Phylogenetic invariants for stationary base composition

Journal of Symbolic Computation

Volumn 41, Issue 2, 2006, Pages 138-150

  Allman, Elizabeth S ^a,c   Rhodes, John A ^a,b  

^a UNIVERSITY OF SOUTHERN MAINE   (United States)

^b BATES COLLEGE   (United States)

^c UNIVERSITY OF ALASKA FAIRBANKS   (United States)

Author keywords

Algebraic statistics; Evolution; Phylogenetic invariants

Indexed keywords

EID: 29744457289     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2005.04.004     Document Type: Article

References (20)

1. E.S. Allman J.A. Rhodes Phylogenetic invariants for the general Markov model of sequence mutation Math. Biosci. 186 2003 113-144
2. Allman, E.S., Rhodes, J.A., 2004. Phylogenetic ideals and varieties for the general Markov model
3. J.A. Cavender J. Felsenstein Invariants of phylogenies in a simple case with discrete states J. Classification 4 1987 57-71
4. G.C. Conant P.O. Lewis Effects of nucleotide composition bias on the success of the parsimony criterion in phylogenetic inference Mol. Biol. Evol. 18 6 2001 1024-1033
5. S.N. Evans T.P. Speed Invariants of some probability models used in phylogenetic inference Ann. Statist. 21 1 1993 355-377
6. J. Felsenstein Inferring Phylogenies 2003 Sinauer Associates Sunderland, MA
7. I.M. Gel'fand M.M. Kapranov A.V. Zelevinsky Discriminants, resultants, and multidimensional determinants In: Mathematics: Theory & Applications 1994 Birkhäuser Boston Inc. Boston, MA
8. D.R. Grayson M.E. Stillman Macaulay 2, a software system for research in algebraic geometry 2002 Available at http://www.math.uiuc.edu/Macaulay2/
9. J. Harris Algebraic Geometry: A First Course 1992 Springer-Verlag New York
10. M.D. Hendy D. Penny Spectral analysis of phylogenetic data J. Classification 10 1993 1-20
11. N. Jacobson Lectures in Abstract Algbebra II. Linear Algebra 1975 Springer-Verlag New York
12. S. Kumar S.R. Gadagkar Disparity index: A simple statistic to measure and test the homogeneity of substitution patterns between molecular sequences Genetics 158 2001 1321-1327
13. J.A. Lake A rate independent technique for analysis of nucleic acid sequences: Evolutionary parsimony Mol. Bio. Evol. 4 1987 167-191
14. P.J. Lockhart M.A. Steel M.D. Hendy D. Penny Recovering evolutionary trees under a more realistic model of sequence evolution Mol. Biol. Evol. 11 4 1994 605-612
15. L. Pachter B. Sturmfels Tropical geometry of statistical models Proc. Natl. Acad. Sci. USA. 101 46 2004 16132-16137 arxiv:q-bio.GN/0401033
16. M.S. Rosenberg S. Kumar Heterogeneity of nucleotide frequencies among evolutionary lineages and phylogenetic inference Mol. Biol. Evol. 20 4 2003 610-621
17. J.G. Sumner P.D. Jarvis Entanglement invariants and phylogenetic branching J. Math. Biol. 51 1 2004 18-36 arXiv:q-bio.PE/0402007
18. M. Steel L. Székely P.L. Erdös P. Waddell A complete family of phylogenetic invariants for any number of taxa under Kimura's 3ST model N.Z. J. Botany 31 31 1993 289-296
19. M.A. Steel L. Székely M.D. Hendy Reconstructing trees from sequences whose sites evolve at variable rates J. Comput. Biol. 1 2 1994 153-163
20. B. Sturmfels S. Sullivant Toric ideals of phylogenetic invariants J. Comput. Biol. 12 2 2005 204-228 arXiv:q-PE/0402015