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Study settingUganda covers 241,037 km2 (4° N, 2° S, 29° E, 35° E) and averages 1100 m above sea level25. Uganda has a total population of 34.6 million people, with 7.4 and 27.2 million living in urban and rural areas, respectively26. It borders Lake Victoria and has an equatorial climate. The study area is mainly plateau, with a few mountains. About 20 percent of Uganda’s area is covered by swamps and water bodies, including the four Great Lakes of East Africa (Lake Edward, Lake Victoria, Lake Albert, and Lake Kyoga). The country has ten national parks housing a high diversity of wildlife and endangered species26. By 2009, agriculture ranked as the second leading contributor to the country’s Gross Domestic Product27.Surveillance data of Bacillus anthracis infectionSurveillance data of livestock and human cases from 2018 were provided by the Ministry of Health (MOH) in Uganda through the Field Epidemiology and Laboratory Training Program and the Uganda Ministry of Agriculture, Animal Industry and Fisheries (MAAIF). Geographical coordinates of anthrax cases among wildlife (from 2004 to 2010) in Queen Elizabeth National Park were obtained from a recently published study4. These cases were mapped to show the distribution of anthrax across Uganda (Fig. 1). It is only recently that Uganda has mandated systematic anthrax surveillance across the country following the outbreak that started in 2018. GPS coordinates gathered by field personnel during outbreak responses were used to map outbreak locations. The human anthrax cases were defined based on the CDC’s clinical criteria (signs and symptoms), presumptive laboratory diagnosis (Gram staining), and confirmatory laboratory diagnosis (bacterial culture, immunohistochemistry, ELISA, and PCR)28. The animal anthrax cases were also defined based on the clinical presentation, presumptive laboratory diagnosis, and confirmatory laboratory diagnosis. All cases were classified as either ‘probable’ or ‘confirmed,’ with probable defined as cases that met both the clinical and presumptive laboratory diagnostic criteria and confirmed defined as cases that met the clinical and confirmatory laboratory diagnostic criteria. A total of 497 livestock (n = 171), humans (n = 32), and wildlife cases (n = 294), both confirmed (n = 32) and probable (n = 465), occurring from 2004 to 2018 were compiled. All methods were performed in accordance with the relevant guidelines and regulations.Figure 1Distribution of anthrax presence and pseudo-absence locations across Uganda. The navy-blue circles show wildlife cases (n = 294) used for model training, the blue triangles show livestock cases (n = 171), and the red diamonds represent human cases (n = 32). The blue polygons show the locations of the 50 km, 75 km, and 100 km buffers which were constructed around the wildlife cases with a distance of 10 km between the buffers and the presence locations. The pink dots show the pseudo-absence points selected within the 50 km buffer, the orange dots show the pseudo-absence points selected within the 75 km buffer, and the white dots show the pseudo-absence points selected within the 100 km buffer. Prediction maps were developed using the Quantum Geographic Information System software (QGIS). URL: https://qgis.osgeo.org (2020).Full size imageEnvironmental variable processingCorrelative studies of environmental risk factors for anthrax outbreaks suggest that temperature6,29,30,31,32,33,34,35,36,37, precipitation6,29,30,31,32,33,34,35,36,37,38,39, elevation6,29,31,32,34,35,37,38,39, soil (type, calcium concentration, pH, carbon content, and moisture)6,30,31,33,34,36,37,39,40,41,42,43, vegetation6,29,31,34,36,37,38,39,40,42,43, and hydrology37,44 are some of the major drivers of B. anthracis suitability. A total of 26 environmental predictors (Fig. 2) were selected for this study based on these known variables. These comprised 19 bioclimatic variables (the mean for the years 1970–2000) collected from the WorldClim database version 2 (https://www.worldclim.org/data/worldclim21.html) at a resolution of 30 s (~ 1 km2)45. Four soil variables, including exchangeable calcium at a depth of 0–20 cm, soil water availability, soil pH (10×) in H2O at a depth of 0 cm, and soil organic carbon at a depth of 0–5 cm, were retrieved from the International Soil Reference and Information Centre (ISRIC) data hub at a resolution of 250 m (https://data.isric.org/geonetwork/srv/eng/catalog.search#/home). Distance to permanent water bodies was derived from a global hydrology map provided by ArcGIS online version 10.6.146. Elevation data of 1 km2 in resolution was obtained from the Global Multi-resolution Terrain Elevation Data (GMTED2010) dataset available from the United States Geological Service. Finally, the monthly Enhanced Vegetation Index (EVI) data for the years 2004, 2005, and 2010 (36 tiles in total) were obtained from The Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Indices (MYD13A3 v.6) at a spatial resolution of 1 km (https://lpdaac.usgs.gov/products/myd13a3v006/). The single variable, mean EVI, was calculated in QGIS by averaging all 36 tiles. The EVI minimizes variations in the canopy background and maintains precision over conditions with dense vegetation.Figure 2Results of correlation between covariates using Pearson’s correlation test. Correlation between covariates was shown by red numbers (negative correlation) and blue numbers (positive correlation). BIO1 = Annual Mean Temperature, BIO2 = Mean Diurnal Range, BIO3 = Isothermality, BIO4 = Temperature Seasonality, BIO5 = Max Temperature of Warmest Month, BIO6 = Min Temperature of Coldest Month, BIO7 = Temperature Annual Range, BIO8 = Mean Temperature of Wettest Quarter, BIO9 = Mean Temperature of Driest Quarter, BIO10 = Mean Temperature of Warmest Quarter, BIO11 = Mean Temperature of Coldest Quarter, BIO12 = Annual Precipitation, BIO13 = Precipitation of Wettest Month, BIO14 = Precipitation of Driest Month, BIO15 = Precipitation Seasonality, BIO16 = Precipitation of Wettest Quarter, BIO17 = Precipitation of Driest Quarter, BIO18 = Precipitation of Warmest Quarter, BIO19 = Precipitation of Coldest Quarter.Full size imageAll environmental variables were resampled using the R package ‘Resample’47 to a resolution of 1 km and clipped to the extent of Uganda. Since data sampling for wildlife data (used in model training) was not done systematically across the study area, target backgrounds buffers (polygon buffers created at certain radii from the training points and used for the random selection of pseudo-absences) were created for model calibration to reduce sampling bias. As there was no information on the sampling radius, a sensitivity analysis was conducted by creating target backgrounds using circular buffers of radius 50 km, 75 km, and 100 km around the presence points used for model training, leaving 10 km between the presence points and the various buffers (Fig. 1). Quantum Global Information System (QGIS) version 3.16 (https://qgis.org) software was then used to add 294 random pseudo-absence points within each buffer polygon giving a ratio of 1:1 for the training presences to pseudo-absences. A recent study explored how four approaches of pseudo-absence creation affect the performance of models across different species and three model types by building both terrestrial and marine models using boosted regression trees, generalised additive mixed models, and generalised linear mixed models48. They then tested four methods for generating pseudoabsences across all the different model types: (1) correlated random walks (RW); (2) reverse correlated RW; (3) sampling pseudoabsences within a buffer area surrounding the presence points; (4) background sampling48. The findings of the study suggested that the separation or distance in the environmental space between the presence locations and the pseudoabsences was the most significant driver of the model predictive ability and explanatory power, and thus finding was consistent across the three model types (boosted regression trees, generalised additive mixed models, and generalised linear mixed models) and both the terrestrial and marine habitats48.The values of the environmental variables were then extracted for each presence and pseudo-absence location using the raster package in R. With these, we did an initial data exploration to check for outliers within the covariates, collinearity, and to explore the relationships between the covariates and the response variables (presence or absence of anthrax). Cleveland dot plots were used to check for possible outliers. Following the outlier checks, variance inflation factors (VIF), pairwise plots, and Pearson correlation coefficients with correction for multiple comparisons were used to measure the statistically significant correlation between the covariates (Fig. 2). For variables that were highly correlated (correlation greater than 0.6) or those with high variance inflation (VIF  > 3), only one was used in the modelling process. Five variables were selected following this analysis: Temperature seasonality (BIO4), elevation, distance to water, soil calcium, and soil water (Table 1).Table 1 Summary of the environmental variables used.Full size tableModelling anthrax suitability across UgandaQGIS v.3.16 (https://qgis.org) and the R statistical package version 4.1.049 were used to conduct data visualization, cleaning, and model analysis (R code used available in a Github repository: https://github.com/valentinandolo/Uganda-Spatial_Model/tree/master). The wildlife cases (n = 294) were used for model training and testing. The remaining human (n = 32) and livestock (n = 171) cases were used for model evaluation. Since the wildlife case locations were recorded from 2004 to 2010, while the livestock and human cases were recorded in 2018, the latter locations were both spatially and temporally distinct from the wildlife cases, making an excellent basis for block cross-validation of the final model performance50. Random partitioning of the data into training and testing sets can inflate the performance of a model and underestimate the error in the spatial prediction evaluation50. Block cross-validation uses spatial blocks that separate the testing and training datasets; thus, the method has been suggested to be a good technique for error estimation and a robust approach for measuring a model’s predictive performance50.The INLA package in R was applied to model the suitability of B. anthracis across Uganda. INLA calculates the spatial interaction effects using a Stochastic Partial Differential Equation (SPDE) method, which estimates a continuous Gaussian Markov Random Field (GMRF) where the correlation between two locations in space is specified by the Matérn correlation which is explained in more detail elsewhere51. The initial step in fitting an SPDE model is the creation of a Constrained Refined Delaunay Triangulation or a mesh to illustrate the spatial process51. R-INLA uses a function called ‘inla.mesh.2d()’ that applies a variety of arguments to build the mesh, these include: loc, loc.domain, boundary, max.edge, and cutoff51. The loc argument contains the point locations which provide information about the area of study and are used to create the triangulation nodes. Alternatively, a polygon of the study area can be used to identify the extent of the domain via loc.domain. We applied the point locations using the loc argument. We then specified the boundary of the mesh as a convex hull. We used the max.edge argument to specify the maximum edge length for the inner mesh domain/triangles and the outer triangles. We did this by first studying the distribution of distances between the point locations for the training presences and pseudo-absences. Most points were within a distance of about 90–100 km away from each other, thus, a possible guess for the range at which spatial autocorrelation persists was 100 km. We used a distance of 20 km as a range guess to create a finer mesh which has been shown to produce more precise models. We specified the maximum edge length for the inner triangles as 20 km divided by 5 (4 km) and the maximum edge length for the outer triangles as 20 km. Finally, the cutoff argument sets the minimum distance allowed between point locations. We divided the maximum edge length for the inner triangles by 5 (4 km divided by 5 = 0.8 km), meaning that points that were closer in distance than 0.8 km were replaced by one vertex to avoid the occurrence of small triangles.The spatial effect, which is a numeric vector, then links each observation within the data to a spatial location, thus, accounting for region-specific variation that cannot be accounted for by the covariates. Following the recommendation by Lindgren and Rue52, multivariate Gaussian distributions with means of zero and a spatially defined covariance matrix were used to model the spatial effect. Several versions of Bayesian hierarchical additive models were created by estimating a Bernoulli generalized additive model (GAM) with and without spatially correlated random effects. The Bernoulli GAM is defined as shown in Eqs. (1) and (2)$${C}_{i} sim Bernoulli left({p}_{i}right),$$
(1)
$$logit left({p}_{i}right)= alpha +sum_{j=1}^{m}{beta }_{j}left({X}_{j,i}right)+ sum_{k=1}^{l}{f}_{k}left({X}_{k,i}right)+ {mu }_{i},$$
(2)
where ({C}_{i}) denotes the observed value, such that: B. anthracis presence or absence at a given location i (i = 1, …, n; n = 588) is given as ({C}_{i}), where ({C}_{i}) =1 if B. anthracis was present, and ({C}_{i})=0 if absent. Logit is the link function for binomial family, ({p}_{i}) is the expected value of the response variable (the probability of B. anthracis suitability) at location i, α is the intercept, ({X}_{j,i}) and ({X}_{k,i}) are the j th and the k th covariates at a location i, ({beta }_{j}) are the beta coefficients, ({f}_{k}) are the smooth functions (cubic regression splines) for k th covariates, and ({mu }_{i}) is the spatial random effect at the location i53. The number of variables in linear term (m) and the non-liner term (l) are different because the variables employed in each term are different. We estimated both linear and non-linear effects for the covariates. Our overall database had 294 B. anthracis pseudo-absences generated randomly across the target background buffers to match the number of species presences recorded. Because we had no prior information, a Gaussian prior distribution with a mean of zero (default no effect prior unless data is informative) was applied for all the model parameters. The posterior mean, standard deviation, and 95% credible intervals were estimated for all the parameters.Model selectionSeveral different candidate models were examined. First, a baseline model was built using only the intercept. A second baseline model was then built, which included the intercept and spatial random effects only. Covariates were added to the second baseline model (intercept plus spatial effects model) without any smoothing function (i.e., only linear effects). The contribution of the spatial random effect was then re-examined by taking it out from the model. Smoothing functions were then added to all covariates, and the same procedure was repeated. Model selection was done using this forward stepwise approach. The final model was run using the three different target background buffers to identify the buffer distance with the lowest Deviance Information Criterion (DIC). The various options were assessed using the DIC54, Watanabe-Akaike information criterion (WAIC), and the Conditional Predictive Ordinate (CPO). The DIC and WAIC were chosen because they are commonly used to assess model performance by measuring the compromise between the goodness of fit and complexity. For CPO, the logarithmic score (− mean(log (CPO)) (LCPO) was calculated and used55. CPO can also be used to conduct internal cross-validation of models using a leave-one-out approach to evaluate the predictive performance of the model. Lower LCPO, DIC, and WAIC estimates suggest superior model performance. Thus, the favoured model had the lowest values across the 3 metrics.Model validation and evaluationModel validation for the favoured model was conducted using an independent evaluation dataset comprising of livestock and human outbreaks occurring at different spatial locations and 8 years after the training data. The omission rate, which indicates the proportion of positive test locations that end up in pixels predicted to be unsuitable for B. anthracis56, was used to validate the model. A low omission rate indicates good model performance. The threshold for suitability was the probability threshold that maximized the sensitivity and specificity of the model. The sensitivity was then derived by calculating the proportion of positive test locations that end up in pixels predicted to be suitable for B. anthracis56. A high sensitivity indicates good model performance.Model predictionThe favoured model selected using the criteria described above was used to generate countrywide prediction maps showing the posterior mean values, standard deviation, and the 95% credible intervals of the probability of B. anthracis suitability. The raster package in R was used to make the prediction maps. Bayesian kriging was done by treating all model parameters as random variables to include uncertainty in the prediction57. This kriging is built into the INLA framework via the SPDE, which allows a Delaunay triangulation to be constructed around the presence and absence locations within the sampling frame52. INLA then conducts model inference and prediction at the same time by considering the prediction points as locations missing the response variable (set to NA)51. Following successful model prediction, additional linear interpolation functions then generate the output for the whole study area scaled from 0 to 1.Ethical approvalEthical approval for this study was provided by the Human Biology Research Ethics Committee, University of Cambridge, UK (Ref: HBREC.2019.02) the School of Veterinary Medicine and Animal Resources Institutional Animal Care and Use Committee, Makerere University, Uganda (Ref: SVAREC/21/2019); and the Uganda National Council for Science and Technology. Informed consent was obtained from all subjects and/or their legal guardian(s). All methods were performed in accordance with the relevant guidelines and regulations. More

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Rule-based mean sowing and maturity datesLocation- and climate-specific mean crop calendars are computed by combining two rule-based approaches published by19 and22 to simulate sowing and physiological maturity dates of grain crops, respectively. The assumption is that farmers select growing seasons based on the mean climatic characteristics of their specific location and on the physiological limitations (base and optimum temperatures for reproductive growth; sensitivity to terminal water stress) of the respective crop species. Accordingly, they select sowing dates and cultivars with phenologies that, on average, meet these adapted maturity dates.The climate is classified into (i) seasonality types, based on the coefficient of variation of monthly mean temperature and precipitation and (ii) temperature levels, based on the temperature of the warmest month as compared to the base and the optimum temperatures for the crop reproductive growth. Optimal temperatures for sowing, optimal temperature ranges for grain filling, as well as indicators of soil moisture conditions (based on precipitation/potential-evapotranspiration ratio (P/PET)), are defined as global parameters for each crop (Supplementary Table 1) and used as thresholds to identify the best timing for sowing and for the start or end of the crop grain-filling phase. To cope with fluctuations of daily values around these thresholds, mean daily temperature, precipitation and potential evapotranspiration are derived by linear interpolation between monthly values.We distinguish between spring and winter crop types. Maize, rice, sorghum, and soybean are simulated as spring crops only, for wheat we simulate both types. For spring crops, farmers sow the crops at the onset of the wet season (first day of the wettest 120 consecutive days), in case of prevailing precipitation seasonality, or on the day of the year when temperatures increase above crop-specific temperature threshold19 (Supplementary Table 1), in case of temperature-driven seasonality.For wheat, we distinguish three types: winter wheat with vernalization is chosen if monthly temperatures fall below 0 °C, but winter is neither too harsh (temperature of the coldest month is higher than −10 °C), nor too long (temperatures fall below the sowing temperature threshold (12 °C) after 15th September (North hemisphere) or 31st March (South hemisphere)19). Winter wheat without vernalization is grown if winters are mild (the temperature of the coldest month is higher than 0 °C) without dormancy. In this case, wheat is sown 75 days before the coldest month of the year. This rule was arbitrarily chosen based on observed wheat sowing dates in mild winter regions. If the conditions for growing any of the winter-wheat types are not met (winter too harsh and too long), then spring wheat (without vernalization) is chosen. Note that the computed sowing dates do not differ between rainfed and irrigated for any of the crops.The mean maturity date is chosen so that the crop grain-filling phase, the most critical for yield formation, occurs under the least stressful conditions possible in that location and climate as follows. Under precipitation seasonality, grain filling starts towards the end of the rainy season, when a P/PET threshold is crossed. Under temperature seasonality, (a) grain filling of spring crops starts in the warmest month of the year (if summer temperatures are optimal), or right after temperatures return within an optimal range; (b) grain filling of winter crops ends in the warmest month of the year (if summer temperatures are optimal), or right before temperatures exceed the optimal range; (c) eventually, maturity is advanced to escape terminal water stress. Note that the grain-filling phase has a static duration of 60 days for maize and 40 days for all the other crops. This assumption is based on empirical relationships between the total growth period and the post-flowering reproductive phase, showing that the partition between the vegetative and reproductive phase of grain crops follows a saturation curve that levels off after 90–100 days of total growth duration54. Different crops are assumed to have only one crop cycle (sowing-to-maturity) per year, therefore neither multi-cropping systems nor crop rotations are accounted for in the decision-making rules. A detailed description of the rules and parameterization can be found in refs. 19, 22.Simulated crop calendars reflect current farmers’ managementSimulated historical crop calendars, driven by the bias-corrected climate dataset WFDEI23, largely agree with observations11,12,13. We compare results both at the country and grid-cell level because, although the observed crop calendars used here are gridded datasets, their underlying sources are often reported per country. The country-level comparison highlights that the agreement is good for most countries, importantly, including those with large cropland area. The area-weighted Mean Absolute Error (MAE) is close or well below 30 days for all considered crops (Fig. 4). The simulated crop calendars compare well with the observed data also at the grid-cell level. Large areas, including major agricultural regions of importance for global yields, show deviations within ±15 days for both sowing and maturity dates (Supplementary Table 2 and Supplementary Figs. 21–24). However, evaluating the accuracy below 30 days is limited by the time resolution of the observations, which is either (i) monthly11 and converted by us into daily values, by taking the mid-day of the reported month, or (ii) daily12,13, but resulting from averages over large time windows (often  > 1 month). Overall, the accuracy of the model is in line with the original evaluations of this rule-base method19,22, as well as with other studies simulating average growing periods across large regions18,20.Fig. 4: Evaluation of simulated crop calendars.Country-level comparison of simulated and observed sowing (A) and maturity (B) dates (day of the year) for five crops. Each circle refers to a country and a crop, the size of the circle is scaled according to the cropland area per country. The area-weighted Mean Absolute Error (MAE, days) is reported for each crop. Crop-calendar simulations are based on WFDEI reanalysis climate forcing23 for the period 1979–2012. The observed crop calendar includes different sources11,12,13.Full size imageSimulation of daily crop phenology and yields with the LPJmL crop modelWe perform a modeling experiment across the global land grid at 0.5° × 0.5° resolution. We used the LPJmL5 crop model24,25 to simulate daily growth and phenological development of five crops, driven by climate projections from four General Circulation Models (GCMs) GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR and MIROC5 under the Representative Concentration Pathways 6.0 (RCP6.0) as provided in bias-adjusted form from the CMIP5 archive by the ISIMIP2b project42. Irrigated and rainfed production systems are simulated separately on their current harvested areas11, which is also used to compute total crop yields at grid-cell and global scale, as the product of yield by crop-specific area. A first 5000-year spin-up simulation is used to initialize all model pools (e.g., soil carbon and nitrogen content). A second spin-up simulation of 390 years is used to introduced effects of historical human-driven land-use change on these pools. A change in cropping area for the future scenarios is not considered in this study.Phenological development is simulated based on the thermal-time model, including the effect of vernalization. All crops are assumed to be insensitive to photoperiod, due to a lack of parameters for multiple-crops and global-scale simulations. Previous global studies15,18 that have focused on maize and wheat only, have found lower performances in the growing-period simulations when using a photo-thermal model, compared to a temperature-only driven approach and thus recommend caution when using the photoperiodic response. State-of-the-art global crop models13,16 also typically do not consider sensitivity to photoperiod or assume that the photoperiodic response of the cultivars chosen in each location are perfectly tuned to the given conditions.Sowing dates are prescribed based on the external rule-based algorithm. Crop cultivars are parametrized based on the phenological units required to reach the corresponding maturity dates (TUreq, °C days). In line with15, TUreq are derived consistently with the phenological module of the crop model LPJmL for each grid cell, crop, and rule-based computed growing period from the respective climate input. They are calculated as the sum of daily mean air temperature increments above a crop-specific base temperature (TU) (Supplementary Table 1) between rule-based sowing and maturity. In addition, winter-wheat cultivars require effective vernalization days (VUreq), that range between 0 (mild winters) and 70 (cold winters), depending on the temperature of the 5 coldest months (Eq. (1))15,18.$${{{{{mathrm{V}}}}}}{{{{{{mathrm{U}}}}}}}_{{{{{{{mathrm{req}}}}}}}}=frac{70}{5}times left(1-frac{{T}_{m}-3}{10-3}right)$$
(1)
where Tm is the mean temperature of the month.From the day of sowing, effective TU for phenological development are accumulated daily, as the difference between the mean air temperature on that day and the crop-specific base temperature for phenological development (Eq. (2)). The vernalization effectiveness is computed daily by a scaling factor (0–1), which is then multiplied to the TU (Eq. (2)). For crops that are insensitive to vernalization, VUd is set equal one.$${{{{{mathrm{T}}}}}}{{{{{{mathrm{U}}}}}}}_{{{{{{{mathrm{req}}}}}}}}=mathop{sum }_{d=1}^{{ndays}}left({max }left(0,{T}_{d}-{T}_{{base}}right)times mathop{sum }_{0}^{d}{{{{{mathrm{V}}}}}}{{{{{{mathrm{U}}}}}}}_{d}right)$$
(2)
where the scaling factor VUd is computed by a three-stage linear response function with a range of optimal temperatures (Eq. 3). Temperature for effective vernalization range between −4 °C and +17 °C, with an optimum range between 3 °C and 10 °C.$${{{{{{{mathrm{VU}}}}}}}}_{d}=left{begin{array}{cc}left({T}_{d}-left(-4right)right)/left(3-10right) & {{{{{{mathrm{if}}}}}}}-4 , < ,{T}_{d} , < , 3\ 1 & {{{{{{mathrm{if}}}}}}};3,le ,{T}_{d},le, 10\ left(17-{T}_{d}right)/left(17-10right) & {{{{{{mathrm{if}}}}}}};10 , < ,{T}_{d} , < , 17\ 0 & {{{{{{mathrm{otherwise}}}}}}}end{array}right}$$ (3) In this study, we have removed the effect of vernalization on slowing down TU accumulation until 10% of the total vernalization requirements is reached. In this way, the crop can accumulate both vernalization units and heat units in fall, so that there is some leaf growth before winter (in LPJmL, the LAI curve depends on accumulated heat units).The LPJmL model simulates phenology as one single phase from emergence to maturity. Although the flowering stage is not simulated as an explicit break point, the fraction of above-ground biomass that is allocated to the storage organs (fHI) depends on the phenological progress (fTUreq, fraction of TUreq that have been fulfilled), with the bulk of the storage organs start filling up after 40% of TUreq have been reached (Eq. (4)). In line with this, the LAI curve reaches a plateau when 45% (wheat) or 50% (other crops) of the TUreq are fulfilled, which could be considered a proxy of the flowering stage.$${{{{{{mathrm{fHI}}}}}}}=100times frac{{{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}}{100times {{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}+{{exp }}^{11.1-10.0times {{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}}}$$ (4) Crop biomass growth is simulated by daily carbon accumulation and allocation to different plant organs (roots, leaves, storage organs, mobile reserves, and stem). The fraction of carbon allocated to each pool is a function of the fraction of completed phenological progress. Water stress increases allocation to the roots and reduces allocation to the leaves. The daily Net Primary Production (NPP) is the result of the Gross Primary Production (daily gross photosynthesis) reduced by the respiration costs. Gross photosynthesis is simulated as a function of absorbed photosynthetically active radiation, CO2 atmospheric mixing ratio, air temperature, day length, and canopy conductance. Photosynthesis rate is given by the minimum between light-limited and Rubisco-limited photosynthesis rates, with distinguished pathways for C3 and C4 crops. Respiration is tissue-specific and it is also driven by temperature. If accumulated NPP is insufficient to satisfy all organ demands, allocation follows a hierarchical order from roots, to leaves, to storage organs, and consequently penalizing the harvest index. Crops are subject to yield failure due to frost events (daily minimum temperature More

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ProductivityWith regard to productivity, in the summer harvest of the 2016–2017 crop year, in which all grain production systems had soybean in common, there were significant differences among crop rotations with species diversification and the double-cropped corn–soybean rotation; performance was better in AS-II, AS-III, AS-IV, AS-V and AS-VI and worst in AS-I. There was no significant difference in productivity among the crop rotations with species diversification (Table 2).Table 2 Productivity (kg ha−1) of the crop rotation systems for the 2014–2015 to 2019–2020 crop years in Londrina, state of Paraná, Brazil.Full size tableFor the summer harvest of the 2019–2020 crop year, in which all the grain production systems again had soybean in common, significant differences were also observed among the production systems. AS-I and AS-V had the lowest productivities, differing from AS-IV and AS-VI, which had the highest productivities. Conversely, the productivities of AS-II and AS-III did not differ significantly from those of the other evaluated systems (Table 2).In the cycle that ended in crop year 2019–2020, compared to the cycle that ended in crop year 2016–2017, there was a reduction in soybean productivity in all the analyzed grain production systems (Table 2). There was also a decrease in the productivity of corn grown in the summer in the 2015–2016 and 2018–2020 crop years. This decrease in productivity observed between the production cycles may be associated with climatic conditions because from 2014–2015 to 2016–2017, there was a good rainfall distribution and few water deficit peaks, while from 2017–2018 to 2019–2020, the water deficit peaks were more constant, especially in 2018–2019 and 2019–2020 (Fig. 1). Notably, there was a greater influence of the El Niño phenomenon on the first production cycle (2014–2017) and of the La Niña phenomenon on the second (2017–2020)28. In southern Brazil, these phenomena correspond to periods of weaker droughts under El Niño conditions and a higher frequency of severe and moderate droughts under La Niña conditions29. The occurrence of a water deficit may limit plant growth and development, particularly during the flowering and grain filling stages. Systems that employ crop rotation with species diversification are less susceptible to production losses due to water deficits30. The results of this study show that crop rotation systems with species diversification, by providing a longer soil cover time for soil protection, either with live plants or from the input of surface straw, together with the respective increase in the soil water storage capacity, can mitigate productivity losses resulting from periods of drought (Fig. 1, Table 2).Another finding is that soybean has higher productivity when grown in systems with greater species diversification, as was the case for AS-IV and AS-VI (Table 2). In general, grain production systems that employ crop rotation with species diversification produce more than those that are not diversified31,32, especially in atypical growing seasons affected by climatic factors limiting crop development33.AS-I and AS-V showed the lowest soybean productivity at the end of the second crop rotation cycle, in the 2019–2020 crop year (Table 2). AS-I had the lowest soybean productivity at the end of the two crop cycles, i.e., in 2016–2017 and 2019–2020, a result that is directly related to corn–soybean double cropping. In the southern region of Brazil, for example, soybean productivity in crop rotation systems with species diversification is 6.2% higher than that in double-crop systems22. In this sense, the results of this study indicate that production systems with little species diversification have lower soybean productivity than those that employ crop rotation with species diversification.At the end of the second crop rotation cycle, in 2019–2020, AS-II and AS-III also showed good soybean productivity, i.e., 3864 kg ha−1 and 3848 kg ha−1, respectively. AS-III had one of the highest grain yields in the summer crops, which may be associated with the use of cover crops in the previous winter. The use of cover crops in the winter growing seasons results in a number of benefits from permanent soil cover because cover crops can improve chemical, physical and biological soil attributes, favoring the accumulation of biomass and organic carbon in the soil34 and prevent soil erosion35. In addition, cover crops control pests, diseases and weeds36 and contribute to weed37 and nematode38 control.Regarding crop dry matter, AS-III, AS-IV, AS-V and AS-VI (Table 3) deposited the most dry matter in the system; the crop dry matter in these systems was greater than that in AS-I and showed no significant difference in relation to that in AS-II. The lower production of dry matter in AS-I is explained by the lack of corn cultivation in the summer. Corn grown in the summer was the crop that most contributed to the accumulation of dry matter in AS-III, AS-IV and AS-VI, compensating for the low averages obtained with beans in AS-V and AS-VI and with safflower in AS-IV. The higher dry matter inputs in AS-IV and AS-VI are because these are the only systems in which corn was grown in the summer for two consecutive years. The average dry matter contributed by corn grown in the summer is 9.9 Mg ha−1, while that from off-season corn and soybeans is 6.5 Mg ha−1 and 4.35 Mg ha−1, respectively.Table 3 Dry matter (Mg ha−1) of the grain production systems for the 2014–2015 to 2019–2020 crop years in Londrina, state of Paraná, Brazil.Full size tableStudies carried out in the Cerrado, Mato Grosso, showed that the minimum amount of plant dry matter deposited by crop rotation systems needed to obtain a balance of C in the soil in the region is between 11.7 and 13.3 Mg ha−139. Therefore, we can deduce that AS-III, AS-IV, AS-V and AS-VI would enter equilibrium; that is, over time, there will be neither accumulation of nor loss of C from the soil. For AS-I and AS-II, we can conclude that over time, C stocks in the soil will be reduced, causing a loss of soil fertility and, consequently, productivity, as shown in Table 2, where the yield of AS-I was lower than that of the most diversified treatments.The results show that crop diversification in grain production systems with the cultivation of commercial or cover crops in the winter benefited soybean and corn production in the summer. In similar studies, species diversification is reported to have increased summer crop productivity over time; specifically, in the U.S. and Canada, corn productivity increased by an average of 28.1%40, and in Canada, corn yield increased by 9.9% and soybean productivity increased by 11.8%41.Economic analysisThe highest mean annual revenue was found for AS-VI, while the lowest was found for AS-III. Regarding the mean annual cost, AS-VI demanded the greatest investment, while AS-III showed the lowest production cost. The highest mean annual profit was also observed for AS-VI, highlighting that the revenue more than offset the costs. As expected, the lowest mean annual profit was found for AS-I, that is, the corn–soybean double-crop system (Fig. 2).Figure 2(a) Mean annual revenue, (b) mean annual cost and (c) mean annual profit of grain production systems with varied levels of species diversity in Londrina, state of Paraná, Brazil.Full size imageThe higher profitability observed for AS-VI indicates that the practice of crop rotation with species diversification in grain production systems increased the grain productivity and economic gains. In this system, the productivity of the commercial crops was positively impacted, and the crops showed excellent yields compared to those in the production systems with lower species diversification. In addition, the winter crops played a key role in the composition of the revenues, especially wheat and bean. As previously noted, the highest mean annual costs of inputs (US$ 685), agricultural operations (US$ 353) and other costs (US$ 177) were found for this system. Within the inputs, the highest cost was for fertilizers (K2O, P2O5, and N), accounting for approximately 22% of the total cost (US$ 280). The higher cost may be related to higher energy demands because in a grain production system, a greater energy volume represents a greater use of inputs42. However, although the cost was the highest, the system was found to be more capable of converting investments into higher productivity and, consequently, into higher revenue and profit. Other studies conducted in Brazil also found economic benefits in crop rotation systems with species diversification, for example, in areas with a predominance of Caiuá sandstone, a region with low-fertility soils, in which the highest profitability was obtained in diversified systems that adopted the highest number of commercial crops, both in the winter and summer growing seasons21. Similarly, in another study in southern Brazil, higher productivities were obtained for more diversified crop rotation systems23. In a long-term study involving soybean, corn, wheat and tropical forage grasses in southern Brazil, higher profits were also found for more diversified production systems22.AS-II had the second highest mean annual profit; this system is characterized by the cultivation of cereals in the winter. The results show that this grain production system is promising, as the use of winter cereal crops had a positive effect on the productivity of the summer crops, leading to increased revenue and profit from the sale of soybean and corn (Supplementary Table S2). With regard to costs, the items that generated the highest expenses in AS-II were inputs, accounting for an average of 54% of the total cost, followed by agricultural operations, which represented an average of 31% of the total, and other costs, accounting for an average of 15% of the total cost (Supplementary Table S2). Studies conducted in other locations also recommend crop rotation systems with the use of cereals, as in the semiarid Northern Great Plains, Canada, where higher productivity and greater profit were found with these cultivation systems compared to a system without species diversification43.AS-V had the third highest mean annual profit. This system is composed of six different crops, and its profitability results were also relevant. Regarding the revenues obtained in the winter growing seasons, beans stood out, accounting for 21% of the total (Supplementary Table S2). One of the problems with AS-V was the cultivation of buckwheat, which, in addition to having a low market price and generating little revenue, also had a high production cost, negatively impacting the entire production system. Thus, if buckwheat had not been cultivated, AS-V could have achieved higher profitability than that observed. With regard to the costs for AS-V, the cost of inputs represented an average of 53% of the total cost, followed by agricultural operations (on average, 31% of the total cost) and other costs (on average, 15% of the total). The cultivation of legumes such as beans in the winter is beneficial for grain production systems because it can favor increased production and, consequently, the profit obtained with subsequent crops44.AS-III had the fourth highest mean annual profit. Although this system did not have the best profitability, it should not be disregarded. This system is focused on the production of straw in the winter and on the revenue generated by the summer crops. However, although cover crops do not generate income for the producer, they indirectly promote gains in subsequent crops. With the maintenance of soil cover, productivity gains and increased revenue are expected in production systems in the medium and long terms21. Cover crops, in general, control pests, diseases and weeds and improve soil conditions36 because they prevent soil compaction and improve soil water infiltration and retention, density, and hydraulic conductivity45. AS-III also had the lowest mean annual production cost; the cost with inputs was on average 35% lower than that observed in the other systems. The lower costs are because the cover crops were not harvested because their benefits are obtained from the biomass generated; thus, the cost is lower than that for systems for which the purpose is to sell grains. One of the great benefits of adopting this system is that the cultivation of cover crops in the winter can reduce the cost of the crop that follows because the amount of inputs involved in the production of the next crop can decrease, as can fuel expenses46. In addition, the lower demand for pesticides makes the system more economical and sustainable and less risky. The quantification and analysis of the items composing the costs of each system are extremely important for producers’ decision-making. However, this analysis requires extreme caution because higher production costs do not necessarily mean lower yields, and similarly, lower costs do not necessarily mean higher profits20,21.AS-IV had the second lowest mean annual profit. This system included winter agroenergy crops. With the exception of canola, the other agroenergy crops grown in this production system showed low profitability. Despite having one of the lowest production costs, the low revenue obtained with agroenergy crops compromised the profitability of AS-IV. Even with the sale of crambe, safflower and canola, the revenues were not sufficient to cover the production costs. Although this system did not show one of the best results, studies with bioenergy crops are being conducted in various regions of the world, and these crops may become an option for southern Brazil, as in the case of Italy, where plants of the family Brassicaceae are being introduced in rotation with cereals as a source of income diversification47.The lowest mean annual profit was observed for AS-I. The low profit is related to the high production costs. Despite having the second highest mean annual revenue, the high production cost compromised the profitability of the system. This result is associated with the lower grain productivity observed in this production system and the fact that it specialized in few crops and focused only on commodities, which are subject to changes in their sale price due to seasonality and market uncertainties, or with the increased susceptibility of this system to problems caused by climatic variations. The crops grown in this system are traded in the international market, and in this case, the producers are only “price takers,”, i.e., they are not able to influence the price of the products48. The prices of commodities may vary; thus, producers may obtain higher or lower revenue due to market fluctuations or volatility. In turn, market fluctuations or volatility are caused by, among other factors, production or external factors, such as exchange rate variations or increased food consumption49,50. AS-I had the highest mean annual pesticide costs, approximately 21% of the total cost (US$ 254). In addition to economic factors, the double-crop system has also generated problems such as the proliferation of pests, diseases and weeds because, in contrast to crop rotation, it does not interrupt the life cycles of pests and diseases51. To control the proliferation of pests, diseases and weeds, the increased use of inputs and an increase in the number of agricultural operations are required52, with a consequent increase in production costs20. This increase in production costs can be observed for winter corn crops, which were more expensive than summer soybean crops. In this system, the mean cost to produce soybean in the summer was US$ 567 per ha, and that to produce corn in the winter was US$ 648. Compared to the other systems studied, the average investment required for the winter growing season was US$ 448 and that for the growing season was US$ 640; that is, the winter crops required 30% less investment than the summer crops (Supplementary Table S3).When considering the real selling price of grains, the highest accumulated profit was observed in AS-VI (Fig. 3); however, in a scenario in which the price of soybeans fluctuates (Fig. 3a) both upward and downward, sensitivity analysis revealed different behaviors. If there was a 44% increase in the selling price of soybeans, the ranking order of the systems would change, making AS-I more profitable. AS-I is the most sensitive to soybean price variations, since in this system, the crop is mainly responsible for generating income and is cultivated in all summers. Thus, the opposite results are also expected. A negative variation in the selling price of soybeans will make AS-I the system with the highest accumulated loss. Price changes can significantly increase or decrease the profitability of producers. Thus, the choice of crops and the number of times a crop appears in each agricultural system determines the profitability of the system as the sale price of the crops varies.Figure 3Price sensitivity analysis (accumulated profit of 6 crop years on the y-axis) of six agricultural systems in Londrina, state of Paraná, Brazil. (a) Soybean; (b) corn; (c) wheat; and (d) bean.Full size imageCorn showed some changes in the order of classification of the systems (Fig. 3b). If the corn sale prices were increased by up to 50%, AS-VI would continue to be the system with the highest accumulated profit. In this scenario, AS-I, composed solely of the corn crop in winter, would cease to be the system with the lowest accumulated profit, occupying the position of AS-III. Different from what happened with the soybean crop, the fluctuations in the corn sale price had less impact on AS-I in terms of accumulated profit. This was because the corn produced in this system accounted for a smaller share of profits and, in some cases, even resulted in losses.Regarding the wheat crop (Fig. 3c), changes in the sale price led to little change in the accumulated profit. Wheat was grown only in AS-II and AS-VI, and in a scenario that considered only the variation in the price of this grain, if its selling price was reduced by up to 47%, AS-VI would continue to be the system with the highest accumulated profit. Changes in the selling price of the bean crop (Fig. 3d) had greater impacts. A 50% increase in the sale price of beans led to a 47% increase in profit in AS-VI.In addition to variations in sale prices, another possible scenario is that crops are stored and sold at later dates. This is possible, as cooperatives are able to provide producers with storage and future sale of grains, extending the time for decision-making. Thus, producers can market products at an optimal time, e.g., when sale prices are better than those on the day of harvest. In this scenario, if corn and soybeans were stored and sold at peak prices recorded each quarter, over the 12 months following the harvest date, the evaluated agricultural systems would show even greater profits. Figure 4 shows the evolution of real prices in tons (USD) of corn and soybeans from July 2014 to March 2021.Figure 4Evolution of corn and soybean prices from July 2014 to March 2020. Data were obtained from the Department of Rural Economy of the Paraná State Secretariat of Agriculture and Supply (DERAL-SEAB). The monetary values are corrected for inflation according to the Brazilian Extended National Consumer Price Index (IPCA) to December 2021.Full size imageIf the sale of soybean and corn was carried out at times of price peaks, the accumulated profit of the systems would vary (Table 4). AS-I, composed exclusively of corn and soybean crops, would become the highest profit system (US$ 3,683). AS-VI, although no longer the highest profit system, would still be one of the systems with the best economic results (US$ 3479). In this scenario, AS-IV would occupy the last position, with the lowest accumulated profit (US$ 2732).Table 4 Profit (USD ha−1) of the grain production systems for the 2014–2015 to 2019–2020 crop years, considering quarterly price peaks in Londrina, state of Paraná, Brazil. .Full size tableIn this scenario, driven by the devaluation of the real against the dollar, the increase in domestic consumption and exports influenced the supply of grains in the market, and agricultural commodities such as soybeans and corn reached high sale values. Thus, it is evident that the market is able to condition the farmer’s profitability, which can influence the results of the analysis, both positively and negatively, according to the daily variations in grain commercialization prices53.From the results, it is evident that species diversification in crop rotation has enabled an increase in both grain productivity and economic gains. It is not enough to simply adopt no-till practices without species diversification in grain production systems31,32; it is necessary for the systems to be aligned with the no-tillage system and conservation agriculture principles. The main reasons for investing in crop diversification are as follows: production of roots and straw to cover the soil surface; improved soil structure and sustained soil biology; nutrient cycling; breaking the cycles of pests, diseases, and weeds; productivity gains; and increased profitability. Thus, the challenge lies in the diffusion of production systems aligned with the principles of the no-tillage system and conservation agriculture, that is, to diversify without failing to produce and obtain gains from grain production. Information on the benefits of grain production systems that employ crop rotation with species diversification, tested and with demonstrated economicity, such as those presented in this study, can therefore be decisive for producers’ decision-making and the adoption of practices aligned with sustainability in agriculture. More

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