Sumner, Jeremy G.; Woodhams, Michael D. Lie-Markov models derived from finite semigroups. (English) Zbl 1411.60113 Bull. Math. Biol. 81, No. 2, 361-383 (2019). MSC: 60J27 22E60 92D15 60J28 PDFBibTeX XMLCite \textit{J. G. Sumner} and \textit{M. D. Woodhams}, Bull. Math. Biol. 81, No. 2, 361--383 (2019; Zbl 1411.60113) Full Text: DOI arXiv
Bergman, Juraj; Schrempf, Dominik; Kosiol, Carolin; Vogl, Claus Inference in population genetics using forward and backward, discrete and continuous time processes. (English) Zbl 1397.92449 J. Theor. Biol. 439, 166-180 (2018). MSC: 92D10 92D15 60J20 60J70 PDFBibTeX XMLCite \textit{J. Bergman} et al., J. Theor. Biol. 439, 166--180 (2018; Zbl 1397.92449) Full Text: DOI Link
Roch, Sebastien; Sly, Allan Phase transition in the sample complexity of likelihood-based phylogeny inference. (English) Zbl 1379.92041 Probab. Theory Relat. Fields 169, No. 1-2, 3-62 (2017). MSC: 92D15 60J20 92D10 PDFBibTeX XMLCite \textit{S. Roch} and \textit{A. Sly}, Probab. Theory Relat. Fields 169, No. 1--2, 3--62 (2017; Zbl 1379.92041) Full Text: DOI arXiv
Sumner, Jeremy G.; Taylor, Amelia; Holland, Barbara R.; Jarvis, Peter D. Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants. (English) Zbl 1383.92056 J. Math. Biol. 75, No. 6-7, 1619-1654 (2017). MSC: 92D15 92B10 62P10 60J20 PDFBibTeX XMLCite \textit{J. G. Sumner} et al., J. Math. Biol. 75, No. 6--7, 1619--1654 (2017; Zbl 1383.92056) Full Text: DOI arXiv
Sumner, Jeremy G. Dimensional reduction for the general Markov model on phylogenetic trees. (English) Zbl 1373.92092 Bull. Math. Biol. 79, No. 3, 619-634 (2017). MSC: 92D15 60J20 PDFBibTeX XMLCite \textit{J. G. Sumner}, Bull. Math. Biol. 79, No. 3, 619--634 (2017; Zbl 1373.92092) Full Text: DOI arXiv
Jarvis, Peter D.; Sumner, Jeremy G. Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model. (English) Zbl 1343.92352 J. Math. Biol. 73, No. 2, 259-282 (2016); correction ibid. 82, No. 7, Paper No. 68, 1 p. (2021). MSC: 92D15 05E05 20G05 17B45 60J20 PDFBibTeX XMLCite \textit{P. D. Jarvis} and \textit{J. G. Sumner}, J. Math. Biol. 73, No. 2, 259--282 (2016; Zbl 1343.92352) Full Text: DOI arXiv
Privault, Nicolas; Guindon, Stéphane Closed form modeling of evolutionary rates by exponential Brownian functionals. (English) Zbl 1354.92054 J. Math. Biol. 71, No. 6-7, 1387-1409 (2015). Reviewer: Fatima T. Adylova (Tashkent) MSC: 92D15 60J65 60J70 PDFBibTeX XMLCite \textit{N. Privault} and \textit{S. Guindon}, J. Math. Biol. 71, No. 6--7, 1387--1409 (2015; Zbl 1354.92054) Full Text: DOI
Fernández-Sánchez, Jesús; Sumner, Jeremy G.; Jarvis, Peter D.; Woodhams, Michael D. Lie Markov models with purine/pyrimidine symmetry. (English) Zbl 1339.60111 J. Math. Biol. 70, No. 4, 855-891 (2015). MSC: 60J27 60J28 22E60 62P10 92D15 92D20 52B99 PDFBibTeX XMLCite \textit{J. Fernández-Sánchez} et al., J. Math. Biol. 70, No. 4, 855--891 (2015; Zbl 1339.60111) Full Text: DOI arXiv
Sumner, J. G.; Fernández-Sánchez, J.; Jarvis, P. D. Lie Markov models. (English) Zbl 1397.92515 J. Theor. Biol. 298, 16-31 (2012). MSC: 92D15 60J20 PDFBibTeX XMLCite \textit{J. G. Sumner} et al., J. Theor. Biol. 298, 16--31 (2012; Zbl 1397.92515) Full Text: DOI arXiv
Asmussen, Søren; Hobolth, Asger Markov bridges, bisection and variance reduction. (English) Zbl 1272.60057 Plaskota, Leszek (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2010. Selected papers based on the presentations at the 9th international conference on Monte Carlo and quasi Monte Carlo in scientific computing (MCQMC 2010), Warsaw, Poland, August 15–20, 2010. Berlin: Springer (ISBN 978-3-642-27439-8/hbk; 978-3-642-27440-4/ebook). Springer Proceedings in Mathematics & Statistics 23, 3-22 (2012). MSC: 60J75 60J22 PDFBibTeX XMLCite \textit{S. Asmussen} and \textit{A. Hobolth}, Springer Proc. Math. Stat. 23, 3--22 (2012; Zbl 1272.60057) Full Text: DOI Link
Sainudiin, Raazesh; Thornton, Kevin; Harlow, Jennifer; Booth, James; Stillman, Michael; Yoshida, Ruriko; Griffiths, Robert; McVean, Gil; Donnelly, Peter Experiments with the site frequency spectrum. (English) Zbl 1220.62141 Bull. Math. Biol. 73, No. 4, 829-872 (2011). MSC: 62P10 92D10 60J22 92C40 65C60 92D15 PDFBibTeX XMLCite \textit{R. Sainudiin} et al., Bull. Math. Biol. 73, No. 4, 829--872 (2011; Zbl 1220.62141) Full Text: DOI
de Oliveira Martins, Leonardo; Kishino, Hirohisa Distribution of distances between topologies and its effect on detection of phylogenetic recombination. (English) Zbl 1422.62323 Ann. Inst. Stat. Math. 62, No. 1, 145-159 (2010). MSC: 62P10 60J85 92D15 PDFBibTeX XMLCite \textit{L. de Oliveira Martins} and \textit{H. Kishino}, Ann. Inst. Stat. Math. 62, No. 1, 145--159 (2010; Zbl 1422.62323) Full Text: DOI
Chen, Gong; Zhou, Qing Heterogeneity in DNA multiple alignments: modeling, inference, and applications in motif finding. (English) Zbl 1203.62184 Biometrics 66, No. 3, 694-704 (2010). MSC: 62P10 92C40 62F15 92D10 65C60 60J20 90C90 PDFBibTeX XMLCite \textit{G. Chen} and \textit{Q. Zhou}, Biometrics 66, No. 3, 694--704 (2010; Zbl 1203.62184) Full Text: DOI Link
Yap, V. B. Similar states in continuous-time Markov chains. (English) Zbl 1170.60329 J. Appl. Probab. 46, No. 2, 497-506 (2009). MSC: 60J27 60J35 92D20 PDFBibTeX XMLCite \textit{V. B. Yap}, J. Appl. Probab. 46, No. 2, 497--506 (2009; Zbl 1170.60329) Full Text: DOI
Minin, Vladimir N.; Suchard, Marc A. Counting labeled transitions in continuous-time Markov models of evolution. (English) Zbl 1145.60323 J. Math. Biol. 56, No. 3, 391-412 (2008). MSC: 60J27 92D15 92D20 PDFBibTeX XMLCite \textit{V. N. Minin} and \textit{M. A. Suchard}, J. Math. Biol. 56, No. 3, 391--412 (2008; Zbl 1145.60323) Full Text: DOI
Lladser, Manuel E.; Betterton, M. D.; Knight, Rob Multiple pattern matching: a Markov chain approach. (English) Zbl 1147.65005 J. Math. Biol. 56, No. 1-2, 51-92 (2008). MSC: 65C40 68Q45 92D20 68R15 60J22 PDFBibTeX XMLCite \textit{M. E. Lladser} et al., J. Math. Biol. 56, No. 1--2, 51--92 (2008; Zbl 1147.65005) Full Text: DOI arXiv
Sumner, J. G.; Jarvis, P. D. Using the tangle: A consistent construction of phylogenetic distance matrices for quartets. (English) Zbl 1104.92049 Math. Biosci. 204, No. 1, 49-67 (2006). MSC: 92D15 60J27 92-08 PDFBibTeX XMLCite \textit{J. G. Sumner} and \textit{P. D. Jarvis}, Math. Biosci. 204, No. 1, 49--67 (2006; Zbl 1104.92049) Full Text: DOI arXiv
Ababneh, Faisal; Jermiin, Lars S.; Robinson, John Generation of the exact distribution and simulation of matched nucleotide sequences on a phylogenetic tree. (English) Zbl 1105.92020 J. Math. Model. Algorithms 5, No. 3, 291-308 (2006). MSC: 92D15 92D20 60J20 92C40 60J22 65C05 65C40 PDFBibTeX XMLCite \textit{F. Ababneh} et al., J. Math. Model. Algorithms 5, No. 3, 291--308 (2006; Zbl 1105.92020) Full Text: DOI
Sumner, J. G.; Jarvis, P. D. Entanglement invariants and phylogenetic branching. (English) Zbl 1066.92040 J. Math. Biol. 51, No. 1, 18-36 (2005). MSC: 92D15 60J20 60J27 92C05 PDFBibTeX XMLCite \textit{J. G. Sumner} and \textit{P. D. Jarvis}, J. Math. Biol. 51, No. 1, 18--36 (2005; Zbl 1066.92040) Full Text: DOI arXiv
Mossel, Elchanan; Steel, Mike A phase transition for a random cluster model on phylogenetic trees. (English) Zbl 1047.92032 Math. Biosci. 187, No. 2, 189-203 (2004). MSC: 92D15 05C05 05C90 92C40 60J20 PDFBibTeX XMLCite \textit{E. Mossel} and \textit{M. Steel}, Math. Biosci. 187, No. 2, 189--203 (2004; Zbl 1047.92032) Full Text: DOI arXiv
Zheng, Qi On the dispersion index of a Markovian molecular clock. (English) Zbl 0989.92018 Math. Biosci. 172, No. 2, 115-128 (2001). MSC: 92D15 60J20 60J27 PDFBibTeX XMLCite \textit{Q. Zheng}, Math. Biosci. 172, No. 2, 115--128 (2001; Zbl 0989.92018) Full Text: DOI
Baake, Ellen What can and what cannot be inferred from pairwise sequence comparisons? (English) Zbl 0940.92017 Math. Biosci. 154, No. 1, 1-21 (1998); erratum ibid. 163, No. 1, 103 (2000). MSC: 92D15 60J99 PDFBibTeX XMLCite \textit{E. Baake}, Math. Biosci. 154, No. 1, 1--21 (1998; Zbl 0940.92017) Full Text: DOI
Kelly, Colleen; Rice, John Modeling nucleotide evolution: A heterogeneous rate analysis. (English) Zbl 0845.92017 Math. Biosci. 133, No. 1, 85-109 (1996). MSC: 92D15 92D20 60J20 60J25 PDFBibTeX XMLCite \textit{C. Kelly} and \textit{J. Rice}, Math. Biosci. 133, No. 1, 85--109 (1996; Zbl 0845.92017) Full Text: DOI
Fu, Yun-Xin; Li, Wen-Hsiung Necessary and sufficient conditions for the existence of certain quadratic invariants under a phylogenetic tree. (English) Zbl 0729.92018 Math. Biosci. 105, No. 2, 229-238 (1991). MSC: 92D15 60J20 92D20 PDFBibTeX XMLCite \textit{Y.-X. Fu} and \textit{W.-H. Li}, Math. Biosci. 105, No. 2, 229--238 (1991; Zbl 0729.92018) Full Text: DOI