In CASCADE we developed a number of dryland vegetation models, starting from existing models and sequentially including additional ecological mechanisms thought to be relevant for drylands' ability to cope with increasing pressures. These mechanisms include:

1. modeling more realistic grazing pressures [25],
2. modeling the effect of fire on drylands [46,76],
3. taking the variability of the external pressure (rainfall) into account [95,96],
4. incorporating different types of feedbacks such as erosion feedbacks known to be important for dryland functioning [76,108],
5. taking different plant functional groups into account as a first step into taking more species characteristics into account [46,76,96,128,130,136–138].

Our results highlight the importance of the role of the spatial aspect of the external pressure [25], demographic stochasticity [139], rainfall intermittency and rate of environmental change [95,96,138], the way species interact with each other (facilitation/competition) [46,76,96,128,130,138,139], and the relevance of different types of ecological feedbacks [76,108] for our understanding of the species composition and the dynamics of dryland ecosystems.

Mathematical modeling can be very insightful as experimental or observation studies are often not able to follow dryland ecosystem dynamics at relevant spatial and temporal scales along wide controlled gradients consisting of multiple stressors, or for extreme stress situations that are expected in the near future. In CASCADE, a number of key mechanisms currently lacking from available models were highlighted at the start of the project and incorporated in already existing models. Generally speaking, two ‘lines’ of models were developed, corresponding to two different types of mathematical formalism which each have advantages and disadvantages.

• On the one hand, interaction particle systems were used for their relative mathematical simplicity and implementation [25,46,108,130,136–138]. They provide a very intuitive representation of space as a grid of cells, where each cell can be in a number of pre-defined states (e.g. occupied by a nurse, occupied by a protégée or empty).We developed a code to ease the use of such models.
• On the other hand, differential equation models were used used for the possibility of representing explicitly ecological and physical mechanistic dynamics using continuous state variables [95,96,128,141], or for their (mathematical) tractability, which allowed for solving them analytically [76,128], and/or to include stochastic elements in the dynamics of the forcing stress (rain, [96]; or fires, [76].

Main results

All the models developed in CASCADE confirm the importance of positive feedbacks in driving the emergence of catastrophic responses at the ecosystem scale as a response to increasing stress. We showed that incorporating a realistic aspect of grazing, which is that grazers tend to eat more at the borders of vegetation patches in a patchy landscape, decreased dryland resilience by increasing the size and the probability of catastrophic shifts under increasing stress (drought or grazing intensity) (see »Dryland responses to grazing and droughts). We found that incorporating a feedback between fire occurrence and vegetation composition promoted, in combination with drought, the emergence of alternative stable states and therefore of possible catastrophic transitions between those states (see »Dryland response to fire).

The connectivity-mediated feedback (i.e. the feedback between vegetation pattern, resource redistribution and productivity) decrease the amount of pressure required to cause a critical shift to a degraded state. Not including these feedbacks into dryland ecological models may lead to an overestimation of ecosystem resilience and therefore failures in the prediction of catastrophic shifts (see »Including ecohydrological feedbacks between vegetation pattern and resource redistribution).

Furthermore, the model results suggest that the upcoming climate change predicted for Mediterranean drylands, and in particular the rainfall patterns, could induce and enhance the occurrence of catastrophic shifts in those ecosystems [95].

The models also highlight counterintuitive results. For example [95], we found that, for a constant annual rainfall rate, both an increase and a decrease in mean rainfall intensity could trigger desertification. (see »Dryland response to changes in rainfall intermittency). This finding was attributed to the fact that water can be lost from the system in two ways. During high intensity rain events, a fraction of the water flows through the vegetation bands and is lost as runoff, while during low intensity events a large portion of the water infiltrates in the bare interbands, where it is not available to plants and eventually lost due to soil evaporation and percolation.

The fire models suggest that the oak forests are very resilient and that in this case, catastrophic shifts may actually be less common than previously thought [46,76] (although alternative states emerge when a positive feedback between vegetation composition and fire occurrence is introduced in the model [76]).

Implications of the models for management

The model developed in CASCADE contribute to the fundamental understanding of what determines the species composition of a given dryland and how that drivers the response of the ecosystem to increasing stress, in particular: why and how alternative stable states, and therefore catastrophic shifts, occur in drylands. This fundamental understanding provides some keys for

1. preventing dryland degradation and
2. restoring degraded ecosystems.

Work in other sections of CASCADiS reports on the merging of those ecological models with socio-economic models to help suggest appropriate management measures (see »Socio-ecological effectiveness of land management).

The grazing model [25] suggests that vegetation patterns provide early warning signals of approaching desertification (i.e. the spatial structure itself). However, spatially heterogeneous grazing does not only altered ecosystem stability (by increasing the probability of catastrophic shift) but could also blur the early warning signals at high grazing pressure. This suggests that we need to be cautious regarding the use of early warning signals of ecosystem degradation when the pressure at play has a spatially-explicit component. It also suggests that additional indicators of degradation need to be developed taking into account the spatial component of the stressor.

Furthermore, model simulations suggest that using a bare-soil connectivity index (Flowlength [108]), in addition to vegetation cover and pattern, may provide more informative early-warning indicators of dryland degradation. Thus, the acceleration of bare-soil connectivity from spatially-explicit time-series data may provide an early warning of imminent shift.

Eventually, quantifying those indicators derived from model studies on field data may help identify field sites that are at the higher risk of irreversible degradation and prioritize those for conservation measures. (For more details regarding the indicators developed via the models see »Appropriate indicators for critical thresholds).

For a given ecosystem studied (e.g. CASCADE study sites of Várzea (Portugal) and Ayora (Spain), see »Dryland response to fire), the models developed allow reaching a better understanding of how different interactions and drivers control the composition of dryland communities and their changes through time. Such a knowledge can be extremely useful in terms of management, e.g. to foster one given community over another (or to prevent being trapped in an undesired community). For example, the model results underline the importance of the practice of planting seedlings from late successional, resprouting species to increase the resistance and resilience to forest fires, which has been already proposed and put into practice by restoration ecologists from the CEAM Cascade unit [142] in the CASCADE site of Ayora (see »Ayora, Spain: Restoration potential for preventing and reversing regime shifts). The modelling approach reinforces such practices as it underlines the importance and the resilience of late successional resprouter species on the time scale of a few generations of these plants, which is well beyond human observation.

Moreover, the essential role of facilitation for both species coexistence and ecosystem resilience highlighted by the models [25,130,138] suggests that it may provide a good opportunity for ecosystem restoration. In a degraded dryland, remaining adults individuals can be used as nurses to increase the recruitment probability of seedlings planted below or close to their canopies [143]. In degraded grazed drylands, the same strategy can be applied using preferentially nurse species adapted against grazing, to improve the early survival of the planted seedlings.

Outlook

The next step of this work could consist in investigating whether it would make sense to try to merge these two sets of approaches into a single framework, which would provide a single model including all the mechanisms investigated here in a single framework. The result of such an effort might very well be that the most adapted framework depends on the precise question asked, on the specific ecosystem studied and on the ecological mechanisms that are relevant for the ecosystem under study. In other words, merging the two approaches into a single one might bear the same types of drawbacks as the ones we are currently facing, which lead us to choose different mathematical formalisms for different questions. To ease the transferability of the CASCADE models to other people, the codes underlying the models were made accessible online with some information (see »Sharing the models). 

Note: For full references to papers quoted in this article see

» References