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Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction-di®usion Models
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- Author(s) / Creator(s)
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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 repro-
ductive 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-di®usion equation in a bounded or
unbounded domain. We develop a spatially explicit theoretical framework
that links species vital rates (mortality or fecundity) and dispersal character-
istics 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 us-
ing 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. -
- Date created
- 2012-01-01
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- Subjects / Keywords
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- Type of Item
- Article (Draft / Submitted)