Global food security is jeopardized by current agricultural practices that prioritize yield over environmental sustainability. These practices contribute to land degradation, biodiversity loss, poor diets, greenhouse gas emissions, and overall unsustainability. Meeting projected increases in food demand (35–56% between 2010–2050) necessitates a transformation of agricultural systems. The debate centers on intensification (increasing production per unit area) versus extensification (expanding cropland). Intensification, while increasing food production, can reduce on-farm biodiversity due to increased pesticide use. Extensification, while potentially improving biodiversity, may lead to deforestation and habitat loss. The land-sharing versus land-sparing debate reflects this dilemma. However, the optimal approach is context-specific; some areas require extensification (where intensification is already unsustainable), while others need intensification (where habitat conversion is the main challenge). This research posits that diversified farming systems (DFS) offer a key element of sustainable intensification (SI), potentially supporting both intensification and extensification depending on the context and socioeconomic conditions. DFS can enhance ecosystem services (pest control, water regulation, soil health), improve yields and resilience, and offer co-benefits in yield quality and system stability. Management practices such as crop rotation, agroforestry, intercropping, and embedding natural habitats can shift farming systems towards SI. Intensively managed systems (monocultures with high agrochemical use) could benefit from diversification through mixed plantings, agroforestry, home gardens, and hedgerows. Extensively managed systems (low input, high diversity, low yields) could intensify through mixed cropping and increased planting density. While evidence supports the benefits of DFS in various contexts (increased food production, economic output, groundwater conservation, carbon mitigation, and biodiversity conservation), the profitability and impact on intensification/extensification remain unclear. This study aims to address this gap by predicting the global suitability of profitable DFS, considering socioeconomic factors and integrating this with biophysical potential for expansion and intensification. The study uses the definition of sustainable intensification as increasing food production per unit hectare without compromising the environment and degrading natural resources, and sustainable extensification as decreasing the depletion of natural resources and environmental impacts while limiting the decrease of food production per unit hectare.

Existing literature highlights the unsustainability of current agricultural practices and the need for transformation. Studies have shown negative impacts of conventional agriculture on biodiversity (Potts et al., 2010; Rhodes, 2018), human diets (Snapp, 2020), and environmental health (Ramankutty et al., 2018). The limitations of both intensification and extensification approaches have been discussed extensively (Matson & Vitousek, 2006; van Zanten et al., 2016; Bateman & Balmford, 2023). Kremen (2015) argues for reframing the land-sparing/land-sharing debate to minimize trade-offs. Research on sustainable intensification (SI) (Pretty & Bharucha, 2014; Angelo & Du Plessis, 2017) suggests context-specific approaches. The benefits of diversified farming systems (DFS) in enhancing ecosystem services and improving yields have been documented (Kremen et al., 2012; Isbell et al., 2017; Beillouin et al., 2021; Jones et al., 2021; Tamburini et al., 2020). However, concerns about lower yields and profits compared to simplified systems persist (Himmelstein et al., 2016; Rosa-Schleich et al., 2019; Sánchez et al., 2022). Studies on cropland suitability distribution (Teka & Haftu, 2012; Zabel et al., 2014) have not focused on the suitability of diversified systems and their profitability, considering factors such as market access and infrastructure (Bowman & Zilberman, 2013). The impact of farmers' decisions based on profitability (Clough et al., 2016; Michler et al., 2019) is also relevant, emphasizing the need to consider socioeconomic factors in predicting the spatial distribution of profitable DFS.

This study employed a maximum entropy (MaxEnt) modeling approach to predict the global spatial distribution of profitable diversified farming systems (DFS). The MaxEnt model, typically used for species distribution modeling, was applied here using locations of profitable DFS as presence data and socioeconomic variables as predictors. The process involved several steps: 1. **Data Collection:** Data on profitable DFS were obtained from a meta-analysis by Sánchez et al. (2022), encompassing various diversified practices (crop rotation, intercropping, agroforestry) and simplified farming systems. Positive effect sizes were classified as profitable. A total of 114 presence and 93 absence records were used. Predictor variables included environmental (cropland area, soil organic carbon), social (population size, density), economic (electricity coverage, travel time to urban centers, ICT coverage, HDI, GDP), and political/governance factors (voice and accountability, rule of law, etc.). Data were rasterized and resampled to a spatial resolution of 2.5 arc minutes. 2. **Variable Selection:** Highly correlated variables (Pearson correlation > 0.8) were excluded. Eight uncorrelated variables were selected for modeling. 3. **Model Creation and Calibration:** The kuenm package in R was used to create 155 candidate MaxEnt models, varying combinations of variables, regularization multipliers, and feature classes (linear, quadratic, product, threshold, hinge). Model selection was based on statistical significance (partial ROC), predictive power (omission rate ≤5%), and model complexity (maximum delta AIC ≤2). Ten-fold cross-validation was used, and the best model (lowest omission rate, least delta AIC, fewest feature classes) was chosen. The cloglog transformation (0-1 range) was used for MaxEnt output. Jackknife results guided the selection of the top 5 predictor variables based on permutation importance: accessibility, cropland area, voice and accountability, nighttime lights, and GDP per capita. 4. **Suitability Mapping:** Four suitability thresholds (maximum training sensitivity plus specificity, balanced training omission, equal training sensitivity and specificity, and 10 percentile training presence) were applied to generate binary suitability maps (presence/absence) to account for uncertainties. 5. **Integration with Cropland Expansion and Intensification Potential:** Data from Zabel et al. (2019) on integrated potential for cropland expansion and intensification were integrated with the DFS suitability map to identify areas suitable for extensification or intensification to achieve sustainable intensification (SI). Bivariate maps were created to visualize the combined potential. The data on integrated potential for cropland expansion and intensification are based on biophysical potential, simulated yields of 17 crops under ideal conditions, and marginal profitability. Areas where high levels of DFS profitability coincided with high potential for intensification or expansion were identified. The data for the presence locations of profitable DFS, as well as the socioeconomic variables used in this study, are available at [https://doi.org/10.60507/FK2/V13Z99](https://doi.org/10.60507/FK2/V13Z99).

The MaxEnt model predicted the global spatial distribution of profitable DFS. Key findings include: * **Global Suitability:** Approximately 47% of the world was found suitable for profitable diversified farming systems. Areas in the Global North exhibited higher suitability compared to the Global South. In the Global South, high suitability was concentrated around cities and along coastlines. Areas with high suitability ranged from 29 to 93 million km² depending on the threshold used. * **Socioeconomic Variable Importance:** Accessibility (distance to cities and markets) and cropland availability were the most crucial factors influencing profitability. Infrastructure variables (accessibility, electricity coverage, cell tower distance) and land allocated for cultivation played significant roles. GDP per capita showed a negative correlation; above USD 60,000, the probability of suitability decreased. Voice and accountability were positively correlated with suitability. * **Suitability for Intensification and Extensification:** Regions with high DFS suitability and high biophysical potential for intensification include sub-Saharan Africa, eastern Brazil, parts of India, Tajikistan, Australia, and Canada. Areas with high DFS suitability and high cropland expansion potential include western Europe, India, China, and parts of Brazil and eastern Europe. West Africa near the Atlantic coast and areas stretching from eastern to southern Africa showed pockets of land suitable for both intensification and expansion, along with high DFS probability. * **Global North vs. Global South:** The Global North tends to be more suitable for profitable DFS due to well-developed infrastructure and established markets offering premium prices for DFS products. In the Global South, suitability is higher near major cities, highlighting the importance of infrastructure for profitability. Limited infrastructure (ICT, electricity coverage) in many Global South countries contributes to high business costs, limited shelf life of produce, and lack of value addition. Governance (voice and accountability) was positively correlated with DFS suitability. This finding contrasts with other studies that find mixed correlations between governance and economic growth. * **Limitations of the Study:** Bioclimatic variables, land cover, crop choice, and adoption rates were not explicitly included in the model due to data limitations and the complexity of modeling diverse crop combinations. However, the findings were combined with data from Zabel et al. (2019) considering biophysical potential for expansion and intensification.

The findings highlight that diversified farming systems (DFS) offer a viable pathway towards sustainable intensification (SI), challenging the either/or dichotomy of land sharing and sparing. The higher suitability of profitable DFS in the Global North compared to the Global South emphasizes the critical role of infrastructure and market access. The negative correlation between GDP per capita and suitability in areas above USD 60,000 suggests that DFS may be more profitable in regions with lower economic development levels. The identification of areas suitable for both intensification and expansion emphasizes the context-specific nature of SI. Different strategies are needed in different contexts. In the Global North, emphasis should be placed on extensification measures in already highly intensified farms. In the Global South, policies should focus on infrastructure development to enhance market access and reduce post-harvest losses. However, caution is needed regarding potential trade-offs, such as land-use change and increased land prices, when considering intensification strategies to compensate for potential losses in biodiversity and other resources. The integration of biophysical potential for expansion and intensification helps pinpoint areas where DFS can most effectively contribute to SI, either through intensification on existing land or through expansion into suitable areas. However, careful consideration is required in expansion to avoid negative impacts on biodiversity. The study underscores the need for a multifaceted approach that balances food production with environmental concerns. Further research is needed to fully explore the interactions between diverse factors affecting DFS profitability.

This study provides a valuable assessment of the global suitability of profitable diversified farming systems (DFS) for achieving sustainable intensification (SI). The findings demonstrate that a significant portion of the world is suitable for DFS, highlighting the potential of this approach to transform agricultural systems. The identified areas suitable for intensification or expansion, combined with socioeconomic factors, offer crucial insights for policy decisions and land-use planning. The study emphasizes the importance of considering contextual factors (infrastructure, market access, governance) when promoting DFS, particularly in the Global South. Further research could explore specific crop combinations, detailed biophysical requirements, and the long-term sustainability of DFS under different climate change scenarios.

The study acknowledges limitations related to data availability and model complexity. Bioclimatic variables, land cover, specific crop choices, and adoption rates were not explicitly incorporated in the MaxEnt model due to data constraints and the challenge of modeling diverse crop combinations at a global scale. The integration of data from Zabel et al. (2019) indirectly accounted for some biophysical aspects, but the combined uncertainties from multiple data sources could affect the results, particularly in regions like China. The use of multiple thresholds aimed to mitigate uncertainties inherent to modeling approaches with imperfect data. However, the results should be interpreted with the awareness that the accuracy and resolution of the findings are limited by the available data and assumptions made in the modeling process. Furthermore, the profitability of DFS may be influenced by factors not considered in this study, including farm management practices, market conditions, and policy support.