Abstract

The process of invasion is fundamental to the study of the dynamics of ecological and epidemiological systems. Quantitatively, a crucial measure of species' invasiveness is given by the rate at which it spreads into new open environments. The so-called "linear determinacy" conjecture equates full nonlinear model spread rates with the spread rates computed from linearized systems with the linearization carried out around the leading edge of the invasion. A survey that accounts for recent developments in the identification of conditions under which linear determinacy gives the "right" answer, particularly in the context of non-compact and non-cooperative systems, is the thrust of this contribution. Novel results that extend some of the research linked to some the contributions covered in this survey are also discussed.

Original languageEnglish (US)
Pages (from-to)1419-1436
Number of pages18
JournalMathematical Biosciences and Engineering
Volume10
Issue number5-6
DOIs
StatePublished - Oct 1 2013

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Keywords

  • Dispersal
  • Ecology
  • Integer difference integral equations
  • Nonlinear reaction diffusion difference equations
  • Population biology

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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