Foundations of spatial ecology: the reification of patches through quantitative description of patterns and pattern repetition

Insect populations tend to be patchy, and the nature of the patches is a cr itical component of ecology. Predator-prey interactions, coexistence of com peting species, survival of rare species as habitat is destroyed, and damag e to crops are just a few examples of spatially-dependent ecological proces ses. For want of tractable quantitative approaches, understanding of spatia l ecology has lagged far behind recognition of its importance. We assert th at a quantitative foundation of a spatial ecology involves the reification of patches as objects of study. We introduce two new measures of patch dyna mics: total covariance for comparing degrees of patchiness between populati ons, and quantile variance for quantifying the constancy of dispersion patt erns through time. These new measures, in combination with the long-establi shed spatial covariance from geostatistics, comprise a rudimentary toolbox for reification of patches and empirical field studies in spatial ecology.