suprefine, a new supertree method
DESCRIPTION
SupreFine, a new supertree method. Shel Swenson September 17th 2009. Reconstructing the Tree of Life. Tree of Life challenges: - millions of species - lots of missing data. Two possible approaches: - Combined Analysis - Supertree Methods. Two competing approaches. - PowerPoint PPT PresentationTRANSCRIPT
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SupreFine, a new supertree method
Shel SwensonSeptember 17th 2009
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Tree of Life challenges:Tree of Life challenges: - millions of species- millions of species - lots of missing data- lots of missing data
Reconstructing the Tree of Life
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Two possible approaches: - Combined Analysis - Supertree Methods
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Two competing approaches
gene 1 gene 2 . . . gene k
. . . Combined Analysis
Sp
ecie
s
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Combined Analysis Methods
gene 1S1
S2
S3
S4
S7
S8
TCTAATGGAA
GCTAAGGGAA
TCTAAGGGAA
TCTAACGGAA
TCTAATGGAC
TATAACGGAA
gene 3TATTGATACA
TCTTGATACC
TAGTGATGCA
CATTCATACC
TAGTGATGCA
S1
S3
S4
S7
S8
gene 2GGTAACCCTC
GCTAAACCTC
GGTGACCATC
GCTAAACCTC
S4
S5
S6
S7
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Combined Analysis gene 1
S1
S2
S3
S4
S5
S6
S7
S8
gene 2gene 3 TCTAATGGAA
GCTAAGGGAA
TCTAAGGGAA
TCTAACGGAA
TCTAATGGAC
TATAACGGAA
GGTAACCCTC
GCTAAACCTC
GGTGACCATC
GCTAAACCTC
TATTGATACA
TCTTGATACC
TAGTGATGCA
CATTCATACC
TAGTGATGCA
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. . .
Analyzeseparately
SupertreeMethod
Two competing approaches
gene 1 gene 2 . . . gene k
. . . Combined AnalysisS
pec
ies
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Why use supertree methods?
• Missing data
• Large dataset sizes
• Incompatible data types (e.g., morphological features, biomolecular sequences, gene orders, even distances based upon biochemistry)
• Unavailable sequence data (only trees)
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Many Supertree Methods
• MRP• weighted MRP• Min-Cut• Modified Min-Cut• Semi-strict Supertree
• MRF• MRD• QILI
• SDM• Q-imputation• PhySIC• Majority-Rule Supertrees
• Maximum Likelihood Supertrees
• and many more ...
Matrix Representation with Parsimony(Most commonly used and most accurate)
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Today’s Outline
• Supertree and combined analysis methods
• Why we need better supertree methods
• SuperFine: a new supertree method that is fast and more accurate than other supertree methods– Strict Consensus Merger (SCM)
– Resolving polytomies
– Performance of SuperFine (compared to MRP and combined anaylses)
– applications and future work
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gene 1 gene 2 . . . gene k
. . .
Ta
xa
Previous Simulation Studies
2. Generate sequence
data
1. Generate Model Tree
4. ConstructSource Trees
. . .
3. Select Subsets
5. Apply SupertreeMethod
6. Compare to Model Tree
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What does lead to missing data?
• Evolution (gain and loss of genes)
• Dataset selection
• Limited resources (time, money, etc.)
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My Simulation Study
1. Generate model trees (100-1000 taxa)
2. Simulate gene gain and loss and generate sequences
3. Simulate techniques for gene and taxon selection• Clade-based datasets
• Scaffold dataset
4. Generate source trees and a combined dataset
5. Apply supertree and combined analysis methods
6. Compare each estimated tree to the model tree, and record topological error
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Experimental Parameters
• Number of taxa in model tree: 100, 500, and 1000– Generate 5, 15 and 25 clade-based datasets, respectively
• Scaffold density: 20%, 50%, 75%, and 100%
• Six super-methods: – Combined analysis using ML and MP– MRP on ML and MP source trees– Weighted MRP on ML and MP source trees(MRP = Matrix Representation with Parsimony)
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A
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D E A
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Quantifying Topological Error
True Tree Estimated Tree
• False positive (FP): An edge in the estimated tree not in the true tree
• False negative (FN): An edge in the true tree missing from the estimated tree
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Comparison of MRP-ML and CA-ML(False Negative Rate)
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Scaffold Density (%)
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We still need supertree methods!
Combined analysis cannot be used for:
– Datasets that are very large
– Incompatible data types
– Unavailable sequence data
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Outline
• Supertree and combined analysis methods• Why we need better supertree methods
• SuperFine: a new supertree method that is fast and more accurate than other supertree methods– Strict Consensus Merger (SCM)
– Resolving polytomies
– Performance of SuperFine (compared to MRP and combined anaylses)
– applications and future work
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Methods that Led to SuperFine
• The Strict Consensus Merger (SCM) (Huson et al. 1999)
• Quartet MaxCut (QMC)(Snir and Rao
2008)
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Strict Consensus Merger (SCM)
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Theorem
Let S be a collection of source trees and T be a SCM tree on S.
Then for every s in S, ∑(T|L(s)) ∑(s), where T|L(s) is the induced subtree of T on the leafset of s.
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Intuition for the Theorem
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Performance of SCM
• Low false positive (FP) rate(Estimated supertree has few false edges)
• High false negative (FN) rate(Estimated supertree is missing many true edges)
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Methods that Led to SuperFine
• The Strict Consensus Merger (SCM) (Huson et al. 1999)
• Quartet MaxCut (QMC)(Snir and Rao
2008)
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Quartet MaxCut (QMC)
QMC is a heuristic for the following optimization problem:
Given a collection Q of quartet trees, find a supertree T, with leaf set L(T) = qQ L(q), that displays the maximum number of quartet trees in Q.
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• 12|34, 23|45, 34|56, 45|67 are compatible quartet trees with supertree
• Adding the quartet 17|23 creates an incompatible set of quartet trees. An “optimal” supertree would be the same as above, because it agrees with 4 out of 5 quartet trees.
Maximizing # of Quartet Trees Displayed
1
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5 6
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3 5
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1 3
424
5 7
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64
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QMC as a Supertree Method
• Step 1: Encode source trees as a set of quartets
• Step 2: Apply QMC
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Idea behind SuperFine
• First, construct a supertree with low false positives using SCM
The Strict Consensus Merger
• Then, refine the tree to reduce false negatives by resolving each polytomy using QMC Quartet Max Cut
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Resolving a single polytomy, v
• Step 1: Encode each source tree as a collection of quartet trees on {1,2,...,d}, where d=degree(v)
• Step 2: Apply Quartet MaxCut (Snir and Rao) to the collection of quartet trees, to produce a tree t on leafset {1,2,...,d}
• Step 3: Replace the star tree at v by tree t
Why?
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Back to Our Example
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Where We Use the Theorem
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For every s in S, ∑(T|L(s)) ∑(s)
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42 3
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Step 1: Encode each source tree as a collection of
quartet trees on {1,2,...,d}
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Step 2: Apply Quartet MaxCut (QMC) to the collection of
quartet trees
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1 4
56QMC
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Replace polytomy using tree from QMC
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False Negative Rate
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Scaffold Density (%)
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False Negative Rate
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Scaffold Density (%)
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False Positive Rate
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Scaffold Density (%)
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Running Time
SuperFine vs. MRP
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MRP 8-12 sec.SuperFine 2-3 sec.
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Scaffold Density (%) Scaffold Density (%)Scaffold Density (%)
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Observations
• SuperFine is much more accurate than MRP, with comparable performance only when the scaffold density is 100%
• SuperFine is almost as accurate as CA-ML
• SuperFine is extremely fast
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Future Work• Exploring algorithm design space for Superfine
– Different quartet encodings
– Not using SCM in Step 1
– Parallel version
– Post-processing step to minimize Sum-of-FN to source trees
• Using Superfine to enable phylogeny estimation– without an alignment
– on many marker combined datasets
• Using Superfine in conjunction with divide-and-conquer methods to create more accurate phylogenetic methods
• Exploration of impact of source tree collections (in particular the scaffold) on supertree analyses
• Revisiting specific biological supertrees