Diversity–stability relationships revisited: scaling rules for biological communities near equilibrium

The debate on diversity–stability relationships has a long history of theoretical interest and plays a central role in development of modern ecology. But such debate has recently re-opened under critical scrutiny both in theoretical and empirical studies. In this paper we use allometric (or energetic) scaling and statistical physics approaches to this problem. On the basis of local Damuth symmetry, a Markov model of transfer of energy between different species, and the fluctuation–dissipation theorem, scaling rules of species number and population variability of biological communities near equilibrium are derived. These scaling rules indicate that the diversity–stability relationship may be an energetic and thermodynamic consequence of ecological systems near equilibrium, not a simple statistical consequence as derived by other recent theoretical work.