Designing parallel algorithms for constructing large phylogenetic trees on Blue Waters

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Designing parallel algorithms for constructing large phylogenetic trees on Blue Waters Erin Molloy University of Illinois at Urbana Champaign General Allocation (PI: Tandy Warnow) Exploratory Allocation (PI: Bill Gropp) NCSA Blue Waters Symposium June 5, 2018 Molloy (PI: Warnow; PI: Gropp) TERADACTAL 1/56

Phylogeny Molloy (PI: Warnow; PI: Gropp) TERADACTAL 2/56

Tree of Life and Downstream Applications Nothing in biology makes sense except in the light of evolution Dobhzansky (1973) Protein structure and function prediction Population genetics Human migrations Metagenomics Infectious Disease Biodiversity Molloy (PI: Warnow; PI: Gropp) TERADACTAL 3/56

Outline Phylogeny estimation pipeline Some standard approaches and their limitations Our new approach to ultra-large phylogeny estimation on Blue Waters Comparison of our approach to existing methods Future work Molloy (PI: Warnow; PI: Gropp) TERADACTAL 4/56

DNA Sequence Evolution Molloy (PI: Warnow; PI: Gropp) TERADACTAL 5/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 6/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 7/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 8/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 9/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 10/56

Phylogeny Estimation Pipelines Molloy (PI: Warnow; PI: Gropp) TERADACTAL 11/56

Distance Methods Input: A matrix D such that D[i, j] indicates the distance between sequence i and sequence j Use multiple sequence alignment to compute pairwise distances Use alignment-free method to compute pairwise distances in an embarrassingly parallel fashion Output: A tree with branch lengths Distance methods use polynomial time. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 12/56

Maximum Likelihood (ML) Tree Estimation Input: A multiple sequence alignment Output: A model tree (topology and other numerical parameters) that maximizes likelihood, that is, the probability of observing the multiple sequence alignment given a model tree The ML tree estimation problem is NP-hard. [Felsenstein,1981; Roch, 2006] ML Heuristic are typically more accurate than distance methods, especially under some challenging model conditions. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 13/56

Maximum Likelihood (ML) Tree Estimation Input: A multiple sequence alignment Output: A model tree (topology and other numerical parameters) that maximizes likelihood or probability of observing the multiple sequence alignment given a model tree The ML tree estimation problem is NP-hard. [Felsenstein,1981; Roch, 2006] ML Heuristic are typically more accurate than distance methods, especially under some challenging model conditions. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 14/56

ML Tree Estimation: N versus L A multiple sequence alignment is an N L matrix. Number of sites or alignment length, L Thousands of sites for single gene analysis Millions of sites for multi-gene analysis Many analyses can be parallelized across sites Because likelihood is computed on each site independently Number of species or sequences, N Many datasets have thousands of species The Tree of Life will have millions Number of tree topologies on N leaves is (2N 5)!! Parallelism is more complicated Molloy (PI: Warnow; PI: Gropp) TERADACTAL 15/56

ML Tree Estimation: N versus L [Stamatakis, 2006; Price et al., 2010; Kozlov et al., 2015] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 16/56

ML Tree Estimation: N versus L [Stamatakis, 2006; Price et al., 2010; Kozlov et al., 2015] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 17/56

ML Tree Estimation: N versus L [Stamatakis, 2006; Price et al., 2010; Kozlov et al., 2015] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 18/56

ML Tree Estimation: N versus L ExaML [Kozlov et al., 2015] can be used for analyzing datasets with 10-20 genes and up to 55,000 taxa, but scalability will be limited to at most 100 cores. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 19/56

ML Tree Estimation: N versus L Molloy (PI: Warnow; PI: Gropp) TERADACTAL 20/56

ML Tree Estimation: N versus L Molloy (PI: Warnow; PI: Gropp) TERADACTAL 21/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 22/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 23/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 24/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 25/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 26/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 27/56

Our Design Goals If we want to build the Tree of Life (millions of sequences!) using Blue Waters, then we need to design an algorithm that can utilize a very large numbers of (not high memory) processors. Based on our observations, it would be good to avoid estimating 1 Multiple sequence alignment on the full set of sequences 2 ML tree on the full multiple sequence alignment 3 Supertree Molloy (PI: Warnow; PI: Gropp) TERADACTAL 28/56

Divide-and-Conquer with DACTAL [Nelesen et al., 2012] [Steel, 1992; Jiang et al., 2001; Bansal et al., 2010] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 29/56

TERADACTAL Algorithm Molloy (PI: Warnow; PI: Gropp) TERADACTAL 30/56

TreeMerge: Step 1 Create a minimum spanning tree on the disjoint subsets. [Kruskal, 1956] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 31/56

TreeMerge: Step 1 Create a minimum spanning tree on the disjoint subsets. [Kruskal, 1956] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 32/56

TreeMerge: Step 2 Merge trees T i and T j into tree T ij such that T ij Li = T i and T ij Lj = T j (multiple solutions). 1 Merge two alignments A i and A j into A ij using an existing technique (e.g., OPAL [Wheeler and Kececioglu, 2007]). 2 Compute distance matrix D ij from merged alignment A ij. 3 Run NJMerge our variant of Neighbor-Joining [Saitou and Nei, 1987] that takes both a distance matrix and a set of constraint trees as input. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 33/56

TreeMerge: Step 2 Merge trees T i and T j into tree T ij such that T ij Li = T i and T ij Lj = T j (multiple solutions). 1 Merge two alignments A i and A j into A ij using an existing technique (e.g., OPAL [Wheeler and Kececioglu, 2007]). 2 Compute distance matrix D ij from merged alignment A ij. 3 Run NJMerge our variant of Neighbor-Joining [Saitou and Nei, 1987] that takes both a distance matrix and a set of constraint trees as input. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 34/56

NJMerge: Constrained Neighbor-Joining Molloy (PI: Warnow; PI: Gropp) TERADACTAL 35/56

NJMerge: Constrained Neighbor-Joining Molloy (PI: Warnow; PI: Gropp) TERADACTAL 36/56

TreeMerge: Step 3 Combine pairs of merged trees using branch lengths, e.g., trees T ij and T jk are combined through T j (blue). NOTE: Unlabeled branches have length one for simplicity. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 37/56

TreeMerge: Step 3 Combine pairs of merged trees using branch lengths, e.g., trees T ij and T jk are combined through T j (blue). NOTE: Unlabeled branches have length one for simplicity. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 38/56

Advantages TERADACTAL No multiple sequence alignment estimation on the full dataset No Maximum Likelihood tree estimation on the full dataset No supertree estimation TreeMerge Polynomial Time Parallel (Step 2) Pairs of alignments and trees can be merged in an embarrassingly parallel fashion. (Step 3) Merged tree pairs can be combined in parallel, as long as they do not share edges in the minimum spanning tree. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 39/56

Simulation Studies Molloy (PI: Warnow; PI: Gropp) TERADACTAL 40/56

Quantifying Tree Error Molloy (PI: Warnow; PI: Gropp) TERADACTAL 41/56

Simulation Study Compare TERADACTAL to 2 alignment-free methods 3 multiple sequence alignment methods (2 shown) 2 distance methods (1 shown) 2 Maximum Likelihood methods (1 Shown) on simulated datasets from Mirarab et al., 2015. 10,000 sequences 4 model conditions each with 10 replicate datasets (1 shown) Molloy (PI: Warnow; PI: Gropp) TERADACTAL 42/56

TERADACTAL Iterations 0.8.71 INDELible M2 0.6 Error Rate 0.4 0.2.14.13.12.12.11 0.0 Iteration 0 1 2 3 4 5 Molloy (PI: Warnow; PI: Gropp) TERADACTAL 43/56

TERADACTAL versus Alignment-Free Methods 0.6.61 INDELible M2 Error Rate 0.4 0.2.41.11 0.0 Method RapidNJ+JD2Stat RapidNJ+KMACS TERADACTAL [Simonsen et al., 2008; Chan et al., 2014; Leimeister and Morgenstern, 2014] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 44/56

TERADACTAL versus Two-Phase Methods (NJ) 0.8.78 INDELible M2 Error Rate 0.6 0.4 0.2.14.11 0.0 Method RapidNJ+MAFFT RapidNJ+PASTA TERADACTAL [Simonsen et al., 2008; Katoh and Standley, 2013; Mirarab et al., 2015] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 45/56

TERADACTAL versus Two-Phase Methods (ML).65 INDELible M2 0.6 Error Rate 0.4 0.2.08.11 0.0 Method RAxML+MAFFT RAxML+PASTA TERADACTAL [Stamatakis, 2006; Katoh and Standley, 2013; Mirarab et al., 2015] Molloy (PI: Warnow; PI: Gropp) TERADACTAL 46/56

Conclusions We designed, prototyped, and tested a method that achieves similar error rates to the leading two-phase phylogeny estimation methods but is highly parallel and avoids 1 Multiple sequence alignment estimation on the full dataset 2 Maximum likelihood tree estimation on the full dataset 3 Supertree estimation Molloy (PI: Warnow; PI: Gropp) TERADACTAL 47/56

Future Work Scale out to one million sequences. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 48/56

Why Blue Waters Blue Waters was used to Demonstrate that codes (e.g., FastTree-2, PASTA, RAxML) could not run on Blue Waters on datasets with 1 million sequences (Run out of memory!) Simulation study completed in < 1 month but would have required > 1 year using our 4 campus cluster nodes Molloy (PI: Warnow; PI: Gropp) TERADACTAL 49/56

Research Products Paper under review at the 17th European Conference on Computational Biology (ECCB 2018). Github: github.com/ekmolloy/teradactal-prototype Molloy (PI: Warnow; PI: Gropp) TERADACTAL 50/56

Other Research Products from General Allocation Nute, Saleh & Warnow Benchmarking statistical multiple sequence alignment. Under review at Systematic Biology. Nute, Chou, Molloy & Warnow (2018). The Performance of Coalescent-Based Species Tree Estimation Methods under Models of Missing Data. BMC Genomics 19(Suppl 5):286. Vachaspati & Warnow (2018). SVDquest: Improving SVDquartets species tree estimation using exact optimization within a constrained search space. Mol Phyl Evol 124:122-136. Github: github.com/pranjalv123/svdquest Vachaspati & Warnow (2018). SIESTA: Enhancing searches for optimal supertrees and species trees. BMC Genomics 19(Suppl 5):252. Github: github.com/pranjalv123/siesta Molloy (PI: Warnow; PI: Gropp) TERADACTAL 51/56

Acknowledgements This work was supported by the National Science Foundation Blue Waters Sustained-Petascale Computing Project (OCI-0725070 and ACI-1238993) General Allocation (PI: Warnow) Exploratory Allocation (PI: Gropp) Graduate Research Fellowship Program (DGE-1144245) Graph-Theoretic Algorithms to Improve Phylogenomic Analyses (CCF-1535977) and the Ira & Debra Cohen Graduate Fellowship in Computer Science. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 52/56

References Felsenstein, J. (1981). Evolutionary trees from DNA sequences: A maximum likelihood approach. Journal of Molecular Evolution 17(6):368 376. Roch, S. (2006). A short proof that phylogenetic tree reconstruction by maximum likelihood is hard. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(1):92 94. Stamatakis, A. (2006). RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models. Bioinformatics 22(21):2688 2690. Price, M.N., P. S. Dehal, and A. P. Arkin. (2010). FastTree 2 Approximately Maximum Likelihood Trees for Large Alignments. PLoS ONE 5(3):1 10. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 53/56

References Kozlov, A.M., A.J. Aberer, and A. Stamatakis. (2015). ExaML version 3: a tool for phylogenomic analyses on supercomputers. Bioinformatics 31. Nelesen, S., et al., (2012). DACTAL: Divide-And-Conquer Trees (almost) without Alignments. Bioinformatics 28(12):i274 i282. Steel, M. (1992). The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification 9:91-116. Jiang, T., P. Kearney, and M. Li. (2001). A polynomial time approximation scheme for inferring evolutationay trees from quartet topologies and its application. SIAM Journal on Computing 30(6):1942 1961. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 54/56

References Bansal, M.S., et al., (2010). Robinson-Foulds Supertrees. Algorithms for Molecular Biology 5(1). Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society 7:48 50. Saitou, N. and M. Nei. (1987). The neighbor-joining method: a new method for reconstruction of phylogenetic trees. Molecular Biology and Evolution 4: 406 425. Mirarab, S., et al., (2015). PASTA: Ultra-Large Multiple Sequence Alignment for Nucleotide and Amino-Acid Sequences. Journal of Computational Biology 22(5):377 386. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 55/56

References Wheeler, T.J. and J. D. Kececioglu. (2007). Multiple alignment by aligning alignments. Bioinformatics 23(13):i559. Chan, C.X. et al., (2014). Inferring phylogenies of evolving sequences without multiple sequence alignment. Scientific Reports 4:6504. Leimeister, C.-A. and B. Morgenstern. (2014). kmacs: the k-mismatch Average Common Substring Approach to alignment-free sequence comparison. Bioinformatics 30(14):2000 2008. Simonsen, M., T. Mailund, and C.N.S. Pedersen. (2008) Rapid Neighbour-Joining. Algorithms in Bioinformatics 5251:113 122. Katoh, K. and D.M. Standley. (2013). MAFFT Multiple Sequence Alignment Software Version 7: Improvements in Performance and Usability. Molecular Biology and Evolution 30(4):772. Molloy (PI: Warnow; PI: Gropp) TERADACTAL 56/56

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