Measuring Spatial Aggregation in Binary Epidemics: Correlative Analysis and the Advantage of Fractal-Based Sampling

Abstract

The incomplete sampling of a binary epidemic is nothing more than the overlap of two spatial patterns: the pattern of diseased plants and the pattern of sampled points. Thus, the information on the spatial arrangement of diseased plants obtained from such a sampling explicitly depends on the geometric locations of the sampled points. A number of procedures for sampling disease incidence are examined. These include samples placed on a regular grid, spatially clustered samples, randomly selected samples, and samples specified by a nested fractal design. The performance of these various sampling schemes was examined using simulated binary epidemics with varying degrees of spatial aggregation over different length scales, generated using a Neyman-Scott cluster process. A modification of spatial correlation analysis specifically geared to binary epidemics is derived and shown to be equivalent to a X2 test comparing the number of infected plant pairs to that expected from a spatially random epidemic. This analysis was applied to the data obtained using the various sampling schemes and the results are compared and contrasted. For the same number of sampling points, the fractal design is most efficient in the detection of contagion and provides spatial information over a larger range of distance scales than other sampling schemes. However, the regular grid sampling scheme consistently yielded an estimate of average disease incidence that had the smallest variance. Sampling patterns consisting of randomly selected points were intermediate in behavior between the two extremes.