Permanent grasslands are often hot spots of biodiversity [1
], which contributes to the temporal stability of their services. The variety of plant species present in grasslands is strongly influenced by long-term management practices [2
], with livestock grazing being the major driving force affecting vegetation dynamics, species distribution and landscape-scale biodiversity in addition to forage quantity and quality [3
]. Biodiversity, encompassing variation within species and across landscapes, may be crucial for the longer-term resilience of ecosystem functions and the services that they underpin [4
]. Biodiversity is intimately connected to ecosystem services through various relationships [5
], with species-rich communities tending to perform better than any individual species.
Biodiversity-ecosystem functioning relationships are affected by the number and identities of species, their evenness within the community, their functional traits, and their interactions. If species loss can be compensated by other species contributing similarly to functioning, the role of individual species may shift with environmental change [6
]. Abiotic change then leads to biotic change and vice versa, and different species can contribute most to any given ecosystem process at different points in time and space [7
]. However, there are limits to species redundancy, and high biodiversity is needed to maintain the many processes operating in multi-functioning ecosystems [8
As concepts of ecosystem functioning have evolved, work has broadened to encompass biodiversity loss within and between trophic levels [10
]. This work has benefited from studies of food webs and more widely of ecological networks [11
]. However, Novak et al. [12
] concluded that such studies can only provide limited predictive capacity while our knowledge of the strengths of interactions between species remains poor. The need for increased predictive capacity is pressing, as the world’s ecosystems undergo unprecedented changes with species being lost from a wide range of ecosystems and trophic levels [13
] and there is a need to consider the role that models can play. In particular, the challenges that grassland systems are facing today imply that aspects related to plant diversity cannot be ignored in modelling studies. Grassland models thus need to consider the nutritional value of multi-species swards [14
], the differing herbage intake of grazing animals between mixtures and pure stands [15
], the dependence of milk protein content on the botanical composition of swards [16
], the beneficial effect of legumes on the nitrogen economy of multi-species swards [15
], and the supporting and regulating services (e.g., pollination, pest control, drought resistance) provided by multi-species swards [17
]. Of primary importance is the need for models to account for the complex and variable relationship between grassland biodiversity and productivity. If primary productivity is not used by grazers or humans, then it may sustain larger biodiversity [18
], although some degree of grazing may stimulate biodiversity [19
]. Further, reducing management intensity (e.g., fertilisation) in grasslands reduces livestock productivity but may enhance the quality of meat [20
]. So trade-offs between biodiversity and the way grassland productivity is exploited exist, and climate change may affect how we prioritise one or the other (e.g., [21
]). We need modelling tools to negotiate these trade-offs (e.g., [24
The literature on grassland modelling is extensive. Google Scholar finds over 2 million articles that include the terms ‘model’ as well as ‘grass’ or ‘grassland’, and 1670 of those have the terms in their title; Web of Science finds 1403 thus titled papers (information retrieved on 20 November 2017). We therefore focus our review on categories of grassland models rather than on specific models. Our primary interest here is in modelling the responses of grasslands of varying degrees of biodiversity to climate change. Of course, the climate not only affects grassland biodiversity and productivity but is itself affected by grassland dynamics at large spatial scales. Grasslands, like all vegetation, affect climate via their albedo and greenhouse gas balance, and may play an important role in mitigating climate change. Vegetation effects on the atmosphere are represented in the latest generation of GCMs (Global Climate Models), but are not further discussed here.
We shall consider both static and dynamic modelling, and modelling aimed at explaining observations as well as modelling aimed at predicting the impact of environmental change. We start off with an overview of data that are available for model development. We then review empirical, process-based and integrated grassland modelling approaches. These are reviewed separately, before discussing their relative strengths and weaknesses, and the scope for using elements from one model type in another. A summary of this model overview is provided in Table 1
. We conclude the paper with a brief outlook toward the future use of new types of data and modelling approaches.
2. Data and Inferences from Experimental and Observational Studies
A large body of data from observational studies and from agricultural and ecological experimentation has been collected for grasslands. Data cover both dry and wet areas across wide latitudinal, longitudinal and altitudinal ranges. Most of the ground-breaking experiments on vegetation biodiversity from the 1980s onward were and are being carried out in grasslands because of the convenient size and lifespan of grassland species [58
]. These experiments have primarily focused on the relation between the number of grass species in swards and the magnitude and stability of primary productivity (e.g., [59
]), with some experiments looking at the impact of water or nutrient availability on this relationship [60
], and interactions with mowing [61
]. In a meta-analysis of 44 grassland biodiversity experiments [63
], it was found that different grassland species tended to complement each other, leading to increased productivity in polycultures compared to monocultures. Hector et al. [64
], analysing data from eight sites, found that grassland biodiversity enhanced the stability of productivity over time primarily because of asynchrony in population development. In most of these experiments, full ground cover was established. In grassland experiments with low ground cover, biodiversity still conferred stability but productivity depended more on ground cover than on species richness [65
]. Also, experiments in Germany by Assaf et al. [66
] suggest that biodiversity has a stronger effect on productivity in unmanaged than in managed grasslands. De Boeck et al. [67
] found by experiment that warming may increase the detrimental effect of species loss on grassland productivity in temperate climates. Soussana & Lüscher [68
] reviewed literature showing that elevated CO2
is likely to benefit legumes and forbes more than grasses. In temperature-limited environments of high-latitudes, warming is likely to benefit legumes more than grasses during the temperate growing season [15
], whereas increased nitrogen deposition will disfavour legumes [60
]. However, it is still highly uncertain how warming will affect the winter survival of different grassland species [70
], and the overall impact of warming and interactions with atmospheric CO2
concentration on grassland biodiversity and productivity at high latitudes is highly uncertain.
Agricultural experimentation on grasslands has tended to focus on the impact of abiotic factors and management on yield and quality of forage. However, experiments on grass-legume interactions (typically using only a single grass species and a single clover species) have been carried out for many decades, including interactions with temperature and nitrogen supply [71
], grazers [15
] and FACE-studies of responses of grasses and legumes to elevated CO2
and fertilisation [74
]. Also, there have been experiments examining the effect on cow milk production and ruminant meat quality of grazing the animals on grasslands of differing species composition and richness (e.g., [75
] and studies mentioned in the Introduction).
In short, there is a fair amount of data available for the further development of models aiming to explain or predict the mutual effects of biodiversity and productivity (e.g., [78
]), and the impact of grazing thereon (e.g., [79
]). In contrast, data are still scarce on how climate change, i.e., changes in weather variables rather than CO2
, may affect these relationships (but see the aforementioned [69
]). Also lacking are data that may help explain observed relationships between biodiversity and productivity in grasslands, such as data on soil dynamics—changes in carbon, nutrient and water pools, and the spatial heterogeneity of these pools [80
]. Such soil data are essential if we want to model long-term impacts of changes in biodiversity. In the 9-year long Jena Experiment (Jena, Germany), soil carbon concentration increase was observed to be highly correlated with sown plant species richness [81
]. In particular, the presence of legumes negatively affected soil carbon concentration while other plant functional groups did not influence it, and any increase in carbon storage was mainly limited by the integration of new carbon into soil from fine root turnover and less by the decomposition of existing soil carbon. Long-term data on managed grasslands have also been produced in resampling studies to detect changes in various diversity indices, likely resulting from grazing and fertilization [82
], but the studies lack information about the history of environmental and anthropogenic drivers.
Increasingly, grassland data are becoming available that cover sizeable areas. Tall tower eddy covariance measurements with large spatial footprints and remote sensing allow coverage of large areas at increasing spatial resolution. These data are used to calibrate grassland models aimed at estimating greenhouse gas fluxes and biomass [85
] but are generally not linked to any biodiversity research. Jing et al. [87
] demonstrated the importance of belowground biodiversity for ecosystem multifunctionality at 60 sites on the Tibetan Plateau, covering an area of over one million km2
. They pointed out the need for more experimental work to assess the degree to which climate modulates the links between belowground biodiversity and ecosystem functionality.
3. Empirical Modelling (Static)
Analysis of biodiversity data has most often been carried out using static empirical models that relate response variables to driving variables in a non-dynamic way. Empirical modelling increasingly goes beyond standard linear regression methods, although those are still found useful for productivity-diversity modelling [28
]. Multivariate regression models (e.g., based on constrained ordination) are commonly used in community ecology of grasslands to explain gradients of species or functional composition by a set of climatic, edaphic and agricultural variables [33
]. Newer methods used in grassland modelling include generalised linear and additive mixed models (GLM, GLMM, GAMM; e.g., [29
]), nonlinear species-interaction models [30
] and structural equation models [31
]. Lee et al. [32
] used mixed-effects modelling to combine the results of grassland experiments with projections of future CO2
and nitrogen deposition, to identify areas where productivity may increase and biodiversity decrease. Other examples of empirical models include statistical modelling of livestock productivity effects on grassland biodiversity [18
] and Amiri et al.’s [34
] geospatial model for optimising choice of grazing area given spatial heterogeneity in vulnerability to drought and erosion.
These statistical techniques allow flexible representation of main and interactive effects. However, as all empirical models, they are valuable as descriptive and analytical tools rather than as means for prediction. Extrapolation of empirical models to new conditions (e.g., due to climate change) remains largely speculative, and we focus the remainder of this review on process-based models.
5. Integrated Modelling
Integrated models, like PBMs, are dynamic models, but with the additional characteristic that interactions with human agents are explicitly simulated. So a PBM could form the non-human ecosystem component of an integrated model. A modern approach to integrated modelling is by means of probabilistic networks (graphical models, e.g., Bayesian belief networks for ecosystem services; [56
]). Typically, integrated models are aimed at policy-makers rather than managers of grasslands (who, as a group, are likely to appear as agents in the integrated models). An integrated model for grasslands is the Sustainability and Organic Livestock Model (SOL-Model) which is “especially designed for an integrated analysis of environmental and socio-economic aspects and their inter-linkages” [57
The strengths of integrated modelling are its comprehensiveness (by including human activities) and, for the network approach, the probabilistic thinking that facilitates uncertainty analysis, risk analysis and decision-support. However, integrated models do propagate the weaknesses, discussed above, of any ecological, biogeochemical or agricultural models that they incorporate, and their complexity may hamper the application of probabilistic techniques for calibration, uncertainty assessment and risk analysis [102
6.1. Modelling Aim and Model Types
This review has focused on one important aim of grassland modelling: to predict the impact of climate change on biodiversity-productivity relationships. In this context, a key question is the following: Will biodiversity loss make grasslands less resilient to climate change in general and extreme events in particular? Although there has been provided some experimental evidence for this (e.g., increased drought resistance at higher biodiversity: [103
]), we have not found that current grassland models are able to reproduce these findings. Continued model development thus remains necessary.
Given that our aim involves environmental change, dynamic models seem more appropriate tools than static empirical ones, and we shall focus on PBMs rather than integrated models. But which type of PBM to use? We believe that the answer depends on whether the PBM is used for short- or long-term prediction.
6.2. Modelling for Short-Term Prediction
In the case of short-term prediction, biodiversity is not likely to change much and can be treated as a fixed boundary condition, not dynamically simulated. We suggest that the way forward in this situation is to start from agricultural models but to add the mechanisms through which a given degree of biodiversity protects grassland from diseases, extreme weather events, erosion and other threats. This implies enriching the agricultural grassland PBMs with elements from ecological and biogeochemical models. However, the assumption of constant biodiversity is unlikely to be adequate for the long-term perspective of climate change.
6.3. Modelling for Long-Term Prediction
For long-term prediction, biodiversity must be considered a dynamic variable. Biogeochemical models may be the model type of choice here, given their strength in long-term prediction [45
], but elements from ecological models need to be added to simulate the biodiversity dynamics. For such model development we need more data on currently poorly quantified aspects of biodiversity, such as its role in erosion prevention, tolerance to extreme events, disease resistance, soil decomposition; see e.g., [104
]. Moreover, elements from agricultural models (in particular the impact of management—fertilisation, irrigation, harvesting etc. and grazing on growth and yield) need to be included in the modelling to allow prediction of future food security.
Climate change is expected to increase drought risks for Mediterranean grasslands [106
]. This may prompt us to investigate the use of modelling approaches developed for non-European semi-arid grazing lands. For example, Benie et al. [86
] modelled the impact of grazing intensity on erosion risk in semi-arid grasslands in the Sahel. For grasslands in cold temperate regions, long-term predictions should also take into account the modifying effect of low temperature related stress on vegetation composition and productivity [52
The process of further developing biogeochemical models using elements from ecological and agricultural models may lead to large and unwieldy models, difficult to parameterise. Therefore, rather than explicitly simulating the growth of many different grassland species and their competition, we could consider adding only a biodiversity metric (e.g., the Shannon index; [107
]) as a dynamically varying state-variable in the model. Such simplification would need to be tested carefully, the more so because long-term prediction may require us to consider other aspects of biodiversity than just plant species richness, e.g., soil biodiversity [87
]. For example, persistence of microbial and faunal biodiversity may be required to maintain organic matter decomposition capacity of soils [108
6.4. The Need for Model Diversity
We conclude that, for estimating the impact of climate change impacts on the biodiversity-productivity relationship in managed grasslands, we shall need process-based modelling as outlined above, with models of different kinds depending on the time-frame and spatial extent of prediction. However, PBMs emphasise the biophysical aspects of the system. For wider goals, such as policy making, integrated models rather than PBMs will be needed, to represent the role of human agents. Rather than incorporating complex PBMs in integrated models, it may be best to keep the model types separate and only include simplified representations of the biophysics possibly based on analysis using PBMs in policy-oriented integrated models.
A difficult methodological issue—alluded to at several points in this review—concerns model complexity. The modelling studies considered here address goals that are typically kept separate: explaining and predicting both biodiversity and productivity, as well as their interactions, under climate change. Given our grown understanding of these processes and interactions, more detail could be represented in models, but this would increase our data needs for model parameterization and testing. The optimum in this trade-off will depend on the specific goals of each study, the available data and the methods employed for model calibration and analysis [98
], and general recommendations are not feasible. The best approach may be to maintain model diversity and stimulate comparisons between different models and modelling paradigms.
In conclusion, we believe that modelling the interaction between climate change and the biodiversity-productivity relationship in grasslands will benefit from model diversity, allowing where needed the merging of elements from ecological, biogeochemical and agricultural models. This will take various forms depending on the spatiotemporal scale of application. Summary models derived from such modelling work (e.g., in the form of generically re-usable components, after Confalonieri et al. [94
]), rather than the PBMs themselves, may then be incorporated in integrated models to support policy-making.
Model development will require new data on mechanisms underlying changes in biodiversity, in particular data on spatial heterogeneity of species distribution and soil characteristics. In this respect, we need data analysis methods that allow interpretation of eddy-covariance flux measurements and remote sensing measurements (albedo, NDVI-derived estimates of LAI and biomass; see Wachendorf et al. [112
] for a review of available methods and their potential application in grassland research) in terms of biodiversity. Such data (or proxies obtained from model analysis, e.g., [113
]) are needed to link models across spatial scales (both upscaling and downscaling). A promising example is the work of Gaitán et al. [114
] who found that satellite observations showed the least amount of drought-induced reduction of NDVI in those Patagonian rangelands that were species-rich.
Increased application of probabilistic methods (such as in Bayesian calibration of PBMs or graphical network modelling for ecosystem services) will be needed to quantify uncertainties associated with model predictions and to support risk analysis [102
]. Network modelling will also facilitate analysis of the trade-offs and synergies between productivity, biodiversity and the various other ecosystem services not examined here [115
The increasing availability of data at various spatial and temporal scales, the existing diversity of dynamic models, and the fast development of probabilistic methods that provide the link between data and models—all these, in our view, portent well for the future of grassland modelling as a tool for explaining and predicting the impact of climate change on biodiversity and productivity.