Sandra Lavorel
email: sandra.lavorel@univ-grenoble-alpes.fr

Anita Bayer

Alberte Bondeau

Sven Lautenbach

Ana Ruiz-Frau

Nynke Schulp

Ralf Seppelt

Peter Verburg

Astrid Van Teeffelen

Clémence Vannier

Almut Arneth

Wolfgang Cramer

Nuria Marba

Pathways to bridge the biophysical realism gap in ecosystem services mapping approaches

Keywords: Ecosystem Service Provider, spatial modelling, biophysical assessment, species distribution, functional traits, large-scale ecosystem model

The mapping of ecosystem service supply has become quite common in ecosystem service assessment practice for terrestrial ecosystems, but land cover remains the most common indicator for ecosystems ability to deliver ecosystem services. For marine ecosystems, practice is even less advanced, with a clear deficit in spatially-explicit assessments of ecosystem service supply. This situation, which generates considerable uncertainty in the assessment of ecosystems' ability to support current and future human well-being, contrasts with increasing understanding of the role of terrestrial and marine biodiversity for ecosystem functioning and thereby for ecosystem services. This paper provides a synthesis of available approaches, models and tools, and data sources, that are able to better link ecosystem service mapping to current understanding of the role of ecosystem service providing organisms and land/seascape structure in ecosystem functioning. Based on a review of literature, models and associated geo-referenced metrics are classified according to the way in which land or marine use, ecological processes and especially biodiversity effects are represented. We distinguish five types of models: proxy-based, phenomenological, nichebased, trait-based and full-process. Examples from each model type are presented and data requirements considered. Our synthesis demonstrates that the current understanding of the role of biota in ecosystem services can effectively be incorporated into mapping approaches and opens avenues for further model development using hybrid approaches tailored to available resources. We end by discussing ways to resolve sources of uncertainty associated with model representation of biotic processes and with data availability.

Introduction

Ecosystem services (ES) originate from spatially structured ecosystems and land/seascapes, and their dynamics over time. Quantifying ES provisioning therefore must account for spatiotemporal patterns and processes. Although this is evident, so far this challenge has been insufficiently resolved [START_REF] Bennett | Linking biodiversity, ecosystem services and to human well-being: Three challenges for designing research for sustainability[END_REF]. Spatially-explicit quantification of ES using georeferenced metrics and GIS-based approaches has recently gained prominence through the needs from policy and decision-makers for global to local ES assessments [START_REF] Maes | Mapping ecosystem services for policy support and decision making in the European Union[END_REF][START_REF] Martinez-Harms | Making decisions for managing ecosystem services[END_REF]. Similar needs follow from emerging practices of land and marine planning [START_REF] Outeiro | Using ecosystem services mapping for marine spatial planning in southern Chile under scenario assessment[END_REF][START_REF] Von Haaren | Integrating ecosystem services and environmental planning: limitations and synergies[END_REF] or land management decision (e.g. in agriculture or forestry; [START_REF] Doré | Facing up to the paradigm of ecological intensification in agronomy: Revisiting methods, concepts and knowledge[END_REF][START_REF] Grêt-Regamey | Facing uncertainty in ecosystem services-based resource management[END_REF][START_REF] Soussana | A European science plan to sustainably increase food security under climate change[END_REF] that incorporate ecosystem services among use allocation and management criteria.

However the reliability of ES mapping varies as a function of the methods employed. For instance in a review of 107 studies, [START_REF] Lautenbach | Blind spots in ecosystem services research and implementation[END_REF] found that, while half of ecosystem service studies were based on relatively simple look-up table approaches attributing fixed values for given land cover types, nearly a third of the studies of ecosystem services conducted between 1966 and 2013 mapped ecosystem services. This mapping is done in most cases based on land use composition ignoring land use configuration and land use intensity [START_REF] Lautenbach | Blind spots in ecosystem services research and implementation[END_REF][START_REF] Mitchell | Reframing landscape fragmentation's effects on ecosystem services[END_REF][START_REF] Verhagen | Effects of landscape configuration on mapping ecosystem service capacity: a review of evidence and a case study in Scotland[END_REF]. More specifically, regulating services have been the most commonly mapped, followed by provisioning services [START_REF] Egoh | Indicators for mapping ecosystem services: a review[END_REF][START_REF] Lautenbach | Blind spots in ecosystem services research and implementation[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF][START_REF] Seppelt | A quantitative review of ecosystem service studies: approaches, shortcomings and the road ahead[END_REF]. For marine and coastal systems, among a total of 27 available studies from an exhaustive search of the Web of Science on ES mapping and ES modelling studies, almost half (52%) focused on Regulation & Maintenance services, of those 22% concentrated on coastal protection (wind & flood protection) and 33% on carbon sequestration and storage. A further third of the studies (33%) focused on provisioning services, particularly on food production (i.e. fish). The rest of the studies (19%) mapped cultural services.

Linked with this increased practice of mapping ES provisioning, several recent reviews have summarised available methods used to map ES. In the following we refer to 'models' as quantitative representations of ES variables depending on abiotic, biotic and social parameters. Overall, statistical models quantifying ES supply based on relationships with biophysical and social variables are prevalent, while process models based on causal relations are still rare [START_REF] Crossman | A blueprint for mapping and modelling ecosystem services[END_REF][START_REF] Egoh | Indicators for mapping ecosystem services: a review[END_REF][START_REF] Lautenbach | Blind spots in ecosystem services research and implementation[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF]. For terrestrial ecosystems, static maps of land use and land cover are the most commonly used indicator for ES in Europe [START_REF] Egoh | Indicators for mapping ecosystem services: a review[END_REF] and the second most common globally [START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF]. This widespread application of methods with weak links to ecosystem processes leads to severe uncertainty in the mapped ES supply from national [START_REF] Eigenbrod | The impact of proxy-based methods on mapping the distribution of ecosystem services[END_REF] to landscape (Lavorel et al., 2011) scales. More advanced approaches incorporate estimates of aboveand sometimes below-ground biomass, along with vegetation type, and soil parameters for the estimation of ecosystem functions from which services are derived. Species observation data, although potentially useful for the estimation of cultural services, is used only rarely.

Contrasting with these statistical models, process models, with explicit description of causal relationships between driver variables and ecosystem functions and properties underpinning ES provision, have primarily been used to map climate regulation and erosion control as well as the provisioning of food, fuel and fibre. Mapping and modelling assessments for marine and coastal ES are still in their infancy (Liquete et al 2013). Considering the 27 available studies from the Web of Science, 31% of the models were geostatistical while less than 20% were process-based.

Beyond the limitations of specific mapping methods, the large variety of primary indicators currently used to express one single ES is a large source of uncertainty for ES maps that limits their usefulness to managers and decision makers [START_REF] Egoh | Indicators for mapping ecosystem services: a review[END_REF]. Level of process understanding, modelling methodology and data sources are three of the critical, yet poorly understood or documented sources of uncertainty for ES maps (Grêt-Regamey et al., 2014a;[START_REF] Hou | Uncertainties in landscape analysis and ecosystem service assessment[END_REF][START_REF] Kandziora | Mapping provisioning ecosystem services at the local scale using data of varying spatial and temporal resolution[END_REF]. A systematic comparison of four sets of ecosystem service maps at the continental scale for five ecosystem services (climate regulation, flood regulation, erosion protection, pollination and recreation) showed considerable disagreement among spatial patterns across Europe (Schulp et al., 2014a), attributed to differences in the mapping aim, indicator definitions, input data and mapping approaches. The four original studies encompassed a land-cover look-up approach [START_REF] Burkhard | Mapping ecosystem service supply, demand and budgets[END_REF], environmental indicator modelling [START_REF] Kienast | Assessing Landscape Functions with Broad-Scale Environmental Data: Insights Gained from a Prototype Development for Europe[END_REF] and two hybrid approaches combining environmental indicators, landscape effects and process modelling [START_REF] Maes | Mapping ecosystem services for policy support and decision making in the European Union[END_REF]Schulp et al., 2008;Stürck et al., 2014;[START_REF] Tucker | Policy Options for an EU No Net Loss Initiative[END_REF]van Berkel and Verburg, 2011). In addition to highlighting the need for mapmakers to clearly justify the indicators used, the methods and related uncertainties, this study provided additional support for the urgent need for better process understanding and data acquisition for ES mapping, modelling and validation. Progress on these issues will be essential to support the uptake of ES spatial assessments for national ecosystem service assessments, national accounts, land planning and broader policy and natural resource management decisions [START_REF] Crossman | A blueprint for mapping and modelling ecosystem services[END_REF][START_REF] Egoh | Indicators for mapping ecosystem services: a review[END_REF].

Given this context, the common use of relatively simple statistical approaches contrasts with increasing evidence on the role of biodiversity for ecosystem functioning and ecosystem services [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF], which has been referred to as a lack of biophysical realism [START_REF] Seppelt | A quantitative review of ecosystem service studies: approaches, shortcomings and the road ahead[END_REF]. Ecosystem service supply is related to the presence, abundance, diversity and functional characteristics of service-providing organisms (also referred to as Ecosystem Service Providers, ESP henceforth; [START_REF] Luck | Quantifying the contribution of organisms to the provision of ecosystem services[END_REF]. Positive relationships have been found between species richness and ecosystem services such as fodder and wood production, regulation of water quality through soil nutrient retention, carbon sequestration or regulation of pest and weed species [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF]. Similarly, the presence of key coastal and marine species has been found to enhance carbon sequestration, coastal protection, food provision or water quality through nutrient retention and particle trapping [START_REF] Fourqurean | Seagrass ecosystems as a globally significant carbon stock[END_REF][START_REF] Mcleod | A blueprint for blue carbon: toward an improved understanding of the role of vegetated coastal habitats in sequestering CO2[END_REF][START_REF] Ondiviela | The role of seagrasses in coastal protection in a changing climate[END_REF][START_REF] Van Zanten | Coastal protection by coral reefs: A framework for spatial assessment and economic valuation[END_REF]. However such observed relationships between species richness and ES often reflect species functional traits and their diversity within communities, rather than species richness per se [START_REF] Diaz | Incorporating plant functional diversity effects in ecosystem service assessments[END_REF]. Lastly, land/sea-scape diversity and connectivity can strongly influence the ES provided by mobile organisms and vegetation [START_REF] Fahrig | Remote Sensing of Ecosystem Services: An Opportunity for Spatially Explicit Assessment[END_REF][START_REF] Mellbrand | Linking Land and Sea: Different Pathways for Marine Subsidies[END_REF][START_REF] Mitchell | Reframing landscape fragmentation's effects on ecosystem services[END_REF]. To provide more reliable estimates of service supply capacity by ecosystems, such fundamental ecological understanding needs to be better incorporated into ES models [START_REF] Bennett | Linking biodiversity, ecosystem services and to human well-being: Three challenges for designing research for sustainability[END_REF]. This paper aims to address the biophysical realism gap in ecosystem service mapping by synthesising available approaches, models and tools, and data sources (with special reference to Europe) for mapping ecosystem services, and focusing on how the role of ecosystem service providing biota can be better incorporated. Based on a review of published mapping studies, modelling methods and associated geo-referenced metrics are classified into five categories according to the way in which the contribution of ecosystem service providing organisms is represented. This review highlights the diversity of individual methods, which increasingly combine different model categories. We end by discussing associated uncertainties and pathways towards resolving them. Our review focuses on assessment of ecosystem capacity to deliver services and does not address the social and economic aspects of ecosystem service demand.

Methods

We reviewed ES biophysical modelling approaches in the literature that incorporate descriptions of ecosystem service providers (ESP) and their contribution to ES supply. Given our objective of analysing the merits and limitations of available models rather than producing a quantitative analysis of the state of the art, for terrestrial systems we did not attempt to reiterate the several systematic reviews that have already been published [START_REF] Lautenbach | Blind spots in ecosystem services research and implementation[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF][START_REF] Seppelt | A quantitative review of ecosystem service studies: approaches, shortcomings and the road ahead[END_REF], while for marine systems a systematic analysis of publications was conducted. As we aimed to assess how biophysical realism was incorporated in different approaches, we chose to classify models and associated geo-referenced metrics according to the way in which the relationships between ESP and biophysical processes are represented, using the following terminology: spatial proxy models, phenomenological models, niche-based models, traitbased models and full process-based models (Figure 1). Briefly, spatial proxy models refer to simple models based on expert knowledge or statistical associations relating abiotic and biotic indicators to ES provision. Phenomenological models add to these by explicitly incorporating effects of land/seascape configuration through spatial processes. Niche-based models deduce ES provision from the geographic distribution of ESP, while trait-based models depict statistical relationships between ecosystem processes and indicators of ESP community functional composition. Lastly, we refer to full process-based models as those incorporating explicit representations of geochemical, physical and biotic processes underpinning ecosystem functioning.

For each category of models we describe and exemplify based on published studies (supported by standard model descriptions presented in Appendix 1Erreur ! Source du renvoi introuvable.) the principles and mechanics of application of these models, with specific reference to how ESP are represented. Main biodiversity components for ESP characterisation and the strengths and weaknesses of different model types for practice are summarised in Table 1. Table 2 summarises main data sources for each model type, with specific reference to Europe for terrestrial (Table 2a) and marine (Table 2b) systems respectively. Lastly, key data sources and strengths and weaknesses for practice are discussed.

Results

Proxy models

We define proxy models as models that relate ES indicators to land or marine cover, abiotic and possibly biotic variables by way of calibrated empirical relationships or expert knowledge. It is desirable, and in practice most common for such models to use selected proxy variables that are based on well-known causal relationships between environmental variables [START_REF] Kienast | Assessing Landscape Functions with Broad-Scale Environmental Data: Insights Gained from a Prototype Development for Europe[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF]. In proxy models habitat type (or biotope) or (more rarely) species composition are considered as the ESP. Most commonly land cover types, ranging from coarse vegetation types (e.g. evergreen vs. deciduous forest) to detailed habitat types such as those of the European Union's Habitats Directive, are associated with levels of ES supply, with the possible incorporation of additional environmental modifiers (e.g. altitude, soil type, climate…). Likewise, for marine ecosystems different habitat types depending on bathymetry or substrate may be used to model ES associated with the presence or activity of particular species.

One simple, and often used method consists in combining look-up tables allocating ES values per land cover with modifying categorical variables describing abiotic factors and ecological integrity [START_REF] Burkhard | Mapping ecosystem service supply, demand and budgets[END_REF]. For example, in the Austrian Stubai valley, [START_REF] Schirpke | Multiple ecosystem services of a changing Alpine landscape: past, present and future[END_REF] combined maps of vegetation types with measures of ES to map past, current or future fodder quantity and quality, carbon sequestration, soil stability, natural hazard regulation and aesthetic value. In traditional forest landscapes of Lapland, [START_REF] Vihervaara | Ecosystem services-A tool for sustainable management of human-environment systems. Case study Finnish Forest Lapland[END_REF] illustrated how multiple biophysical and social data sources can be combined to quantify regulation service supply by different biotopes. In marine ecosystems, bathymetry, habitat distribution, sediment type, wave and currents regime, tidal range and water temperature are most frequently used proxies. Liquete et al. (2013) developed a proxy-based model to assess coastal protection at European level based on 14 biophysical and socioeconomic variables describing coastal protection capacity, coastal exposure and demand for protection. Statistical models developed from observations or analysis of regional data sets may also be applied. Multiple regression models, Generalized Additive Models [START_REF] Yee | Generalized additive models in plant ecology[END_REF] or more sophisticated methods for capturing uncertainty in relationships, such as Bayesian modelling [START_REF] Grêt-Regamey | Facing uncertainty in ecosystem services-based resource management[END_REF]) may be used here. In general, the application of models developed at larger scale to smaller extents and greater resolution generates uncertainty as they do not capture context-dependent relationships [START_REF] Purtauf | Landscape context of organic and conventional farms: Influences on carabid beetle diversity[END_REF] and the effects of finer-grained relevant variables such as soils. Sitespecific models may be developed based on field data collection (as encouraged by Martinez-Harms and Balvanera, 2012 -see Lavorel et al., 2011) and on remote sensing data (Table 2, Figure 2). On the other hand, the validity of up-scaling from site-specific models to larger spatial scales depends on whether sites represent the average conditions at the larger scale. It has further been shown by Grêt-Regamey et al. (2014b) that spatially explicit information about non-clustered, isolated ES tends to be lost at coarse resolution, mainly in less rugged terrain, which calls for finer resolution assessments in such contexts.

In the marine case, proxy models have generally been used to map the distribution of coastal vegetation such as mangrove coverage, which then has been used to estimate carbon sequestration and storage. In contrast, proxy models have had a limited application for the assessment of "underwater" marine ES, and we contend that this mainly reflects the limitations of remote sensing for correctly determining underwater habitat coverage.

Strengths and weaknesses for practice Sophisticated proxy models have been recommended for national assessment of ecosystem services [START_REF] Maes | Mapping and Assessment of Ecosystems and their Services: Indicators for ecosystem assessments under Action 5 of the EU Biodiversity Strategy to 2020[END_REF]. They help move from a pure 'benefit transfer' approach based on land cover [START_REF] Eigenbrod | The impact of proxy-based methods on mapping the distribution of ecosystem services[END_REF]MAES Tier 1), to more precise assessments (MAES Tier 2) using classic GIS methods accessible to all [START_REF] Kienast | Assessing Landscape Functions with Broad-Scale Environmental Data: Insights Gained from a Prototype Development for Europe[END_REF]. Also, they can be easily combined with socio-economic variables in order to provide at least first level assessments of benefits [START_REF] Burkhard | Mapping ecosystem service supply, demand and budgets[END_REF][START_REF] Grêt-Regamey | Linking GIS-based models to value ecosystem services in an Alpine region[END_REF][START_REF] Vihervaara | Ecosystem services-A tool for sustainable management of human-environment systems. Case study Finnish Forest Lapland[END_REF] and allow consistent mapping of different ecosystem services, which is essential for avoiding data artefacts when studying trade-offs. Model applications are however constrained by the availability of different data layers depending on scales and regions. For instance, while effects of soil parameters on regulation services (e.g. carbon sequestration, erosion control) are well understood by scientists and practitioners, soil maps are often not available at suitably fine resolution.

Phenomenological models

Phenomenological models are based on qualitative or semi-quantitative relationships between ESP and ES supply, based on an understanding of biological mechanisms underpinning ES supply. In difference to simple proxy models, at least part of the parameters and relationships are transferred from in-depth process-based studies or meta-analyses of observations. They assume, but do not represent explicitly, a mechanistic relationship between elements of the landscape, considered as ESP units, and the provisioning of ES. This often implies considering landscape configuration explicitly, contrary to simple land cover proxy models. This relationship might be represented by a functional relationship between landscape attributes and services, or might also incorporate spatial configuration. For example, the ES supply of a forest patch might depend on land cover, patch size and additional attributes such as soil quality or topography. However, quantitative biodiversity indicators are not commonly used in this type of models that are often dominated by the influence of land cover/use, although biodiversity indicators might be used, e.g. by incorporating a statistical relationship between plant or bird species richness and recreational value of a location. Typically, these approaches are used at the regional to the global scale since the assumed relationships ignore most often smaller scale details and focus on patterns emerging at coarser scales.

Phenomenological approaches have been applied for ecosystem services provided by mobile organisms and ecosystem services relating to lateral flows for which consideration of spatial configuration is essential [START_REF] Mitchell | Reframing landscape fragmentation's effects on ecosystem services[END_REF][START_REF] Verhagen | Effects of landscape configuration on mapping ecosystem service capacity: a review of evidence and a case study in Scotland[END_REF]). As a simple example of mobile ESP, in the Swiss valley of Davos, the cultural service of habitat for the protected bird species Capercaillie was modelled by combining habitat suitability criteria relating to quality and spatial pattern with GIS-modelled vegetation distribution [START_REF] Grêt-Regamey | Linking GIS-based models to value ecosystem services in an Alpine region[END_REF]. Phenomenological approaches that incorporate landscape configuration are commonly used to model pollination through the interplay between habitats suitable for wild pollinators and demand from insect-pollinated crops (Grêt-Regamey et al., 2014a;[START_REF] Lautenbach | Analysis of historic changes in regional ecosystem service provisioning using land use data[END_REF][START_REF] Maes | A European assessment of the provision of ecosystem services[END_REF]Schulp et al., 2014b). Based on a metaanalysis by [START_REF] Ricketts | Landscape effects on crop pollination services: are there general patterns[END_REF] these models represent realized pollination as a decay function based on the distance between pollinator habitat and fields with pollinationdependent crops. The InvESt pollination model (Lonsdorf et al., 2009) includes the location of crops to be pollinated and the habitat quality for different pollinator species or guilds, as well as the availability of floral resources. More sophisticated versions also limit the number of cells that can be pollinated by pollinator source [START_REF] Lautenbach | Analysis of historic changes in regional ecosystem service provisioning using land use data[END_REF]Grêt-Regamey et al. (2014a) used knock-off thresholds based on connectivity to modulate habitat quality.

The assessment of water quality regulation and recreation by [START_REF] Lautenbach | Analysis of historic changes in regional ecosystem service provisioning using land use data[END_REF], and the universal soil loss equation (USLE) and related approaches [START_REF] Wischmeier | Predicting rainfall erosion losses -a guide to conservation planning[END_REF] for the quantification of erosion control [START_REF] Schirpke | Multiple ecosystem services of a changing Alpine landscape: past, present and future[END_REF] represent examples of commonly used phenomenological approaches for ES depending on lateral flows.

In the marine environment phenomenological models have been rarely used, however [START_REF] Townsend | Overcoming the challenges of data scarcity in mapping marine ecosystem service potential[END_REF] developed a method whereby services were defined from a series of principles based on ecosystem functioning and linked to marine biophysical parameters to develop ES maps for an area in New Zealand (Figure 3). Other studies have used phenomenological models to link the coverage of key habitats and their level of connectivity to fisheries production [START_REF] Yee | Comparison of methods for quantifying reef ecosystem services: A case study mapping services for St[END_REF].

Strengths and weaknesses for practice

Phenomenological approaches depend on the validity of the qualitative or semi-quantitative relationships underlying the model. Typically, the required parameters are transferred from other study sites or obtained through meta-analysis. Results should therefore be interpreted as indicators of the direction or spatial variation of an effect or of the relative importance of an effect (e.g. by comparing different land use scenarios or historic land use data) rather than absolute values. The strength of the approach it incorporates land use configuration effects while requiring only limited data. It can therefore be used to get first estimates at scales where data availability is limited, such as the regional scale, or for the assessment of past conditions for which required data for more sophisticated approaches will not become available.

Niche-based models

We define as niche-based models of ES models that assess ES supply based on the presence (or abundance) of ESP (often species) depending on their geographic distribution (Figure 4). ES can be modelled by aggregating distribution maps for different ESP if there are more than one contributing species, thus considering for instance the number of ESP species as a proxy for ES supply. A frequent limitation to such an approach is the lack of continuous distribution maps of ESP occurrence. To overcome this, Species Distribution Modelling (SDM) [START_REF] Elith | Species Distribution Models: Ecological Explanation and Prediction Across Space and Time[END_REF][START_REF] Guisan | Predicting species distribution: offering more than simple habitat models[END_REF] can be used to produce statistical relationships that predict the probability of occurrence of a given species (or group of species) over geographic areas depending on parameters such as climate, soil or land use, and generate continuous distribution maps of these taxa. There are also more sophisticated, mechanistic models, which (akin to full process models -see below) model species distributions based on physiological mechanisms (e.g. temperature tolerance thresholds, temperature responses), phenology (the timing of specific life cycle events such as bud burst or flowering in plants) or animal behaviour. The contribution of e.g. different species or functional groups to the ES of interest is assessed based on specific traits (e.g. trophic guilds) or expert knowledge.

Niche-based models may in particular apply to cultural services provided by well-identified species (e.g. protected species, species of particular aesthetic value) or to provisioning services by particular species such as in the case of wild foods (Schulp et al., 2014c). In Mediterranean regions provisioning services such as timber, fuelwood or cork production can be related to the presence of particular species (e.g. Fagus sylvatica or Quercus ilex, or Quercus suber respectively) and to forest species richness [START_REF] Vilà | Species richness and wood production: a positive association in Mediterranean forests[END_REF][START_REF] Von Essen | Cork before cattle: Quantifying Ecosystem Services in the Portuguese Montado and Questioning Ecosystem Service Mapping[END_REF], while spiritual and aesthetic values are supported by Quercus suber and Pinus halepensis, and the regulation of fire hazards is promoted by Quercus suber but negatively affected by Pinus halepensis [START_REF] Lloret | Mediterranean vegetation response to different fire regimes in Garraf Natural Park (Catalonia, Spain): field observations and modelling predictions[END_REF]. Niche-based modelling was applied to model biocontrol of vertebrate and invertebrate pests by terrestrial vertebrates (birds, mammals, reptiles) in Europe, considering predator species richness as a proxy for biocontrol potential (Civantos et al., 2012). As SDMs enable the projection of ESP distribution under changing environmental conditions, this approach showed that under future climate change scenarios pest control would be substantially reduced, especially in southern European countries, whereas in much of central and northern Europe climate change would likely to benefit pest-control providers. In coastal and marine environments niche-based models have been primarily used to model the distribution of mangroves and thus their carbon capture and storage capacity [START_REF] Hutchison | Predicting Global Patterns in Mangrove Forest Biomass[END_REF][START_REF] Sunny | A global predictive model of carbon in mangrove soils[END_REF] and fisheries production, based on species distribution models (Jordan et al., 2012).

In principle, any method of aggregation is possible, although so far species richness for ESP (i.e. added contributing species) has been considered as the proxy for ES without applying any weighting to different species. Though in their infancy, approaches considering relationships between taxonomic, phylogenetic and functional diversity and their links to ES [START_REF] Flynn | Functional and phylogenetic diversity as predictors of biodiversity-ecosystem-function relationships[END_REF] are good candidates to expand existing ones. These approaches build on the premise that since functional diversity, or functional composition tend to be better related to ES supply than species richness or diversity [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF], then niche-based models of species distributions could be translated to functional diversity in order to generate projections of ES. The incorporation of phylogenetic diversity, which can be easily computed based on taxonomic data granted the availability of phylogenetic data (e.g. [START_REF] Thuiller | Consequences of climate change on the tree of life in Europe[END_REF], adds a further means to approach functional diversity and thereby to quantify ES [START_REF] Cadotte | Using Phylogenetic, Functional and Trait Diversity to Understand Patterns of Plant Community Productivity[END_REF].

Strengths and weaknesses for practice

Overall, niche-based modelling of species distributions is a well-developed approach with free accessible tools, suitable for future scenario projections (.e.g BIOMOD: [START_REF] Thuiller | BIOMOD -a platform for ensemble forecasting of species distributions[END_REF]Maxent: Elith et al., 2011). Species distribution data are often the critical bottleneck for niche-based approaches. Limitations of SDM and strengths and weaknesses of different distribution modelling methods have been discussed extensively (e.g. [START_REF] Bellard | Impacts of climate change on the future of biodiversity[END_REF][START_REF] Elith | Species Distribution Models: Ecological Explanation and Prediction Across Space and Time[END_REF], and improvements proposed [START_REF] Zurell | Benchmarking novel approaches for modelling species range dynamics[END_REF]. Apart from the intrinsic limitations of the approach, such as ignoring population dynamics, species interactions, or potential adaptive responses, the main avenue for improvement towards the application to ES modelling regards the understanding and quantitative specification of relationships between ESP and ES supply. This gap requires both greater ecological understanding [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF][START_REF] Nagendra | Impacts of land change on biodiversity: making the link to ecosystem services[END_REF], and research into the demand for ES in terms of the identities and relative weights of contributing species.

Trait-based models

There is increasing evidence for the relevance of traits of organisms as ES providers [START_REF] De Bello | Functional traits underlie the delivery of ecosystem services across different trophic levels[END_REF][START_REF] Lavorel | Plant functional effects on ecosystem services[END_REF][START_REF] Luck | Quantifying the contribution of organisms to the provision of ecosystem services[END_REF]. Trait-based models quantify ES supply based on statistical, quantitative relationships between an ecosystem property underpinning ES supply and trait-based metrics, as well as, if significant additional effects of abiotic parameters such as climate or soil variables [START_REF] Gardarin | Plant trait-digestibility relationships across management and climate gradients in French permanent grasslands[END_REF]Lavorel et al., 2011). (Lavorel et al., 2011) demonstrated that trait-based models reduce uncertainty in ES prediction over space as compared to models based on land use alone, or even land use and soil variables [START_REF] Eigenbrod | The impact of proxy-based methods on mapping the distribution of ecosystem services[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF]. Such models are constructed based on empirical measures of ecosystem functioning, which are then related to explanatory variables including: land cover/use, trait-based metrics quantifying functional diversity of ESP [START_REF] Mouchet | Functional diversity measures: an overview of their redundancy and their ability to discriminate community assembly rules[END_REF], soil variables and, for regional to continental scale or topographically complex landscapes climate / microclimate variables. Models may combine metrics for several individual traits, e.g. plant height and leaf nitrogen concentration to model grassland productivity (Lavorel et al., 2011); or use multi-trait metrics such as a compound index of different traits, e.g. the leaf economics spectrum [START_REF] Laliberté | Cascading effects of long-term land-use changes on plant traits and ecosystem functioning[END_REF][START_REF] Lienin | Plant trait responses to the environment and effects on multiple ecosystem properties[END_REF][START_REF] Mokany | Functional identity is more important than diversity in influencing ecosystem processes in a temperate native grassland[END_REF] or multivariate trait diversity (e.g. [START_REF] Conti | Plant functional diversity and carbon storage -an empirical test in semiarid forest ecosystems[END_REF][START_REF] Mokany | Functional identity is more important than diversity in influencing ecosystem processes in a temperate native grassland[END_REF]. A review of known relationships between indicators of ecosystem biogeochemical functioning for plants, relevant to the modelling of ES such as for instance fodder or timber production, climate regulation through carbon sequestration or the maintenance of water quality, suggested that, for available studies so far, community mean values of single traits tended to capture most of the variance in these ecosystem properties [START_REF] Lavorel | Plant functional effects on ecosystem services[END_REF]. The recent extension to ES associated with other biota such as soil fauna and microorganisms [START_REF] Mulder | Connecting the Green and Brown Worlds: Allometric and Stoichiometric Predictability of Above-and Below-Ground Networks[END_REF], insects [START_REF] Ibanez | Optimizing size thresholds in a plant-pollinator interaction web: towards a mechanistic understanding of ecological networks[END_REF][START_REF] Moretti | Linking traits between plants and invertebrate herbivores to track functional effects of environmental changes[END_REF], terrestrial vertebrates [START_REF] Luck | Extending trait-based frameworks to vertebrates and improving their application to the study of ecosystem services[END_REF], aquatic invertebrates [START_REF] Engelhardt | Relating effect and response traits in submersed aquatic systems[END_REF] or marine fish [START_REF] Albouy | From projected species distribution to food-web structure under climate change[END_REF] holds high promises. Multitrophic traitbased models quantify ecosystem services resulting from the interaction between several trophic levels such as pollination, biotic control of pests and weeds or maintenance of soil fertility (Grigulis et al., 2013;Lavorel et al., 2013a). These models capture not only the effects of environmental change on ES via their effects on e.g. plant traits, but by also integrating the traits that underpin biotic interactions between plants and other organisms such as pollinators [START_REF] Pakeman | Using plant functional traits as a link between land use and bee foraging abundance[END_REF], herbivores [START_REF] Ibanez | Plant functional traits reveal the relative contribution of habitat and food preferences to the diet of four subalpine grasshoppers[END_REF], or soil microorganisms [START_REF] De Vries | Abiotic drivers and plant traits explain landscape-scale patterns in soil microbial communities[END_REF][START_REF] Legay | The relative importance of above-ground and below-ground plant traits as drivers of microbial properties in grasslands[END_REF], and their effects of ES supply (Grigulis et al., 2013;[START_REF] Moretti | Linking traits between plants and invertebrate herbivores to track functional effects of environmental changes[END_REF]. In principle, and similar to niche-based models, a wide range of modelling methods are suitable, although selected methods must allow spatially-extensive extrapolation over space for which explanatory variables are available, and preferably across time under scenarios.

As an example, models of mountain grassland ES supply were developed based on plant traits (Lavorel et al., 2011), and further complemented by traits of soil microorganisms (Grigulis et al., 2013). In these models which focused principally on components of carbon and nutrient cycling, ecosystem properties were linked to plant height and easily measureable leaf traits such as dry matter content and nitrogen concentration, with additional effects of soil parameters. Both traits and soil parameters were related to grassland management to produce ES maps (Figure 5). These models were also applied to project effects of combined climate and socio-economic scenarios translated into grassland management projections and parameterised from observations and experiments [START_REF] Lamarque | Plant trait-based models identify direct and indirect effects of climate change on bundles of grassland ecosystem services[END_REF].

The initial construction of trait-based ES models requires observational or experimental data sets measuring ecosystem properties underpinning ES supply along with community composition of ESP. ESP community composition can then be combined with original, sitelevel trait data, or data extracted from trait data bases, but considering uncertainties resulting from intraspecific trait variability [START_REF] Kazakou | Are trait-based species rankings consistent across data sets and spatial scales?[END_REF][START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF]. Scenario projections can be parameterised by combining projected values for land use and environmental parameters with new community-level trait values calculated based on species compositional turnover from e.g. state-and-transition models [START_REF] Quétier | Linking vegetation and ecosystem response to complex past and present land use changes using plant traits and a multiple stable state framework[END_REF] and on intraspecific variability measured along environmental gradients [START_REF] Albert | Intraspecific functional variability: extent, structure and sources of variation within a French alpine catchment[END_REF] or through experiments [START_REF] Jung | Intraspecific trait variability mediates the response of subalpine grassland communities to extreme drought events[END_REF].

Increasing trait data availability through communal data bases and remote sensing offers high promises for the development of trait-based models of ES (Table 2a). There are definite geographic gaps, but overall European vegetation tends to be increasingly well covered, although more extreme environments such as Mediterranean or alpine, where intraspecific variability hinders the use of data measured in more temperate regions, still require collection efforts.

Strengths and weaknesses for practice

Although trait-based models of ES supply are in their infancy they rely on rapidly increasing conceptual and empirical evidence. Such models also provide a mechanistic basis for the understanding of biophysical bundles and trade-offs in ES supply [START_REF] Lavorel | How fundamental plant functional trait relationships scale-up to trade-offs and synergies in ecosystem services[END_REF][START_REF] Mouillot | Functional Structure of Biological Communities Predicts Ecosystem Multifunctionality[END_REF]. The existence of so called 'response -effects overlaps' [START_REF] Lavorel | Predicting the effects of environmental changes on plant community composition and ecosystem functioning: revisiting the Holy Grail[END_REF][START_REF] Suding | Scaling environmental change from traits to communities to ecosystems: the challenge of intermediate-level complexity[END_REF] enables mechanistic ES projections under future scenarios using relatively simple models [START_REF] Lamarque | Plant trait-based models identify direct and indirect effects of climate change on bundles of grassland ecosystem services[END_REF]. As with any statistical model however, the greatest care should be taken when attempting to apply such models beyond the parameter space for which they were derived. So far trait-based ES models have rarely been validated across sites, although inter-site analyses have identified generic traitbased models of fodder production, fodder digestibility and litter decomposability [START_REF] Fortunel | Plant functional traits capture the effects of land use change and climate on litter decomposability of herbaceous communities in Europe and Israel[END_REF][START_REF] Gardarin | Plant trait-digestibility relationships across management and climate gradients in French permanent grasslands[END_REF]Lavorel et al., 2013b), and the model by [START_REF] Gardarin | Plant trait-digestibility relationships across management and climate gradients in French permanent grasslands[END_REF] was applied to map fodder quality at national scale [START_REF] Violle | Vegetation Ecology meets Ecosystem Science: permanent grasslands as a functional biogeography case study[END_REF]. Lastly, traitbased models will become increasingly attractive as trait data bases become more generally available, although the lack of soil data layers in many regions will remain problematic.

Full process-based models

Full process-based models of (terrestrial) ecosystems rely on the explicit representation, using mathematical formulations, of ecological, physical, and biogeochemical processes that determine the functioning of ecosystems. The predictive algorithms simulate a large range of variables, which can then be post-processed to quantify ES. Process-based models have been most widely applied to quantify i) climate regulation [START_REF] Bayer | Historical and future quantification of terrestrial carbon sequestration from a Greenhouse-Gas-Value perspective[END_REF]Duarte et al., 2013;[START_REF] Metzger | A spatially explicit and quantitative vulnerability assessment of ecosystem service change in Europe[END_REF][START_REF] Naidoo | Global mapping of ecosystem services and conservation priorities[END_REF][START_REF] Ooba | Biogeochemical model (BGC-ES) and its basin-level application for evaluating ecosystem services under forest management practices[END_REF][START_REF] Watanabe | Dynamic emergy accounting of water and carbon ecosystem services: A model to simulate the impacts of land-use change[END_REF], ii) water supply, water quality, flood and erosion regulation [START_REF] Gedney | Detection of a direct carbon dioxide effect in continental river runoff records[END_REF]Lautenbach et al., 2012a;[START_REF] Lautenbach | Optimization-based trade-off analysis of biodiesel crop production for managing an agricultural catchment[END_REF][START_REF] Logsdon | A quantitative approach to evaluating ecosystem services[END_REF], iii) food, fodder, and bioenergy provision [START_REF] Bateman | Bringing Ecosystem Services into Economic Decision-Making: Land Use in the United Kingdom[END_REF][START_REF] Beringer | Bioenergy production potential of global biomass plantations under environmental and agricultural constraints[END_REF]Lindeskog et al., 2013;[START_REF] Müller | Hotspots of climate change impacts in sub-Saharan Africa and implications for adaptation and development[END_REF], iii) natural hazard regulation [START_REF] Elkin | A 2 °C warmer world is not safe for ecosystem services in the European Alps[END_REF], but also in the wider frame of habitat characterisation [START_REF] Hickler | Projecting the future distribution of European potential natural vegetation zones with a generalized, tree species-based dynamic vegetation model[END_REF][START_REF] Huntingford | Highly contrasting effects of different climate forcing agents on terrestrial ecosystem services[END_REF]. Here, we discriminate between large-scale and local to landscape scale process-based models.

Appendix 1 lists examples using Dynamic Vegetation Models (DVM) (LPJ-GUESS and LPJmL: Bondeau et al., 2007;[START_REF] Sibyll | Contribution of permafrost soils to the global carbon budget[END_REF]Sitch et al., 2003;Smith et al., 2001), Earth System Models (ESM) (JULES andORCHIDEE: Cox, 2001, Krinner et al., 2005;[START_REF] Zaehle | Carbon and nitrogen cycle dynamics in the O-CN land surface model: 1. Model description, site-scale evaluation, and sensitivity to parameter estimates[END_REF], hydrological models (SWAT and others: Neitsch et al., 2005;Stürck et al., 2014), forest dynamic models (e.g. [START_REF] Elkin | A 2 °C warmer world is not safe for ecosystem services in the European Alps[END_REF]Bugmann, 1996) and models for ecological restoration (e.g. [START_REF] Chen | A gap dynamic model of mangrove forest development along gradients of soil salinity and nutrient resources[END_REF]Duarte et al., 2013). Figure 6 represents the typical steps of ES assessments with process-based models and possible mapping outputs.

Large-scale process models

Several large-scale process models have been used for ES quantification. Dynamic Vegetation Models (DVMs) and Earth System Models (ESMs) are large-scale models that provide functional representations of plant and ecosystem processes that are universal rather than specific to one biome or region [START_REF] Prentice | Encyclopedia of Biodiversity[END_REF]. Hydrological models represent water-related processes within river catchments [START_REF] Gudmundsson | Evaluation of nine large-scale hydrological models with respect to the seasonal runoff climatology in Europe[END_REF]. Global models typically apply a spatial resolution of 0.5°x0.5°, but can be run at finer resolution, or even ecosystem scale if the required drivers are available. In that case, model adjustment might be necessary (e.g. re-calibration, re-formulation to better account for important processes of the region). Applications of these models that include a representation of regional specific features are often designed for local to regional scale application, like forest dynamic models and crop models. This type of models uses a set of process formulations for representing key biogeochemical and physical processes as a function of prevailing atmospheric CO 2 concentration, climate, soil characteristics and eventually land use and management or nutrient deposition. Vegetation is represented as a mixture of plant functional types (PFTs) or species that are distinct in terms of bioclimatic limits and ecological parameters (see [START_REF] Lavorel | Plant functional types : are we getting any closer to the Holy Grail ?[END_REF][START_REF] Woodward | Plant functional types and climatic change: Introduction[END_REF], simulated or prescribed. Age or size classes may be distinguished, but more typically the modelled properties represent averages of the entire grid cell population of a given PFT [START_REF] Prentice | Dynamic Global Vegetation Modeling: Quantifying Terrestrial Ecosystem Responses to Large-Scale Environmental Change[END_REF], possibly under a given management type. Soil profile is described using up to ten layers. Hydrological models consider also shallow and deep aquifer storages, and a river routing module simulates the discharge to the rivers network. "Fast" processes are modelled on a daily or sub-daily basis and include energy and gas exchange, photosynthesis, respiration and plant-soil water exchanges. Processes with seasonal dynamics such as plant phenology, growth and biomass allocation are implemented on a daily or monthly basis. Mortality, disturbance, management, are represented on an annual or sub-annual basis, eventually stochastically. By using a small number of PFTs which represent a low-dimensional continuum of plant trait combinations, process-based models generally underestimate the functional diversity of biota in favour of a manageable number of classes. Yet the rise of super computers allows to run DVMs with flexible individual traits [START_REF] Sakschewski | Leaf and stem economics spectra drive diversity of functional plant traits in a dynamic global vegetation model[END_REF], making it possible to account for functional diversity.

Local to landscape scale process models

At local to landscape scales, forest dynamic models with similar philosophy and structure as DVMs have been used for the assessment of bundles of ecosystem services including timber production, natural hazard regulation (avalanches, rockfalls), carbon sequestration, conservation of forest diversity for greater drought resilience and habitat for protected bird species [START_REF] Elkin | A 2 °C warmer world is not safe for ecosystem services in the European Alps[END_REF][START_REF] Grêt-Regamey | Linking GIS-based models to value ecosystem services in an Alpine region[END_REF][START_REF] Temperli | Adaptive management for competing forest goods and services under climate change[END_REF].

As another type of full-process models with strong potential for ES modelling, watershed models have been designed to simulate hydrological flows and often water quality at the landscape to regional scale. Soil infiltration, surface and subsurface flows as well as evapotranspiration and snowmelt are the main hydrological processes. For modelling water quality the transport and turnover of nutrients and other chemicals need to be represented as well as soil erosion processes, along with agricultural practices. Given the importance of vegetation for the water cycle a vegetation growth model is part of all watershed models. Specifically differences between different plants (or plant functional types) are considered for water use, and in nutrient use for crops. As an example, Stürck et al. (2014) quantified the supply of flood control by running a hydrological model for a number of representative catchment types to quantify the regulating effect of different land use types in different positions in the catchments. Results were extrapolated on a European map accounting for catchment type, location in the catchment, land use and soil conditions. The soil water assessment tool (SWAT) (Neitsch et al., 2005) is an example of an advanced watershed model applied to agricultural landscapes map water purification services (Lautenbach et al., 2012a), to assess fresh water provisioning, fuel provisioning, erosion regulation and flood regulation [START_REF] Logsdon | A quantitative approach to evaluating ecosystem services[END_REF] and to describe trade-offs between food and fodder provisioning, biofuel provisioning, water quality regulation and discharge regulation [START_REF] Lautenbach | Optimization-based trade-off analysis of biodiesel crop production for managing an agricultural catchment[END_REF] depending on crop rotations and crop management.

For marine ecosystems, the Ecopath with Ecosim (EwE) modelling approach supports predictions of changes in fish to evaluate ecosystem effects of fishing, explore management policy options, analyse impacts and placement of marine protected areas, predict movement and accumulation of contaminants and tracers and model the effects of environmental changes. At the core of EwE is Ecopath, a static, mass-balance snapshot of fisheries based on a set of linear equations combining net production that reflects the balance of catch, predation and other sources of mortality, migration, biomass accumulation, with respiration and unassimilated food. , The Ecosim and Ecospace modules then build on this basic massbalance module to simulate respectively temporal dynamics using differential equations, and spatial dynamics using spatially explicit distribution of habitat types and fishing effort, along with lateral movement. Alcamo et al. (2005) applied EwE to model fish consumption and production for three important regional marine fisheries (North Benguela, Central North Pacific and Gulf of Thailand) under the four Millennium Ecosystem Assessment global scenarios, showing that for all scenarios fish catch (by weight) was maintained in North Benguela, not maintained in the Central North Pacific, whereas results were scenariosensitive in the Gulf of Thailand. Another process-based model is available for the long-term carbon sequestration expected from seagrass restoration programmes (Duarte et al., 2013) by combining models of patch growth, patch survival in seagrass planting projects and estimates of seagrass CO 2 sequestration per unit area for the five seagrass species commonly used in restoration programmes. Results enable the estimation of an optimal planting density to maximise C sequestration.

Strengths and weaknesses for practice

There is a substantially overlapping set of physiological and ecological principles that is used across process-based models to represent ecosystem dynamics and matter flows, providing robustness and scalability to these models for ES quantification. However, predictions of response variables, e.g. net primary productivity, vary considerably among individual largescale models (e.g. [START_REF] Denman | Climate 2007: The Physical Science Basis[END_REF][START_REF] Friedlingstein | Climate-carbon cycle feedback analysis. Results from the C4MIP model intercomparison[END_REF][START_REF] Sitch | Trends and drivers of regional sources and sinks of carbon dioxide over the past two decades[END_REF]. This is due to the lack of a universal set of benchmarks e.g. for terrestrial carbon cycle modelling, and the lack of consensus about several aspects of ecological processes [START_REF] Prentice | Encyclopedia of Biodiversity[END_REF]. Conversely, local and landscape scale process models can be limited by detailed parameterization and calibration needs and by availability of case-specific validation data.

Most process models have not been designed to model ecosystem services but to model the underlying ecosystem functions from which an ecosystem service is derived directly or indirectly. The great strength of this approach is that it allows scenario analysis and if-thenelse experiments if the model has been proven to capture the essential system behaviour. Because they model processes and their fundamental biological and physical interactions they also appear particularly promising for exploring mechanisms underpinning synergies and trade-offs between ES [START_REF] Viglizzo | Partition of some key regulating services in terrestrial ecosystems: Meta-analysis and review[END_REF].

Discussion

Mobilising scientific understanding to assess the spatial distribution of ecosystem services is a tremendous challenge to support environmental assessment, planning and sustainable futures [START_REF] Bennett | Linking biodiversity, ecosystem services and to human well-being: Three challenges for designing research for sustainability[END_REF][START_REF] Maes | An indicator framework for assessing ecosystem services in support of the EU Biodiversity Strategy to[END_REF]. Because ES lie at the interface between social and environmental systems, this endeavour requires an integrated assessment of the social and ecological factors determining the production of ecosystem services (Reyers et al., 2013;[START_REF] Villamagna | Capacity, pressure, demand, and flow: A conceptual framework for analyzing ecosystem service provision and delivery[END_REF]. In this review, we have focused solely on how the biophysical condition of ecosystems, as influenced by biotic, abiotic and management factors, determines ES supply, thus not considering ES demand, and how it influences ES flows and feedbacks to biophysical condition. Mapping ES demand is an even more challenging objective [START_REF] Wolff | Mapping ecosystem services demand: A review of current research and future perspectives[END_REF], and will ultimately need to be coupled in integrated spatial ES assessments (e.g. Schulp et al., 2014b;Schulp et al., 2014c;Stürck et al., 2014).

In the following we discuss future avenues for further improvement of the mapping of ES supply by increasing biophysical realism, but this will need proceed along with parallel progress in accounting for ES demand. [START_REF] Plant | Ecosystem services as a practicable concept for natural resource management: some lessons from Australia[END_REF] identified the lack of an 'ES toolbox' as a barrier to the adoption of ES by natural resource managers. While this paper does not attempt to produce such a tool box, it provides a basis for guiding model choice by scientists and practitioners. Here, we identified two important dimensions which enable the incorporation of greater biophysical realism in models supporting ES mapping and can be developed into different model categories regardless of their baseline complexity. First, while simple land cover information is most commonly used to map ES, effects of land use configuration and land use intensity that can be captured by phenomenological models are too often ignored [START_REF] Verhagen | Effects of landscape configuration on mapping ecosystem service capacity: a review of evidence and a case study in Scotland[END_REF]. Recent practice also shows the benefits of incorporating explicit land use rather than simple land cover information for the simplest proxy-based models all the way to advanced full process-based models Second, approaches incorporating explicitly the role of ES providing biota are emerging as powerful methods to reduce uncertainty in ES mapping. This includes models quantifying individual species effects, species diversity, functional traits, and ecosystem functions described in this review, and for which tools and data are becoming increasingly available. Our review also helps the selection of appropriate methods according to spatial scale, given that scale effects have so far been poorly considered in ES research (Grêt-Regamey et al., 2014b). Review of practice highlights [START_REF] Temperli | Adaptive management for competing forest goods and services under climate change[END_REF] the predominant effect of scale on model selection for practical case studies, (2) the prospect within a single case study to combine different model types, of varying complexity and detail in the representation of biotic effects, depending on specific ES of interest, skills and data / resources availability.

Future avenues for increasing biophysical realism in ES mapping

The last point highlights that our categories of methods are not necessarily exclusive and there may be more of a continuum between approaches. Hybridization is a fruitful avenue for model improvement depending on context, scale, skills and data availability. This is illustrated by a number of published examples and ongoing developments that gradually help progressing from MAES Tier 2 to Tier 3, by gradually incorporating more mechanistic approaches [START_REF] Grêt-Regamey | A tiered approach for mapping ecosystem services[END_REF], and especially a greater integration of explicit biodiversity effects into mapping of ES supply. For instance, Grêt-Regamey et al. ( 2008) demonstrated how statistical, phenomenological and process-based models of varying level of complexity can be coupled with a GIS platform in order to assess ecosystem services at landscape scale. Stürck et al. (2014) used a hybridization between a process-based hydrological model and a spatial proxy, look-up approach to map flood regulation across Europe by determining the regulating capacity of different land use-soil combinations within a catchment. [START_REF] Schirpke | Multiple ecosystem services of a changing Alpine landscape: past, present and future[END_REF] coupled the USLE phenomenological model of soil erosion with a semi-mechanistic statistical model of plant root trait effects on soil retention to quantify effects of land use change on soil stability. Large scale full-process models are also evolving towards the integration of trait-based approaches rather than using a small number of fixed Plant Functional Types. First, global vegetation models can be reformulated to incorporate plant traits and their trade-offs as drivers of vegetation distribution [START_REF] Reu | The role of climate and plant functional trade-offs in shaping global biome and biodiversity patterns[END_REF]. Second, recent models have started considering direct trait-based formulation [START_REF] Scheiter | Impacts of climate change on the vegetation of Africa: an adaptive dynamic vegetation modelling approach (aDGVM)[END_REF][START_REF] Zaehle | Carbon and nitrogen cycle dynamics in the O-CN land surface model: 1. Model description, site-scale evaluation, and sensitivity to parameter estimates[END_REF] and/or parameterisation [START_REF] Verheijen | Impacts of trait variation through observed traitclimate relationships on performance of an Earth system model: a conceptual analysis[END_REF][START_REF] Wullschleger | Plant functional types in Earth system models: past experiences and future directions for application of dynamic vegetation models in high-latitude ecosystems[END_REF]. Lastly, for landscape to regional scales so-called 'hybrid' DVMs pave the way to the integration of niche-based models with dispersal models [START_REF] Midgley | BioMove -an integrated platform simulating the dynamic response of species to environmental change[END_REF] and with trait-based process models [START_REF] Boulangeat | Optimizing plant functional groups for dynamic models of biodiversity: at the crossroads between functional and community ecology[END_REF], thereby opening new perspectives for the refinement of the trait-based modelling of ES supply under scenarios of climate change [START_REF] Boulangeat | FATE-HD: A spatially and temporally explicit integrated model for predicting vegetation structure and diversity at regional scale[END_REF]. Together, all these recent developments illustrate how increasing fundamental understanding on the role of different facets of biodiversity for ecosystem functioning and ecosystem services [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF] can be incorporated into the spatially explicit modelling of ecosystem service supply.

Quantifying and mapping marine ecosystem services has lagged behind efforts for terrestrial ecosystems, but this is in the process of changing (Liquete et al., 2013;[START_REF] Maes | Mapping ecosystem services for policy support and decision making in the European Union[END_REF]. Data and methods to assess the provision of services from the marine environment are far behind to those available for terrestrial environments (Barbier, 2012;[START_REF] Costanza | The ecological, economic, and social importance of the oceans[END_REF]. The gap is greatest when it comes to the mapping of ES, the main reasons behind this is the lack of high-resolution spatial information for habitat and species distribution and the incomplete understanding of ecosystem processes and functions within a highly dynamic threedimensional environment with fluid boundaries [START_REF] Maes | Mapping ecosystem services for policy support and decision making in the European Union[END_REF]. However, efforts towards mapping marine habitats are increasing. In order to rapidly move towards biophysically realistic mapping, some large fundamental knowledge gaps regarding ecosystem processes need to be resolved. First, there is a lack of information at which scales ecosystem processes and functions occur and how these relate to the provisioning of services. Second, the relationships between biodiversity and ecosystem functions in marine ecosystems are still poorly known [START_REF] Bergström | Modeling and predicting the growth of the mussel, Mytilus edulis: implications for planning of aquaculture and eutrophication mitigation[END_REF][START_REF] Moore | Distribution of Mangrove Habitats of Grenada and the Grenadines[END_REF]. The literature search on marine models/mapping conducted as part of this review highlighted a considerable number of studies which stopped at the assessment or prediction of ESP distributions without taking the next step in analysing their implications for ES provision (e.g. [START_REF] Albouy | From projected species distribution to food-web structure under climate change[END_REF][START_REF] Bergström | Modeling and predicting the growth of the mussel, Mytilus edulis: implications for planning of aquaculture and eutrophication mitigation[END_REF][START_REF] Moore | Distribution of Mangrove Habitats of Grenada and the Grenadines[END_REF]. Although this is not an easy problem, experience from terrestrial ecosystems in the integration of biotic processes and biodiversity effects into ES quantification and mapping may speed up progress for marine and coastal ecosystems.

Uncertainty and validation of spatially-explicit models of ES supply

While the importance of quantifying uncertainties and of model validation is accepted knowledge in the environmental and ecological modelling community [START_REF] Bennett | Characterising performance of environmental models[END_REF][START_REF] Dormann | Components of uncertainty in species distribution analysis: a case study of the Great Grey Shrike[END_REF][START_REF] Jakeman | Ten iterative steps in development and evaluation of environmental models[END_REF][START_REF] Laniak | Integrated environmental modeling: A vision and roadmap for the future[END_REF], these have been two enduring challenges for spatial explicit ES assessment [START_REF] Crossman | A blueprint for mapping and modelling ecosystem services[END_REF][START_REF] Martinez-Harms | Methods for mapping ecosystem service supply: a review[END_REF][START_REF] Seppelt | A quantitative review of ecosystem service studies: approaches, shortcomings and the road ahead[END_REF].

Uncertainty can be conceptually separated into uncertainty about the model structure, uncertainty of model parameterization, uncertainty in the data and last but not least the conceptual uncertainty of the definition of an ecosystem service and underlying processes. In reality all these different components interact: data availability -especially at larger scalesdrives in many situations the choice of proxys and the model structure for assessing an ES [START_REF] Andrew | Spatial data, analysis approaches, and information needs for spatial ecosystem service assessments: a review[END_REF]. The use and parameterization of a model is limited by the availability of data -this can in turn lead to suboptimal decision about model structure which leads in turn to an increase in uncertainty. Choosing strongly simplified proxy-models to best match data availability may lead to ignoring the most important processes determining ecosystem service supply, and especially biotic processes. For ecosystem services that predominantly rely on mobile biota -such as pest control, or pollination -increased system understanding on how the different components of biodiversity affect ES provisioning of the services supports the development of more robust models suitable for spatial and temporal extrapolation [START_REF] Kremen | Pollination and other ecosystem services produced by mobile organisms: a conceptual framework for the effects of land-use change[END_REF]. At the same time, using the most advanced process models in the absence of data to parameterise them at the desired scale does not necessarily lead to higher accuracy. Still, incorporating at least phenomenological understanding into ES models would likely increase reliability and robustness of ES assessments and maps. The use of remote sensing data to estimate ecosystem service proxies [START_REF] Ayanu | Quantifying and Mapping Ecosystem Services Supplies and Demands: A Review of Remote Sensing Applications[END_REF][START_REF] De Araujo Barbosa | Remote sensing of ecosystem services: A systematic review[END_REF] and to derive information on biodiversity [START_REF] O'connor | Earth observation as a tool for tracking progress towards the Aichi Biodiversity Targets[END_REF][START_REF] Schmidtlein | Mapping plant strategy types using remote sensing[END_REF] (Table 2) is promising to overcome some of the data limitations, although the derivation of information from remote sensing data requires the use of additional models that bring in their own sources of uncertainty [START_REF] Foody | Front Matter, Uncertainty in Remote Sensing and GIS[END_REF].

In the previous sections we have illustrated how better biodiversity process understanding can be incorporated to reduce uncertainty in ES models. The uncertainty introduced by a selected model structure can be assessed by comparing models of different structure, as recently done for species-distribution models [START_REF] Buisson | Uncertainty in ensemble forecasting of species distribution[END_REF][START_REF] Morin | Comparing niche-and process-based models to reduce prediction uncertainty in species range shifts under climate change[END_REF]. Such comparisons can be used to highlight areas or situations in which models strongly agree or disagree. Schulp et al. (2014a) followed this approach by comparing ES maps from five distinct studies at the European scale, and such practice is now gaining currency to assess the value of novel model developments. Another strategy is the use of model ensembles for forecasts and assessments. This strategy which is common practice for fullprocess models is now spreading for niche-based and trait-based based models (e.g. [START_REF] Araújo | Ensemble forecasting of species distributions[END_REF][START_REF] Gritti | Estimating consensus and associated uncertainty between inherently different species distribution models[END_REF][START_REF] Thuiller | BIOMOD -a platform for ensemble forecasting of species distributions[END_REF].

As the availability on species, phylogenetic and functional biodiversity increases currently, along with remote sensing derived information, data availability is likely to become less limiting for using more advanced models (Table 2). But then uncertainty in biodiversity input data could propagate in ES models [START_REF] Dong | Land use mapping error introduces strongly-localised, scale-dependent uncertainty into land use and ecosystem services modelling[END_REF]. Researchers will then need to estimate the effects of increasing model complexity both on feasibility of parameterisation and on sensitivity to uncertainty in the input data, and to carefully assess potential mismatches in temporal and spatial scale of the new data [START_REF] Orth | Does model performance improve with complexity? A case study with three hydrological models[END_REF][START_REF] Perrin | Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments[END_REF]. First, a specific source of uncertainty in ES assessment relates to the scale of the input data. Although the selection of the modelling scale should be driven by the requirements of the end user (the scale of the decision to be made) (Grêt-Regamey et al., 2014b), data availability seriously limits the degrees of freedom for the selection of input data. There should always be a match between the resolution for ESP biota and environmental data. This in particular applies to climate, where downscaled layers need to be available or calculated for adequate species distribution or process modelling. Conversely, care should also be taken in combining high resolution soil maps with biota data with a coarser resolution (Grêt-Regamey et al., 2014b). Second extrapolating models beyond the range of calibration data is a critical source of uncertainty. Black box statistical models, e.g. some phenomenological, niche-based or trait-based models that have been (over-)fitted to data without ensuring a robust model structure are especially prone to effects of extrapolation. In general, for an analysis of temporal changes or for assessing management options the projected effects should be compared to the sensitivity of the model outputs against reasonable parameter changes: if the direction of the effect changes or if the magnitude of the response is weaker than the sensitivity of the model one should hesitate to draw strong conclusions from the model. Examples for this approach can be found in [START_REF] Lautenbach | Analysis of historic changes in regional ecosystem service provisioning using land use data[END_REF] and (Schulp et al. (2014b). It is also possible to test the sensitivity towards the uncertainty in the input data, an approach followed in Lautenbach et al. (2012b).

Thus, ES map users should be aware of the different sources of uncertainty and map creators should at least list them with respect to their application. In addition to this qualitative step a quantitative assessment of the uncertainties of model output should be given. If observed data is used for model parameterisation and calibration, it should be always possible to quantify the uncertainty attached. If no observed data is available against which model output could be compared sensitivity analysis is an option to quantify uncertainties. Lastly, validation of ES models is complicated by the fact that many ES cannot be directly measured. Water purification for example has to rely on water quality data not on measured purification rates (Lautenbach et al., 2012a). Therefore, model validation is often pattern-oriented, considering proxy-data, and tries to at least capture the system behaviour instead of specific process variables.

Ultimately, comparing the gains from improved biophysical process understanding to the possible propagation of uncertainties in biodiversity and ecosystem process data will determine the net benefits from using models of increasing biophysical complexity.

Conclusion

In order to achieve the ambitious political agenda for biodiversity, and to support sustainable development that both preserves and benefits from natural capital and ecosystem services, considerable progress is still needed in the practice of quantifying ecosystem service supply. Today a rich array of methods are available, especially for terrestrial systems, that enable the incorporation of biodiversity effects on ecosystem functioning into quantitative, spatiallyexplicit assessments of ecosystem service supply. We have summarised the main characteristics, strengths and weaknesses of different approaches for mapping ES supply, highlighting their complementarity depending on scale, assessment objectives and context, available skills and data. Review of practice illustrates the predominant effect of scale on model selection, and the ability within a single case study to combine different model types, of varying complexity and detail in the representation of biodiversity effects, depending on specific ES of interest, skills and data / resources availability. Besides, model categories are not necessarily exclusive and there may be more of a continuum between approaches. Recent model developments, with innovative hybridization across model types illustrate how increasing fundamental understanding on the role of different facets of biodiversity for ecosystem functioning and ecosystem services can be incorporated into the spatially explicit modelling of ecosystem service supply. As the availability of biodiversity data (species, phylogenetic and functional) increases and the potential for remote sensing of taxonomic and functional diversity becomes realised, the application of more 'biodiversity realistic' models should be able to move to from research to practice. Considerable challenges remain for assessments to embrace good practice in model uncertainty quantification and validation, an upstream research need to still be addressed. Lastly, while the mapping of terrestrial ecosystem service supply is now reaching greater maturity, for marine ecosystems research is still in its infancy. Urgent research needs regard a better understanding of marine biodiversity effects on ecosystem functioning, and at which scales this influences ecosystem service supply. The availability of high resolution data also proves to be an obstacle that needs to be cleared before sound practice can be achieved. Daily or monthly average air surface temperature, precipitation (daily precipitation or monthly precipitation and wet days), incoming shortwave radiation (or sunshine hours per day). Various sources depending on scale and considered time frame, e.g. 0.5° from CRU TS 3.1 [START_REF] Mitchell | An improved method of constructing a database of monthly climate observations and associated high-resolution grids[END_REF], usually in combination with CMIP5 scenario climate data (e.g. MPI-ES-LR after Giorgetta et al., 2013).

Figures

global soil map (FAO, 1991) atmospheric CO2 concentration

LPJmL (Bondeau et al. 2007)

Daily or monthly average air surface temperature, daily precipitation (or monthly precipitation and wet days), cloudiness or shortwave and longwave radiation. Various sources depending on the scale, e.g. 0.5° from CRU TS 3.1 [START_REF] Mitchell | An improved method of constructing a database of monthly climate observations and associated high-resolution grids[END_REF] 11 PFTs e.g. according to [START_REF] Ahlström | Robustness and uncertainty in terrestrial ecosystem carbon response to CMIP5 climate change projections[END_REF]; 11 CFTs (Lindeskog et al., 2013) LPJmL (Bondeau et al. 2007) 9 PFTs (Sitch et al., 2003) (Neitsch et al., 2005). The model integrates all relevant processes for watershed modeling including water flow, nutrient transport and turnover, vegetation growth, land use, and water management at the sub-basin scale. It considers five different pools of nitrogen in the soils (Neitsch et al., 2005): two inorganic (ammonium and nitrate) and three organic (fresh organic nitrogen and active and stable organic nitrogen). Nitrogen is added to the soil by fertilizer, manure or residue application, fixation by bacteria, and atmospheric deposition. Nitrogen losses occur by plant uptake, leaching, volatilization, denitrification and erosion. The continental scale of the model may oversimplify the local coastal processes, since they cannot be taken into account a the continental scale and resolution. Coastal studies generally lack the step of aggregation of data and knowledge transfer from local case studies to regional ones. Due to the lack of large scale datasets or methodologies some important factors could not be included in the model (e.g. local sediment Budget, subsidence, main direction of morphologic features with respect to wave action, coastal development and management, low vs. high coasts, health of the ecosystems, the specific non-linear response of habitats for protection among others). Further information on limitations or aspects that could improve the model are discussed in the paper. A primary limitation is that the Erosion Protection model assumes that all erosion leads to a loss of land. Further, the model estimates coastal protection services provided by habitats in terms of the reduction in damages due to erosion from storm waves, not surge. Some coastal habitats have the ability to attenuate surge in addition to waves (e.g., marshes, coastal forests), while other nearshore subtidal habitats do not (e.g., eelgrass). the model has technical limitations. The first is the lack of high quality GIS data that are readily available. The theoretical limitations of the Nearshore Waves and Erosion model are more substantial. As mentioned earlier, wave evolution is modeled with a 1D model. This assumes that the bathymetry is longshoreuniform (i.e. the profile in front of the site is similar along the entirety of the stretch of shoreline). Because this is unlikely true, the model ignores any complex wave transformations that occur offshore of the site of interest

HILLFLOW

InVEST

InVEST Food provision (Guerry et al 2012)

Production of maps that identify the most important marine and coastal areas across a variety of fishing fleets It does not model behavior , for that reason it is not well suited to the evaluation of how human uses may change in response to changes in the marine environment.

InVEST Marine renewable energy (Guerry et al 2012)

Not stated in the paper Not stated in the paper

InVEST Recreation (Guerry et al 2012)

Not stated in the paper The model does not presuppose that any predictor variable has an effect on visitation. Instead, the tool estimates the magnitude of each predictor's effect based on its spatial correspondence with current visitation in the area of interest. It requires the assumption that people's responses to attributes that serve as predictors in the model will not change over time.

In other words, in the future, people will continue to be drawn to or repelled by the attributes as they are currently.

Hydrodynamic model (Temmerman et al 2012)

Not stated in the paper Not stated in the paper

Hydrodynamic model (Shepherd et al 2007)

Cost benefit analysis (CBA) demonstrates that managed realignment provides positive economic advantages. In a wider sense the case study demonstrates how CBA of managed realignment schemes should be undertaken so that the potential social cost of realignment can be better understood

The model and CBA is based in many assumptions (e.g. sedimentation rate 1.5 or 6mm per year) and uncertainties (e.g. habitat values or nitrogen removal), however the assumptions are conservative, if anything it will have underestimated the value of the service Mangrove's wind protection [START_REF] Das | Mangroves can provide protection against wind damage during storms[END_REF] The study found that not accounting for the role of mangroves significantly overestimates actual wind damage. The model indicates that the cumulative C sequestered increases rapidly over time and with planting density. The value corresponding to this C sequestration suggests that the costs of seagrass restoration projects may be fully recovered by the total CO2 captured in societies with a carbon tax in place

The model presented delivers rough, but conservative, estimates of the average CO2 capture capacity associated with seagrass restoration projects. These estimates are conservative because they focus on the mean, whereas plant-ing of seagrass patches for CO2 capture can be managed to achieve maximum capture, which could double the esti-mates provided above. In addition, the model considers clonal spread alone, whereas the restored meadows would produce seeds as they develop, contributing to accelerate colonization beyond the limits imposed by clonal growth, accelerating space occupation and therefore carbon capture.

Role of eelgrass in ES, food web modeling (Plummer et al 2013)

Increased eelgrass coverage was most associated with increases in commercial and recreational fishing with some small decreases in one non-market activity, bird watching. When ES categories were considered (aggregations of individual groups of species) there was little evidence of strong tradeoffs among marine resources; that is, increasing eelgrass coverage was essentially either positive or neutral for all services examined Not stated in the paper

Mercury sequestration (Anastacio et al 2013)

tool to analyze system behavior and to make projections regarding mercury sequestration. This is particularly relevant in the case of human interventions (i.e. engineering) for the optimization of this ecosystem service the value calculated does not include sequestration by other plants sharing the habitat with B. maritimus. For this reason we should expect that the total value for mercury sequestration by wetland plants will be higher since other plant species are present in the studied area

Spatial model of coastal ecosystem services (Barbier 2012)

The basic model demonstrates how spatial production of ecosystem services affects the location and extent of landscape conversion. An extension allows for the risk of ecological collapse, when the critical size of the remaining landscape that precipitates the collapse is not known. Both models are simulated using the example of spatial variation in ecosystem services across a mangrove habitat that might be converted to shrimp aquaculture.

Not stated in the paper

FigureFigure 2 -

 2 Figure 1 service s

  Figure 3 marine e -Phenomen ecological pr nological mo rinciples. Ada del developm apted from T ment for ma Townsend et pping marin t al., 2014. e ecosystem m services based

  Not stated in the paper

  Wind barriers like mangroves reduces tangential wind and contributes subtantially to reduce wind-caused damage to structures While the simplicity of the model makes it very tractable for use in empirical studies in poor regions, further model development and better data would shed more light on the particular mechanisms Ecological production functions generally are observed at fine spatial scales for brief spans of time, whereas the resulting ecosystem services and their economic values may be delivered over broad geographic and temporal scales. This paper demonstrates methods of modeling and estimation that link fishery production and its associated economic indicators to the distributions and attributes of coastal habitats across scales ranging from habitat patches to large ocean basins.Not stated in the paper CO 2 capture potential of seagrass restoration(Duarte et al, 2013)

(Smith et al. 2001, Sitch et al. 2003).

	IVM-FloodRegulation LPJ-GUESS	precipitation regime (Haylock et al.,	soil water holding capacity	DEM and forest and
	(Stürck et al, 2014)	2008)	classification (FAO, 2009)	agricltural management
				variables
	SWAT	precipitation, temperature (min and max),	number and thickness of	terrain (slope)
	(Lautenbach et al.	solar radiation, wind speed, humidity,	layers, hydrologic soil
	2012)	potential evapotranspiration, daily	class, soil porosity,
		resolution, spatial resolution: climate	saturated hydraulic
		stations. Depending on the method used	conductivity, porosity, field
		to calculate evapotransipiration. Values	capacity, water content at
		can also be estimated using a weather	wilting point, clay/silt/sand
		generator.	content, organic matter
			content, bulk density,…
			available resolution of soil
			together with land cover
			resolution defines the
			Harmonized World Soil achiveable resolution	atmospheric CO2
	HILLFLOW	precipitation, temperature (min and max),	Database (version 1.2) soil texture, saturated	concentration DEM: altitude, slope,
	(Leitinger et al. 2015)	solar radiation, wind speed, humidity,	(2012) aggregated to 0.5• water content, field	aspect
		potential evapotranspiration, daily	resolution and classified capacity, residual soil
		resolution, spatial resolution: climate	according to the USDA water content, saturated
		stations.	soil texture classification hydraulic conductivity, soil
		and GPCC	(http://edis.ifas.ufl.edu/ depth, macropores
		(Rudolf et al 2010), 0.25° from WATCH	ss169).
		Forcing Data (Weedon et al. 2011) and
		ERA-Interim (ECMWF).

Trait-based models of grassland ES (Lavorel et al. 2011, Grigulis et al. 2013)

	IVM-tourism (Van Berkel & Verburg, 2011) LPJ-GUESS (Smith et al. 2001, Sitch et al. 2003)	Applicable across the EU; using easy Global quantification; historical and future	Only applicable at this scale; expert based Limitations in resolution (0.5°x0.5°), applicable up
			accesible datasets transitions; high detail in representation of	approach makes it inherently subjective; to contry/regional level (i.e. Downscaling aspired in
			vegetation dynamics (age cohorts and gap	preferences and suitable indicators might change Scottish Exemplar)
			dynamics), closed carbon and nitrogen	over time; dos not generate reliable results in all
			cycles	regions
	Biocontrol (Civantos et al. 2012) LPJmL (Bondeau et al. 2007)	Climate-and land use-based distributions Closed carbon cycle, consistent	Usual limits of species distribution modelling Currently no nitrogen cycle
			of service providing species. Easy to representation of the biogeochemical
			project given scenarios. Contribution of processes bewteen the different plant
			individual species may be combined with types.
			different weights e.g. depending on diets
			(although currently even weights)
			Mechanistic understanding of ES supply;	Generic nature of models under checking (inter-site
			functional understanding of ES trade-offs /	comparison). May need adaptation for different
			bundles. Easy to project given scenarios.	bioclimatic regions
		Soil moisture, deep water	Process-based	Mechanistic model of water evaporation, lateral flow and
	(Leitinger et al. 2015)	seepage		deep seepage depending on vegetation demand, soil
				properties and terrain

IVM-FloodRegulation (Stürck et al, 2014)

	Multiscale ecological Multiscale ecological InVEST Coastal	Provisioning, nutrition, biomass (food production) protection Spatial proxy-based	Phenomenological Fishery landings, effort data, habitat GIS coverages, survival rates for local & regional NA (estuary) coastal protection The InVEST Coastal Protection
	and economic models and economic models (Guerry et al., 2012)			habitat types, salinity, economic value salmon fisheries model quantifies the protective
	salmon, shrimp & blue salmon, shrimp & blue			services provided by natural
	crab (Jordan et al crab				habitats of nearshore environments
	2012) (Jordan et al 2012) Mangrove's wind	x		mangrove	distance from mangrove forest, mangrove in terms of avoided erosion and mangrove
	Coastal protection Coastal protection protection		coastal protection	forest	Spatial proxy-based continental (EU) Bathymetry, topography, slope, geomorphology, submarine habitats, Three data sources: forest extent forest flood mitigation. The model's profile
	(Liquete et al 2013) (Liquete et al 2013) (Das et al, 2013)				EU Corine Land Cover emerged habitats, wave regime, tidal range, relative sea level, storm generator prepares a	1D
					(CLC) surge, population density, infrastructures, artificial surface, main cultural bathymetry transect of a shoreline,
	InVEST Marine carbon storage & InVEST Food provision (Guerry et al InVEST Marine renewable energy (Guerry et al 2012) (Guerry et al 2012) 2013) InVEST Recreation (Plummer et al 2012) modeling in ES, food web Role of eelgrass et al 2012) (Guerry et al 2012) 2013) sequestration (Guerry renewable energy (Liquete et al InVEST Marine Coastal protection CO 2 capture x Role of eelgrass in ES, potential of seagrass food web modeling restoration (Plummer et al 2013) (Duarte et al, InVEST Marine carbon 2013) Role of eelgrass in ES, 2012) et al 2012) (Plummer et al 2013) provision (Guerry et al blue crab (Jordan food web modeling InVEST Food salmon, shrimp & economic models (Guerry et al 2012) storage & sequestration ecological and Multiscale x	Combination of flood regulation demand and supply to identify prioritiy areas where flood regulation can be enhanced using natural vegetation. Spatial proxy-based local / regional / cover, soils and flood regulation from single catchments to the entire EU. Method is difficult to apply at smaller scales commercial and recreational fisheries continental marine mammals, detrital pools), NA producers, invertebrates, fishes, birds, Spatial proxy-based local / regional / continental NA emigration rate, biological groups (primary rates of prey, immigration rate, mortality, biomass, growth efficiency, consumption marine Carbon storage & sequestration Energy recreational activities visitation rates, Food provision maximum capacity) Performance tables, capabilities (e.g. technological Spatial proxy-based local / regional / (height, peak period, continental wave condition data marine NA Extrapolation of estimates for relation between land sites seagrass patch growth, parch survival in seagrass seagrass providing information about its dataset v.15 from the year 2000 with a resolution of 100 m (EEA 2011); meadows planting projects, estimates of seagrass meadows backshore and the location of No abiotic variables stated CO2 sequestration per unit area for five natural habitats. The transect is seagrass species used to estimate the total water level and shoreline erosion in the and modelled seabed Carbon stored, rate of C accumulation in sediments, economic presence and absence of habitat maps (MESH 2010; EUSeaMap JNCC price of harvestd product, harvest rate information multiple ES (provisioning, cultural, supporting) Spatial proxy-based local Fishing fleet distribution, value of landings, fishing grounds distribution, NA 2010) information such as market/non-market value of stored/sequestered carrying capacity Carbon stock biomass, net recruitment per year, marine nearshore marine habitats

InVEST Food provision (Guerry et al 2012)

					energy based on wave conditions
					and	technology-specific
					ccapabilities.
	InVEST Recreation (Guerry et al	Spatial proxy-based	Recreation	The InVEST recreation model
	2012)				predicts the spread of person-days
					of recreation, based on the
					locations of natural habitats and
					other features that factor into
					people's decisions about where to
					recreate
	Hydrodynamic	model	Phenomenological	Mediation of flows (flood protection) Hydrodynamic model simulations of
	(Temmerman et al., 2012)				flood attenuation by a tidal marsh,
					with particular focus on the effects
					of spatial patterns of vegetation
					dieoff. Tidal marsh die-off, which
			Spatial proxy-based	Food provision	InVESt model estimates the may increase with ongoing global
					quantity and monetary value of fish change (e.g. because sea level
					haversted by commercial fisheries. rise), is expected to have non-linear
					Appropiate to use for single species effects on reduced coastal
					or groups of species with similar life protection against flood waves.
					stories.	It	estimates	annual
					production of fish. Another section
					of the model can be used to
					analyse	the	production	and
					monetary value of farmed fish and
					shellfish and quantify by-products of
					farming.
	InVEST Marine renewable energy	Spatial proxy-based	Energy	Models energy production from
	(Guerry et al 2012)				waves an models off-shore wind
					energy production. The model
					asseses potential wave power and

Hydrodynamic model (Shepherd et al., 2007)

								benefit analysis of the managed and biological proxies in others.
	Mercury		sequestration	Process-based	Mediation of waste, toxics and	realignment is conducted too. Modelling of growth and mercury
	Mangrove's wind protection (Das (Anastácio et al., 2013)	Phenomenological	Mediation of flows (wind protection) Modeling of wind attenuation and other nuisances (HG) sequestration by
	and Crépin, 2013)						protection offered by mangroves in Bolboschoenus maritimus on the
								the event of wind-related damage most contaminated area of a
								during storms, specially in areas temperate shallow coastal lagoon
								affected by tangential wind historically subjected to heavy Hg
	Ecosim/EcoPath (Alcamo et al.,	Niche-based	Provisioning, nutrition, biomass	Fish production (landings) is load, under gradients of climate
	2005)					(fish production)		estimated driven variables. Simulation of B. for three regional
								fisheries (Guf of Thailand, Central maritimus mercury sequestration
								North Pacific North Benguela) for 4 under different environmental
								different scenarios. The model scenarios involving increases and
								computes dynamic changes in decreases in temperature, salinity
								selected marine ecosystems as a and cloud cover. The largest effects
								function of fishing efforts (Pauly et were related to high salinity
								al. 2000). For its fish production scenarios but all variables
								estimates, the EcoSim/EcoPath presented an inverse relation with
								model takes into account not only Hg-sequestration
	Spatial	model	of	coastal	NA	mediation of	flows (storm	the future source of feed for Modelling of ecological production
	ecosystem services (Barbier,		protection) & fish density	aquaculture, functions that decline across a but also future
	2012)				Phenomenological	Maintenance of physical, chemical	Hydrodynamic model to estimate subsidies for the fishing industry, coastal landscape
						and biological conditions (nutrient	nutrient removal and carbon the management objectives of
						removal and carbon sequestration)	sequestration in a UK estuary fishing (either to optimize
								covered with tidal wetlands and employment or profits), and the
								mudflats, based on sediment impact of climate change on shifts
								dynamics and composition. The in species distribution and
								model abundance (Pauly et al. 2003). For also estimates the
								associated value of habitat created all scenarios, fish catch (by weight)
								under a scenario of extensive is maintained in the North Benguela
								managed realignment. A cost fishery, not maintained in the
								Central North Pacific, and has

Acknowledgements

This study was funded by project OPERAs FP7-ENV-2012-two-stage-308393. AB and WC acknowledge Labex OT-Med (ANR-11-LABX-0061) funded by the French Government Investissements d'Avenir program of the French National Research Agency (ANR) through the A*MIDEX project (ANR-11-IDEX-0001-02)

 2015). Criteria were rated according to expert opinion and synthesis of published studies.

Model type

Primary data sources for Europe Remote sensing data

Proxy

Land cover maps

Vegetation data bases [START_REF] Chytrý | Vegetation survey: a new focus for Applied Vegetation Science[END_REF]. European Vegetation Archive (EVA)

Global Index of Vegetation-Plot Databases (http://www.givd.info) [START_REF] Dengler | The Global Index of Vegetation-Plot Databases (GIVD): a new resource for vegetation science[END_REF] Potential lack of data layers (e.g. soils))

Mapping thematic variables like Land Use/Land Cover, Vegetation, Forest, Wetland, Water, Burnt area, etc.

Regional scale (for mapping landscape units), medium spatial resolution data like multitemporal MODIS, Spot Vegetation or MeteoSat data to follow vegetation dynamic.

Local scale (for mapping precise thematic variables): high spatial resolution Landsat8 or Sentinelle-2 (for passive RS data), RadarSat or TerraSar (for active RS data). [START_REF] Ayanu | Quantifying and Mapping Ecosystem Services Supplies and Demands: A Review of Remote Sensing Applications[END_REF][START_REF] Burkhard | Mapping ecosystem service supply, demand and budgets[END_REF][START_REF] Kuenzer | Earth observation satellite sensors for biodiversity monitoring: potentials and bottlenecks[END_REF][START_REF] Pettorelli | Satellite remote sensing for applied ecologists: opportunities and challenges[END_REF]

Phenomenologic al

Maps or proxy of landscape elements (van der Zanden et al., 2013) Topographic information including Digital Elevation Models: road networks, river networks (Lehner et al., 2004), coastlines (USGS HYDRO1K, 2015)

Biophysical data including soil data (European Soil database see Panagos et al., 2012) As for proxy models

Niche-based

Occurrence data for all European terrestrial vertebrate species: 187 mammals [START_REF] Mitchell-Jones | The Atlas of European Mammals[END_REF], 445 breeding birds [START_REF] Hagemeijer | EBCC atlas of European breeding birds : their distribution and abundance[END_REF], and 149 amphibians and reptiles [START_REF] Gasc | Atlas of amphibians and reptiles in Europe[END_REF].

Refined data for 275 mammals, 429 birds and 102 amphibians across the Palearctic at 300 m resolution by incorporating 46 GlobCover land use/land cover classes [START_REF] Maiorano | Threats from Climate Change to Terrestrial Vertebrate Hotspots in Europe[END_REF]. Clustering at 10' by [START_REF] Zupan | Spatial mismatch of phylogenetic diversity across three vertebrate groups and protected areas in Europe[END_REF].

Extensive distribution data available for 1280 higher plants; digitized Atlas Flora Europeae. Trees: exhaustive data at 1 km² resolution ( http://www.efi.int/portal/virtual_library/information_services/mapping_service s/tree_species_maps_for_european_forests/).

More comprehensive species distribution data available on a country per country basis, and for specific regions within a same country.

Availability of phylogenies currently increasing, especially in Europe. Megaphylogenies for higher plants, mammals and birds for Europe [START_REF] Thuiller | Consequences of climate change on the tree of life in Europe[END_REF], with further complements for the Palearctic and amphibians by (Zupan Texture variables like object size and shape, compactness, homogeneity/heterogeneity, neighborhood relationships, fragmentation, connectivity, relevant for plant type specification and habitats characterization.

Global scale, Meteosat or SpotVegetation.

Regional scale, medium spatial resolution data like multitemporal MODIS; can characterize vegetation dynamics. [START_REF] Ayanu | Quantifying and Mapping Ecosystem Services Supplies and Demands: A Review of Remote Sensing Applications[END_REF][START_REF] Burkhard | Mapping ecosystem service supply, demand and budgets[END_REF][START_REF] Kuenzer | Earth observation satellite sensors for biodiversity monitoring: potentials and bottlenecks[END_REF][START_REF] Pettorelli | Satellite remote sensing for applied ecologists: opportunities and challenges[END_REF][START_REF] Pettorelli | Satellite remote sensing for applied ecologists: opportunities and challenges[END_REF].

Trait data for functional diversity: see trait-based models

Trait-based

Community composition data -locally measured or from vegetation data bases as for proxy-based models. There are currently no public community composition data bases for animals Site-level measurements following standard methods [START_REF] Cornelissen | Handbook of protocols for standardised and easy measurement of plant functional traits worldwide[END_REF].

Communal plant trait data bases, e.g. TRY (Kattge et al., 2011) Trait data bases for birds [START_REF] Pearman | Phylogenetic patterns of climatic, habitat and trophic niches in a European avian assemblage[END_REF], mammals (PanTHERIA [START_REF] Jones | PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals[END_REF]), amphibians (http://amphibiaweb.org/), fish (FishBase (Froese and Pauly)), phytoplankton [START_REF] Litchman | Trait-based community ecology of phytoplankton[END_REF], lotic invertebrates [START_REF] Nicole | A Database of Lotic Invertebrate Traits for North America[END_REF], soil invertebrates (e.g. [START_REF] Salmon | Linking species, traits and habitat characteristics of Collembola at European scale[END_REF] for Collembola).

Plant/Canopy height using laser scanning (LiDAR).

Leaf phenology: satellite multi-temporal data or timelaps cameras (class by spatial resolution from coarse to fine) : AVHRR NDVI time series, MODIS, Sentinelle-2, RadarSat-2, Pleiades ; or aerial photos/hyperspectral data using airborne sensor.

Using Radiative Transfer Models (RTM), leaf mass per area (for Specific Leaf Area SLA estimation), leaf water content using RTM and/or SWIR wavelengths of RS data (for leaf dry matter content), chlorophyll content (for leaf nitrogen concentration estimation).

Methods operational at individual/population/community/ecosystem scales depending on RS data source. [START_REF] Homolová | Review of optical-based remote sensing for plant trait mapping[END_REF][START_REF] Kuenzer | Earth observation satellite sensors for biodiversity monitoring: potentials and bottlenecks[END_REF] Full processlarge-scale Climate forcing from observations (e.g. [START_REF] Mitchell | An improved method of constructing a database of monthly climate observations and associated high-resolution grids[END_REF][START_REF] Rudolf | The new "GPCC Full Data Reanalysis Version 5" providing high-quality gridded monthly precipitation data for the global land-surface is public available since[END_REF][START_REF] Weedon | Creation of the WATCH Forcing Data and Its Use to Assess Global and Regional Reference Crop Evaporation over Land during the Twentieth Century[END_REF] or from a suite of climate models (e.g. CMIP5, [START_REF] Taylor | An Overview of CMIP5 and the Experiment Design[END_REF] Atmospheric CO 2 concentration from observations for the past and models for the future RCPs (e.g. [START_REF] Keeling | Atmospheric CO2 records from sites in the sio air sampling network[END_REF].

Land-use data historical reconstructions and future scenarios (e.g., [START_REF] Fader | Virtual water content of temperate cereals and maize: Present and potential future patterns[END_REF][START_REF] Von Essen | Cork before cattle: Quantifying Ecosystem Services in the Portuguese Montado and Questioning Ecosystem Service Mapping[END_REF], Hurtt et al., 2011[START_REF] Kaplan | The effects of land use and climate change on the carbon cycle of Europe over the past 500 years[END_REF], Klein Goldewijk et al., 2011, 2010, Ramankutty and Foley 1999).

Highly generalized classes of soil texture (e.g. by FAO/IIASA/ISRIC/ISSCAS/JRC, 2012).

Drainage direction map (e.g. [START_REF] Döll | Validation of a new global 30-min drainage direction map[END_REF] for models that apply a river routine scheme allowing for studying ecosystem services related to water flows

Global N deposition (e.g. [START_REF] Lamarque | Historical (1850-2000) gridded anthropogenic and biomass burning emissions of reactive gases and aerosols: Methodology and application[END_REF]2011) and N fertilization of croplands (e.g. by [START_REF] Zaehle | Carbon benefits of anthropogenic reactive nitrogen offset by nitrous oxide emissions[END_REF] for models accounting for C-N 1) RS data provide model inputs, 2) RS data for calibrating model parameters, 3) RS data for evaluation of models output. Models that are run for scenario studies obviously must be prognostic models that are not fed by RS data.

Frequent terrestrial indicators that are derived from RS data are e.g. Land use / Land cover, topography, phenology, gross primary production, evapotranspiration, but see the reviews in [START_REF] Turner | Integrating Remote Sensing and Ecosystem Process Models for Landscape-to Regional-Scale Analysis of the Carbon Cycle[END_REF], [START_REF] Andrew | Potential contributions of remote sensing to ecosystem service assessments[END_REF]. At the global scale, the often used satellite instruments are Landsat, Meteosat, Spot-Vegetation, NOAA-AVHRR, ATSR, MISR, SeaWiFS (e.g. [START_REF] Ayanu | Quantifying and Mapping Ecosystem Services Supplies and Demands: A Review of Remote Sensing Applications[END_REF][START_REF] Kelley | A comprehensive benchmarking system for evaluating global vegetation models[END_REF][START_REF] Randerson | Systematic assessment of terrestrial biogeochemistry in coupled climate-carbon models[END_REF].

Remote Sensing derived land use data (e.g. [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF] for forest extent, loss, and gain from 2000 to 2012) are typical model inputs.

Seasonal fraction of absorbed photosynthetically active radiation (fPAR) can be used as input by process-models [START_REF] Potter | Terrestrial ecosystem production: A process model based on global satellite and surface data[END_REF], but they are also useful tools for the validation of full process-models that simulate the fPAR based on the modelling of biophysical processes (Bondeau et al., 2007;Lindeskog et al., 2013).

interations Population density maps (Klein [START_REF] Goldewijk | Three centuries of global population growth: A spatial referenced population density database for 1700 -2000[END_REF][START_REF] Klein Goldewijk | Long-term dynamic modeling of global population and built-up area in a spatially explicit way: HYDE 3.1[END_REF] when this is required by fire disturbance modelling Communal plant trait data bases for PFT parameterisation, e.g. TRY (Kattge et al., 2011).

Full processlocal-landscapescale

Input data (historical and scenarios) as for large-scale process-based models with the additional possibility for local-landscape scale data -Fisheries landings, effort data, habitat GIS coverages, survival rates for habitat types, salinity (Jordan et al., 2012) Trait-based -Seagrass patch growth, parch survival in seagrass planting projects, estimates of seagrass CO 2 sequestration per unit area (Duarte et al., 2013) Full process -largescale -Submarine habitat cover [START_REF] Yee | Comparison of methods for quantifying reef ecosystem services: A case study mapping services for St[END_REF] Full process -locallandscape-scale -Use of biogeochemical model; Dissolved Organic Carbon; Particulated Organic Carbon; nutrients; carbonates; zooplankton; microzooplankton; phytoplankton [START_REF] Canu | Estimating the value of carbon sequestration ecosystem services in the Mediterranean Sea: An ecological economics approach[END_REF] Appendix 1 Use of dynamic simulations in a food web model of central Puget Sound, Washington, USA developed in the Ecopath with Ecosim software, to examine how the marine com-munity may respond to changes in coverage of native eelgrass (Zostera marina), and how these modeled responses can be assessed using an ecosystem services framework, expressing these services with economic currencies in some cases

Model name

Main strengths Limitations

Coastal protection (Liquete et al 2013)

The assessment shown in the paper could help assist the comparison between European regions and to further national or regional scale studies of ecosystem services. In Europe it can have a direct application on the EU Biodiversity Strategy, the EU Floods Directive. On an international scale, this approach could be taken by CBD (Convention on biological diversity) countries.