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dc.contributor.authorLewis, Mark A.
dc.contributor.authorLi, Bingtuan
dc.date.accessioned2016-02-28T06:07:52Z
dc.date.available2016-02-28T06:07:52Z
dc.date.issued2012-08-15
dc.identifier.citationLewis MA, Li B (2012) Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models. Bull Math Biol 74: 2383–2402. Available: http://dx.doi.org/10.1007/s11538-012-9757-6.
dc.identifier.issn0092-8240
dc.identifier.issn1522-9602
dc.identifier.pmid22893042
dc.identifier.doi10.1007/s11538-012-9757-6
dc.identifier.urihttp://hdl.handle.net/10754/599701
dc.description.abstractHow 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. © 2012 Society for Mathematical Biology.
dc.description.sponsorshipThe authors thank two anonymous reviewers for their helpful comments and suggestions. This research was supported by NSERC Discovery and Accelerator grants and by a Canada Research Chair. M. A. L. gratefully acknowledges a Research Fellowship from Oxford Centre for Collaborative and Applied Mathematics, supported by Award No KUK-CI013-04 made by King Abdullah University of Science and Technology (KAUST).This research was partially supported by the National Science Foundation under Grant DMS-616445 and Grant DMS-1225693.
dc.publisherSpringer Nature
dc.subjectDifference equation
dc.subjectMinimal domain size
dc.subjectReaction-diffusion equation
dc.subjectSpreading speed
dc.subjectTraveling wave
dc.titleSpreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models
dc.typeArticle
dc.identifier.journalBulletin of Mathematical Biology
dc.contributor.institutionUniversity of Alberta, Edmonton, Canada
dc.contributor.institutionUniversity of Louisville, Louisville, United States
kaust.grant.numberKUK-CI013-04
dc.date.published-online2012-08-15
dc.date.published-print2012-10


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