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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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Photosynthetic characteristicsWater and nitrogen coupling treatment had a significant effect on the photosynthetic characteristics (Fig. 1). Generally, the net photosynthetic rates of the treatments were in the following order: CK, W1N1, W1N3, W3N1, W3N3, W2N1, W1N2, W3N2, W2N3, and W2N2. The treatments with low water and low nitrogen had significantly lower net photosynthetic rates than W2N2. The stomatal conductance and transpiration rate changed in similar patterns. The net photosynthetic rate showed a unimodal trend with the increase of nitrogen application at the same irrigation level. Under the same nitrogen application level, the net photosynthetic rate increased first and then decreased slowly with the increase of irrigation amount, with the highest photosynthetic rates in the order of W2  > W3  > W1. The net photosynthetic rate was the highest, with a mean value was 13.87 μmol m−2 s−1, in treatment W2N2. The results showed that severe water stress and excessive nitrogen were not conducive to the absorption and utilization of water and nutrients by crop roots, which led to the decrease of the photosynthetic rate. The effect of water and nitrogen treatment on the intercellular CO2 concentration was significant (Fig. 1). Under the condition of excessive water or nitrogen, the photosynthesis of Isatis indigotica decreased, and the intercellular CO2 concentration showed a trend opposite to that of the net photosynthetic rate.Compared with N, P, and K deficiency treatments, water–N coupling could increase the Pn of crops, which was the same as that of other fruit trees and vegetables13. Accumulated photoassimilates in the third internode of the upper part of the main stems, as well as in the flag leaf sheath, are mobilized in a higher proportion and can contribute to grain filling in rice plants subjected to water stress in the tillering phase14. The Pn, Gs, and Tr of maize leaves at the seedling stage decreased significantly, while the Ci increased significantly when the nitrogen application rate was low15.The experiments with Isatis indigotica demonstrate that the Pn, Gs, and Tr under the same irrigation level first increased and then decreased with the increase of the nitrogen application rate. The net photosynthetic rate, transpiration rate, and stomatal conductance of Isatis indigotica were improved by rational nitrogen application. Studies have reported similar findings in Isatis indigotica; with the decrease of N level, the net photosynthetic rate, transpiration rate, and stomatal conductance of leaves gradually decreased, while the intercellular CO2 concentration increased16,17. Under reasonable water and nitrogen coordination conditions, the synergistic effect of water and nitrogen increased, which effectively promoted the photosynthesis of Isatis indigotica. Under the condition of too much nitrogen or too little water, the antagonism of water and nitrogen was obvious, and the photosynthesis of Isatis indigotica was inhibited to a certain extent.Yield and water use efficiencyThe Isatis indigotica yield values presented are the average of two consecutive years of water–nitrogen trials (Fig. 2). The I. indigotica yields differed significantly between the water–nitrogen treatments; the W2N2 and W2N3 treatments had the highest yields at 7277.5 and 6820.5 kg hm−2, respectively. The lowest yield of 3264.5 kg hm−2 was recorded in the control treatment. The yields of all treatments were significantly higher than that of the control treatment. The yields of the W2N2 and W2N3 treatments were significantly higher than those of the W1N1 and the W3N1 treatments. With the increase of the nitrogen application rate, the yield first increased and then decreased under the same irrigation conditions.The water use efficiency values of Isatis indigotica presented are the average of 2 consecutive years of water–nitrogen trials (Fig. 2). The water use efficiency of Isatis indigotica differed significantly between the water–nitrogen treatments; the W1N2 and W2N2 treatments had the highest yields at 20.78 and 19.63 kg mm−1 hm−2, respectively. The lowest yield of 13.65 kg mm−1 hm−2 was recorded in the W3N1 treatment. The water use efficiency values of the W1N2 and W2N2 treatments were significantly higher than that of the W3N3 treatment, which was the treatment with excess water and nitrogen fertilizer. The water use efficiency decreased with the increase of irrigation under the same nitrogen application conditions. The water use efficiency first increased and then decreased with the increase in nitrogen application rate under the same irrigation conditions. The W2N2 treatment had the highest yield and water use efficiency. Therefore, the water–nitrogen coupling mode of medium water and medium nitrogen application achieved the highest yield and effectively saved water. This was mainly due to the moderate water and nitrogen to promote the photosynthesis of Isatis indigotica and lead to more dry matter accumulation, so as to increase the yield.Generally, appropriate water deficits can improve crop yield and water use efficiency18,19, and rational fertilization can increase crop yield, such as in fruit trees and vegetables20,21,22. The yield increase in the current experiment was probably related to reasonable water stress and reasonable nitrogen application; the W2N2 treatment had the highest yield and water use efficiency. However, excessive water and nitrogen reduced the yield and water use efficiency of Isatis indigotica. This was consistent with recent research reports23,24. Compared with the local flooding irrigation and excessive nitrogen fertilizer mode, the W2N2 treatment with moderate water and nitrogen application not only obtained a high yield but also significantly improved the water use efficiency. This method could reduce the effect of excessive water and fertilizer application on soil productivity and would be a better water and nitrogen management model for local Isatis indigotica production.QualityThe Isatis indigotica quality values presented are the average of two consecutive years of water–nitrogen trials (Fig. 3). These quality indicators mainly include the following content indicators: indigo, indirubin, (R, S)-goitrin, and polysaccharides. The Isatis indigotica quality indicators differed significantly between the water–nitrogen treatments. The CK treatment had the highest values of all quality indicators. Each quality indicator decreased gradually with the increase of water content under the same nitrogen application conditions. Each quality indicator decreased gradually with the increase of nitrogen application under the same water conditions. The (R, S)-goitrin content of the W2N2 treatment decreased by 6.5% compared with CK and by 3.9% compared with the W1N1 treatment.Water is the medium for improving crop quality. Generally, the crop quality was improved by a suitable water deficit25,26,27 and reasonable fertilization28,29,30. The quality of Isatis indigotica in the current experiment increased gradually with the decrease of water. The water deficit treatment increased the content of effective components and improved the quality of Isatis indigotica. The content of the effective components in all treatments reached the pharmacopoeia standard12. The quality indicator values of each treatment in the current experiment were significantly lower than those of the CK treatment, but there was little difference in the quality indicator values between each treatment. Moreover, the yield of the control treatment was much lower than that of other treatments. Therefore, the effective quality content of the control treatment was lower than other treatments. Excessive water and nitrogen inputs were not conducive to quality, which was not consistent with recent research reports31. Generally, the water-nitrogen coupling type of W2N60 was antagonism basing on the average yield of winter wheat in the 10 years32. Some scholars have studied the irrigation of jujube that WUE and ANUE of jujube cannot reach the maximum at the same time. Different ratio of water and nitrogen will produce coupling and antagonism33. The results showed that total N applications over 200 kg ha−1 did not increase yield or quality. Water deficit treatment could be increased the content of effective components and improve the quality of Isatis indigotica. Due to the high evaporation, moderate water stress and effective use of nitrogen fertilizer, the active components of Isatis indigotica were easier to accumulate in its roots. The synergistic effect of water and nitrogen will lead to the accumulation of active components in Isatis indigotica. More

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