Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 235, Issue 4, Pages 463-475Publisher
ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2005.01.026
Keywords
coupled map lattice; integro-difference equations; host-pathogen; predator-prey; dispersal-driven instability
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Recently there has been a great deal of interest within the ecological community about the interactions of local populations that are coupled only by dispersal. Models have been developed to consider such scenarios but the theory needed to validate model outcomes has been somewhat lacking. In this paper, we present theory which can be used to understand these types of interaction when population exhibit discrete time dynamics. In particular, we consider a spatial extension to discrete-time models, known as coupled map lattices (CMLs) which are discrete in space. We introduce a general form of the CML and link this to integro-difference equations via a special redistribution kernel. General conditions are then derived for dispersal-driven instabilities. We then apply this theory to two discrete-time models; a predator-prey model and a host-pathogen model. (c) 2005 Elsevier Ltd. All rights reserved.
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