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, yet it has remained a high-level and unquantifiable concept. Here, we introduce a quantitative framework rooted in non-equilibrium statis-tical physics to measure irreversibility in general ecological systems. Through theoretical analyses, we demonstrate that irreversibility serves as a model-free indicator of a system's distance from 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, non-parametric, and model-free formalism to assess the non-equilibrium nature of empirical ecological communities, with the potential to integrate dynamical, energetic, and informational perspectives in ecology.