Vegetation patterns in limited resource ecosystems: a statistical mechanics model and Monte Carlo simulations

Abstract

The model considers individuals (plants) forming the living biomass as particles having an excluded area and a facilitation/competition pair interaction that is controlled by four parameters. Two are related to the plant morphology while the others to the plant?plant interaction strength. By using the principle of maximum entropy and Monte Carlo simulations in the grand canonical ensemble, vegetation patterns and clusters are obtained thatresemble those of stressed ecosystems. The shape and size of these clusters strongly depend on potential external resources or natural environmental resources. A non-linear relation between the biomass density and the activityof the environmental resources as well as a shift in the vegetation cover are predicted. The model seems to be a powerful tool for the description of systems with limited resources.