Spreading speed and linear determinacy for two-species competition models.

• Author(s) / Creator(s)

  • Lewis, Mark A.
  • Bingtuan Li
  • Hans F. Weinberger

•  One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper

• Date created

  2002-01-01

• Subjects / Keywords

  • Spreading speeds
  • Linear determinacy
  • Lotka-Volterra
  • Linear conjecture

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3M03Z46V

• License

  © 2002 Springer. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.