CIPRES: Enabling Tree of Life Projects

1. CIPRES: Enabling Tree of Life Projects Tandy Warnow The University of Texas at Austin

2. Phylogeny From the Tree of the Life Website,University of Arizona Orangutan Human Gorilla Chimpanzee

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 and NP-hard optimization problems NSF funds many projects towards this goal, under the Assembling the Tree of Life program

5. Cyber Infrastructure for Phylogenetic Research Purpose: to create a national infrastructure of hardware, algorithms, database technology, etc., necessary to infer the Tree of Life. Group: approx. 36 biologists, computer scientists, and mathematicians from 18 institutions. Funding: $11.6 M (large ITR grant from NSF).

6. EPFL (Switzerland) Bernard Moret Georgia Tech David Bader UCSD/SDSC Fran Berman Alex Borchers John Huelsenbeck Terri Liebowitz Mark Miller University of Connecticut Paul O Lewis University of Pennsylvania Junhyong Kim Susan Davidson Sampath Kannan Val Tannen Texas A&M Tiffani Williams UT Austin Tandy Warnow David M. Hillis Warren Hunt Robert Jansen Randy Linder Lauren Meyers Daniel Miranker University of Arizona David R. Maddison University of British Columbia Wayne Maddison North Carolina State University Spencer Muse American Museum of Natural History Ward C. Wheeler NJIT Usman Roshan UC Berkeley Satish Rao Steve Evans Richard M Karp Brent Mishler Elchanan Mossel Eugene W. Myers Christos M. Papadimitriou Stuart J. Russell Rice Luay Nakhleh SUNY Buffalo William Piel Florida State University David L. Swofford Mark Holder Yale Michael Donoghue Paul Turner CIPRES Members

7. CIPRES algorithms research (sample) • Improved heuristics for NP-hard optimization problems (MP, ML, tree alignment) • Obtaining better mathematical theory for phylogeny reconstruction methods under Markov models of evolution • Supertree methods • Constructing networks rather than trees (detecting and reconstructing reticulate evolution) • Whole genome phylogeny

8. This talk • Phylogeny reconstruction through a divide-and-conquer strategy using chordal graph theory • “Absolute fast converging” methods • Improved heuristics for NP-hard optimization problems

9. -3 mil yrs AAGACTT AAGACTT -2 mil yrs AAGGCCT AAGGCCT AAGGCCT AAGGCCT TGGACTT TGGACTT TGGACTT TGGACTT -1 mil yrs AGGGCAT AGGGCAT AGGGCAT TAGCCCT TAGCCCT TAGCCCT AGCACTT AGCACTT AGCACTT today AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT DNA Sequence Evolution

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

11. Local optimum Cost Global optimum Phylogenetic trees Phylogenetic reconstruction methods • Heuristics for NP-hard optimization criteria (Maximum Parsimony and Maximum Likelihood) • Polynomial time distance-based methods: Neighbor Joining, FastME, etc. 3. Bayesian MCMC methods.

12. Evaluating phylogeny reconstruction methods • In simulation: how “topologically” accurate are trees reconstructed by the method? • On real data: how good are the “scores” (typically either MP or ML scores) obtained by the method, as a function of time?

13. -3 mil yrs AAGACTT AAGACTT -2 mil yrs AAGGCCT AAGGCCT AAGGCCT AAGGCCT TGGACTT TGGACTT TGGACTT TGGACTT -1 mil yrs AGGGCAT AGGGCAT AGGGCAT TAGCCCT TAGCCCT TAGCCCT AGCACTT AGCACTT AGCACTT today AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT DNA Sequence Evolution

14. Markov models of DNA sequence evolution General Time Reversible (GTR) Markov Model: • The state at the root is random • The model tree is a pair consisting of a rooted binary tree T with edge lengths, where w(e) indicates the number of times a site changes on edge e. • There is a 4x4 symmetric substitution matrix for the sites, so that if a site changes on an edge, it uses the matrix to determine the probability of each change. • The evolutionary process is Markovian • All sites evolve identically and independently

15. Distance-based Phylogenetic Methods

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

17. Neighbor joining has poor accuracy on large diameter model 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 0 0 400 800 1200 1600 No. Taxa

18. Problems with current techniques for MP Shown here is the performance of the TNT software for maximum parsimony on a real dataset of almost 14,000 sequences. The required level of accuracy with respect to MP score is no more than 0.01% error (otherwise high topological error results). (“Optimal” here means best score to date, using any method for any amount of time.) Performance of TNT with time

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

20. “Boosting” phylogeny reconstruction methods • DCMs “boost” the performance of phylogeny reconstruction methods. DCM Base method M DCM-M

21. Graph-theoretic divide-and-conquer (DCM’s) • Define a triangulated (i.e. chordal) graph so that its vertices correspond to the input taxa • Compute a decomposition of the graph into overlapping subgraphs, thus defining a decomposition of the taxa into overlapping subsets. • Apply the “base method” to each subset of taxa, to construct a subtree • Merge the subtrees into a single tree on the full set of taxa.

22. Some properties of chordal graphs • Every chordal graph has at most n maximal cliques, and these can be found in polynomial time: Maxclique decomposition. • Every chordal graph has a vertex separator which is a maximal clique: Separator-component decomposition. • Every chordal graph has a perfect elimination scheme: enables us to merge correct subtrees and get a correct supertree back, if subtrees are big enough.

23. A separator-component DCM (cartoon)

24. Strict Consensus Merger (SCM)

25. DCMs (Disk-Covering Methods) • DCMs for polynomial time methods improve topological accuracy (empirical observation), and have provable theoretical guarantees under Markov models of evolution • DCMs for hard optimization problems reduce running time needed to achieve good levels of accuracy (empirically observation)

26. Statistical consistency, convergence rates, and absolute fast convergence

27. Neighbor Joining’s sequence length requirement is exponential! • Atteson: Let T be a General Markov model tree defining additive matrix D. Then Neighbor Joining will reconstruct the true tree with high probability from sequences that are of length at least O(lg n emax Dij).

28. DCM1-Boosting [Warnow et al. SODA 2001] • DCM1+SQS is a two-phase procedure which reduces the sequence length requirement of methods. Exponentially converging method Absolute fast converging method DCM1 SQS

29. Improving upon NJ • Construct trees on a number of smaller diameter subproblems, and merge the subtrees into a tree on the full dataset. • Our approach: • Phase I: produce O(n2) trees (one for each diameter) • Phase II: pick the “best” tree from the set.

30. DCM1 Decompositions Input: Set S of sequences, distance matrix d, threshold value 1. Compute threshold graph 2. Perform minimum weight triangulation (note: if d is an additive matrix, then the threshold graph is provably chordal). DCM1 decomposition : Compute maximal cliques

31. DCM1-boosting distance-based methods[Nakhleh et al. ISMB 2001 and Warnow et al. SODA 2001] • Theorem: DCM1-NJ converges to the true tree from polynomial length sequences 0.8 NJ DCM1-NJ 0.6 Error Rate 0.4 0.2 0 0 400 800 1200 1600 No. Taxa

32. What about solving MP and ML? • Maximum Parsimony (MP) and maximum likelihood (ML) are the major phylogeny estimation methods used by systematists.

33. 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.

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

35. Local optimum Cost Global optimum Phylogenetic trees 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).

36. Problems with current techniques for MP Best methods are a combination of simulated annealing, divide-and-conquer and genetic algorithms, as implemented in the software package TNT. However, they do not reach 0.01% of optimal on large datasetsin 24 hours. Performance of TNT with time

37. 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.

38. How can we improve upon existing techniques?

39. Our objective: speed up the best MP heuristics Fake study Performance of hill-climbing heuristic MP score of best trees Desired Performance Time

40. DCM Decompositions Input: Set S of sequences, distance matrix d, threshold value 1. Compute threshold graph 2. Perform minimum weight triangulation DCM2 decomposition: Separator plus components DCM1 decomposition : Max cliques

41. Empirical observation • No DCM based upon the threshold graphs gave us an improvement over the best heuristics for MP!

42. How can we improve upon existing techniques?

43. A conjecture as to why current techniques are poor: • Our studies suggest that trees with near optimal scores tend to be topologically close (RF distance less than 15%) from the other near optimal trees. • The best heuristics for MP are based upon the TBR move to explore tree space: there are O(n3) neighbors of every tree, most of which have large RF distances. • So TBR may be useful initially (to reach near optimality) but then more “localized” searches are more productive.

44. Using DCMs differently • Observation: DCMs make small local changes to the tree • New algorithmic strategy: use DCMs iteratively and/or recursively to improve heuristics on large datasets • We needed a decomposition strategy that produces small subproblems quickly.

45. Input: Set S of sequences, and guide-tree T We use a new graph (“short subtree graph”) G(S,T)) Note: G(S,T) is chordal! 2. Find clique separator in G(S,T) and form subproblems New DCM3 decomposition • DCM3 decompositions • can be obtained in O(n) time • (2) yield small subproblems • (3) can be used iteratively

46. DCM3 decompositions

47. Iterative-DCM3 T Base method DCM3 T’

48. Comparison of DCMs (13,921 sequences) Base method is the TNT-ratchet. “Optimal” refers to the best score found by any method using any amount of time, to date.

49. Rec-I-DCM3 significantly improves performance Current best techniques DCM boosted version of best techniques Comparison of TNT to Rec-I-DCM3(TNT) on one large dataset

50. Conclusions (and comments) • Rec-I-DCM3 improves upon the best performing heuristics for MP. • The improvement increases with the difficulty of the dataset. • DCMs also boost the performance of ML heuristics (not shown). • Rec-I-DCM3 will be in the first software release from the CIPRES project