Detecting and forecasting tipping points from sample variance alone

TL;DR

This paper introduces TIPMOC, a statistical framework that uses sample variance to detect and forecast bifurcations in complex systems, improving reliability and interpretability over traditional early warning signals.

Contribution

The paper presents TIPMOC, a novel method that leverages power-law divergence of variance to detect and predict tipping points using only sample variance data.

Findings

TIPMOC accurately detects bifurcations in simulations.

It reliably forecasts the timing of tipping points.

The method maintains low false positive rates under various conditions.

Abstract

Anticipating tipping points in complex systems is a fundamental challenge across domains. Traditional early warning signals (EWSs) based on critical slowing down, such as increasing sample variance, are widely used, but their ability to reliably indicate imminent bifurcations and forecast their timing remains limited. Here, we introduce TIPMOC (TIpping via Power-law fits and MOdel Comparison), a parametric framework designed to statistically detect the approach of a bifurcation and estimate its future location using only the sample variance. TIPMOC exploits the mathematical property that variance diverges with a characteristic power-law form near codimension-one bifurcations. By sequentially monitoring system variance as a control parameter changes, TIPMOC statistically adjudicates between linear and power-law divergence at each step. When evidence favors power-law divergence, TIPMOC forecasts the impending tipping point and estimates its position; otherwise, it avoids false positives. Through numerical simulations, we demonstrate TIPMOC's robustness and accuracy in both detection and timing prediction across different types of dynamics and bifurcation. TIPMOC shows low false positive rates and performs well even with uneven sampling and colored noise. This method thus enhances the interpretability and practical utility of classical EWSs, serving as both a transparent add-on and a stand-alone statistical tool for forecasting regime shifts in diverse complex systems.