Information-Geometric Early Warning Signals in Complex Adaptive Systems: A Simulation Study Linking Fisher Information to Fluctuation–Dissipation Dynamics

This preprint investigates whether information-geometric quantities derived from 
multivariate abundance data can approximate instability signals predicted by 
fluctuation–dissipation theory (FDT) in stochastic dynamical systems.

We introduce the CRTI (Covariance–Response Temperature Index) estimator 
T_est = Tr(F⁻¹)/Tr(F), constructed from the empirical Fisher Information Matrix, 
and evaluate its performance against the theoretically grounded observable 
T_true = Tr(Σ)/Tr(Σ⁻¹) derived from stochastic generalized Lotka–Volterra (gLV) dynamics.

A reduced ensemble simulation (10 replicates, S=15 species, 30 timesteps) yields 
mean Spearman correlation ρ(T_true, T_est) = 0.983, demonstrating that the 
information-geometric estimator closely tracks the true fluctuation–dissipation 
signal even in small-sample regimes.

Simulation code is included as supplementary material.

early warning signals · Fisher information · fluctuation-dissipation theory · critical transitions · generalized Lotka-Volterra · information geometry · complex systems · regime shifts · critical slowing down · compositional data · microbiome · ecological networks

Resource Type Publication → Preprint
License Creative Commons Attribution 4.0 International (CC BY 4.0)
Language English