Evolving gene frequencies in a population with three possible alleles at a locus

被引：3
作者：
Bradshaw-Hajek, B. H. [1 ]
Broadbridge, P. [2 ]
Williams, G. H. [3 ]
机构：
[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia
[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia
[3] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2008年 / 47卷 / 1-2期
关键词：
reaction-diffusion equations; traveling wave solutions; changing gene frequencies; gene propagation;
D O I：
10.1016/j.mcm.2007.02.015
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A number of models involving reaction-diffusion equations have been developed by different authors to describe the changes in frequency of alleles in a population. Each of these models describes the case in which there are only two possible alleles at the locus in question. In the present paper, we are interested in the more realistic possibility of three alternative alleles. A system of reaction-diffusion equations can be developed to describe this situation. After transforming to the traveling wave coordinates, we introduce a nonlinear transformation which allows us to find exact solutions under certain conditions imposed on two of the parameters. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：210 / 217
页数：8
相关论文
共 15 条
[1]  
Aronson D. G., 1975, LECT NOTES MATH, V446, P5
[2]  
BAZYKIN AD, 1969, EVOLUTION, V23, P685, DOI 10.1111/j.1558-5646.1969.tb03550.x
[3]  
Bradshaw-Hajek BH, 2004, MATH COMPUT MODEL, V39, P1151, DOI [10.1016/S0895-7177(04)90537-7, 10.1016/j.mcm2003.03.009]
[4]   Huxley and Fisher equations for gene propagation: An exact solution [J].
Broadbridge, P ;
Bradshaw, BH ;
Fulford, GR ;
Aldis, GK .
ANZIAM JOURNAL, 2002, 44 :11-20
[5]   The wave of advance of advantageous genes [J].
Fisher, RA .
ANNALS OF EUGENICS, 1937, 7 :355-369
[6]  
Fisher RA., 1923, P ROY SOC EDINB B, V42, P321, DOI [DOI 10.1017/S0370164600023993, 10.1017/S0370164600023993]
[7]  
Kolmogorov A., 1937, Bull. Moscow State Univ. Ser. A: Math. Mech, V1, P1
[8]  
LITTLER R A, 1975, Mathematical Biosciences, V25, P151, DOI 10.1016/0025-5564(75)90058-9
[9]   NOTE ON THE ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF THE KPP EQUATION [J].
MOET, HJK .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1979, 10 (04) :728-732
[10]  
Pialek J, 1997, GENETICS, V145, P493
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