Data-driven identification of reliable sensor species to predict regime shifts in ecological networks

Abstract

Signals of critical slowing down are useful for predicting impending transitions in ecosystems. However, in a system with complex interacting components not all components provide the same quality of information to detect system-wide transitions. Identifying the best indicator species in complex ecosystems is a challenging task when a model of the system is not available. In this paper, we propose a data-driven approach to rank the elements of a spatially distributed ecosystem based on their reliability in providing early-warning signals of critical transitions. The proposed method is rooted in experimental modal analysis techniques traditionally used to identify structural dynamical systems. We show that one could use natural system fluctuations and the system responses to small perturbations to reveal the slowest direction of the system dynamics and identify indicator regions that are best suited for detecting abrupt transitions in a network of interacting components. The approach is applied to several ecosystems to demonstrate how it successfully ranks regions based on their reliability to provide early-warning signals of regime shifts. The significance of identifying the indicator species and the challenges associated with ranking nodes in networks of interacting components are also discussed.

Practical Guide of Using Kendall's τ in the Context of Forecasting Critical Transitions

“…First, there exist a probability distribution over the possible values of Kendall's τ corresponding to each measurement. Hence, a positive Kendall's τ does not guarantee that the system is moving toward a transition unless its significance is confirmed [13,15,16]. Even for a signal measured from a stationary system, one might obtain a positive value for Kendall's τ .…”

“…In addition, identifying the trend of early warning signals might not be trivial due to stochastic fluctuations in the reported values of early warning signals over time. As a result, Kendall's τ coefficient is often used to quantify the trend of statistics related to the critical slowing down phenomenon [8,13]. Kendall's τ is a measure of the correlation between the rank order of the observed values and their order in time [14].…”

“…Even for a signal measured from a stationary system, one might obtain a positive value for Kendall's τ . In addition, the values of Kendall's τ are affected by parameters such as window size, sample rate and the length of the time series corresponding to data collection and analysis steps [13,15,16]. Hence, one needs to examine the effects of different parameters on the distribution of the trend statistic Kendall's τ .…”

Data-driven prediction in dynamical systems: recent developments

“…As a result, developing simple and tractable data-driven system identification methods via a limited number of recorded observations has been the motivation of recent research. These methods focus on the discovery of dynamical systems from high-dimensional data [46][47][48][49][50][51][52][53][54][55] and making predictions of system dynamics based on the identified model. Examples include data-driven identification methods based on nonlinear regression [56], empirical dynamic modelling [57], normal form methods [58], nonlinear Laplacian spectral analysis [59], eigensystem realization algorithms [60], dynamic mode decomposition (DMD) [52,54] and artificial neural networks [61,62].…”

“…Data-driven prediction methods have also offered a solution to the formidable challenge of predicting catastrophic events in a variety of complex systems. Recent studies have shown that features extracted from data can be used to predict critical transitions [165] and extreme events [166] in the dynamics of a variety of complex systems, including aeroelastic systems [39,40,44,167,168], ecological systems [51,[169][170][171][172][173][174][175], epidemiological systems [176][177][178][179], traffic flow systems [158,180] and fluid flows [166,[181][182][183].…”