Uncertainty in ensembles of global biodiversity scenarios — TEI-tagged view

Wilfried ThuillerpersName, Maya GuéguenpersName, Julien RenaudpersName, Dirk N. KargerpersName, Niklaus E. ZimmermannpersName (2019date). “Uncertainty in ensembles of global biodiversity scenarios.” Nature Communicationstitle·j.

Object of study — projections of climatic suitabilityterm·key for ~11,500 vertebrate species under combinations of SDMsterm·mth, GCMsterm·mth and RCPsterm·dom

Research question — how large the uncertainties in biodiversity scenariosterm·mth are, and where they come from

Contribution — evidence that multiple SDMsterm·mth, RCPsterm·dom, dispersalterm·key assumptions and GCMsterm·mth are necessary in any biodiversity scenarioterm·mth assessment

Full text — tagged

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Uncertaintyterm·key in ensemblesterm·key of global biodiversity scenariosterm·mth Abstract While there is a clear demand for scenarios that provide alternative states in biodiversity with respect to future emissions, a thorough analysis and communication of the associated uncertainties is still missing. Here, we modelled the global distribution of ~11,500 amphibian, bird and mammal species and project their climatic suitabilityterm·key into the time horizon 2050 and 2070, while varying the input data used. By this, we explore the uncertainties originating from selecting species distribution modelsterm·mth (SDMsterm·mth), dispersalterm·key strategies, global circulation modelsterm·mth (GCMsterm·mth), and representative concentration pathwaysterm·dom (RCPsterm·dom). We demonstrate the overwhelming influence of SDMsterm·mth and RCPsterm·dom on future biodiversity projections, followed by dispersalterm·key strategies and GCMsterm·mth. The relative importance of each component varies in space but also with the selected sensitivity metrics and with species’ range size. Overall, this means using multiple SDMsterm·mth, RCPsterm·dom, dispersalterm·key assumptions and GCMsterm·mth is a necessity in any biodiversity scenarioterm·mth assessment, to explicitly report associated uncertainties.

Introduction The launch of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Servicesterm (IPBESterm) in 2012 and the ongoing activities of the Intergovernmental Panel for Climate Changeterm·key (IPCC) have led the ecological communities to conceive and produce biodiversity modelsterm·mth and scenarios 1 , 2 . We define here biodiversity modelsterm·mth as any type of quantitative model that aims at predicting the spatial or/and temporal distribution of a population, species or groups of species. Biodiversity scenariosterm·mth, the application of these models to plausible trajectories of different aspects of the future (e.g. future climate), rely on several complex components that depend on each other (Fig. 1 in ref. 2 ). When focusing on biodiversity trends under climate changeterm·key, biodiversity modelsterm·mth are first trained or fitted under current climatic conditions. Next, these models project future biodiversity patterns based on climate projections from global circulation modelsterm·mth (GCMsterm·mth) that in turn rely on socio-economic scenarios, expressed as representative concentration pathwaysterm·dom (RCPsterm·dom 3 ). This chain of dependencies implies that the coupled choice of a GCMterm·mth and a RCPterm·dom is not straightforward 4 . Analyzing the biodiversity response with respect to RCPsterm·dom is crucial to test and report how climate changeterm·key and its mitigation could ultimately influence biodiversity, with consequences for management and conservation. However, the variation among climate changeterm·key projections from different GCMsterm·mth can be so high that the interest of choosing one RCPterm·dom over another is no longer seen a necessity 4 . With regards to biodiversity impact modelling, the situation is even more complex since biodiversity modelsterm·mth themselves proved to generate considerable variability 5 , 6 . In other words, the choice of a biodiversity modelterm·mth, a GCMterm·mth and a RCPterm·dom matters and the uncertainties originating from these choices should be considered in decision-making or biodiversity conservation. In both the climate and ecological modelling communities, researchers are generating and increasingly using ensemblesterm·key of projections from a range of GCMsterm·mth, biodiversity modelsterm·mth and RCPsterm·dom to quantify the uncertaintyterm·key arising from these apparently subjective choices 7 , 8 . However, while several studies have highlighted the potential consequences of ignoring this variability originating from different choices in biodiversity scenariosterm·mth 9 , 10 , most studies still produce single projections based on a single biodiversity modelterm·mth and a single GCMterm·mth and only superficially discuss their results in the light of socio-economic pathways (see e.g. 11 ). Fig. 1 Relative influence of the different sources of variation on species’ level sensitivity metrics. The plot represents the relative influence of the choice of species distribution modelsterm·mth (SDMsterm·mth), global circulation modelsterm·mth (GCMsterm·mth) and representative concentration pathwaysterm·dom (RCPsterm·dom) on the variance of change in climatic suitabilityterm·key (left) and loss of suitable climate (right) for all modelled species. The deviance was calculated across all species by means of a nested ANOVAterm·mth and the partitioning is represented by the percentage of explained deviance (note that the unexplained deviance is not represented here). ANOVAs were run for three different TSSterm·mth thresholds (0.4, 0.6, and 0.7) above which individual SDMsterm·mth were retained for assessing the model results Here, we demonstrate the importance of considering multiple approaches (e.g. biodiversity modelsterm·mth, GCMsterm·mth and RCPsterm·dom) but also multiple ecological decisions (e.g. quality of the data, species dispersalterm·key limitation) on biodiversity scenariosterm·mth. To obtain plausible and robust results useful for biodiversity assessments like IPBESterm 12 , we run an extensive climate changeterm·key impact assessment study by modelling the current and future climatic suitabilityterm·key of ~11,500 vertebrate species at the global scale (Supplementary Fig. 1 ). More specifically, we model the distribution of 1351 amphibian, 7248 bird, and 2896 mammal species as a function of current climate using four species distribution modelsterm·mth (SDMterm·mth) that are cross-validated four times and projected their future climatic suitabilityterm·key as a function of 14 combinations of GCMsterm·mth and RCPsterm·dom and for two dispersalterm·key strategies (‘no dispersalterm·key’ and ‘limited dispersalterm·key’). This totaled to five million single projections from which we define two species-level sensitivity metrics (change in climatic suitabilityterm·key and loss in climatic suitabilityterm·mth better) and pixel-level variation in community metrics (change in species richness, change in spatial turnover per region and temporal turnover per pixel). We then use nested ANOVAsterm·mth to disentangle the relative importance of the choices of dispersalterm·key strategies, SDMsterm·mth, GCMsterm·mth and RCPsterm·dom on the variability of the results.

Results Species-level uncertaintyterm·key analyses At the species-level, the influence of SDMterm·mth, GCMterm·mth and RCPterm·dom differed with respect to the sensitivity metric and dispersalterm·key scenario used (Fig. 1 ). When assuming limited dispersalterm·key, the choice of SDMsterm·mth causes a more than ten times higher deviance in the change of suitable habitats than the choice of the other two components. In other words, the subjective selection of a specific SDMterm·mth has an overarching influence on the final result compared to the choices of GCMsterm·mth and RCPsterm·dom. Interestingly, when considering only the loss in climatic suitabilityterm·mth (‘no dispersalterm·key’ scenario), RCPsterm·dom are the most important element causing variation, followed by SDMsterm·mth and GCMsterm·mth (Fig. 1 ). The observed difference in the explained deviance between the two dispersalterm·key assumptions arises from the discrepancy in SDMsterm·mth in projecting the future climatic suitabilityterm·key of species 13 . While SDMsterm·mth generally agree well when predicting the current distribution of species (as is targeted by the no dispersalterm·key assumption, Supplementary Fig. 2 ), they are known to widely differ when projecting future distributions 14 . This effect is evident even when keeping only SDMsterm·mth that reach very high predictive accuracies (TSSterm·mth > 0.7, Fig. 1 ). In other words, it is not only the quality of the SDMsterm·mth that explains a large proportion of variance in model output, but also their internal structure. Indeed, relatively complex models (i.e. random forest) use a variety of combinations of features that can lead to similar geographical predictions under current conditions, but that can vastly differ to other models when transferred to future conditions, especially under conditions that have been used for calibrating the modes. Some of the particular combinations of features could represent true complex interactions between species’ occurrences and environmental conditions, but sometimes they could result of over-fittingterm·dom and spurious combinations, that once projected in new conditions lead to misleading results. The ensemble projectionterm·mth of the bearded woodpecker ( Dendropicos namaquus , Lichtenstein 1793) exemplifies this aspect (Supplementary Fig. 3 ). The results reveal marked differences for SDMterm·mth in projected future climatic suitabilityterm·key which leads to difficulties when interpreting the results in the light of socio-economic pathways. On the other hand, the loss in (current) climatic suitabilityterm·key does not vary as much for SDMterm·mth and rather show strong differences for RCPterm·dom. Novel conditions are usually far away from the current range of species, which also explain that SDMsterm·mth are a more important driver of over-all uncertaintyterm·key when dispersalterm·key in accounted for, than when considering only current loss of suitable habitats. Interestingly, the same trend was also found to be a function of species’ range size (Fig. 2 ). When considering dispersalterm·key, the effect of SDMsterm·mth on total projection uncertaintyterm·key was highest for rare species. However, when considering the loss of currently suitable climatic habitat (as is targeted by the no dispersalterm·key assumption), the influence of RCPsterm·dom on projection uncertaintyterm·key increases with species range sizes. For the rarest species, both SDMsterm·mth and RCPsterm·dom have the highest contributions to explain uncertainties, while for large-ranged species, the influence of RCPsterm·dom on the total variance in future climatic suitabilityterm·key is largest. The same pattern emerges when considering the effects of selecting RCPsterm·dom for a given GCMterm·mth (Supplementary Fig. 4 ). Here, under limited dispersalterm·key, the deviance due to SDMsterm·mth is such that there is no influence of RCPsterm·dom on the final results. Only when considering the loss in climatic suitabilityterm·mth (LCSterm·mth), the effect of RCPsterm·dom is discernible where the median LCSterm·mth is around 65% under the RCPterm·dom 8.5 and 30% under the RCPterm·dom 2.6 (Supplementary Fig. 4 ). With regards to biodiversity management, our results indicate that only when considering the loss of currently suitable climate that one can assess the effects of climate changeterm·key adaptation plans or of emission scenarios. Fig. 2 Relative influence of the different sources of variation on species’ level sensitivity metrics in function of species range size. The plot represents the relative influence of SDMsterm·mth, GCMsterm·mth, and RCPsterm·dom on overall species sensitivity to climate changeterm·key in response to species’ range size. A TSSterm·mth threshold of 0.7 was used for all analyses. Species ranges were classified for equal size at the log scale Pixel-based uncertaintyterm·key analyses The overall variation originating from the combination of SDMsterm·mth, GCMsterm·mth and RCPsterm·dom markedly differed between pixel-based metrics and among species groups (Fig. 3 ). Under the ‘no dispersalterm·key’ assumption the amphibians showed lower variation than the other groups, while the variation in the other metrics was generally higher for amphibians. This is probably reflecting that amphibian species are slightly less easy to model (Supplementary Fig. 2 ) at that particular resolution (100 km) and scale (global) and generally occur in location where RCPsterm·dom and GCMsterm·mth also diverge most (Supplementary Figs. 5 – 8 ). Interestingly, the change in α-diversityterm·dom was particularly sensitive to the choice of SDMsterm·mth, which explained by far most of the deviance for that metric (Fig. 3 ). This was much less the case for the estimates of relative species turnover and loss per pixel were a larger proportion of the deviance was additionally explained by the RCPsterm·dom, with the strongest effects for the time horizon 2070. While SDMsterm·mth explained a constant portion of the deviance, the percentage of explained deviance by RCPterm·dom scenarios increased considerably for 2070 (Fig. 3 ). This result confirms that when using sensitivity metrics that account for dispersalterm·key limitation (e.g. change in α-diversityterm·dom), the uncertaintyterm·key due to the choice of SDMsterm·mth becomes particularly important and may hide variations due to RCPsterm·dom. Fig. 3 Absolute influence of the different sources of variation on pixel-based sensitivity metrics. The plot represents the absolute influence of the choice of species distribution modelsterm·mth (SDMsterm·mth), global circulation modelsterm·mth (GCMsterm·mth) and representative concentration pathwaysterm·dom (RCPsterm·dom) on the change in α-diversityterm·dom per-pixel (Δα), temporal species turnover (βt) and percentage of species loss per pixel (% loss). The deviance was calculated across all pixels together by means of a nested ANOVAterm·mth and the partitioning is represented by the absolute deviance to show the difference in deviance between metrics. Dark and light grey correspond to the horizon 2041–2060 and 2061–2080, respectively. Total deviance bar shows the total deviance that was explained by all components in the ANOVA. The central line of each box correspond to the median, the bounds of box represent the 25 and 75% quantiles, and the whiskers represent the quantiles 0.05 and 95% Interestingly, the relative influence of SDMsterm·mth, GCMsterm·mth, and RCPsterm·dom markedly varied in space at the scale of the IPBESterm sub-region (Fig. 4 , Supplementary Fig. 9 ) but also at the pixel-scale (Supplementary Figs. 10 – 15 ). This was particularly true for the effect of selecting GCMsterm·mth, which on average have a low effect, but appear relatively strong in explaining the deviance in both %loss (percent of currently suitable area lost) and Δβs (percent change in total diversity per IPBESterm sub-region divided by the mean α-diversityterm·dom per sub-region), under ‘no dispersalterm·key’ in all of the Europe and Central Asia region, and in the North Africa and the Australia sub-regions for birds, and to a lesser extent for mammals and amphibians (Fig. 4 ). Similarly, the deviance explained by RCPsterm·dom for βt (temporal turnover) was much higher than the one explained by SDMsterm·mth in Africa and South America, while this was opposite in Europe, Central Asia and North America (Fig. 4 ). These varying effects can be explained by the spatial structure of the predicted changes in the different sensitivity metrics (Supplementary Figs. 10 – 15 ). For instance, the areas with the highest projected changes in the percentage of species loss by 2070 were mostly located in Africa and South America, areas where most of the variation was explained by RCPsterm·dom (Supplementary Fig. 12 ). A similar result was obtained for changes in α-diversityterm·dom (Supplementary Fig. 11 ), where the areas with the highest expected changes (Northern Americas, Northern Africa, some areas in Central Asia) coincide with areas for which the largest deviance was explained by RCPsterm·dom again. Fig. 4 Spatial variation of the relative influence of the different sources of variation. The maps represent the relative influence (i.e. % of explained variance) of the choice of species distribution modelsterm·mth (SDMsterm·mth), global circulation modelsterm·mth (GCMsterm·mth) and representative concentration pathwaysterm·dom (RCPsterm·dom) on the change in α-diversityterm·dom per-pixel (Δα), temporal species turnover (βt), percentage of species loss per pixel and change in β-diversity per IPBESterm sub-region (Δβs). Results are for the time period 2061–2080 (see Supplementary Fig. 9 for the period 2041–2060). Top row corresponds to amphibians, middle row to birds, and bottom-row to mammals Discussion In our comprehensive study, we have demonstrated the importance of considering multiple biodiversity modelsterm·mth, multiple GCMterm·mth, and, of course, multiple emission scenarios. Here, by covering the global scale and a larger range of organisms, we also demonstrate how the uncertaintyterm·key in sensitivity metrics varies in space, in time, as a function of the organism, and ultimately, as a function of the sensitivity metric used. When considering sensitivity metrics that account for species dispersalterm·key capacity, the influence of the modelling algorithms becomes overwhelming. Statistical SDMsterm·mth are known to markedly differ when projecting species distributions across space and time and this is why several packages include multiple algorithms to explore this variation (e.g. 15 ). Importantly, even when selecting only the best performing models (TSSterm·mth > 0.7), SDMsterm·mth still caused highest contributions to uncertaintyterm·key, followed by GCMsterm·mth, and then RCPsterm·dom.

For biodiversity management, this could have important implications. There is indeed growing interest in climate change refugiaterm·dom 16 , a concept that provides a theoretical basis for the identification of species-specific safe areas under climate changeterm·key. In that respect, targeted species translocation is sometimes advocated as a potential solution to safeguard species for conservation that would otherwise become extinct in the face of climate changeterm·key 17 , 18 . While considerable controversy has emerged regarding the selection of geographic areas translocation 19 , it is often suggested that SDMterm·mth are an appropriate tool for selecting areas for translocations that are becoming suitable in the future 18 . Our results suggest that should SDMsterm·mth be used for guiding conservation translocation, it should be done carefully, since SDMsterm·mth tend to cause high levels of uncertaintyterm·key. Running multiple state-of-the-art SDMsterm·mth forced by several GCMsterm·mth seems to be the best and only option to provide ensembleterm·key future projections for assessing options for translocations. Ensemble projectionsterm·mth provide information what areas are suitable in most models and scenarios, which reduces translocation uncertaintiesterm·dom compared to using projections from a single SDMterm·mth with a single climate forcing only.

Alternatively, in situ conservation planning focuses on protecting or managing species where they currently occur and protect them from other, negative effects. To guide efforts to areas within the current range that are least affected by climate changeterm·key, the use of multiple GCMterm·mth and especially RCPsterm·dom is very important.

Interestingly, when focusing on sensitivity metrics related to species loss or temporal turnover, the uncertaintyterm·key related to variation in SDMsterm·mth is not necessarily larger than in GCMsterm·mth and is lower than in RCPsterm·dom, which is as expected. When researchers do not have the computational capability to implement a full treatment of uncertaintyterm·key, focusing on those metrics might be an avenue. In terms of conservation planning, it also means that optimization algorithms that rather focus on securing diversity (both α- and β-diversities in a complementarity way) should be less affected by uncertaintyterm·key from GCMsterm·mth and SDMsterm·mth. They should thus mostly concentrate their efforts on assessing the effects of emission scenarios. Alternatively, there are also alternative modelling techniques that explicitly focus on community-level metrics (i.e. pixel-based). Since those approaches do not rely on stacking individual SDMterm·mth, they are less prone to bias coming from aggregating models with different quality 20 . However, modelling α- and β-diversity explicitly is not as straightforward than modelling individual species 21 . Similar analyses than the one proposed here but with community-level modelling approaches will be interesting to understand whether they are less influential on projection outputs than SDMsterm·mth. In this study, we have also proposed novel ways of communicating both the uncertainties and their sources either per region, sub-region or pixel. This shall help pave the way to better communicate and map both the metric and the variance in this metric from the different sources of uncertaintyterm·key. Yet, it shall also illustrate how the importance of these different sources varies in space and time and that conservation actions or biodiversity management should account for those variations. We have seen that sources of uncertaintyterm·key can strongly vary in space depending on the quality of biodiversity modelsterm·mth for some particular groups or the variability of projections among GCMterm·mth (Supplementary Figs. 5 – 8 ).

Biodiversity scenariosterm·mth are not meant to predict the future precisely, but rather to project the range of possible futures allowing to better understand uncertainties and alternative visions of this future. These visions allow for considering how different political options, represented here by the RCPsterm·dom, might influence the persistence of biodiversity under a wide range of possible futures. However, to be useful, one has to acknowledge also other sources of variations that may influence the overall modelling exercise 12 . There are different types of biodiversity modelsterm·mth, and here while considering only a single type (i.e. statistical SDMterm·mth), we show that different algorithms could lead to substantial variability in the sensitivity metrics used. This variation may blur the utility of using several RCPsterm·dom to discuss their impact on biodiversity persistence. This issue was long recognized in climate sciences such that it is no longer conceivable to show projected climatic trends from a single GCMterm·mth only. Rather, ensemblesterm·key of climate trajectories are usually shown (or least statistics thereof) and offered to users through data portals (e.g. CMIP5). The biodiversity modelling community needs to more consistently follow this path and report and communicate the variability resulting from the different options in biodiversity modelsterm·mth (e.g. SDMsterm·mth, dispersalterm·key scenarios) and input data (e.g. GCMterm·mth, RCPterm·dom). However, the range of biodiversity modelterm·mth types, algorithms, input data or parameterizations is so large that it seems currently impossible to report the variability even across biodiversity modelterm·mth types. However, we urge that variabilities originating from modelling algorithms, input data and external forces be assessed and reported comprehensively for better informing science, users and decision-makers in exploring options for the future.

Methods Statistical analyses All analyses have been carried out in the R environment (specific functions within specific package are indicated in parentheses).

Data We used the distribution maps provided by the Amphibian and Mammal Red List Assessment ( http://www.iucnredlist.org/ ) for 5547 and 4616 species, respectively. For birds, breeding range distribution maps were extracted from BirdLife ( http://www.birdlife.org/ ) for 9993 species. Ranges were converted to 100 km × 100 km equal-area grid cells, a resolution previously validated as the finest justifiable for these data globally 22 . Grid cells within the distribution range of each species were thus converted to presence points, while those outside their distribution ranges were converted as absence points. We finally focused on 1351 amphibian, 7248 bird and 2896 mammal species after removing species occurring in <20 grid cells, as well as domestic and aquatic species. We consider 20 presence points the minimum to successfully fit response curves to four different predictor variables.

Climatic data Current climate (1979–2013) was represented by four bioclimatic variables from the CHELSA dataset 23 up-scaled from a 1 km to a 100 km resolution. The chosen variables were as follows: annual mean temperature, annual temperature range, annual sum of precipitation and precipitation seasonality (coefficient of variation in monthly sum of precipitations).

Projected future climate variables were taken from five GCMsterm·mth driven by four scenarios of RCPsterm·dom in a factorial manner as explained in Supplementary Fig. 1 . The five selected models originate from the CMIP5 collection of model runs used in IPCC’s 5th Assessment Report (IPCC 2013). The five models from which data were taken are: CESM1-BGC 24 run by National Center for Atmospheric Research (NCAR); CMCC-CMS 25 run by the Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC); CM5A-LR 26 run by the Institut Pierre-Simon Laplace (IPSL); MIROC5 27 run by the university of Tokyo; and ESM-MR 28 run by Max Planck Institute for Meteorology (MPI-M).

Future climatic conditions of the four climatic variables were also taken from the CHELSA dataset 23 , which provides CMIP5 scenarios at a native resolution of 30 arc seconds. Future conditions from coarser resolution GCMsterm·mth had been achieved using climatologically aided interpolation. We took the difference between selected GCMsterm·mth from CMIP5 at a 0.25° grid cell size for current conditions (1979–2013) and the selected future periods (2041–2060, 2061–2080) and interpolated them using b-spline interpolation to the resolution of 30 arc seconds of CHELSA. The resulting difference was then added to (for temperature) or multiplied with (for precipitation) to the CHELSA climatologies of the 1979–2013 baseline period. As our study used 100 km grid cells, the native CHELSA resolution was upscaled by calculating mean within values per each 100 km grid cell.

Species distribution modelsterm·mth An ensembleterm·key of projections of SDMterm·mth was obtained for the 11,495 selected species. The ensembleterm·key included projections with Generalized Additive Models, Boosting Regression Trees, Generalized Linear Models and Random Forests. Models were calibrated for the baseline period using 70% of observations randomly sampled from the initial data and evaluated against the remaining 30% data using the true skill statisticterm·mth (TSSterm·mth 29 ). Presence data were randomly drawn from the gridded range maps. For absences, we considered data in a reasonable buffer around the presence data to avoid having over-optimistic predictive accuracies 30 . To be consistent with assumed realistic dispersalterm·key distances (see next paragraph) and in line with previous analyses, we selected absence data in 2000, 3000, and 4000 km buffer around amphibian, mammal and bird species ranges, respectively. This analysis was repeated four times, thus providing a four-fold internal cross-validation of the models (biomod package 15 ). The quality of the models was ‘very high’ to ‘excellent’ with an average TSSterm·mth of 0.83 (Supplementary Fig. 2 ). Since the quality of the models strongly affect projection uncertainties, we tested three thresholds below which models were removed from projection ensemblesterm·key. We used a threshold of TSSterm·mth = 0.4, which is usually considered a minimum for retaining reliable models 29 . We also used thresholds of 0.6 and 0.7, and investigated their effects on uncertainties of species-based sensitivity metrics. For all further analyses, the most drastic threshold (TSSterm·mth = 0.7) was then used (red lines in Supplementary Fig. 2 ).

For each species, all calibrated models (4 SDMsterm·mth × 4 repetitions) were then used to project the potential distribution of each species under both current and projected future climatic conditions (Supplementary Fig. 1 ).

Dispersalterm·key limitation Since most species have a sub-global distribution, we adjusted the area from which species are modelled and for which projections are made. In other words, for amphibian, bird and mammal species, the modelled and projected area included all grid cells within 2000, 3000 and 4000 km of species’ current distributions, respectively. This represents a maximal dispersalterm·key distance and excludes regions and climatic conditions that are outside of what is conceivably within reach for these species 30 . These estimates likely underestimate the true dispersalterm·key limitation of most species but give a more reliable estimate than assuming unlimited dispersalterm·key during this century. For most analyses, we also assumed a ‘no dispersalterm·key’ scenario. This ‘no dispersalterm·key’ scenario is useful to investigate whether and where area of currently suitable climate habitat will remain to be suitable for species in the future. This is a very important aspect for in situ conservation.

Sensitivity metrics All species projections under future conditions (5,149,760 in total) were converted to a metric of species sensitivity. CCSterm·mth measures the relative change in climatic suitabilityterm·key. It corresponds to the difference between the total suitable climatic area projected into the future under the assumption of limited dispersalterm·key and the total suitable area projected under current conditions, with the resulting quantity being divided by the total suitable area projected on the current conditions. Under the ‘no dispersalterm·key’ hypothesis, we derived LCSterm·mth, which measure the relative loss in climatic suitabilityterm·mth. This metric quantifies a species’ risk of habitat loss within its current area of occupancy.

At the pixel-level, we calculated several metrics commonly used in biodiversity scenarioterm·mth modelling. First, we calculated the relative (percent) change in species richness (Δα-diversityterm·dom) and the relative (percent) loss of species per pixel (% loss). Second, we calculated the temporal species turnover per pixel under the assumption of limited dispersalterm·key (βt = [No. of species lost + No. of species gained]/[current species richness + No. of species gained]). Finally, to be useful for the global assessment of the IPBESterm, we also estimated the change in spatial turnover (Δβs) within each of the IPBES-subregions (Supplementary Fig. 16 ), calculated as the relative (percent) change in total diversity per sub-region (γ-diversity) divided by the mean α-diversityterm·dom per sub-region. Δβs was calculated under both no dispersalterm·key and limited dispersalterm·key assumptions.

Variance partitioning of the uncertaintyterm·key For both species-based sensitivity metrics and pixel-based variation in community metrics, we conducted a set of variance partitioning to understand the main drivers of the variance.

All sensitivity metrics are based on a large amount of simulationsterm·mth (e.g. 448 projections per species) that vary as a result cross-validation sub-setting of initial data, dispersalterm·key scenario, and choice of SDMterm·mth, GCMterm·mth, and RCPterm·dom. First, the effects of cross-validation explained <1% of total variation and thus we decided not to consider it for further analyses. Cross-validated models were considered as four independent runs of the same models. Second, since our sensitivity metrics were defined for different dispersalterm·key assumptions, we did not consider dispersalterm·key in the variance partitioning, but contrasted the results as a function of it. Finally, we partitioned the effects of SDMsterm·mth, GCMsterm·mth and RCPsterm·dom on the final metrics using a nested ANOVAterm·mth, in which SDMsterm·mth were the first level, followed by GCMsterm·mth and RCPsterm·dom, which were considered as crossed effects (SDMterm·mth/GCMterm·mth:RCPterm·dom). We implemented a nested ANOVAterm·mth since SDMsterm·mth are first fitted irrespective of GCMsterm·mth and RCPsterm·dom, yet they differ strongly in how they affect projected suitable habitats when applied to GCMsterm·mth and RCPsterm·dom. Therefore, we considered the effects from GCMterm·mth and RCPterm·dom as nested within the effects of SDMsterm·mth. We are aware that most analyses have been done with a full factorial (non-nested) design so far. For the sake of consistency, we also performed a full-factorial ANOVAterm·mth that showed the same results. Since we believe the nested ANOVAterm·mth is more correct, we kept it as main effect in this study. From the nested ANOVAterm·mth, we focused on the deviance explained by each component.

For the species-level sensitivity metrics, we evaluated several selection criteria below which SDMsterm·mth were not retained for final ensemble projectionsterm·mth (see Species distribution modelsterm·mth part). Here, the nested ANOVAsterm·mth were performed for three TSSterm·mth thresholds (0.4, 0.6 and 0.7) and the results were compared to assess whether the explained variance that come from SDMsterm·mth is driven by the quality of retained SDMsterm·mth. Since we observed increasing variability caused by SDMsterm·mth when using too low thresholds, we kept the highest threshold TSSterm·mth (TSSterm·mth = 0.7) to ensures that only very good models were retained.

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