Absence of detailed balance in ecology

¹ Dipartimento di Fisica “G. Galilei”, Università di Padova, CNISM and INFN - via Marzolo 8, 35131 Padova, Italy, EU
² Institute of Integrative and Comparative Biology, University of Leeds - Miall Building, Leeds LS2 9JT, UK, EU
³ Department of Physics, University of Maryland - College Park, MD 20742, USA

Received: 5 July 2012
Accepted: 16 October 2012

Abstract

Living systems are typically characterized by irreversible processes. A condition equivalent to the reversibility is the detailed balance, whose absence is an obstacle for analytically solving ecological models. We revisit a promising model with an elegant field-theoretic analytic solution and show that the theoretical analysis is invalid because of an implicit assumption of detailed balance. A signature of the difficulties is evident in the inconsistencies appearing in the many-point correlation functions and in the analytical formula for the species area relationship.