Some inequalities for theoretical spatial ecology

Abstract

An important open problem in fully-structured spatial population dynamics, particularly those of competing plant communities, is a rigorous justification of the key assumption required for the pair-approximations of lattice models in statistical mechanics introduced to theoretical ecology by H. Matsuda, K. Sato and Y. Iwasa, among others. A similar assumption is made in the derivation of the spatially continuous moment equations introduced by B.M. Bolker and S. Pacala (1997, Theor. Popul. Biol., 52: 179-197). Towards this aim, upper bounds of the k-th central moment in the contact process of a single spatial dimension are precisely derived. The proof of this result explains, from an analytical perspective, why moment closure methodologies of spatial ecology can be so effective. doi:10.1017/S1446181113000266