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

被引：12

作者：

Chalub, Fabio A. C. C. ^{[1
,2
]}

Souza, Max O. ^{[3
]}

机构：

[1] Univ Nova Lisboa, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] Univ Nova Lisboa, Ctr Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

[3] Univ Fed Fluminense, Dept Matemat Aplicada, BR-24020140 Niteroi, RJ, Brazil

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2008年 / 47卷 / 7-8期

关键词：

evolutionary dynamics; statistical mechanics; degenerate parabolic differential equations; Moran process; Kimura equation; replicator dynamics;

D O I：

10.1016/j.mcm.2007.06.009

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

There are many different models - both continuous and discrete - used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dynamics are all well known models, that might lead to different conclusions. We present a discussion of a unified framework to embrace all these models, in the large population regime. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：743 / 754

页数：12

共 19 条

[1] FLUID DYNAMIC LIMITS OF KINETIC-EQUATIONS .1. FORMAL DERIVATIONS [J].

BARDOS, C ;

GOLSE, F ;

LEVERMORE, D .

JOURNAL OF STATISTICAL PHYSICS, 1991, 63 (1-2) :323-344

[2] FLUID DYNAMIC LIMITS OF KINETIC EQUATIONS-II CONVERGENCE PROOFS FOR THE BOLTZMANN-EQUATION [J].

BARDOS, C ;

GOLSE, F ;

LEVERMORE, CD .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (05) :667-753

[3] On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit [J].

Bechouche, P ;

Mauser, NJ ;

Selberg, S .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2005, 2 (01) :129-182

[4]

CHALUB FAC, IN PRESS ASYMPTOTIC

[5]

CHALUB FAC, 2006, CONTINUOUS LIMIT MOR

[6] Global convergence of a kinetic model of chemotaxis to a perturbed Keller-Segel model [J].

Chalub, FACC ;

Kang, K .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (04) :686-695

[7] Kinetic models for chemotaxis and their drift-diffusion limits [J].

Chalub, FACC ;

Markowich, PA ;

Perthame, B ;

Schmeiser, C .

MONATSHEFTE FUR MATHEMATIK, 2004, 142 (1-2) :123-141

[8] The diffusion limit of transport equations derived from velocity-jump processes [J].

Hillen, T ;

Othmer, HG .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 61 (03) :751-775

[9]

Hofbauer J., 1998, Evol. Games Popul. Dyn., DOI DOI 10.1017/CBO9781139173179

[10]

KIMURA M, 1962, GENETICS, V47, P713

← 1 2 →