Discrete versus continuous models in evolutionary dynamics: From simple to simpler-and even simpler-models

Mathematical and Computer Modelling

Volumn 47, Issue 7-8, 2008, Pages 743-754

  Chalub, Fabio A C C ^a   Souza, Max O ^b  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

^b FLUMINENSE FEDERAL UNIVERSITY   (Brazil)

Author keywords

Degenerate parabolic differential equations; Evolutionary dynamics; Kimura equation; Moran process; Replicator dynamics; Statistical mechanics

Indexed keywords

DIFFERENTIAL EQUATIONS; GENE EXPRESSION; MATHEMATICAL MODELS; STATISTICAL METHODS;

DEGENERATE PARABOLIC DIFFERENTIAL EQUATIONS; EVOLUTIONARY DYNAMICS; KIMURA EQUATION; MORAN PROCESS; REPLICATOR DYNAMICS;

EVOLUTIONARY ALGORITHMS;

EID: 40249095977     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.06.009     Document Type: Article

References (19)

1. Bardos C., Golse F., and Levermore C.D. Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Comm. Pure Appl. Math. 46 5 (1993) 667-753
2. Bardos C., Golse F., and Levermore D. Fluid dynamic limits of kinetic equations. I. Formal derivations. J. Statist. Phys. 63 1-2 (1991) 323-344
3. Bechouche P., Mauser N.J., and Selberg S. On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit. J. Hyperbolic Differ. Equ. 2 1 (2005) 129-182
4. Chalub F.A.C.C., and Kang K. Global convergence of a kinetic model for chemotaxis to a perturbed Keller-Segel system. Nonlinear Anal. 64 4 (2006) 686-695
5. Chalub F.A.C.C., Markowich P.A., Perthame B., and Schmeiser C. Kinetic models for chemotaxis and their drift-diffusion limits. Monatsh. Math. 142 1-2 (2004) 123-141
6. F.A.C.C. Chalub, M.O. Souza, Asymptotic limits of continuous Moran processes: The Kimura equation and the replicator dynamics (in preparation)
7. F.A.C.C. Chalub, M.O. Souza, The continuous limit of the Moran process and the diffusion of mutant genes in infinite populations. arXiv:math.AP/0602530, 2006, Pre-print
8. Hillen T., and Othmer H.G. The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math. 61 3 (2000) 751-775 Electronic
9. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge, UK
10. Kimura M. On the probability of fixation of mutant genes in a population. Genetics 47 (1962) 713-719
11. Markowich P.A., Ringhofer C.A., and Schmeiser C. Semiconductor Equations (1990), Springer-Verlag, Vienna
12. Masmoudi N. Some recent developments on the hydrodynamic limit of the Boltzmann equation. Mathematics & Mathematics Education (Bethlehem, 2000) (2002), World Sci. Publishing, River Edge, NJ 167-185
13. Masmoudi N., and Nakanishi K. Nonrelativistic limit from Maxwell-Klein-Gordon and Maxwell-Dirac to Poisson-Schrödinger. Int. Math. Res. Not. 13 (2003) 697-734
14. Masmoudi N., and Saint-Raymond L. From the Boltzmann equation to the Stokes-Fourier system in a bounded domain. Comm. Pure Appl. Math. 56 9 (2003) 1263-1293
15. N.J. Mauser, Semi-relativistic approximations of the Dirac equation: First and second order corrections. in: Proceedings of the Fifth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics (Maui, HI, 1998), vol. 29, 2000, pp. 449-464
16. Moran P.A.P. The Statistical Process of Evolutionary Theory (1962), Clarendon Press, Oxford
17. Othmer H.G., and Hillen T. The diffusion limit of transport equations. II. Chemotaxis equations. SIAM J. Appl. Math. 62 4 (2002) 1222-1250 Electronic
18. Sparber C., and Markowich P. Semiclassical asymptotics for the Maxwell-Dirac system. J. Math. Phys. 44 10 (2003) 4555-4572
19. Traulsen A., Claussen J.C., and Hauert C. Coevolutionary dynamics: From finite to infinite populations. Phys. Rev. Lett. 95 (2005) 238701