Maximum Entropy Production allows a simple representation of heterogeneity in arid ecosystems

S. J. SCHYMANSKI, A. KLEIDON, M. STIEGLITZ AND J. NARULA

(Submitted to Philosophical Transactions B (27 February 2009)

Abstract

Feedbacks between water use, biomass and infiltration capacity in semiarid ecosystems have been shown to lead to the spontaneous formation of vegetation patterns in a simple model. The formation of patterns permits the maintenance of larger overall biomass at low rainfall rates compared with homogeneous vegetation. This results in a bias of models run at larger scales neglecting subgrid-scale variability. In the present study, we investigate the question whether subgrid-scale heterogeneity can be parameterised as the outcome of optimal partitioning between bare soil and vegetated area. We find that a two-box model reproduces the time-averaged biomass of the patterns emerging in a 100 by 100 grid model if the vegetated fraction is optimised for maximum entropy production. This suggests that the proposed optimality-based representation of subgrid-scale heterogeneity may be generally applicable to different systems and at different scales. The implications for our understanding of self-organised behaviour and its modelling are discussed.