Approximating spatially exclusive invasion processes

Joshua V. Ross and Benjamin J. Binder
Phys. Rev. E 89, 052709 – Published 15 May 2014

Abstract

A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.

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  • Received 28 January 2014
  • Revised 6 April 2014

DOI:https://doi.org/10.1103/PhysRevE.89.052709

©2014 American Physical Society

Authors & Affiliations

Joshua V. Ross* and Benjamin J. Binder

  • School of Mathematical Sciences, University of Adelaide, South Australia, 5005 Australia

  • *joshua.ross@adelaide.edu.au

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Vol. 89, Iss. 5 — May 2014

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