The Law of Alignment Applied to Ecological Systems: Cumulative Regeneration Imbalance and Ecological Collapse
Abstract
Ecological collapse is commonly modeled as a threshold event in biomass or as a nonlinear critical transition. This paper introduces a structural alternative: collapse as a joint-state boundary event under cumulative regeneration imbalance. In finite regenerative systems, sustained extraction in excess of regenerative capacity generates a nonnegative cumulative misalignment variable that weakens effective drift and compresses the viability basin. Collapse is therefore modeled as a stochastic boundary-hitting event in the joint state space (Sₜ, Mₜ), rather than as a function of stock alone. The paper develops: • A recursive regeneration-adjusted misalignment metric• A joint-state structural formulation of ecological fragility• A monotone boundary-hitting theorem under degradation• An exponential barrier-compression result in the small-noise regime• A regenerative stability budget condition• A state-feedback control framework under degradation memory Documented fishery collapses, including Atlantic cod and Peruvian anchoveta, are shown to be structurally consistent with cumulative stress dynamics. Environmental shocks are interpreted as amplifiers of accumulated imbalance rather than sole collapse drivers. The framework is falsifiable and empirically testable using multi-stock panel data (e.g., RAM Legacy Stock Assessment Database). The contribution is structural and classificatory: collapse is reinterpreted as the predictable outcome of sustained proportional deviation in finite regenerative systems.
Fields of Study & Subjects
Ecosystem dynamics and resilience
Mathematical and Theoretical Epidemiology and Ecology Models
Marine and fisheries research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint