Spreading speed and linear determinacy for two-species competition models

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

Research output: Contribution to journalArticlepeer-review

197 Scopus citations


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 [11].

Original languageEnglish (US)
Pages (from-to)219-233
Number of pages15
JournalJournal of Mathematical Biology
Issue number3
StatePublished - Sep 1 2002


  • Linear conjecture
  • Lotka-Volterra
  • Spreading speed linear determinacy

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