Early-warning signals of critical transition: Effect of extrinsic noise

An early warning indicator trained on stochastic disease-spreading models with different noises

The timely detection of disease outbreaks through reliable early warning signals (EWSs) is indispensable for effective public health mitigation strategies. Nevertheless, the intricate dynamics of real-world disease spread, often influenced by diverse sources of noise and limited data in the early stages of outbreaks, pose a significant challenge in developing reliable EWSs, as the performance of existing indicators varies with extrinsic and intrinsic noises. Here, we address the challenge of modelling disease when the measurements are corrupted by additive white noise, multiplicative environmental noise and demographic noise into a standard epidemic mathematical model. To navigate the complexities introduced by these noise sources, we employ a deep learning algorithm that provides EWS in infectious disease outbreaks by training on noise-induced disease-spreading models. The indicator's effectiveness is demonstrated through its application to real-world COVID-19 cases in Edmonton and simulated time series derived from diverse disease spread models affected by noise. Notably, the indicator captures an impending transition in a time series of disease outbreaks and outperforms existing indicators. This study contributes to advancing early warning capabilities by addressing the intricate dynamics inherent in real-world disease spread, presenting a promising avenue for enhancing public health preparedness and response efforts.

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Physics-based early warning signal shows that AMOC is on tipping course

One of the most prominent climate tipping elements is the Atlantic meridional overturning circulation (AMOC), which can potentially collapse because of the input of fresh water in the North Atlantic. Although AMOC collapses have been induced in complex global climate models by strong freshwater forcing, the processes of an AMOC tipping event have so far not been investigated. Here, we show results of the first tipping event in the Community Earth System Model, including the large climate impacts of the collapse. Using these results, we develop a physics-based and observable early warning signal of AMOC tipping: the minimum of the AMOC-induced freshwater transport at the southern boundary of the Atlantic. Reanalysis products indicate that the present-day AMOC is on route to tipping. The early warning signal is a useful alternative to classical statistical ones, which, when applied to our simulated tipping event, turn out to be sensitive to the analyzed time interval before tipping.

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems, there are ongoing debates as to when warning signs can be extracted from data. In this work, we shed light on this debate by considering different types of underlying noise. Thereby, we significantly advance the general theory of warning signs for nonlinear stochastic dynamics. A key scenario deals with stochastic systems approaching a bifurcation point dynamically upon slow parameter variation. The stochastic fluctuations are generically able to probe the dynamics near a deterministic attractor to reveal critical slowing down. Using scaling laws near bifurcations, one can then anticipate the distance to a bifurcation. Previous warning signs results assume that the noise is Markovian, most often even white. Here, we study warning signs for non-Markovian systems including coloured noise and α -regular Volterra processes (of which fractional Brownian motion and the Rosenblatt process are special cases). We prove that early warning scaling laws can disappear completely or drastically change their exponent based upon the parameters controlling the noise process. This provides a clear explanation as to why applying standard warning signs results to reduced models of complex systems may not agree with data-driven studies. We demonstrate our results numerically in the context of a box model of the Atlantic Meridional Overturning Circulation.

Effects of stochasticity and social norms on complex dynamics of fisheries

Recreational fishing is a highly socioecological process. Although recreational fisheries are self-regulating and resilient, changing anthropogenic pressure drives these fisheries to overharvest and collapse. Here, we evaluate the effect of demographic and environmental stochasticity for a social-ecological two-species fish model. In the presence of noise, we find that an increase in harvesting rate drives a critical transition from high-yield-low-price fisheries to low-yield-high-price fisheries. To calculate stochastic trajectories for demographic noise, we derive the master equation corresponding to the model and perform a Monte Carlo simulation. Moreover, the analysis of the probabilistic potential and mean first-passage time reveals the resilience of alternative steady states. We also describe the efficacy of a few generic indicators in forecasting sudden transitions. Furthermore, we show that incorporating social norms on the model allows a moderate fish density to maintain despite higher harvesting rates. Overall, our study highlights the occurrence of critical transitions in a stochastic social-ecological model and suggests ways to mitigate them.

Detecting and distinguishing tipping points using spectral early warning signals

Theory and observation tell us that many complex systems exhibit tipping points—thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein–Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator–prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.

No evidence for critical slowing down prior to human epileptic seizures

There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.

A systematic study of the determinants of protein abundance memory in cell lineage

Proteins are essential players of life activities. Intracellular protein levels directly affect cellular functions and cell fate. Upon cell division, the proteins in the mother cell are inherited by the daughters. However, what factors and by how much they affect this epigenetic inheritance of protein abundance remains unclear. Using both computational and experimental approaches, we systematically investigated this problem. We derived an analytical expression for the dependence of protein inheritance on various factors and showed that it agreed with numerical simulations of protein production and experimental results. Our work provides a framework for quantitative studies of protein inheritance and for the potential application of protein memory manipulation.