title: Approximating spatially exclusive invasion processes.
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.
authors.affiliation: School of Mathematical Sciences, University of Adelaide, South Australia, 5005 Australia.
authors.forename: Joshua V
authors.initials: JV
authors.lastname: Ross
authors.affiliation: School of Mathematical Sciences, University of Adelaide, South Australia, 5005 Australia.
authors.forename: Benjamin J
authors.initials: BJ
authors.lastname: Binder
mesh_terms: D002465:Cell Movement; D003198:Computer Simulation; D058865:Introduced Species; D008390:Markov Chains; D008954:Models, Biological; D013269:Stochastic Processes