Philippa Kaur

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Root morphological traitsThe wild-type parent ISR42-8 produced longer root length (RL) than the modern cultivar parent Golf and tested lines (Table S2, Fig. 1A.h,A.f [h = hydroponic; f = field]). The tested lines of the two evolving barley populations displayed significant variations under hydroponic conditions. Barley lines evolved under OCS had on average 3484 mm longer roots compared to CCS under hydroponic treatment (Fig. 1A.h, Table 2). Complementary results under field conditions show as well higher RL for the OCS lines, even though the variance was significantly less pronounced (Fig. 1A.f). In addition, a less evident variance was observed in the field within both groups compared to the hydroponic (Fig. 1A.d). Across both experimental setups, the observed range of RL was higher in the OCS lines [Standard deviation (SD)OCS = 883, SDCCS = 597] (Table 2).Figure 1Significantly variant root morphological phenotypes. Boxplots illustrate the overall distribution of observed data points for the parents Golf and ISR 42-8 as well as for the conventional (CCS) and organic (OCS) lines. Density plots highlight the overall distribution of organic and conventional adapted lines. (A)—Root length (RL)—the sum of all roots harvested in millimeters (mm), illustrated for all four groups. (A.h)—root length measured in the hydroponic experiment; (A.f)—field experiment; A.d—distribution histogram for root length in both field and hydroponic experiment for CCS and OCS adapted lines. (B)—the ratio of root length to volume (L/V). Data available for hydroponics (B.h), field (B.f), and distribution of the ratio of root length to volume illustrated in B.d. (C.f)—Root mass density (RMD) from the field; (D.f)—Root angle (RA) from the field, distribution of the root angle illustrated in (D.d); (E.f)—root tip per plant count from the field, corresponding histogram visualized in (E.d). (F.f)—root fork per plant count from the field.Full size imageTable 2 Comparison of organic and conventional population root phenotypes under field and hydroponic evaluation.Full size tableThe root length to volume (L/V) is an important indicator of the soil volume that can be explored by the roots. Under hydroponics conditions, variations were found for L/V between the parental genotypes as well as between the OCS and CCS populations (Tables 2 & S3). The organic lines were characterized by a significantly higher L/V, indicating a much more distinct exploration of the soil by these lines (Fig. 1B.h,B.f). In comparison to field, highest diversity in L/V was found under hydroponic experiments within both OCS and CCS populations (Fig. 1B.d).The root mass density (RMD) is the ratio of root volume for a given root mass and is a key indicator of root thickness. Although significant variations existed between ISR42-8 and Golf under hydroponics conditions, such significant variations were not found between the OCS and CCS groups (P = 0.09) (Fig. 1C.f and Tables 2 and S3).The root angle (RA) measurements were only performed under field conditions since plants grown under hydroponics conditions were placed in uniform growing vessels and the direction of root growth is restricted by tubes. Significant variation was observed for the RA between the two parental lines, which was also reflected in the CCS and OCS lines (Fig. 1D.f). ISR42-8 was characterized by an 11.5° average narrower RA than Golf (Table S3). The RA was 4.1° bigger in the OCS compared to the CCS population (P = 0.005) (Table 2). However, a higher diversity in RA was observed in the OCS compared to the CCS lines (Fig. 1D.d, Table 2).In addition to the RA, the number of root tips and forks was measured under field conditions only. Both tips and forks indicate a similar pattern, where the OCS lines produced on average more for both PForks = 0.014, PTips = 0.0041 (Fig. 1E.f,F.f). After applying a P-adjustment, the number of forks count was no longer significantly different between OCS and CCS (PForks = 0.07, Table 2). Complementary, ISR 42-8 was observed to produce more tips and forks than Golf, which remained highly significant even after probability adjustment (Fig. 1E.f,F.f, Table S3). The distribution and the standard deviation of observed phenotypes highlight once more the fact that the OCS lines tend to have a higher variation (Fig. 1E.d, Table 2). Similarly, a significant increasing trend was recorded in root surface area (RSA) and root average diameter (RAD) by ISR42-8 as compared to Golf under hydroponics (Table S3). Contrasting to the parental genotypes, no variation was observed between OCS and CCS lines for RSA (Table 2).Root anatomical traitsWithin the observed anatomical traits, four were considered due to their relevance and variation between the systems. In both hydroponic and field experiments, significant variations were observed for the late metaxylem number (LMXN) between the parental lines as well as OCS and CCS lines (Tables 2 & S3, Fig. 2A.h,A.f). An increased LMXN for ISR 42-8 compared to Golf was observed (Fig. 2A.h). Regarding the CCS and OCS lines, a heterogenic scenario was presented over both experimental setups. While the median LMXN under CCS was identical with ISR 42-8 in the seedling stages of plant development (Fig. 2A.h), it was much lower in flowering stages under field conditions (Fig. 1A.f). Additionally, the LMXN was significantly higher in the CCS lines in the seedling stage compared to OCS lines, vice-versa LMXN was observed at the flowering time point (Fig. 2A.d).Figure 2Significantly variant root anatomical traits. Boxplots illustrate the overall distribution of observed data points for the parents Golf and ISR 42-8 as well as for the conventional (CCS) and organic (OCS) lines. (A) –Late metaxylem number (LMN)—the sum of all roots harvested and expressed by plant−1, illustrated for all four groups. A.h—Late metaxylem number measured in the hydroponic experiment; A.f—field experiment; A.d—distribution histogram for late metaxylem number in both field and hydroponic experiment for CCS and OCS adapted lines. (B)—Aerenchyma area (AA). Data available for hydroponics (B.h), field (B.f), and distribution of the aerenchyma area illustrated in (B.d). (C.f)—Total cortical area (TCA) from the field; (D.f)—Root cross-section area (RA) from the field, distribution of the total cortical area and root cross-section area illustrated in C.d and D.d, respectively.Full size imageThe intercellular space, represented by the aerenchyma area (AA), was observed to be significantly more pronounced in the tested CCS compared to OCS lines in both environments (Fig. 2B.h,B.f). Furthermore, the OCS population did not show significant differences to both parents under hydroponics conditions, however, when grown under field conditions, it was noted that Golf had a significantly higher AA mean value as compared to the OCS population (Table S3). As illustrated by the values, the AA expended from early to late stages by a magnitude of 10-folds (Fig. 2B.d). In general, although the two parents did not indicate phenotypic variations, OCS and CCS lines showed significant variations (Table S4).A 0.12 mm2 decreased average total cortical area (TCA) was recorded in the OCS compared to the CCS population under field conditions (P = 0.003, Fig. 2C.f), although substantial variations for TCA was observed within OCS and CCS populations (Fig. 2C.d). The root cross-section area (RXA) is a two-dimensional axis of the root which is an important indicator of root thickness. In the hydroponic examination of the seedling stage, significant variations existed between the CCS and ISR42-8 as well as OCS population (Tables 2 and S3). The complementary study under field conditions observed a noticeable variation for OCS from both parental genotypes and the CCS (Table S3). About 0.13 mm2 increased average value for RXA was identified for CCS (Fig. 2D.f), while consistent significant variations were also observed between the populations in the under field experiment, where 0.13 mm2 increased average value for RXA was identified for CCS (Fig. 2D.f). Analog (Fig. 2D.d). Analogue to the AA, the RXA indicates a lower root extension in the OCS compared to the CCS population. For the stele area (SA), significant variations were only observed at the flowering stage, where ISR42-8 generally had the highest SA and varies significantly between Golf and its progeny lines (Tables 2 and S3).Shoot-related traitsBeyond the root-related phenotypic observations, above-ground characteristics were also recorded to assess the root-borne shoot dynamics (Figs. 3 and S2). Among the OCS and CCS populations and the parents, ISR42-8 had the longest duration of emergence. While CCS-adapted lines took on average 5.8 days of emergence (DE), OCS-adapted lines emerged 1.8 days later (7.6 days) (Fig. S2). No variation was observed for the tiller number (TN) throughout all tested groups, while ISR 42-8 tends to produce much more leaf number (LN), accompanied by a lower plant height (PH) and higher shoot dry weight (SDW) (Table S4, Fig. S2). The OCS and CCS plants significantly differed in PH as well as SDW (Fig. 3B,C). The LN was marginally above the probability threshold of 0.05 (p = 0.058, Fig. 3A), with a clear tendency of increased variability in phenotypic variation (Fig. 3D). Similar trend was recorded for the SDW (Fig. 3F).Figure 3Above-ground plant characteristics. Boxplots illustrate the overall distribution of observed data points for the parents Golf and ISR 42-8 as well as for the conventional (CCS) and organic (OCS) lines under the hydroponic experiment. (A)—Leaf number (LN) expressed by; (B)—Plant height (PH) and C-Shoot dry weight (SDW). The data distribution of the leaf number, plant height and shoot dry weight is illustrated in (D,E,F), respectively.Full size imageInterconnection of root-shoot traitsWe performed inter-trait correlation analysis to unravel association among root traits and in between root and shoot phenotypes (Fig. 4). Pearson correlation coefficient revealed significant correlations among root-shoot traits. LN, PH and SDW had strong positive associations with all root architectural traits under hydroponic conditions (P  0.30) in both CCS and OCS, while DE has negative association with all shoot traits (r = −0.17 to −0.48) (Fig. 4A.h,B.h). A consistent negative relationship was observed for L/V with shoot traits such as LN, PH and SDW and root morphological traits such as RL, RSA and RAD in both CCS and OSC populations (Fig. 4A.h,B.h). A strong negative association existed between RL and all shoot morphological, root architectural and anatomical traits in both populations, except for L/V where a weak negative (r = −0.09) association was displayed only in the OCS. Likewise, all above-ground traits and all root architectural traits exhibited significant positive associations with all root anatomical features in both groups with an exception for the AA (Fig. 4A.h,B.h). Moreover, correlation analysis revealed strong positive relationships in both groups of SDW and root dry weight (RDW) to all above-ground traits, below-ground traits including, RL, SA, and RAD, as well as in all root anatomical traits (Fig. 4A.h,B.h). This means that the growth of tissue and organ is proportional to the increase in total dry biomass. More importantly, we observed a significant positive correlation among most of the root morphological, architectural, and anatomical traits in both OCS and CCS adapted populations, with few exceptions such as L/V (Fig. 4A.h,B.h).Figure 4Correlation matrix for shoot morphological (only in hydroponic conditions; A.h and B.h), root architectural and anatomical traits in two groups of barley populations and their parental lines grown across two growing conditions. (A)—conventional and (B)—organic cropping systems. (A.h)—conventional under hydroponic, (B.h)—organic under hydroponic, (A.f)—conventional under field, and B.f—organic under field conditions. The color scale represents Spearman’s ranked correlation coefficient. A larger circle size indicates a smaller p-value; blank cells represent that correlation was non-significant at P  −0.90) and RDW (r =   > −0.80) (Fig. 4A.f,B.f) for CCS and OCS populations respectively, which means that narrower the angle of the nodal roots, the longer was the root system. The two root branching traits, the number of tips and number of roots forks which were known to be associated and dependent on the RL have a strong positive correlation reflected by r = 0.81 and 0.90 in CCS and r = 0.74 and 0.84 in OCS developed lines, respectively, while they have a significant negative correlation with RA (r = −0.72 to −0.77) in both barley groups. In addition, RA had also strong negative relationship to RDW contributing architectural traits including, RMD (r = −0.81 to −0.84) and L/V (r = −0.34 to −0.44). However, no positive associations were observed for RA and all root anatomical traits in both OCS and CCS populations (Fig. 4A.f,B.f).Allometry analysisThe correlation analysis identified interconnection among root and shoot-related traits. Therefore, we checked if these correlations can be explained by allometric relations (Tables 3 and 4).Table 3 Summary of allometric analysis of root-shoot system traits under hydroponic condition.Full size tableTable 4 Summary of allometric analysis of root-shoot system traits under field condition.Full size tableIn the hydroponic environment, we observed a total of ten allometric relations, from which six were annotated to the PH. The PH was allometrically related to the SDW, the RSA, the RV, the RDW, the SRL, and the RMD (Table 3). Besides, the SDW was allometrically associated with the RSD. Furthermore, the TCA was related to the RXA. Finally, an allometry relationship was detected between the LMXN and AA (Table 3).In the field experimental setup, we detected in total ten allometric relations (P  More

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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

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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

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