1. Algorithms for Inferring the Tree of Life
Tandy Warnow
Dept. of Computer Science
The University of Texas at Austin

2. Phylogeny Orangutan Gorilla Chimpanzee Human
From the Tree of the Life Website, University of Arizona
Orangutan
Gorilla
Chimpanzee
Human
A phylogeny is a tree representation for the evolutionary history relating the species we are interested in.
This is an example of a 13-species phylogeny.
At each leaf of the tree is a species – we also call it a taxon in phylogenetics (plural form is taxa). They are all distinct.
Each internal node corresponds to a speciation event in the past.
When reconstructing the phylogeny we compare the characteristics of the taxa, such as their appearance, physiological features, or the composition of the genetic material.

3. Evolution informs about everything in biology
Big genome sequencing projects just produce data – so what?
Evolutionary history relates all organisms and genes, and helps us understand and predict
interactions between genes (genetic networks)
drug design
predicting functions of genes
influenza vaccine development
origins and spread of disease
origins and migrations of humans

4. Reconstructing the “Tree” of Life
Handling large datasets: millions of species,
NP-hard problems,
Lots of computer science
research to do

5. Steps in a phylogenetic analysis
Gather data
Align sequences
Estimate phylogeny on the multiple alignment
Estimate the reliable aspects of the evolutionary history (using bootstrapping, consensus trees, or other methods)
Perform post-tree analyses.

6. DNA Sequence Evolution
-3 mil yrs
-2 mil yrs
-1 mil yrs
today
AAGACTT
TGGACTT
AAGGCCT
AGGGCAT
TAGCCCT
AGCACTT
AGCGCTT
AGCACAA
TAGACTT
TAGCCCA
AAGACTT
TGGACTT
AAGGCCT
AGGGCAT
TAGCCCT
AGCACTT
AAGGCCT
TGGACTT
TAGCCCA
TAGACTT
AGCGCTT
AGCACAA
AGGGCAT
TAGCCCT
AGCACTT

7. Phylogeny Problem U V W X Y X U Y V W AGGGCAT TAGCCCA TAGACTT TGCACAA
TGCGCTT X U Y V W

8. Phylogenetic reconstruction methods
Hill-climbing heuristics for hard optimization criteria (Maximum Parsimony and Maximum Likelihood)
Phylogenetic trees
Cost
Global optimum
Local optimum
Polynomial time distance-based methods: UPGMA, Neighbor Joining, FastME, Weighbor, etc.

9. Performance criteria Running time. Space.
Statistical performance issues (e.g., statistical consistency) with respect to a Markov model of evolution.
“Topological accuracy” with respect to the underlying true tree. Typically studied in simulation.
Accuracy with respect to a particular criterion (e.g. tree length or likelihood score), on real data.

10. How can we infer evolution?
While there are more than two sequences, DO
Find the “closest” pair of sequences and make them siblings
Replace the pair by a single sequence

11. That was called “UPGMA”
Advantages: UPGMA is polynomial time and works well under the “strong molecular clock” hypothesis.
Disadvantages: UPGMA does not work well in simulations, perhaps because the molecular clock hypothesis does not generally apply.
Other polynomial time methods, also distance-based, work better. One of the best of these is Neighbor Joining.

12. Quantifying Error FN: false negative (missing edge) FP: false positive
(incorrect edge)
50% error rate FP

13. Neighbor joining has poor performance on large diameter trees [Nakhleh et al. ISMB 2001]
Simulation study based upon fixed edge lengths, K2P model of evolution, sequence lengths fixed to 1000 nucleotides.
Error rates reflect proportion of incorrect edges in inferred trees.
0.8 NJ
0.6
Error Rate
0.4
0.2
400
800
1200
1600
No. Taxa

14. Other standard polynomial time methods don’t improve substantially on NJ (and have the same problem with large diameter datasets).
What about trying to “solve” maximum parsimony or maximum likelihood?

15. Maximum Parsimony Input: Set S of n aligned sequences of length k
Output:
A phylogenetic tree T leaf-labeled by sequences in S
additional sequences of length k labeling the internal nodes of T
such that is minimized, where H(i,j) denotes the Hamming distance between sequences at nodes i and j

16. Maximum parsimony (example)
Input: Four sequences
ACT
ACA
GTT
GTA
Question: which of the three trees has the best MP scores?

17. Maximum Parsimony
ACT
GTA
ACA
ACT
GTT
ACA
GTT
GTA
GTA
ACA
ACT
GTT

18. Maximum Parsimony ACT GTA ACA ACT GTT GTA ACA ACT 2 1 1 2 GTT 3 3 GTT
MP score = 7
MP score = 5
GTA
ACA
ACA
GTA 2 1 1
ACT
GTT
MP score = 4
Optimal MP tree

19. Maximum Parsimony: computational complexity
ACT
ACA
GTT
GTA 1 2
MP score = 4
Finding the optimal MP tree is NP-hard
Optimal labeling can be
computed in linear time O(nk)

20. Solving NP-hard problems exactly is … unlikely
#leaves
#trees 4 3 5 15 6
105 7
945 8
10395 9
135135 10 20
2.2 x 1020
100
4.5 x 10190
1000
2.7 x
Number of (unrooted) binary trees on n leaves is (2n-5)!!
If each tree on 1000 taxa could be analyzed in seconds, we would find the best tree in
2890 millennia

21. Approaches for “solving” MP/ML
Hill-climbing heuristics (which can get stuck in local optima)
Randomized algorithms for getting out of local optima
Approximation algorithms for MP (based upon Steiner Tree approximation algorithms).
Phylogenetic trees
Cost
Global optimum
Local optimum

22. Problems with current techniques for MP
Shown here is the performance of a heuristic maximum parsimony analysis on a real dataset of almost 14,000 sequences. (“Optimal” here means best score to date, using any method for any amount of time.) Acceptable error is below 0.01%.
Performance of TNT with time

23. Observations
The best MP heuristics cannot get acceptably good solutions within 24 hours on most of these large datasets.
Datasets of these sizes may need months (or years) of further analysis to reach reasonable solutions.
Apparent convergence can be misleading.

24. Empirical problems with existing methods
Heuristics for Maximum Parsimony (MP) and Maximum Likelihood (ML) cannot handle large datasets (take too long!) – we need new heuristics for MP/ML that can analyze large datasets
Polynomial time methods have poor topological accuracy on large diameter datasets – we need better polynomial time methods

25. My research
Focused on the design and analysis of algorithms for large-scale phylogeny reconstruction and multiple sequence alignment.
Objective: the design of new algorithms with better performance than existing algorithms, as evidenced by mathematical theory, experiment, or empirical studies.
Collaborations with biologists for modelling and data analysis.
Current group: four PhD students, one postdoc, and two undergrads.

26. What happens after the analysis?
The result of a phylogenetic analysis is often thousands (or tens of thousands) of equally good trees.
How should we analyze the set of trees?
How can we store the set of trees?
Current approaches use consensus methods, as well as other techniques, to try to infer what is likely to be the characteristics of the “true tree”. Current techniques use too much space, take too much time, and are not sufficiently informative.

27. General comments
There is interesting computer science research to be done in computational phylogenetics, with a tremendous potential for impact.
Algorithm development must be tested on both real and simulated data.
The interplay between data, stochastic models of evolution, optimization problems, and algorithms, is important and instructive.