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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

CA methods in ecology paper

Escape from the cell: Spatially explicit modelling with and without grids

Bithell, M. and W. D. Macmillan.

Ecological Modelling

Jan 10, 2007
Volume: 200
Issue: 1-2
Pages: 59-78

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 ndividuals 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.

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Old Post 01-07-2008 08:52 PM
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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

My review - this is a useful methods paper for CAs in ecology, specifically for models in which mobile animals diffuse across a grid of terrain and resource features, interacting with other animals within the model in the process. The paper is useful for making several practical suggestions. I am less convinced on a few of their recommendations, but if one picks and chooses among their ideas the paper is helpful overall.

One flaw is a kind of excess of literalism in the statement of the possible problem, as they imagine putting 2m sized animals into km wide grid squares, imagining that they need very fine grain for some details and wide total ranges for other matters. Better modeling thinking is the main thing needed there, not a change of method. Which effect is one trying to capture with the model, and what scale does it actually operate on? There is essentially no reason to let animal scale dictate anything about grid scale.

The suggestion to record a number of animals in each cell rather than tracking each of them as an "atom" of unit-cell size is clearly correct, if hopefully fairly obvious. The more technical idea to encode the data in what is in effect sparse array format is also useful and probably less obvious. It is much less clear to me that it helps to encode positions within cells in lists of real numbers, sort of boid style - if you are going to bother tracking real number precise locations, the overlying grid is not all that useful to begin with. Perhaps it can track some coarse terrain or resource variables for you, I suppose.

It seems to me simpler and more promising to abstract interactions within one cell, or to get reasonable formulae for them from prior simulation and just use a resulting value, function, or table to handle the rest of the within-cell detail (probability of "collision" e.g.).

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