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Species-level dataSpecies range maps were derived from BirdLife International and NatureServe50 and the IUCN51. The threat data were from the IUCN Threats Classification Scheme (Version 3.2), which contains 11 primary threat classes and almost 50 subclasses52. In Red List assessments, assessors assign those threats that impact the species. For birds, the scope of the impact is also recorded categorically as the percentage of the species population that the threat impacts (unknown, negligible, 90%) and the severity, describing the scale of the impact on population declines: unknown, no decline, negligible declines, fluctuations, slow but significant declines (30%).Model development approachWe designed our analytical framework with three considerations in mind. First, the threat location information is limited: for each species, the data only describe whether a species is threatened by a given activity anywhere within its range (data on the timing, scope and severity of threats are available only for birds and are not spatially explicit). Second, we wanted to compare the spatial patterns of threat against independent data on spatial distributions of human activities. Third, for many activities, the relationship between human activity (for example, hunting or invasive species and diseases) and biodiversity response is poorly understood. We therefore chose not to incorporate known patterns of human activity as explanatory variables in our models.In the absence of global datasets on the spatial patterns of the impact probability of each threat, we used a simulation approach to develop our models and assess the ability of different model parameterizations to reproduce our simulated threat. This process had four steps (Extended Data Fig. 1).Simulated threat intensity mapsFirst, we simulated a continuous synthetic threat across sub-Saharan Africa. The concept behind this is that a credible model should be able to reproduce a ‘true’, synthetic threat pattern on the basis of information comparable to that available in the Red List. To test this, we generated a set of synthetic, continuous surfaces of threat intensity with different levels of spatial autocorrelation and random variation (Supplementary Fig. 1). This was achieved by taking a grid of 50 km × 50 km (2,500 km2) pixels across the Afrotropic biogeographic realm (i.e., sub-Saharan Africa). Threat intensity was modelled as a vector of random variables, Z, one for each pixel i, generated with a correlation structure given by the distance matrix between points weighted by a scalar value, r, indicating the degree of correlation (equations (1–3)). Four values of r were used: 1 × 10−6, which yields very strong autocorrelation; 1 × 10−4, which yields strong autocorrelation; 0.05, which yields moderate autocorrelation; and 0.3, which produces a low-correlation, localized pattern (Supplementary Fig. 1). The model included the following equations:$${mathbf{Z}}(r) = U^{mathrm{T}}{mathrm{Norm}}left( {n,0,1} right)$$
(1)
$$W = UU^{ast}$$
(2)
$$W = {mathrm{e}}^{left( { – rD} right)}$$
(3)
where r is a scalar determining the degree of spatial autocorrelation (as r decreases, the autocorrelation increases), D is the Euclidean distance matrix between each pair of pixels, W is the matrix of weights for the threat intensity, U and U* are the upper triangular factors of the Choleski decomposition of W and its conjugate transpose, UT is the transpose of U and n is the number of pixels.We chose the Afrotropic biogeographic realm (sub-Saharan Africa) as our geography within which to develop the modelling approach because it permitted more rapid iterations than a global-scale simulation while also retaining characteristics of importance for the model evaluation such as strong environmental gradients and heterogeneity in species richness. However, for the simulation, no information from the geography or overlapping species ranges was used, except the spatial configuration of the polygons. Thus, the use of the Afrotropic realm was purely to avoid generating thousands of complex geometries for the purpose of the simulation. Using a real geography and actual species ranges ensures that our simulation contains conditions that are observed in reality (for example, areas of high and low species richness also observed in the real world). We took the simulated threat maps generated through this process to be our ‘true’ likelihood of a randomly drawn species that occurs in that location being impacted by the synthetic threat (Supplementary Fig. 1).Simulating the red-listing processSecond, we wanted to simulate the red-listing process whereby experts evaluate whether a threat is impacting a species on the basis of the overall threat intensity within its range. For this, we used the range maps for all mammal species in Africa and assigned a binary threat classification (that is, affected or not affected) to each species on the basis of the values of the synthetic threat within each species’ range. We assumed that the binary assessment of threat for a species is based on whether the level of impact across a proportion of its range is judged as significant. This step was intended to replicate the real red-listing process, where assessors define threats that impact the species on the basis of an assessment of the information available on threatening mechanisms and species responses. In practice, this was done by overlaying the real range maps for mammals over the four simulated threat surfaces and assessing the intensity of synthetic threat within each species range map. We wanted to assign species impacts considering that species will be more likely to be impacted if a greater part of their range has a high threat intensity. Understanding how to set a threshold for what intensity would constitute sufficient threat to be assessed as affected is a complicated exercise. We thus tested three thresholds to capture different assumptions. These thresholds were chosen after discussion with leading experts on the red-listing process. More specifically, we calculated the 25th, 50th and 75th percentiles of threat intensity across pixels within the species range. We then used a stochastic test to convert these quantiles to binary threat class, C. For each species, we produced a set of ten draws from a uniform distribution bounded by 0 and 1. If over half of the draws were lower than the threat intensity quantile, the species was classified as threatened for that percentile.The above simulation assumes perfect knowledge of the threat intensities across the species range, which might not always be the case in the actual red-listing process. In real life, certain areas within species ranges are less well known for a suite of different reasons. To incorporate some uncertainty about the knowledge of the red-listing experts about the ‘true’ threat intensity, we constructed a layer to describe the spatial data uncertainty associated with the Red List. This aspect was intended to simulate the imperfect knowledge of the simulated ‘Red List assessors’. This layer was calculated as the proportion of species present in a given location that are categorized as Data Deficient—in other words, there is insufficient information known about the species to assess its extinction risk using the IUCN Red List Criteria (Extended Data Fig. 7). Then, when calculating the 25th, 50th and 75th percentiles of threat intensity across each range, we weighted this calculation by one minus the proportion of Data Deficient species, so that more uncertain places (those with a greater proportion of Data Deficient species) contributed less to the calculation than locations where knowledge was more certain. These were then converted to a binary threat class accounting for uncertainty in expert knowledge among the simulated ‘assessors’, CUncertain, using the same stochastic process described above for the calculation of C.This step produced, for each species, a threat classification analogous to the threat classification assigned by experts as part of the IUCN Red List process. Six sets of threat classifications were produced for each synthetic threat surface, on the basis of the 25th, 50th and 75th percentiles with perfect (C0.25, C0.5 and C0.75) or uncertain (CUncertain-0.25, CUncertain-0.5 and CUncertain-0.75) spatial knowledge.Model formulation and selectionThird, using all species polygons with assigned threat assessments from step 2 (that is, affected or not affected), we fitted nine candidate models and predicted the estimated probability of impact for each grid cell. Then, in a fourth step, we compared the predicted probabilities of impact produced in step 3 with the original synthetic threat maps created in step 1 to test the predictive ability of our models.The Red List threat assessment does not contain information on where in the range the impact occurs. Therefore, a species with a very small range provides higher spatial precision about the location of the impact, whereas a species with a large range may be impacted anywhere within a wide region. To address this lack of precision in the impact location, we took the area of each species range to serve as a proxy for the spatial certainty of the impact information. The certainty that a species was impacted or not impacted in a given cell depended on its range size, R. The models we evaluated therefore incorporated R in different ways (Supplementary Table 1).The models were fitted as a binomial regression with a logit link function. For each pixel, the model predicts the probability of impact, PTh—in other words, the probability that if you sampled a species at random from those that occur in that pixel, the species would be impacted by the activity being considered. To account for uncertainties in the simulation of the threat assessment process (thresholds for impact and perfect or imperfect knowledge), models were fitted to the six sets of threat codes (C0.25, C0.5, C0.75, CUncertain-0.25, CUncertain-0.5 and CUncertain-0.75), and the root mean squared error (RMSE) was calculated between PTh and the simulated threat intensity, Z(r), for each value of r. For each simulation, we ranked the different models according to their model fit as measured by the RMSE. We assessed these ranks across all simulations and sets of threat codes. We evaluated the models on the basis of the ranks of RMSE, across the threat code sets and threat intensity maps. Rank distributions for each model are shown in Extended Data Fig. 2, and the results from these models are shown in Supplementary Tables 1 and 2.All models were correlated (Pearson’s r2  > 0.5), albeit with some variation between model types and across the simulation parameters (Supplementary Fig. 2). However, some models had greater predictive accuracy when evaluated using the RMSE. The top four ranking models were, in order of decreasing summed rank, (1) inverse of cube root of range size as a weight, (2) inverse 2.5 root of range size as a weight, (3) inverse square root of range size as a weight and (4) inverse natural logarithm of range size as a weight. The fact that these four models showed good model fit suggests that the best model structure had a measure of range size as a weight but that the model was not particularly sensitive to the transformation of range size.The best-fitting model across the range of simulation parameters was an intercept-only logistic regression where the response variable was the binary threat code (1 = threatened, 0 = not threatened) for each species in the pixel and where the inverse cube root of the range size of each species was used as a weight. The model was concordant across the set of simulated datasets with a relationship that was predominantly linear with r2 between 0.47 and 0.7, depending on simulation parameters for Z(r) in 0.05, 10−4 and 10−6, centred around unity and with the RMSE ranging between 0.129 and 0.337 depending on simulation parameters (Supplementary Figs. 2 and 3). The choice of the inverse cube root range size weight was based on the performance of this against eight other model types (Supplementary Fig. 4 and Supplementary Table 1).We conducted a decomposition of variance in model performance using a binomial regression model, with RMSE as the dependent variable and model type, knowledge level and autocorrelation structure as the independent factorial variables. This showed that knowledge about the threats underlying each species range and how that threat information is used in the assessment explained the vast majority (94.7%) of the variation in RMSE outcomes (Supplementary Fig. 4).For birds, further information on the scope of the threat was available as an ordinal variable describing the fraction of range that the threat covers. We explored the use of scope in our models but concluded that to avoid arbitrary decisions about the scope of non-threatened species (where they are either not threatened anywhere or threatened in only a small part of their range), and for consistency with other taxonomic groups, we would model birds using the same model structure as used for mammals and amphibians (see the Supplementary Methods for further details).Mapping probability of impactOnce the best-performing model was identified using the simulated data, we then used this model on the actual Red List threat and range data to develop threat maps. This model produced threat maps for each taxonomic group (amphibians, birds and mammals) of the probability of impact, PTh, for each individual threat. For a given pixel, threat and taxonomic group, this estimates the probability that a randomly sampled species with a range overlapping with that pixel is being impacted by the threat, while taking into account spatial imprecision in the Red List data.Threat maps were generated using range map data and threat assessments from the IUCN Red List18. We intersected range maps for 22,898 extant terrestrial amphibians (n = 6,458), birds (n = 10,928; excluding the spatial areas within the range that are associated with ‘Passage’—where the species is known or thought very likely to occur regularly during relatively short periods of the year on migration) and mammals (n = 5,512; including those with uncertain ranges) with a global 50 km × 50 km (2,500 km2) resolution, equal-area grid for the terrestrial world. This provided, for each 50 km × 50 km pixel, a list of the species whose range overlapped it, along with the associated range size of each species. For each pixel and taxonomic group (amphibians, birds and mammals) independently, we then modelled the probability of impact, PTh,Activity (for example, PTh,Logging for logging, PTh,Agriculture for agriculture or PTh,Pollution for pollution), for each of the six threats: agriculture, hunting and trapping, logging, pollution, invasive species and diseases, and climate change. We focused on these as the six main threats as defined by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services4, but our methodological framework is flexible and could be expanded to other threats in the IUCN classification19. We used only taxonomic groups with a sufficiently high total number of species and where they have been comprehensively assessed so that potential biases associated with the groups of species prioritized by experts are avoided.Calculating uncertainties for the threat probabilityWe estimated a measure of uncertainty associated with our impact probability predictions using maps of the proportions of Data Deficient species in each cell within each taxonomic class (amphibians, birds or mammals) as a measure of knowledge certainty in that cell. The rationale for this approach is that places with more Data Deficient species with unknown threatened status should have greater uncertainty in the probability of impact. We therefore created greater variation in the data where there were more Data Deficient species. We used the knowledge-certainty map to probabilistically draw a sample of 100 threat codes for each species, on the basis of the median Data Deficiency across the species range. The random sample changed the species threat code with a probability related to the proportion of Data Deficient species within its range. If the median proportion of Data Deficient species was zero, then we assumed that there was a small probability (0.005) that the species could have been incorrectly coded. Where the median proportion was greater than zero, the probability increased linearly. So, for a species with 5% Data Deficient species within its range, the sample changed the species threat code with a probability close to 5%; if the median proportion was equal to 0.5, then the probability of the species being incorrectly assigned was equal to 0.5. We then fitted the impact probability model with each of the 100 species threat codes and generated a distribution of predicted threat probabilities in each grid cell, from which we took the 95% confidence intervals as the uncertainty estimates (Extended Data Figs. 8–10).Evaluating modelled threat patternsWe evaluated the spatial patterns of threat on the basis of the real Red List threat assessment data against empirical data in two independent ways. First, we compared the probability of impact from logging and agriculture combined within forested biomes (that is, corresponding to remotely detected forest loss, which we refer to as the probability of impact from forest loss, PTh,Forest-loss) with data on forest cover change10. Forest cover change was aggregated from their native 30 m × 30 m (900 m2) resolution pixels to our 50 km × 50 km resolution pixels using Google Earth Engine. For each 50 km × 50 km pixel, we calculated the total area lost between 2000 and 2013 and the area lost as a proportion of the area in 2000. We restricted our analysis to forested biomes: (1) tropical and subtropical moist broadleaf forests, (2) tropical and subtropical dry broadleaf forests, (3) tropical and subtropical coniferous forests, (4) temperate broadleaf and mixed forests, (5) temperate coniferous forests and (6) boreal forests/taiga, following the World Wildlife Fund’s ecoregions classification53. The relationship between forest loss and the probability of impact from forest loss as captured by agriculture and logging overall showed a significant positive correlation: PTh,Forest-loss increased with increasing forest cover loss (P  More

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Independent reference samplesThe authentic, independent strawberry (Fragaria × ananassa) reference samples used for model validation in this study were provided by Agroisolab GmbH (Jülich, Germany). The samples were collected either directly by the company or on their behalf through authorized sample collectors between 2007 and 2017. The primary purpose of such authentic reference samples is the direct comparison between their stable isotope compositions (oxygen, hydrogen, carbon, nitrogen, or sulfur) to those of samples of suspect origin. Accompanying metadata for each reference sample included information about the geographic origin as community name, postal code, or location coordinates, and information about the month and year the strawberry sample was picked. In total, we used δ18O values from 154 reference samples. Most samples were collected in the UK, Germany, Sweden, and Finland (Fig. 1). All reference samples were grown on open strawberry-fields rather than artificial greenhouse conditions. All berry samples were collected from cultivated, non-endangered plant species (“garden strawberry”), and the research conducted complies with all relevant institutional, the corresponding national, and also international guidelines and legislation.After collection in the field, samples were stored in airtight containers and shipped directly to Agroisolab, where they were stored frozen prior to analysis. In order to analyze the oxygen stable isotope composition of the organic strawberry tissue, the lipids were solvent-extracted with dichloromethane for a at least 4 h, using a Soxhlet extractor. The remaining samples were dried and milled to a fine powder. 1.5 mg of the powder was weighed into silver capsules. The silver capsules were equilibrated for at least 12 h in a desiccator with a fixed relative humidity of 11.3%. After a further vacuum drying the samples were measured via high-temperature furnace (Hekatech, Wegberg, Germany) in combination with an Isotope-ratio mass spectrometer (IRMS) Horizon (NU Instruments, Wrexham, UK). The pyrolysis temperature was 1530 °C and the pyrolysis tube consisted of covalent-bound SiC (Agroisolab patented). The reproducibility of the measurement was better than 0.6 ‰.Oxygen isotope model calculationPlant physiological stable isotope models simulate the oxygen isotopic composition of leaf water or organic compounds synthesized therein as δ18O values in per mil (‰), where δ18O = (18O/16O)sample/(18O/16O)VSMOW − 1, and VSMOW is Vienna Standard Mean Ocean Water as defined by the VSMOW-Standard Light Antarctic Precipitation (SLAP) scale. The Craig-Gordon model57, which was developed to mathematically describe the isotopic enrichment of standing water bodies during evaporation and later modified for plants, is the basis for modelling plant water δ18O values23,58. Plant source water is the baseline for the model, which is the precipitation-derived soil water that plants take up through their roots without isotope fractionation51,59,60. The 18O enrichment of water within leaves is described by the following equation (Eq. 1)36,61:$$ Delta^{18} {text{O}}_{{text{e leaf}}} = left( {1 +upvarepsilon ^{ + } } right)left[ {left( {1 + {upvarepsilon }_{{text{k}}} } right)left( {1 – {text{e}}_{{text{a}}} /{text{e}}_{{text{i}}} } right) + {text{e}}_{{text{a}}} /{text{e}}_{{text{i}}} (1 + Delta^{18} {text{O}}_{{{text{Vapor}}}} )} right]{-}1 $$
(1)

where Δ18Oe_leaf is the oxygen isotopic enrichment above source of water at the evaporative site in leaves, ε+ is the equilibrium fractionation between liquid water and water vapor, εk is the kinetic fractionation associated with the diffusion through the stomata and the boundary layer. ea/ei is the ratio of ambient vapor pressure in the atmosphere to intercellular vapor pressure in the leaf. Δ18OVapor is the isotopic composition of the ambient vapor above source water, which in this study is assumed to be in equilibrium with the source water (Δ18OV = − ε+)62,63. This assumption can be used, if the atmosphere is well mixed, and plants’ source water derives from recent precipitation events. For crops, growing in the temperate climate of the mid latitudes this is usually the case, especially over the long time periods (several weeks) over which strawberries grow. If such a model is applied in other climatic zones (e.g. tropics), this assumption should, however, be reevaluated64. The equilibrium fractionation factor (ε+)65,66 and kinetic fractionation factor (εk)67 can be calculated with the following equations (Eqs. 2 and 3):$$upvarepsilon ^{ + } = left[ {exp left( {frac{1.137}{{left( {273 + T} right)^{2} }}*10^{3} – frac{0.4156}{{273 – T}} – 2.0667*10^{ – 3} } right) – 1} right]*1000 $$
(2)

where T is the leaf temperature in degrees Celsius. In our calculations, leaf temperature was set to 90% of the monthly mean air temperature, which describes a realistic leaf-energy balance scenario for well-watered crops68,69, and also yielded the best model performance with respect to the reference data. As leaf to air temperature differences have a strong influence on leaf water δ18O values, this assumption needs to be independently tested in future applications. For example, changing leaf temperature from 20 °C to 22 °C at a constant air temperature of 20 °C and a source water δ18O value of -10 ‰ will affect leaf water δ18O values by + 1.4 ‰.$$upvarepsilon _{{text{k}}} = frac{{28{text{r}}_{{text{s}}} + 19{text{r}}_{{text{b}}} }}{{{text{r}}_{{text{s}}} + {text{r}}_{{text{b}}} }} $$
(3)

where rs is the stomatal resistance and rb is the boundary layer resistance in m2s/mmol, which is the inverse of the stomatal and boundary layer conductance. For our model calculations, we consistently used stomatal conductance values of 0.4 mol/m2s, stomatal resistance values of 1 m2s/mol70.The Craig-Gordon model predicted leaf water values are often enriched in 18O relative to measured bulk leaf water δ18O values26,27. This is because the model describes the δ18O values of water at the site of evaporation while measurements typically give bulk leaf water δ18O values36,71. The two-pool modification to the Craig-Gordon model corrects for this effect by separating bulk leaf water into a pool of evaporatively enriched water at the site of evaporation (δ18Oe_leaf derived from the Craig-Gordon model, Eq. 1) and a pool of unenriched plant source water (δ18Osource water)25. δ18Oe_leaf is calculated as follows:$$updelta ^{18} {text{O}}_{{{text{e}}_{text{leaf}}}} = , (Delta^{18} {text{O}}_{{{text{e}}_{text{leaf}}}} +updelta ^{18} {text{O}}_{{text{source water}}} ) , + , (Delta^{18} {text{O}}_{{{text{e}}_{text{leaf}}}} * ,updelta ^{18} {text{O}}_{{text{source water}}} )/1000) $$
(4)
In the two-pool modified Craig-Gordon model (Eq. 5), the proportion of unenriched source water is described as fxylem36.$$updelta ^{18} {text{O}}_{{text{leaf water}}} = , left( {1 , {-}f_{xylem} } right) , * ,updelta ^{18} {text{O}}_{{{text{e}}_{text{leaf}}}} + , left( {f_{xylem} * ,updelta ^{18} {text{O}}_{{text{source water}}} } right) $$
(5)
Values for fxylem in leaf water generally range from 0.10 to 0.3336,37,38,39,40 but higher values have also been observed72. For strawberry plants, leaf water fxylem values were recently shown to vary between 0.24 and 0.3428.Organic molecules in leaves generally reflect the δ18O values of the bulk leaf water plus additional isotopic effects occurring during the assimilation of carbohydrates and post-photosynthetic processes21,22,34. The fractionations occur when carbonyl-group oxygen exchanges with leaf tissue water during the primary assimilation of carbohydrates (trioses and hexoses)42. This process causes 18O enrichment, described as εwc42, and has been determined to be ~  + 27 ‰21,22,73.During the synthesis of cellulose from primary assimilates, sucrose molecules are broken down to glucose and re-joined, allowing some of the carbonyl group oxygen to further exchange with water in the developing cell. The isotopic fractionation (εwc) during this process is assumed to be the same as in the carbonyl oxygen exchange during primary carbohydrate assimilation (~ + 27 ‰)41,42. During the formation of cellulose, the δ18O values of the primary assimilates are thus partially modified by the water in the developing cell33. Equation (6) describes this process34$$updelta ^{18} {text{O}}_{{{text{cellulose}}}} = {text{ p}}_{{text{x}}} {text{p}}_{{{text{ex}}}} *left( {updelta ^{18} {text{O}}_{{text{source water}}} + ,upvarepsilon _{{{text{wc}}}} } right) , + , left( {1 , – {text{p}}_{{text{x}}} {text{p}}_{{{text{ex}}}} } right) , * , left( {updelta ^{18} {text{O}}_{{text{leaf water}}} + ,upvarepsilon _{{{text{wc}}}} } right) $$
(6)

where δ18Ocellulose is the oxygen isotopic composition of cellulose, pex is the fraction of carbonyl oxygen in cellulose that exchanges with the medium water during synthesis, and px is the proportion of unenriched source water in the bulk water of the cell where cellulose is synthesized33. Bulk water in developing cells where cellulose is synthesized, i.e. in the leaf growth-and-differentiation zone, has been found to primarily reflect the isotope composition of source water43. Therefore, px in Eq. 6 is likely larger than fxylem in Eq. (5). For practical reasons, the parameters px or pex are typically not determined individually, but as the combined parameter pxpex45. For cellulose in leaves of grasses, crops, and trees pxpex has been found to range from 0.25 to 0.5445,46,47,48,49.In this study as in many applied examples where plant δ18O values are used for origin analysis we attempt to simulate the δ18O values of dried bulk tissue. Bulk dried plant tissue (δ18Obulk) contains in addition to carbohydrates compounds such as lignin, lipids, and proteins, which can be 18O-depleted compared to carbohydrates50. Since this needs to be accounted for in the model, we included the parameter c into the model. As pxpex and c cannot be determined separately they are used as a combined model parameter in our approach pxpexc:$$updelta ^{18} {text{O}}_{{{text{bulk}}}} = {text{ p}}_{{text{x}}} {text{p}}_{{{text{ex}}}} {text{c}}*left( {updelta ^{18} {text{O}}_{{text{source water}}} + ,upvarepsilon _{{{text{wc}}}} } right) , + , left( {1 – {text{ p}}_{{text{x}}} {text{p}}_{{{text{ex}}}} {text{c}}} right) , * , left( {updelta ^{18} {text{O}}_{{text{leaf water}}} + ,upvarepsilon _{{{text{wc}}}} } right) $$
(7)
Bulk dried tissue δ18O values of strawberries in Cueni et al. (in review) did not differ statistically from pure cellulose δ18O values in strawberries. Consequently, pxpex and pxpexc are identical for strawberries and ranges from 0.41 to 0.51. This approach allows the calculation of bulk dried tissue δ18O values without the knowledge of cellulose δ18O values, which is the case for the data set used in this study, and contrasts to the approach by Barbour & Farquhar (2000), where bulk dried tissue δ18O values are assessed by an offset (εcp) to the cellulose δ18O values.Model parameter selectionTo find the best values of the key model parameters for the prediction of strawberry bulk dried tissue δ18O values, we used different combinations of the values for the parameters. Specifically, we compared average parameter values from the literature that were derived from leaves and parameter values that were specifically derived for berries (Cueni et al. in review) to test if a leaf-level parameterization of the model is sufficient or if a berry-specific parameterization is necessary for producing satisfying model prediction. These values were either (i) fxylem and pxpex values reported in literature for leaf water and cellulose from various species that were averaged, (ii) values averaged for leaves (fxylem) and berries (pxpexc) of berry producing plants, or (iii) values for leaves (fxylem) and berries (pxpexc) specifically obtained for strawberry plants. For the general leaf-derived parameter values we used mean literature values originally obtained for leaf water and leaf cellulose δ18O for different species and averaged these values (0.22 for fxylem36,37,38,39,40 and 0.40 for pxpex45,46,47,48,49) (Table 1). For berries (average of the values of raspberries and strawberries) the mean leaf-derived fxylem value was 0.26 and the value for pxpexc was determined to be 0.46 (Table 1) (data derived from Cueni et al. in review). For strawberry plants, the leaf-derived fxylem value we used was 0.30, and the value for bulk dried tissue (pxpexc) was determined to be 0.46 (Table 1) (data derived from Cueni et al. in review). Since the pxpexc values of different berry species did not differ, this resulted in a total of six different model input parameter combinations.Table 1 Values of the model parameters (fxylem and pxpex/pxpexc) used for the simulations of strawberry bulk dried tissue δ18O values.Full size tableEnvironmental model input data selectionIn order to apply the strawberry parametrized bulk dried tissue oxygen model on a spatial scale, spatially gridded climate and precipitation isotope data layers were used as model inputs. The accurate simulation of geographically distinct δ18O values, however, requires the use of the most appropriate and best available input variables. We therefore tested the importance of the temporal averaging and lead time of the input data relative to the picking date of the berry. We defined these collectively as the “integration time” of the input data. Climate of the growing season46,53, and precipitation δ18O values of rain-events prior and during the growing season51,54,55 have been shown to shape plant tissue water and organic compound δ18O values. The major objective of our study was thus a careful evaluation of the most appropriate type and integration time of model input variables needed for this kind of model simulation. Moreover, to find the best data source provided, we also used several different spatial climate and precipitation isotope datasets in our evaluations (Table 2).Table 2 (a) Table showing the different climatic (air temperature and vapor pressure) and isotope (precipitation and vapor δ18O) data products, (b) as well as the different integration times and names used in the study used to simulate strawberry bulk dried tissue δ18O values.Full size tableTwo precipitation isotope data products were compared (Table 2): (1) The mean monthly precipitation δ18O grids by Bowen (2020), which are updated versions of the grids produced by Bowen and Revenaugh (2003) and Bowen et al. (2005) (Online Isotopes in Precipitation Calculator, OIPC Version 3.2). They provide global grids of monthly long-term mean precipitation isotope values. The resolution of these global grids is 5’. (2) Precipitation isotope predictions from Piso.AI (Version 1.01)32. This source provides values for individual months and years based on station coordinates32. Both data sets were on the one hand used for the precipitation δ18O input data of the model, and also to extrapolate the vapor δ18O values from sets (see model description above), which we treated as two individual, independent input data sets.For the climatic drivers of the model (air temperature and vapor pressure), we used the gridded data products from the Climatic Research Unit (CRU) (TS Version 4.04)29 and the E-OBS gridded dataset by the European Climate Assessment & Dataset (Version 22.0e)30 (Table 2). The CRU dataset provided global gridded monthly mean air temperature, and mean vapor pressure with a resolution of 0.5°. The E-OBS dataset included European daily mean air temperature and relative humidity gridded data, with a resolution of 0.1 arc-degrees. We calculated monthly mean air temperature and relative humidity grid layers, on the basis of these daily mean air temperature and relative humidity grids, respectively.Fruit tissue formation takes place over a period of several weeks leading up to picking date46,53. This results in a lead time between the date that best represents the mean climate conditions, and source water and vapor stable isotope signal influencing the isotope signal during tissue formation, and the picking date. As integration time of the input data, we therefore investigated lead times of 1, 2, 3, and 4 months, as well as the three months leading up to the picking date (Table 2). Moreover we also used more general European strawberry growing season averages76, independent of either the sampling month (yearly May to July mean) or the sampling year (2007 to 2017 May to July mean) (Table 2). Precipitation isotope data means were calculated as amount-weighted averages using CRU mean monthly precipitation data. This means that the long term mean precipitation δ18O values taken from OIPC were weighted by yearly specific CRU monthly precipitation totals for the case of the three months or growing season averages for individual years, and by average monthly precipitation totals (May, June, and July) from 2007 to 2017 for the long-term growing season calculation. The same assessment was also made using precipitation values from Piso.AI.Validation of model with reference samplesUsing the plant physiological model described above, we calculated the strawberry bulk dried tissue δ18O values for the location and the growing time of each authentic reference sample. For the model input data, we tested variable combinations using each of the eight integration times described in Table 2, along with all combinations of the data sources outlined in Table 2. This resulted in a total of 65,536 combinations of input variables per model parameter combination (fxylem and pxpex/pxpexc, Table 1), yielding model results to be evaluated against the measured reference samples. Our approach can be described with the following equation:$$updelta ^{18} {text{O}},{text{plant }} = fleft( {{text{air}},{text{temp}}left( {text{s,t}} right),{text{ relative}},{text{humidity}}left( {text{s,t}} right), updelta ^{18} {text{O}},{text{precip}}.left( {text{s,t}} right),updelta ^{18} {text{O}},{text{vapor }}left( {text{s,t}} right)} right) $$
(8)

where δ18O plant is the simulated δ18O value of the strawberry, s is the data product for the specified input variable (Table 2), and t is the integration time of the specified variable (Table 2).For the crucial model parameters fxylem and pxpex/pxpexc we on the one hand used the values proposed for leaves by literature (for pxpex), and on the other hand average of the values of raspberries and strawberries and strawberry-specific values determined from Cueni et al. (in review) (for pxpexc). In all calculations an εwc value of + 27 ‰ was used. To calculate mean monthly relative humidity values from the provided CRU vapor pressure data, site specific elevation was extracted from the ETOPO1 digital elevation model77, and used to calculate the approximate atmospheric pressure. These values were then used in combination with air temperature to calculate the saturation vapor pressure after Buck (1981), in order to assess relative humidity (relative humidity = vapor pressure/saturation vapor pressure). The R-script of the model is available on “figshare”, find the URL in the data availability statement.Statistical analysesStatistical analyses were done using the statistical package R version 3.5.379. The relationships of the range δ18O values observed with latitude, and between CRU and E-OBS mean air temperature were compared with a linear regression model, and with an alpha level that was set to α = 0.05. The results of the 65,536 models for each of the six physiological parameter combinations were compared with the measured δ18O bulk dried tissue values of the authentic reference samples (n = 154) by calculation of the root mean squared error (RMSE).Calculation of prediction mapsPrediction maps showing the regions of possible origin of a sample with unknown provenance are the product that is of interest in the food forensic industry. We calculated the prediction maps shown in Fig. 5 for three example δ18O values of strawberries collected in July 2017: (i) + 20 ‰ representing a mean Finish/Swedish sample, (ii) + 24.5 ‰ representing a mean German sample, and (iii) + 27 ‰ representing a mean southern European sample.The prediction maps were calculated in a two-step approach. First, we calculated a map of the expected strawberry bulk dried tissue δ18O values of berries grown in July 2017. For this we used the average berry model input parameters (fxylem and pxpexc, Table 1), and the best fitting model input data and integration time combination, which we assessed beforehand (Fig. 2). We thus used CRU mean air temperature and vapor pressure from June 2017, precipitation δ18O values from OIPC as an average from April, May and June, and vapor δ18O values calculated from OIPC precipitation δ18O values from April. Since using spatial maps as model input data, this calculation resulted in a mapped model result. In a second step, we calculated the prediction maps. For this we first subtracted the δ18O value of the bulk dried tissue of the sample strawberry from the mapped result of the best berry-specific model. This was done for each pixel value of the map. This resulted in a map showing the difference of the sample δ18O value and the predicted map δ18O value for each pixel of the map. The places (pixels) that are predicted to have the same δ18O value as the sample strawberry thus are represented by a value of zero. Based on the prediction error of the best berry-specific model (RMSE = 0.96 ‰), the one sigma (68%) and two sigma (95%) confidence intervals around the areas showing no difference to the δ18O value of the suspected sample could be assessed. This means that the bigger the difference between the simulated δ18O value and the sample value, the lower the probability of provenance of the sample. In other words, a difference between the sample’s δ18O value and the predicted δ18O value of 0 ‰ to ± 0.96 ‰ equals a possible provenance of at least 68% (one sigma), and a difference between ± 0.96 ‰ and ± 1.92 ‰ reflects a possible provenance between 68 and 27% (two sigma). Regions on the map with bigger differences than ± 1.92 ‰ represent regions of possible provenance, lower than 5% (bigger than two sigma). More

Spatial databaseWe collected species occurrences from the most accurate and available source of data for each taxonomic group. For mammals, birds, reptiles and amphibians, we used the IUCN spatial database to assign realm identity for each species15. By doing this, we assigned a realm for 5489 mammal species, 10,787 bird species, 5489 reptile species and 5833 amphibian species. Since IUCN spatial database does not cover all species, we completed our database with two additional sources of species occurrences: (1) the WWF WildFinder species database23, except for mammals where we used the latest version of the species distribution provided by ref. 24. If (1) was not available, we used (2) the global biodiversity information facility (GBIF). Using WWF WildFinder, we assigned a realm for 1634 bird species, 7378 reptile species and 2006 amphibian species. 437 mammal species were assigned using ref. 24. From GBIF, we downloaded all the records belonging to the four classes of animals (Mammals50, Aves51, Reptiles52 and Amphibians53). Before using the spatial data, we cleaned the dataset following a cleaning procedure that was similar to but more conservative than other currently available methods (e.g. CoordinatesCleaner, BDCleaner54). First, records were screened, and only those with (1) coordinates; (2) a taxonomic rank of “species” were kept. From this list, we filtered out the records with clearly false locality coordinates (e.g. latitude equal to longitude, both latitude and longitude equal to 0, and longitude/latitude outside the possible range (i.e. −180; 180 for longitude and −90; 90 for latitude)). Those are the most common errors encountered with GBIF occurrence data55. In addition, we removed the records from living specimens (i.e. from zoos, botanical gardens), conserved specimens (i.e. museums), and unknown sources. We also excluded the species with less than 50 records within each realm as a low number of records can be due to misidentifications, which might have strong effects on our analyses. We finally refined the dataset by overlaying the occurrences within the six biogeographic realms (see below) and dropping the species that fall outside of the polygons. This spatial overlay process was conducted using the ‘sp’ library56 in R. The number of species for which realm was assigned using GBIF was 1 ( More