1. Inferring phylogenetic trees: Distance and maximum likelihood methods
GENOME 373: Genomic Informatics
Prof. William Stafford Noble

2. Outline Distance methods Maximum likelihood Fitch-Margoliash
Neighbor joining
UPGMA
Maximum likelihood

3. One-minute responses Is the parsimony model biologically accurate?
No. Parsimony ignores back-mutation, parallel mutation, etc.
The following tree can have a score of 2 or 3, correct?
Correct. However, the idea of parsimony is to select the tree with the smallest number of mutations along the tree.
Is it biologically acceptable to make the assumptions of the JC model?
No. The assumptions are made for statistical reasons – essentially, we often don’t know the proper values for the more parameter-rich models.
What other considerations can be taken to get a better tree?
The most important ones are site-by-site variation in mutation rate, and dependencies between adjacent sites.
Is there any way to check whether the tree obtained is significant?
You can check whether individual branches are significant using something called “bootstrap analysis.”
Still unclear how to use these trees in a biological way.
Primarily, these trees are used to understand evolutionary history.
Will we be using any of the phylogeny software in this class?
No.

4. One-minute responses
What’s a real event that is your “oracle” that tells you the true evolutionary history of substitutions for Jukes-Cantor?
There is no oracle, and luckily, you don’t need one in order for Jukes-Cantor to work.
It was difficult to understand how you were computing parsimony scores at first.

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

6. Star topology Sum of all branches is S*=a+b+c+d+e.
Summing all distances in the matrix counts each edge four times (e.g., dAB, dAC, dAD and dAE).
Hence, the sum of all distances in the matrix is 4S*.

7. Adding one branch Sum of branches is S = a + b + c + d + e + f
= (dAC + dAD + dAE + dBC + dBD + dBE)/6 + dAB/2 + (dCD + dCE + dDE)/3

8. Neighbor joining
Add one branch to the star topology and compute the difference between S* and S.
Repeat for each pair of leaves in the tree.
Choose the pair that yields the largest difference (the closest neighbors).
Join that pair.
Repeat until all pairs are joined.

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

10. UPGMA Scer Spar Smik Sbay Skud Scas Sklu 30 40 32 323 253 31 26 17 20130 40 32
323
253 31 26 17
201
229 25 35
290
219
298
227
316
243
322
300
315 95
226

11. UPGMA Find the smallest off-diagonal element in the matrix. Scer Spar
Smik
Sbay
Skud
Scas
Sklu 30 40 32
323
253 31 26 17
201
229 25 35
290
219 37
298
227
316
243
322
300
315 95
226
Find the smallest off-diagonal element in the matrix.

12. UPGMA Compute the average between the two rows and columns. Scer Spar
Smik
Sbay
Skud
Scas
Sklu 30 40 32
323
253 31 26 17
201
229 25 35
290
219 37
298
227
316
243
322
300
315 95
226
Compute the average between the two rows and columns.

13. UPGMA Scer Spar Smik Sbay Skud Scas Sklu 30 36 323 253 31 21.5 201 22930 36
323
253 31
21.5
201
229
31.5
32.5
294
222.5
316
243
322
300
315 95

14. UPGMA Each merger creates a subtree. Smik Sbay Scer Spar Smik-Sbay
Skud
Scas
Sklu 30 36
323
253 31
21.5
201
229
31.5
32.5
294
222.5
316
243
322
300
315 95
Smik
Sbay
Each merger creates a subtree.

15. Maximum likelihood for each possible tree
for each column of the alignment
compute the likelihood of the column, given the tree
return the tree with the highest likelihood
Similar to parsimony, but capable of using a model of evolution.
Computationally expensive.
DNAML is the Phylip program for maximum likelihood. FastDNAML is a fast clone (

16. Computing the likelihood
ACGCGTTGGG
ACGCAATGAA
ACACAGGGAA +
Pr(column|tree,model) T T A G
What is the probability of observing this column, given this tree and an assumed model of evolution?

17. Computing the likelihoodA C G A A A A A A T T T T A G T A G T A G
Solution: Enumerate all possible assignments to the internal nodes. Compute the probability of each tree, and sum.

18. Computing the likelihood
ACGCGTTGGG
ACGCAATGAA
ACACAGGGAA + A
Pr(column|tree,model) T A T T A G
What is the probability of observing this column, given this assigned tree and an assumed model of evolution?

19. Computing the likelihood
The probability of observing a substitution from A to T on a branch of length m is given by the evolutionary model.
πA, πC, πG, πT
The probability of the ancestral observation being A is just πA. A m T A T T A G

20. Computing the likelihood
πA, πC, πG, πT L0 A L1 L2 T A L5 L3 L4 L6 T T A G
The desired probability is the product of the probabilities of the branches.
L(tree) = L0  L1  L2  L3  L4  L5  L6

21. Computing the likelihoodA C G A A A A A A T T T T A G T A G T A G
tree1
tree2
tree3
The probability of the tree is the sum of the probabilities of the individual trees.
L(tree) = L(tree1) + L(tree2) + L(tree3) + …

22. Maximum likelihood revisited
for each possible tree
for each column of the alignment
for each assignment of internal nodes
for each branch
compute the probability of that branch
assigned tree probability ← multiply branch probabilities
column probability ← sum assigned tree probabilities
tree probability ← multiply column probabilities
return the tree with the highest probability

23. Maximum likelihood revisited
for each possible tree
for each column of the alignment
for each assignment of internal nodes
for each branch
compute the probability of that branch
assigned tree probability ← multiply branch probabilities
column probability ← sum assigned tree probabilities
tree probability ← multiply column probabilities
return the tree with the highest probability
Multiply probabilities of independent events.
Add probabilities of mutually exclusive events.

24. Overview Parsimony Distance methods Maximum likelihood
Computing distances
Finding the tree
Fitch-Margoliash
Neighbor-joining
UPGMA
Maximum likelihood