How to See a Tree for a Forest?How to See a Tree for a Forest?Combining Phylogenetic Trees – Combining Phylogenetic Trees –

Reasons, Methods, and ConsequencesReasons, Methods, and Consequences

Tanya Y. Berger-WolfDIMACS and UIC

The affinities of all the beings of the same class have sometimes been represented by a great tree… As buds give rise by growth to fresh buds, and these if vigorous, branch out and overtop on all

sides many a feeble branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken

branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications.

Charles Darwin, 1859

Phylogeny Reconstruction

Orangutan Chimpanzee HumanGorilla

Phylogeny Reconstruction Process

1. Get an estimate of evolutionary distance between species

2. Treat the species as a set of points with pairwise distance measure

3. Find a tree that optimizes{parsimony, likelihood, function of your choice}on that set of points

Phylogeny Reconstruction Problems

1. Get an estimate of evolutionary distance between species

2. Treat the species as a set of points with pairwise distance measure

3. Find a tree that optimizes{parsimony, likelihood, function of your choice}on that set of points

• DNA not sufficient for deep evolution and too simple• Genomes are better but no good distance measures• Other types of data are subjective and no good models• Constraints on possible topologies• Species are sampled not at the same level and frequency

so some points are “more equal than others”• Large datasets: efficient storage, query, and representation

Computational Pitfalls

• Resulting optimization problems are hard

• No good bounds

• Existing heuristics expensive on large datasets

• Same score – many topologies

• True tree is unknown

⇓When to stop and what to return?

Consensus Methods

ABCDE

ACBDE

ABCDE

+

=

Consensus is what many people say in chorus but do not believe as individuals

Abba Eban (1915 - 2002), Israeli diplomat In "The New Yorker," 23 Apr 1990

Consensus Methods: StrictMcMorris et al. (83)

E

ABCD

E

ABCD

E

ABCD

AB CD ABCDABCDE

AB ABC DEABCDE

BCD ABCDABCDE

Strict: contains clades common to all trees

E

ABCD

Consensus Methods: MajorityMargush & McMorris (81), McMorris et al. (83), Barthelemy & McMorris (86)

E

ABCD

E

ABCD

E

ABCD

AB CD ABCDABCDE

AB ABC DEABCDE

BCD ABCDABCDE

Majority: contains clades common to majority

AB CD ABCD AB ABC DE BCD ABCD

E

ABCD

Stopping Maximum Parsimony(joint work with T.Williams, B.M.E.Moret, U.Roshan, T.Warnow)

If return Majority Consensus of the top scoring trees how early can we stop without changing the outcome? What stopping criteria?

Biological datasets: •three567: “three-gene” (rbcL, atpB, and 18s) DNA sequences (Soltis et al., 2000)

•aster328: ITS RNA sequences from the plant Asteracaeae (Gutell Lab, ICMB, UT Austin)

•ocho854: rbcL DNA sequences (Goloboff, 1999)

•lipsc439: rDNA sequences of Eukaryotes (Goloboff, 1999)

•john921: Avian Cytochrome b DNA sequences (Johnson, 2001)

•eern476: Metazoan DNA sequences (Goloboff, 1999)

•will2000: Eukaryotic sRNA sequences (Gutell Lab, ICMB, UT Austin)

•rbcL500: rbcL DNA sequences (Rice et al., 1997)

•mari2594: rbcL DNA sequences (Kallerjo et al., 1998)

Experiment DesignATTCGGAAGCGATAGCTGAATCGATCGATCGTATTACGTTAGCTAGTATGCAGCGGAG

Biological dataset

Run parsimony ratchet (PAUP*)500 iterations, 5 repetitionsSave the tree at each iteration

Majority consensus ofoptimal trees (PAUP*)

Output consensus tree

…Optimal - best scoring treesin all repetitions

Majority consensus ofbest and second bestso far

Results

rbcl500

02468

10121416

0 50 100 150 200 250 300 350 400 450 500

Iteration

RF

rate

(%)

0.001

0.01

0.1

1

MP

Sco

re (%

)

Optimal-best MRC

Best-second best MRC

Score error (from optimal)

Results

aster328

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500

Iteration

RF

rat

e (%

)

0.001

0.01

0.1

1

MP

Sco

re (

%)

Optimal-best MRC

Best-second best MRC

Score error (from optimal)

rbcl500

02468

10121416

0 50 100 150 200 250 300 350 400 450 500

Iteration

RF

rat

e (%

)

0.001

0.01

0.1

1

MP

Sco

re (

%)

Optimal-best MRC

Best-second best MRC

Score error (from optimal)

ocho854

0

5

10

15

20

0 50 100 150 200 250 300 350 400 450 500

Iteration

RF

rat

e (%

)

0.0001

0.001

0.01

0.1

1

MP

Sco

re (

%)

Optimal-best MRC

Best-second best MRC

Score error (from optimal)

mari2594

0

5

10

15

20

0 50 100 150 200 250 300 350 400 450 500

Iteration

RF

rat

e (%

)

0.0001

0.001

0.01

0.1

1

MP

Sco

re (

%)

Optimal-best MRC

Best-second best MRC

Score error (from optimal)

Online Consensus: Strict

C(SC) = C(Ti)i=1

k

C(SCi) = C(Tj) = C(Tj) C(Ti) = C(SCi-1)C(Ti)j=1

ij=1

i-1

Running time for a new tree - θ (n) and is optimal

Online Consensus: Majority

Running time for a new tree - θ (n) and is optimal

c є C(M) if and only if |C(Ti) s.t. c є C(Ti)| > k—2

C(Mi) C(Mi-1) C(Ti)∩—

∩

• Maintain the set of clades so far with counters• Update counters for the previous majority and the new tree• Use good implementation of a dictionary data structure (Amenta et al, 2003)

Conclusions

• No need to work hard to get good enough trees?

• Work to get “good” (?) trees, not optimal

• Stopping criteria

• Consensus is not the best representation. What else?

• This is a wide open research area

Using a Different Path:Heterogeneous Data

(joint work with Tandy Warnow)

Heterogeneous Data

Molecular data: DNA and genomes

Pros Cons

• Have distance measure

• Unambiguous• Many characters

• No data for extinct species

• Difficulties with ancient evolutionary events

• Recombination, repeated evolution

Heterogeneous Data

Paleontological, morphological, geographical, historical data

Pros Cons

• Easy to sample• Sometimes is the

only available information

• Has been used for a century

• Character states hard to determine

• Genetic basis not known

• No distance measure• Subjective

Data As ConstraintsConstraints, not distance!• Positive: these species are together

(phylogenetic trees, presence of a morphological character)

• Negative: these species are not together (above + geography, fossils)

• Temporal: these events happened in this order (fossils, history)

• Frequency: this even happens more often than another (adaptation mechanisms)

E

ABCD

Consensus Methods: Greedy

E

ABCD

E

ABCD

E

ABCD

AB CD ABCDABCDE

AB ABC DEABCDE

BCD ABCDABCDE

Greedy: resolves majority by adding compatible clades

E

ABCD

AB CD ABCD

E

ABCD

AB ABC DE

E

ABCD

Consensus Methods: AMTPhillips & Warnow (95)

E

ABCD

E

ABCD

E

ABCD

AB CD ABCDABCDE

AB ABC DEABCDE

BCD ABCDABCDE

Asymmetric Median Tree: maximum (weighted) collection of compatible clades

ABABC

ABCD

BCDDE

CD

AB CD ABCD ABCDE

AB ABC ABCD ABCDE

AB CD ABCD ABCDE

Consensus of Positive Constraints

Formalize constraint, go through existing consensus methods, see if satisfies or can be extended

Positive Constraints Strict + res Maj + res Grdy AMT Input

All input have isomorphic T... all output have T One input has isomorphic T, no contradictions output have T All input have clade all output have One input has clade , no con- tradictions output have

ππ

ππ

Partially from Steel et al. 2000

1. a and b are separated by C

2. C is closer to a than b – same as positive

Negative Constraints Strict + res Maj + res Grdy AMT Input

All input have 1 .all output…. have 1 One input has 1, no contradictions output have 1

Consensus of Negative Constraints

More Conclusions

• Existing methods are insufficient

• (Consensus with respect to temporal, frequency constraints)

• Developing new methods that preserve 4 types of constraints

• Network phylogeny

• Error measure and evaluation of quality

• This is a wide open research area

Work was supported by the National Science Foundation postdoctoral

fellowship grant EIA 02-03584

Thank you

"The significant problems we face cannot be solved at the same level of thinking we were at when we created them."

- Albert Einstein (1879-1955)

"A little inaccuracy sometimes saves a ton of explanation."

- H. H. Munro (Saki) (1870-1916)

Controlled Breeding(joint work with Cris Moore and Jared Saia)

Given an initial population of animals design a mating strategy that achieves a

breeding goal (within shortest time)

Controlled Breeding: Background

• Conservation Biology and Agriculture

• Breeding strategies: designed and evaluated empirically or using stochastic time-step modeling

• Empirical evaluation – too slow!

• Stochastic modeling – mathematically and biologically inappropriate.

• Classic algorithm design problem

Breeding All Possible Animals

Given k binary strings of length nDesign an algorithm that Produces all possible strings With the smallest expected # matings

Greedy: mate two animals with the highest probability of producing new

Upper bound: 2.32•2n

Breeding a Target Animal

Given k strings of length nDesign an algorithm that Produces a target string With the smallest expected # matings

Alg 1: breed for one trait at a timeO(n lg n)

Alg 2: breed the animals closest to the target

O(n2)

Algorithm: One Trait at a TimeAddOneTrait (11…100...0, 00…010…0)

x = 11…100…0y = 00…010…0While (y has < i+1 ones) do

Mate x and y twicey = string with 1 in bit (i+1)

Return y

The Algorithm (e1,e2,…,en)x = e1

For x = 2..n dox = AddOneTrait(x,ei)

More Realistic Breeding

• Gender

• Variable probability of outcome

• Deaths

• Minimize number of generations

• Goal: maximum diversity

• On-line: maintain the distribution

•