Early warning signals of catastrophic regime shifts in semi-arid vegetation-soil systems with slow transients

Abstract

Real world complex systems, such as ecosystems, can undergo abrupt and radical qualitative changes in their states. This comes about when the system crosses a critical threshold, also referred to as a tipping point. Such dramatic shifts between alternative stable states, known as catastrophic regime shifts or critical transitions, are inevitably accompanied by sizeable ecological and economic losses; it therefore gets inestimably valuable to forewarn and avert them. Although prognosticating ecological transitions is a seemingly problematic issue, auspiciously, the detection of a general class of diagnostic indices – the so-called early warning signals, has been recently demonstrated by different methods utilising simple mathematical models. These warning indicators are essentially statistical anomalies starting to be seen ahead of the unwanted collapse, appearing to be applicable to a broad variety of dynamical systems. Recent studies made clear that it can be that many systems might exhibit slow transients between the alternative domains of attraction owing to low rates of change in the system after a tipping point has been crossed. Reviewing the crux of the concept of critical transitions in complex dynamic systems together with the proposed early warning indicators, we centre around a dryland ecosystem that undergoes a catastrophic regime shift from a vegetated to a bare desert ecological state through a fold bifurcation. We systematically explore the rate of change during the transient of the system along with the detectability of the potential early warning signals. The main goal of the study is to acquire more insight into the transient behaviour of semi-arid land surface systems that exhibit long transient periods, evaluating how fast the transition unfolds after transgressing a threshold and what are the early warning signals that may be detected in such systems. We employed a two-dimensional lumped model which describes the dynamics of two coupled environmental compartments – a slow component, the soil subsystem and a fast, the vegetation subsystem – under the effect of grazing pressure. A scenario analysis demonstrates that soil parameters (i.e., bare bedrock weathering rates) significantly influence how quickly the transition unfolds after crossing the tipping point. Importantly, the shift between the contrasting states can be either rapid, unfolding over a period of a few years or unexpectedly slow, responding over centuries or more. Early warning signals in biomass can be observed in the form of increasing variance and declining skewness prior to the critical point, whereas statistical signatures of soil time series seemed to fail detecting the critical change. Further, when the system exhibits a transient phase (unfolding very slowly), early indicators hardly provide a timely warning of the actual shift. Our findings underline the great uncertainty involved when it comes to predict critical transitions explained by the prolonged transient phase together with the system dynamics after transcending the critical point.