Identifiability of Large Phylogenetic Mixture Models

Bulletin of Mathematical Biology

Volumn 74, Issue 1, 2012, Pages 212-231

  Rhodes, John A ^a   Sullivant, Seth ^b  

^a UNIVERSITY OF ALASKA FAIRBANKS   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Parameter identifiability; Phylogenetic mixture model

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; MOLECULAR EVOLUTION; PHYLOGENY; STATISTICAL MODEL;

EVOLUTION, MOLECULAR; MODELS, GENETIC; MODELS, STATISTICAL; PHYLOGENY;

EID: 84855863369     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-011-9672-2     Document Type: Article

References (33)

1. Allman, E. S., & Rhodes, J. A. (2003). Phylogenetic invariants for the general Markov model of sequence mutation. Mathematical Biosciences, 186(2), 113-144.
2. Allman, E. S., & Rhodes, J. A. (2006). The identifiability of tree topology for phylogenetic models, including covarion and mixture models. Journal of Computational Biology, 13(5), 1101-1113.
3. Allman, E. S., & Rhodes, J. A. (2008). Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites. Mathematical Biosciences, 211(1), 18-33.
4. Allman, E. S., & Rhodes, J. A. (2008). Phylogenetic ideals and varieties for the general Markov model. Advances in Applied Mathematics, 40(2), 127-148.
5. Allman, E. S., & Rhodes, J. A. (2009). The identifiability of covarion models in phylogenetics. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 6(1), 76-88.
6. Allman, E. S., Ané, C., & Rhodes, J. A. (2008). Identifiability of a Markovian model of molecular evolution with gamma-distributed rates. Advances in Applied Probability, 40, 229-249. arXiv: 0709. 0531.
7. Allman, E. S., Matias, C., & Rhodes, J. A. (2009). Identifiability of parameters in latent structure models with many observed variables. Annals of Statistics, 37(6A), 3099-3132.
8. Allman, E. S., Petrović, S., Rhodes, J. A., & Sullivant, S. (2010). Identifiability of two-tree mixtures for group-based models. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8(3), 710-722.
9. Allman, E. S., Matias, C., & Rhodes, J. A. (2011). Parameter identifiability in a class of random graph mixture models. Journal of Statistical Planning and Inference, 141, 1719-1736.
10. Chai, J., & Housworth, E. A. (2011, to appear). On Rogers's proof of identifiability for the GTR+Γ+I model. Systematic Biology.
11. Chang, J. T. (1996). Full reconstruction of Markov models on evolutionary trees: identifiability and consistency. Mathematical Biosciences, 137(1), 51-73.
12. Cox, D., Little, J., & O'Shea, D. (1997). Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra (2nd edn.). New York: Springer.
13. Degnan, J. H., & Salter, L. A. (2005). Gene tree distributions under the coalescent process. Evolution, 59, 24-37.
14. Eriksson, N. (2005). Tree construction using singular value decomposition. In Algebraic statistics for computational biology (pp. 347-358). New York: Cambridge University Press.
15. Felsenstein, J. (2004). Inferring phylogenies. Sunderland: Sinauer.
16. Huelsenbeck, J. P., & Suchard, M. A. (2007). A nonparametric method for accommodating and testing across-site rate variation. Systematic Biology, 56(6), 975-987.
17. Kim, J. (2000). Slicing hyperdimensional oranges: the geometry of phylogenetic estimation. Molecular Phylogenetics and Evolution, 17(1), 58-75.
18. Kruskal, J. B. (1976). More factors than subjects, tests and treatments: an indeterminacy theorem for canonical decomposition and individual differences scaling. Psychometrika, 41(3), 281-293.
19. Kruskal, J. B. (1977). Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra and Its Applications, 18(2), 95-138.
20. Landsberg, J. M. (2011). The geometry of tensors with applications. Manuscript.
21. Le, S. Q., Lartillot, N., & Gascuel, O. (2008). Phylogenetic mixture models for proteins. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 363, 3965-3976.
22. Matsen, F. A., & Steel, M. A. (2007). Phylogenetic mixtures on a single tree can mimic a tree of another topology. Systematic Biology, 56(5), 767-775.
23. Matsen, F. A., Mossel, E., & Steel, M. (2008). Mixed-up trees: the structure of phylogenetic mixtures. Bulletin of Mathematical Biology, 70(4), 1115-1139.
24. Mossel, E., & Vigoda, E. (2005). Phylogenetic MCMC algorithms are misleading on mixtures of trees. Science, 309, 2207-2209.
25. Pagel, M., & Meade, A. (2004). A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data. Systematic Biology, 53(4), 571-581.
26. Pagel, M., & Meade, A. (2005). Mixture models in phylogenetic inference. In O. Gascuel (Ed.), Mathematics of evolution and phylogeny (pp. 121-142). Oxford: Oxford University Press.
27. Rannala, B. (2002). Identifiability of parameters in MCMC Bayesian inference of phylogeny. Systematic Biology, 51(5), 754-760.
28. Rhodes, J. A. (2010). A concise proof of Kruskal's theorem on tensor decomposition. Linear Algebra and Its Applications, 432(7), 1818-1824.
29. Semple, C., & Steel, M. (2003). Oxford lecture series in mathematics and its applications: Vol. 24. Phylogenetics. Oxford: Oxford University Press.
30. Štefankovič, D., & Vigoda, E. (2007). Phylogeny of mixture models: Robustness of maximum likelihood and non-identifiable distributions. Journal of Computational Biology, 14(2), 156-189.
31. Strassen, V. (1983). Rank and optimal computation of generic tensors. Linear Algebra and Its Applications, 52/53, 645-685.
32. Wakeley, J. (2008). Coalescent theory. Greenwood Village: Roberts & Company.
33. Wang, H. C., Li, K., Susko, E., & Roger, A. J. (2008). A class frequency mixture model that adjusts for site-specific amino acid frequencies and improves inference of protein phylogeny. BMC Evolutionary Biology, 8, 331.