NDLI: The influence of space dimension on the large-time behavior in a reaction–diffusion system modeling diallelic selection

Content Provider	Springer Nature Link
Author	Winkler, Michael Souplet, Philippe
Copyright Year	2010
Abstract	We study a mathematical model from population genetics, describing a single-locus diallelic (A/a) selection–migration process. The model consists of a coupled system of three reaction–diffusion equations, one for the density of each genotype, posed in the whole space $${\mathbb R^n}$$ . The genotype AA is advantageous, due to a smaller death rate, and we consider the fully recessive case where the other two genotypes aa and Aa have the same (higher) death rate. In the nondiffusive (spatially homogeneous) case, the disadvantageous gene a is always eliminated in the large time limit. In the presence of diffusion, when the birth rate exceeds a certain threshold value, we prove that this conclusion is still true for dimensions n ≤ 2, whereas for n ≥ 3 there exist initial distributions for which the advantageous gene A ultimately disappears. This is the first rigorous result of this type for the full system, and it solves a problem which seems to have been open since the celebrated work of Aronson and Weinberger (Lecture notes in mathematics, vol 446, Springer, New York, pp 5–49, 1975; Adv Math 30, 33–76, 1977), where similar results had been obtained for a simplified scalar model, that they derived as an approximation of the full system. Interestingly, we moreover show that, at the threshold value of the birth rate, the cut-off dimension shifts from n = 2 to n = 6.
Ending Page	421
Page Count	31
Starting Page	391
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	3
Volume Number	62
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-04-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fisher approximation Population dynamics (general) Second-order parabolic systems Extinction Selection Reaction–diffusion system Mathematical Biology in General Applications of Mathematics Population genetics Problems related to evolution Asymptotic behavior of solutions
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The influence of a line with fast diffusion on Fisher-KPP propagation

Extinction and spreading of a species under the joint influence of climate change and a weak Allee effect: a two-patch model

Global classical solutions for reaction–diffusion systems with nonlinearities of exponential growth

Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks

Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks

Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equations

A Fisher-KPP model with a fast diffusion line in periodic media

Spreading Speeds and Traveling Waves for Non-cooperative Reaction–Diffusion Systems

Long time behavior of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions

The influence of space dimension on the large-time behavior in a reaction–diffusion system modeling diallelic selection

Similar Documents

The influence of a line with fast diffusion on Fisher-KPP propagation

Extinction and spreading of a species under the joint influence of climate change and a weak Allee effect: a two-patch model

Global classical solutions for reaction–diffusion systems with nonlinearities of exponential growth

Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks

Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks

Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equations

A Fisher-KPP model with a fast diffusion line in periodic media

Spreading Speeds and Traveling Waves for Non-cooperative Reaction–Diffusion Systems

Long time behavior of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions

The influence of space dimension on the large-time behavior in a reaction–diffusion system modeling diallelic selection