Spatial proxy calculation

The inoculum density of soilborne pathogens is dependent on the climate and cropping system [14]. Even though some authors report favorable temperatures for the disease (e.g. above 18°C) [14](e.g. between 22–32°C) [18], and growth, survival and chlamydospore germination, the adaptation to climatic variations in both temperate and tropical regions, turns the FSSC into a cosmopolitan pathogen [15].Growing drivers, such as the temperature and soil moisture, coupled with the nutrients and organic matter content in soil, directly affect the viability of chlamydospores (the resistance structures of several Fusarium species) and the seasonality of the FSSC [20]. The same variables affect directly host root development in different cropping systems [14].

FSSC chlamydospores are broadly distributed in soil throughout the year, and growing hyphae exhibit great saprophytic ability [21]. In this study, a database of FSSC inoculum density records managed by Embrapa Arroz e Feijão (Santo Antônio de Goiás, Brazil) supported the pathogen spatial proxy estimate. That database was composed of 2,311 soil samples from commercial farms that belonged to 103 municipalities in 10 Brazilian states assessed from 2002 to 2015. Common beans were always present in the cropping history of sampling sites. In general, samples were taken at 0–10 cm topsoil from commercial farms where common bean-maize-soybean is the main cropping sequence, chosen by farmers due to commercial demands. Eventually, cropping sequences included sorghum, millet, vegetables, or forage crops. Each soil sample was submitted to serial dilution and deep plating in Nash-Snyder semi-selective medium. The FSSC colonies were identified and their colony forming units (CFUs) per soil gram considered to estimate FSSC inoculum density. Former strain pathogenicity tests with the inoculum layer method [22] showed that all isolates caused average or high dry root rot severity to the common bean [19], supporting the modeling studies with feasible field records of inoculum density (S1 Table).

Disease data were retrieved from publications with field records of dry root rot on common bean crops. Scientific papers, short communications, and technical documents were selected according to the infestation histories of the sampling sites. Only those publications for which experiments had been conducted in sites naturally infested with the FSSC or in sites with historical records of dry root rot were kept. Ten publications sufficiently met the selection requisites and the geographic coordinates of their experimental sites, and therefore, were registered to support 46 disease occurrences (S1 Table).

To find the best spatial proxy for the disease, with a reliable spatial reference, we estimated the Spearman’s correlation coefficient between the disease occurrence and FSSC inoculum density records. Three inoculum densities were selected according to published data regarding the disease severity/inoculum density relationship. The inoculum densities adopted were the following: 1200 CFU/g of soil based on field experiments and controlled environment tests with the common bean and FSSC [23]; 3700 CFU/g of soil in greenhouse experiments with the same pathosystem as above [24]; and 4500 CFU/g of soil based on greenhouse tests to estimate the dry root rot severity according to increasing concentrations of FSSC chlamydospores [17]. The inoculum density that most correlated with dry root rot records was then considered a spatial proxy for the disease.

Climate and climate change information

Climate data, used here to calibrate models of potential distribution, were downloaded from the WorldClim website (www.worldclim.org/current). This database was produced via the interpolation of data from ground weather stations referring to the years of 1950–2000 [25]. On WorldClim, climate data are available as raster files containing grid-based information at different spatial resolutions. We upscaled the downloaded rasters to the resolution of 0.5 degrees of lat/long. Although our inoculum dataset allowed a finer resolution analysis to be conducted, we opted for a relatively coarser spatial resolution. Because the exact location of the sampling sites was not known, the resolution of spatial data on disease occurrence (extracted from publications) was usually rough. Several papers indicated only the municipality and not the exact locations (and the associated environmental conditions) of the experimental sites. However, most municipalities to which studies usually referred were smaller than 50km². Therefore, we assumed that a 0.5 lat/long degree could adequately encompass the average enviromental conditions associated with all of the possible locations where experiments could have been conducted. In this way, the loss of some important local environmental information was compensated for by more accurate patterns on a worldwide scale, due to more generalized relationships between climate and disease occurrence.

In addition to estimating the potential distribution of dry root rot in the present- day, we also evaluated the potential impacts of climate change on disease spread. To do so, we projected the disease distribution models into future climate scenarios. Scenarios of climate change were taken from two “Representative Concentration Pathways”—RCPs—from the Intergovernmental Panel on Climate Change (IPCC). Each RCP is based on a greenhouse gas concentration trajectory that the IPCC adopted for its Fifth Assessment Report (AR5) [26]. The RCP 2.6 estimates an increase of global warming of 1°C by 2050 (average for 2041–2060), whereas the RCP 8.5 projects an increase of 2°C. The same scenarios are used for 2070 (average for 2061–2080) with the RCP 2.6 (1°C) and the RCP 8.5 (3.7°C) [26]. Each RCP scenario is calculated from monthly temperature and precipitation averages, which the climate forecasts known as Atmospheric and Oceanic General Circulation Models (AOGCMs) generated [27]. Bioclimatic variables therefore are calculated from monthly temperature and precipitation values, representing annual climatic trends, seasonality, and extremes. Those climate parameters are usually considered environmental constraints for biological species and systems [28].

Although AOGCMs have been widely used to project the impacts of climate change on species distribution, different forecasts may provide different outcomes [27]. Variation in the AOGCMs chosen to project distribution models for the future can thus affect maps of potential distribution, creating a well-known source of uncertainty [29]. We therefore accounted for that known source of uncertainty by selecting different AOGCMs and projecting the disease distribution models onto all of them. The following climate forecasts were chosen: the Community Climate System Model (CCSM4) version 4 [30], the Hadley Centre Global Environmental Model version 2 (HADGEM2) [31], and the Model for Interdisciplinary Research on Climate (MIROC5) [32].

These climate forecasts are based on robust modelling algorithms, although each one has a different bias in terms of temperature and precipitation estimates [27]. The CCSM4, for example, has biases in average precipitation distribution in the tropical Pacific Ocean [30], and the HADGEM2 shows some bias toward warmer temperatures in the continental Northern Hemisphere and a colder bias in South America [31]. Lastly, MIROC5 also shows a cooling bias in the North Atlantic [32]. Therefore, no AOGCM is efficient in everything [27]. Such biases may, however, be ameliorated by considering different AOGCMs as a source of variation in model outcomes to improve the predictions of distribution models [33].

Climate forecasts provide predictions for several environmental variables based on temperature and precipitation—the bioclimatic variables. However, not all of these predictors are used in modelling procedures, to avoid correlation and collinearity-related problems. We therefore selected the predictors to be used in modelling procedures, by using logistic regressions. Logistic regressions are meant here to evaluate which bioclimatic variables would be the best disease predictors by calculating slopes without or with low collinearity and, at the same time, showing satisfactory biological explanations. All bioclimatic variables were considered as predictors. The response variable in such logistic regressions was disease occurrence (presence or absence), defined by the best spatial proxy, which was described earlier in the text. Logistic regression was performed with the R function glm, the binomial family, and the logit link. The binomial family is adequate for presence-absence data, and the logit link is the natural log of the odds in which the response variable equals one of the categories (zero and one categories). Non-significant predictor variables were removed. Further, collinearity between predictor variables was avoided with a cutoff on Pearson’s correlation coefficient (r < 0.25), which is considered statistically significant (p < 0.05) [34]. Those procedures led to the following bioclimatic variables, to be used as predictors in subsequent distribution models: Isothermality (mean diurnal range/temperature annual range), maximum temperature of the warmest month, precipitation seasonality (coefficient of variation), and precipitation of the warmest quarter.

The bioclimatic variables were therefore selected to allow appropriate statistical analyses. However, biological and ecological reasons also exist for justifying their choice as the best climate predictors [35]. Two chosen bioclimatic variables are based on the maximum and seasonal temperature, which admittedly alters the occurrence of diaseases. The precipitation seasonality is also a known driver of soilborne pathogen growth [4]. The rationale of modelling disease distribution based on optimal temperature ranges may not be efficient for predicting where disease does not occur [35]. Climatic constraints (maximum and minimum) may, however, lead to insights on the growth, development, and fitness of species over a period of time [35]. Periods of drought and rain in regions that exhibit high climatic seasonality may therefore influence the FSSC. These climate constraints [36,37] are indeed known to affect chlamydospore and conidia germination, spore viability, and agressiveness in different cropping systems [14].

Distribution models for the Fusarium solani species complex

In this work, the study model comprised a soilborne pathogen (FSSC) and a host (common bean), used here to assess dry root rot distribution. As explained before, we used a spatial proxy defined by the inoculum threshold that best represented disease occurrence. Therefore, we modeled the pathogen environmental requirements found at locations where in-situ inoculum density seems ideal for disease manifestation. The environmental requirements of a pathogen are usually linked to disease occurrence via conditions (abiotic factors) and resources (biotic factors, which may be consumed and are subjected to competition) required for the pathogen’s survival and breed [38]. However, models based solely on ecological niches of pathogens may not lead to accurate maps of disease risk because the presence of a pathogen does not necessarily implicate in disease manifestation [39]. Thus, by using not only the pathogen presence but also the density most correlated to disease manifestation, we modeled the environmental conditions most strongly related to the dry root rot occurrence. The resulting host × pathogen × environment interaction is therefore the pathogen niche projected for disease occurrence and represented in maps of climatic suitability of dry rot root in common beans.

Common bean crops account for about 3.1 million hectares cropped in all Brazilian regions, especially in the South, Southeast, and Center-West regions, which themselves are responsible for 3,327.8 thousand tons of the crop [40]. In Brazil, diseased fields are frequently reported, especially due to conducive weather and the omnipresence of susceptible cultivars [41]. In this study, models of FSSC distribution were calibrated with data retrieved for the Brazilian territory extent, although projections were made worldwide. We did so because the access to the exclusive database on inoculum densities allowed us to characterize regions in the pathogen’s climatic niche, e.g., the environmental preferences and constraints [42–44], in a way not repeatable with other countries’ datasets.

By calibrating our distribution models exclusively with Brazilian data, we therefore assume that the relationship among the disease occurrence, inoculum density, and environmental requirements can be extrapolated to other regions with similar climatic conditions. This approach, although possibly new in plant disease epidemiology, is widely used in other niche-related areas, such as biological invasion risk assessments [45]. By using such an approach, our attempt here is to provide a first visual map of the dry root rot potential distribution worldwide, but not a guide for supporting local farmers and crop managers. Our models probably do not capture local climate peculiarities due to territorial data restrictions, even though disease projections may match disease records elsewhere. Therefore, we caution that the world maps provided here should not be used beyond their intended purpose.

Another known source of uncertainty in distribution models, beyond AOGCM climate forecasts, is the modelling method used to establish the relationship between the occurrence of the object of interest and the environment it occupies. Different modelling methods may provide dramatically distinct projections [8]. To minimize such discrepancies, we considered only a few different methods and weighted their projections according to their performances. That model-weighting procedure, also called “model ensembling”, assumes that by encompassing different possible projections and their respective performances, uncertainty in the modelling method is therefore minimized [46]. Such ensembles should not, however, encompass all classes of modelling methods, as they may have different requirements for model building and thus non-comparable results [47]. We therefore accounted for model uncertainty by ensembling among projections from different methods but also respecting theoretical restrictions regarding outcome comparisons.

Our ensembles of distribution models were performed within two main classes of models: 1) the statistical methods and 2) the machine-learning methods. No ensemble was performed between both classes of methods. Statistical or regression-based methods (e.g., a generalized linear model [GLM], a generalized additive models [GAM], and multivariate adaptive regression splines [MARS] allow for encompassing a large number of relationships between occurrences and environmental factors and usually have good explanatory power regarding the distribution-related ecological processes [47]. In this class of methods, precision and generality are balanced, which leads to moderately flexible although accurate predictions [48]. Machine-learning methods, in contrast, employ data-mining algorithms—such as GARP (Genetic Algorithm for Rule Set Production), random forest, and artificial neural networks—in an attempt to maximize the relationship between environmental predictors and biological responses [47]. Machine-learning methods usually lead to highly accurate but more clinger distribution predictions (rigid predictions) [48]. In machine-learning methods, generality is penalized for the sake of accuracy, and model complexity usually prevents a clear interpretation of parameter relationships [47].

The regression-based methods used in this work were a GAM and a GLM because they are compatible in building requirements [48]. The GAM was implemented with the function of gam using the binomial family and selecting 10,000 pseudo-absences randomly sampled from all occurrence points within our defined extent. Meanwhile, the GLM was adjusted with a linear function using a binomial family, being performed for stepwise proceeding, and using 10,000 pseudo-absences with random sampling, to avoid collinearity issues [48]. All analyses were performed in “sp” [49], “raster” [50], and “Biomod2” [51] packages within the R environment (R Development Core Team).

The machine-learning methods used in this study were the random forest and classification tree analysis. Random forest is a general technique of random decision forests. Here, we used 1,000 pseudo-absences collected with a random selection of points outside of the suitable area estimated with a rectilinear surface envelope from the large presence number (surface range envelope model “SRE”) [48]. Finally, we performed a classification tree analysis (CTA) with the same random forest framework described above, to assure model outcome compatibility. All models were fitted with 100 runs.

In a data-splitting process, 75% of our occurrence data were used for training and 25% for testing the model performance [48]. Model weighting was based on the True Skill Statistics (TSS), a measure of model performance that the prevalence of occurrences does not affect [52]. Sensitivity is the probability that the model correctly rates the presence of data, and specificity is the probability that it correctly rates an absent data. Values of TSS (TSS = sensitivity + specificity -1) range from -1 to +1, where values close to +1 indicate high accuracy, whereas values equal to or smaller than zero are usually considered not better than random. Less biased than other criteria, the TSS is the measure of choice for distribution predictions [53]. We used a cutoff (TSS < 0.5) to select exclusively the models with the best accuracy, i.e., models with TSS smaller than this figure were removed and not considered in posterior weighting procedures. Therefore, a weight (the TSS value) was attributed to each cell-based prediction of environmental suitability, which resulted in an averaged ensemble for each modelling method.

Ensemble models were projected onto current climate maps to provide estimates of potential distribution for the FSSC. The same ensemble models were then projected onto predictions of future climate forecasts, which were previously collected. Therefore, suitable regions were identified for disease distribution in the present-day time and in different scenarios for climate change. Projections were made on both a country (Brazil) and a worldwide scale to predict the disease risks of dry root rot on growing regions of common beans elsewhere [54]. All of the modelling procedures were performed with the R “Biomod2” package in R (R Development Core Team).

Uncertainty analysis

Despite considering different projections, i.e., the ensembling procedure, we were also interested in determining which were the main drivers of total uncertainty in the model outcomes. To disentangle the variation present in our results, we adjusted linear mixed models with residual maximum-likelihood estimation (REML). Prior to that, we performed an estimability test of the effects in the mixed model in R [55] to check if it could be used to correctly describe factor rankings. We therefore built the mixed model considering the “year” (year 2050 and year 2070) as a random factor and considering “AOGCMS,” “RCPs,” and “modelling methods” as fixed factors. The Gauss-Markov function of the parameters was considered to be estimable if built by a linear combination of mathematic expectations. The best empirical linear unbiased estimates (eBLUEs) for fixed factors and the empirical best linear unbiased predictors (eBLUPs) were also performed for random factors. Thus, we separated the percentage of variation attributed to each factor. Because our model outcomes are maps, uncertainty was calculated for each grid cell. Therefore, uncertainty maps could be obtained for total variation and for the variation attributed to each factor. All maps presented in this paper are original and were created in R and ArcGIS 10.1 (ESRI, Redlands, CA, USA).