Semi-arid grazing systems and climate change: a survey of present modelling potential and future needs

Authors


Britta Tietjen, Plant Ecology and Nature Conservation, Potsdam University, Maulbeerallee 2, 14469 Potsdam, Germany (fax: +49 331977 1948; e-mail: tietjen@uni-potsdam.de).

Summary

  • 1Sustainable land use under climate change requires detailed knowledge of the system dynamics. This applies particularly for the management of domestic livestock in semi-arid and arid grazing systems, where the risk of degradation is high and likely climate change may have a strong impact. A suitable way to assess potential future trends of these complex systems is through the application of simulation models.
  • 2We reviewed 41 models published between 1995 and 2005 simulating semi-arid and arid livestock grazing systems. The models were categorized according to the model aim and type, their temporal and spatial scale, and several indicators of model complexity. Additionally, we developed a list of model requirements for adequately simulating the effects of climate change. Based on these requirements, we evaluated the potential of current models to simulate impacts of climate change and determine important shortcomings.
  • 3Three general model types could be distinguished, namely state and transition, difference and differential equation, and rule-based models. Over time, we found that the number of models aiming to improve management strategies increased, while there were fewer models that aimed to understand system dynamics. This was accompanied by a trend to simplify model descriptions of hydrological relationships.
  • 4Important shortcomings of current models included the impact of increased CO2 levels on plant productivity and the ability to resolve changes in intra-annual precipitation patterns. The consideration of both external drivers is crucial under climate change, hence sustainable long-term decision making is currently lacking important information.
  • 5Synthesis and applications. Sustainable livestock management in semi-arid and arid systems requires knowledge about effects of future climate change to adjust livestock density adequately. Producers’ experiences from current weather conditions are not necessarily transferable to future conditions, thus models could help to support management. However, an analysis of current models has shown that few existing models are able to assess the impacts of the predicted climate change. Therefore, we call for the development of new dynamic grazing models that provide land managers with the necessary tools to face the threat of future climate changes.

Introduction

Semi-arid to arid rangelands form nearly 30% of the world's land surface (Stafford Smith 1996; Sivakumar, Das & Brunini 2005). These regions are characterized by a ratio of mean annual rainfall to mean annual potential evapotranspiration of between 0·2 and 0·5 for semi-arid and 0·05 and 0·2 for arid areas (UNEP 1992). An important type of land use in these regions is the production of livestock; according to Puigdefábregas (1998), drylands (areas with rainfall lower than the evaporative demand) support about 50% of the world's livestock. The low mean annual rainfall in semi-arid and arid regions is typically associated with a high variability (Schlesinger et al. 1990) that directly influences primary production (Noy-Meir 1973; Walker et al. 1981; Le Houérou, Bingham & Skerbek 1988; Fang et al. 2001) and hence exerts a major influence on the carrying capacity of the system for livestock. The greater the variability in the climatic conditions, the lower the long-term stocking rate, for example because livestock populations take time to rebuild after die-offs (Illius, Derry & Gordon 1998).

Livestock management also strongly influences vegetation dynamics. World-wide, plant species composition has changed because of land utilization by domestic livestock (Watkinson & Ormerod 2001); an increase in grazing pressure can lead to a reduction of palatable grasses and herbs coupled with an increase in both unpalatable grasses and herbs and woody plants (Perrings & Walker 1997; Anderies, Janssen & Walker 2002; Cingolani, Posse & Collantes 2005). This shift in plant species composition has been shown to be accompanied by reductions in primary productivity (Illius & O’Connor 1999). Because of these probable changes, sustainable management of semi-arid grazing systems requires profound knowledge of the system dynamics (Watkinson & Ormerod 2001).

Climate change is likely to exacerbate any difficulties arising in the management of semi-arid and arid areas. Although forecasts on a regional scale remain difficult (Weltzin et al. 2003), important trends of climate change can be derived from general change patterns. There is evidence of an increased variance of precipitation everywhere: wet areas become wetter and dry areas become dryer (Dore 2005). The reduction in total annual rainfall in semi-arid and arid areas is caused by a decreased frequency of rainfall events. Yet at the same time, the intensity of single precipitation events increases (Easterling et al. 2000).

These changes clearly have an impact on the vegetation of semi-arid and arid regions. More intense rainfall events with no change in total rainfall quantity can lead to lower and more variable soil water content (Fay et al. 2003). As a consequence, the above-ground net primary production is reduced. This reduction is accompanied by a decrease in the livestock carrying capacity, which leads to an exacerbation of overgrazing (Weltzin et al. 2003). Additionally, higher temperatures are likely to intensify water stress through increased potential evapotranspiration (Hughes 2003). At the same time, increased atmospheric carbon dioxide (CO2) could mitigate these effects by increasing water use efficiency (Drake, Gonzàlez-Meler & Long 1997) but it could also change species composition in favour of woody shrubs, with negative implications for nutritive values (Campbell & Stafford Smith 2000).

The enhanced risk of land degradation caused by climate change requires careful management planning for future livestock production. For this, reliable predictions about future trends of vegetation dynamics under uncertain climatic and land-use conditions are crucial. Models offer one way to make predictions that link weather conditions to vegetation dynamics and describe feedback mechanisms between the components of the system. Sustainable management strategies can then be identified to assist long-term planning under uncertain or variable climatic conditions. Numerous models have been developed to assess the feedback between precipitation, vegetation and herbivores. Modelling of semi-arid to arid grazing systems started in the 1960s and 1970s (Wright & Dent 1969; Tadmor et al. 1977; Noy-Meir 1978) and became an important issue in the scientific community in the 1990s, with many different research questions and approaches (e.g. the SAVANNA model; Coughenour 1992). These different approaches need to be evaluated for their success in optimizing management strategies with regard to future variable climate conditions and whether there are still gaps to close.

In this review, we analysed models of semi-arid and arid grazing systems developed from 1995 to 2005, and then elaborated which criteria have to be fulfilled in order to simulate grazing systems under a changing climate. Based on this analysis, we assessed which of the existing models are able to simulate the effects of climate change to allow an evaluation of sustainable management strategies. The identification of important shortcomings led to recommendations for future research.

State-of-the-art of grazing models

We assessed peer-reviewed articles published between 1995 and 2005 that described simulation models of semi-arid and arid grazing systems. The list of publications was not exhaustive; however, with 41 publications it presented a broad overview of the modelling process of grazing systems with domestic livestock in the past 10 years. We assessed five main components of the models: the type of model, its spatiotemporal resolution, the number and type of constituent elements (model complexity), feedbacks and scenarios.

We differentiated two modelling aims: understanding of system dynamics (Understanding) and analysing management strategies (Management), although some models addressed both aspects. We characterized the modelling technique by distinguishing three general model types. State and transition (S&T) models described the state of the vegetation by dominant vegetation types (VT) and transitions between those states. These transitions could be triggered by natural events or management actions (Westoby, Walker & Noy-Meir 1989). Difference and differential equation models calculated the change of each variable (e.g. vegetation biomass and herbivore density) and their interactions using a system of difference/differential equations. This type of models could be subclassified into time discrete finite difference equations (FDE), time continuous ordinary differential equations (ODE) and time continuous and spatially explicit partial differential equations (PDE). Rule-based models (Rule) described processes by rules. In the reviewed publications, such models divided the total area into grid cells. Every cell was characterized by its state, which changed as a result of succession processes, external drivers or interactions with other cells.

In contrast with the more conceptual models that aimed to enhance the understanding of the system dynamics, the models used to assess management strategies were mostly developed for one or more specific sites. Thus, we also report the continents to which the models were applied. Additionally, we examined whether a model validation was carried out. However, we did not judge the sophistication of the validation, for example whether the model was tested on different sites or for several management strategies.

As the introduced models used various temporal and spatial scales, we considered both the extent (maximum value) and resolution. The simulated time span was classified in terms of the decision horizon of a manager. We distinguished short-term (1–5 years), medium-term (5–50 years) and long-term decision making (> 50 years). The temporal resolution was classified into three groups relating to whether models worked on (i) a daily, (ii) a seasonal or (iii) an annual basis. Some models operated on an annual basis but included a submodel operating at a shorter time scale, and were assigned to both groups. In spatial models, the spatial extent and spatial resolution were classified similarly. The spatial extent ranged from less than 1 ha to more than 5000 ha; the resolution ranged from a single plant to more than 50 m.

Those variables relating to the complexity of the system indicated the extent to which water, vegetation and herbivores were described in the model and whether fire could be simulated. Water availability to plants was classified into three groups: it was either described simply by rainfall, explicitly by a single soil layer, or by more than one layer, for example by several soil layers or by surface water and one soil layer. The complexity of vegetation was given by three classes describing the number of vegetation types (VT): total vegetation (one aggregated VT), two VT or more than two VT. Publications that described vegetation in another way, for example by green vs. dry biomass, were classified separately. Herbivores were either modelled implicitly by vegetation reduction or explicitly (simple or detailed).

Feedbacks described an additional aspect of the system complexity related to the influence a component of the system exerted on another component. Where fire was modelled, we analysed whether the vegetation influenced the frequency or intensity of fire.

One advantage of models is their ability to compare different scenarios. As climate change and the evaluation of management strategies were the focus of this review, we investigated whether different climate and management scenario analyses were carried out in the publications.

Results

the model overview

The models were mainly applied to regions in Africa and Australia, but included regions in Asia, North and South America. A detailed classification of these publications is given in the supplementary material (Table S1); a list of the included publications can also be found in Table 1. While both the understanding of system dynamics and the optimization of management strategies were frequent aims of models, emphasis on management strategies has grown recently (Fig. 1a). The number of spatially explicit models has declined in parallel, as most models evaluating different management options did not consider spatial elements (Fig. 1b). Overall, there has been a decline in the proportion of rule-based models, with a concomitant increase in the proportion of difference and differential equation models (Fig. 1c,d). Although conceptual state and transition approaches have been developed since Westoby, Walker & Noy-Meir's (1989) first description (Stringham, Krueger & Shaver 2003), simulation studies with these models were rare. Rule-based models were mainly applied to questions related to the understanding of system dynamics, and the prevalence of these models was similar to that of state and transition models.

Table 1.  Evaluation of the reviewed publications by applying the following criteria: (i) can intra-annual precipitation be tracked adequately, (ii) is soil moisture regarded explicitly, (iii) are the effects of temperature/evapotranspiration incorporated in the model, (iv) can an altered CO2 level be considered, and is the influence of vegetation on (v) the infiltration and (vi) the fire frequency considered. ‘X’ denotes publications that fulfil the given criterion and ‘–’ those that do not fulfil the criterion. With respect to the influence of vegetation on infiltration or on fire, we only give a positive evaluation where vegetation influences the processes infiltration and fire explicitly
PublicationIncorporation of
Intra-annual precipitationSoil moistureTemperature/ evapotranspirationCO2Influence of vegetation on
InfiltrationFire*
  • *

    Where fire is simulated, otherwise blank.

  • Annual or other aggregated precipitation with additional information about the precipitation patterns within this time span.

  • Daily precipitation data.

Adler & Hall (2005) 
Adler, Raff & Lauenroth (2001)
Allen-Diaz & Bartolome (1998)X
Anderies, Janssen & Walker (2002) 
Ares, Bertiller & Bisigato (2003) 
Benie et al. (2005)X 
Bestelmeyer et al. (2004) 
Beukes, Cowling & Higgins (2002)X
Boer & Stafford Smith (2003)XXXX 
Diaz-Solis et al. (2003)X 
Dunkerley (1997)XXX
Glasscock, Grant & Drawe (2005)XX
Hahn, Richardson & Starfield (1999) 
Hahn et al. (2005) 
HilleRisLambers et al. (2001)XXX 
Hunt (2001) 
Illius & O’Connor (2000)X 
Illius, Derry & Gordon (1998)X 
Jackson & Bartolome (2002)X
Janssen, Anderies & Walker (2004)X
Janssen et al. (2000)X
Jeltsch et al. (1996)XXX
Jeltsch et al. (1997a)XXXX
Jeltsch et al. (1997b)XXXX
Perrings & Walker (1997) 
Pickup (1995)XXX
Plant et al. (1999)X 
Pickup (1996)XXX 
Pulina et al. (1999) 
Rietkerk & van de Koppel (1997)X 
Sparrow, Friedel & Stafford Smith (1997)XXX 
Stigter & van Langevelde (2004)XXXX 
van de Koppel & Rietkerk (2000)XXX 
van de Koppel et al. (2002)XXX 
Wang & Hacker (1997)XXXX
Weber & Jeltsch (2000)XX 
Weber et al. (1998)XXX 
Wiegand & Milton (1996) 
Witten, Richardson & Shenker (2005) 
Wu et al. (1996)XX 
Zeng et al. (2005)XXX 
Figure 1.

Overview of model properties. The numbers or proportions of models with specific model properties are given to show (a) trends in the model aim; (b) the percentage of publications (within one aim) that are spatially explicit, describe a model validation, take the influence of vegetation on the infiltration into account and simulate fire events; (c) trends in the model type; and (d) the chosen model type dependent on the model aim, with state and transition (S&T) models, difference or differential equation (FDE, ODE, PDE) models and rule-based (Rule) models. Models falling into two categories (see Table 1) are double-counted.

Trade-offs were found in the complexity of the model components water, vegetation and herbivores. None of the models simulated all of these components in great detail. Generally, only one or two model components were considered in detail, while the remaining components were simplified. The aim of the model mostly dictated whether water or herbivores were modelled in more detail. Models of system dynamics tended to concentrate on the role of water together with one or multiple water layers, whereas models dealing with management questions often simply considered rainfall or ignored the amount of rainfall completely (Fig. 2a). In those models the role of herbivores tended to be more complex (Fig. 2b). Vegetation was frequently modelled using two vegetation types, usually shrubs and grasses or herbs (Fig. 2c).

Figure 2.

Complexity of model components dependent on the model aim. The percentage of publications is shown, which can be categorized into the following complexity classes: (a) water is described by rainfall, explicitly by one layer, by more than one layer or neglected; (b) herbivores are simulated implicitly by vegetation reduction or explicitly in a simple or a detailed way; and (c) vegetation is described by different numbers of aggregated vegetation types (VT) or modelled in a differing way, indicated by ‘other classes’.

About three-quarters of the models considered two to four feedback components between water, vegetation and herbivores. Mostly, the impact of water and herbivores on vegetation was simulated explicitly. In contrast, less than half of the models simulated infiltration dependent on vegetation (Fig. 1b) or included the dependence of herbivores on the vegetation. The remaining models assumed the stocking rate to be constant. Where herbivores were modelled explicitly, herbivore growth was assumed to be dependent on reproduction and weight gain. About one-third of the models included disturbances caused by fire (Fig. 1b), with fire mostly directly linked to vegetation as fuel load.

Less than half of the publications described any attempt to validate the model. Validations were more often carried out for models dealing with management questions than for models aiming to improve our general understanding of system dynamics (Fig. 1b). When regarding the latter model aim in more detail, two main foci were distinguished: models analysing the influence of grazing heterogeneity on vegetation dynamics, for example as a result of watering points, and models analysing pattern formation in the landscape or stable states of the system in general. Additional, more detailed information about the model aims is given in the supplementary material (Table S2).

Inter-annual variable rainfall was considered in nearly every model but only a few evaluated different rainfall scenarios, for example by comparing different mean precipitation levels. No analyses of trends in rainfall intensity and distribution caused by climate change were found. In contrast, most models included an analysis of several stocking rates or other management strategies.

modelling climate change

Models working at the temporal scale of several decades should be able to respond to changes as a result of predicted climatic shifts such as higher temperatures, more variable precipitation and increased CO2 levels. These variables will have an impact on process rates and the strength of feedback mechanisms, and thus on the total system. We developed a criteria list that identified important model requirements to simulate the effects of climate change on a semi-arid or arid grazing system. Subsequently, the criteria will be applied to the publications reviewed earlier in order to evaluate the potential performance of present modelling approaches simulating climate change and to identify shortcomings. However, note that the original intention of the publications was not necessarily to analyse the effects of climate change.

model requirements

World-wide, precipitation patterns are predicted to become less frequent but more intense events (Easterling et al. 2000). Although the general effects of climate on production are well documented, the effects of extreme events are less well understood (Campbell & Stafford Smith 2000). Several publications emphasized the importance of considering intra-annual precipitation changes (Schlesinger et al. 1990; Puigdefábregas 1998; Knapp et al. 2002; Fay et al. 2003; Weltzin et al. 2003) in order to investigate the impact of climate change on ecosystems (Porporato, Daly & Rodriguez-Iturbe 2004).

Soil moisture as a key driver of vegetation dynamics (Wight & Hanks 1981) should be included in any model that simulates impacts of climate change. Soil moisture is dependent on infiltration and precipitation as well as run-off, interception and evapotranspiration, in turn determined by the prevailing temperature. Thus, to assess the effects of climate change on soil moisture and hence on the vegetation, variable temperature or evapotranspiration should be considered explicitly. This also applies for the possible mitigating effect of increased atmospheric CO2. While experiments have shown increased plant growth under increased CO2 (Drake, Gonzàlez-Meler & Long 1997), this may affect different vegetation types differently and may alter the tree–grass balance in savannas (Bond, Midgley & Woodward 2003). This will result in important changes in plant species composition, thereby altering conditions for livestock production (Campbell & Stafford Smith 2000). Therefore, models dealing with climate change should also incorporate the effects of changed CO2 conditions in the atmosphere.

Climate change will have an impact on mechanisms within the systems, thus all relevant feedbacks between the system variables should be simulated explicitly. One important mechanism concerning changing precipitation patterns is the influence of the current vegetation on soil moisture. A decrease in vegetation cover leads to increased run-off and decreased infiltration, in turn decreasing the water availability to plants (O’Connor, Haines & Snyman 2001). Infiltration cannot simply be described by a rate dependent on precipitation because it is also dependent on the current vegetation cover. Land degeneration processes must also be considered. Similarly, altered vegetation biomass caused by climate change can lead to changes in fire frequency and intensity (Turner & Romme 1994; Williams, Karoly & Tapper 2001; Govender, Trollope & van Wilgen 2006), thus fixed fire probabilities are inadequate when assessing the effects of climate change.

potential of present models to simulate climate change

None of the models reviewed were able to simulate climate change effectively according to our criteria (Table 1). One main limitation was the neglect of atmospheric CO2 in all models. Additionally, only a few models were able to describe changes in precipitation patterns accurately, as the majority of models used an annual or seasonal time resolution. Models incorporating higher temporal resolution operated at a daily level (Sparrow, Friedel & Stafford Smith 1997; Illius, Derry & Gordon 1998; Illius & O’Connor 2000; Boer & Stafford Smith 2003; Stigter & van Langevelde 2004), on a coarser scale with additional information about precipitation patterns within this time (Wu et al. 1996; Wang & Hacker 1997; Benie et al. 2005), or were event driven (Plant et al. 1999). Although models described by Jeltsch et al. (1997a,b) and Weber et al. (1998) included daily rainfall data, these data were aggregated to annual soil moisture in a way that did not allow changes in precipitation patterns within 1 year to be simulated. Generally, there was a trend towards modelling the water component in a less complex way. The proportion of models describing the water dynamics of two or more layers decreased strongly from 1995 until 2005, while the proportion of models simulating rainfall or ignoring rainfall variance increased (Fig. 3a). This was also true for the proportion of models simulating the influence of the current vegetation on the infiltration (Fig. 3b). In contrast, no clear trend was found for consideration of temperature and evapotranspiration. Where fire was simulated, its frequency or intensity depended mostly on the fuel load provided by the vegetation cover. Of the 41 publications, only two met all criteria (except for the incorporation of CO2), namely the models developed by Boer & Stafford Smith (2003) and Stigter & van Langevelde (2004).

Figure 3.

Temporal development of the complexity of the water component. The proportion of models is shown (a) simulating the water component in a specific complexity class and (b) incorporating temperature/evaporation and the influence of vegetation on infiltration.

Discussion

Numerous models have been developed to describe herbivore–plant interactions in arid and semi-arid regions. Several organizations promote and test the use of these models as decision support tools for grazing management (FAO 1998; LEAD 2006).

Climate change could result in changes in the system dynamics that are not covered by previous experience. Models explicitly simulating the effects of climate change on semi-arid and arid grazing systems could help land managers to adapt to a new situation. The effects of alternative livestock densities could be tested for different climate scenarios, from which optimal stocking rates could be established. Models are required that can track a changing climatic environment in long-term simulations of grazing systems. However, our review of existing methods shows that current models of semi-arid and arid grazing systems focus on differing research questions and are unable to make predictions about changes in system dynamics as a result of climate change. Notably, models including increased CO2 levels in the atmosphere are missing. Few grazing models simulated water dynamics in any detail, despite the emergence of a new field called ecohydrology (Rodriguez-Iturbe 2000; Porporato et al. 2002; Rodriguez-Iturbe & Porporato 2004; Wilcox & Newman 2005). Ecohydrology is concerned with the coupled dynamics of water and vegetation, for example to analyse the influence of precipitation patterns on water availability to plants (Loik et al. 2004; Porporato, Daly & Rodriguez-Iturbe 2004) and to explain vegetation patterns (Okayasu & Aizawa 2001; von Hardenberg et al. 2001; Rietkerk et al. 2004).

The inclusion of CO2 in a grazing model was, for example, undertaken by Howden et al. (1999) for the more humid south-eastern part of Queensland, Australia. In their modelling approach, they extended the pasture and animal production model GRASP (McKeon et al. 1990) to simulate the effects of CO2 and other climate change scenarios. This approach could also be applied to existing models of arid and semi-arid regions. It would also be expedient to use a model describing more than one vegetation type, because the response of species to climate change and also to herbivores can differ greatly.

A promising model is the ARENA model, developed by Boer & Stafford Smith (2003) for north Australian rangelands. It is a grid-based difference equation model that aims to simulate long-term changes in vegetation composition dependent on the grazing regime and fire. The model fulfils five out of six criteria, but the impact of CO2 would have to be added in order to simulate the impacts of climate change. Different management scenarios can be evaluated by changing the stocking rate, the daily intake per animal equivalent or the start and end day of the grazing season. The model simulates growth of three vegetation types, namely annual and perennial herbaceous vegetation and woody vegetation.

A model meeting four out of five criteria was the conceptual approach by Stigter & van Langevelde (2004); fire was not evaluated because it was not included into this model. Ordinary differential equations are solved analytically as well as numerically to find a strategy to achieve maximal yield in a pastoralist–herbivore–vegetation system without falling below a critical vegetation biomass density. Like the ARENA model, it uses daily precipitation data; however, in this model only one management year is simulated. As the model is conceptual and not meant to simulate specific rangelands, it was not validated. Thus, it is probably not appropriate to be used as management tool for a ‘real’ grazing system.

Other models that could reasonably be extended are the rule-based models described by Jeltsch et al. (1997a,b) and Weber et al. (1998). As an improvement to these models, the water component should be described with higher temporal resolution. This should easily be possible, as daily rainfall data are already used, but currently it is aggregated to annual soil moisture. Additionally, temperature and CO2 would have to be included in the model.

Other models also met key criteria but essentially they were conceptual approaches that aimed to enhance the understanding of the system dynamics and could not be applied directly to manage specific grazing systems (van de Koppel & Rietkerk 2000; HilleRisLambers et al. 2001; van de Koppel et al. 2002; Zeng et al. 2005). These models concentrate on analytical solutions of the system dynamics and assume constant parameter values. However, because they describe water dynamics in a detailed way, it would be interesting to look at numerical solutions with variable precipitation and evapotranspiration.

The development of new models meeting the criteria described in this study is of great interest because they would facilitate comparisons between the outputs of different modelling approaches. Researchers could learn from ecohydrologcal models, which were introduced above, or from digital global vegetation models (DGVM). DGVM have been developed primarily to simulate terrestrial ecosystem responses to rapid climate change (Cramer et al. 2001). DGVM link general circulation models (GCM) with vegetation dynamics, which are described by physiological, biophysical and biogeochemical processes. The effects of enhanced atmospheric CO2 levels can be included explicitly in DGVM (Foley et al. 1996; Haxeltine & Prentice 1996; Woodward, Lomas & Betts 1998; Cox 2001; Sitch et al. 2003). However, DGVM can have limitations in areas subject to pronounced seasonal water deficits, as Smith, Prentice & Sykes (2001) showed in a comparison of an individual-based model and a DGVM in a wide range of locations.

Which model type shows promise for future model development depends on the research question. State and transition models are appealing because they take account of the knowledge of farmers and can be based directly on observations. Additionally, irreversible changes can be tracked easily. However, changing drivers of the system dynamics are difficult to include and possible states of the system have to be specified in advance. In particular, feedbacks between system variables are not regarded explicitly. Thus simulating the effects of climate changes could be problematical. These difficulties would not arise with difference or differential equations as neither the drivers nor the states of system variables are fixed. However, comprehension of this model type is less intuitive, which could decrease the confidence of farmers in model results. Additionally, accounting for discontinuity of driving forces or including spatial heterogeneity can cause some difficulties. Rule-based models provide a similar intuitiveness as state and transition models and encounter similar difficulties when it comes to changed drivers, which have to be included in the rule set in advance.

An additional question in model development is whether space matters, i.e. if models should be spatially explicit or not. This can be dependent on the underlying model aim and the landscape structure, for example if soil structure or topography are quite heterogeneous, spatial considerations may be important. Because of the dependence of the suitability of the model approach on the model aim, we do not make a general recommendation about appropriate future model types. Instead, we encourage scientists to test and compare different approaches and to combine them.

To summarize, there is a clear need for models simulating the effects of climate change on arid and semi-arid grazing systems as decision support tools for producers. Present approaches disregard the impact of the level of atmospheric CO2 on the ecosystem and are often not able to account for changing precipitation patterns, but some models could reasonably be extended. To overcome present shortcomings, future research on sustainable, long-term management of domestic livestock in arid in semi-arid regions should set a focus on climate change and its impacts on the system.

Acknowledgements

We thank an anonymous referee, Kai Lessmann, Max Rietkerk, Peter Vesk and the editor Phil Hulme for their valuable comments and suggestions. This study was supported by the Heinrich-Böll-Foundation and by the GLOWA Jordan River project, which is financed by the German Federal Ministry for Education and Research (BMBF), contract 01LW0306(A). The authors alone are responsible for the content of this publication.

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