Partial differential equations in ecology: spatial interactions and population dynamics

• Author(s) / Creator(s)

  • Veit, R. R.
  • Banks, J. E.
  • Holmes, E. E.
  • Lewis, M. A.

• Most of the fundamental elements of ecology, ranging from individual behavior to species abundance, diversity, and population dynamics, exhibit spatial variation. Partial differential equation models provide a means of melding organism movement with population processes and have been used extensively to elucidate the effects of spatial variation on populations. While there has been an explosion of theoretical advances in partial differential equation models in the past two decades, this work has been generally neglected in mathematical ecology textbooks. Our goal in this paper is to make this literature accessible to experimental ecologists. Partial differential equations are used to model a variety of ecological phenomena; here we discuss dispersal, ecological invasions, critical patch size, dispersal-mediated coexistence, and diffusion-driven spatial patterning. These models emphasize that simple organism movement can produce striking large-scale patterns in homogeneous environments, and that in heterogeneous environments, movement of multiple species can change the outcome of competition or predation.

• Date created

  1994

• Subjects / Keywords

  • Differential equations
  • Coexistence
  • Invasions
  • Ecological models
  • Reaction-diffusion
  • Spatial models
  • Spatial patterning
  • Diffusive instabilities
  • Dispersal
  • Diffusion

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3NP1WH9V

• License

  © 1994 Ecological Society of America. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.