NDLI: Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction

Content Provider	Springer Nature Link
Author	Lewis, Mark A. Li, Bingtuan
Copyright Year	2012
Abstract	How growth, mortality, and dispersal in a species affect the species’ spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction–diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction–diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species’ spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.
Starting Page	2383
Ending Page	2402
Page Count	20
File Format	PDF
ISSN	00928240
Journal	Bulletin of Mathematical Biology
Volume Number	74
Issue Number	10
e-ISSN	15229602
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-08-15
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Difference equation Reaction–diffusion equation Spreading speed Traveling wave Minimal domain size Cell Biology Mathematical and Computational Biology Life Sciences
Content Type	Text
Resource Type	Article
Subject	Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences

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