# American Institute of Mathematical Sciences

January  2000, 6(1): 221-236. doi: 10.3934/dcds.2000.6.221

## Mutation, selection, and recombination in a model of phenotype evolution

 1 Faculte des Sciences et Techniques, 25, rue Philippe Lebon, B.P. 540, 76058 Le Havre, France 2 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States

Received  October 1999 Published  December 1999

A model of phenotype evolution incorporating mutation, selection, and recombination is investigated. The model consists of a partial differential equation for population density with respect to a continuous variable representing phenotype diversity. Mutation is modeled by diffusion, selection is modeled by differential phenotype fitness, and genetic recombination is modeled by an averaging process. It is proved that if the recombination process is suffciently weak, then there is a unique globally asymptotically stable attractor.
Citation: P. Magal, G. F. Webb. Mutation, selection, and recombination in a model of phenotype evolution. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 221-236. doi: 10.3934/dcds.2000.6.221
 [1] Fatih Bayazit, Ulrich Groh, Rainer Nagel. Floquet representations and asymptotic behavior of periodic evolution families. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4795-4810. doi: 10.3934/dcds.2013.33.4795 [2] N. I. Karachalios, Hector E. Nistazakis, Athanasios N. Yannacopoulos. Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 711-736. doi: 10.3934/dcds.2007.19.711 [3] Zhong Tan, Zheng-An Yao. The existence and asymptotic behavior of the evolution p-Laplacian equations with strong nonlinear sources. Communications on Pure and Applied Analysis, 2004, 3 (3) : 475-490. doi: 10.3934/cpaa.2004.3.475 [4] Angela A. Albanese, Elisabetta M. Mangino. Analytic semigroups and some degenerate evolution equations defined on domains with corners. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 595-615. doi: 10.3934/dcds.2015.35.595 [5] Zhipeng Qiu, Jun Yu, Yun Zou. The asymptotic behavior of a chemostat model. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 721-727. doi: 10.3934/dcdsb.2004.4.721 [6] Mykhailo Potomkin. Asymptotic behavior of thermoviscoelastic Berger plate. Communications on Pure and Applied Analysis, 2010, 9 (1) : 161-192. doi: 10.3934/cpaa.2010.9.161 [7] Hunseok Kang. Asymptotic behavior of a discrete turing model. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 265-284. doi: 10.3934/dcds.2010.27.265 [8] Yu Wu, Xiaopeng Zhao, Mingjun Zhang. Dynamics of stochastic mutation to immunodominance. Mathematical Biosciences & Engineering, 2012, 9 (4) : 937-952. doi: 10.3934/mbe.2012.9.937 [9] Chunpeng Wang. Boundary behavior and asymptotic behavior of solutions to a class of parabolic equations with boundary degeneracy. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 1041-1060. doi: 10.3934/dcds.2016.36.1041 [10] Yong Liu. Even solutions of the Toda system with prescribed asymptotic behavior. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1779-1790. doi: 10.3934/cpaa.2011.10.1779 [11] M. Grasselli, V. Pata. Asymptotic behavior of a parabolic-hyperbolic system. Communications on Pure and Applied Analysis, 2004, 3 (4) : 849-881. doi: 10.3934/cpaa.2004.3.849 [12] Jingyu Li. Asymptotic behavior of solutions to elliptic equations in a coated body. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1251-1267. doi: 10.3934/cpaa.2009.8.1251 [13] Minkyu Kwak, Kyong Yu. The asymptotic behavior of solutions of a semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 1996, 2 (4) : 483-496. doi: 10.3934/dcds.1996.2.483 [14] Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017 [15] Ciprian G. Gal, M. Grasselli. On the asymptotic behavior of the Caginalp system with dynamic boundary conditions. Communications on Pure and Applied Analysis, 2009, 8 (2) : 689-710. doi: 10.3934/cpaa.2009.8.689 [16] Sergio Frigeri. Asymptotic behavior of a hyperbolic system arising in ferroelectricity. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1393-1414. doi: 10.3934/cpaa.2008.7.1393 [17] Carmen Cortázar, Manuel Elgueta, Fernando Quirós, Noemí Wolanski. Asymptotic behavior for a nonlocal diffusion equation on the half line. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1391-1407. doi: 10.3934/dcds.2015.35.1391 [18] Michel Chipot, Karen Yeressian. On the asymptotic behavior of variational inequalities set in cylinders. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4875-4890. doi: 10.3934/dcds.2013.33.4875 [19] Bernard Brighi, S. Guesmia. Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain. Conference Publications, 2007, 2007 (Special) : 160-169. doi: 10.3934/proc.2007.2007.160 [20] Lie Zheng. Asymptotic behavior of solutions to the nonlinear breakage equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 463-473. doi: 10.3934/cpaa.2005.4.463

2021 Impact Factor: 1.588