1. New methods for simultaneous estimation of trees and alignments
Tandy Warnow
The University of Texas at Austin
Joint work with K. Liu, S. Raghavan, S. Nelesen, and C.R. Linder

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

3. Evolutionary History Helps us
predict gene function
develop drugs and vaccines
understand disease spread
understand human origins
Phylogenetics: estimating evolutionary histories
All organisms on earth are related through their evolutionary history. Understanding these relationships is critical to answering many biological and biomedical questions. For example, evolutionary histories can be used to develop effective vaccines, and to understand the spread of a disease through a population. The field responsible for estimating these evolutionary histories is Phylogenetics, and the histories themselves are called phylogenies or phylogenetic trees.
One of the big goals in phylogenetics is to construct the tree of life, a phylogenetic tree that relates all organisms on earth. Supertrees methods are one tool for reconstructing very large phylogenies, and will be critical in progressing towards constructing the tree of life. My focus has been to develop supertree methods that can help us get closer to this goal.
Before we see how supertree methods can be used to construct large-scale phylogenies, let’s look at a small example of a phylogeny.
Tree of Life
From AToL website

4. Many, Many Trees (2n-5)! 2 (n-1)! # of Species # of Unrooted Trees 4 315 6
105 7
945 8
10,395 9
135,135 10
2,027,025 20
2.2 x 10
100
4.5 x 10x
1000
2.7 x 10 x
190
2900
(2n-5)!
2 (n-1)!
n-1

5. Computational phylogenetics
Heuristics for NP-hard problems
Statistical aspects of estimation methods under Markov models of evolution
Detection and reconstruction of reticulate evolution
Comparative genomics
Datamining sets of trees and alignments
Visualization of large trees and alignments
Supertree methods
Simultaneous estimation of trees and alignments
(plus similar issues for historical linguistics)

6. Computational phylogenetics
Heuristics for NP-hard problems
Statistical aspects of estimation methods under Markov models of evolution
Detection and reconstruction of reticulate evolution
Comparative genomics
Datamining sets of trees and alignments
Visualization of large trees and alignments
Supertree methods
Simultaneous estimation of trees and alignments
(plus similar issues for historical linguistics)

7. This talk
SATé (Simultaneous Alignment and Tree Estimation), Science 2009, Liu et al.
Standard methods for estimating sequence alignments and phylogenetic trees have unacceptably high error
SATé produces high accuracy with 24 hour analyses on datasets with up to 1000 taxa
New methods (unpublished), both more accurate and faster than SATé
SATé-II
BLuTGEN (only produces a tree)
Potential for major impact for large-scale phylogeny estimation

8. DNA Sequence Evolution
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

9. U V W X Y X U Y V W AGGGCAT TAGCCCA TAGACTT TGCACAA TGCGCTT
Unrooted trees are equivalent to a rooted tree with branch lengths and the root node omitted.
Rooting is a separate problem which is not discussed in this talk. V W 9

10. Deletion
Mutation
…ACGGTGCAGTTACCA…
…ACCAGTCACCA… 10

11. …ACGGTGCAGTTACCA… …ACGGTGCAGTTACCA… …AC----CAGTCACCA… …ACCAGTCACCA…
Deletion
Mutation
…ACGGTGCAGTTACCA…
…ACGGTGCAGTTACCA…
…AC----CAGTCACCA…
…ACCAGTCACCA…
The true multiple alignment
Reflects historical substitution, insertion, and deletion events
Defined using transitive closure of pairwise alignments computed on edges of the true tree
Homology = nucleotides lined up since they come from a common ancestor.
Indel = dash. 11

12. Input: unaligned sequences
S1 = AGGCTATCACCTGACCTCCA
S2 = TAGCTATCACGACCGC
S3 = TAGCTGACCGC
S4 = TCACGACCGACA

13. Phase 1: Multiple Sequence Alignment
S1 = AGGCTATCACCTGACCTCCA
S2 = TAGCTATCACGACCGC
S3 = TAGCTGACCGC
S4 = TCACGACCGACA
S1 = -AGGCTATCACCTGACCTCCA
S2 = TAG-CTATCAC--GACCGC--
S3 = TAG-CT GACCGC--
S4 = TCAC--GACCGACA

14. Phase 2: Construct tree S1 = AGGCTATCACCTGACCTCCA
S2 = TAGCTATCACGACCGC
S3 = TAGCTGACCGC
S4 = TCACGACCGACA
S1 = -AGGCTATCACCTGACCTCCA
S2 = TAG-CTATCAC--GACCGC--
S3 = TAG-CT GACCGC--
S4 = TCAC--GACCGACA S1 S2 S4 S3

15. Many methods Phylogeny methods Bayesian MCMC Maximum parsimony
Maximum likelihood
Neighbor joining
FastME
UPGMA
Quartet puzzling
Etc.
Alignment methods
Clustal
POY (and POY*)
Probcons (and Probtree)
MAFFT
Prank
Muscle
Di-align
T-Coffee
Opal
Etc.
RAxML: best heuristic for large-scale ML optimization 15

16. Question: How well do two-phase methods perform?
ROSE simulation:
1000, 500, and 100 sequences
Evolution with substitutions and indels
Varied gap lengths, rates of evolution
Estimated alignments using leading methods
Used RAxML to compute trees
Recorded tree error (missing branch rate)
Recorded alignment error
Liu et al., Science 2009

17. Simulation Studies Unaligned Sequences Compare True tree and alignment
S1 = AGGCTATCACCTGACCTCCA
S2 = TAGCTATCACGACCGC
S3 = TAGCTGACCGC
S4 = TCACGACCGACA
Unaligned Sequences
S1 = -AGGCTATCACCTGACCTCCA
S2 = TAG-CTATCAC--GACCGC--
S3 = TAG-CT GACCGC--
S4 = TCAC--GACCGACA
S1 = -AGGCTATCACCTGACCTCCA
S2 = TAG-CTATCAC--GACCGC--
S3 = TAG-C--T-----GACCGC--
S4 = T---C-A-CGACCGA----CA S1 S2 S3 S4 S1 S4 S3 S2
Compare
True tree and alignment
Estimated tree and alignment

18. Quantifying Error True Tree Estimated TreeC A B C D E A D FN B E
True Tree
Estimated Tree
False negative (FN) - aka “missing branch” : An edge in the true tree missing from the estimated tree

19. 1000 taxon models, ordered by difficulty
1. 2 classes of MC: easy, moderate-to-difficult
2. true alignment
3. 2 classes: ClustalW, everything else
Alignment error, measured this way, isn't a perfect predictor of tree error, measured this way.
1000 taxon models, ordered by difficulty 19

20. Problems with the two-phase approach
Manual alignment is time consuming and subjective.
Current alignment methods fail to return reasonable alignments on large datasets with high rates of indels and substitutions.
Systematists discard potentially useful markers if they are difficult to align.
This issues seriously impact large-scale phylogeny estimation (and Tree of Life projects)

21. S1 S4 S2 S3
S1 = AGGCTATCACCTGACCTCCA
S2 = TAGCTATCACGACCGC
S3 = TAGCTGACCGC
S4 = TCACGACCGACA
and
S1 = -AGGCTATCACCTGACCTCCA
S2 = TAG-CTATCAC--GACCGC--
S3 = TAG-CT GACCGC--
S4 = TCAC--GACCGACA
Statistical simultaneous estimation methods (BALiPhy, Alifritz, Statalign) are not scalable.
POY and related methods are not more accurate than standard two-phase methods. 21

22. SATé: (Simultaneous Alignment and Tree Estimation)
Liu, Nelesen, Raghavan, Linder, and Warnow
Search strategy: search through tree space, and realigns sequences on each tree using a novel divide-and-conquer approach.
Optimization criterion: alignment/tree pair that optimizes maximum likelihood under GTR+Gamma (RAxML GTRMIX, treating gaps as missing data).
Science, 19 June 2009, pp

23. SATé Algorithm
Tree
Obtain initial alignment and estimated ML tree

24. SATé Algorithm Obtain initial alignment and estimated ML tree Tree
Use tree to compute new alignment
Alignment

25. SATé Algorithm Obtain initial alignment and estimated ML tree Tree
Estimate ML tree on new alignment
Use tree to compute new alignment
Alignment

26. SATé Algorithm Obtain initial alignment and estimated ML tree Tree
Estimate ML tree on new alignment
Use tree to compute new alignment
Alignment
If new alignment/tree pair has worse ML score, realign using a different decomposition
Repeat until termination condition (typically, 24 hours)

27. SATé iteration (Actual decomposition produces 32 subproblems)
Merge subproblems
Estimate ML tree on merged alignment
Decompose based on input tree
Align subproblems
ABCD e

28. 1000 taxon models, ordered by difficulty
Say the only thing changing here is the alignment method. 28

29. 1000 taxon models, ordered by difficulty
For moderate-to-difficult datasets, SATe gets better trees and alignments than all other estimated methods. Close to what you might get if you had access to true alignment.
Opens up a new realm of possibility: Datasets currently considered “unalignable” can in fact be aligned reasonably well. This opens up the feasibility of accurate estimations of deep evolutionary histories using a wider range of markers.
TRANSITION: can we do better? What about smaller simulated datasets? And what about biological datasets?
24 hour SATé analysis, on desktop machines
(Similar improvements for biological datasets)

30. Why is SATé so accurate?
Not because it’s good to optimize ML under a model treating gaps as missing data - we prove that this optimization problem is a bad approach.
Instead, the key is the divide-and-conquer strategy (with ML giving a small but statistically significant additional improvement).

31. SATé iteration (Actual decomposition produces 32 subproblems)
Merge subproblems
Estimate ML tree on merged alignment
Decompose based on input tree
Align subproblems
ABCD e

32. Since the Science paper…
Two new (unpublished) methods, both more accurate than the Science SATé:
SATé-II: different re-alignment strategy, but same general algorithm design. Fast version gives highly accurate results in just a few hours on datasets with 1000 taxa.
BLuTGEN: designed for very large datasets, or those where an alignment on the entire dataset is not possible. Only produces a tree.

33. SATé-II: same as SATé-I except for decompositionB D C
Merge subproblems
Estimate ML tree on merged alignment
Decompose based on input tree
Align subproblems
ABCD e

34. SATé-2 vs. SATé: only difference is the division into subsets
Recursive decomposition:
An edge is taken from the tree, dividing the taxa into two subsets.
This is repeated until each set is “small enough”
Each subset is aligned, and then alignments are merged into an alignment on the entire dataset.

35. 1000 taxon models ranked by difficulty

36. SATé-I vs. SATé-II SATé-II Faster and more accurate than SATé-I
Longer analyses or use of ML to select tree/alignment pair slightly better results

37. Limitations of SATé-I and -IIB D C A B
Decompose dataset C D
Align subproblems A B C D
Estimate ML tree on merged alignment
ABCD
Merge sub-alignments

38. BLuTGEN Input: unaligned sequences
Output: tree on the sequence dataset
Note: BLuTGEN does not produce a multiple alignment on the full dataset.

39. BLuTGEN BLAST-based Existing Method: RAxML(MAFFT) pRecDCM3
Unaligned Sequences
Overlapping
subsets
pRecDCM3
A tree for each subset
New supertree method: SuperFine
A tree for the entire dataset

40. 1000 taxon models ranked by difficulty
For moderate-to-difficult datasets, SATe gets better trees and alignments than all other estimated methods. Close to what you might get if you had access to true alignment.
Opens up a new realm of possibility: Datasets currently considered “unalignable” can in fact be aligned reasonably well. This opens up the feasibility of accurate estimations of deep evolutionary histories using a wider range of markers.
TRANSITION: can we do better? What about smaller simulated datasets? And what about biological datasets?
We examine BLuTGEN on the two hardest model conditions
1000S1 = M14 and 1000M1 = M15

41. Using pRecDCM3
Missing Edge Rate

42. pRecDCM3 vs. SATé
Missing Edge Rate

43. Further Improvements with Iteration
Missing Edge Rate

44. BLuTGEN
Results shown based upon three iterations, starting with RAxML(MAFFT).
Same levels of accuracy obtained when using the BLAST-based approach.
Nelesen, Linder, and Warnow. In preparation.

45. Analyses of Gutell rRNA datasets
BLuTGEN yields dramatic improvements in topological accuracy over two-phase methods, and slight improvements over SATé-I, with just a few iterations.
Two largest datasets:
7,350 16S sequences spanning the Tree of Life (all 3 domains)
27,643 16S bacterial sequences.

46. BLuTGEN vs. SATé BLuTGEN iterations:
1-2.5 hours for 1000 taxon (simulated) datasets
25 hours on 7350 taxon (16S.T) dataset
68 hours on 27,643 taxon (16S B.ALL) dataset
SATé-2 iterations:
2-12 hours for 1000 taxon (simulated) datasets
75 hours on the 7350 taxon (16S.T) dataset
253 days on the 27,643 taxon (16S B.ALL) dataset:
Alignment production 121 hours
RAxML tree estimation 248 days (one month with 8 processors, fastest version of RAxML)

47. BLuTGEN on 16S.B.ALL
6 iterations of BLuTGEN on a 27,000 taxon dataset; each iteration takes 3 days

48. Summary
Both SATé-I and SATé-II produce more accurate trees and alignments than standard methods, and SATé-II is much faster and more accurate than SATé-I.
BLuTGEN is designed for very large-scale phylogeny estimation problems, especially where SATé-II cannot be used (or where its use would require extreme computational resources).
Together, these methods make it possible to analyze a much larger range of genes in systematic studies, and may transform Tree of Life efforts.

49. Related Research SuperFine: new supertree method
Divide-and-conquer methods to speed up
Constructing species phylogenies from gene trees
Whole genome phylogenetics
Historical Linguistics, including reticulate evolution detection and reconstruction
Metagenomic analyses, esp. phylogenetic placement

50. Acknowledgments
National Science Foundation: Assembling the Tree of Life (ATOL), ITR, and IGERT grants ( , , )
Students: Kevin Liu, Serita Nelesen, Sindhu Raghavan, and Shel Swenson
Randy Linder, Integrative Biology, UT-Austin