problems with large-scale phylogeny tandy warnow, ut-austin department of computer sciences center...

Problems with large-scale phylogeny

Tandy Warnow, UT-AustinDepartment of Computer SciencesCenter for Computational Biology

and Bioinformatics

Phylogeny

Orangutan Gorilla Chimpanzee Human

From the Tree of the Life Website,University of Arizona

DNA Sequence Evolution

AAGACTT

TGGACTTAAGGCCT

-3 mil yrs

-2 mil yrs

-1 mil yrs

today

AGGGCAT TAGCCCT AGCACTT

AAGGCCT TGGACTT

TAGCCCA TAGACTT AGCGCTTAGCACAAAGGGCAT


AAGACTT

TGGACTTAAGGCCT


AAGGCCT TGGACTT

AGCGCTTAGCACAATAGACTTTAGCCCAAGGGCAT

Molecular Systematics

TAGCCCA TAGACTT TGCACAA TGCGCTTAGGGCAT

U V W X Y

U

V W

X

Y

Quantifying Error

FN: false negative (missing edge)FP: false positive (incorrect edge)

50% error rate

FN

FP

Methods and Conjectures

• Popular methods: Neighbor-Joining (polynomial time, distance-based), heuristics for Maximum Parsimony and Maximum Likelihood

• Big debates about which is better, and when



• Big debates about which is better, and when• Our research shows: big differences between NJ

and MP, on large enough trees



• Big debates about which is better, and when• Our research shows: big differences between NJ

and MP, on large enough trees• Our research also shows that current techniques

(in the best software packages) can be sped up, to solve MP and ML faster.

Computational challenges for Assembling the Tree of Life

8 million species for the Tree of Life -- cannot currently analyze more than a few hundred (and even this takes years)

• We need new methods for inferring large phylogenies - hard optimization problems!

• We need new software for visualizing large trees• We need new database technology• Not all phylogenies are trees, so we need methods

for inferring phylogenetic networks

Our research projects

DCM-boosting phylogenetic reconstruction methods (improving the accuracy of NJ and speeding-up MP and ML)

Phylogenetic reconstruction from gene ordersReticulate evolution detection and

phylogenetic network reconstructionVisualization of large trees

DCM-boosting NJ

Outline: Convergence rates (how long do the

sequences need to be for methods to reconstruct the true tree with high probability?)

DCM-boosting Neighbor-JoiningExperimental study comparing DCM-NJ to

NJ on large trees

The Jukes-Cantor model of DNA sequence evolution

• A random DNA sequence evolves down the tree from the root

• The positions within the sequence evolve independently and identically

• If the nucleotide at a particular position changes on an edge, it changes with equal probability to the other nucleotides

The General Markov model of DNA sequence evolution

• A random DNA sequence evolves down the tree from the root

• The positions within the sequence evolve independently and identically (or under a distribution of rates across sites)

• Each edge has a 4x4 stochastic substitution matrix governing the evolution of a random site on the edge

Statistical Performance Issues

• Statistical consistency: does the reconstruction method return the true tree with high probability from long enough sequences?

• “Convergence Rate”: at what sequence length will the reconstruction method return the true tree with high probability?

• Robustness: if we violate the model conditions, what can we say about the performance of the method?

Absolute fast convergence vs. exponential convergence

Theoretical Comparison of Methods

• Theorem 1 [Warnow et al. 2001]DCMNJ is absolute fast converging for the GM model.

• Theorem 3 [Atteson 1999]NJ is exponentially converging for the GM model (but is not known to be afc).

DCM1: a divide-and-conquer strategy to improve NJ’s accuracy

Phase I: Basic step: Divide the dataset into many small diameter subproblems. Construct NJ trees on each subproblem, and merge subtrees, using the “Strict Consensus Merger”. Refine the resultant tree using PAUP*’s constrained search. Do the basic step for each way of setting the diameter.Phase II: Pick the “best tree” out of the set of O(n2) trees.

Strict Consensus Merger

1 2

3

4 65

1 2

37 4

1

3

2

4

1 2

3 4

1 2

3 4

1

2

3

4

5

6

7

DCM-Boosting [Warnow et al. 2001]

• DCM+SQS is a two-phase procedure which reduces the sequence length requirement of methods.

DCM SQSExponentiallyconvergingmethod

Absolute fast convergingmethod

• DCMNJ+SQS is the result of DCM-boosting NJ.• We can replace SQS by MP or ML, and get

better empirical performance (though not provably afc)

DCM-boosting Neighbor Joining

• DCM-boosting makes distance-based methods more accurate (we have established this for other distance-based methods, too)

NJDCM-NJ

0 400 800 16001200No. Taxa

0

0.2

0.4

0.6

0.8

Erro

r Rat

e

Summary of DCM-NJ

• These are the first polynomial time methods that improve upon NJ (with respect to topological accuracy) and are never worse than NJ.

• The advantage obtained with DCMNJ+MP and DCMNJ+ML increases with number of taxa, deviation from a molecular clock, and rate of evolution.

• In practice these new methods are slower than NJ (minutes vs. seconds), but still much faster than MP and ML (which can take days).

Time is a bottleneck for MP and ML

Phylogenetic trees

MP scoreGlobal optimum

Local optimum

• Systematists tend to prefer trees with the optimal maximum parsimony score or optimal maximum likelihood score; however, both problems are hard to solve

• (Our experimental studies show that NJ doesn’t do as well as MP when trees are big and have high rates of evolution, so NJ and other fast methods aren’t sufficiently reliable.)

MP/ML heuristics

Time

MP scoreof best trees

Performance of hill-climbing heuristic

Fake study

DCM-boosting Speeding up MP/ML heuristics

Time

MP scoreof best trees

Performance of hill-climbing heuristic

Desired Performance

Fake study

Maximum Parsimony

ACT

GTT ACA

GTA ACA ACT

GTAGTT

ACT

ACA

GTT

GTA

Maximum Parsimony

ACT

GTT

GTT GTA

ACA

GTA

12

2

MP score = 5

ACA ACT

GTAGTT

ACA ACT3 1 3

MP score = 7

ACT

ACA

GTT

GTAACA GTA1 2 1

MP score = 4

Optimal MP tree

Maximum Parsimony: computational complexity

ACT

ACA

GTT

GTAACA GTA

1 2 1

MP score = 4

Finding the optimal MP tree is NP-hard

Optimal labeling can becomputed in linear time O(nk)

The DCM technique for speeding up MP/ML searches

DCM2-MP/ML

• Step 1: pick a threshold at which the threshold graph is connected, and divide the dataset into two overlapping subsets.

• Step 2: Compute trees on each subset using a heuristic for MP or ML

• Step 3: Merge subtrees using the Strict Consensus Merger

• Step 4: Refine the resultant tree using PAUP* constrained search

DCM2 vs hill-climbing

Biological dataset of 388 rRNA sequences. Maximum subproblem size = 70%

What we see

• Some datasets decompose well, and DCM gives real advantage

• The bigger the dataset, and the more careful the heuristic search, the less good the decomposition has to be for DCM to give an advantage

• Outlier identification may help

Other projects (briefly)

• Gene order phylogeny: GRAPPA (our free software) is the fastest and most accurate software for reconstructing phylogenies from gene order and content data. Joint project with Bob Jansen (UT) and Bernard Moret (UNM), and others.

• Reticulate evolution inference. Our research shows no existing method for reconstructing networks work, and that methods (such as ILD) for detecting reticulation fail. Joint project with Randy Linder (UT) and Bernard Moret.

Acknowledgements

• Funding: The David and Lucile Packard Foundation, and The National Science Foundation.• Collaborators: Bernard Moret (UNM), Daniel Huson (Tubingen),

Lisa Vawter (Aventis), Katherine St. John (CUNY), Randy Linder (UT), Bob Jansen (UT)

• Students: Luay Nakhleh, Usman Roshan, Jerry Sun, and Li-San Wang

Phylolab, U. TexasPlease visit us athttp://www.cs.utexas.edu/users/phylo/

problems with large-scale phylogeny tandy warnow, ut-austin department of computer sciences center...

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