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Quantifying genetic innovation: mathematical foundations for the topological study of reticulate evolution. (English) Zbl 1433.92030

MSC:
92D15 Problems related to evolution
55N31 Persistent homology and applications, topological data analysis
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[1] M. Adamaszek and H. Adams, The Vietoris-Rips complexes of a circle, Pacific J. Math., 290 (2017), pp. 1-40. · Zbl 1366.05124
[2] M. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier, Vietoris-rips and cech complexes of metric gluings, in Proceedings of the 34th International Symposium on Computational Geometry (SoCG 2018), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. · Zbl 1422.55037
[3] M. Adamaszek, H. Adams, and S. Reddy, On Vietoris-Rips complexes of ellipses, J. Topology Anal., (2017), pp. 1-30. · Zbl 1426.05182
[4] M. Arenas, G. Valiente, and D. Posada, Characterization of reticulate networks based on the coalescent with recombination, Molecular Biol. Evolution, 25 (2008), pp. 2517-2520.
[5] U. Bauer and M. Lesnick, Induced matchings and the algebraic stability of persistence barcodes, J. Comput. Geom., 6 (2015), pp. 162-191. · Zbl 1405.68398
[6] D. Bezemer, A. van Sighem, V. V. Lukashov, L. van der Hoek, N. Back, R. Schuurman, C. A. B. Boucher, E. C. J. Claas, M. C. Boerlijst, R. A. Coutinho, and F. de Wolf, Transmission networks of HIV-1 among men having sex with men in the Netherlands, AIDS (London, England), 24 (2010), pp. 271-282.
[7] A. J. Blumberg and M. Lesnick, Universality of the Homotopy Interleaving Distance, preprint, arXiv:1705.01690, 2017.
[8] P. G. Cámara, A. J. Levine, and R. Rabadán, Inference of ancestral recombination graphs through topological data analysis, PLoS Comput. Biol., 12 (2016), e1005071.
[9] P. G. Cámara, D. I. S. Rosenbloom, K. J. Emmett, A. J. Levine, and R. Rabadán, Topological data analysis generates high-resolution, genome-wide maps of human recombination, Cell Systems, 3 (2016), pp. 83-94.
[10] G. Carlsson, Topology and data, Bull. Amer. Math. Soc., 46 (2009), pp. 255-308. · Zbl 1172.62002
[11] G. Carlsson, Topological pattern recognition for point cloud data, Acta Numer., 23 (2014), pp. 289-368, https://doi.org/10.1017/s0962492914000051. · Zbl 1398.68615
[12] A. H. Chan, P. A. Jenkins, and Y. S. Song, Genome-wide fine-scale recombination rate variation in drosophila melanogaster, PLoS Genetics, 8 (2012), e1003090.
[13] J. Chan, G. Carlsson, and R. Rabadán, Topology of viral evolution, Proc. Natl. Acad. Sci., 110 (2013). · Zbl 1292.92014
[14] F. Chazal, D. Cohen-Steiner, M. Glisse, L. Guibas, and S. Oudot, Proximity of persistence modules and their diagrams, in Proceedings of the 25th Annual Symposium on Computational Geometry, ACM, 2009, pp. 237-246. · Zbl 1380.68387
[15] F. Chazal, D. Cohen-Steiner, L. Guibas, F. Mémoli, and S. Oudot, Gromov-Hausdorff stable signatures for shapes using persistence, in Proceedings of the Symposium on Geometry Processing, Eurographics Association, 2009, pp. 1393-1403.
[16] F. Chazal, V. de Silva, M. Glisse, and S. Oudot, The Structure and Stability of Persistence Modules, Springer Briefs Math., Springer, New York, 2016, https://doi.org/10.1007/978-3-319-42545-0. · Zbl 1362.55002
[17] F. Chazal, V. De Silva, and S. Oudot, Persistence stability for geometric complexes, Geom. Dedicata, 173 (2014), pp. 193-214. · Zbl 1320.55003
[18] D. Cohen-Steiner, H. Edelsbrunner, and J. Harer, Stability of persistence diagrams, Discrete Comput. Geom., 37 (2007), pp. 103-120. · Zbl 1117.54027
[19] W. Crawley-Boevey, Decomposition of pointwise finite-dimensional persistence modules, J. Algebra Appl., 14 (2015), 1550066. · Zbl 1345.16015
[20] J. Davies and D. Davies, Origins and evolution of antibiotic resistance, Microbiol. Molecular Biol. Rev., 74 (2010), pp. 417-433.
[21] R. Durrett, Probability: Theory and Examples, Cambridge University Press, Cambridge, UK, 2010. · Zbl 1202.60001
[22] H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, AMS, Providence, RI, 2010. · Zbl 1193.55001
[23] J. S. Eden, M. M. Tanaka, M. F. Boni, W. D. Rawlinson, and P. A. White, Recombination within the pandemic norovirus GII.4 lineage, J. Virology, 87 (2013), pp. 6270-6282.
[24] K. Emmett, D. Rosenbloom, P. Cámara, and R. Rabadán, Parametric Inference Using Persistence Diagrams: A Case Study in Population Genetics, arXiv:1406.4582 [q-bio.QM], 2014.
[25] K. J. Emmett and R. Rabadán, Characterizing scales of genetic recombination and antibiotic resistance in pathogenic bacteria using topological data analysis, in Brain Informatics and Health, Lecture Notes in Comput. Sci. 8609, Springer, New York, 2014, pp. 540-551.
[26] R. Forman, A user’s guide to discrete Morse theory, Sém. Lothar. Combin., 48 (2002), B48c. · Zbl 1048.57015
[27] D. Gusfield, ReCombinatorics: The Algorithmics of Ancestral Recombination Graphs and Explicit Phylogenetic Networks, MIT Press, Cambridge, MA, 2014. · Zbl 1316.92001
[28] D. Gusfield, S. Eddhu, and C. Langley, Efficient reconstruction of phylogenetic networks with constrained recombination, in Proceedings of the Bioinformatics Conference, IEEE, 2003, pp. 363-374.
[29] S. Harker, M. Kramár, R. Levanger, and K. Mischaikow, A comparison framework for interleaved persistence modules, J. Appl. Comput. Topol., 3 (2019), pp. 85-118, https://doi.org/10.1007/s41468-019-00026-x. · Zbl 1443.55001
[30] A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, UK, 2002. · Zbl 1044.55001
[31] R. R. Hudson and N. L. Kaplan, Statistical properties of the number of recombination events in the history of a sample of DNA sequences, Genetics, 111 (1985), pp. 147-164.
[32] D. P. Humphreys, M. R. McGuirl, M. Miyagi, and A. J. Blumberg, Fast estimation of recombination rates using topological data analysis, Genetics, 211 (2019), pp. 1191-1204.
[33] D. H. Huson, R. Rupp, and C. Scornavacca, Phylogenetic Networks: Concepts, Algorithms and Applications, Cambridge University Press, Cambridge, UK, 2010.
[34] T. Ito, J. N. S. S. Couceiro, S. Kelm, L. G. Baum, S. Krauss, M. R. Castrucci, I. Donatelli, H. Kida, J. C. Paulson, R. G. Webster, and Y. Kawaoka, Molecular basis for the generation in pigs of influenza A viruses with pandemic potential, J. Virology, 72 (1998), pp. 7367-7373.
[35] M. Kahle, Random geometric complexes, Discrete Comput. Geom., 45 (2011), pp. 553-573. · Zbl 1219.05175
[36] O. Kallenberg, Foundations of Modern Probability, Springer, New York, 2006. · Zbl 0996.60001
[37] D. Kozlov, Combinatorial Algebraic Topology, Algorithms Comput. Math. 21, Springer, Berlin, 2008, https://doi.org/10.1007/978-3-540-71962-5. · Zbl 1130.55001
[38] S. L. Lauritzen, Graphical Models, Oxford University Press, New York, 1996. · Zbl 0907.62001
[39] J. Munkres, Elements of Algebraic Topology, Prentice-Hall, Englewood Cliffs, NJ, 1984, http://www.worldcat.org/isbn/0131816292. · Zbl 0673.55001
[40] S. R. Myers and R. C. Griffiths, Bounds on the minimum number of recombination events in a sample history, Genetics, 163 (2003), pp. 375-394.
[41] T. Nora, C. Charpentier, O. Tenaillon, C. Hoede, F. Clavel, and A. J. Hance, Contribution of recombination to the evolution of human immunodeficiency viruses expressing resistance to antiretroviral treatment, J. Virology, 81 (2007), pp. 7620-7628.
[42] S. Y. Oudot, Persistence Theory: From Quiver Representations to Data Analysis, Math. Surveys Monogr., AMS, Providence, RI, 2015. · Zbl 1335.55001
[43] L. Parida, F. Utro, D. Yorukoglu, A. P. Carrieri, D. Kuhn, and S. Basu, Topological signatures for population admixture, in International Conference on Research in Computational Molecular Biology, Springer, 2015, pp. 261-275. · Zbl 1355.92077
[44] R. Rabadán and A. J. Blumberg, Topological Data Analysis for Genomics and Evolution: Topology in Biology, Cambridge University Press, Cambridge, UK, 2019. · Zbl 07030669
[45] M. D. Rasmussen, M. J. Hubisz, I. Gronau, and A. Siepel, Genome-wide inference of ancestral recombination graphs, PLoS Genetics, 10 (2014), e1004342.
[46] H. Rohde, J. Qin, Y. Cui, D. Li, N. J. Loman, M. Hentschke, W. Chen, F. Pu, Y. Peng, J. Li, et al., Open-source genomic analysis of Shiga-toxin-producing E. coli O104: H4, New England J. Medicine, 365 (2011), pp. 718-724.
[47] A. Solovyov, G. Palacios, T. Briese, W. I. Lipkin, and R. Rabadán, Cluster Analysis of the Origins of the New Influenza A (H1N1) Virus, Euro Surveillance: European Communicable Disease Bulletin, 14, 2009.
[48] Y. S. Song, Y. Wu, and D. Gusfield, Efficient computation of close lower and upper bounds on the minimum number of recombinations in biological sequence evolution., Bioinformatics (Oxford, England), 21 (2005), i413.
[49] T. Stadler, R. Kouyos, V. von Wyl, S. Yerly, J. Boni, P. Burgisser, T. Klimkait, B. Joos, P. Rieder, D. Xie, H. F. Gunthard, A. J. Drummond, and S. Bonhoeffer, Estimating the basic reproductive number from viral sequence data, Molecular Biol. Evolution, 29 (2011), pp. 347-357.
[50] Cohort profile: The Swiss HIV Cohort study, Internat. J. Epidemiology, 39 (2010), pp. 1179-1189.
[51] V. Trifonov, H. Khiabanian, R. Rabadán, et al., Geographic dependence, surveillance, and origins of the 2009 influenza A (H1N1) virus, New England J. Medicine, 361 (2009), pp. 115-119.
[52] J. Wakeley, Coalescent Theory, An Introduction, Roberts & Co., Devon, UK, 2007. · Zbl 1366.92001
[53] L. Wang, K. Zhang, and L. Zhang, Perfect phylogenetic networks with recombination, J. Comput. Biol., 8 (2001), pp. 69-78.
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