Alexandros Stamatakis LRR TU München Contact: stamatak@cs.tum

Parallel & Distributed Systems and Algorithms for Inference of Large Phylogenetic Trees with Maximum Likelihood Alexandros Stamatakis LRR TU München Contact: stamatak@cs.tum.edu

Outline • Motivation • Introduction to phylogenetic tree inference • Statistical inference methods • Maximum Likelihood & associated problems • Solutions: • 2 simple heuristics • parallel & distributed implementation • Results • Conclusion • Availability & Future Work Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Motivation: Towards a „Tree of Life“ • 30.000 organisms available, current trees <= 1000 Where we are: Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Motivation: Towards a „Tree of Life“ • 30.000 organisms available, current trees <= 1000 Where we want to get: Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Phylogenetic Tree Inference • Input: „good“ multiple alignment of a distinguished, highly conserved part of DNA sequences • Output: unrooted binary tree with the sequences at its leaves (all nodes: either degree 1 or 3) • Various methods for phylogenetic tree inference • Differ in computational complexity and quality of trees • Most accurate methods: Maximum Likelihood Method (ML) and Bayesian Phylogenetic Inference: + most sound and flexible methods + other methods not suited for large/complex trees -- most computationally intensive methods Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ML and Bayesian methods • T.Williams et al (March 2003) comparative analysis with simulated data shows: MrBayes is best program • Guidon et al (May 2003) PHYML very fast & accurate ML program for real & simulated data: faster than MrBayes • ML (PHYML, RAxML2): + Significantly faster than MrBayes + Reference/starting trees for bayesian methods -- Less powerful statistical model • Bayesian Inference (MrBayes): + Powerful statistical model -- MCMC convergence problem • Memory requirements for 1000/10000-taxon alignment: • RAxML: 200MB/750MB • PHYML: 900MB/8.8GB • MrBayes: 1150MB/unknown Alexandros Stamatakis: Phylogenetic Inference with RAxML2

MCMC Convergence Problem Alexandros Stamatakis: Phylogenetic Inference with RAxML2

What does ML compute? • Maximum Likelihood calculates: • Topologies • Branch lengths v[i] • Likelihood of the tree S1 v1 v5 S3 S4 v3 v7 v4 v2 S2 v6 S5 Goal: Find tree topology wich maximizes likelihood Problem I: Number of possible topologies is exponential in n Problem II: Computation of likelihood value + branch length optimization is expensive Solution: Algorithmic Optimizations (previous work) + New heuristics +HPC Alexandros Stamatakis: Phylogenetic Inference with RAxML2

New Heuristics for RAxML • Two common methods to build a tree: • Progressive addition of organisms e.g. stepwise addition algorithm • Use a (random, simple) starting tree containing all organisms and optimize likelihood by application of topological changes • RAxML (Randomized Axelerated Maximum Likelihood) computes parsimony starting tree with dnapars -> fast and relatively „good“ initial likelihood • dnapars uses stepwise addition -> randomized sequence input order to obtain distinct starting trees • Optimize starting tree by application of rearrangements • Accelerate rearrangements by two simple ideas Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ST2 ST1 ST3 ST6 ST4 ST5 Subtree Rearrangements Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Subtree Rearrangements ST2 ST1 ST3 ST6 ST4 ST5 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Subtree Rearrangements +1 ST2 ST1 ST3 ST6 ST4 ST5 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Subtree Rearrangements ST2 ST1 Optimize all branches ST3 ST4 ST5 ST6 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Subtree Rearrangements ST2 ST1 Need to optimize all branches ? ST3 ST4 ST5 ST6 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Idea 1: Local Optimization of Branch Length ST2 ST1 ST3 ST6 ST4 ST5 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Why is Idea 1 useful? • Local optimization of branch lengths: • Update less likelihood vectors -> significantly faster • Allows higher rearrangement settings -> better trees • Likelihood depends strongly on topology • Fast exploration of large number of topologies • Straight-forward parallelization • Store best 20 trees from each rearrangement step • Branch length optimization of best 20 trees only • Experimental results justify this mechanism Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ST2 ST1 ST3 ST6 ST4 ST5 Idea 2:Subsequent Application of Topological Changes Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ST2 ST1 ST2 ST1 ST6 ST4 ST5 ST3 ST6 ST4 ST5 Idea 2:Subsequent Application of Topological Changes ST3 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ST2 ST1 ST2 ST1 ST6 ST4 ST5 ST3 ST2 ST1 ST6 ST4 ST5 ST6 ST4 ST5 Idea 2:Subsequent Application of Topological Changes ST3 ST3 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

ST2 ST1 ST6 ST4 ST5 ST2 ST1 ST6 ST4 ST5 Idea 2:Subsequent Application of Topological Changes ST2 ST1 ST3 ST3 ST6 ST4 ST5 ST1 ST2 ST3 ST3 ST6 ST4 ST5 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Why is Idea 2 useful? • During inital 5-10 rearrengement steps many improved topologies are encountered • Acceleration of likelihood improvment in initial optimization phase • Enables fast optimization of random starting trees Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Remainder of this Talk • Motivation • Introduction to phylogenetic tree inference • Statistical inference methods • Maximum Likelihood & associated problems • Solutions: • 2 simple heuristics • parallel & distributed implementation • Results • Conclusion • Availability & Future Work Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Basic Parallel & Distributed Algorithm • Basic idea: Distribute work by subtrees instead of topologies (e.g. parallel fastDNAml) • Simple Master-Worker architecture • Subsequent application of topological changes introduces non-determinism ST2 ST1 ST3 ST6 ST4 ST5 Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Basic Parallel & Distributed Algorithm • Basic idea: Distribute work by subtrees instead of topologies (e.g. parallel fastDNAml) • Simple Master-Worker architecture • Subsequent application of topological changes introduces non-determinism ST2 ST1 ST3 ST6 ST4 ST5 MPI_Send(ST3_ID, tree) Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Basic Parallel & Distributed Algorithm • Basic idea: Distribute work by subtrees instead of topologies (e.g. parallel fastDNAml) • Simple Master-Worker architecture • Subsequent application of topological changes introduces non-determinism ST2 ST1 MPI_Send(ST2_ID, tree) ST3 ST6 ST4 ST5 MPI_Send(ST3_ID, tree) Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Differences between Parallel & Distributed Algorithm • Parallel: best tree list of max(20, #workers) maintained and merged at the master • Parallel: Master distributes max(20, #workers) as toplogy-strings to workers for branch length optimization • Distributed: Each worker maintains local best list of 20 trees • Distributed: Worker performs fast branch length optimizations locally on all 20 trees -> returns only best topology to the master Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Sequential Results • 50 distinct simulated 100-taxon alignments • Measured average execution times & topological distance (RF-rate) from „true“ tree • PHYML: 35.21 seconds, RF-rate: 0.0796 • MrBayes: 945.32 seconds, RF-rate: 0.0741 • RAxML: 29.27 seconds, RF-rate: 0.0818 • 9 distinct real alignments containing 101-1000 taxa • Measured execution times & final likelihood values • RAxML yields best-known likelihood for all data sets • RAxML faster than PHYML & MrBayes Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Sequential Results: Real Data Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Parallel Results: Speedup 1000_ARB Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Distributed Results: First Tests • Platforms: • Infiniband-Cluster: 10 Intel Xeon 2.4 GHz • Sunhalle: 50 Sun-Workstations for CS students • Alignments: • 1000_ARB • 2025_ARB • Larger trees to come .......... • Results: • Program executed correctly & terminated • RAxML@home yielded best-known tree for 2025_ARB Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Biological Results: 1st ML 10.000-taxon tree • Calculated 5 parsimony starting trees + 3-4 initial rearrangement steps sequentially on Xeon 2.4GHz • Further rearrangements of those 5 trees in parallel on 32 or 64 Xeon 2.66GHz at RRZE • Accumulated CPU hours/tree ~ 3200hours • Best ln likelihood: -949539 worst: -950026 • Problems: • Quality assessment? bootstrap not feasible • Consense crashes for > 5 trees • MrBayes/PHYML crash on 32-bit/4GB • MrBayes crashed on Itanium • Visualization? Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Conclusion • RAxML not able to handle protein data • RAxML not able to perform model parameter optimization • BUT: • RAxML easy to parallelize/distribute • Accurate & fast for large trees • Significantly lower memory requirements than MrBayes/PHYML • Conclusion: Imlement model parameter optimization & protein data in RAxML Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Availability & Future Work • Further development & distribution of RAxML@home • Big production runs with RAxML@home • Survey: ML supertrees vs. integral trees • Alignment split-up methods for ML supertrees • RAxML implementation on GPUs • RAxML2 download, benchmark, code: wwwbode.in.tum.de/~stamatak • RAxML@home development: www.sourceforge.com/projects/axml Alexandros Stamatakis: Phylogenetic Inference with RAxML2

Alexandros Stamatakis LRR TU München Contact: stamatak@cs.tum