Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges
Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree...
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| Veröffentlicht in: | Random structures & algorithms Jg. 40; H. 3; S. 350 - 384 |
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| Abstract | Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stochastic models of evolution. The fast converging reconstruction algorithms introduced in the last decade dramatically reduced the sequence length required to guarantee accurate reconstruction of the entire tree. However, if the tree in question contains even few edges which cannot be reliably reconstructed from the input sequences, then known fast converging algorithms may fail to reliably reconstruct all or most of the other edges. This calls for an adaptive approach suggested in this paper, called adaptive fast convergence, in which the set of edges which can be reliably reconstructed gradually increases with the amount of information (length of input sequences) available to the algorithm.
This paper presents an adaptive fast converging algorithm which returns a partially resolved topology containing no false edges: edges that cannot be reliably reconstructed are contracted into high degree vertices. We also present an upper bound on the weights of those contracted edges, which is determined by the length of input sequences and the depth of the tree. As such, the reconstruction guarantee provided by our algorithm for individual edges is significantly stronger than any previously published edge reconstruction guarantee. This fact, together with the optimal complexity of our algorithm (linear space and quadratic‐time), makes it appealing for practical use. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 350–384, 2011 |
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| AbstractList | Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stochastic models of evolution. The
fast converging
reconstruction algorithms introduced in the last decade dramatically reduced the sequence length required to guarantee accurate reconstruction of the entire tree. However, if the tree in question contains even few edges which cannot be reliably reconstructed from the input sequences, then known fast converging algorithms may fail to reliably reconstruct all or most of the other edges. This calls for an adaptive approach suggested in this paper, called
adaptive
fast convergence, in which the set of edges which can be reliably reconstructed gradually increases with the amount of information (length of input sequences) available to the algorithm.
This paper presents an adaptive fast converging algorithm which returns a partially resolved topology containing no false edges: edges that cannot be reliably reconstructed are contracted into high degree vertices. We also present an upper bound on the weights of those contracted edges, which is determined by the length of input sequences and the depth of the tree. As such, the reconstruction guarantee provided by our algorithm for individual edges is significantly stronger than any previously published edge reconstruction guarantee. This fact, together with the optimal complexity of our algorithm (linear space and quadratic‐time), makes it appealing for practical use. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 350–384, 2011 Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stochastic models of evolution. The fast converging reconstruction algorithms introduced in the last decade dramatically reduced the sequence length required to guarantee accurate reconstruction of the entire tree. However, if the tree in question contains even few edges which cannot be reliably reconstructed from the input sequences, then known fast converging algorithms may fail to reliably reconstruct all or most of the other edges. This calls for an adaptive approach suggested in this paper, called adaptive fast convergence, in which the set of edges which can be reliably reconstructed gradually increases with the amount of information (length of input sequences) available to the algorithm. This paper presents an adaptive fast converging algorithm which returns a partially resolved topology containing no false edges: edges that cannot be reliably reconstructed are contracted into high degree vertices. We also present an upper bound on the weights of those contracted edges, which is determined by the length of input sequences and the depth of the tree. As such, the reconstruction guarantee provided by our algorithm for individual edges is significantly stronger than any previously published edge reconstruction guarantee. This fact, together with the optimal complexity of our algorithm (linear space and quadratic‐time), makes it appealing for practical use. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 350–384, 2011 |
| Author | Gronau, Ilan Snir, Sagi Moran, Shlomo |
| Author_xml | – sequence: 1 givenname: Ilan surname: Gronau fullname: Gronau, Ilan organization: Department of Computer Science, Technion - Israel Institute of Technology, Haifa, 32000 Israel – sequence: 2 givenname: Shlomo surname: Moran fullname: Moran, Shlomo email: gronau@gmail.com; moran@cs.technion.ac.il organization: Department of Computer Science, Technion - Israel Institute of Technology, Haifa, 32000 Israel – sequence: 3 givenname: Sagi surname: Snir fullname: Snir, Sagi email: ssagi@research.haifa.ac.il organization: Department of Evolutionary and Environmental Biology and The Institute of Evolution, University of Haifa Mount Carmel, Haifa 31905 Israel |
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| Cites_doi | 10.1016/S0304-3975(99)00028-6 10.1007/978-3-642-02008-7_32 10.2307/2412305 10.1016/0022-5193(77)90351-4 10.1016/B978-1-4832-3211-9.50009-7 10.1089/10665270252935467 10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.0.CO;2-R 10.1090/S0002-9947-03-03382-8 10.1016/0025-5564(81)90043-2 10.1137/S0097539798342496 10.1089/106652799318337 10.1007/BF01731581 10.1016/B978-0-12-307550-5.50005-8 10.1016/0025-5564(78)90089-5 10.1007/PL00008277 10.1016/j.mbs.2005.11.003 10.1007/11732990_24 10.1016/j.jtbi.2009.05.028 10.1109/TCBB.2007.1010 10.1093/oso/9780198566106.003.0014 10.1016/0020-0190(89)90216-0 10.1145/1132516.1132540 10.1007/978-0-387-21736-9 10.1137/S089548010138790X |
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| References_xml | – reference: K. Zaretskii, Constructing a tree on the basis of a set of distances between the hanging vertices, Uspekhi Mat Nauk 20 ( 1965), 90-92, [in Russian]. – reference: M. Waterman, T. Smith, M. Singh, W. Beyer, Additive evolutionary trees, J Theor Biol 64 ( 1977), 199-213. – reference: N. Saitou, M. Nei, The neighbor-joining method: A new method for reconstructing phylogenetic trees, Mol Biol Evol 4 ( 1987), 406-425. – reference: T. Cormen, C. Leiserson, R. Rivest, C. Stein, Introduction to algorithms, 2nd edition, MITP, 2001. – reference: M. Kimura, A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences, J Mol Evol 16 ( 1980), 111-120. – reference: F. Robinson, R. Foulds, Comparison of phylogenetic trees, Math Biosci 53 ( 1981), 131-147. – reference: M. Lacey, J. Chang, A signal-to-noise analysis of phylogeny estimation by neighbor-joining: Insufficiency of polynomial length sequences, Math Biosci 199 ( 2006), 188-215. – reference: M. Cryan, L. Goldberg, P. Goldberg, Evolutionary trees can be learned in polynomial time in the two-state general markov model, SIAM J Comput 31 ( 2001), 375-397. – reference: I. Gronau, S. Moran, I. Yavneh, Towards optimal distance functions for stochastic substitution models, J Theor Biol 260 ( 2009), 294-307. – reference: E. Mossel, Distorted metrics on trees and phylogenetic forests, IEEE/ACM Trans Comput Biol Bioinform 4 ( 2007), 108-116. – reference: J. Cavender, Taxonomy with confidence, Math Biosci 40 ( 1978), 271-280. – reference: M. Steel, L. Szekely, Inverting random functions II: Explicit bounds for discrete maximum likelihood estimation, with applications, SIAM J Discrete Math 15 ( 2002), 562-575. – reference: M. Csürös, Fast recovery of evolutionary trees with thousands of nodes, J Comput Biol 9 ( 2002), 277-297. – reference: J. Culberson, P. Rudnicki, A fast algorithm for constructing trees from distance matrices, Inform Process Lett 30 ( 1989), 215-220. – reference: E. Mossel, Phase transitions in phylogeny, Trans Am Math Soc 356 ( 2004), 2379-2404. – reference: K. Atteson, The performance of neighbor-joining methods of phylogenetic reconstruction, Algorithmica 25 ( 1999), 251-278. – reference: L. Wasserman, All of statistics, Springer, New York, 2004. – reference: P. L. Erdös, M. A. Steel, L. A. Szekely, T. J. Warnow, A few logs suffice to build (almost) all trees (II), Theoret Comput Sci 221 ( 1999), 77-118. – reference: J. Farris, A probability model for inferring evolutionary trees, System Zool 22 ( 1973), 250-256. – reference: D. Huson, S. Nettles, T. Warnow, Disk-Covering, a fast-converging method for phylogenetic tree reconstruction, J Comput Biol 6 ( 1999), 369-386. – reference: P. L. Erdös, M. A. Steel, L. A. Szekely, T. J. Warnow, A few logs suffice to build (almost) all trees (I), Random Struct Algorithm 14 ( 1999), 153-184. – reference: J. Felsenstein, Inferring phylogenies, Sinauer Associated, Inc., Sunderland, MA, 2004. – volume: 260 start-page: 294 year: 2009 end-page: 307 article-title: Towards optimal distance functions for stochastic substitution models publication-title: J Theor Biol – volume: 22 start-page: 250 year: 1973 end-page: 256 article-title: A probability model for inferring evolutionary trees publication-title: System Zool – start-page: 729 year: 2008 end-page: 738 – start-page: 444 year: 2003 end-page: 453 – year: 2001 – volume: 40 start-page: 271 year: 1978 end-page: 280 article-title: Taxonomy with confidence publication-title: Math Biosci – start-page: 186 year: 2001 end-page: 195 – start-page: 1 year: 1971 end-page: 27 – volume: 4 start-page: 108 year: 2007 end-page: 116 article-title: Distorted metrics on trees and phylogenetic forests publication-title: IEEE/ACM Trans Comput Biol Bioinform – volume: 199 start-page: 188 year: 2006 end-page: 215 article-title: A signal‐to‐noise analysis of phylogeny estimation by neighbor‐joining: Insufficiency of polynomial length sequences publication-title: Math Biosci – start-page: 384 year: 2005 end-page: 412 – volume: 14 start-page: 153 year: 1999 end-page: 184 article-title: A few logs suffice to build (almost) all trees (I) publication-title: Random Struct Algorithm – volume: 15 start-page: 562 year: 2002 end-page: 575 article-title: Inverting random functions II: Explicit bounds for discrete maximum likelihood estimation, with applications publication-title: SIAM J Discrete Math – volume: 9 start-page: 277 year: 2002 end-page: 297 article-title: Fast recovery of evolutionary trees with thousands of nodes publication-title: J Comput Biol – start-page: 451 year: 2009 end-page: 465 – start-page: 159 year: 2006 end-page: 168 – volume: 64 start-page: 199 year: 1977 end-page: 213 article-title: Additive evolutionary trees publication-title: J Theor Biol – volume: 356 start-page: 2379 year: 2004 end-page: 2404 article-title: Phase transitions in phylogeny publication-title: Trans Am Math Soc – volume: 6 start-page: 369 year: 1999 end-page: 386 article-title: Disk‐Covering, a fast‐converging method for phylogenetic tree reconstruction publication-title: J Comput Biol – start-page: 21 year: 1969 end-page: 132 – volume: 30 start-page: 215 year: 1989 end-page: 220 article-title: A fast algorithm for constructing trees from distance matrices publication-title: Inform Process Lett – year: 2008 – volume: 25 start-page: 251 year: 1999 end-page: 278 article-title: The performance of neighbor‐joining methods of phylogenetic reconstruction publication-title: Algorithmica – start-page: 281 year: 2006 end-page: 295 – year: 2004 – volume: 20 start-page: 90 year: 1965 end-page: 92 article-title: Constructing a tree on the basis of a set of distances between the hanging vertices publication-title: Uspekhi Mat Nauk – volume: 53 start-page: 131 year: 1981 end-page: 147 article-title: Comparison of phylogenetic trees publication-title: Math Biosci – volume: 31 start-page: 375 year: 2001 end-page: 397 article-title: Evolutionary trees can be learned in polynomial time in the two‐state general markov model publication-title: SIAM J Comput – volume: 221 start-page: 77 year: 1999 end-page: 118 article-title: A few logs suffice to build (almost) all trees (II) publication-title: Theoret Comput Sci – start-page: 387 year: 1971 end-page: 395 – volume: 16 start-page: 111 year: 1980 end-page: 120 article-title: A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences publication-title: J Mol Evol – volume: 4 start-page: 406 year: 1987 end-page: 425 article-title: The neighbor‐joining method: A new method for reconstructing phylogenetic trees publication-title: Mol Biol Evol – ident: e_1_2_12_13_2 doi: 10.1016/S0304-3975(99)00028-6 – ident: e_1_2_12_11_2 doi: 10.1007/978-3-642-02008-7_32 – ident: e_1_2_12_14_2 doi: 10.2307/2412305 – ident: e_1_2_12_34_2 doi: 10.1016/0022-5193(77)90351-4 – ident: e_1_2_12_19_2 doi: 10.1016/B978-1-4832-3211-9.50009-7 – ident: e_1_2_12_7_2 doi: 10.1089/10665270252935467 – ident: e_1_2_12_12_2 doi: 10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.0.CO;2-R – ident: e_1_2_12_25_2 doi: 10.1090/S0002-9947-03-03382-8 – start-page: 444 volume-title: In SODA: ACM‐SIAM Symposium on Discrete Algorithms year: 2003 ident: e_1_2_12_21_2 – ident: e_1_2_12_29_2 doi: 10.1016/0025-5564(81)90043-2 – ident: e_1_2_12_6_2 doi: 10.1137/S0097539798342496 – start-page: 387 volume-title: Mathematics in the Archeological and Historical Sciences year: 1971 ident: e_1_2_12_3_2 – ident: e_1_2_12_18_2 doi: 10.1089/106652799318337 – ident: e_1_2_12_20_2 doi: 10.1007/BF01731581 – start-page: 186 volume-title: In SODA: ACM‐SIAM Symposium on Discrete Algorithms year: 2001 ident: e_1_2_12_24_2 – ident: e_1_2_12_28_2 doi: 10.1016/B978-0-12-307550-5.50005-8 – ident: e_1_2_12_4_2 doi: 10.1016/0025-5564(78)90089-5 – volume: 20 start-page: 90 year: 1965 ident: e_1_2_12_35_2 article-title: Constructing a tree on the basis of a set of distances between the hanging vertices publication-title: Uspekhi Mat Nauk – start-page: 729 volume-title: In IEEE Symposium on Foundations of Computer Science (FOCS), Philadelphia, PA year: 2008 ident: e_1_2_12_30_2 – ident: e_1_2_12_2_2 doi: 10.1007/PL00008277 – volume-title: Introduction to algorithms year: 2001 ident: e_1_2_12_5_2 – ident: e_1_2_12_22_2 doi: 10.1016/j.mbs.2005.11.003 – ident: e_1_2_12_16_2 – ident: e_1_2_12_9_2 doi: 10.1007/11732990_24 – ident: e_1_2_12_17_2 doi: 10.1016/j.jtbi.2009.05.028 – volume-title: Inferring phylogenies year: 2004 ident: e_1_2_12_15_2 – ident: e_1_2_12_26_2 doi: 10.1109/TCBB.2007.1010 – start-page: 384 volume-title: Mathematics of evolution and phylogeny, Chapter 14 year: 2005 ident: e_1_2_12_27_2 doi: 10.1093/oso/9780198566106.003.0014 – ident: e_1_2_12_8_2 doi: 10.1016/0020-0190(89)90216-0 – ident: e_1_2_12_10_2 doi: 10.1145/1132516.1132540 – ident: e_1_2_12_23_2 – ident: e_1_2_12_33_2 doi: 10.1007/978-0-387-21736-9 – volume: 4 start-page: 406 year: 1987 ident: e_1_2_12_31_2 article-title: The neighbor‐joining method: A new method for reconstructing phylogenetic trees publication-title: Mol Biol Evol – ident: e_1_2_12_32_2 doi: 10.1137/S089548010138790X |
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| Snippet | Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA)... |
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| SubjectTerms | adaptive fast converging fast converging optimal time algorithms phylogenetic reconstruction |
| Title | Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges |
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| Volume | 40 |
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