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Lattice data geoprocessing and temporal extentWe latticed the data49 using a worldwide grid composed of 18,874 hexagonal 7774 km2 units, built using Discrete Global for R (https://github.com/r-barnes/dggridR)50. All the information we processed on yellow fever cases, on urban and sylvatic vectors presences, and on zoogeographic, spatial and environmental variables (see details on this information below) was aggregated at this spatial resolution. We used zonal statistics to calculate average variable values using ArcMAP 10.7.The temporal extent for our analysis was divided into three periods: the late 20th century (1970–2000), the early 21st century (2001–2017), and the period 2018–2020. Predictions estimated by the late 20th century models were validated using cases reported in the early 21st century, and predictions from the early 21st century models were validated with records from 2018‒2020. Although the limit between periods at the turn of the century is arbitrary, it reflects: 1) Distributional changes in the ranges of the Ae. aegypti and Ae. albopictus vectors51; 2) after 1999, the yellow fever genotype I has spread outside the endemic regions, and the genotype I modern-lineage has caused all major yellow fever outbreaks detected in non-endemic regions of South America since 200013; 3) the maximum potential of globalization was realised at the beginning of the 21st century with the opening of international borders, the widespread access to the Internet and to cell phones, and the generalization of online travel booking and of low-cost flights34. The end of the second period, 2017, was chosen in order to include three years with occurrence of yellow fever cases in south-western Brazil (and two since its occurrence in Angola and the DRC), while retaining three later years for predictive testing purposes (details on this testing are given below).Yellow fever datasetsWe used georeferenced cases of yellow fever in humans for a period of 51 years (from 1970 to 2020). This study period starts immediately after the suspension of the use of DDT due to to the appearance of resistance of Ae. aegypti in the late 1960s in several countries, after 50 years of eradication efforts10. We took from Shearer et al.6 the distribution of yellow fever cases for the period 1970–2016. We extracted additional cases for the period 1970–2020 from various sources (Supplementary data 1), including ProMED-mail: Program of International society for infectious diseases; World Health Organization (WHO): Yellow fever outbreak weekly situation reports, Rapport de situation fievre jaune en RD Congo and Weekly epidemiological record; Health Ministry of different countries: Epidemiological Bulletins of yellow fever in Brazil, Peru, Colombia, and Paraguay; Pan American Health Organization (PAHO): Epidemiological Update Yellow Fever; European Centre for Disease Prevention and Control (ECDC): Communicable disease threats report and Rapid risk assessment report; Nigeria Centre for Disease Control (NCDC): Situation report, yellow fever outbreak in Nigeria and Global Infectious Disease and Epidemiology Online Network (GIDEON). The reported cases were complemented with publications available since 2016 with geo-referenced information on case location (Supplementary data 1). In addition, information was also sought on cases reported in French and Portuguese from local news reports in Africa.We only represented in the hexagonal lattice the reported cases of yellow fever that had a precise location or that were referred to administrative unit was smaller than or of similar size to the hexagons. This dataset was transformed into a binary variable per study period representing the presence (n = 218 hexagons in the late 20th century; 493 hexagons in the early 21st century, see Supplementary data 2) or absence (n = 18,656 hexagons in the late 20th century; 18,381 hexagons in the early 21st century), hereafter the distribution of reported cases of yellow fever.Vector datasetThe georeferenced presences of vectors involved in the urban cycle of yellow fever (i.e., the mosquitoes Ae. aegypti and Ae. albopictus) were taken from “The global compendium of the Ae. aegypti and Ae. Albopictus occurrence”26 for the period 1970–2014. We complemented these records with georeferenced data scientifically validated for the period 2014–2017, taken from VectorBase (https://www.vectorbase.org/) and Mosquito Alert (http://www.mosquitoalert.com/). We included both species because, although Ae. Aegypti is the main vector of yellow fever, Ae. albopictus can also transmit the yellow fever virus to humans4,52.In addition, we included georeferenced occurrence data of sylvatic vectors (Haemagogus janthinomys, H. leucocelaenus and Sabethes chloropterus in South America; Ae. africanus and Ae. vittatus in Africa), which were obtained from Vectormap (vectormap.si.edu) and Gbif (https://gbif.org).We represented in the hexagonal lattice the reported occurrence of mosquitoes that had a precise location or were located in administrative smaller than or of similar size to the hexagons. With this information, we built binary variables representing the presence or absence of each mosquito species in each hexagon. For species involved in the urban cycle, we built two binary variables per species: one for the late 20th century, and another for the early 21st century. For species involved in the sylvatic cycle, we merged the data of late 20th century and early 21st century in order to build a binary variable per species, due the scarcity of data and under the assumption that their distributions have been stable during the four last decades53,54,55.Zoogeographic, spatial and environmental variablesWe built zoogeographic variables based on chorotypes, or types of distribution ranges, of all non-human primate species, as all are potentially vulnerable to yellow fever56. A chorotype is a distribution pattern shared by a group of species57. For obtaining these zoogeographic variables, we proceeded in 4 steps: (1) Distribution maps of non-human primates were obtained from the IUCN for South-America and Africa; (2) the species ranges were classified hierarchically using the classification algorithm UPGMA according to the Baroni-Urbani & Buser´s similarity index58; (3) we evaluated the statistical significance of all clusters obtained as a result of the classification using RMacoqui 1.0 software (http://rmacoqui.r-forge.r-project.org/)59; (4) in each hexagon, the number of species belonging to each chorotype was quantified. We generated a zoogeographic model based on the non-human primates chorotypes by running a forward-backward stepwise logistic regression using presence/absence of yellow fever cases and the number of species of each chorotype as dependent and predictor variables, respectively. This procedure was made for two periods: late 20th century and early 21st century. Henceforth, only the selected chorotype variables were considered in the baseline disease favourability models explained below.We built a yellow fever spatial variable for each continent (South-America and Africa), which were calculated through the trend surface approach, by performing a backward-stepwise logistic regression of the distribution of yellow fever cases on a ensemble of variables defined for polynomial combinations of longitude (X) and latitude (Y) up to the third degree: X, Y, XY, X2, Y2, X2Y, XY2, X3, and Y3. We transformed probability values derived from logistic regression into spatial favourability values by applying the Favourability Function60,61, using the following equation:$$F=frac{P}{1-P}Big/left(frac{{n}_{1}}{{n}_{0}}+frac{P}{1-P}right)$$
(1)
where P is the spatial probability of occurrence of at least a case of yellow fever at each hexagon, and n1 and n0 are the numbers of hexagons with presence and absence of yellow fever cases, respectively. We built a different spatial variable for each continent and time period.We used environmental variables related to the following factors: climate, human activity, topography, hydrography, biome, ecosystem type, and forest loss. For details about the source and description of the environmental variables selected, see Supplementary Table 3.Pathogeographical approach to transmission risk modellingOur objectives were to construct a global yellow fever transmission risk map, and to identify areas where primates contribute to increased risk, using the methodology previously used to analyse the worldwide dynamic biogeography of zoonotic and anthroponotic dengue34 (see flowchart in Fig. 1 and Supplementary Methods). We produced a transmission model focused on the late 20th century and another for the early 21st century.The risk of transmission was assessed by combining a first model describing areas favourable to the presence of yellow fever, i.e., the “baseline disease model”; and another model describing areas favourable to the presence of mosquitoes known to act as vectors, i.e., the “vector model”. For this combination, we used the fuzzy intersection62, i.e., the risk of transmission at each hexagon was valued at the minimum between favourability in the baseline disease model and favourability in the vector model.In this way, we considered that the vectors are a limiting factor, and that the risk of transmission derives from the degree to which the environmental conditions are simultaneously favourable for the presence of vectors and for disease cases to occur63. In order to analyze the spatio-temporal dynamic of yellow fever, we made comparable models for the late 20th century and the early 21st century, using predictor variables that are available for both periods. Later, we made a 21st-century enhanced model that optimized the predictive capacity of availabe information in the search for current risk areas. For this purpose, we included, in the variable set, predictors that are only accessible for the 21st century (e.g., high-resolution population density, livestock, irrigation, infrastructures, intact forest, and GlobCover land cover classes; see Supplementary Table 3).Baseline disease modelsThe baseline disease model in the late 20th century was expressed in terms of favourability values, using the Eq. (1) (see above). This time, P was calculated through a multivariable forward-backward stepwise logistic regression of the 20th-century yellow fever presences/absences on a set of zoogeographic, environmental and spatial variables. This was made in two blocks: 1) a stepwise selection of environmental and spatial variables; 2) a later stepwise addition of chorotypes whose presence contribute to improve significantly the likelihood of the model based only on the first block. Variables for each block were preselected using RAO´s score tests (which estimated the significance of its association to the distribution of yellow fever cases), and Benjamini and Hochberg´s (1995) false discovery rate (FDR) to control for Type I errors, which could pass due to the number of variables analysed. We also avoided excesive multicollinearity by preventing that variables with Spearman correlation values >0.8 were included in the same model. In case this happened, only the variable with the most significant RAO´s score-test value was retained, and the multivariable model was re-run. The parameters in the models were estimated using a gradient ascent machine learning algorithm, and the significance of these paremeters was assessed using the test of Wald. The goodness of fit of the models was established using the test of Hosmer and Lemeshow, which checks the significance of the difference between expected and observed values, so that non significant differences mean that the fit is good. We used IBM-SPSS Statistics 24 software package to perform the models and all the associated tests.We subsequently updated the baseline disease model to explain the distribution of yellow fever cases in the early 21st century. Compared to the procedure described for the 20th-century model, we included a new block before the two ones mentioned above. Thus, the methodological sequence was as follows: (1) forcing the input, as a predictor variable, of the logit of the late 20th century baseline disease model (the logit being the linear combination of variables in the 20th-century model); (2) making a later stepwise selection of spatial and environmental variables; and (3) a stepwise addition of chorotypes that contribute to improving the model’s likelihood. In this way, we took into account that the current spread of yellow fever is influenced by the inertia of previous situations. This is equivalent to assuming that there is temporal autocorrelation (i.e., disease cases in the early 21st century are more probable to occur in areas where they already occurred in the late 20th century). In the 21st-century model, the variables entering in blocks (2) and (3) represent the drivers potentially favouring the spread34. The preselection of variables for blocks (2) and (3) and the control for excessive multicollinearity between environmental variables were made as explained for the late 20th-century model.Vector modelsWe produced a favourabuility model for each vector species for the late 20th century and for the early 21st century separately. We built multivariable favourability models for urban vectors using the distribution of each urban mosquito species in the late 20th century and the spatial and environmental variables for the late 20th century, following the same procedure used for block (1) in the 20th-century baseline disease model. We also updated each urban vector model for the early 21st century as in the baseline disease model, using the procedure described for blocks (1) and (2).A single model, referred to both the late 20th and the early 21st centuries, was made for sylvatic vectors, for the reasons explained above. Finally, we built up the vector models for the late 20th century and for the early 21st century by joining all individual vector models of each period using the fuzzy union64 (i.e., considering for each hexagon the maximum value shown by any of the species models). This criterion was taken into account because, if the pathogen were present, the occurrence of a single vector species would involve potential for yellow fever transmission.Model fit assessment and validation of its predictive capacityFavourability models were assessed according to their classification and discrimination capacities respect to the training data set (i.e., to the observations used for model training). The classification capacity was based on two classification thresholds: F = 0.5, which represents the neutral favourability, and F = 0.2, below which the risk of transmission was considered to be low61. Six classification assessment indices were used65: (1) sensitivity (i.e., proportion of presences correctly classified in favourable hexagons), (2) specificity (i.e., proportion of absences correctly classified in unfavourable hexagons), (3) CCR (i.e., proportion of presences and absences correctly classified in favourable hexagons respectively), (4) TSS (that is sensitivity + specifity – 1), (5) underprediction rate (i.e., proportion of favourable areas that are recorded to have presences), and (6) overprediction rate (i.e., proportion of favourable areas that are not recorded to have presences). The discrimination capacity was assessed using the area under the receiver operating characteristic (ROC) curve (AUC)66.The validation of the predictive capacity of the late 20th century disease and transmission-risk models was done by evaluating, with the same indices used above, classification and discrimination capacities with respect to the cases of the period 2001‒2020. The predictive capacity of the models for the early 21st century was validated with respect to the yellow fever cases reported in the period 2018‒2020.Relative importance of the zoogeographical factorWe estimated the pure contribution of non-human primates to the baseline disease model, i.e., how much of the variation in favourability for yellow fever cases was explained exclusively by the zoogeographical factor, by performing a variation partitioning analysis67. This implied the use of the zoogeographic model and a spatio-environmental model constructed with the environmental and spatial variables that entered the baseline disease model. This approach also allowed us to calculate how much is the variation of the baseline disease model attributable simultaneously to the zoogeographical and other factors. We built maps identifying the zones where the non-human primates could increase yellow fever cases in humans, that is, where the presence of primates could favour the occurrence of yellow fever regardless of correlations with other factors. To map these areas we identified the hexagons that fulfilled these conditions: 1) favourability values for the baseline disease model were ≥ 0.2; and 2) the difference between the favourability values provided by the baseline disease model and the spatio-environmental model was positive and ≥ 0.01.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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Species DataWe analyse long-term high-quality monitoring data on 1,478 species of birds, mammals, small rodents, butterflies, moths, forest understory vascular plants and freshwater phytoplankton sampled across 6,504 individual sites along an ~1,200 km latitudinal gradient in Finland. Because of differences in sampling methods and in spatial and temporal coverage, each dataset was analysed separately. We note that most species have a distributional range larger than Finland and that for the current purposes, niche space was estimated based on empirical data compiled within Finland alone.BirdsBird data have been collected using line transect censuses in Finland since the 1970s21. The data are collected yearly based on a one‐visit census in which birds are counted along transects with lengths typically 3–6 km. Transects are previously established (that is, with known locations) and not all transects are sampled every year. The census period is June, with observations typically carried between 3:00 and 9:00 am, when the singing activity of birds is highest in dry weather conditions. The observer walks alone at a speed of approximately 1 km h−1 depending on the density of birds along the transect using a map, compass or global positioning system. The census is carried out earlier in southern Finland (June 1–20) compared with northern Finland (June 10–30) due to later breeding phenology in northern latitudes. The line transect is divided into a main belt and a supplementary belt. The main belt is 50 m wide (25 m on each side of the transect line), and the supplementary belt represents the area beyond the main belt as far as birds can be detected. Every observation is assigned to either the main or the supplementary belt. Birds crossing the main belt belong to the supplementary belt even if first observed above the main belt. Species‐specific annual proportions of displaying birds and birds in the main belt remained stable between 1987–2010, indicating that there have been no major changes in species detectability36. The data are curated by the Finnish Museum of Natural History. We used records between 1978 and 2017, including a total of 189 species sampled in 1,105 transects after applying our selection criteria (‘Study design and data preparation’ below).MammalsA systematic monitoring programme of counts of mammal snow tracks was established in 1989 by the Natural Resources Institute Finland (Luke; Game triangle data37,38). The wildlife triangle scheme is based on a network of 4 + 4 + 4 km triangle-shaped transects (totalling 12 km per triangle) with fixed locations, covering the entire country. The triangles are located in forested areas covering the main forest types and are usually situated in hunting areas with the observations carried out by volunteers (mainly hunters). Around 2,000 triangles have been established and about half of these are counted annually. In the winter count, the transect is walked or skied during one day and all snow tracks of 24 mammal species crossing the count line are recorded, usually from mid-January to mid-March (when snow cover conditions are good). The number of crossings are typically related to the transect length and number of days since last snowfall, when snow tracks have been accumulating. Snowfall can be replaced with a pre-count, where the existing tracks are marked or erased, to be disregarded during the actual count. We used records between 1989 and 2017, including a total of 18 species sampled in 1,958 sites after applying our selection criteria (‘Study design and data preparation’ below).Small rodentsSince the 1960s, the Natural Resources Institute Finland (Luke) carries out an inventory of vole species to support forest management planning (small rodents data39). Data were collected biannually in spring (mid‐March to mid‐June) and autumn (mid‐August to mid‐October) in forested and field habitats in 34 locations throughout Finland. Individual trapping sites within locations were often not constant over the study period, primarily due to changes in land use. New sites were selected to be as close and as similar as possible to earlier sites regarding habitat characteristics. Trapping was conducted in two habitat types in almost all locations: spruce (Picea abies) or mountain birch (Betula pubescens) forests and in open grassland habitats, primarily old agricultural land no longer in use. We used records between 1978 and 2017, including a total of 15 species sampled in 19 sites after applying our selection criteria (‘Study design and data preparation’ below).ButterfliesWe combined two similar surveys of butterflies conducted in agricultural landscapes in Finland. The first is a butterfly monitoring network based on volunteer transects initiated by the Finnish Environment Institute (SYKE)40. Between 1999 and 2017, the network included 101 sites, with an average of 47 sites recorded annually (range 30–59). At each site, the walking route (transect) is kept constant from year to year and walked repeatedly during the summer. Along each transect, the number of individuals for each species is recorded from a 5 × 5 × 5 m3 cube ahead of the observer41. The transects are monitored by volunteer butterfly enthusiasts with high species identification skills, who are asked to conduct a minimum of seven annual visits per transect, approximately once a fortnight from late May to late August. Weekly counts are recommended and are usually carried out on nearly half of the transects. The sampling period is typically no longer than 16 weeks and less than ten weeks in the northernmost transects. The second survey type spans between 2001 and 2014 and consists of 68 standardized transects of 1 km length in southern Finland and the Åland islands. These transects were sampled by researchers with a constant sampling frequency of seven counts per summer42. The median transect length of the combined data is 1.95 km (mean = 2.41 km). We used records between 1999 and 2017, including a total of 68 species sampled in 98 transects after applying our selection criteria (‘Study design and data preparation’ below).MothsData on moths have been collected under the National Moth Monitoring scheme (Nocturna) between 1993 and 201743,44, which is coordinated by the Finnish Environment Institute (SYKE). Nocturnal moths were sampled using ‘Jalas’ light traps45 equipped with 125 W Hg vapour or 160 W mixed-light bulbs, located mainly in forested areas across Finland. Traps are located in the same location from year to year and are usually emptied weekly. Sampling occurred every night from early spring to late autumn (usually between April and October). Sampling effort (that is, trapping period) was constant across years for each trap, but given that sampling aimed to cover the entire moth activity period at each location, the trapping period was longer in more southern traps. Volunteers empty the traps and identify the specimens43, with a variable number of traps being sampled per year. The taxonomic skills of the volunteer lepidopterists were typically excellent, and data quality control and cross checking was carried out by the monitoring coordinators43,44,46. The data used here consist of species records collected from 65 traps with at least eight years of sampling. We used records between 1993 and 2017, including a total of 615 species after applying our selection criteria (‘Study design and data preparation’ below).Understory vascular plants of forestsUnderstory vegetation was surveyed on a systematic network of 1,700 sites established on mineral soil in forested land between 1985 and 1986 (as part of the 8th Finnish National Forest Inventory47). This network consists of clusters, each including four sites with 400 m intervals. The clusters were located 16 km apart from each other in southern Finland, and 24 km and 32 km apart in northern Finland along east–west and north–south axes, respectively. All 1,700 sites were resurveyed in 1995, and a subset of 443 sites were resurveyed in 2006. The spatial extent of sampling was comparable across surveys covering the whole country. In all three surveys, vascular plant species (dwarf shrubs, herbs, ferns and graminoids, including also tree and shrub seedlings and saplings up to 50 cm tall) were identified and species’ cover (0.1–100%) was visually estimated; this was based on three to six permanent square‐shaped sampling plots of 2 m2, located 5 m apart from each other within each site. The data are curated by the Natural Resources Institute Finland (Luke). For this analysis, we selected all sites with four sampling plots. The average of species cover across these four sampling plots is used as an estimate of species abundance at each site. This included occurrence records from 1,518, 1,673 and 443 sites in years 1985, 1995 and 2006, respectively. After applying the selection criteria (‘Study design and data preparation’ below), the data included a total of 109 species sampled in 1,712 sites.PhytoplanktonThe National Finnish Phytoplankton Monitoring Database maintained by the Finnish Environment Institute (SYKE; open data portal http://www.syke.fi/en-US/Open_information) comprises nationwide phytoplankton community data of lake surface water samples. We used data collected in the late summer months with samples taken during early July to late August, reflecting the peak productivity season of lake phytoplankton communities. To ensure consistent sampling methodology, we included only data between the years 1977 and 2017. All phytoplankton samples were preserved with acid Lugol’s solution and analysed using the standard Utermöhl technique48. We used records between 1978 and 2017, including a total of 464 species sampled in 1,544 sites after applying our selection criteria (‘Study design and data preparation’ below).Study design and data preparationBefore running the joint species distribution models (below), we converted abundance data into presence records. Each site was assigned to one of the four bioclimatic zones in Finland49—from south to north: hemiboreal (HB), southern boreal (SB), middle boreal (MB) and northern boreal (NB). We combined the two southernmost regions by pooling the occurrence records to obtain a better distribution and number of samples given the much smaller extent of the HB zone. Each occurrence record was also assigned to a different decade based on the year of sampling: decade 1 (1978–1987), decade 2 (1988–1997), decade 3 (1998–2007) and decade 4 (2008–2017) (Fig. 1). Scarce records before 1978 were excluded. Splitting the data into discrete zone and decade subsets allowed us to use independent (and computationally manageable) data to jointly model species responses within each taxonomic group and to disentangle any contrasting imprints of climatic changes between regions and periods. Each subset therefore covered a wide range of climatic conditions for each taxon, with the majority including ten years of data. While the number of sites varied over decades, zones and taxa, the change was not systematic, neither over time nor across taxonomic groups—that is, there was no consistent pattern of more sampling in later decades, and for each group, there could be more sampling sites in a given zone in a later or in an earlier decade (Supplementary Table S2). In addition, the frequency distribution of the pairwise distances between all sites remained similar across decades in each zone (Supplementary Fig. S4), suggesting no changes in the spatial aggregation of sites over time. Furthermore, our analyses are model based and thus explicitly account for the number and distribution of sampling sites, while making inference on both environmental covariates and spatial random effects50. Thus, the variation in the number and distribution of sampling sites affects the uncertainty on trend estimates, rather than affecting the estimates themselves.Species were included if they had a minimum of ten occurrences in each zone × decade combination. Finally, due to the difficulty of obtaining reliable model estimates from very sparse data, we set two additional criteria, including only data subsets with at least 20 samples and at least six species; this meant that despite data being available, some subsets were not included in the analyses (for instance, small rodents in NB).Environmental dataFor each site across the different taxonomic datasets and for each year sampled, we extracted values of daily mean temperature, daily precipitation sum and daily snow depth from the Finnish Meteorological Institute (https://etsin.fairdata.fi/datasets/fmi?keys=Finnish%20Meteorological%20Insitute&terms=organization_name_en.keyword&p=1&sort=best; first accessed in April 2019 and updated in May 2020). These datasets are part of the Finnish Meteorological Institute ClimGrid, which is a gridded daily climatology dataset of Finland, with a spatial resolution of 10 × 10 km 51. From these, we calculated values of annual mean temperature, total precipitation and number of days with snow cover. We extracted annual NAO values from the Climate Analysis Section, National Center for Atmospheric Research (NCAR), Boulder, Colorado, United States52. The NAO index is calculated based on surface sea level pressure difference between the Subtropical (Azores) High and the Subpolar (Iceland) Low, with a high index (NAO +) indicating cool summers and mild and wet winters, whereas low values (NAO −) indicate cold dry winters53. We explored whether other climatic variables might also be relevant for our analysis. Specifically, we additionally calculated January temperature, July temperature, temperature range, mean temperature standard deviation, temperature seasonality, growing degree days (over 5 °C), summer precipitation, precipitation range and mean snow depth. For calculating these additional variables, we extracted daily maximum and minimum temperature data from the ClimGrid data. We evaluated the correlation patterns among these variables and found they were highly correlated, particularly with annual values (Supplementary Fig. S5). As such, we included annual mean and summed values in our models because the relevance of the more detailed variables is likely to vary among taxa. Using annual values also facilitates comparisons with other studies and climate scenarios and allows overcoming issues regarding the overlap between some variables and seasonal sampling of the different species surveys.Quantifying climatic change patternsWe used two approaches to quantify changes in the different climatic variables. First, we used linear regressions with an interaction term between decade and bioclimatic zone to test whether changes over time differed between the different zones in our analysis framework. Second, for a more spatio-temporally resolved assessment of changing patterns we used the k-means clustering method to characterize regions of common climatic profiles for each variable considering all available data over space and time. We set k = 4, resulting in four groups of respectively similar variable conditions. Subsequently we calculated the mean and standard deviation of each resulting cluster for all variables and highlighted the average climate regimes over the whole latitudinal gradient and decades.Joint species distribution modellingWe used a joint species distribution modelling framework to (1) determine how the different climatic variables affected species occurrence patterns and (2) assess whether their relative importance in structuring assemblages has changed over time or across latitude. We fitted separate spatially explicit models for each combination of taxonomic group × bioclimatic zone × decade, yielding a total of 63 models. We modelled the probability of species presence in response to temperature, precipitation and snow cover with quadratic and to NAO with a linear function. Because we model presence data, we used probit regression models. Towards (1), we used the species responses to the climatic variables to quantify the proportion of species at the lower end of their niche (that is, occurrences increasing along the climatic gradient), at the upper end of their niche (that is, occurrences decreasing along the gradient) or at the optimum of their niche (that is, occurrences peaking within the gradient; Fig. 2b; ‘Scoring species’ position within niche domains’ below) within each bioclimatic zone and decade. Towards (2), we compared the proportion of explained variance attributed to each variable and examined whether their relative contribution shifted through time and/or space.For each taxon × bioclimatic zone × decade combination, we fitted latent-variable joint species distribution models using the Hierarchical Modelling of Species Communities (HMSC) framework. HMSC is a multi-variate Bayesian generalized linear mixed-effect model framework, which allows joint modelling of the responses of entire species assemblages and explicit modelling of spatial and temporal autocorrelation18,54,55. We used spatially structured latent variables which were originally proposed by Ovaskainen et al. 56. and later expanded to big spatial data by Tikhonov et al. 57. We fitted the models with the ‘Hmsc’ v 3.0.9 package55 in R58 with a probit link function and assuming the default prior distributions. As fixed effects, we included the climatic variables described above, estimating a second-order polynomial term for all covariates except for NAO, for which we estimated a linear term only. To account for variation in other (unmeasured) environmental variables and potential year-to-year variation not captured by the climatic covariates, we included the random effects of site and year, respectively. All models had the same structure for all the taxon × zone × decade subsets, except for the understory vegetation data for which we did not include the covariate NAO nor the random effect of year because these data were collected only in three individual years, corresponding to a single year per decade in our analytical framework (Fig. 1). Finally, due to computational bottlenecks for large data subsets, some model runs failed to complete with available resources; when this was the case, we randomly subsetted 1,000 records before re-fitting the models (specifically, bird and phytoplankton subsets for the last decade in SB and six mammal subsets for MB and SB in the second, third and fourth decades). We performed posterior sampling using four Markov Chain Monte Carlo chains, each collecting 250 samples, yielding a total of 1,000 samples. We used a thinning interval of 100 and excluded the first 12,500 iterations as burn-in, only sampling the subsequent 25,000 iterations per chain. For phytoplankton in the southernmost region in decade 4, we used a thinning of 10 due to computational constraints due to large site and species numbers. To evaluate Markov Chain Monte Carlo convergence, we examined the distribution of the potential scale reduction factor over the parameters related to the fixed effects and the random effects (equivalent to the Gelman-Rubin statistic59). We assessed model fit via the Area Under the Curve (AUC) statistic60 and model discriminatory power was quantified by Tjur’s R2, which is recommended as a standard measure of discriminatory power for binary outcomes61.To quantify shifts in the explanatory power associated with each covariate, we assessed variance component estimates, that is, the relative explanatory power of each environmental covariate in the HMSC models18,54. We estimated how the relative importance of the covariates in explaining species occurrences varied over time by fitting linear regression models to the species variance component estimate values as a function of decade (using the function ‘lm’ in R) and then compared these changes across zones for the different taxonomic groups (Fig. 4). These model comparisons were carried out after weighing the variance component values by each model’s ability to explain species occurrence patterns (that is, discriminatory power quantified using Tjur’s R2 values).Scoring species’ position within niche domainsTo analyse whether a species occurred at the lower end, at the optimum or at the upper end of its climatic niche within a particular bioclimatic zone and decade, we assessed the species’ responses to each of the climatic variables as follows. First, we classified a species as non-responsive to a specific climate variable within the measured range of that variable if the posterior distribution of the corresponding beta parameter estimates included zero with a probability of more than 10% (corresponding to having less than 90% posterior probability for the response). The non-zero responses were then classified as positive, negative or ‘bell-shaped’ based on the sign of the derivative of the response over the observed environmental gradient. A positive response corresponds to a species being at the lower end of its niche, ‘bell-shaped’ response corresponds to a species being at the optimum of its niche, and a negative response corresponds to a species being at the upper end of its niche. In cases where the derivative is positive/negative at both ends of the environmental gradient, responses were classified as either positive or negative, respectively. Cases where the derivative changed from positive to negative required subsequent evaluation. More specifically, if the derivative was positive or negative over less than 20% of the gradient, we classified the response as negative or positive, respectively. If the derivative was positive or negative over more than 80% of the gradient, we classified the response as positive or negative, respectively. Finally, if the derivative was positive or negative over at most 60% of the environmental gradient, we classified the response as bell-shaped. We evaluated whether this threshold affected the overall results by implementing the same classification using two other criteria for the derivatives being positive or negative: over less than 10% and more than 90% of the environmental gradient, and over less than 30% and more than 70% of the gradient. This showed that our classification of species’ responses was robust to these choices (Supplementary Fig. S6). This classification procedure did not apply to the beta parameters for NAO because we did not include a polynomial term for this covariate, as explained above. Thus, we obtained the number of species for each taxon × bioclimatic zone × decade model that showed responses to the different covariates and calculated the proportion of these species relative to the total number of species in each model (Fig. 3 and Extended Data Fig. 2).Comparing overall species composition between decadesWe compiled the species list present in each decade and each zone for the different taxonomic groups and compared these lists between consecutive decades, that is, comparing decades 1 and 2, 2 and 3, and 3 and 4. For each comparison, we noted how many species were present in both decades (‘shared’ = A), were present only in the first decade in the comparison (‘unique to earlier decade’ = C) or were present only in the last decade in the comparison (‘unique to later decade’ = B). We did this exercise for all taxa in all zones, plotting the sum of ‘shared’ and ‘unique species in each decade’ (Supplementary Fig. S2) and all the consecutive decade comparisons for each taxon (Supplementary Fig. S1). To quantify these patterns over a larger temporal extent, we implemented the same procedure but only comparing the first and last decades sampled for each taxon (Supplementary Figs. S1 and S2; note that for butterflies, these analyses are identical, because this taxon was sampled only in decades 3 and 4).Quantifying community dissimilarityTo assess how community composition changed over space and time, we calculated overall dissimilarity among all the sampling units within a given zone and decade—that is, we quantified variation in composition among sites within a given spatio-temporal extent, regardless of their location. Dissimilarity indices range between 0 and 1, representing cases where all or no species are shared between sites, respectively. We used the same occurrence matrices that were analysed with the HMSC models, that is, the raw species data matrices. We used the function ‘beta.sample’ in the ‘betapart’ package v 1.5.262,63 to calculate total dissimilarity (Sørensen index), which can be additively decomposed into the turnover (Simpson index) and nestedness components64. ‘beta.sample’ randomly selects a specified number of sites to generate distributions of the multiple‐site dissimilarity measures. This is important because the number of sites affects the estimated compositional change values. For each taxonomic group, we first determined the minimum number of sites among the different zone × decade combinations, which was used to define the number of sites to be randomly sampled from the original occurrence matrix, performing this subsampling 1,000 times. We then plotted the mean and standard deviation of these distributions to compare compositional change for each taxonomic group across the different zones and decades. We focus on the turnover metric (that is, species replacement among sites independent of changes in species richness; Extended Data Fig. 3), as it was systematically the main component of dissimilarity except for the small rodent data where the nestedness component had a relatively higher contribution to total dissimilarity. We show the results for the three metrics in Supplementary Fig. S3.Reporting SummaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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Experimental dataThe dataset used in this study is the global long-term air quality indicator data of 5577 regions from 2010 to 2014 extracted by Betancourt et al.14 based on the TOAR database (https://gitlab.jsc.fz-juelich.de/esde/machine-learning/aq-bench/-/blob/master/resources/AQbench_dataset.csv)29. As shown in Fig. 3, the monitoring sites include 15 regions, including EUR (Europe), NAM (North America), and EAS (East Asia), and are mainly distributed in NAM (North America), EUR (Europe) and EAS (East Asia). The dataset mainly includes the geographical location information of the monitoring site, such as longitude and latitude, the area to which it belongs, altitude, etc., and the site environment information, such as population density, night light intensity, and vegetation coverage. Since it is difficult to directly quantify factors such as the degree of industrial activity and the degree of human activity, environmental information such as the average light intensity at night and population density are used as proxy variables for the above factors. The ozone indicator records the hourly ozone concentration from air quality observation points in various regions and aggregates the collected ozone time series in units of one year into one indicator. Using a longer aggregation period can be used to average short-term weather fluctuations. The experimental data have a total of 35 input variables, including 4 categorical attributes and 31 continuous attributes. The predictor variable is the average ozone concentration in each region from 2010 to 2014. The specific variable names and descriptions14 are shown in the supplementary materials. A total of 4/5 of the total samples were used as the training set, and 1/5 were used as the test set.Figure 3Global distribution of monitoring sites.Full size imageResults of BO-XGBoost-RFEAccording to the XGBoost-RFE algorithm for feature selection, XGBoost-RFE combined with the cross-validation method is used to calculate the selected feature set in each RFE stage for fivefold cross-validation, and the mean absolute error (MAE) is used as the evaluation criterion to finally determine the number of features with the lowest mean absolute error (MAE). At the same time, the Bayesian optimization algorithm is used to adjust the hyper-parameters of XGBoost-RFE, and then the feature subset with the lowest cross-validation mean absolute error (MAE) is obtained. The main parameters of the XGBoost model in this article include the learning_rate, n_estimators, max_depth, gamma, reg_alpha, reg_lambda, colsample_bytree, and subsample. All parameters used in the model are shown in the supplementary material. Within the given parameter range, the Bayesian optimization algorithm is used, the mean absolute error (MAE) of the XGBoost-RFE fivefold cross-validation is used as the objective function, and the number of iterations is controlled to be 100. We obtained the hyperparameter combination corresponding to the lowest MAE and the corresponding optimal feature subset. The iterative process of Bayesian optimization is shown in Fig. 4.Figure 4Iterative process of Bayesian optimization.Full size imageThe parameter range and optimized value of XGBoost-RFE are shown in Table 1. The XGBoost-RFE feature selection results under the above optimized hyperparameters are shown in Fig. 5. The number of features in the feature subset with the lowest mean absolute error is 22, and the MAE is 2.410.Table 1 Main hyper-parameter range and optimized value.Full size tableFigure 5XGBoost-RFE feature selection results: Cross-validation MAE under optimal hyperparameter combination.Full size imageAdditionally, the XGBoost-RFE feature selection model without Bayesian optimization is compared with the algorithm in this study. The default parameters of the underlying model XGBoost are set to learning_rate as 0.3, max_depth as 6, gamma as 0, colsample_bytree as 1, subsample as 1, reg_alpha as 1, and reg_lambda as 0. The comparison results are shown in Table 2. The results show that the XGBoost-RFE cross-validation MAE without parameter tuning is larger than that of the algorithm in this study, and the dimension of the feature subset obtained is also higher than that of the algorithm in this study.Table 2 Comparison of MAE and feature num before and after BO.Full size tablePrediction resultsTo test the prediction accuracy of the prediction model with the optimal subset obtained by BO-XGBoost-RFE, three indexes, MAE, RMSE and R2, are used to evaluate the prediction results, and the expressions are as follows:$$begin{array}{*{20}c} {MAE = frac{1}{n}mathop sum limits_{i = 1}^{n} left| {left( {y_{i} – widehat{{y_{i} }}} right)} right|} \ end{array}$$
(8)
$$begin{array}{*{20}c} {RMSE = sqrt {frac{1}{n}mathop sum limits_{i = 1}^{n} left( {y_{i} – widehat{{y_{i} }}} right)^{2} } } \ end{array}$$
(9)
$$begin{array}{*{20}c} {R^{2} = 1 – frac{{mathop sum nolimits_{i = 1}^{n} left( {widehat{{y_{i} }} – y_{i} } right)^{2} }}{{mathop sum nolimits_{i = 1}^{n} left( {y_{i} – overline{{y_{i} }} } right)^{2} }}} \ end{array}$$
(10)
n indicates the number of samples, yi is the true value, (widehat{{y_{i} }}) is the predicted value and (overline{{y_{i} }}) indicates the mean value of the predicted value.The XGBoost-RFE feature selection algorithm based on Bayesian optimization in this study is compared with feature selection using full features and features selected by the Pearson correlation coefficient, which measures the correlation between two variables. In this study, the correlation with predictor variables was selected to be less than 0.1, and the variables with correlations greater than 0.9 were deleted to avoid multicollinearity.XGBoost, random forest, support vector regression machine, and KNN algorithms were used to predict ozone concentration with full features, features selected by Pearson’s correlation coefficient, and features based on BO-XGBoost-RFE. According to the evaluation indicators described above, the comparison of the prediction performance results of the three algorithms before and after dimensionality reduction can be obtained. The MAE, RMSE and R2 results of each prediction model are shown in Table 3.Table 3 MAE, RMSE and R2 of each prediction model.Full size tableAmong the four prediction models, random forest has the lowest MAE and RMSE and the highest R2 based on three different dimensions of data and therefore has the best prediction performance. The prediction accuracy of all four prediction models based on Pearson correlation is lower than that based on BO-XGBoost-RFE, indicating that only selecting features by correlation cannot accurately extract important variables. Although the RMSE of the support vector regression model based on BO-XGBoost-RFE is slightly lower than the RMSE based on full features, the prediction accuracy of XGBoost, RF, KNN after feature selection of BO-XGBoost-RFE is higher than that based on full features and Pearson correlation. Among the four prediction models, random forest has obtained the highest prediction accuracy. The MAE based on BO-XGBoost-RFE is 5.0% and 1.4% lower than that based on the Pearson correlation coefficient and the full-feature-based model, and the RMSE is reduced by 5.1%, 1.8%, R2 improved by 4.3%, 1.4%. Additionally, the XGBoost model achieved the greatest improvement in accuracy. The MAE was reduced by 5.9% and 1.7%, the RMSE was reduced by 5.2% and 1.7%, and the R2 was improved by 4.9% and 1.4% compared with the Pearson correlation coefficient-based and full-feature-based models, respectively. This indicates that feature selection based on BO-XGBoost-RFE effectively extracts important features, improves prediction accuracy based on multiple prediction models, and has better dimensionality reduction performance.Figure 6 shows the importance of each feature obtained by using the random forest prediction model, reflecting the degree of influence of each variable on the prediction results of the global multi-year average near-ground ozone concentration. The most important variables that affect the prediction results according to the ranking of feature importance are altitude, relative altitude, and latitude, followed by night light intensity within a radius of 5 km, population density and nitrogen dioxide concentration, while the proxy variables for vegetation cover have a relatively weak effect on the prediction of ozone concentration.Figure 6Feature importance in random forest.Full size image More