A practical algorithm for recovering the best supported edges of an evolutionary tree (extended abstract)

It is now routine for biologists to conduct evolutionary analyses of large DNA and protein sequence datasets. A computational bott leneck in these analyses is the recovery" of the topology of the evolutionary tree for a set of sequences. This paper presents a practical solution to this challenging problem. In particular, a new technique, called hypercleaning, is presented that can be combined with various tree-building algorithms to efficiently reconstruct from sequence da ta the best supported edges of the evolutionary tree. More precisely, the hypercleaning technique computes from sequence da ta a small subset of edges that is likely to contain most edges of the correct tree. A tree-building algorithm then a t tempts to identify edges in the subset that are compatible with each other and hereby produces an evolutionary tree. We also propose a simple greedy agorithm that builds a tree by *. -~4-d~ress: D~partement d'Informatique Fondamentale et Applications, LIRMM, Universit4 de Montpellier II, France. Part of this work was done at the D~partement de Math~matiques, EURISE, Universit~ de Saint-Etienne, France. E-mail: vberry@lirmm.fr tSupported in part by a Bioinformatics Postdoc Fellowship from the CIAR, Evolutionary Biology Program and by NSERC and CGAT grants to D. Sankoff. Address: CRM Universit~ de Montrdal. E-mail: bryantQcrm.umontreal. ca **Supported in part by NSERC Research Grant OGP0046613, a CITO grant, and a UCR startup grant. Department of Computer Science, University of California, Riverside, CA 92521. jiang@cs.ucr. edu. On leave from McMaster University. ~Supported in part by a CITO grant and NSERC Research Grant 160321. Address: Department of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. Email: pkearney@math.uwaterloo.ca ISupported in part by NSERC Research Grant OGP0046506, a CITO grant, and the Steacie Fellowship. Address: Department of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. E-mail: mli~math.uwaterloo.ca IIDepartment of Computer Science, Memorial University of Newfoundland, St. John's, NF AIB 3X5, Canada. Work done at McMaster University. Email: harold@garfield.cs. umn.edu **Department of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. E-mail: h2zbang~wh.math.uwaterloo.ca screening the edges provided by hypercleaning in the decreasing order of support from sequence data. This technique is a substantial improvement over previous algor i thms in its ability to recover edges of the evolutionary tree. Hypercleaning also incorporates a detailed error model tha t relates errors in the data to the topology of the evolutionary tree. The results of a simulation study that strongly support the practicality, efficiency and effectiveness of hypercleaning are also presented. 1 I n t r o d u c t i o n Advances in D N A sequencing technology this decade have resu l t ed in an exponen t i a l g rowth in the amoun t of sequence d a t a avai lable for biological analys is [8]. As a consequence, it is now rou t ine for biologists to c onduc t evo lu t i ona ry ana lyses of large sequence d a t a s e t s [16, 17, 21]. However , s t a n d a r d me thods for inferr ing evo lu t iona ry t rees f rom sequence da ta , such as m a x i m u m l ikel ihood [14] and m a x i m u m pa r s imony [26], a re p lagued by c o m p u t a t i o n a l difficulties. An e vo lu t i ona ry t ree T for a set S of sequences is a r oo t ed and edge weighted t ree where the leaves of T are l abe led b i jec t ive ly by S. The topo logy of T ( tha t is, T w i t h o u t edge weights) descr ibes the spec ia t ion events r esu l t ing in the evolu t ion of sequences in S from the root . The edge weights of T are p ropo r t i ona l to t he a m o u n t of evolu t ion (sequence subs t i tu t ions , inser t ions and dele t ions) be tween spec ia t ion events. Th i s p a p e r presen ts new insights on the difficult c o m p u t a t i o n a l p rob lem of de t e rmin ing the topology of an unknown evo lu t iona ry t ree T given only the set S of sequences t ha t label the leaves of T. This problem is of p rac t i ca l i m p o r t a n c e since once the topology of T is known, T can be roo ted and edge weights d e t e r m i n e d , resul t ing in a hypo thes i s descr ib ing the e vo lu t i ona ry h i s tory of the sequences in S. De te rmining the t o p o l o g y of T is cons idered to be the most difficult c o m p u t a t i o n a l s t ep in the recons t ruc t ion of T f rom S. I t is we l l -known t h a t t he topo logy of an evolut i ona ry t ree can be specif ied by its set of edgeinduced b ipa r t i t i ons . An evo lu t i ona ry t ree T l abe led by S