Modelling early warning signals for critical transitions in a water-controlled grazing system

In systems subject to gradually changing conditions abrupt and sometimes irreversible shifts between two stable states can take place if a certain threshold is exceeded. These so called critical transitions also occur in arid ecosystems subject to grazing or changing climatic conditions. The transition from a vegetated to a barren state is problematic as it plays a key role in global desertification. Fortunately, early warning signals for this transition in the form of vegetation patterns can often be observed in these ecosystems. In addition, more general signals related to the principle of critical slowing down may be found, as they appear in many systems that approach a transition. This study aims to gain more insight in the behaviour of arid ecosystems and the early warning signals that may be found in these systems. A model was developed and evaluated on early warning signals. The main transition in this model is based on feedbacks between grazing and vegetation growth. When grazing exceeds vegetation growth, the systems collapses. This type of transition was studied before, but in this model water – the resource that was assumed to limit vegetation growth – is explicitly modelled. This allows spatial hydrological processes to be modelled and enables the transition to be forced with hydrological parameters like rainfall intensity and frequency. Furthermore, early warning signals for the transition may be detected in the hydrological compartments of the model. For the transition in this system early warning signals in vegetation density can be found in the form of decreasing skewness and increasing variance and correlation. These signals can be found both in spatial data and time series data. Depending on the relation between vegetation density and infiltration, the signals can also be found in time series of annual discharge, with exception of changing skewness. The variability of the climate however, may result in a weakening of the trends in these indicators. Furthermore, the signals can also be observed when the transition is gradual. Changes in precipitation are less likely to cause a shift in the modelled system compared to intensified grazing. Besides the shift induced by grazing-growth feedbacks another transition is hidden in this system. Feedbacks related to interactions between vegetation and its limiting resource are responsible for this second transition and result in self-organisation of vegetation in vegetation bands. These bands may also serve as early warning signals for this transition. It was hypothesized that the formation of vegetation bands depends both on soil properties and variability in climate and vegetation cover