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Photosynthetic pigmentsBased on the analysis of variance, data of Photosynthetic pigments as presented in Table 1 indicate that photosynthetic pigments as chlorophyll a (Chl. a) had non-significant for three Canola genotypes AD201 (G1), Topaz (G2) and SemuDNK 234/84 (G3), but chlorophyll b (Chl. b) and chlorophyll a/b ratio (Chl. a/b) had significant difference for three genotypes. Chl. a, Chl. b and Chl. a/b were positively responded to different N application i.e. without nitrogen fertilization (control F0), 95 kg N ha−1 (F1), 120 kg N ha−1 (F2) and 142 kg N ha−1 (F3) (without yeast); and integrated between nitrogen fertilization and yeast extract (YE) treatments as follows: 95 kg N ha−1 + YE (F4), 120 kg N ha−1 + YE (F5) and 142 kg N ha−1 (F6) (with yeast), data indicated that F5 and F6 gave the highest values of Chl. a and Chl. a/b ratio and lowest values of Chl. b Table 1. Interaction data showed that three Canola genotypes that were fertilized with N without yeast or with yeast had a slight difference with statistically significant in chl. a. The highest values of Chl. an obtained by G2 under F5 treatment followed by G1 under F6 treatments. In respect to Chl. a/b ratio, statistical analysis showed that Interaction between Canola genotypes treated with N applications without or with yeast had a significant difference whereas the highest values were recorded when Canola genotypes G3 and G2 fertilized with F6 and F5 with slight differences. While the interaction was significant between N treatments and Canola genotypes for Chl. b. and Canola genotype (G1) gave the highest value when treated with F1. Generally, F6 and F5 improve the contents of chl. a and chl. a/b ratio for three Canola genotypes Table 1. Chl. contents were increased in plants grown under middle and high N conditions as compared with plants grown under low N conditions, which significantly affected photochemical processes20. N is a fundamental element for leaf plants, insufficient N supply lead to decreased photosynthetic rate in plants21, this occurs to many factors such as a decrease in pigment degradation22, reduction in stomatal conductance23 and a decline in the light and dark reaction of photosynthesis. Canola is a nitrophilous plant, wherein a high concentration of NO3 in the culture media results in higher Chl. contents in the plant leave compared with controls20. The Chl. a/b ratio can be a valuable indicator of N element within a leaf because this ratio must be positively related to the ratio of PSII cores to light-harvesting chlorophyll-protein complex (LHCII)24. LHCII contains the majority of Chl. b, consequently it has a lower Chl a/b ratio than other Chl. binding proteins associated with PSII25. Thus, Chl. a/b ratios should increase with decreasing N availability, especially under high light conditions26, the Chl. a/b ratio and the ratio of PSII to Chl. are independent of N availability for spinach27, and lower Chl. a/b ratios were noticed when plants were subjected to low N28, while Kitajima and Hogan29 revealed that the Chl. a/b ratio increased when Chl. content decreased in response to N restriction in photosynthetic cotyledons in leaves of seedlings of four tropical woody species in the Bignoniaceae, and Bungard et al.30 demonstrated that there is a tiny response in Chl. a/b ratios to light or N. The yeast includes bio-regulators i.e. plant growth regulators and endogenous plant hormones, which enhance photosynthesis, also it produces 5-Aminolevulinic acid which is vital to tetrapyrrole biosynthesis and biochemical processes in plants, including heme and Chl. biosynthesis25.Table 1 Photosynthetic pigments for the three Canola genotypes under different N applications without and with yeast extract.Full size tableYield and its attributesComparing of mean data through the Duncan Multiple Range Test in the probability level of 5%, data showed significant differences among the Canola genotypes for the highest plant (cm), branches number/plant, and pods number/plant. On contrary, there wasn’t a significant difference for seed number/pods, seed yield (t ha−1), biological yield (t ha−1), and harvest index, wherein G2 gave the highest value for the highest plant (cm). In the same trend, G2 gave the highest values of branches No./plant and pods No./plant followed by G3 for the previous two treats Table 2. All examined N without or with yeast caused a significant difference in yield and its attributes, wherein F6 positively affected on abovementioned traits and gave the highest values on the highest plant (cm), branches No./plant, pods No./plant, seed No./pods, seed yield (t ha−1), and harvest index. While the highest values of biological yield (t ha−1) were obtained with F3, F6, and F5, respectively Table 2.Table 2 Growth, yield and its attributes for the three Canola genotypes under different N applications without and with yeast extract.Full size tableThe interaction between the Canola genotype and different N rates without or with yeast extract as shown in Table 2, demonstrated a significant difference. Data showed that the highest values of plant height and pods No./plant were recorded by G2 under F6 and the highest values of branches No./plant, seed No./pods, and seed yield (t ha−1) got by G3 and G2 under F6. There was a slight difference with statistically significant biological yield (t ha−1) and highest values established by G1 under F3 and F6; and G2 and G3 under F3, F5, and F6 respectively; and the highest values of harvest index recorded by G1, G2 and G3. under F6. Generally, data proved that 142 kg N/ h−1 + YE (F6) was enhanced the yield and its components of three Canola genotypes i.e. AD201 (G1), Topaz (G2), and SemuDNK 234/84 (G3). Many researchers reported that there are significant differences among Canola varieties and growth and yield traits are significantly increased by increasing N rates11. Increasing N fertilizer rates significantly increased most of the yield and its components31, N enhances metabolites synthesized by the plant which leads to more transformation of photosynthesis to reproductive parts, and induces different physiological mechanisms to access the nutrient32. Yeast extract as bio-fertilizer had a significant and positive effect on plant height and yield traits of Canola. The role of bread yeast in increasing the growth and yield traits; may be due to the content of yeast to many important nutrients elements i.e. N, Mg, Ca, Zn, Cu, and Fe, and the production of some growth regulators such as Auxin and Gibberellin and cytokinin which is necessary for plant biological processers especially photosynthesis and cell division and elongation33. Also, Yeast extract had stimulatory effects on cell division and enlargement, protein and nucleic acid synthesis, and chlorophyll formation34, in addition to its content of cryoprotective agent, i.e. sugars, protein, amino acids, and also several vitamins35. Consequently, it improves growth, flowering, and fruit set and formation and increases yield34.Correlation of Canola seed yield and chlorophyll a/b ratioPartial correlation coefficients of Canola seed yield and Chl. a/b ratio is given in Fig. 1. This result showed that seed yield was positively correlated with Chl. a/b ratio when the amount of N applied without or with yeast extract is increased. Chl. a/b ratio can be an important indicator of N within a leaf, this ratio must be positively related to photosynthesis and biological processers which reflect on seed yield.Figure 1Correlation of Canola seed yield (t/h) and chlorophyll a/b ratio as affected by different nitrogen rates without and with yeast extract.Full size imageCorrelation of Canola seed yield and its attributesCorrelations of seed yield and yield components of Canola are a function of the plant height, number of branches/plant, number of pods/plant, and number of seeds/pod as shown in Fig. 2a–d. These results proved that grain yield was strongly positively correlated with some of the abovementioned traits when N fertilization increased without or with yeast extract. Sufficient N contributes to enhance physiological processes, improves growth, flowering, seed formation, and the seed yield finally.Figure 2(a) Correlation of Canola seed yield (t/h) and plant height (cm) as affected by different nitrogen rates without and with yeast extract, (b) Correlation of Canola seed yield (t/h) and branch No/plant as affected by different nitrogen rates without and with yeast extract, (c) Correlation of Canola seed yield (t/h) and pods No/ plant as affected by different nitrogen rates without and with yeast extract, and (d) Correlation of Canola seed yield (t/h) and seeds No/ pod as affected by different nitrogen rates without and with yeast extract.Full size imageChemical propertiesRegarding results of the oil yield (t ha−1), seed oil %, protein %, N % in seed, and N% in straw as presented in Table 3, data showed significant differences among three Canola genotypes; AD201 (G1), Topaz (G2) and SemuDNK 234/84 (G3), excepted oil yield had non-significant difference. G1 was surpassed in oil %; G2, G3 surpassed in protein % and N % in seed, and G3 surpassed in N% in straw. Different N fertilization applies without or with yeast extract had a significant effect on the abovementioned traits, wherein F6 treatment gave the highest oil yield, protein %, N % in seed, and N% in straw, while seed oil % significantly increased with F1 and F4 treatments. There was significant interaction concerning with abovementioned traits, Table 3, as well as the highest values of seed oil yield (t ha−1), protein % in seeds, and nitrogen % in seeds were obtained with G1, G2, and G3 when treated with F6. Wherein the highest values of oil % were obtained by G1 under F1 and F4 treatments. Concerning N% in straw was increased by increasing the rate of N fertilizer application and the highest value was recorded by adding F6 to G336. Seed oil percentage was decreased by increasing nitrogen rates; the effect of interaction between Canola cultivars and nitrogen fertilization treatments was significant on seed oil. % High rates of N led to decreases in seed oil % and increase in protein concentrations in Canola seed37, the increase in seed protein % because N is an integral part of protein and the protein of Canola.Table 3 Effect of different N applications without and with yeast extract on oil yield, oil %, protein %, N % in seed and N% in straw for the three Canola genotypes.Full size tableCorrelation of Canola seed yield and seed oil percentageA strong negative correlation was detected between seed oil percentage as shown in Fig. 3. The result indicates that seed oil percentage decreases with increasing in different N fertilization rates without or with yeast extract. That’s a negative correlation between seed yield and seed oil %; it might be due to N application which results in delaying maturity leading to poor seed filling and a greater proportion of green seed38.Figure 3Correlation of Canola seed yield (t h−1) and oil % as affected by different nitrogen rates without and with yeast extract.Full size imagePhysico-chemical properties of Canola oilThe effects of different N application rates without or with yeast extract on Canola genotypes on physico-chemical properties i.e. Acid value (mg g−1), saponification number (mg g−1) and peroxide value (mg kg−1) were shown in Table 4. Data of chemical properties of Canola oil showed significant differences among Canola genotypes, the highest acid value and peroxide value were obtained from G2 followed by G1 and G3, respectively, while the highest saponification number was obtained by G3 followed by G1 and G2, respectively.Table 4 Oil properties for three Canola genotypes under different N applications without and with yeast extract.Full size tableData had significant differences among different N application rates without or with yeast extract, by increasing the N rated from F0 to F6 caused decreases in Acid value, Saponification number, and peroxide value. Also, data showed a significant interaction between Canola genotypes and different N application rates without or with yeast extract for all abovementioned traits, wherein the highest values of saponification number were obtained by G1 and G3 under F0 treatment. In addition, the highest values of peroxide value and the acid value were obtained by G2 with F0. The acid value is a physicochemical indicator38, wherein oils which have higher acid value posse poor quality39, on another hand, Low acid value of Canola genotype shows their higher oil quality. The peroxide value varied between 7.1 and 9.06 meq. O2/kg indicates that the tested vegetable oils are fresh, and the lowest initial peroxide value is suitable for consumption40. High saponification value indicated that Canola oil possesses normal triglycerides and may be useful in the production of liquid soap and shampoo41. Saponification number was significantly different among genotypes and a higher nitrogen rate resulted in an increase in the unsaponifiable matter and led to a decrease in oil acid value and saponification value42.Fatty acids composition percentages in Canola oilThe main values of fatty acids composition percentages in Canola oil were determined and calculated in the second season Table 5. Gas–liquid chromatographic analysis showed that, saturated fatty acids (Palmitic, 16:0, Stearic, 18:0, Arachidic, 20:0, and Behenic, 22:0) represent about 9.1 of the total fatty acids. Palmitic was the dominant acid among the saturated ones. In respect of unsaturated fatty acids i.e., Oleic acid (18:1), Linoleic (18:2), Linolenic (18:3), and Erucic (22:1), they all represent about 90.9% of total fatty acids. Therefore, Oleic acid (18:1) was the major fatty acid in Canola oil (59.43%) followed by Linoleic (20.80%) and Linolenic (9.02%). Erucic acid was less than 2%.Table 5 Saturated and unsaturated fatty acids (%) in seeds of the three Canola genotypes and different N applications without and with yeast extract.Full size tableData in Table 5, showed slight differences in saturated fatty acids between Canola varieties. AD201(G1) variety contained more amount of Palmitic (4.78%) and Stearic (1.52%) acids followed by Topaz (G2) for Palmitic and SemuDNK 234/84 (V3) for Stearic. However, Behenic acid (1.20%) was higher in G3 than G2 (1.17%), while G2 was the highest in Arachidic acid than G3 variety. These results are in line with those obtained by El Habbasha et al.43. They reported that AD 201, Silvo, and Topas (G2) were different in their oil contents of saturated and unsaturated fatty acids. Canola varieties were also slightly differed in their content of the unsaturated fatty acids Table 5, G3 variety contained more amounts of Oleic (60.36%) acid followed by the G2 variety. G1 recorded the lowest amount of Oleic acid (58.36%) in comparison with the other two varieties. On the other hand, G1 showed a high increment in Linoleic and Linolenic acids followed by G3 for Linoleic and Linolenic acids. The second oil quality breeding objective is to reduce the percentage of Linolenic acid from the percent 8–10% to less than 3% while maintaining or increasing the level of Linoleic acid44. Lower Linolenic acid is desired to improve the storage characteristics of the oil, while higher Linolenic acid content may be nutritionally desirable. Similar observations were reported by Ref.45. Topaz variety recorded the highest value for Erucic acid (1.77%) followed by AD201 variety, whereas Semu DNK gave the lowest value (1.45%). The increase in Erucic acid content in the Topaz variety may be due to the decrease in Oleic acid content46. Stated that the concentrations of Oleic and Erucic acids were negatively correlated and a high Oleic acid concentration ( > 50%) was always associated with a low Erucic acid concentration ( More

Changes of straw degradation characteristics at different culture stagesCorn straw degradation ratioCorn straw weight loss in M44 at F1 reached 35.90% at 15 ℃ for 21 days, which was greater than that at F5, F8, and F11 by 2.33%, 3.01%, and 3.35%, respectively. There were no significant differences between F8 and F11(Fig. 1).Figure 1Corn straw degradation ratio was measured at different culture stages. The same small letter means there was no significant difference, and different small letters indicate significant differences at p  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