SupreFine,%20a%20new%20supertree%20method

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SupreFine, a new supertree method

• Shel Swenson
• September 17th 2009

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Reconstructing the Tree of Life
Tree of Life challenges - millions of species
- lots of missing data
Two possible approaches - Combined Analysis -
Supertree Methods
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Two competing approaches
Species
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Combined Analysis Methods
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Combined Analysis
gene 2
gene 3
gene 1
S1
TCTAATGGAA
TATTGATACA
? ? ? ? ? ? ? ? ? ?
S2
GCTAAGGGAA
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
S3
TCTAAGGGAA
TCTTGATACC
? ? ? ? ? ? ? ? ? ?
S4
TCTAACGGAA
GGTAACCCTC
TAGTGATGCA
S5
GCTAAACCTC
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
S6
GGTGACCATC
? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
S7
TCTAATGGAC
GCTAAACCTC
TAGTGATGCA
S8
TATAACGGAA
CATTCATACC
? ? ? ? ? ? ? ? ? ?
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Two competing approaches
Species
Combined Analysis
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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 ...

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Todays Outline
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• 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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Previous Simulation Studies
1. Generate Model Tree
3. Select Subsets
2. Generate sequence data
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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

• Generate model trees (100-1000 taxa)
• Simulate gene gain and loss and generate
  sequences
• Simulate techniques for gene and taxon selection
• Clade-based datasets
• Scaffold dataset
• Generate source trees and a combined dataset
• Apply supertree and combined analysis methods
• 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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Quantifying Topological Error
True Tree
Estimated Tree
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Comparison of MRP-ML and CA-ML(False Negative
Rate)
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, ?(TL(s)) ? ?(s), where
  TL(s) is the induced subtree of T on the leafset
  of s.

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Corollary

• Let S be a collection of source trees, T be a SCM
  tree T on S, and let v be a vertex of T. Let T
  be a subtree of T rooted at a vertex u adjacent
  to v, such that v is not a vertex of T
• Then for every s in S, one of the following
  holds
• L(s) ? L(T)
• L(s) ? L(T) ?
• L(s) ? L(T) L(s) - L(T) ? ?(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) ?q?Q L(q), that
  displays the maximum number of quartet trees in
  Q.

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Maximizing of Quartet Trees Displayed

• 1234, 2345, 3456, 4567 are compatible quartet
  trees with supertree
• Adding the quartet 1723 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.

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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
  ddegree(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
For every s in S, ?(TL(s)) ? ?(s)
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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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QMC
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Theorem

• For each source tree, and each polytomy v of
  degree d, the encoding of each source tree with
  leaf labels 1,2,...,d is well-defined and
  produces no conflicting quartet trees.

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Replace polytomy using tree from QMC
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False Negative Rate
Scaffold Density ()
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False Negative Rate
Scaffold Density ()
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False Positive Rate
Scaffold Density ()
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Running Time
SuperFine vs. MRP
Scaffold Density ()
Scaffold Density ()
Scaffold Density ()
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Running Time
SuperFine vs. MRP
MRP 8-12 sec. SuperFine 2-3 sec.
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