Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis

The main focus of this article is to present and relate four different frameworks in which spatially explicit individual-based models (IBMs) can be defined. These frameworks differ in the way space and time are modeled; each can be treated either discretely or continuously. The emphasis is put on constructing and simulating one of the simplest single-species IBMs in each spatio-temporal framework, discussing some of their technical subtleties, and deriving corresponding mean-field models when the homogeneous mixing conditions are assumed to hold. The four frameworks are more supplements than competitors. Since at almost every step of IBM construction several alternatives are a priori plausible I discuss the most important ones in more details. This article seems to be the first attempt to collect and synthesize information of this kind that is scattered over the literature. (C) 2002 Elsevier Science B.V. All rights reserved.