Quantifying irreversibility of ecological systems

Irreversibility--the asymmetry of population dynamics when played forward versus backward in time--is a fundamental property of ecological dynamics. Despite its early recognition in ecology, irreversibility has remained a high-level and unquantifiable concept. Here, we introduce a quantitative framework rooted in non-equilibrium statistical physics to measure irreversibility in general ecological systems. Through theoretical analyses, we demonstrate that irreversibility quantifies the degree to which a system is out of equilibrium, a property not captured by traditional ecological metrics. We validate this prediction empirically across diverse ecological systems structured by different forces, such as rapid evolution, nutrient availability, and temperature. In sum, our study provides a rigorous formalism for quantifying irreversibility in ecological systems, with the potential to integrate dynamical, energetic, and informational perspectives in ecology.