An algebraic analysis of the two state Markov model on tripod trees

Mathematical Biosciences - Tập 237 - Trang 38-48 - 2012
Steffen Klaere1, Volkmar Liebscher2
1Department of Statistics and School of Biological Sciences, The University of Auckland, Auckland, New Zealand
2Institut für Mathematik und Informatik, Universität Greifswald, Germany

Tài liệu tham khảo

Bryant, 2005, Likelihood calculation in molecular phylogenetics, 33

Lazarsfeld, 1968

Pearl, 1986, Structuring causal trees, J. Complexity, 2, 60, 10.1016/0885-064X(86)90023-3

Allman, 2009, Identifiability of parameters in latent structure models with many observed variables, Ann. Stat., 37, 3099, 10.1214/09-AOS689

Allman, 2008, Phylogenetic ideals and varieties for the general Markov model, Adv. Appl. Math., 40, 127, 10.1016/j.aam.2006.10.002

Allman, 2003, Phylogenetic invariants for the general Markov model of sequence mutation, Math. Biosci., 186, 113, 10.1016/j.mbs.2003.08.004

Baake, 1998, What can and what cannot be inferred from pairwise sequence comparisons?, Math. Biosci., 154, 1, 10.1016/S0025-5564(98)10044-5

Sturmfels, 2005, Toric ideals of phylogenetic invariants, J. Comput. Biol., 12, 457, 10.1089/cmb.2005.12.457

Evans, 1993, Invariants of some probability models used in phylogenetic inference, Ann. Stat., 21, 355, 10.1214/aos/1176349030

Sumner, 2009, Markov invariants and the isotropy subgroup of a quartet tree, J. Theor. Biol., 258, 302, 10.1016/j.jtbi.2009.01.021

Zwiernik, 2012, Tree-cumulants and the identifiability of binary tree models, Bernoulli, 18, 290, 10.3150/10-BEJ338

Yang, 2000, Complexity of the simplest phylogenetic estimation problem, Proc. Roy. Soc. B, 267, 109, 10.1098/rspb.2000.0974

Cavender, 1978, Taxonomy with confidence, Math. Biosci., 40, 271, 10.1016/0025-5564(78)90089-5

Farris, 1973, A probability model for inferring evolutionary trees, Syst. Zool., 22, 250, 10.2307/2412305

Neyman, 1971, Molecular studies of evolution: a source of novel statistical problems, 1

Hendy, 1989, A framework for the quantitative study of evolutionary trees, Syst. Zool., 38, 297, 10.2307/2992396

Rayner, 2009, Towards a better understanding of correlation, Stat. Neerl., 63, 324, 10.1111/j.1467-9574.2009.00425.x

Chor, 2000, Multiple maxima of likelihood in phylogenetic trees: an analytic approach, Mol. Biol. Evol., 17, 1529, 10.1093/oxfordjournals.molbev.a026252

Strimmer, 2000, Likelihood Analysis of Phylogenetic Networks Using Directed Graphical Models, Mol. Biol. Evol., 17, 875, 10.1093/oxfordjournals.molbev.a026367