Absence of Detailed Balance in Ecology

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.