The Law of Alignment Applied to Ecological Systems: Cumulative Regeneration Imbalance and Ecological Collapse

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Authors: Ramzi Najjar
Cited by: 0

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