How to analyze spatial structure and model spatio-temporal development of epiphytes?

The spatial dimension of plant disease development has often been neglected by most epidemiologists, despite its importance. Yet several tools are available for analysis and modeling of epidemics, both in time and space. Methods for spatial analysis include clustering index calculation, distribution fitting, power law, relationships between incidences at different spatial scales, mapping, geostatistics, and distance indices with SADIE software. The tools for spatio-temporal modeling include spatially explicit or spatially implicit models. Among the spatially explicit models, we find reaction-diffusion, network, or individual-based models, cellular automata, and lattice models, including some metapopulation models. Spatially implicit models are based on the introduction of a correction factor, the percolation theory, or statistical approximations. This review presents a rough guide to spatio-temporal approaches, in the hope that their use will become widespread in the community of epidemiologists, even among nonspecialists in spatial information. The tools that can be used to analyze and model the spatial structure of epidemics are reviewed in the context of their application to phytopathology. The diffusion of this information should promote a better understanding of epidemics and the design of innovative management strategies.