Rounsevell Mark
email: mark.rounsevell@kit.edu

Arneth Almut

Brown Calum

William W L Cheung

Gimenez Olivier

Holman Ian

Leadley Paul

Luján Criscely

Mahevas Stephanie

Maréchaux Isabelle

Pélissier Raphaël

Vieilledent Ghislain

Wintle Brendan A 12

Shin Yunne-Jai

Mark D A Rounsevell

Identifying uncertainties in scenarios and models of socioecological systems in support of decision-making

Keywords: uncertainty, scenarios, socio-ecological models, decision-making

There are many sources of uncertainty in scenarios and models of socio-ecological systems, and understanding these uncertainties is critical in supporting informed decision-making about the management of natural resources. Here, we review uncertainty across the steps needed to create socioecological scenarios, from narrative storylines to the representation of human and biological processes in models and the estimation of scenario and model parameters. We find that socio-ecological scenarios and models would benefit from moving away from "stylized" approaches that do not consider a wide range of direct drivers and their dependency on indirect drivers. Indeed, a greater focus on the social phenomena is fundamental in understanding the functioning of nature on a human-dominated planet. There is no panacea for dealing with uncertainty, but several approaches to evaluating uncertainty are still not routinely applied in scenario modeling, and this is becoming increasingly unacceptable. However,

Introduction

"The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts" [START_REF] Russell | History of Western Philosophy[END_REF] . With this phrase, Bertrand Russell highlights the imperative of embracing uncertainty rather than fooling ourselves into thinking that it does not exist. This holds especially true for how we understand the natural world, including the increasingly important role of humans in socio-ecological systems. We know that socio-ecological systems are complex. They are non-linear, bifurcate, have feedbacks and tipping points, all of which makes their future development inherently uncertain and difficult to predict. Indeed, the future is a place we can never know; we cannot observe it, and we cannot measure it. Yet, decision makers are challenged with planning short to long-term strategies for preserving biodiversity and the contributions of nature to people [START_REF]Biodiversity and Ecosystem Services for Europe and Central Asia (Secretariat of the Intergovernmental Science-Policy Platform for Biodiversity and Ecosystem Services[END_REF] and so, we need to anticipate what the future may hold.

The scientific response to this challenge has been the development of scenarios to explore the uncertainty space of plausible, but unknown, futures [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF] . Scenarios are not predictions, but are "a plausible and often simplified description of how the future may develop based on a coherent and internally consistent set of assumptions about key driving forces and relationships" [START_REF]Ecosystems and Human Well-being: Biodiversity Synthesis[END_REF] . Scenarios are commonly underpinned by qualitative descriptions (narrative storylines) of the underlying direct and indirect drivers of change including policy options [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF][START_REF] Rounsevell | Developing qualitative scenario storylines for environmental change assessment[END_REF] , which are often translated into impacts on biodiversity, ecosystem services and complex socio-ecological systems using models in a storyline and simulation approach [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF] . Hence, scenarios can be qualitative, quantitative or both. As such, scenarios and models are invaluable tools in guiding long-term, strategic policies that prompt management actions and increase public awareness of the future threats to nature [START_REF] Acosta | The methodological assessment report on scenarios and models of biodiversity and ecosystem services[END_REF] .

Due to the complexity of socio-ecological systems, but also to advances in knowledge and observation capacity, models are being developed with increasing complexity, involving many processes and feedbacks, and integrating multiple components of the ecosystem, from the physical environment to human societies. Examples include, land use models [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF] , agent-based models [START_REF] Brown | Societal breakdown as an emergent property of largescale behavioural models of land use change[END_REF] , marine ecosystem models [START_REF] Tittensor | A protocol for the intercomparison of marine fishery and ecosystem models: Fish-MIP v1.0[END_REF][START_REF] Travers | Towards end-to-end models for investigating the effects of climate and fishing in marine ecosystems[END_REF] , models of trophic levels [START_REF] Harfoot | Emergent Global Patterns of Ecosystem Structure and Function from a Mechanistic General Ecosystem Model[END_REF] , dynamic vegetation models [START_REF] Pavlick | The Jena Diversity-Dynamic Global Vegetation Model (JeDi-DGVM): a diverse approach to representing terrestrial biogeography and biogeochemistry based on plant functional trade-offs[END_REF][START_REF] Prentice | Dynamic Global Vegetation Modeling: Quantifying Terrestrial Ecosystem Responses to Large-Scale Environmental Change[END_REF] , state and transition landscape models [START_REF] Daniel | State-and-transition simulation models : a framework for forecasting landscape change[END_REF] and niche-based models of species response to climate and land use change [START_REF] Buisson | Uncertainty in ensemble forecasting of species distribution[END_REF] . There has been a strong focus on developing comprehensive modelling tools from empirical evidence [START_REF] Medlyn | Using models to guide field experiments: a priori predictions for the CO 2 response of a nutrient-and water-limited native Eucalypt woodland[END_REF][START_REF] Cury | Ecosystem oceanography for global change in fisheries[END_REF] , but until now, far less effort has been dedicated to exploring the uncertainties within these models, especially when used to quantify scenarios.

Identifying and quantifying future uncertainties may be key in achieving buy-in from stakeholders, to prompt evidence-based decision-making, and to shift mind-sets on the perception of the future threats to biodiversity, ecosystems and ecosystem services. To increase the influence of scenario and modelling analyses on policy and to trigger appropriate management responses, the Intergovernmental science-policy Platform on Biodiversity & Ecosystem Services (IPBES) has strongly encouraged the use of scenarios and models, but warns that these "should be applied with care, taking into account uncertainties and unpredictability associated with model-based projections" [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF] . A critical challenge for improving scenarios and models of socio-ecological systems is to augment the scientific capacity in quantifying the uncertainty within and among model projections [START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF] .

Here, we review the current state of knowledge about the uncertainties associated with scenarios and models of socio-ecological systems within the context of decision-making, by which we mean the policy decisions made within private or public sector organisations. In doing so, we seek to address some of the key challenges raised by Elsawah et al. (2020) [START_REF] Elsawah | Science of the Total Environment Scenario processes for socio-environmental systems analysis of futures : A review of recent efforts and a salient research agenda for supporting decision making[END_REF] that relate to uncertainty, such as the role of stakeholder engagement in the co-development of scenarios, linking scenarios across multiple geographical, sectoral and temporal scales, improving the links between qualitative and quantitative scenarios, addressing surprises, addressing scenario consistency, communicating scenarios and linking scenarios to decision making. We do not aim to undertake an exhaustive evaluation of scenarios and model types. Instead, we use examples from a very wide range of scenarios and models to illustrate a comprehensive review of sources of uncertainty. A comprehensive review of sources of uncertainty in scenarios and models does not require a comprehensive review of scenarios and models. A wider ranging review can be found in the IPBES (2016) [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF] assessment of scenarios and models.

We provide an overview of how uncertainty is treated within socio-ecological systems analysis and how understanding these uncertainties can enhance confidence in the creation of the next generation of scenarios and models. This is novel in both tackling a comprehensive review of sources of uncertainty in scenarios and models, exploring the implications of these uncertainties for decisionmaking and in setting-out a number of potential solutions and recommendations for how to deal with these uncertainties.

Types of uncertainties

We focus on three categories of uncertainty: scenario uncertainty, model uncertainty and decisionmaking uncertainty (see Table 1) across terrestrial and marine realms. We explore the whole chain of steps needed to create socio-ecological scenarios and models that are useful for decision-makers, from narrative storylines, the representation of human and biological processes in models, the estimation of model parameters and model initialisation and evaluation. Some of these sources of uncertainty relate to differences in worldviews, some to the limits of our current knowledge and others to our capacity to represent processes within models including the reliability of model input data across spatial and temporal scales. Figure 1 shows the types of uncertainty (from Table 1) in the steps from observational data, model development, the construction of qualitative storylines and quantitative scenario projections that together provide input to decision-making.

Scenario Uncertainty

Linguistic uncertainty

Linguistic uncertainty has been classified into five distinct types: vagueness, context dependence, ambiguity, indeterminacy of theoretical terms and under-specificity [START_REF] Regan | A taxonomy and treatment of uncertainty for ecology and conservation biology[END_REF] . Of these, ambiguity and vagueness arguably occur most commonly, largely because scenario terminology is often based on common language words. Indeed, the word 'scenario' itself derives from the language of the theatre.

Yet, different communities can sometimes attribute different meanings to the same 'precise' word, i.e. their use is ambiguous. For example, the word 'pathways' is used as a synonym for 'projections' or 'trajectories' (as in the shared socio-economic pathways [START_REF] O'neill | A new scenario framework for climate change research: The concept of shared socioeconomic pathways[END_REF] ), or alternatively it is used to describe a set of time-dependent actions that are required to achieve a future vision 2 . Using the term in one sense can lead to confusion if it is interpreted as being used in the other sense. Vagueness relates to statements with insufficient precision. For example, 'population growth will increase strongly over the coming 50 years' tells us nothing about what a strong population growth actually looks like. Is it a doubling of population, or tripling, or something else? These different types of linguistic uncertainty commonly occur in narrative storylines, and they are especially important considerations when communicating the outcomes of scenario processes to decision-makers. Recent development of information technology provides a means to minimize linguistic uncertainty by building ontologies, i.e. an ensemble of formal definitions of concepts and their relationships within the domain of interest, and their synonyms or equivalents in closely related domains. While domain-specific ontologies exist in ecology that facilitate data mining and sharing [START_REF] Madin | Advancing ecological research with ontologies[END_REF] , to our knowledge, there is no widely accessible controlled vocabulary or thesaurus standardizing the meaning of the basic concepts used in scenarios of socio-ecological systems, as is the case with ontologies related to the Intergovernmental Panel on Climate Change (IPCC) [START_REF] Sleeman | Ontology-Grounded Topic Modeling for Climate Science Research[END_REF] .

Narratives storyline uncertainty

The first step in the construction of scenarios is often the development of qualitative, narrative storylines [START_REF] Rounsevell | Developing qualitative scenario storylines for environmental change assessment[END_REF] . These describe alternative trajectories in the key drivers of change (and their interactions) with a focus on socio-economic change. Socio-economic trajectories can also be associated with changes in physical conditions, such as climate change, where a change in climate is assumed to be internally consistent with drivers of, for example, societal consumption patterns and industrialisation [START_REF] Van Vuuren | A new scenario framework for Climate Change Research: scenario matrix architecture[END_REF] . The uncertainties associated with the development of narrative storylines arise from how to create this internal-consistency using mental models [START_REF] Metzger | A spatially explicit and quantitative vulnerability assessment of ecosystem service change in Europe[END_REF] , as well as the difficulty of imagining futures for which there are no historical analogues and representing a sufficient range of possible futures [START_REF] Maier | An uncertain future, deep uncertainty, scenarios, robustness and adaptation: How do they fit together[END_REF][START_REF] Trutnevyte | Reinvigorating the scenario technique to expand uncertainty consideration[END_REF] . This affects the 'plausibility' of narrative storylines in terms of whether the assumed causal relationships reflect real-world development, or the worldviews of the storyline developer. A particular case of this problem are 'black swans', which reflect shocks or surprises to a system, i.e. events that are unexpected or assumed to have a low probability of occurring, but which have a high impact [START_REF] Taleb | The black swan: The impact of the highly improbable (Random house)[END_REF] . Black Swans by their very nature can be difficult to anticipate or imagine, and are often unprecedented historically. The most appropriate way of dealing with uncertainties in storyline development is to clearly state and document the assumptions that underpin a narrative, and to communicate these assumptions when reporting a scenario study [START_REF] Metzger | How personal judgment influences scenario development: an example for future rural development in Europe[END_REF] .

Most narrative storylines focus on the supply-side of natural resource systems (e.g. crop production, or fish harvesting), and say little about the demand-side (e.g. consumption patterns such as dietary preferences) or the economic and institutional transformations that implicitly underlie the storylines.

Although many 'stylised' scenarios exist for diets, e.g. what would be the consequences for biodiversity of people becoming vegetarian or vegan [START_REF] Henry | The role of global dietary transitions for safeguarding biodiversity[END_REF][START_REF] Vuuren | the need for negative emission technologies[END_REF] , these do not account for the transitions from where we are today to this assumed future situation [START_REF] Brown | Achievement of Paris climate goals unlikely due to time lags in the land system[END_REF] . Hence, the uncertainties associated with these transitions are not explicit.

Existing storylines of marine ecosystems largely focus on a narrow set of direct drivers, such as fishing or climate change [START_REF] Lotze | Global ensemble projections reveal trophic of ocean biomass declines with climate change[END_REF] , or short-term policy interventions (such as protected areas or management of fishing effort). Moreover, the consideration of indirect drivers such as seafood demand from changes in population, consumption patterns or international trade, are not explicit in most marine storylines.

Recent studies increasingly focus on expanding the scope of uncertainties by developing storylines that consider multiple drivers and policy interventions, in particular the interactions between climate change, fishing and management [START_REF] Gaines | Improved fisheries management could offset many negative effects of climate change[END_REF][START_REF] Dueri | Food security, biomass conservation or economic profitability? Projecting the effects of climate and socioeconomic changes on the global skipjack tuna fisheries under various management strategies[END_REF][START_REF] Maury | From shared socio-economic pathways (SSPs) to oceanic system pathways (OSPs): Building policy-relevant scenarios for global oceanic ecosystems and fisheries[END_REF] .

Terrestrial studies have a longer tradition of evaluating multiple, often cross-scale drivers in developing narrative storylines [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF] . However uncertainties arise from an overreliance on climate change as a driver, and not accounting for other drivers that are critical for socio-ecological systems, such as invasive alien species, trade in wild species or air and water pollution 2 . Furthermore, uncertainties also arise from failure to account for indirect, cross-sectoral interactions [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF] .

Participatory approaches, by which narrative storylines are co-created with stakeholders, add richness and diversity to storyline development, and strengthen the link between storylines and scenario quantification with models [START_REF] Kok | European participatory scenario development: strengthening the link between stories and models[END_REF] , but are highly dependent on the selection of individual stakeholders and the extent of their explicit and tacit knowledge. Stakeholder mapping exercises [START_REF] Kok | European participatory scenario development: strengthening the link between stories and models[END_REF] that seek to maximise stakeholder diversity are one way of resolving this problem. Participatory approaches are well developed in the marine realm especially in fisheries management and marine spatial planning [START_REF] Planque | A participatory scenario method to explore the future of marine social-ecological systems[END_REF][START_REF] Gopnik | Coming to the table: Early stakeholder engagement in marine spatial planning[END_REF] .

Scenario parameter uncertainty

Simulation models can quantify the outcomes of narrative storylines for specific indicators. This requires the translation of the qualitative statements within a storyline into quantitative model inputs, which in itself has potential to introduce additional uncertainties [START_REF] Rounsevell | Developing qualitative scenario storylines for environmental change assessment[END_REF] . We draw a distinction here between 'scenario parameter uncertainty' and 'model parameter uncertainty'. Scenario parameter uncertainty derives from the translation of qualitative narratives into quantitative values, and so is dependent on the scenario itself, i.e. the quantitative values vary across scenarios. For example, a scenario parameter could be the number of people in a high, medium or low population growth storyline. In general scenario parameters relate to the socio-economic components of socio-ecological systems and may themselves be model inputs. Model parameter uncertainty refers to the estimation of parameters within the functions that represent modelled processes, e.g. a rate constant or capacity, and often, but not always, relate to the biophysical components of socio-ecological systems. Hence, model parameter uncertainty depends on the system and the model of that system, and is independent of a scenario. Scenario parameter quantification often uses best guess estimates that sometimes draw on uncertain, historical analogues. However, the majority of these studies do not account for the uncertainties associated with the process of estimating scenario parameters themselves. A few exceptions to this have defined 'credible' parameter ranges [START_REF] Pedde | Bridging uncertainty concepts across narratives and simulations in environmental scenarios[END_REF] , or have used conditional probabilistic futures methods [START_REF] Henry | Food supply and bioenergy production within the global cropland planetary boundary[END_REF] .

In the conditional probabilistic approach, probability distribution functions (PDFs) are created for the scenario parameters that are conditional on the assumptions within a scenario storyline, thus reflecting the uncertainty range in the estimation of a scenario parameter [START_REF] Henry | Food supply and bioenergy production within the global cropland planetary boundary[END_REF][START_REF] Brown | Analysing uncertainties in climate change impact assessment across sectors and scenarios[END_REF][START_REF] Engström | Assessing uncertainties in global cropland futures using a conditional probabilistic modelling framework[END_REF] . When combined with Monte Carlo sampling across the PDFs and multiple model simulations this approach is able to explore the range of scenario outcomes that are contingent on the uncertainties of scenario parameter inputs, although subjective assumptions and choices made in Monte Carlo sampling can introduce uncertainty in model outcomes [START_REF] Beulke | User subjectivity in Monte Carlo modeling of pesticide exposure[END_REF] . Conditional probabilistic approaches have been used to explore whether scenario parameter uncertainty leads to divergent or (more commonly) convergent outcomes across scenarios [START_REF] Brown | Analysing uncertainties in climate change impact assessment across sectors and scenarios[END_REF] . Being computationally intensive, this method is less tractable for models with long runtimes, which constrains its application for many large-scale models. However, run-times are also affected by the temporal and spatial resolution as well as the spatial extent of a model, and computational capacity is becoming increasingly less important.

Apart from these examples of scenario parameter uncertainty being quantified and communicated, there is little quantification of the uncertainties arising from different management and policy actions to achieve 'stylised' scenarios 2 , e.g. assumptions of vegetarianism [START_REF] Vuuren | the need for negative emission technologies[END_REF] , maximizing long term fishing catches [START_REF] Costello | Global fishery prospects under contrasting management regimes[END_REF] , and the rate of change in fishing technologies that have been identified as key drivers of increasingly effective fishing effort that impacts marine biodiversity [START_REF] Rousseau | Evolution of global marine fishing fleets and the response of fished resources[END_REF] . Management practices are especially important when representing adaptation processes within models in which responses are consistent with time-varying, scenario-specific barriers and enablers e.g. societal values and governance [START_REF] Holman | Improving the representation of adaptation in climate change impact models[END_REF] . Overall, there are considerable gaps in current knowledge about scenario parameter uncertainty.

Model uncertainty

Structural uncertainty

Models simplify the representation of the real world in different ways and so produce different responses to the same scenario assumptions. These responses depend on how a model is structured and parameterised and on the timescale, all of which can lead to structural model uncertainty. Hence, modelling is the art of making choices in a given context, and structural uncertainties reveal the variety of these choices [START_REF] Levins | The strategy of model building in population biology[END_REF][START_REF] Prentice | Reliable, robust and realistic: the three R's of next-generation land-surface modelling[END_REF] . The more knowledge we try to formalize within models through process-based understanding, the more uncertainty we may potentially cause or reveal. One could argue that simple, parsimonious, models are better than complex models for robust forecasting [START_REF] Evans | Do simple models lead to generality in ecology?[END_REF][START_REF] Yatat | A tribute to the use of minimalistic spatially-implicit models of savanna vegetation dynamics to address broad spatial scales in spite of scarce data[END_REF] , but there is no universal evidence of a relationship between model complexity and model robustness. Parsimonious models that are based on observed trends may lead to low uncertainty within the range of conditions for which they were calibrated, but can lead to high uncertainty when applied over longer time scales or in scenarios with large deviations from current trends [START_REF] Cheaib | Climate change impacts on tree ranges: model intercomparison facilitates understanding and quantification of uncertainty[END_REF][START_REF] Bugmann | Tree mortality submodels drive simulated long-term forest dynamics: assessing 15 models from the stand to global scale[END_REF] . However, focusing on parsimony misses the point about why we build models. We model to experiment with elements of the natural world in order to explore, explain and understand how they work [START_REF] Evans | Do simple models lead to generality in ecology?[END_REF] .

Many models of climate, land use and biodiversity are increasing in complexity by the addition of components, processes and model coupling [START_REF] De Weirdt | Seasonal leaf dynamics for tropical evergreen forests in a process-based global ecosystem model[END_REF][START_REF] Robinson | Modelling feedbacks between human and natural processes in the land system[END_REF][START_REF] Xu | Diversity in plant hydraulic traits explains seasonal and inter-annual variations of vegetation dynamics in seasonally dry tropical forests[END_REF] . More complex models may, arguably, be better at representing system dynamics over longer time-scales or under changing conditions than simpler models [START_REF] Fisher | Vegetation demographics in Earth System Models: A review of progress and priorities[END_REF] . For example, oversimplifying biodiversity representation in vegetation models has long been an impediment to detailed understanding and robust projections of ecosystem dynamics and distribution [START_REF] Moorcroft | How close are we to a predictive science of the biosphere?[END_REF][START_REF] Purves | Predictive models of forest dynamics[END_REF] . This has motivated a finer representation of species or traits diversity [START_REF] Sakschewski | Leaf and stem economics spectra drive diversity of functional plant traits in a dynamic global vegetation model[END_REF][START_REF] Pavlick | The Jena Diversity-Dynamic Global Vegetation Model (JeDi-DGVM): a diverse approach to representing terrestrial biogeography and biogeochemistry based on plant functional trade-offs[END_REF][START_REF] Maréchaux | An individual-based forest model to jointly simulate carbon and tree diversity in Amazonia: description and applications[END_REF][START_REF] Van Bodegom | Going beyond limitations of plant functional types when predicting global ecosystem-atmosphere fluxes: Exploring the merits of traits-based approaches[END_REF] , which allows better exploration of the role of the interactions between diversity and ecosystem functioning in shaping the future of natural systems [START_REF] Mokany | Integrating modelling of biodiversity composition and ecosystem function[END_REF][START_REF] Sakschewski | Resilience of Amazon forests emerges from plant trait diversity[END_REF] . However, this does not necessarily lead to less uncertainty, since the representation of feedbacks and path-dependency may lead to dramatic changes in system behaviour, potentially increasing the range of possible responses and associated uncertainty. Furthermore, increasing model complexity may also lead to problems with the traceability of the origins of uncertainty and inconsistencies between different model components [START_REF] Voinov | Integronsters'', integral and integrated modeling[END_REF] . These problems may be further compounded within models that include stochastic process representations, leading to internal variability, and multiple model outcomes. However, stochastic approaches based, for example, on Monte Carlo methods can be useful in representing uncertainty in model structure [START_REF] Jarnevich | Developing an expert elicited simulation model to evaluate invasive species and fire management alternatives[END_REF] .

Models can support improved understanding of how resource management can adapt to environmental change and thereby inform decision-making and policy processes. However, a better representation of adaptation processes is required in models in general. For example, substantial differences have been found between the extensive, available empirical knowledge about societal adaptation processes and their representation in models of land and water sectors [START_REF] Holman | Improving the representation of adaptation in climate change impact models[END_REF] . Only a minority of models take account of the management choices that underpin adaptation measures or the constraints (financial, institutional, social, etc.) that may limit the uptake and effectiveness of adaptation [START_REF] Brown | Behavioral models of climate change adaptation and mitigation in land-based sectors[END_REF] ; factors which are likely to be influenced (positively or negatively) by the scenario setting.

The pervasiveness of simplistic, over-optimistic approaches to simulate the role of adaptation in reducing impacts and vulnerabilities or in exploiting the benefits associated with climate and socioeconomic changes means that studies may produce findings that cannot meaningfully inform decisionmaking about appropriate adaptation strategies.

Incremental model improvement aims to increase a model's ability to predict plausible responses to uncertain, environmental change conditions. The drawback of incremental improvements is that they can cause 'lock-in' of an existing model structure or ways of doing things [START_REF] Van Nes | A strategy to improve the contribution of complex simulation models to ecological theory[END_REF] . Moreover, even incremental changes in model structure require substantial investment in time and effort. The exploration of alternative structural specifications in models is often done for local to regional scale studies [START_REF] De Weirdt | Seasonal leaf dynamics for tropical evergreen forests in a process-based global ecosystem model[END_REF][START_REF] Joetzjer | Assimilating satellite-based canopy height within an ecosystem model to estimate aboveground forest biomass[END_REF][START_REF] Naudts | A vertically discretised canopy description for ORCHIDEE (SVN r2290) and the modifications to the energy, water and carbon fluxes[END_REF] . At the global level, the investment required to build new models maybe substantially larger than maintaining existing models. Global scale models often need long-term institutional funding, thus limiting the number of research groups that have the capacity for such effort. Hence, the diversity of model structures and modelling paradigms is low in global-scale modelling compared with regional scale models [START_REF] Kim | A protocol for an intercomparison of biodiversity and ecosystem services models using harmonized land-use and climate scenarios[END_REF] . For example, many global scale economic models still use optimisation approaches based on the assumptions of neoclassical economics that are known to be limited [START_REF] Rounsevell | Towards decision-based global land use models for improved understanding of the Earth system[END_REF] .

Better understanding of structural uncertainty is often achieved by trying to learn from model intercomparison exercises [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF][START_REF] Cheaib | Climate change impacts on tree ranges: model intercomparison facilitates understanding and quantification of uncertainty[END_REF] (see Box 1) or the comparison of model results with observed data [START_REF] Powell | Confronting model predictions of carbon fluxes with measurements of Amazon forests subjected to experimental drought[END_REF][START_REF] Restrepo-Coupe | Do dynamic global vegetation models capture the seasonality of carbon fluxes in the Amazon basin? A data-model intercomparison[END_REF] . Model inter-comparisons and the closely related ensemble modelling approach have proven highly beneficial for improving the credibility of climate change projections such as through the Coupled Model Intercomparison Project (CMIP [START_REF] Taylor | An overview of CMIP5 and the experiment design[END_REF] ). Similar multi-model efforts, in which different models that address a similar question are run using a standardised simulation protocol and the same input data, are only starting for impact models projecting future terrestrial [START_REF]Biodiversity and Ecosystem Services for Europe and Central Asia (Secretariat of the Intergovernmental Science-Policy Platform for Biodiversity and Ecosystem Services[END_REF][START_REF] Kim | A protocol for an intercomparison of biodiversity and ecosystem services models using harmonized land-use and climate scenarios[END_REF] and marine biodiversity (Fish-MIP [START_REF] Lotze | Global ensemble projections reveal trophic of ocean biomass declines with climate change[END_REF][START_REF] Tittensor | A mid-term analysis of progress toward international biodiversity targets[END_REF] ).

The comparison of model outputs with observational data [START_REF] Mouquet | Predictive ecology in a changing world[END_REF] , or benchmarking, can provide pointers towards the conditions under which a model performs better or worse, as well as revealing the sources of uncertainty. Diverse sets of observations are needed to assess both the magnitude, and seasonal and interannual variability of modelled outputs [START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF] . Specialised experiments, such as free-air carbon enrichment studies, herbivore exclosures or remotely-sensed trait information [START_REF] Asner | Airborne laser-guided imaging spectroscopy to map forest trait diversity and guide conservation[END_REF][START_REF] Tanentzap | Carbon storage in terrestrial ecosystems: do browsing and grazing herbivores matter?[END_REF][START_REF] Walker | Predicting long-term carbon sequestration in response to CO2 enrichment: How and why do current ecosystem models differ?[END_REF] can also be used to test the realism of specific simulated processes. Taken together, these datasets can be used to test whether models correctly capture existing relationships between variables (or incorrectly assume existing relationships, which are not supported by observations). At least for vegetation models, studies have begun to systematically explore the use of scoring of model performance against a range of observations [START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF] . Two further common approaches to model improvement are: 1) the addition or respecification of certain model components, and 2) the simple calibration of model parameters to increase the model fit to data. Calibration may lead to either overfitting of the model or to issues relating to equifinality. In overfitting, a calibrated model may represent a specific place and time very well, but it sacrifices generality when applied to other places and times. The comparison between individual models and an 'ensemble mean' might unintentionally also lead to the model being 'retuned' to fit better to the average model response.

Equifinality occurs when different functional or process representations in a model lead to the same outcome [START_REF] Beven | Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology[END_REF][START_REF] Luo | Parameter identifiability, constraint, and equifinality in data assimilation with ecosystem models[END_REF][START_REF] Rykiel | Testing ecological models: the meaning of validation[END_REF] . This reduces the range of the modelled outputs, but at the same time may conceal structural uncertainty, since it can be difficult to track which mechanisms within a model lead to the equifinal outcomes. The effect of equifinality can be evaluated by comparing the overall model outcomes against independent datasets [START_REF] Fisher | Vegetation demographics in Earth System Models: A review of progress and priorities[END_REF] , but also by comparing different process representations within the model itself. This is important when assumptions are made, for example, in how to model the management choices that underpin land use change [START_REF] Medlyn | On the validation of models of forest CO2 exchange using eddy covariance data: some perils and pitfalls[END_REF] . While different approaches to representing management choices may, in the short term, lead to similar land use outcomes, they may wrongly represent longer-term adaptation and behaviour under resource constraints. In this case, empirical data on management choices may be more useful in validating the model process than validating the short-term model outcomes.

In a review of land use models, little over half were validated independently, and many conflated calibration with validation [START_REF] Brown | Behavioral models of climate change adaptation and mitigation in land-based sectors[END_REF][START_REF] Van Vliet | A review of current calibration and validation practices in land-change modeling[END_REF] . Although this can be explained to some extent by the limited availability of consistent empirical datasets for different time periods, it still increases the risk of overfitting in many model applications. In other words, a model both trained and validated on historical data may not accurately project the full range of outcomes in a non-stationary future. However, calibration to improve model fit can, in part, compensate for the subjective decisions made by modellers concerning the selection of observed input datasets (e.g. which meteorological, economic or demographic variables), alternative process algorithms (e.g. reference evapotranspiration), and initial conditions (e.g. land use classes and their distribution) [START_REF] Remesan | Effect of baseline meteorological data selection on hydrological modelling of climate change scenarios[END_REF][START_REF] Remesan | Effect of baseline snowpack assumptions in the HySIM model in predicting future hydrological behaviour of a Himalayan catchment[END_REF] . Nevertheless, the consequences of these choices may still be unclear when the model is perturbed beyond the historical conditions represented in the calibration data, leading to potentially large uncertainty in the magnitude and direction of impacts [START_REF] Remesan | Effect of baseline snowpack assumptions in the HySIM model in predicting future hydrological behaviour of a Himalayan catchment[END_REF] .

Input data uncertainty

It is difficult to decouple model structural uncertainty from model input data uncertainty, since models with a different structure commonly use different input data [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF][START_REF] Prestele | Hotspots of uncertainty in land-use and landcover change projections: a global-scale model comparison[END_REF] . Models of socio-ecological systems are data demanding for parameterization, calibration, and initialization of simulations, including large demands for baseline data. Uncertainties in the use of data can emerge from measurement errors, data scarcity, or a mismatch between the resolution and scope of the available data, and the needs of the model. These uncertainties are amplified when models include additional processes, represent processes at finer spatial scales or expand the spatial and temporal scope of simulations. For example, data availability has been assessed for several mechanisms known to play a key role in mediating species responses to climate change, such as physiological processes, evolutionary potential and species interactions [START_REF] Urban | Improving the forecast for biodiversity under climate change[END_REF] . Even for the best-studied species, data were at best incomplete if not entirely absent. In recent years, the scientific community has gone to great lengths to increase access to biodiversity data through the development of networks of high-quality monitoring systems (observation systems, instrumented sites and remote sensing sensors) [START_REF] Gillespie | Measuring and modelling biodiversity from space[END_REF][START_REF] Pereira | Essential biodiversity variables[END_REF][START_REF] Muller-Karger | Advancing Marine Biological Observations and Data Requirements of the Complementary Essential Ocean Variables (EOVs) and Essential Biodiversity Variables (EBVs) Frameworks[END_REF][START_REF] Miloslavich | Essential ocean variables for global sustained observations of biodiversity and ecosystem changes[END_REF] , data repositories (e.g. GBIF.org; obis.org) or, citizen science programmes [100][101][102] .

For correlative species distribution models 103,104 , the lack of accuracy and comprehensiveness of the species data and of the relevance and completeness of the predictors can critically impact the relevance of the fitted niche models and hence of the resulting outcomes 105,106 . Data deficiencies and biases in this specific approach include samples of species' occurrences that are too small or do not include absences, or have missing covariates; the latter being known to introduce significant spatial correlation in the errors of the analysis [107][108][109][110] .

Trait-based approaches have been developed to leverage limited data and allow model prediction for a broad range of species, including poorly studied ones. Traits are individual features that inform individual performance 111 . Both correlative and process-based models have used trait parameters to simulate higher-level processes. This includes population growth rate or range shifts in plant [START_REF] Van Bodegom | Going beyond limitations of plant functional types when predicting global ecosystem-atmosphere fluxes: Exploring the merits of traits-based approaches[END_REF][112][113][114] , fish [115][116][117] , or reptile and amphibian communities 118 . Trait data availability is increasing rapidly (e.g. open digital repository 119,120 ; www.fishbase.org), but it remains highly variable across taxonomic groups and geographic areas. It is also strongly correlated with the ease in measuring traits: so-called "soft" structural traits have been more often measured than "hard" physiological traits, although the latter often provide key information on species responses to non-present analogue conditions, such as tolerance to drought or higher temperatures [121][122][123] . Additionally, functional ecologists often report species mean trait values, resulting in a lack of assessment of intraspecific trait variability 123 in spite of increasing evidence for its role in species adaptation and coexistence [124][125][126][127] . These are both crucial in establishing biodiversity projections 128 .

Uncertainties related to initial conditions are less well studied in socio-ecological models 129 , although they have been identified as important in some studies. For example, variability in the data used to represent initial land use conditions between different models of land use change contributed a substantial part to the variation across future land use projections [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF] with distinct spatial differences in the level of uncertainty [START_REF] Prestele | Hotspots of uncertainty in land-use and landcover change projections: a global-scale model comparison[END_REF] . Differences in initial data can arise from different definitions of the same land cover type and different data acquisition approaches [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF][START_REF] Prestele | Hotspots of uncertainty in land-use and landcover change projections: a global-scale model comparison[END_REF] . Similarly, errors in the initialization of forest structure in large scale simulations of vegetation models can result from limited sampling and coarse resolution, for example of large scale, remote-sensing products, and have been found to propagate in subsequent model prediction uncertainty [START_REF] Joetzjer | Assimilating satellite-based canopy height within an ecosystem model to estimate aboveground forest biomass[END_REF]130,131 .

Several methods are available to address input data uncertainties. Hierarchical modelling techniques and other statistical methods can address different sources of uncertainty explicitly in modelling frameworks 127,132,133 . Sensitivity and uncertainty analyses [START_REF] Brown | Analysing uncertainties in climate change impact assessment across sectors and scenarios[END_REF]134,135 can help identify and prioritize the need to reduce parameter uncertainty given limited time and resources and hence guide the empirical effort of data collection through iterative cycles of data-model fusion [START_REF] Medlyn | Using models to guide field experiments: a priori predictions for the CO 2 response of a nutrient-and water-limited native Eucalypt woodland[END_REF]136,137 . In stochastic sensitivity analyses (sometimes called "perturbed physics experiments"; see Box 1) model-internal parameter values are sampled across parameter-space to explicitly and transparently test parameter-value uncertainty 138 . These analyses are computationally expensive and so, have not been sufficiently exploited with coupled and integrated models. But, a number of studies have demonstrated their application both in offline models (e.g., related to vegetation or land-use change modelling) and in coupled models (e.g., related to carbon cycle-climate feedbacks) [START_REF] Henry | Food supply and bioenergy production within the global cropland planetary boundary[END_REF][START_REF] Engström | Assessing uncertainties in global cropland futures using a conditional probabilistic modelling framework[END_REF][139][140][141][142] . Results help to identify and rank those parameters to which a model output is most sensitive, but can also inform sensitivity analysis of other models for those values. The outcomes aid the interpretation of e.g., model ensembles as the magnitude of uncertainty seen in a single model's output from stochastic parameter sensitivity analysis can be compared to the spread in output within a model ensemble.

Data assimilation techniques can bridge the gap between data availability and model requirements. In particular, inverse modelling such as Approximate Bayesian Computation use a wide range of data to refine values of input parameters [143][144][145][146] . With these methods, parameter distributions provided by the available data (prior parameter estimate) are iteratively adjusted (posterior parameter estimate) by comparing simulation outputs with observed data at different scales, e.g. element fluxes derived from eddy-flux measurements 147 , tree size distribution derived from inventory data 148 or remote-sensing products 149 .

A promising avenue in terms of data assimilation is the spectrometry imagery of functional diversity [START_REF] Asner | Airborne laser-guided imaging spectroscopy to map forest trait diversity and guide conservation[END_REF]150 , which, at least for terrestrial ecosystems, can help to bridge the gap between biodiversity data available from field surveys and the amount of data required to better control for uncertainty in continental and global scale models. This raises new technical challenges in terms of data standardisation (corrections and inter-calibration of remote sensing images) and methods for data extraction 151 . It also raises the issue that the input data themselves often derive from modelled products. For example, in modelling the terrestrial C-cycle, the same level of uncertainty is possible for several DGVMs forced by the same climate scenario (based on a single emissions scenario and climate model), as for a single DGVM forced by inputs from several climate scenarios (with different emissions and climate models) 152 .

Error propagation uncertainty

Uncertainties from error propagation arise in coupled model systems when the inputs to one model (e.g., a model of climate impacts on ecosystems) derive from the outputs of another model (e.g., a climate model). In some cases, several models are coupled together leading to serious error propagation especially at the end of the chain of coupled models 153,154 . Error propagation becomes even more important when there are dynamic feedbacks between models.

Coupled models are common in integrated assessment, which seeks to explore the interactions between, as well as within, different socio-ecological systems [START_REF] Robinson | Modelling feedbacks between human and natural processes in the land system[END_REF] . Integrated assessment models (IAMs) focus, for example, on the connections between the economy, the energy system and land cover change 155 at global scale levels. However, regional integrated assessment models have also demonstrated the importance of adopting a cross-sectoral approach for impact assessments [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF] . Indeed, the impacts of climate change as reported by the IPCC may be over-or underestimated because they fail to account for cross-sectoral interactions [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF] . A source of uncertainty in coupled models is when simplified, meta-models replace complex models in order to facilitate data flows across systems [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF]134 .

However, these uncertainties may be acceptable since the indirect effects of one sector on another sector are often more important than the changes within a single sector itself [START_REF] Harrison | Climate change impact modelling needs to include cross-sectoral interactions[END_REF] . Similar issues arise for models that do not consider cross-scale impacts, since one scale level is highly dependent on the boundary conditions defined by a higher-scale level [START_REF] Rounsevell | Towards decision-based global land use models for improved understanding of the Earth system[END_REF] .

Different methods can evaluate the uncertainties arising from error propagation, with qualitative methods being of particular utility. Dunford et al. (2015) 154 combined formal numerical approaches, modeller interviews and network analysis to provide a holistic uncertainty assessment of a regional integrated assessment model that considered both quantifiable and unquantifiable uncertainty. Maps of modeller confidence (the counterpart of uncertainty) were created from fuzzy-set methods and network analysis to show that validation statistics are not the only factor driving modeller confidence.

Several other factors such as the quality and availability of validation data, the meta-modelling process, trust between modellers, derivation methods, and pragmatic factors such as time, resources, skills and experience were also found to be important 154 .

For most simple models (e.g. linear Gaussian models), the variance of the prediction associated with error propagation can be computed analytically, paying attention to the dependence between variables and the associated covariance 156 . In the majority of cases, modelling involves complex models that are non-linear and non-Gaussian for which variance computation is analytically intractable. In such cases, error propagation can be evaluated through simulation using, for example, Monte-Carlo methods 157 . A Monte Carlo-based approach to evaluate the propagation of uncertainties in a regional integrated assessment model, showed that rather than the uncertainties 'exploding' in importance there was convergence across a range of contrasting scenarios [START_REF] Brown | Analysing uncertainties in climate change impact assessment across sectors and scenarios[END_REF] . This implies that if fully understood, uncertainties arising from error propagation can be managed successfully. However, the assessment of error propagation through simulation is computationally demanding and, in general, only applicable to models with rapid run-times.

Model output-input chains and feedbacks can become complex and lead to unacceptable levels of uncertainty for decision-making 154 . Where possible, major sources of uncertainties (data, model, parameters) should be identified a priori to allow propagating errors with a minimum number of simulations. Comprehensive sensitivity analysis is also useful in identifying emergent uncertainties 134 .

Structured sensitivity analysis (also referred to as scenario-neutral approaches and impact response surfaces) is valuable in evaluating whether the emergent behaviour in coupled models as a response to simple perturbations is consistent with understanding or influenced by error propagation, although sensitivity analysis as a method has been criticised 158 . Hierarchical Bayesian models can be useful tools to incorporate and propagate errors from multiple sources (data, parameters, models), through the computation of the predictive posterior distribution 159 .

Uncertainties in decision-making and decision methods

Intrinsic uncertainties in decision-making

Uncertainty pertaining to environmental processes and ecological theory is interesting from an academic perspective, but it becomes a practical issue when it impinges on the ability of managers, planners and policy makers to make relevant science-based decisions to achieve societal objectives.

In spite of multiple uncertainties, decisions are still made about natural resource management.

However, the decision-making process is itself messy and difficult to predict, depending as it does on the context, on the individuals involved (with their conscious and unconscious biases) , on the breadth of values attributed to nature (including non-quantifiable ones), on the efficient exchange of knowledge between science and policy, and on time-lags in policy implementation 160 . Decision making is often disorganised and politicised, and has to deal with many trade-offs, as well as co-benefits, making it difficult to generalise about how uncertainty in scenarios and models affects decision making processes. There is a significant body of work in decision theory and operations research on dealing with epistemic uncertainty in decision making. However, further understanding is still needed of the relationship between science and the social and political processes of decision-making, and this is an important area of future research in environmental management.

What can be stated is that different degrees of uncertainties and levels of controllability may be more effectively managed by different strategies and approaches [START_REF] Ferrier | The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services[END_REF] . Controllability here refers to the degree of control that a decision-maker has over the system being managed. Controllability tends to be higher when decision horizons are shorter, when the decision-maker has direct and sole jurisdiction over the places and/or resources being managed, or when stakeholders do not vary widely in their aspirations for the outcomes of management. Controllability covaries with uncertainties over temporal and spatial scales. Controllability tends to be higher at local and national scales relative to regional and global scales 161 . When the system is highly controllable and uncertainties about the future are low, it may be most effective to implement optimal control tactics. Optimal control tactics generally involve "predictthen-act" such as determining catch or fishing quotas 162 . In situations where controllability is low and uncertainty is high, robustness analysis 163 in support of scenario planning 164 may be favoured 165 .

In this section, we further discuss how uncertainties in scenarios and models can contribute to decision-making uncertainty, as well as the tools that are available to address these uncertainties and their limitations

How uncertainties are communicated to decision-makers

How uncertainties are accounted for in decision-making is strongly dependent on how these uncertainties are communicated to decision-makers. In international science-policy processes such as IPCC or IPBES, formalised uncertainty language is used to communicate levels of confidence in the assessment of scientific evidence 166 , including results from scenarios and models. This approach is generally qualitative, although attempts have also been made to use quantitative probabilistic statements. Whether this approach is effective in communicating uncertainty to policy communities is debatable 167 , although some benefit to decision-makers is likely since government-approved assessment reports continue to use uncertainty language.

How uncertainties are accounted for in decision-making is also strongly dependent on how these uncertainties manifest into the different indicators that are provided to decision-makers, e.g. Living Planet Index 168 , species richness 169 , extinction risk 170 , monetary value of ecosystem services 171 .

Communicating alternative scenario outcomes thus requires appropriate indicators that are understandable and meaningful to decision-makers, and above all responsive to different drivers in an expected way, i.e. with low uncertainty. Within the same scenario or model, the way the output variables are transformed, integrated and combined into indicators does not result in the same level of uncertainty 172 , or in the same strength of the signal-to-noise ratio 171 . The granularity of an indicator can be key (from population, to multispecies, to whole community level for example), as well as the choice of the spatial and temporal scales at which it is integrated. The portfolio statistical concept developed in economics and used by analogy in ecology, explains why dynamics may be extremely volatile at small scales (and high biodiversity granularity, e.g. population biomass), but less variable at more aggregated scales (and low biodiversity granularity, e.g. community biomass) 173 . International initiatives such as GEOBON (https://geobon.org), GOOS (www.goosocean.org) and the Biodiversity Indicators Partnership (www.bipindicators.net) have proposed a number of indicators and Essential Biodiversity Variables to characterize changes in biodiversity status under global change. However the selection of indicators has been done mostly under the criteria of measurability and accessibility at the global scale [START_REF] Pereira | Essential biodiversity variables[END_REF][START_REF] Miloslavich | Essential ocean variables for global sustained observations of biodiversity and ecosystem changes[END_REF] , but the performance of indicators in capturing changes and associated uncertainty has rarely been tested in a systematic way 174,175 .

It is not possible to say whether communicating to decision-makers the uncertainties in scenarios and models of socio-ecological systems actually changes decision-making in practice or not. There is no objective measure of the 'success' of communicating uncertainties, nor is there a counterfactual to explain whether alternative decisions would have been made in the absence of knowledge about uncertainties.

How decision-making tools address uncertainties

A great number and variety of tools exist to support decision-makers in dealing with various kinds of uncertainty when making decisions [START_REF] Acosta | The methodological assessment report on scenarios and models of biodiversity and ecosystem services[END_REF] . A key role of decision support tools is to provide a framework that allows decision makers and stakeholders to separate deliberations about what represents a desired outcome (competing objectives and preferences that arise from differing values) from deliberations about the facts of the matter; the probability that a particular course of action will result in a particular outcome. Therefore, it can be useful to think about different decision support tools in terms of how they deal with competing values and uncertainty (see Figure 2). Decision support tools vary in terms of how they deal with spatial scale and extent, cultural and administrative complexity, multiple stakeholders and competing values and uncertainty [START_REF] Acosta | The methodological assessment report on scenarios and models of biodiversity and ecosystem services[END_REF] . In Figure 2, we outline a small sample of the decision support approaches that deal with uncertainty to varying degrees with the aim of highlighting the breadth of opportunities for addressing competing values and models using existing decision support approaches, and these approaches are summarised in Annex 1.

In spite of the widespread development of decision support tools, the capacity of these tools to support objective decision-making may often be limited, especially where high levels of complexity and uncertainty make interpretability difficult. For example, when uncertain trade-offs between different ecosystem services are at stake, tools designed to support decisions are usually required to impose artificial boundaries or quantifications, to limit and render comparable the broad, diverse range of services in question [176][177][178][179] . This implicitly involves the same value-based judgement under uncertainty that a decision-maker would be faced with in the absence of such a tool, but often obscures its subjective nature. More systematic biases also exist. Knowledge about socio-ecological systems is growing so rapidly and on so many fronts that it is very difficult to capture accurately. Social science knowledge in particular is consistently neglected, perhaps because most tool developers are natural scientists 180,181 . This also contributes to the neglect of cultural services, and their uncertainties, in ecosystem services assessments 182 . Even tools that sacrifice coverage are likely to prove to be too complex and uncertain to be used and understood by stakeholders as originally intended 176 . Decision-support tools therefore run the risk of obscuring uncertainty and subjectivity rather than helping to overcome it. This can be revealed, and to some extent overcome, where tools are used in participatory settings that allow for interrogation of assumptions, representation and outcomes by a range of stakeholders 183 . Comprehensive uncertainty evaluation can play an important role in this process 184 , but is not itself sufficient. Rather, improved and more comprehensive methods of accounting for subjectivity and uncertainty within nominally objective decision-processes remain a priority 185 .

Discussion: ways forward

It is important to recognise the many sources of uncertainties that exist in scenarios and models of socio-ecological systems. It is also important to avoid these uncertainties becoming a disincentive for action when facing environmental challenges, within either the science or decision-making domains.

Importantly, decision-makers should not use uncertainty as an excuse for inaction. There is no panacea for dealing with uncertainty, but a portfolio of approaches may provide an opportunity to better understand and cope with uncertainty. This portfolio might include a range of methods from Model Inter-comparison Projects (MIPs), validation against independent data, error propagation analysis to learning from uncertainty to guide model improvement. Table 2 provides a summary of the approaches to addressing uncertainty that are discussed throughout this article. Figure 3 also provides a visual representation of these approaches with referencing to Table 2. Together, these provide a checklist of the types of actions that can be implemented when dealing with uncertainties of scenarios and models of socio-ecological systems within the context of supporting decision-making.

A number of ways of dealing with uncertainty are still not routinely applied in scenario modelling and this is becoming increasingly unacceptable. For instance, statistical parameter uncertainty analysis may not be possible for all parameters for all models, but it can be done at least for a subset of model parameters. Likewise, the confrontation of models with data is inadequately done. In many cases, there may be insufficient data to do this properly, but using this as an excuse to do nothing at all is simply wrong. In situations where data are lacking, one should start with qualitative "common sense" tests, such as Turner et al. (2018) 192 who identified future projected rates of change in bioenergy adoption to be three times faster than the historical precedent, for the most rapidly changing land use.

Likewise, creating better scenarios of uncertain futures would benefit from consideration of a wider range of socio-economic and natural system drivers going beyond a focus on climate change alone 2 . This includes, for instance, drivers of biodiversity loss such as biomass extraction, invasive alien species and pollution 2 . Many scenarios are also weak at relating indirect drivers (i.e. the underlying socioeconomic-political causes of change) to direct drivers. We need to move beyond the representation of stylised scenarios of, for example, consumption patterns, to scenarios and models that account for the role of human behavioural processes in affecting ecological change. This includes better representation of how policy and conservation initiatives affect people with the knock-on effects this has for ecosystems 193 . This is critical in better evaluating the considerable role of humans in causing ecological degradation, and in informing the decision processes that can do something about it through restoration and effective ecosystem management 194 .

Within this review, we have focused on models and scenarios of socio-ecological systems. However, it is clear from the literature that there is a bias towards the 'ecological' aspects rather than the 'social' aspects of such systems, such that many modelling approaches do not adequately capture the full range of interacting human and natural processes. We view this as a major research gap in current modelling and scenario exercises, and suggest that further development in this field would benefit from a greater focus on the social phenomena that are critical in understanding the functioning of nature on a human dominated planet.

Uncertainty is often seen as the problem whilst instead it could be interpreted as a 'space' to manage socio-ecological systems in more desirable directions. Uncertainty also helps to target future effort in model development and to identify areas that lack understanding and so, are priorities for future research. However, structural uncertainty needs to go beyond the improvement of model components and details, by re-evaluating the fundamental principles and assumptions of a model structure.

Furthermore, part of the total uncertainty in the future of socio-ecological systems actually derives from current and future decisions, and thus, from a decision-maker or citizen point of view, represents less of an 'uncertainty' than our 'societal leeway' or choices. Disentangling and documenting the different sources of uncertainties in socio-ecological systems is critical in allowing the design and initiation of informed and efficient actions. Many things about the future will always be uncertain, but we may wish to avoid the foolish and the fanatical by adopting the wisdom of doubt. Data and knowledge about socio-ecological systems are increasing rapidly, and knowledge improvement is often concomitant with awareness raising about system complexity. This leads to the paradox that, as Decision-making tools. The variety of decision-supporting methods, e.g. multi-criteria decision analysis.

Box 1: Model benchmarking, inter-comparison projects and ensembles

Benchmarking is the repeated confrontation of models with a range of observations to establish a track record of model developments. Observational datasets in themselves are uncertain [START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF]197 , so benchmarking needs transparent information on which observations were used. Some global models already routinely undergo a systematic confrontation against data when new processes are added (e.g. for the terrestrial carbon cycle [198][199][200][201][202][203] ). Recent approaches allow scoring of model performance against a wide range of observations for global vegetation models [START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF] . Observational data for benchmarking include multiple-site and remote sensing products of e.g., fraction of absorbed photosynthetically active radiation, gross primary productivity, net primary productivity, burnt area, river discharge or atmospheric CO2 concentration. Specialised experiments or datasets, such as free-air carbon enrichment studies, herbivore exclosures or remotely-sensed trait information [START_REF] Asner | Airborne laser-guided imaging spectroscopy to map forest trait diversity and guide conservation[END_REF][START_REF] Tanentzap | Carbon storage in terrestrial ecosystems: do browsing and grazing herbivores matter?[END_REF][START_REF] Walker | Predicting long-term carbon sequestration in response to CO2 enrichment: How and why do current ecosystem models differ?[END_REF] can also be used to test the realism of specific simulated processes. Diverse data are needed to assess both magnitude, and seasonal and interannual variability of modelled processes [START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF] . These datasets can be used to test whether models correctly capture existing relationships between variables (or incorrectly assume existing relationships, which are not supported by observations). Physics, climate and biogeochemistry observations are generally more numerous, systematically measured and available on different spatio-temporal scales, whereas biodiversity data are more disparate and contain many gaps (e.g. the GOOS marine initiative 204 ), so benchmarking is much more challenging for biodiversity models.

In models of climate, oceans and ecosystem dynamics, stochastic sensitivity analyses (sometimes called "perturbed physics experiments") are applied (see also section Parameter Uncertainty)

where model-internal parameter values are sampled across a parameter-space to explicitly and transparently test parameter-value uncertainty 138 . These analyses are computationally expensive and so, have not been sufficiently exploited with coupled and integrated models. But, a number of been argued that "optimal adaptation is not a good representation of the past, and probably is not a good representation of the future, because social and political constraints get in the way" 155 ; constraints that are likely to be significant across the scenario space 189 .

Structured Decision

Making (SDM) 190 An integrative decision-making framework that sets out a deliberative process for identifying acceptable trade-offs in complex decision problems.

SDM is considered integrative because it often embeds other relatively simple tools such as MCDA in stakeholder consultation processes that may utilise sophisticated, model-based predictions of benefit of different decision options.

Management strategy evaluation (MSE) 162

A modelling framework for assessing by simulation the consequences of several management strategies and providing a ranking of them according to their ability to reach management objectives. Its efficiency to link modelbased knowledge to decision-making relies on co-produced objectives, uncertainty, interpretation of outputs and ranking scenarios.

Delphi technique 191

Used in decision support in political environments when decisions affect strong factions with opposing preferences. It emphasizes anonymity of judgments during multiple rounds of deliberation and elicitation.

Info-gap decision theory 163

A methodology for supporting model-based decisions under severe uncertainty. It seeks to maximize robustness and opportuneness (upside of uncertainty) of decisions using three key components; an uncertainty model, a system model and an objective function (called a 'performance requirement'). Info-gap is interesting in that it is specifically focussed on uncertainty in decision making and hence the uncertainty modelling aspects of the framework are particularly strongly developed.

Table 1 .

 1 technical knowledge increases, what we ignore is increasingly more important than what we know. Uncertainty in science should not imply uncertainty in making decisions that respond to environmental problems 195 . Ironically, scientists see the quantification of uncertainty as underpinning scientific rigour, whereas others see it as a sign of weakness in the underlying science 196 . Too often, such a fallacy has become a flawed means of discouraging the endorsement of policies against environmental problems, such as climate change or biodiversity. Knowledge of uncertainty should inspire action rather than indifference and guide decision-making, rather than prevent it 195 . Sources of uncertainty and their description in scenarios and models of socio-Linguistic uncertainty. The use of similar terms to mean different things in different research communities, e.g. pathways, ensembles, boundary conditions. Narratives storyline uncertainty. The limits to imagining unknown futures (e.g., unknown unknowns). This can relate, for example, to alternative world-views or the uncertainties associated with participatory processes arising from internal consistency and knowledge limitations. Scenario parameter uncertainty. The estimation of quantitative parameters from narrative storylines that are subsequently used in models. Scenario parameter uncertainty follows from the interpretation of quantitative values from qualitative narratives, e.g. the number of people in a 'high population growth' scenario. ) uncertainty. The uncertainties associated with the choice and the representation of processes in models. Input data uncertainties. The variability in baseline data conditions that are used to initialise a model, including thematic classification, i.e. how classes are defined in, for example, land use maps. Error propagation uncertainty. The amplification (or dampening) of the transmission of errors across multiple coupled models. The role of meta-modelling and indirect effects (such as cross-sectoral interactions). Data interpretation for decision-making. Selective use of data or information from different sources and their interpretation. Analysing at relevant spatio-temporal scales. The selection of spatio-temporal scales at which simulated data are analysed, and the granularity of derived indicators (e.g., level of integration across biodiversity facets, merging subsets of ecosystem services).

Figure 1 .

 1 Figure 1. Sources of uncertainty in scenarios and models of socio-ecological systems within the

Figure 2 .

 2 Figure 2. A sample of decision tools to support decision making in the presence of competing values

Table 2 . Potential solutions and recommendations to address uncertainty in models and scenarios of socio-ecological systems for different sources of uncertainty.

 2 See Table1and the visual presentation in Figure3. This list does not preclude other relationships between solutions and uncertainty sources that may be feasible.

	For these sources of uncertainty
	Scenario	Model	Decision-making
	uncertainty	uncertainty	uncertainty

Acknowledgements

This work is part of the USBIO project funded by the LabEx CeMEB (ANR-10-LABX-04-01). MR, AA and CB would like to acknowledge the funding of the Helmholtz Association. YJS acknowledges funding support from the Biodiversa and Belmont Forum project SOMBEE (BiodivScen ERA-Net COFUND programme, ANR contract n°ANR-18-EBI4-0003-01), the European Union's Horizon 2020 research and innovation programme under grant agreements No 869300 (FutureMARES) and No 817578 (TRIATLAS), and the Pew Fellows Program in Marine Conservation at The Pew Charitable Trusts. RP was partly funded by the FACCE Era-Gas project 3DForMod (ANR contract n°ANR-17-EGAS-0002-01).

OG was partly funded by CNRS "Mission pour l'interdisciplinarité" through its "Osez l'interdisciplinarité" call and the French National Research Agency (grant ANR-16-CE02-0007). WLC acknowledges funding support from NSERC Discovery Grant (RGPIN-2018-03864).

Author contributions

All authors contributed to the conceptualisation, writing and editing of the manuscript.

Declaration of interests

The authors declare no competing interests. 1. More details about the numbered methods for addressing uncertainties are provided in Table 3. The colour-coding refers to the sources of uncertainty (see Table 1), with the gradient-shaded boxes indicating methods that apply to more than one uncertainty source.

studies have demonstrated their application both in offline models (e.g., related to vegetation or land-use change modelling) and in coupled models (e.g., related to carbon cycle-climate feedbacks) [START_REF] Henry | Food supply and bioenergy production within the global cropland planetary boundary[END_REF][START_REF] Engström | Assessing uncertainties in global cropland futures using a conditional probabilistic modelling framework[END_REF][139][140][141][142] . Results help to identify those parameters to which a model is most sensitive, but can also inform sensitivity analysis of other models for those values. The outcomes aid the interpretation of e.g., model ensembles as the magnitude of uncertainty seen in a single model's output from stochastic parameter sensitivity analysis can be compared to the spread in output within a model ensemble.

The currently most widely used approaches to quantify model uncertainty in climate change, landuse change, exploitation and ecosystem modelling are inter-comparisons and modelensembles [START_REF] Alexander | Assessing uncertainties in land cover projections[END_REF][205][206][207][208] . Ensemble modelling has proven highly beneficial for improving the credibility of climate change projections with international model inter-comparison efforts such as the Coupled Model Inter-comparison Project (CMIP) [START_REF] Taylor | An overview of CMIP5 and the experiment design[END_REF] . It is only starting for impact models projecting future terrestrial [START_REF]Biodiversity and Ecosystem Services for Europe and Central Asia (Secretariat of the Intergovernmental Science-Policy Platform for Biodiversity and Ecosystem Services[END_REF][START_REF] Kim | A protocol for an intercomparison of biodiversity and ecosystem services models using harmonized land-use and climate scenarios[END_REF] and marine biodiversity (Fish-MIP [START_REF] Tittensor | A protocol for the intercomparison of marine fishery and ecosystem models: Fish-MIP v1.0[END_REF]209 ).

In model inter-comparisons, different models that address a similar question are run using a standardised simulation protocol and the same input data. Output comparison helps to identify whether models agree or disagree in the simulated time series or spatial patterns. In some cases, an ensemble mean is used based on the notion that the average across a range of models would 'average-out' some of the structural and parameter-related uncertainties and yield more robust results [START_REF] Buisson | Uncertainty in ensemble forecasting of species distribution[END_REF][START_REF] Prestele | Hotspots of uncertainty in land-use and landcover change projections: a global-scale model comparison[END_REF]138 . However, the comparison between individual models and the 'ensemble mean' might unintentionally also lead to the model being 're-tuned' to fit better to the average model response. Furthermore, 'families' of similar models (or with similar development heritage) tend to bias the mean, as they are each given the same weight as a genuinely different model. So far, most ensemble studies do not identify and exclude (or give different weight to) models that fail to fulfil certain quality-assurance criteria (based on scores in a benchmarking exercise). This has started, however, to be the case for the terrestrial models used in the annual global carbon budget calculation 210 . In view of the often still untested model structural and parameter uncertainties, deriving probabilistic estimates of uncertainty from model ensembles must be viewed critically 138 . Annex 1. Description of different decision support tools as presented in Figure 2.

Cost-benefit analysis (CBA), or benefitcost analysis 186

Applicable if all expected consequences of a decision are assigned a value. Uncertainty can be partially addressed by computing expected benefit cost ratios that explicitly incorporate probabilities of benefits and costs, providing bounds around cost-benefit ratios, and analysing the sensitivity of the CBA ranking of options by systematically varying costs and benefits of each option within plausible bounds and exploring how these uncertainties impact on the ranking of options.

Multi criteria decision analysis (MCDA) 187

Analyses trade-offs between decision options according to multiple objectives (criteria) by explicitly separating the tasks of causal judgment and value judgment.

Outranking

Designed for complex choice problems with multiple criteria and multiple participants. Out-ranking indicates the degree of dominance of one alternative over another. The outranking methods enable the utilisation of incomplete value information and judgments about the likelihood of outcomes.

Stochastic dynamic programming (SDP) 188

finds optimal sequences of decisions under uncertainty. It is particularly useful in sequential decision problem to identify the optimal decision to take now, knowing that future decisions will adapt to future conditions. For that reason, SDP has been used in several Adaptive Management decision problems. Whilst these methods will work well within the uncertainty of a single scenario, there are doubts about whether they can meaningfully find an optimal solution across multiple, uncertain scenarios. For example, it has Scenario Planning 164 A tool for exploring possible, probable and/or preferable futures, and identifying strategies or options that are robust to a range of possible situations. Unlike forecasting, which aims to accurately predict future events, the focus of scenario planning is to explore possible futures that may arise under different conditions and what those different futures might mean for current decisions.