five different evolutionary relationships among the taxa!

23. All of these rearrangements show the same evolutionary relationships between the taxaC D B A C D
Rooted tree 1a B A C D B C A D D C A B A B D C A B C D

24. Think for yourself How many unrooted trees are there with 4 taxa?
How many rooted trees are there with 4 taxa?

25. Each unrooted tree theoretically can be rooted anywhere along any of its branchesx = C A B D E F
(2N - 3)!! = # unrooted trees for N taxa

26. Finding the best tree Search strategies Number of (rooted) trees
Exact
Exhaustive
Branch and bound
Algorithmic
Greedy algorithms (including Neighbor-joining)
Heuristic
Systematic; branch-swapping (NNI, SPR, TBR)
Stochastic
Markov Chain Monte Carlo (MCMC)
Genetic algorithms
Number of (rooted) trees
3 taxa -> 3 trees
4 taxa -> 15 trees
10 taxa -> trees
25 taxa -> 1,19·1030 trees
52 taxa -> 2,75·1080 trees
Finding the optimal tree is an NP-complete problem

27. Rooting Trees Molecular Clock Extrinsic Evidence (Outgroup)B C D 10 2 3 5
d (A,D) = = 18
Midpoint = 18 / 2 = 9
Molecular Clock
Root=midpoint, longest span
Extrinsic Evidence (Outgroup)
select fungus as root for plants
outgroup

28. Steps in Analysis Input: Alignment Choose substitution model
Build Trees
Algorithm based vs Criterion based
Distance based vs Character-based

29. Practicalities Quality of input data critical
Examine data from all possible angles
distance, parsimony, likelihood
Assess the variation in your data in some way

30. Types of data used in phylogenetic inference:
Character-based methods: Use the aligned characters, such as DNA or protein sequences, directly during tree inference.
Taxa Characters
Species A ATGGCTATTCTTATAGTACG
Species B ATCGCTAGTCTTATATTACA
Species C TTCACTAGACCTGTGGTCCA
Species D TTGACCAGACCTGTGGTCCG
Species E TTGACCAGTTCTCTAGTTCG
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
Example 1:
Uncorrected
“p” distance
(=observed percent
sequence difference)
Example 2: Kimura 2-parameter distance
(estimate of the true number of substitutions between taxa)

31. Types of computational methods:
Clustering algorithms: Use pairwise distances. Are purely algorithmic methods.
Optimality approaches: Use either character or distance data.
minimum branch lengths,
fewest number of events,
highest likelihood
Clustering algorithms: Use pairwise distances. Are purely algorithmic methods, in which the algorithm itself defines the the tree selection criterion. Tend to be very fast programs that produce singular trees rooted by distance. No objective function to compare to other trees, even if numerous other trees could explain the data equally well. Warning: Finding a singular tree is not necessarily the same as finding the "true” evolutionary tree.
Optimality approaches: Use either character or distance data. First define an optimality criterion (minimum branch lengths, fewest number of events, highest likelihood), and then use a specific algorithm for finding trees with the best value for the objective function. Can identify many equally optimal trees, if such exist.
Warning: Finding an optimal tree is not necessarily the same as finding the "true” tree.

32. Molecular phylogenetic tree building methods:
COMPUTATIONAL METHOD
Clustering algorithm
Optimality criterion
DATA TYPE
Characters
Distances
PARSIMONY
MAXIMUM LIKELIHOOD
UPGMA
NEIGHBOR-JOINING
MINIMUM EVOLUTION
LEAST SQUARES
Are mathematical and/or statistical methods for inferring the divergence order of taxa, as well as the lengths of the branches that connect them. There are many phylogenetic methods available today, each having strengths and weaknesses. Most can be classified as follows:

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

34. Distance Methods Measure distance (dissimilarity) Methods
UPGMA (Unweighted pair group method with Arithmetic Mean)
NJ (Neighbor joining)
FM (Fitch-Margoliash)
ME (Minimal Evolution)

35. Inferring Trees and Ancestors
CCCAGG
CCCAAG->
CCCAAG
CCCAAA->
CCCAAA
CCCAAC

36. UPGMA: Clustering

37. 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 is defined as:
where |Ci| and |Cj| denote the number of sequences in cluster i and j, respectively.

38. 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)

39. 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.

40. 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

41. 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

42. Step 3: merge D and G A B C E F DG - 63 94 79 67 23 83 20 58 89 62 10945 98
104
DNA/RNA overview

43. 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

44. Step 5 AF B C E DG - 61 92 79 65 23 62
107 94 45 98
DNA/RNA overview

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

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

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

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

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

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

51. Classification of phylogenetic
inference methods
COMPUTATIONAL METHOD
Optimality criterion
Clustering algorithm
PARSIMONY
MAXIMUM LIKELIHOOD
Characters
DATA TYPE
MINIMUM EVOLUTION
LEAST SQUARES
UPGMA
NEIGHBOR-JOINING
Distances

52. Clustering methods (UPGMA & N-J)
Optimality criterion: NONE. The algorithm itself builds
‘the’ 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.

53. Minimum evolution (ME) methods
Optimality criterion: The tree(s) with the shortest sum of
branch lengths (or 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.

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

55. 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.
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”:

56. 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

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

58. 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

59. 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: ?

60. 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.

61. 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

62. 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

63. 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

64. Likelihoods of a more interesting tree
Data for one site is shown on the tree
Edge lengths are defined as =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

65. Confidence assesment
Bootstrap

66. 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.

67. 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
- Can be computationally slow
Maximum likelihood
+ Model based
- Model based
- Computationally veeeeery slow

68. Computation
For large data sets (many taxa) exact solutions for any method employing an optimality criterion (parsimony, likelihood, minimum evolution) are not possible

69. 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

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

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

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

73. What we have studied…
Canis
Gadus
Mus

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

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

76. To conclude– Trash in, trash out : Alignment crucial
Try several methods, for consistency
Beware of paraloges
If recombinations possible: each site its tree.