Gene Order Phylogeny

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Gene Order Phylogeny

• Tandy Warnow
• The Program in Evolutionary Dynamics, Harvard
  University
• The University of Texas at Austin

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• Cyber-Infrastructure for Phylogenetic RESearch
  (http//www.phylo.org)
• Main research Large-scale phylogenetics,
  reticulate evolution, gene order phylogeny,
  complex simulations, and databases
• Funded by 11.6M ITR Grant from NSF
• 40 biologists, computer scientists, and
  mathematicians collaborating on the project

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CIPRes Members
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Limitations of DNA phylogenetics

• Deep evolutionary histories may not be
  recoverable from DNA sequence phylogeny due to
  lack of specificity -- too much noise (homoplasy)
  and insufficient sequence length
• The systematics community has looked to rare
  genomic changes for better sources of
  phylogenetic signal

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Whole-Genome Phylogenetics
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Genomes As Signed Permutations
1 5 3 4 -2 -6or6 2 -4 3 5 1 etc.
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Genomes Evolve by Rearrangements
1 2 3 4 5 6 7 8 9 10

• Inversion (Reversal)

• Transposition

• Inverted Transposition

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Other types of events

• Duplications, Insertions, and Deletions (changes
  gene content)
• Fissions and Fusions (for genomes with more than
  one chromosome)
• These events change the number of copies of each
  gene in each genome (unequal gene content)

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Genome Rearrangement Has A Huge State Space

• DNA sequences 4 states per site
• Signed circular genomes with n genes
  states, 1
  site
• Circular genomes (1 site)
• with 37 genes (mitochondria)
  states
• with 120 genes (chloroplasts)
  states

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Why use gene orders?

• Rare genomic changes huge state space and
  relative infrequency of events (compared to site
  substitutions) could make the inference of deep
  evolution easier, or more accurate.
• Our research shows this is true, but accurate
  analysis of gene order data is computationally
  very intensive!

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Phylogeny reconstruction from gene orders

• Distance-based reconstruction estimate pairwise
  distances, and apply methods like
  Neighbor-Joining or Weighbor
• Maximum Parsimony find tree with the minimum
  length (inversions, transpositions, or other edit
  distances)
• Maximum Likelihood find tree and parameters of
  evolution most likely to generate the observed
  data

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Maximum Parsimony on Rearranged Genomes (MPRG)

• The leaves are rearranged genomes.
• Find the tree that minimizes the total number of
  rearrangement events (e.g., inversion phylogeny
  minimizes the number of inversions)

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Optimization problems for gene order phylogeny

• Breakpoint phylogeny find the phylogeny which
  minimizes the total number of breakpoints
  (NP-hard, even to find the median of three
  genomes)
• Inversion phylogeny find the phylogeny which
  minimizes the sum of inversion distances on the
  edges (NP-hard, even to find the median of three
  genomes)

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Inversion phylogenies

• When the data are close to saturated, even the
  best distance-based analyses are insufficiently
  accurate. In these cases, our initial
  investigations suggest that the inversion
  phylogeny approach may be superior.
• Problem finding the best trees is enormously
  hard, since even the point estimation problem
  is hard (worse than estimating branch lengths in
  ML).

Local optimum
Tree length
Global optimum
Phylogenetic trees
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Observations

• For equal gene content, heuristics for the
  inversion phylogeny problem are extremely
  accurate, even under model conditions in which
  transpositions are dominant.
• For unequal gene content, the parsimony style
  problems are too computationally intense -- but
  NJ (neighbor joining) with a new distance
  estimator (Moret et al. 2004) works extremely
  well.

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Software

• BPAnalysis (Sankoff) open source, restricted to
  the breakpoint phylogeny reconstruction
• GRAPPA (Moret et al.) open source, restricted to
  single chromosome genomes, but can handle both
  equal and unequal gene content
• MGR (Pevzner et al.) multiple chromosome,
  limited to equal gene content, performs well if
  the dataset is small (less than 10 genomes)
• Bayesian analysis by Bret Larget (not yet
  released).

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Merciera
Wahlenbergia
Tiodanus
Legousia
Asyneuma
Trachelium
Symphyandra
Campanula
Codonopsis
Tobacco
Adenophora
Cyananthus
The strict consensus of 24 trees, each with
inversion length of 64. Finished within 40
minutes on a laptop using GRAPPA version 1.8
Platycodon
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GRAPPA (Genome Rearrangement Analysis under
Parsimony and other Phylogenetic Algorithms)

• http//www.cs.unm.edu/moret/GRAPPA/
• Heuristics for maximum parsimony style problems
  for equal gene content
• Fast polynomial time distance-based methods
• Contributors U. New Mexico,U. Texas at Austin,
  Universitá di Bologna, Italy
• Freely available in source code at this site.
• Project leader Bernard Moret (UNM)
  (moret_at_cs.unm.edu)

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Speeding up MP and ML DCM3

• Tandy Warnow
• Radcliffe Institute
• The University of Texas at Austin

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Reconstructing the Tree of Life
Handling large datasets millions of species
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Methods for phylogenetic inference

• Polynomial time methods, mostly based upon
  estimating evolutionary distances
• Heuristics for hard optimization problems (such
  as maximum parsimony and maximum likelihood)
• Bayesian methods

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Main research objectives

• Determine the best current methods available for
  MP and ML, and then improve upon them
• Focus on performance within one day, one week, or
  one month, on large real datasets (1K to 20K
  sequences for MP)
• Final objective is hundreds of thousands (or
  millions) of sequences.

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Initial results

• Very large datasets are hard for both MP and ML,
  no matter what software is used
• Suboptimal solutions to MP yield reasonable
  estimates of the optimal MP trees - but only if
  they are within .01 of optimal MP score
• Improving upon techniques for searching treespace
  will yield improvements for both MP and ML

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Datasets
Obtained from various researchers and online
databases

• 1322 lsu rRNA of all organisms
• 2000 Eukaryotic rRNA
• 2594 rbcL DNA
• 4583 Actinobacteria 16s rRNA
• 6590 ssu rRNA of all Eukaryotes
• 7180 three-domain rRNA
• 7322 Firmicutes bacteria 16s rRNA
• 8506 three-domain2org rRNA
• 11361 ssu rRNA of all Bacteria
• 13921 Proteobacteria 16s rRNA

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Problems with current techniques for MP
Average MP scores above optimal of best methods
at 24 hours across 10 datasets
Best current techniques fail to reach 0.01 of
optimal at the end of 24 hours, on large datasets
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Problems with current techniques for MP
The best current method (default TNT) fails to
reach acceptable levels of accuracy (0.01 of
optimal) within 24 hours on many large datasets
-- evidence suggests that this level will not be
reached for weeks or months (or more) of further
analysis.
Performance of TNT with time
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Observations

• The best methods 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.

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Observations

• The best methods 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.

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Observations

• The best methods 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.

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Disk-Covering Methods (DCMs)

• DCMs are divide-and-conquer methods that our
  group has developed for use in phylogeny
  reconstruction
• DCM2 was designed for speeding up maximum
  parsimony and maximum likelihood heuristics. DCM2
  was good enough for PAUP.
• DCM3 is a recent improvement over DCM2 which
  enables iteration (and gives smaller subproblems)
  - and is good enough for TNT.

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Boosting MP heuristics

• DCMs boost the performance of phylogeny
  reconstruction methods.

DCM
Base method M
DCM-M
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DCM3 technique for speeding up MP searches
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Iterative-DCM3
T
DCM3
Base method
T
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New DCMs

• DCM3
• Compute subproblems using DCM3 decomposition
• Apply base method to each subproblem to yield
  subtrees
• Merge subtrees using the Strict Consensus Merger
  technique
• Randomly refine to make it binary
• Recursive-DCM3
• Iterative DCM3
• Compute a DCM3 tree
• Perform local search and go to step 1
• Recursive-Iterative DCM3

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Boosting MP heuristics

• We examine DCMs using DCM2 and DCM3, and using
  recursion and/or iteration.

DCM
Base method M
DCM-M
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Performance Study

• How well do these boosted versions of the best
  MP heuristics perform, compared to the best MP
  heuristics?
• We examine performance with respect to optimal
  MP scores (best found so far, using any method)
  for a number of very large datasets, over 24
  hours.
• The benchmark MP heuristic is the default TNT.

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Datasets
Obtained from various researchers and online
databases

• 1322 lsu rRNA of all organisms
• 2000 Eukaryotic rRNA
• 2594 rbcL DNA
• 4583 Actinobacteria 16s rRNA
• 6590 ssu rRNA of all Eukaryotes
• 7180 three-domain rRNA
• 7322 Firmicutes bacteria 16s rRNA
• 8506 three-domain2org rRNA
• 11361 ssu rRNA of all Bacteria
• 13921 Proteobacteria 16s rRNA

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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
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Rec-I-DCM3(TNT) vs. TNT(Comparison of scores at
24 hours)
Base method is the default TNT technique, the
current best method for MP. Rec-I-DCM3
significantly improves upon the unboosted TNT by
returning trees which are at most 0.01 above
optimal on most datasets.
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Summary

• Rec-I-DCM3 is a powerful technique for escaping
  local optima, and boosts the performance of the
  best heuristics for solving MP
• The improvement increases with the difficulty of
  the dataset - Rec-I-DCM3(TNT) is 50 times faster
  than TNT on our hardest datasets, but we expect
  even bigger speedups in our next version
• DCMs also boost the performance of Maximum
  Likelihood heuristics (not shown)

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Acknowledgements

• Collaborators Bernard Moret (UNM), Usman Roshan
  (UT-Austin), and Tiffani Williams (UNM)
• Funding NSF, The David and Lucile Packard
  Foundation, The Radcliffe Institute for Advanced
  Study, The Institute for Cellular and Molecular
  Biology at UT-Austin, and The Program in
  Evolutionary Dynamics at Harvard University
• Software will be part of the CIPRES Projects
  first distribution - see http//www.phylo.org

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• Cyber-Infrastructure for Phylogenetic RESearch
  (http//www.phylo.org)
• Main research Large-scale phylogenetics,
  reticulate evolution, gene order phylogeny, and
  databases
• Funded by 11.6M ITR Grant from NSF
• 40 biologists, computer scientists, and
  mathematicians collaborating on the project