Mean deep coalescence cost under exchangeable probability distributions

Discrete Applied Mathematics

Volumn 174, Issue , 2014, Pages 11-26

  Than, C V ^a   Rosenberg, N A ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Deep coalescence; Evolutionary models; Exchangeability; Lineage sorting; Phylogeny

Indexed keywords

BIOLOGY; COSTS; GENES; PROBABILITY DISTRIBUTIONS;

BALANCED TREES; EVOLUTIONARY MODELS; EXCHANGEABILITY; GENE TREE; NEW SPECIES; PHYLOGENY; YULE MODEL;

FORESTRY;

BIOLOGY; COSTS; FORESTRY; GENES;

EID: 84902285345     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2014.02.010     Document Type: Article

References (28)

1. D. Aldous Probability distributions on cladograms D. Aldous, R. Pemantle, Random Discrete Structures IMA Volumes in Mathematics and its Applications vol. 76 1996 Springer-Verlag New York 1 18
2. M.S. Bansal, J.G. Burleigh, and O. Eulenstein Efficient genome-scale phylogenetic analysis under the duplication-loss and deep coalescence cost models BMC Bioinformatics 11 2010 S42
3. M.G.B. Blum, and O. François On statistical tests of phylogenetic tree imbalance: the Sackin and other indicies revisited Math. Biosci. 195 2005 141 153
4. J.K.M. Brown Probabilities of evolutionary trees Syst. Biol. 43 1994 78 91
5. L.L. Cavalli-Sforza, and A.W.F. Edwards Phylogenetic analysis: models and estimation procedures Am. J. Hum. Genet. 19 1967 233 257
6. M. DeGiorgio, J. Syring, A.J. Eckert, A.I. Liston, R. Cronn, D.B. Neale, and N.A. Rosenberg An empirical evaluation of two-stage species tree inference strategies using a multilocus dataset from North American pines BMC Evol. Biol. 2014 in press
7. J.H. Degnan, and N.A. Rosenberg Gene tree discordance, phylogenetic inference and the multispecies coalescent Trends Ecol. Evol. 24 2009 332 340
8. J. Felsenstein The number of evolutionary trees Syst. Zool. 27 1978 27 33
9. G.W. Furnas The generation of random, binary unordered trees J. Classification 1 1984 187 233
10. R.L. Graham, D.E. Knuth, and O. Patashnik Concrete Mathematics: A Foundation for Computer Science second ed. 1994 Addison-Wesley Reading, Massachussetts
11. E.F. Harding The probabilities of rooted tree-shapes generated by random bifurcation Adv. Appl. Probab. 3 1971 44 77
12. J.F.C. Kingman On the genealogy of large populations J. Appl. Probab. 19A 1982 27 43
13. M. Kirkpatrick, and M. Slatkin Searching for evolutionary patterns in the shape of a phylogenetic tree Evolution 47 1993 1171 1181
14. R. Klein, and D. Wood On the path length of binary trees J. Assoc. Comput. Mach. 36 1989 280 289
15. D.E. Knuth The Art of Computer Programming Vol. 1: Fundamental Algorithms third ed. 1997 Addison-Wesley Reading, Massachussetts
16. H.T. Lin, J.G. Burleigh, and O. Eulenstein The Deep Coalescence Consensus Tree Problem is Pareto on Clusters Lecture Notes in Bioinformatics vol. 6674 2011 172 183
17. W.P. Maddison Gene trees in species trees Syst. Biol. 46 1997 523 536
18. W.P. Maddison, and L.L. Knowles Inferring phylogeny despite incomplete lineage sorting Syst. Biol. 55 2006 21 30
19. P. Pamilo, and M. Nei Relationships between gene trees and species trees Mol. Biol. Evol. 5 1988 568 583
20. J. Phipps The numbers of classifications Can. J. Bot. 54 1976 686 688
21. N.A. Rosenberg The shapes of neutral gene genealogies in two species: probabilities of monophyly, paraphyly, and polyphyly in a coalescent model Evolution 57 2003 1465 1477
22. M.J. Sackin "Good" and "bad" phenograms Syst. Zool. 21 1972 225 226
23. M. Steel, and A. McKenzie Properties of phylogenetic trees generated by Yule-type speciation models Math. Biosci. 170 2001 91 112
24. C. Than, and L. Nakhleh Species tree inference by minimizing deep coalescences PLoS Comput. Biol. 5 2009 e1000501
25. C.V. Than, and N.A. Rosenberg Consistency properties of species tree inference by minimizing deep coalescences J. Comput. Biol. 18 2011 1 15
26. C.V. Than, and N.A. Rosenberg Mathematical properties of the deep coalescence cost IEEE/ACM Trans. Comput. Biol. Bioinform. 10 2013 61 72
27. G.U. Yule A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis, F.R.S. Philos. Trans. R. Soc. Lond. Ser. B 213 1925 21 87
28. L. Zhang From gene trees to species trees II: species tree inference by minimizing deep coalescence events IEEE/ACM Trans. Comput. Biol. Bioinform. 8 2011 1685 1691