Models in Spatial Analysis

Which model and which spatial analysis? The spatial dimension plays a key role in many social phenomena. On the one hand things are unequally distributed through space, creating spatial differentiation, segregation, discontinuities. On the other hand there is a feedback loop between a society's organization and a space's configuration. Most of the time, the modeling of spatial phenomena and processes requires the combination of knowledge and skills from various fields, some involving the theme of research, others originating from computer science, statistics, physics or mathematics. These latter subjects are relevant because they provide stimulating methodological prospects to theorists interested in the organization of space and the evolution of its structures (whether they be geographers, urban planners, archaeologists, ecologists, agriculture scientists, etc.). Besides, they also offer useful technical frameworks for formalizing the thematician's theoretical models. On the other hand, the latter provide problems and data that can be used to implement and test models designed by mathematicians, statisticians and computer scientists. In such context the phrase spatial model takes on different meanings. Even though researchers in different fields may agree on a relatively broad definition of the concept of a " model " as " a schematic representation of reality, developed with the goal of understanding and explaining it " 1 , the referents are significantly different from one subject to another. In order to illustrate the diversity of meanings that come with the word " model " in a given application, in the following sections we will rely for the most part on two concrete examples. In the first, the goal is to modelize the evolution of the spatial distribution of the population over a few decades, and in the second, of the land use. From a methodological perspective, each of these two examples involves dealing with and modeling " spatial dynamics ". However, modeling spatial dynamics can 1 A definition close to that of P. Haggett [HAG 65] used by F. Durand-Dastès in Chapter 1. Author manuscript, published in "Models in Spatial Analysis, Lena Sanders (Ed.) (2007) xv-xxvii" Models in Spatial Analysis take on several different meanings: it can consist of describing changes as clearly as possible, or of finding causality underlying the type and speed of the observed evolution. These two approaches, the former used to describe and the latter to explain, should logically complement each other and be conducted one after the other. In practice, however, the …