2026/03/22 by Bernd von Mallinckrodt · 1 voice
Biochemistry, Genetics and Molecular Biology · Environmental Science · #Ecosystem dynamics and resilience #Gene Regulatory Network Analysis #Sustainability and Ecological Systems Analysis
paper · doi:10.5281/zenodo.19161205
openalex publication_date 2026/03/22 · openalex created_date 2026/03/23 · openalex updated_date 2026/07/01
This document provides a fully specified empirical test protocol for the CRTI (Constraint–Response Transition Index) framework, designed to evaluate mechanism-dependent collapse dynamics in complex adaptive systems. The protocol operationalizes the distinction between bifurcation-driven collapse (M1) and structural compression collapse (M3) through explicitly defined proxy measures for structural compression (Φ) and adaptive capacity (R), together with a composite diagnostic index T = R / Φ. A central contribution is the conditional validation of effective rank as a proxy for accessible state space entropy, supported by external benchmarking against analytically tractable Gaussian systems. The validity domain is explicitly restricted (Gaussian conditions, moderate anisotropy, d ≤ 10, sufficient sample size), and three failure modes—anisotropy, multimodality, and heavy-tailed distributions—are formally identified and incorporated into the protocol via pre-specified diagnostic tests and fallback estimators. The empirical design is implemented for the Peter Lake whole-ecosystem phosphorus manipulation experiment, a canonical benchmark for critical slowing down (CSD). Mechanism classification is determined a priori using experimental metadata and external forcing structure, ensuring strict non-circularity between classification and proxy evaluation. All statistical tests, thresholds, and decision rules are defined in advance, including Mann–Kendall trend testing with autocorrelation correction, minimum detectable effect sizes, and bootstrap confidence intervals. The protocol is structured to be falsifiable. Explicit falsification criteria are defined for proxy behavior, diagnostic performance, and mechanism classification consistency. The design separates mechanism identification, proxy validation, and empirical testing into independent stages, enabling rigorous evaluation without circular dependencies. This document serves as a Methods Companion to the main CRTI manuscript and is intended for direct reproducibility, reviewer-level scrutiny, and extension to additional systems. It represents a transition from a conceptual framework to a testable empirical program, with clearly stated validity conditions and limitations. Keywords complex systems critical transitions early warning signals mechanism-dependent collapse structural compression adaptive capacity entropy proxy effective rank mutual information system resilience bifurcation dynamics ecological regime shifts Peter Lake experiment empirical protocol reproducibility non-circular inference information theory state space entropy