1. Phylogenetic Analysis

2. Review of Linux ls cd
mkdir
less cp mv
cat
pwd
>

3. Perl Variables Statements $DNA="A"; @DATA=('A', 'B');
%TABLE=(A=>'A', N=>'[AC]',);
Statements
print
length
open
close
substr
push
pop
shift
unshift

4. #!/usr/bin/perl –w
$word = 'MNIDDKL';
if($word eq 'QSTVSGE') {
print "QSTVSGE\n"; }
elsif($word eq 'MRQQDMISHDEL') {
print "MRQQDMISHDEL\n";
elsif ( $word eq 'MNIDDKL' ) {
print "MNIDDKL-the magic word!\n";
else {
print "Is \”$word\“ a peptide?\n";
exit;

5. $x = 10;
$y = -20;
if ($x <= 10) { print "1st true\n";}
if ($x > 10) {print "2nd true\n";}
if ($x <= 10 || $y > -21) {print "3rd true\n";}
if ($x > 5 && $y < 0) {print "4th true\n";}
if (($x > 5 && $y < 0) || $y > 5) {print "5th true\n";}

6. $position = 0;
while ( $position < length $DNA) {
$base = substr($DNA, $position, 1);
if ( $base eq 'C' or $base eq 'G') {
++$count_of_CG; }
$position++;
for ( $position = 0 ; $position < length $DNA ; ++$position ) {

7. The Most Common Sequence Formats

8. Converting Formats
Don’t re-compute your MSA if it is not in the right format
Convert your file using one of the online conversion tools
The 3 most popular reformatting utilities:
Fmtseq The most complete
RESDSEQ Very popular and robust
SeqCheck Can clean FASTA sequences

10. Editing your MSA If your MSA looks bad . . .
Don’t torture the online server
Edit the MSA yourself locally
Never, ever, ever (ever) use a standard word processor
Always use a dedicated MSA editor
The most popular online tool is Jalview
You can get it at

12. MSA => LOGO Graph A LOGO graph summarizes an MSA
Tall letters indicate highly conserved positions
Short letters indicate poorly conserved positions
LOGO graphs are ideal for identifying conserved patterns
weblogo.berkeley.edu/

13. Molecular Evolution and Phylogenetic Reconstruction

14. Evolutionary Tree of Bears and Raccoons

15. Human Evolutionary Tree (cont’d)

16. Human Migration Out of Africa
1. Yorubans
2. Western Pygmies
3. Eastern Pygmies
4. Hadza
5. !Kung 1 2 3 4 5

17. Reading Your Tree There’s a lot of vocabulary in a tree
Nodes correspond to common ancestors
The root is the oldest ancestor
Often artificial
Only meaningful with a good outgroup
Trees can be un-rooted
Branch lengths are only meaningful when the tree is scaled
Cladograms are often scaled
Phenograms are usualy unscaled

18. Rooted and Unrooted Trees
In the unrooted tree the position of the root (“oldest ancestor”) is unknown. Otherwise, they are like rooted trees

19. Type of Trees (Cladogram)

20. Type of Trees (Phylogram)

21. Orthology and Paralogy
直系（垂直）同源和旁系（平行）同源
Orthologous genes
Separated by speciation
Often have the same function
Paralogous genes
Separated by duplications
Can have different functions
In the graph:
A is paralogous with B
A1 is orthologous with A2

22. Which Sequences ? Orthologous sequences Paralogous sequences
Produce a species tree
Show how the considered species have diverged
Paralogous sequences
Produce a gene tree
Show the evolution of a protein family

23. Building the Right MSA
Your MSA should have as few gaps as possible. Most time should remove columns with gaps.
Some variability but not too much!
Some conservation but not too much!

24. Building the Right Tree
There are three types of tree-reconstruction methods
Distance-based methods
Statistical methods
Parsimony methods
Statistical methods are the most accurate
Maximum likelihood of success
Bayesian methods
Statistical methods take more time
Limited to small datasets

25. Distance in Trees: an Exampej
d1,4 = = 68

26. Compute a Distance Matrix
Evolutionary Distance - number of substitutions
per 100 amino acids (for proteins) or nucleotides (for DNA)
A C T G T A G G A A T C G C
A A T G A A A G A A T C G C
3 observed changes
A C T G T A G G A A T C G C
A C T G C A G G A A T A G C
A A T G A A A G A A T C G C
6 actual changes

27. Edit Distance vs Tree Distancej
d1,4 = = 68
D1,4 may be smaller than 68, as some changes may not be observed

28. Fitting Distance Matrix
Given n species, we can compute the n x n distance matrix Dij
Evolution of these genes is described by a tree that we don’t know.
We need an algorithm to construct a tree that best fits the distance matrix Dij

29. Reconstructing a 3 Leaved Tree
Tree reconstruction for any 3x3 matrix is straightforward
We have 3 leaves i, j, k and a center vertex c
Observe:
dic + djc = Dij
dic + dkc = Dik
djc + dkc = Djk

30. Reconstructing a 3 Leaved Tree (cont’d)
dic + djc = Dij
+ dic + dkc = Dik
2dic + djc + dkc = Dij + Dik
2dic + Djk = Dij + Dik
dic = (Dij + Dik – Djk)/2
Similarly,
djc = (Dij + Djk – Dik)/2
dkc = (Dki + Dkj – Dij)/2

31. Additive Distance Matrices
Matrix D is ADDITIVE if there exists a tree T with dij(T) = Dij
NON-ADDITIVE otherwise

32. The Four Point Condition (cont’d)
Compute: 1. Dij + Dkl, 2. Dik + Djl, 3. Dil + Djk 2 3 1
2 and 3 represent the same number: the length of all edges + the middle edge (it is counted twice)
1 represents a smaller number: the length of all edges – the middle edge

33. The Four Point Condition: Theorem
The four point condition for the quartet i,j,k,l is satisfied if two of these sums are the same, with the third sum smaller than these first two
Theorem : An n x n matrix D is additive if and only if the four point condition holds for every quartet 1 ≤ i,j,k,l ≤ n

34. Distance Based Phylogeny Problem
Goal: Reconstruct an evolutionary tree from a distance matrix
Input: n x n distance matrix Dij
Output: weighted tree T with n leaves fitting D
If D is additive, this problem has a solution and there is a simple algorithm to solve it

35. Using Neighboring Leaves to Construct the Tree
Find neighboring leaves i and j with parent k
Remove the rows and columns of i and j
Add a new row and column corresponding to k, where the distance from k to any other leaf m can be computed as:
Dkm = (Dim + Djm – Dij)/2
Compress i and j into k, iterate algorithm for rest of tree

36. Finding Neighboring Leaves
To find neighboring leaves we simply select a pair of closest leaves.

37. Finding Neighboring Leaves
To find neighboring leaves we simply select a pair of closest leaves.
WRONG

38. Finding Neighboring Leaves
Closest leaves aren’t necessarily neighbors
i and j are neighbors, but (dij = 13) > (djk = 12)
Finding a pair of neighboring leaves is
a nontrivial problem!

39. Neighbor Joining Algorithm
In 1987 Naruya Saitou and Masatoshi Nei developed a neighbor joining algorithm for phylogenetic tree reconstruction
Finds a pair of leaves that are close to each other but far from other leaves: implicitly finds a pair of neighboring leaves
Advantages: works well for additive and other non-additive matrices, it does not have the flawed molecular clock assumption

40. Overview
Based on the current distance matrix calculate the matrix Q (defined later).
Find the pair of taxa for which has its lowest value Qij. Add a new node to the tree, joining these taxa to the rest of the tree.
Calculate the distance from each of the taxa in the pair to this new node.
Calculate the distance from each of the taxa outside of this pair to the new node.
Start the algorithm again, replacing the pair of joined neighbors with the new node and using the distances calculated in the previous step.

41. Basic Algorithm

43. D Q

44. D Q

45. D Q

46. Another Example A B C D E F 5 4 7 6 8 10 9 11

47. Q(ij)=(N-2)d(ij) - [r(i) + r(j)]A B C D E F 5 4 7 6 8 10 9 11
Q(ij)=(N-2)d(ij) - [r(i) + r(j)] A B C D E F

48. Q A B C D E F
-52
-46
-40
-42
-44

49. Tree (So far) D(AU) =d(AB) / 2 + [r(A)-r(B)] / 2(N-2) = 1
D(BU) =d(AB) -D(AU) = 4
Tree (So far)

50. d(CU) = [d(AC) + d(BC) - d(AB)] / 2 = 3
d(DU) = [d(AD) + d(BD) - d(AB) ]/ 2 = 6
d(EU) = [d(AE) + d(BE) - d(AB) ]/ 2 = 5
d(FU) = [d(AF) + d(BF) - d(AB) ]/ 2 = 7
New Matrix U C D E F 3 6 5 7 8 9

51. Q(ij)=(N-2)d(ij) - [r(i) + r(j)]U C D E F 3 6 5 7 8 9
Q(ij)=(N-2)d(ij) - [r(i) + r(j)]
r(U)= =21
r(C)=24
r(D)=27
r(E)=24
r(F)=32 U C D E F

52. U C D E F -36 -30 -32 D(UW) =d(UC) / 2 + [r(U)-r(C)] / 2(N-2) = 1
D(CW) =d(UC) -D(UW) = 2 U C D E F
-36
-30
-32

53. Programs
BIONJ
WEIGHBOR
FastME

54. UPGMA: Unweighted Pair Group Method with Arithmetic Mean
UPGMA is a clustering algorithm that:
computes the distance between clusters using average pairwise distance
assigns a height to every vertex in the tree, effectively assuming the presence of a molecular clock and dating every vertex

55. UPGMA’s Weakness
The algorithm produces an ultrametric tree : the distance from the root to any leaf is the same
UPGMA assumes a constant molecular clock: all species represented by the leaves in the tree are assumed to accumulate mutations (and thus evolve) at the same rate. This is a major pitfalls of UPGMA.

56. UPGMA’s Weakness: Example2 3 4 1
Correct tree
UPGMA

57. Clustering in UPGMA Given two disjoint clusters Ci, Cj of sequences,1
dij = ––––––––– {p Ci, q Cj}dpq
|Ci|  |Cj|
Note that if Ck = Ci  Cj, then distance to another cluster Cl is:
dil |Ci| + djl |Cj|
dkl = ––––––––––––––
|Ci| + |Cj|

58. UPGMA Algorithm Initialization: Assign each xi to its own cluster Ci
Define one leaf per sequence, each at height 0
Iteration:
Find two clusters Ci and Cj such that dij is min
Let Ck = Ci  Cj
Add a vertex connecting Ci, Cj and place it at height dij /2
Delete Ci and Cj
Termination:
When a single cluster remains

59. UPGMA Algorithm (cont’d)1 4 3 2 5

60. UPGMA Building Phylogenetic Trees by UPGMA: Example:
The distance matrix

61. UPGMA

62. UPGMA

63. UPGMA

64. UPGMA

65. UPGMA

66. UPGMA

67. UPGMA

68. UPGMA

69. UPGMA

70. UPGMA

71. UPGMA

72. UPGMA

73. UPGMA
What are the distance between: W and X (Calculate).

74. UPGMA

75. UPGMA

76. UPGMA
What are the distance between: Y and C (Calculate).

77. UPGMA

78. UPGMA