Absence of Detailed Balance in Ecology
Jacopo Grilli, Sandro Azaele, Jayanth R. Banavar, Amos Maritan

TL;DR
This paper demonstrates that ecological models often assumed to have detailed balance are actually inherently irreversible, complicating analytical solutions and revealing inconsistencies in correlation functions and species-area relationships.
Contribution
The paper critically revisits a field-theoretic ecological model, showing the invalidity of its assumptions of detailed balance and highlighting the implications for analytical solutions.
Findings
Inconsistencies in many-point correlation functions
Failure of the species area relationship formula
Absence of detailed balance in ecological processes
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.
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