1. Inferring phylogenetic trees: Distance methods
Prof. William Stafford Noble
Department of Genome Sciences Department of Computer Science and Engineering
University of Washington

2. One-minute responses
Thank you for this lecture. It was very interesting.
I think I’m starting to program like a pro.
I wish to hear more on how we can understand better the evolutionary relationships among species, preferably among distinct human populations.
I think I enjoyed today’s lecture. More especially the class problems!
70% of the course has been understood by me.
Tell us more about interpretations.
Python part was easy to follow today.
Python part was very easy to follow. I did not have any problem for the first time.
The lecture was well understood.
The Python part was not so easy for me, but OK.
I appreciate the revision every day, it is very helpful.
Can we learn how to have better output from Python (form / appearance)?
Can we work at this stage on real human genetic data?

3. Outline Parsimony Distance methods Maximum likelihood
Computing distances
Finding the tree
Maximum likelihood

4. Revision What is the input to a phylogenetic inference problem?
A multiple alignment of DNA or protein sequences.
What is the output?
A binary tree showing the inferred evolutionary relationships.
For what types of phylogenetic inference problems is maximum parsimony the right approach?
Small numbers of input sequences.
Closely related sequences.
What are the two computational problems that must be solved in a maximum parsimony approach?
Enumerating all possible tree topologies.
Evaluating the parsimony score for a given topology.

5. Revision
Evaluate the parsimony score of the given tree with respect to the first column of the given alignment.
Skud
Sbay R S
Score = 1
Scer
Svin
Scer RTGH
Skud RTGV
Sbay RVGV
Smik SVGH
Spom STIL
Svin RLGH
Smik
Spom

6. Revision Repeat, but use the second column of the alignment. Scer RTGH
Skud
Sbay T V L
Score = 2 X
Scer
Smik
Scer RTGH
Skud RTGV
Sbay RVGV
Smik SVGH
Spom STIL
Svin RLGH
Svin
Spom

7. Selecting a method Choose set of related sequences Obtain multiple
alignment
Is there
strong
sequence
similarity?
Yes
Maximum
parsimony
methods No
Is there clearly
recognizable
sequence
similarity
Yes
Distance
methods No
Maximum
likelihood
methods

8. Distance methods Multiple sequence alignment Pairwise distance matrix
Phylo-
genetic
tree

9. The distance between species 1 and 2 is the sum of X and Y.
Calculating distance
ACTGAACGTAACGC X Y
Species 2: AATGAAAGAATCGC
Species 1: ACTGTAGGAATCGC
Species 1: ACTGTAGGAATCGC
Species 2: AATGAAAGAATCGC
The distance between species 1 and 2 is the sum of X and Y.

10. True evolutionary history
Ancestral
Species 1
Species 2 A
C T G A A C G T A A C G C A
C T G A  C  T A C  G G T  A A A  C  T C G C A
C  A T G A A C  A G T  A A A  T C G C  T  C
Single substitution
Multiple substitutions
Coincidental substitutions
Parallel substitutions
Convergent substitution
Back substitution

11. Jukes-Cantor model
Assume the same probability of change at all positions and all times.
dAB is the proportion of changed sites in the alignment.
KAB is the expected number of changes per position.
Derivation at

12. 3 observed changes in 20 sites
Jukes-Cantor model
Species 1
Species 2
3 observed changes in 20 sites A
C T G A  C  T A C  G G T  A A A  C  T C G C A
C  A T G A A C  A G T  A A A  T C G C  T  C

13. Computing JK distances
Proportion of changed sites
Species 1: ACGTGATCGGTGA
Species 2: ACTTGATGCCTAG
Species 3: A-TTACGTAATGG
Species 4: A-TTGATGGCGTA 1 2 3 4
Pairwise distances 1 2 3 4

14. Computing JK distances
Proportion of changed sites
Species 1: ACGTGATCGGTGA
Species 2: ACTTGATGCCTAG
Species 3: A-TTACGTAATGG
Species 4: A-TTGATGGCGTA 1 2 3 4
6/12
8/12
5/12
7/12
4/12
9/12
Pairwise distances 1 2 3 4 ?

15. Computing JK distances
Proportion of changes sites
Species 1: ACGTGATCGGTGA
Species 2: ACTTGATGCCTAG
Species 3: A-TTACGTAATGG
Species 4: A-TTGATGGCGTA 1 2 3 4
6/12
8/12
5/12
7/12
4/12
9/12
From this matrix, we calculate the tree.
Pairwise distances 1 2 3 4
0.82

16. Other models Jukes-Cantor Kimura F84, HKY Tamura-Nei
The simplest possible model
Kimura
2 parameters
Differentiates between transitions and transversions.
F84, HKY
5 parameters
Allows arbitrary base frequencies.
Tamura-Nei
6 parameters
Combination of F84 and HKY.
General time-reversible model
12 parameters
Only assumes Pr(x→y) = Pr(y→x)

17. Distance methods Fitch-Margoliash Neighbor-joining UPGMA Multiple
sequence
alignment
Pairwise
distance
matrix
Phylo-
genetic
tree

18. UPGMA Unweighted pair group method with arithmetic mean.
Also known as agglomerative hierarchical clustering.
Basic idea: iteratively connect the two most closely related sequences.

19. UPGMA Scer Spar Smik Sbay Skud Scas Sklu 31 40 32 30 323 253 26 37 30031 40 32 30
323
253 26 37
300
229 25 35
290
219
298
227
316
243 95

20. UPGMA Find the smallest off-diagonal element in the matrix. Scer Spar
Smik
Sbay
Skud
Scas
Sklu 31 40 32 29
323
253 26 37 30
300
229 25 35
290
219
298
227
316
243 95
Find the smallest off-diagonal element in the matrix.

21. UPGMA Compute the average between the two rows and columns. Scer Spar
Smik
Sbay
Skud
Scas
Sklu 31 40 32 29
323
253 26 37 30
300
229 25 35
290
219
298
227
316
243 95
Compute the average between the two rows and columns.

22. UPGMA Scer Spar Smik Sbay Skud Scas Sklu 31 36 29 323 253 31.5 30 30031 36 29
323
253
31.5 30
300
229
32.5
294
223
316
243 95

23. UPGMA Each merger creates a subtree. Smik Sbay Scer Spar Smik-Sbay
Skud
Scas
Sklu 31 36 29
323
253
31.5 30
300
229
32.5
294
223
316
243 95
Smik
Sbay
Each merger creates a subtree.

24. Perform the next merger
Scer
Spar
Smik-Sbay
Skud
Scas
Sklu 31 36 29
323
253
31.5 30
300
229
32.5
294
223
315
243
316 95
Smik
Sbay

25. Smik Sbay Scer Spar Smik-Sbay Skud Scas Sklu 31 36 29 323 253 31.5 3031 36 29
323
253
31.5 30
300
229
32.5
294
223
315
243
316 95
Smik
Sbay

26. Smik Sbay Skud Scer Spar Smik-Sbay Skud-Scer Scas Sklu 31.5 30.5 300
31.5
30.5
300
229
34.25
294
223
319.5
248 95
Smik
Sbay
Skud
Scer

27. What is next? Smik Sbay Skud Scer Spar Smik-Sbay Skud-Scer Scas Sklu
31.5
30.5
300
229
34.25
294
223
319.5
248 95
Smik
Sbay
Skud
Scer

28. Formatting with %
Insert % between a string and a tuple to get formatted output.
Use %s for strings, %d for integers, and %f or %g for floats.
Use %f for a fixed number of decimal places, %e for exponent, %g for either.
%g rounds to specified number of digits of precision
%g uses either fixed or exponential notation, depending on the value
Use leading numbers to specify width.
Replace with * to provide width as an input.
Full details at

29. Problem #1
Write a program that reads sequences from a given file and prints, in aligned columns, the sequence ID, length and frequency of each letter. You may assume that each sequence is no more than 100,000 characters.
Version 1: Use the alphabet ACGT and a fixed width for the sequence ID.
Version 2: Adjust the field width of the sequence ID based on the longest sequence ID.
Version 2: Use the alphabet of the given sequences. Print fields in alphabetical order.
Version 3: Add a header line to your output file.
./compute-seq-stats.py sample-dna.txt
Read 11 sequences from sample-dna.txt.
ce1cg A=0.17 C=0.12 G=0.31 T=0.40
ara A=0.34 C=0.23 G=0.18 T=0.24
bglr A=0.41 C=0.13 G=0.07 T=0.39
crp A=0.35 C=0.20 G=0.22 T=0.23
cya A=0.24 C=0.19 G=0.21 T=0.36
deop A=0.29 C=0.11 G=0.25 T=0.34
gale A=0.30 C=0.23 G=0.12 T=0.34
ilv A=0.22 C=0.26 G=0.17 T=0.35
lac A=0.22 C=0.22 G=0.22 T=0.34
male A=0.31 C=0.24 G=0.28 T=0.17
malk A=0.26 C=0.15 G=0.37 T=0.22

30. > ./compute-seq-stats-4.py ribosomal.txt
Read 13 sequences from ribosomal.txt.
Longest sequence ID = 32.
20 letters in alphabet.
Alphabet=['A', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'V', 'W', 'Y'].
Sequence Len A C D E F G H I K L M N P Q R S T V W Y
gi| |ref|XP_ |
gi| |emb|CCD
gi| |gb|EMH
gi| |pdb|3ZEY|U
gi| |ref|XP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_
gi| |ref|NP_