2019
DOI: 10.1016/j.aim.2018.11.021
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Phylogenetic complexity of the Kimura 3-parameter model

Abstract: In algebraic statistics, the Kimura 3-parameter model is one of the most interesting and classical phylogenetic models. We prove that the ideals associated to this model are generated in degree four, confirming a conjecture by Sturmfels and Sullivant.

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Cited by 7 publications
(4 citation statements)
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References 41 publications
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“…1.10 (Guindon and Gascuel, 2003;Darriba et al, 2012). The three-parameter model 2 with gamma distribution (TPM2+G) (Michalek and Ventura, 2019) was chosen for the 18S rDNA sequences and Tamura-Nei with gamma distribution (TrN +G) (Tamura and Nei, 1993) for the cox1. Phylogenetic trees were generated using the package Bayesian Evolutionary Analysis by Sampling Trees (BEAST v1.10.4) (Bouckaert et al, 2019), and an.xml input file was created with Bayesian Evolutionary Analysis Utility (BEAUti v1.10.4) with 10 7 Markov chain Monte Carlo (MCMC) generations and a burn-in length of 10 3 .…”
Section: Phylogenetic and Species Delimitation Analysesmentioning
confidence: 99%
“…1.10 (Guindon and Gascuel, 2003;Darriba et al, 2012). The three-parameter model 2 with gamma distribution (TPM2+G) (Michalek and Ventura, 2019) was chosen for the 18S rDNA sequences and Tamura-Nei with gamma distribution (TrN +G) (Tamura and Nei, 1993) for the cox1. Phylogenetic trees were generated using the package Bayesian Evolutionary Analysis by Sampling Trees (BEAST v1.10.4) (Bouckaert et al, 2019), and an.xml input file was created with Bayesian Evolutionary Analysis Utility (BEAUti v1.10.4) with 10 7 Markov chain Monte Carlo (MCMC) generations and a burn-in length of 10 3 .…”
Section: Phylogenetic and Species Delimitation Analysesmentioning
confidence: 99%
“…Codon positions included in the analyses were 1st + 2nd + 3rd + Noncoding. During phylogenetic analysis of the three genes, Kimura 3 parameter and Jukes-Cantor evolutionary models were followed [36,37]. The models assumed the rates and patterns of substitution were uniform among the four nucleotide sites.…”
Section: Phylogenetic Analysismentioning
confidence: 99%
“…As described above, we are interested in the geometry of network-based Markov models, in particular, their dimensions. Such work is along the lines of Sturmfels and Sullivant ( 2005 ), Eriksson et al ( 2005 ), Allman and Rhodes ( 2007 ), Allman and Rhodes ( 2008 ), Casanellas and Fernández-Sánchez ( 2008 ), Zwiernik and Smith ( 2011 ), Casanellas and Fernández-Sánchez ( 2011 ), Michałek ( 2011 ), Casanellas et al ( 2017 ), Michałek and Ventura ( 2019 ), and Casanellas et al ( 2021 ), which study the geometry of tree-based Markov models. Indeed, by moving to and taking Zariski closures, images of the parameterization maps correspond to algebraic varieties whose study can aid in model selection (see Pachter and Strumfels ( 2005 ), Drton et al ( 2009 ), and Sullivant ( 2018 ) for discussions).…”
Section: Introductionmentioning
confidence: 99%