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 critical component of ecology. Predator-prey interactions, coexistence of competing species, survival of rare species as habitat is destroyed, and damage to crops are just a few examples of spatially-dependent ecological processes. For want of tractable quantitative approaches, understanding of spatial ecology has lagged far behind recognition of its importance. We assert that a quantitative foundation of a spatial ecology involves the reification of patches as objects of study. We introduce two new measures of patch dynamics: total covariance for comparing degrees of patchiness between populations, and quantile variance for quantifying the constancy of dispersion patterns through time. These new measures, in combination with the long-established spatial covariance from geostatistics, comprise a rudimentary toolbox for reification of patches and empirical field studies in spatial ecology.