Stability and Complexity on a Lattice: Coexistence of Species in an Individual-Based Food Web Model

Theoretical studies of the stability of food webs have generally not incorporated space as a contingency affecting coexistence of species. Here, I considered the importance of spatial heterogeneity on the stability of an individual-based food web model. Individual agents diffused on a lattice of cells and interacted according to a set of probabilistic interaction coefficients. Simulations were run on both uniform and non-uniform lattices. The model had two modes: (1) a mean-field mode with global interactions, and (2) a spatially localized mode in which species interacted within local neighborhoods. Equilibrium number of species were compared among different simulations varying web connectance, interaction strength, and lattice heterogeneity. The addition of spatial heterogeneity to the lattice further altered relationships among species richness, web connectance, and interaction strength, and increased coexistence among species. The results did not support the stability criterion derived by May. However, an inverse relationship between web connectance and species richness was observed suggesting that the product of connectance and species richness may govern the stability of real, finite webs.