arXiv subjects

Tristan Gamot

Publications and source records attributed to Tristan Gamot.

3 recordsLinked to original sources

arXiv2026

An analytical framework to unify ecological and engineering resilience near critical transitions

The capacity of dynamical systems to resist and recover from perturbations, broadly referred to as resilience, is commonly expressed by two complementary quantities: ecological and engineering resilience. As many complex systems exhibit critical transitions, or tipping points, understanding how these resiliences jointly change nearby them is central to characterising and anticipating such shifts. Here, we develop a theoretical framework that clarifies this for bifurcation-induced tipping, i.e., critical transitions triggered by the crossing of a local bifurcation. Using normal form theory, we derive explicit scaling laws for commonly used resilience metrics as functions of the distance to the bifurcation point in parameter space, and show that these extend to general models up to a scaling factor. They are particularly relevant for detecting tipping, where the relative behaviour of metrics matters more than their absolute values. The rates at which metrics decrease as the bifurcation is approached depend on both the type of bifurcation and the metric considered. Furthermore, our results show that, sufficiently close to a local bifurcation, resiliences are intrinsically linked. Our predictions, which replace previously proposed scalings based on heuristic arguments, are validated for three representative models covering all commonly encountered local bifurcations in one-dimensional systems.

q-bio.PE↗

arXiv2026

On the robustness of Mann-Kendall tests used to forecast critical transitions

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time series. Recent results on the lack of validity of this assumption urge a robustness analysis of these approaches. While the issue is relevant across a wide range of applications, we illustrate it here in the context of detecting early warning signals (EWS) of critical transitions, which are used across a variety of research domains, and where commonly applied methods generate autocorrelation. We present a broad analysis, covering all types of critical transitions commonly investigated in EWS studies. We compare empirical distributions of the Mann-Kendall statistic computed from classical EWS indicators preceding critical transitions to the theoretical distributions hypothesized by Mann-Kendall tests. We detect mismatches leading to inflated type I error rates, which would routinely lead to announcing a critical transition while it is not occurring. In contrast to a recent recommendation, we conclude that the use of Mann-Kendall tests for trend detection in the context of forecasting critical transitions should be avoided. We point out several alternative methods available instead.

stat.AP↗

arXiv2025

On the Gaussian distribution of the Mann-Kendall tau in the case of autocorrelated data

Non-parametric Mann-Kendall tests for autocorrelated data rely on the assumption that the distribution of the normalized Mann-Kendall tau is Gaussian. While this assumption holds asymptotically for stationary autoregressive processes of order 1 (AR(1)) and simple moving average (SMA) processes when sampling over an increasingly long period, it often fails for finite-length time series. In such cases, the empirical distribution of the Mann-Kendall tau deviates significantly from the Gaussian distribution. To assess the validity of this assumption, we explore an alternative asymptotic framework for AR(1) and SMA processes. We prove that, along upsampling sequences, the distribution of the normalized Mann-Kendall tau does not converge to a Gaussian but instead to a bounded distribution with strictly positive variance. This asymptotic behavior suggests scaling laws which determine the conditions under which the Gaussian approximation remains valid for finite-length time series generated by stationary AR(1) and SMA processes. Using Shapiro-Wilk tests, we numerically confirm the departure from normality and establish simple, practical criteria for assessing the validity of the Gaussian assumption, which depend on both the autocorrelation structure and the series length. Finally, we illustrate these findings with examples from existing studies.

stat.ME↗