Alberti, Frederic Genetic recombination as a generalised gradient flow. (English) Zbl 1475.92109 Monatsh. Math. 196, No. 4, 645-663 (2021). Summary: It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated. MSC: 92D10 Genetics and epigenetics 92C40 Biochemistry, molecular biology Keywords:recombination; chemical reaction networks; gradient flow; Lyapunov function; partitioning process PDFBibTeX XMLCite \textit{F. Alberti}, Monatsh. Math. 196, No. 4, 645--663 (2021; Zbl 1475.92109) Full Text: DOI arXiv References: [1] Akin, E., The Geometry of Population Genetics (1979), Berlin: Springer, Berlin · Zbl 0437.92016 · doi:10.1007/978-3-642-93128-4 [2] Baake, E.; Baake, M., Haldane linearisation done right: solving the nonlinear recombination equation the easy way, Discrete Contin. Dyn. Syst. A, 36, 6645-6656 (2016) · Zbl 1353.92064 · doi:10.3934/dcds.2016088 [3] Baake, E., Baake, M.: An exactly solved model for mutation, recombination and selection. Can. J. Math. 55, 3-41 (2003). arXiv:0210422, and erratum, Can. J. Math60 (2008) 264 · Zbl 1056.92040 [4] Baake, E., Baake, M.: Ancestral lines under recombination, to appear. In: Baake, E., Wakolbinger, A. (eds.) Probabilistic Structures in Evolution. EMS Publishing House, in preparation · Zbl 1231.92052 [5] Baake, E., Baake, M., Salamat, M.: The general recombination equation in continuous time and its solution. Discrete Contin. Dyn. Syst. A 36, 63-95 (2016), and addendum, arXiv:1409.1378 · Zbl 1325.34064 [6] Bellaïche, A.; Risler, JJ, Sub-Riemannian Geometry (1996), Basel: Birkhäuser, Basel · doi:10.1007/978-3-0348-9210-0 [7] Bürger, R., The Mathematical Theory of Selection, Recombination, and Mutation (2000), Chichester: Wiley, Chichester · Zbl 0959.92018 [8] Bürger, R., Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration, J. Math. Biol., 58, 939-978 (2009) · Zbl 1204.92050 · doi:10.1007/s00285-008-0236-5 [9] Ethier, SN; Kurtz, TG, Markov Processes—Characterization and Convergence (1986), New York: Wiley, New York · Zbl 0592.60049 · doi:10.1002/9780470316658 [10] Feinberg, M., Foundations of Chemical Reaction Network Theory (2019), Cham: Springer, Cham · Zbl 1420.92001 · doi:10.1007/978-3-030-03858-8 [11] Hofbauer, J., Population dynamics and reaction systems—some crossovers, Oberwolfach Rep., 28, 1753-1756 (2017) [12] Hofbauer, J., Müller, S.: Genetic recombination as a chemical reaction network. Math. Model. Nat. Phenom. 10, 84-99 (2015). arXiv:1503.01155 · Zbl 1371.92089 [13] Lyubich, YI, Mathematical Structures in Population Genetics (1992), Berlin: Springer, Berlin · Zbl 0747.92019 · doi:10.1007/978-3-642-76211-6 [14] Mielke, A., A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Nonlinearity, 24, 1329-1346 (2011) · Zbl 1227.35161 · doi:10.1088/0951-7715/24/4/016 [15] Walschap, G., Metric Structures in Differential Geometry (2004), New York: Springer, New York · Zbl 1083.53002 · doi:10.1007/978-0-387-21826-7 [16] Yong, W., Conservation-dissipation structure of chemical reaction systems, Phys. Rev. E, 86, 67101, 1-3 (2012) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.