How to See a Tree for a Forest? Combining Phylogenetic Trees – Reasons, Methods, and Consequences Tanya Y. Berger-Wolf DIMACS 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 OrangutanChimpanzeeHumanGorilla

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 A B C D E A C B D E A B C D E + = Consensus is what many people say in chorus but do not believe as individuals Abba Eban ( ), Israeli diplomat In "The New Yorker," 23 Apr 1990

Consensus Methods: Strict McMorris et al. (83) E A B C D E A B C D E A B C D AB CD ABCD ABCDE AB ABC DE ABCDE BCD ABCD ABCDE Strict: contains clades common to all trees E A B C D

Consensus Methods: Majority Margush & McMorris (81), McMorris et al. (83), Barthelemy & McMorris (86) E A B C D E A B C D E A B C D AB CD ABCD ABCDE AB ABC DE ABCDE BCD ABCD ABCDE Majority: contains clades common to majority AB CD ABCDAB ABC DEBCD ABCD E A B C D

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 Design ATTCGGAAGCGATAGCTGA ATCGATCGATCGTATTACGT TAGCTAGTATGCAGCGGAG Biological dataset Run parsimony ratchet (PAUP*) 500 iterations, 5 repetitions Save the tree at each iteration Majority consensus of optimal trees (PAUP*) Output consensus tree … Optimal - best scoring trees in all repetitions Majority consensus of best and second best so far

Results

Online Consensus: Strict C(SC) = C(T i )  i=1 k C(SC i ) = C(T j ) = C(T j )  C(T i ) = C(SC i-1 )  C(T i )  j=1 i  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(T i ) s.t. c є C(T i )| > k — 2 C(M i ) C(M i-1 ) C(T i ) ∩ — ∩ 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 ProsCons 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 ProsCons 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 Constraints Constraints, 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 A B C D Consensus Methods: Greedy E A B C D E A B C D E A B C D AB CD ABCD ABCDE AB ABC DE ABCDE BCD ABCD ABCDE Greedy: resolves majority by adding compatible clades E A B C D AB CD ABCD E A B C D AB ABC DE E A B C D

Consensus Methods: AMT Phillips & Warnow (95) E A B C D E A B C D E A B C D AB CD ABCD ABCDE AB ABC DE ABCDE BCD ABCD ABCDE Asymmetric Median Tree: maximum (weighted) collection of compatible clades AB ABC ABCD BCD DE 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 ConstraintsStrict+ resMaj+ resGrdyAMTInput 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   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 ConstraintsStrict+ resMaj+ resGrdyAMTInput 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 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 ( ) "A little inaccuracy sometimes saves a ton of explanation." - H. H. Munro (Saki) ( )

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 n Design 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: n

Breeding a Target Animal Given k strings of length n Design an algorithm that Produces a target string With the smallest expected # matings Alg 1: breed for one trait at a time O(n lg n) Alg 2: breed the animals closest to the target O(n 2 )

Algorithm: One Trait at a Time AddOneTrait (11… , 00…010…0) x = 11…100…0 y = 00…010…0 While (y has < i+1 ones) do Mate x and y twice y = string with 1 in bit (i+1) Return y The Algorithm (e 1,e 2,…,e n ) x = e 1 For x = 2..n do x = AddOneTrait(x,e i )

More Realistic Breeding Gender Variable probability of outcome Deaths Minimize number of generations Goal: maximum diversity On-line: maintain the distribution