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Each sedimentary sequence from the three excavated ponds (Tampolove [TAMP], Ankatoke [ANKA], and Andranobe [ANDR]) includes a layer of clay (defined as zone 2), which separates the surface soil formation (zone 1) from the underlying fossiliferous muddy sand and bedrock (zone 3, Figs. S4–S7 & S9). Details regarding the composition of this sediment and its microfossils are given in Appendix-Results-Excavation (Figs. S9–S12).Subfossils and chronologyCoastal survey recovered mostly zebu bones on exposed sandy surfaces, some pygmy hippo and giant tortoise bones on the margins of shallow ponds, and giant tortoise carapace under overhanging limestone outcrops (Appendix-Results-Survey, Fig. S3). A high proportion of surface bone failed 14C analysis (~ 55%, Table S1), yet the successfully analyzed specimens (n = 8) span up to 3390–3220 calibrated years before present (cal BP, PSUAMS 8681, 3150 ± 15 14C BP, a hippo molar). Pond deposits that are relatively deep include bones that cover a relatively long period of time (Figs. S14–S16, Dataset S6). This span ranges from ~ 6000 years at TAMP (~ 120 cm deep) to ~ 2500 years at ANDR (~ 100 cm deep), with the oldest bones present in the fossiliferous sedimentary zone 3 and scarce bones in the overlying clay (zone 2).Zone 3Most bones in this layer are relatively intact and include readily identifiable pygmy hippo long bones and cranial fragments (e.g., Fig. S13a,f), giant tortoise carapace and plastron fragments (Fig. S13d), ratite eggshell and long bones (Fig. S13c,m), and crocodile scutes, cranial fragments, and teeth (Fig. S13b). Scarce bones of a duck (genus Anas) were recovered at ANDR. Remains of subfossil lemurs were scarce or absent, but they may be represented by an unknown type of bone fragment identified through protein fingerprinting (ANDR-1-5-55, Dataset S3). The widespread success of collagen extraction from these bones attests to the excellent preservation of organics in this zone. ANKA also includes keratin (mostly in the form of crocodile claws, e.g., Fig. S13i), as well as two rounded agates found associated with ratite eggshell (Fig. S13m).Remains of a juvenile pygmy hippo were recovered from both TAMP and ANDR (a femur and tibia, respectively, Dataset S3). The epiphyses of some of the pygmy hippo long bones have gnaw marks (Fig. S13f), and none of the bones include chop marks. In association with these bones towards the top of this zone are some large ( > 1 cm diameter) charcoal fragments and scarce bones of bushpig (Fig. S13k) and zebu (Fig. S13e). Protein fingerprinting identified a screened fragment of a non-zebu bovid in ANKA zone 3 and confirmed that a tentatively identified bushpig canine fragment (ANKA 1-4-151) belonged to a hippo. This zone at TAMP and ANDR also includes occasional mangrove whelk (Terebralia palustris) shells (Fig. S13g). These whelks currently live at least ~ 500 m distant from these ponds, and whelk shells at ANDR each have an irregular hole above the operculum.The span of time represented by bones in zone 3 ranges up to ~ 4000 years (~ 6000–2000 cal BP at TAMP, Fig. S14). Confirmed introduced animal bones from zone 3 failed direct 14C analysis. There are multiple examples of directly 14C-dated bone in close stratigraphic association that nonetheless differ in age by  > 1000 years, and there are a couple of examples of bones from the same individual that are separated stratigraphically. For example, two giant tortoise carapace and plastron fragments from TAMP that have indistinguishable 14C ages are separated by 22 cm of sediment (PSUAMS 8670 comes from 112 cm depth, and PSUAMS 8668 comes from 90 cm depth).Although ANKA produced what is thus far the oldest directly 14C dated pygmy hippo bone from a coastal subfossil site (PSUAMS 9383, 4380 ± 25 BP, 5030–4840 cal BP), the mean calibrated age of hippos from the Tampolove excavations (n = 11, x̄ = 2858 cal BP, SD = 972 yr) is significantly less than that of the giant tortoises (n = 9, x̄ = 4582 cal BP, SD = 705 yr, t(18) = − 4.4, p  2000 years older than a closely associated charcoal sample (38 cm depth, PSUAMS 8849, 575 ± 30 14C BP, 630–510 cal BP), which makes this molar comparable in age to bone from zone 3. Consequently, the youngest directly 14C-dated ancient bone from the Tampolove excavations comes from the lowermost zone 3: a pygmy hippo’s vertebra recovered at 90 cm depth at TAMP (PSUAMS 8730, 1865 ± 15 14C BP, 1819–1705 cal BP). Though poorly constrained in time, the deposition of zone 2 sediment came sometime within the past two millennia, which witnessed marine regression and dry intervals recorded in both the δ18O record of a nearby speleothem27 and the salinization of a nearby pan36. Previously directly 14C-dated bone collected around Tampolove attests to the local persistence of at least pygmy hippos and giant tortoises until the start of the last millennium (n = 15), and an atlas from Lamboara/Lamboharana is in fact the most recent confidently dated pygmy hippo bone from the island (PSUAMS 5629, 1100 ± 15 14C BP, 980–930 cal BP).Figure 4Cutmarked pygmy hippo femur recovered from Tampolove during recent excavation at ~ 40 cm depth (TAMP-1-2-61, above), and previously-recovered and directly 14C-dated (~ 3500 and 1600 cal BP37) cutmarked pygmy hippo femora from the nearby site of Lamboara/Lamboharana that are currently housed in the National Museum of Natural History in Paris (MAD 1709 & MAD 1710, below). Four views highlight three locations of cutmarks on the broken shaft of TAMP-1-2-61, and the inset frames show 20 × magnification of these areas, with corresponding orientations given by red lines. Note that the false color insets of TAMP-1-2-61 are meant to highlight linear edges and crevices, and the overview photos of all three femur fragments are on the same scale.Full size imageZone 1A fragment of iron (from TAMP, 16 cm depth) and sparse ceramic fragments (from ANKA, 3 & 9 cm depth) are present only in zone 1, and three 14C dates from TAMP and ANKA suggest that these specimens span the past ~ 200 years (Figs. S14–S15).CharcoalThe directly 14C dated charcoal spans all three stratigraphic zones yet consistently dates to the past millennium (Figs. S14–16). Multiple charcoal samples from different excavated ponds have practically indistinguishable 14C ages (Table S2), and much of the charcoal from Tampolove formed during peaks in the deposition of macrocharcoal at nearby Namonte (17 km distant; Fig. 5A). The onset of directly 14C-dated charcoal deposition approximately coincides with a decrease in Asafora speleothem δ18O values and with multiple directly 14C-dated first and final local occurrences of large animals. While directly 14C dated charcoal is limited to the past millennium, microcharcoal particles were abundant in all TAMP sediment samples (x̄ ± SD = 2.0 × 106 ± 2.8 × 106 particles). Additionally, microcharcoal is relatively abundant near the bottom of TAMP and ANKA, which contains bones that span ~ 6000–2000 cal BP (Fig. 5B).Figure 5Records of fire, drought, and faunal turnover from the vicinity of Tampolove within the past 1200 years, with dashed horizontal lines for reference (5A), and macrocharcoal concentrations from the excavated ponds, with depth intervals containing directly 14C-dated charcoal that spans the past millennium marked in red (5B). The past 1200 years includes the entire summed calibrated distribution of the 10 directly dated prebomb charcoal fragments from the Tampolove excavations. The calibrated probability distributions associated with the latest dates from endemic megafauna bone (giant tortoises and pygmy hippos) and earliest dates from introduced animal bone (zebu cattle and bushpigs) are shown as black distributions, and 95% of each distribution is bracketed. Considering directly dated remains within the past 4 ka from hippos (n = 26), giant tortoises (n = 18), and zebu (n = 9) and the assumption that bones were deposited uniformly over time, the grey distributions and bracketed 95% credible intervals give estimates of extirpation and arrival times. As in Fig. 3, the red line on the Asafora record follows from BCPA.Full size image More

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Data sourcesWe analyzed records of confirmed and suspected livestock deaths attributed to anthrax occurring from 1 January 2006 to 31 December 2020 across Kenya (available online along with full code for the analysis in this paper https://github.com/spatialmodels/Kenyan_anthrax_model). The case records covering the entire country were reported from the Kenya Directorate of Veterinary Services (KDVS) located in Nairobi and the five Regional Veterinary Investigation Laboratories located in Nakuru, Eldoret, Karatina, Kericho, and Mariakani. The anthrax outbreaks were considered as any livestock (cattle, goats, sheep, pigs, camels) or wildlife deaths confirmed through clinical and laboratory diagnosis. Clinical diagnosis was defined as an acute disease accompanied by sudden death, bleeding from body orifices, swelling, lack of rigor mortis, and oedema of the neck and face in pigs. Laboratory confirmation was done through methylene blue staining to identify the characteristic bacterial capsule and the rod-shaped bacilli in clinical specimens collected from the infected carcasses.We extracted data from old paper records of livestock anthrax cases into Microsoft Excel. These records comprised the location of the livestock outbreaks, name of the farmer, number of animals dead and herd size, species affected, date, method of diagnosis, and the details of the reporting veterinary doctor. Since the locations of livestock anthrax outbreaks were reported at sub-county/district levels (districts refer to the old naming given to current sub-counties before the rollout of the current constitution), we recorded the geographic coordinates of livestock cases at the district level. During data cleaning, we removed duplicate coordinates, outliers, and entries with missing variables. In the end, we had 540 livestock cases that we used for analysis. The spatial granularity and prolonged surveillance period of these data allow for a more detailed perspective on the major drivers of anthrax across Kenya. We also collected wildlife data from the Kenya Wildlife Service (KWS). Most of the data from KWS was lacking information on the geographic coordinates of the outbreaks, so we visited the actual locations and collected the coordinates. We recorded 20 wildlife cases that we used to validate the performance of the spatial model.Processing socio-economic and ecological covariatesWe gathered geospatial data on ecological and socio-economic correlates of B. anthracis ecology and distribution. For the spatial model, we obtained the following variables: rainfall, vegetation, elevation, distance to permanent water bodies, and soil patterns. For the spatiotemporal models, we used human population estimates (total population, population density, and male and female population per sub-county), host population (livestock producing households, total number of indigenous, exotic dairy, and exotic beef cattle per sub-county), and agricultural practices that lead to soil disturbance (agricultural area under cultivation, number of farming households, and crop-producing households).We chose seven environmental covariates for the spatial model based on known correlates of B. anthracis suitability identified from previous peer-reviewed studies9,10,13,15,21,22,23. These comprised three soil variables, including soil pH (× 10) in H2O at a depth of 0 cm, exchangeable calcium at a depth of 0–20 cm, and soil water availability (volume of water per unit volume of soil) retrieved at a resolution of 250 m from the International Soil Reference and Information Centre (ISRIC) data hub (https://data.isric.org/geonetwork/srv/eng/catalog.search#/home). We used the shallowest depth available because although the bacterial spores can persist in the surface soil for up to five years and indefinitely in much deeper soils24, the spores in the surface soils are more likely to trigger host infection25. We retrieved monthly Enhanced Vegetation Index (EVI) data from 1 January 2006 to 31 December 2020 (180 tiles in total) from The Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Indices (MYD13A3 v.6) at a resolution of 1 km2 (https://lpdaac.usgs.gov/products/myd13a3v006/). The mean EVI was then calculated using QGIS by averaging all 180 tiles. EVI reduces variations in the canopy background and retains precision over dense vegetation conditions. Monthly Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) rainfall data from rain gauge and satellite observations was retrieved from the United States Geological Service (USGS) at a resolution of 0.05 degrees (https://climateserv.servirglobal.net/map). Since the rainfall data also comprised 180 tiles, the mean rainfall was calculated by averaging all 180 tiles using QGIS. We also collected data on the distance to permanent water bodies from a global hydrology map obtained from ArcGIS version 10.6.1.26 and elevation data at 1 km2 resolution from the Global Multi-resolution Terrain Elevation Data (GMTED2010) dataset available from USGS (Table 1).Table 1 Summary of the environmental variables used in the spatial model including variable name, unit, and spatial resolution.Full size tableFor the spatiotemporal sub-county-based models, we accessed the population data per sub-county (total population, male population, female population, and population density) from the 2019 Kenyan census report provided via the Humanitarian Data Exchange platform (https://data.humdata.org/dataset/kenya-population-per-county-from-census-report-2019). We also obtained data on livestock population (numbers of exotic dairy and beef cattle, and indigenous cattle), area of agricultural land in hectares, number of farming households, and the number of households actively practicing agriculture (crop production and livestock production) aggregated to the sub-county level from the 2019 Kenya Population and Housing Census volume IV provided by the OpenAfrica platform (https://open.africa/dataset/2019-kenya-population-and-housing-census).We conducted data exploration to check for outliers, collinearity, and the relationships between the covariates and the response variables. We used Cleveland dot plots to check for outliers. We measured collinearity using variance inflation factors (VIF), Pearson correlation coefficients, and pairs plots. For VIF scores, the covariates with scores higher than 3 were eliminated one-by-one until all the scores were equal to or less than 3. All the covariates included in the study had correlation coefficient values of less than 0.6 (Figs. 1, 2).Figure 1Results of correlation between covariates using Pearson’s correlation coefficient test for the spatial model. Correlation between covariates is shown by red numbers (negative correlation) and blue numbers (positive correlation). Correlations with a p-value  > 0.01 are regarded as insignificant and the correlation coefficient values are left blank. The figure was generated using R software v. 4.1.028.Full size imageFigure 2Results of correlation between covariates using Pearson’s correlation coefficient test for the spatiotemporal model. Correlation between covariates is shown by red numbers (negative correlation) and blue numbers (positive correlation). Correlations with a p-value  > 0.01 are regarded as insignificant and the correlation coefficient values are left blank. The figure was generated using R software v. 4.1.028.Full size imageSpatial model analysisWe used R version 4.1.0 together with the packages raster version 4.1.127, and R-INLA version 4.1.128 to conduct the data processing and statistical modelling. The R-INLA package applies the INLA framework in designing models. We used Quantum Global Information System (QGIS) version 3.16 (https://qgis.org) to create a 50 km buffer polygon around all the observed livestock outbreak points. We then created a 20 km2 grid within this buffer and counted the number of points within each grid cell to create a regular lattice with a given number of counts per cell. We then extracted the coordinates of the centroids of each cell to create marked locations with a given number of livestock cases per location. We essentially converted the data into a count process (number of livestock outbreaks per location). We had 95 cells with one or more counts which formed our new presence locations. We then randomly selected 95 pseudoabsences within the 50 km buffer polygon but at a distance of 10 km from the presence locations as shown in Fig. 3.Figure 3Spatial distribution of thinned livestock anthrax case locations across Kenya from 2006 to 2020. The map shows livestock anthrax case locations (n = 540) thinned to pixels of 20 km2 to form 95 new marked locations. The orange dots show the new presence locations which are marked points with colour intensity representing the number of livestock cases per location. The white triangles show the random pseudo-absence locations. The yellow squares are the wildlife cases obtained from the Kenya Wildlife Service. The green polygon is the background calibration buffer used to derive the random pseudo-absence locations. This map was generated using Quantum Geographical Information Systems (QGIS) v. 3.16.11 (https://www.qgis.org/en/site/forusers/download.html).Full size imageWe defined a Zero-inflated Poisson (ZIP) regression model with spatially correlated random effects, implemented as a generalized additive model (GAM) with anthrax incidence as the response variable. The model is defined as shown in Eqs. (1), (2), and (3)$${C}_{i} sim zero-inflated, Poisson left({mu }_{i},{p}_{i}right),$$
(1)
$$expectedleft({C}_{i}right)=left(1- {p}_{i}right)times {mu }_{i},$$
(2)
$$mathrm{log}left({mu }_{i}right)= alpha + sum_{j}{beta }_{j}{X}_{j,i}+ sum_{k}{delta }_{k,i}+{u}_{i},$$
(3)
where (Ci) denotes the observed number of anthrax livestock cases at location i, ({mu }_{i}) and ({p}_{i}) are parameters of the ZIP distribution. (expectedleft({C}_{i}right)) refers to the expected number of outbreaks at location i, (alpha) is the intercept, (beta) are the beta coefficients for the covariates, X is the matrix with all the covariates, (delta k) are the non-linear effects (cubic regression splines), and ({u}_{i}) is the spatial random effect at location i.To test whether the addition of the GAM smoothers and the spatially correlated random effects improved the fit of the model, we also considered candidate models without smoothers and spatial random effects. We tested three versions of the spatial model: the first used distance to water, elevation, and EVI as linear covariates without spatial random effects, the second applied non-linear terms to elevation and EVI also without spatial random effects, and the final model was similar to the second model but with the addition of spatial random effects. We then measured the DIC values of the candidate models to select the final spatial model.We conducted model validation by assessing the posterior distributions of the parameters and the residuals for adherence to the distributional assumptions. We checked whether the residuals were independent and normally distributed. We also plotted a sample variogram to check for any residual spatial auto-correlation using a well-defined method29. We then ran 1000 simulations to check whether the model was capable of handling zeros.The estimated model was used to map posterior predicted distributions for the incidence of anthrax disease (plotted as mean and 95% credible intervals). We validated the model using independent evaluation data withheld from the model calibration. This evaluation dataset comprises the wildlife cases collected from KWS. We then calculated the sensitivity by estimating the proportion of wildlife case locations correctly identified by the model, using the minimum presence training threshold (minimum value of the fitted presence training points).Spatiotemporal model analysisOur second objective was to investigate the socio-economic, population-based drivers of livestock anthrax risk at the sub-county level. These socioeconomic variables are usually collected at the sub-county level. Therefore, we developed a second areal model with the number of observations per sub-county as the new response variable. The occurrence data, gathered by the Kenya Directorate for Veterinary Services (KDVS), consisted of monthly case reports of livestock anthrax cases collected by all 290 sub-counties across Kenya between January 2006 to December 2020. We analyzed the whole monthly case time series from the year 2006 to 2020 and mapped out the annual counts of confirmed and suspected livestock anthrax cases across Kenya at the sub-county level to analyse the spatial and temporal trends throughout the surveillance period. The sub-county shapefiles that were used for mapping and modelling were derived from Humanitarian Data Exchange version 1.57.16 under a Creative Commons Attribution for Intergovernmental Organisations license (https://data.humdata.org/dataset/ken-administrative-boundaries).Due to the sparsity of data, we aggregated the monthly case counts and modelled the quarterly occurrence and incidence of anthrax at the sub-county-level scale, including spatial and temporal effects, to determine the spatial socio-economic drivers of livestock anthrax disease risk across Kenya. We used R-INLA version 4.1.1 (26) to conduct the data processing and statistical modelling. We used quarterly case counts that were confirmed per sub-county across the 15 years of surveillance (2006–2020) as a measure of anthrax incidence. Due to the zero-inflated and over-dispersed nature of the distribution, which is difficult to fit incidence counts, we employed a two-stage modelling approach using the hurdle model distribution to separately model anthrax occurrence (presence or absence) across all sub-counties via logistic regression, and incidence counts using a zero-inflated Poisson distribution. We were then able separately to estimate the contributions of the various socio-ecological factors that drive disease occurrence (the presence or absence of anthrax) and total incidence counts.We model the quarterly anthrax occurrence (n = 290 sub-counties over 60 quarters; 17,400 observations) where ({Y}_{i,t}) refers to the binary presence (denoted as 1) or absence (denoted as 0) of anthrax in sub-county i during year t, and ({P}_{i,t}) is the probability of anthrax occurrence, thus:$${Y}_{i,t} sim Bernoullileft({P}_{i,t}right).$$
(4)
We model quarterly anthrax incidence counts ({C}_{i,t}) using a zero-inflated Poisson process with parameters ({mu }_{i,t}) and ({p}_{i,t}) (see Eq. (5)). Equation (6) denotes the expected values for the ZIP distribution at sub-county i during year t.$${C}_{i,t} sim Zero-inflated, Poisson left({mu }_{i,t},{p}_{i,t}right),$$
(5)
$$expectedleft({C}_{i,t}right)=left(1- {p}_{i,t}right)times {mu }_{i,t}.$$
(6)
Both the Bernoulli and the ZIP distributions are modelled separately as functions of the covariates and the spatial and temporal random effects using a general linear predictor as shown in Eqs. (7) and (8):$$logit left({P}_{i,t}right)= alpha + sum_{j}{beta }_{j}{X}_{j,i}+{u}_{i,t}+{v}_{i,t}+{y}_{i,t},$$
(7)
$$mathrm{log}left({mu }_{i,t}right)= alpha + sum_{j}{beta }_{j}{X}_{j,i}+{u}_{i,t}+{v}_{i,t}+{y}_{i,t},$$
(8)
$${y}_{i,t}= {y}_{i,t-1}+ {w}_{i,t},$$
(9)
where α denotes the intercept; (X) signifies a matrix made up of the socio-economic covariates accompanied by their linear coefficients denoted as (beta); spatiotemporal reporting trends at the sub-county level were accounted for in the models using spatially structured (({u}_{i,t}); conditional autoregressive) and unstructured noise (({v}_{i,t}); i.i.d—independent and identically distributed) random-effects specified jointly as a Besag–York–Mollie model30,31, as well as temporally structured (({y}_{i,t})) random effects of the first order where ({w}_{i,t}) is a pure noise term that is normally distribute with a mean of zero and a variance of σ2. We used uninformative priors with a Gaussian distribution for the fixed effects and penalized complexity priors for the hyperparameters of all the random effects.For the two spatiotemporal models, we applied linear effects for all the variables: population density, total population, number of exotic dairy cattle, agricultural land area, and number of livestock producing households. We scaled the continuous covariates by standardizing them (to a mean of 0 and standard deviation of 1) before fitting the linear fixed effects.We used R-INLA to conduct model inference and selection and used DIC to evaluate the model fit for both the occurrence and incidence models. For both models (occurrence and incidence), we created 4 candidate models, compared them, and selected the model with the lowest DIC as the final model. The candidate models included: a baseline intercept only model; a second model with the intercept and covariates; a third model with the intercept, covariates, and the spatial random effects; and a fourth model with the intercept, covariates, spatial random effects, and a temporal trend.We evaluated the posterior distributions of the parameters and the residuals for adherence to the distributional assumptions. We assessed the residuals to check whether they were independent and normally distributed. We also plotted the residuals against the covariates to check for any non-linear patterns using a well-defined method29. We then ran 1000 simulations to check whether the model was capable of handling zeros.Ethics statementLicence to conduct the research was granted by the National Council for Science, Technology, and Innovation (NACOSTI) under reference number 651983, and the Kenya Wildlife Service under reference number KWS-0003-01-21. More

We used a hierarchical Bayesian modeling approach to evaluate the relationship between the spring phenology of tree and wildflower species and various climate drivers (see Methods). Following model selection, our final model structure included fixed effects of average spring (March–April) temperature and elevation, as well as species-level random effects. We show continental distributions of spring temperature values in Fig. 1b (means and standard deviations are listed in Table S2). We report estimates for spring temperature sensitivities from the final model structure in the main text. Parameter estimates for elevation sensitivities as well as the model performance of other potential drivers and combinations of drivers are reported in Tables S3 and S4. An extended discussion of model assumptions and limitations is included in the Supplementary Information.Sensitivity differences by strataTree leaf out phenology (LOD) was substantially more sensitive to average spring temperature in North America (mean = −3.62 days °C−1; 95% credible interval (CI) = [−3.76, −3.49]) than in Europe (mean = −2.79; CI = [−3.27, −2.30]) and Asia (mean = −2.62; CI = [−2.97, −2.26]; Fig. 2). These values are consistent with previously reported phenological sensitivities in North America7 (−5.5 to −3.3 days °C−1) and Europe8 (−4.1 to −3.0 days °C−1), as the credible intervals from our results overlap with the reported credible intervals of prior studies. However, the Asian LOD sensitivity was less sensitive than previously reported27 (−3.50 to −3.03 days °C−1), potentially owing to differences in species selection28 or model structure. Previously reported sensitivities were determined in separate studies using either observational data7,8 or long-term observation-based weather station data27. The general consistency between our findings suggests that phenology data from herbarium collections are good indicators of patterns in natural systems29,30,31, a point supported by a recent study of phenological sensitivity derived from herbaria and from observed citizen science data32. These herbarium-based results provide evidence that phenological sensitivity differs across the temperate forest biome (but see ref. 33 for evidence of differences in response to warming and chilling accumulation). To our knowledge, our study is the first to contrast overstory and understory phenology across multiple continents and, therefore, to find differences in phenological sensitivity between trees and forest wildflowers across continents. We recommend future studies explore these differences using alternative approaches and methodologies that focus on the physiological basis for and mechanisms that underlie these patterns.Fig. 2: Posterior estimated means and 95% credible intervals for spring temperature sensitivity.Shapes represent parameter estimates for wildflower First Flower Date (FFD, blue circles; n = 1418, 618, and 1060 for Asia, Europe, and North America, respectively) and canopy tree Leaf Out Date (LOD, yellow triangles; n = 899, 532, and 995, for Asia, Europe, and North America, respectively). Estimates are considered different from 0 if credible intervals do not overlap the dashed 0 line and are considered different from each other if credible intervals do not overlap.Full size imageIn contrast to trees, wildflower sensitivity to spring temperature was similar across all three continents and exhibited no strong differences (i.e., overlap in 95% Bayesian credible intervals) among continents (means and 95% credible intervals in brackets: North America = −3.14, [−3.28, −3.00]; Europe = −3.02, [−3.48, −2.56]; Asia = −3.12, [−3.36, −2.86]; Fig. 2). These values are also generally consistent with those reported elsewhere in the literature (i.e., 95% credible intervals overlap with those reported in other studies; −2.2, [−3.7, −0.76] days °C−1 in North America7 and −3.6, [−4.04, −3.18] days °C−1 in Europe9), although we are unaware of any studies that have estimated phenological sensitivity for Asian forest wildflowers in days °C−1. Ge et al.3 report herbaceous plant sensitivity of −5.71 days per decade in Asia (±7.90 standard deviation; based primarily on long-term observational data), which appears to be roughly consistent with our model results, but the difference in units makes this more speculative than the other comparisons. Discrepancies in mean responses between this study and others may be due in part to different types of data (herbarium specimens versus field observations) and to choice in focal taxa, as temperature sensitivity has been shown to vary widely across taxa28.Particularly noticeable in our results was that r2 coefficients of predicted versus observed phenology were much higher in North America (0.70 and 0.76 for wildflower and tree models, respectively) compared to Asian (0.40 and 0.44, respectively) and European models (0.41 and 0.25, respectively). This difference in model performance could be due to the higher interannual variability of spring temperatures in North America33, leading to greater selective pressure for strong sensitivity to spring temperatures in North American plants. This difference could explain why North American species exhibit higher correlation of phenology with average spring temperatures (Table S4). Alternatively, European and Asian species may have stronger phenological responses to alternative spring forcing windows, winter chilling temperatures, or photoperiod, relative to the March–April temperature period used in this study (see Methods). We think the latter explanation is unlikely, given the strong correlations of phenology with spring temperature across all continents (see Supplementary Information – Justification for March–April Temperature Window).Herbarium-based phenological models may be improved by accounting for spatial autocorrelation within the dataset. For example, Willems et al.9 found that including spatial autocorrelation significantly improved predictability of European herbaceous flowering phenology, even when accounting for multiple drivers of spring phenology. We followed a similar approach as their study and found similar improvements in model performance with the addition of spatial autocorrelation (Tables S3–S4) that had substantial positive effects on r2 values of Asian and European models. However, spatial distributions of specimens differed substantially among continents (see Figs. S2–S4), and these differences could lead to artifacts that make results unreliable to interpret (see Supplementary Information). Therefore, we focus here on results for models without spatial autocorrelation while acknowledging that spatial aggregation of herbarium specimens in Europe and Asia may be partially responsible for the relatively lower r2 values. We encourage other researchers to explore this question further both with our data set and other datasets.Climate change and spring light windowsThe relative difference between wildflower and tree sensitivity varied substantially among continents, with wildflowers being approximately equally as sensitive to spring temperature as trees in Asia and Europe but substantially less sensitive (i.e., 95% BCI do not overlap) than trees in North America (Fig. 2). Importantly, these differences were driven by changes in tree phenological sensitivities among continents and resulted in different expectations for spring light window duration (i.e., the difference in time between estimated wildflower flowering date and canopy tree leaf out date) on different continents under current climate conditions (Fig. 3), based on modeled leaf out and flowering under a climate scenario derived from average climate conditions from 2009–2018 (Fig. S5).Fig. 3: Current estimated phenological escape duration in northern temperate deciduous forests.Estimated mean difference between wildflower First Flower Date (FFD) and canopy tree Leaf Out Date (LOD) (in days) under current climate conditions (averaged from 2009–2018, see methods) in a Asia, b Europe, and c North America. Negative values indicate tree LOD is estimated to occur before wildflower FFD. Estimations were cropped by the estimated area of broadleaf and mixed-broadleaf forest (see methods). Dark gray regions indicate areas where the consensus land classification is More