Abstract
Forecasting bifurcations such as critical transitions is an active research area of relevance to the management and preservation of ecological systems. In particular, anticipating the distance to critical transitions remains a challenge, together with predicting the state of the system after these transitions are breached. In this work, a new model-less method is presented that addresses both these issues based on monitoring recoveries from large perturbations. The approach uses data from recoveries of the system from at least two separate parameter values before the critical point, to predict both the bifurcation and the post-bifurcation dynamics. The proposed method is demonstrated, and its performance evaluated under different levels of measurement noise, with two ecological models that have been used extensively in previous studies of tipping points and alternative steady states. The first one considers the dynamics of vegetation under grazing; the second, those of macrophyte and phytoplankton in shallow lakes. Applications of the method to more complex situations are discussed together with the kinds of empirical data needed for its implementation.
Highlights
Multiple stable dynamics coexist in ecological systems that have thresholds and breaking points
We demonstrate here the proposed method with simulation data generated with two established ecological models whose bi-stable dynamics have been studied extensively: a vegetation grazing ecosystem [1, 6, 9, 20, 21] and a feedback system between macrophytes and phytoplankton in shallow lakes [19, 22,23,24]
We focus on bi-stable systems because of their relevance to tipping points, not just in ecology but in a wide variety of fields concerning the dynamics of
Summary
Multiple stable dynamics coexist in ecological systems that have thresholds and breaking points. Transitions from one stable dynamics to another can often lead to drastic changes such as the extinction of species or the loss of ecosystems’ function [1, 2] These changes are sometimes referred to as critical transitions in ecology to refer to catastrophic shifts. Specific types of bifurcations have different names in different fields, for instance fold or saddle-node bifurcations in mathematics are referred to as first order phase transitions in physics and as critical transitions in ecology. These bifurcations occur when two fixed points of the system eliminate each other when they come together, and results in a jump or discontinuity in the bifurcation diagram.
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