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Escape from the cell: Spatially explicit modelling with and without grids
Institution:1. Department of Geography, University of Cambridge, Downing Place, Cambridge CB2 3EN, United Kingdom;2. University of East Anglia, Norwich NR4 7TJ, United Kingdom;1. Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA;2. Information Science Directorate, US Army Research Office, Durham, NC 27709, USA;1. Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China;2. Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China;3. Department of Physics, Zhejiang University, Hangzhou 310027, China;1. EuroMov, Universite Montpellier-1, 700 av du Pic Saint-Loup, 34090 Montpellier, France;2. Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA;1. Centro Nacional de Investigaciones Metalúrgicas (CENIM-CSIC), Avenida Gregorio del Amo, 8. 24080 Madrid, Spain;2. Instituto de Nanociencia de Aragón (INA), Edificio I+D, c/Mariano Esquillor s/n, 50018 Zaragoza, Spain;2. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois;3. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
Abstract:This paper is concerned with the representation of individuals embedded in a two- (or three-) dimensional environment, and with the techniques that can be used to simulate the evolution of the spatial patterns both of the populations of those individuals and of their environment. Its scope is therefore that of individual based or agent based modelling, of a general type, including herbivore populations, predator-prey models or any other type that is concerned with the spatial patterning evolving from recruitment, interaction and/or movement of discrete individuals. The aim is to discuss a modelling technique that allows more flexibility in the representation of the positions of individuals than is typically the case for cellular automata (CA), but which also deals efficiently with the problem of searching for neighbours when individual positions can vary nearly continuously. A scaling problem is discussed that arises when the range over which individuals interact is much smaller than the size of the domain. It is argued that validation of CA models involving discrete individuals is made more difficult when the system scale exceeds the size of individuals by a large factor. However, even when the domain size is small, if interaction between individuals is mediated by their size, imposition of a fixed grid upon the dynamics may cause important phenomena to be misrepresented or missed altogether. We suggest that cellular automata, as usually formulated, do not deal adequately with this type of problem, and introduce a particle-in-cell (PIC) method to deal with it in intermediate cases. Alternative data structures are discussed for dealing with more extreme cases, including the possibility of modelling an indefinitely large domain using a changing set of cells (PIC:SI).
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