Some inequalities for theoretical spatial ecology

Abstract

Inequalities for spatial competition verify the pair approximation of statistical mechanics introduced to theoretical ecology by Matsuda, Satō and Iwasa, among others. Spatially continuous moment equations were introduced by Bolker and Pacala and use a similar assumption in derivation. In the present article, I prove upper bounds for the kth central moment of occupied sites in the contact process of a single spatial dimension. This result shows why such moment closures are effective in spatial ecology.