Absence of Detailed Balance in Ecology

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.