Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction-di®usion Models

  • Author(s) / Creator(s)
  • 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
  • Subjects / Keywords
  • Type of Item
    Article (Draft / Submitted)
  • DOI
  • License
    Attribution-NonCommercial 4.0 International