Document Type

Article

Publication Date

1990

Publication Title

Proceedings of the Royal Society of Edinburgh Section A-Mathematics

Abstract

Monotone travelling wave solutions are known to exist for Fisher's equation which models the propagation of an advantageous gene in a single locus, two alleles population genetics model. Fisher's equation assumed that the population size is a constant and that the fitnesses of the individuals in the population depend only on their genotypes. In this paper, we relax these assumptions and allow the fitnesses to depend also on the population size. Under certain assumptions, we prove that in the second heterozygote intermediate case, there exists a constant θ*>0 such that monotone travelling wave solutions for the reaction–diffusion system exist whenever θ > θ*. We also discuss the stability properties of these waves.

Volume

115

Issue

1-2

First Page Number

1

Last Page Number

18

DOI

10.1017/S0308210500024525

Publisher Statement

© 1990, Cambridge University Press. Available on publisher's site at http://dx.doi.org/10.1017/S0308210500024525.

Included in

Mathematics Commons

Share

 
COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.