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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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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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Sample collectionA survey was conducted among the residents of nine counties in Kenya (Mombasa, Kisumu, Machakos, Nairobi, Makueni, Bomet, Kericho, Kiambu, and Narok) and GPS location coordinates were recorded and later used to build the predictive model (“Infestation dynamics of bedbugs in residential communities” section). These counties represent diversity in cultural practices, livelihood strategies (such as fishing, tourism, farming), and infrastructure development. Also, they comprise different altitudes above sea level, temperatures, and differing in average annual rainfall.Samples identification using morphological identification keysIn each county where the survey was conducted, bedbug samples was taken and preserved in ethanol 70% for morphological identification. Cimex belonging to Cimicidae family is the common genus adapted to human environment and reported throughout the world and comprising species such as Cimex lectularius and C. hemipterus that are hematophagous mainly feeding on human blood5. The key morphological features used in identifying bedbugs include: (1) the head has a labrum that appears as a free sclerite at the extreme anterior margin, ecdysial lines form a broad V, eyes project from the sides composed of several facets and the antennae are 4-segmented, (2) thorax is subdivided into prothorax, mesothorax and metathorax, (3) legs have all other normal parts except pulvilli and arolia, tarsus is 3-segmented with 2 simple claws, (4) the abdomen has 11 more-or-less segmented recognizable segments, 7 pairs of spiracles borne on the second to eighth segments, hosts the genital structures, paramere in males and mesospermalege in females45. Bedbug specimen morphological features were examined using Leica EZ24 HD dissecting microscope (Leica Microsystems, UK) and photos documented using the associated software.Survey for household’s knowledge and perceptions on bedbugsThis study was a community-based cross-sectional survey conducted from November–December 2020 with respect of the rules/guidlines introduced by the Ministry of Health to contain the COVID-19 pandemic in Kenya (wearing mask, social distance, washing hand, etc.). It was based on a stratified, systematic random sampling where 100 respondents were selected from each county.A total number of 900 respondents were randomly selected and the household head or the representative showing willingness and consent was interviewed face-to-face. The interview was conducted using a semi-structured questionnaire prepared in the English language (Appendix A). The questionnaire was translated into the local native language (Kiswahili) to avoid biasness and improve the understanding between the enumerator and the respondent. Prior to the commencement of the survey and authentic data collection, a pre-testing exercise was performed by training enumerators on a similar socio-demographic pattern. This was useful for improving the quality of data, ensuring validity, familiarizing the enumerators with the questionnaire, and data handling.The information collected using the semi-structured questionnaire included residents’ socio-economic profiles, knowledge, and perceptions on the pest, bedbug incidence, and management practices. The socio-economic profile factors addressed in the survey comprised gender, age, education, access to basic social amenities, and household size. The study also prioritized the financial consequences, the severity of the bites, perceptions of respondents on the pest, and management practices for its control.Survey data were checked for errors, completeness, summarized, and entered in Microsoft-Excel. It was then cleaned and transferred to Statistical Package for Social Science (SPSS) version 25 software (IBM Corp., Armonk, NY) for purposes of descriptive statistics (means and percentages).In contrast, in instances where more than one reason was given for a single question, percentages were calculated based on each group of similar responses. Chi-square was performed to determine the differences regarding socio-demographic characteristics, knowledge, and perceptions on bedbugs and control practices. Additionally, data were disaggregated by gender and age categories to understand the existing differences among the various respondent categories. Besides, F-test statistics was performed on the ages of respondents to determine the mean, standard deviation and statistical significance. The level of significance was considered when the p-value was below 5%.Infestation dynamics model of bedbugModel simulation assumptionsHouses infestation dynamics was studied following Susceptible-Infested-Treatment (SIT) model46. Therefore, houses in the community are classified into three groups: susceptible, infested or treated. Within a house, bedbug population dynamics was ignored, while it was considered from one house to another where infested houses have some potential to spread the infestation to other houses in the community. A population of bedbugs in an infested house has some probability per unit of time of becoming extinct either naturally or after treatment. In the infestation dynamics, the rate of house infestation depends on the number of infested houses, the movement of people from one house to another and the proportion of treated houses in the community. We assume that infested houses (I) spread the infestation at the rate β and only a fraction S/N of the houses is susceptible (S) to infestation. Infested houses become extinct at a certain rate known as rate γ. Infested houses are treated at the rate τ and the protection conferred is lost at the rate α. Ordinary differential equation developed to study SIT model were used in this study46. All the models used have the generic formulations displayed below:$$frac{dS}{dt}=frac{beta }{N}SI+gamma I+alpha T$$
(1)
$$frac{dI}{dt}=frac{beta }{N}SI-(gamma +tau )I$$
(2)
$$frac{dT}{dt}=tau I-alpha T$$
(3)
where β  > 0, τ  > 0, α ≥ 0 and γ  > 0. The total population size is N = S(t) + I(t) + t(t). The initial conditions satisfy at S(0)  > 0, I(0)  > 0, T(0) ≥ 0 and S(0) + I(0) = N, where N is the constant total population size, dN/dt = 0.Infestation dynamics models implementationThe method used to implement the infestation dynamics model of the pest is based on the system thinking approach with its archetypes [Causal Loop Diagram (CLD), Reinforcing (R) and Balancing (B)] by a mental and holistic conceptual framework. This is important for mapping how the variables, issues, and processes influence each other in the complex interactions of bedbugs within and between houses and their impacts. Despite these archetypes being qualitative, they are necessary for elucidating and disclosing the basic feedback configurations that occur in houses and their environs when infested with pests like bedbugs. A dynamic model was generated by converting the causal loop diagram (CLD) obtained using stocks, flows, auxiliary links, and clouds. Consequently, these in turn were translated into coupled differential equations for simulations.The SIT model was translated into causal loop diagram where arrows show the cause-effect relations where positive sign indicates direct proportionality of cause and effect while negative sign shows inverse proportionality relations, and two different scenarios have been assessed: (1) homogeneous houses where there is a single community of houses of the same quality, and (2) heterogeneous houses where there is a community of good and bad houses. Ancient houses presenting slits/fissures with less cleanliness and filled with old or secondhand furniture at low grade are considered bad houses as they may sustain high level of bedbug infestation; and new houses don’t provide well enough conditions for bedbug population to survive, and they are called in the model good houses47. Bad houses are considered to act as sources while good houses act as sinks, but all together are randomly distributed where each house has the same probability to contact good or bad houses.In the scenarios of homogeneous houses, the causal loop diagram (Fig. 7) has two feedback loops: (a) one positive, as the number of infested houses increases, the probability to get susceptible houses infested also increases resulting in infested houses increase; (b) one negative, as the infested houses increases, the treated houses increase resulting in susceptible houses decrease. The causal loop diagram is displayed in Fig. 7A while Fig. 7B showed the stocked and flows diagram and axillary variables obtained from causal loop diagram.Figure 7Susceptible-Infested-Treatment (SIT) model translated into causal loop diagram (A) and stock and flow diagram (B) for homogeneous houses and causal loop diagram (C) and stock and flow diagram (D) for heterogeneous houses in the community.Full size imageSusceptible, infested, and treated houses are stocks in the system, representing the number of houses susceptible, infested, and treated, respectively at a given point of time. The rates represent in and out-flows of the diagram. Auxiliary and constants that drive the behavior of the system were connected using information arrows within them and flows and stocks to represent the relations among variables in terms of equations.In the scenarios of heterogeneous houses, the causal loop diagram (Fig. 7C) comes with the two previous feedback loops but for each category of house. In addition, there is a fifth feedback loop that connect bad house to good house and vice versa.Therefore, as the infested bad houses increase, the probability to infest good houses increases. The more they are exposed the more they get infested. In turn, as the infested good houses increase, the chance to infest susceptible bad houses increases and the more they are exposed, the more they get infested, resulting in the increase of infested bad houses. The stocks and flows diagram of each of the two categories of houses occurred with interconnexion relationships between the two categories (Fig. 7D).Models’ simulationsThe survey data (“Bedbug Genus identification” section) on prevalence, knowledge, perceptions and self-reported; in addition, the respondents’ reported control mechanisms and their average time of effectiveness (Appendix B, Table S1) were used for model simulations. The different control methods reported were reclassified in three control approaches: chemical control, other control methods (including exposure to direct sunlight, use of hot water, painting, application of diesel, paraffin and wood ash, use of Aloe Vera extract and Herbs), and combination of chemical and other control methods. All the models commodities and units were checked before performing the simulations. Simulation and implementation of the models were done using Vensim PLP 8.1 platform (Ventana systems, Harvard, USA). It consists of a graphical environment that usually permits drawing of Causal Loop Diagram (CLD), stocks, flow diagrams and to carry out simulations. After we simulated the infestation dynamics under the two scenarios, we explored the effect of the different control methods.Spatial distribution analysis of bedbugs using MaxEnt modelEnvironmental data for MaxEntThe environmental variables used as the other maxent input were obtained by deriving bioclimatic, land cover, and elevation data. Bioclimatic variables and elevation (Digital Elevation Model; DEM) data were obtained from the Global Climate Data official website, Worldclim (http://www.worldclim.org/bioclim.htm)48 including 19 bioclimatic variables (Appendix B, Table S2). The land cover data were downloaded from the Global Land Cover Facility (GLCF).In order to reduce collinearity between predictors, a collinearity test was performed on all the variables by filtering them according to the following steps36: firstly, the MaxEnt model was run using the distribution data of bedbugs and 19 bioclimatic variables to obtain the percent contribution of each variable to the preliminary prediction results. Secondly, following the generation of the percentage contribution of all the variables, we then imported all distribution points in Arc-GIS and extracted the attribute values of the 19 variables. Furthermore, the “virtual species” package49 in R-software (R Foundation for Statistical Computing, Vienna, Australia) was used to explore the extracted variables’ clusters spatial correlation using Pearson’s correlation coefficient and the cluster tree (Fig. 8). Thus, the final number of predictor variables after screening was 5 establishing the potential geographical distribution of bedbug, which includes Temperature Seasonality (bio4), Precipitation of Driest Month (bio14), Temperature Annual Range (bio7), Precipitation of Driest Quarter (bio17) and Precipitation of Warmest Quarter (bio18) (Appendix B, Table S2). The land cover was considered because studies have shown its importance on insect spatial distribution50,51,52 and it was setled as a categorical variable53. Elevation was selected as variable because it greatly influences species’ occurrence and dispersal by affecting the temperature, precipitation, vegetation, and sun characteristics (direction, intensity, etc.) on the earth’s surface54,55,56. The study variables had different resolutions and were therefore, resampled to 1 km. The variables were clipped to Kenya and Africa boundaries and converted to ASCII (Stands for “American Standard Code for Information Interchange”) format using the ‘raster’ package49 in R statistical software (R Foundation for Statistical Computing, Vienna, Australia).Figure 8Key model predictor variables.Full size imageDistribution modelling in Kenya and AfricaIn our study, we used the maximum entropy distribution modelling method. This is because it has been recommended to have the ability to perform best and remain effective despite the use of small sample size relative to the other modelling methods57.Our selected bioclimatic variables (5) and occurrence/prevalence data for bedbugs were then imported into MaxEnt model and the options of ‘Create response curves’ and ‘Do jackknife’ were selected to measure variable importance’ options. The model output file was selected as ‘Logistic’, the commonly used approach is the random portioning of distribution datasets into ‘training’, and ‘test’ sets57,58. MaxEnt model was run with a total number of 5000 iterations and five replicates for better convergence of the model and rescaled within the range of 0–1000 suitability scores using ‘raster’ package49 in R statistical software (R Foundation for Statistical Computing, Vienna, Australia).The modelling performance/MaxEnt accuracy was evaluated by choosing the area under the receiver operating characteristics (ROC) curve (AUC) as the estimation index. This was important for the calibration and validation of the robustness of MaxEnt model evaluation. Furthermore, the area under the ROC curve (AUC) was necessary as an additional precision analysis59. The range of AUC values greater than 0.7 was considered a fair model performance, while those greater than 0.9 indicated that the model was considered an excellent model performance. Therefore, by considering the AUC values, the excellently performing model was selected to analyze the suitability of bedbugs in Kenya and Africa59,60,61,62.The ASCII format output was then imported into QGIS 3.10.2 (using the QGIS 3.10.2 software, https://qgis.org/downloads/), following its conversion into a raster format file using R software. This was useful for the classification and visualization of the distribution area63,64. The potential suitable distribution of bedbugs was extracted using the Kenyan and African maps. At the same time, Jenks’ natural breaks were also used to reclassify and classify the suitability into five categories, namely: unsuitable (P  More