Modeling the impact of improved seed varieties on common beans productivity in agroecological zones of Tanzania: A stochastic simulation approach

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Kadigi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7237495/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Beans are a critical source of food and income for smallholder farmers in Tanzania; yet, their productivity remains low due to a reliance on traditional varieties and limited adoption of inputs. This study evaluates the impact of improved seed varieties on bean productivity across diverse agroecological zones (AEZs) in Tanzania, employing a stochastic simulation approach. Drawing on nationally representative data from the 2019/20 National Sample Census of Agriculture (NSCA), we compared yield distributions for farms using local versus improved seeds. Monte Carlo simulations assessed the probabilities of achieving productivity thresholds of 0.6 t/ha (low) and 1.5 t/ha (high) during both long and short rainy seasons. Findings reveal that improved seeds significantly increase the likelihood of higher yields, particularly in the short rainy season. In zones such as the Lake and Eastern regions, improved seed users had a 42–49% probability of surpassing the global standard of 1.5 t/ha, compared to only 34% for local seed users. However, this yield gain was accompanied by slightly higher variability and risk of yield failure. The long rainy season presented less favorable conditions, with over 50% of farms, regardless of seed type, yielding less than 0.6 t/ha and minimal chances of exceeding 1.5 t/ha. Spatial variability was evident, with improved seeds showing stronger effects in the Lake, Eastern, and Northern zones. Notably, local seeds continued to demonstrate profitability during the short rainy season. The study recommends improving access to improved seeds, enhancing extension services, and implementing input subsidies for marginalized AEZs. These findings support policy interventions that boost resilience, productivity, and food security, aligning with Sustainable Development Goal 2 (Zero Hunger). The study also highlights the need for spatially differentiated strategies and provides empirical evidence to inform adaptive agricultural policy and investment planning. stochastic simulation local seeds improved seeds bean productivity agroecological zones Tanzanian Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Common beans ( Phaseolus vulgaris L. ) constitute a vital component of the daily diet for millions of households in developing countries, serving as both a staple food and a crucial source of protein, micronutrients, and cash crop legumes (Mkuna, 2022 ). Globally, beans are recognized for their role in enhancing food and nutritional security, particularly among low-income populations who rely heavily on plant-based protein sources (Beebe et al., 2000 ; Paredes et al., 2009 ; Assefa et al., 2006 ; Blair et al., 2010 ; Mukankusi et al., 2019 ). Rich in iron, zinc, fiber, and essential amino acids, beans significantly contribute to reducing micronutrient deficiencies and combating undernutrition, particularly among children and women of reproductive age (Petry et al., 2015 ; Huertas et al., 2023 ; Muthoni & Nyamongo, 2009 ; Katungi et al., 2010 ; Wortmann & Allen, 1994 ). Globally, common bean production covers approximately 30 million hectares, with an annual production of over 28 million metric tons. Latin America and Sub-Saharan Africa (SSA) are the largest producers and consumers, with countries such as Brazil, Mexico, Kenya, and Tanzania among the top contributors (Beebe et al., 2012 ; Jansa et al., 2011 ). In SSA alone, beans occupy a central position in both rainfed agriculture and local diets, providing up to 20% of daily protein intake in some rural communities (Wortmann et al., 1998; Buruchara et al., 2011 ; Farrow & Muthoni-Andriatsitohaina, 2020). Despite this critical role, bean productivity remains substantially below global standards in most SSA countries, averaging between 0.6 and 0.8 t/ha, compared to the global potential yield range of 1.3–1.5 t/ha (Terán & Singh, 2002 ; Buruchara et al., 2011 ; Farrow & Muthoni-Andriatsitohaina, 2020; Rubyogo et al., 2010 ; Hummel et al., 2018 ; Katungi et al., 2009 ; Beebe et al., 2008 ; Rao et al., 2013 ). In East Africa (EA), common beans are among the top five most widely cultivated food crops, grown by over 30 million smallholder farmers, largely under low-input, rainfed systems (Asfaw, 2011 ; Asfaw et al., 2012 ; Bruno et al., 2018 ). Tanzania stands as one of the leading producers in the region, with over 1.2 million hectares dedicated to bean farming, yielding more than 900,000 metric tons annually (URT, 2021). The crop is cultivated across diverse agroecological zones, including the Northern Highlands, Southern Highlands, Lake Zone, and the Western Zone, where it supports both household food security and market-oriented farming (Justus et al., 2021 ; Hamazakaza et al., 2014 ; Letaa et al., 2015 ; Hillocks et al., 2006 ; Ndakidemi et al., 2006 ; Tryphone et al., 2013 ). However, despite its significance, bean production in Tanzania continues to face myriad challenges that constrain productivity. These include low adoption of improved seed varieties, recurrent droughts, erratic rainfall, pest and disease outbreaks (notably angular leaf spot, root rots, and bean fly), soil fertility depletion, and limited access to extension services and inputs such as certified seeds and fertilizers (David & Sperling, 1999 ; Rubyogo et al., 2010 ; Assefa et al., 2006 ; Beebe et al., 2012 ; Jansa et al., 2011 ; Jiménez, 2019 ; Parker et al., 2022 ). Furthermore, much of Tanzania's bean production is conducted using local landraces, which, although well-adapted to local conditions, have lower yield potential and poor resistance to biotic and abiotic stresses compared to improved varieties (Lunze et al., 2012 ; Birnholz et al., 2018 ; Barasa, 2022 ). Over the past two decades, several initiatives have been introduced by governments and development partners in SSA to address these constraints and boost bean productivity. These include regional programs such as the Pan-Africa Bean Research Alliance (PABRA) and the Eastern Africa Agricultural Productivity Project (EAAPP), as well as national interventions like Tanzania’s Agricultural Sector Development Programme (ASDP I & II). These programs have promoted the dissemination of improved bean varieties, capacity building in seed systems, and participatory breeding to align varieties with farmer preferences and local agroecological realities (Buruchara et al., 2011 ; Rubyogo et al., 2010 ; Monyo & Varshney, 2016 ; Daudi et al., 2018 ). Despite these interventions, adoption of improved bean varieties remains patchy, and their impacts on farm-level productivity have not been rigorously quantified, particularly across Tanzania's varied agroecological zones. Many existing studies tend to generalize productivity outcomes without accounting for ecological heterogeneity or input interaction effects (Mwongera et al., 2017 ). Moreover, most empirical assessments rely on cross-sectional data or linear regressions that fail to capture stochastic variation in productivity, limiting their relevance for risk-based decision-making in smallholder farming systems (Antle, 2006 ; Antle & Valdivia, 2006 ). There is a critical need for robust, simulation-based models that can evaluate the probability of achieving target yields under various seed adoption scenarios across ecological gradients. Specifically, quantifying whether improved seed adoption can enable smallholders to attain the global benchmark of 1.3–1.5 t/ha is essential for guiding evidence-based investment in seed systems, policy design, and agricultural research targeting (Terán & Singh, 2002 ; Beebe et al., 2008 ; Giller et al., 2009 ; Rao et al., 2013 ; Vanlauwe et al., 2014 ; Sommer et al., 2014 ). Nevertheless, such assessments remain limited in the literature, particularly those that incorporate stochastic elements to reflect real-world production risk and uncertainty. This study seeks to fill this critical gap by employing a stochastic simulation approach to model the potential impact of improved bean varieties on productivity across Tanzania’s major agroecological zones. Using nationally representative data and yield probability distributions, the simulation assesses whether the adoption of improved seed varieties, either alone or in combination with other inputs, can enable smallholders to reach or exceed the global productivity threshold. The stochastic framework also facilitates estimation of risk-adjusted yield outcomes and policy-relevant probability metrics, thereby supporting more informed investment decisions in Tanzania’s bean sector. The primary objective of this study is to determine whether the adoption of improved bean seed varieties can enable farmers in Tanzania’s diverse agroecological zones to achieve or surpass the global yield standard of 1.3–1.5 t/ha. This work not only contributes to the academic discourse on productivity modeling and input adoption but also provides critical insights for stakeholders in Tanzania’s agricultural policy, seed systems development, and climate-resilient farming initiatives. 2.0 Materials and Methods 2.1. Study Area This research focuses on the impacts of improved seed on common bean yield across all regions of Tanzania (Fig. 1 ), which are categorized into six agroecological zones (AEZs). The AEZs include the Central Zone (CZ), Eastern Zone (EZ), Lake Zone (LZ), Northern Zone (NZ), the Southern Highlands Zone (SHZ), and Western Zone (WZ). The composition of each zone includes: The Central Zone (CZ) covers the central regions of Tanzania (Dodoma and Singida). The Eastern Zone (EZ) covers Morogoro, Dar es Salaam, Tanga, and the Coastal region. The Western Zone (WZ) covers the Kigoma and Tabora regions. Lake Zone (LZ) includes Mara, Shinyanga, Simiyu, Geita, Mwanza, and Kagera. The Northern zone (NZ) covers the Arusha, Kilimanjaro, and Manyara regions. The Southern Highlands zone (SHZ) includes the Mbeya, Iringa, Songwe, Njombe, Ruvuma, Katavi, and Rukwa regions. Tanzania’s AEZs are characterized by distinct environmental features, including rainfall patterns, temperature, altitude, soil types, and seasonal moisture distribution, all of which significantly influence crop productivity (URT, 2021). These biophysical conditions and variations in farming systems and land use practices contribute to differences in crop responses across regions. By grouping bean farms according to these AEZs, the study assesses how improved common bean varieties influence yields under different agro-environmental settings. This approach ensures that the results reflect national diversity while remaining applicable to localized planning and extension services (Tittonell & Giller, 2013 ). Disaggregating the analysis by AEZs enables a more detailed comparison of the performance of improved varieties across diverse production landscapes. Such spatially explicit evaluation is crucial for formulating region-specific strategies that address unique agronomic constraints and potential (Sheahan & Barrett, 2017 ; Kadigi et al, 2025 ). Furthermore, this zonal analysis sheds light on how different regions respond to climatic variability, soil fertility limitations, and resource availability, key factors in building resilient and adaptive farming systems (Vanlauwe et al., 2015 ). Acknowledging Tanzania’s ecological heterogeneity provides a robust foundation for targeting productivity-enhancing interventions and tailoring input recommendations. Ultimately, this spatial classification helps identify priority zones for improved variety support, contributing to evidence-based decision-making that improves bean yields and promotes sustainable agricultural development (Pretty & Bharucha, 2014 ; Struik & Kuyper, 2017 ). 2.2. Overview of Beans Production in Tanzania Beans are the most widely cultivated pulses in Tanzania, grown extensively during both the short and long rainy seasons. According to the 2019/20 National Sample Census of Agriculture (NSCA), over 1.04 million households in the short rainy season and 1.52 million households in the long rainy season were engaged in bean production, predominantly in Mainland Tanzania. During the same agricultural year, the total planted area under beans was 826,685 hectares, with 99.6% of this land managed by smallholder farmers. Kagera, Kigoma, and Manyara regions recorded the largest planted areas, while Mtwara had the least (URT, 2021). Out of the total planted area, approximately 86.1% was eventually harvested, resulting in 661,699 tons of beans, with 659,497 tons by smallholders and 2,202 tons by large-scale farms. Kagera contributed the most to national output, followed by Manyara and Kigoma. Productivity levels varied across regions, with an average yield of 0.9 tons/ha nationwide. Notably, Zanzibar achieved higher productivity (1.6 tons/ha) compared to Mainland Tanzania, with Mwanza and Geita reporting the highest yields on the mainland (1.3 tons/ha). These statistics reflect the significance of beans as a food security and income crop, particularly among smallholder farmers in Tanzania (URT, 2021). 2.2. Data Sources Tanzania has undertaken multiple rounds of the National Sample Census of Agriculture (NSCA), with the most recent being conducted in 2019/2020. This follows earlier rounds completed in 1971/72, 1994/95, 2002/03, and 2007/08. The present study primarily draws on data from the 2019/20 NSCA while also incorporating information from the 2007/08 census to adjust historical comparisons and contextualize the latest figures. The NSCA is managed by the National Bureau of Statistics (NBS) and serves as a key source of agricultural data in Tanzania. It offers comprehensive coverage of rural farming households, documenting aspects such as landholding size, types and levels of crop production, livestock ownership, and the application of agricultural inputs like fertilizers and improved seeds. Additionally, the survey gathers insights into rural infrastructure, livelihood conditions, and household living standards, providing a critical basis for evaluating agricultural performance and the outcomes of development initiatives (URT, 2021). To ensure national representativeness, the NSCA applies a rigorous two-stage sampling strategy. In the first phase, Census Enumeration Areas (CEAs) are selected using the 2012 Population and Housing Census as a sampling frame. These CEAs serve as Primary Sampling Units (PSUs) and are strategically selected from various regions and districts to ensure comprehensive geographical coverage. In the second phase, agricultural households within these selected PSUs are randomly sampled, with an emphasis on those involved in crop and livestock production. The final survey sample comprises 2,820 PSUs, consisting of 2,670 from Mainland Tanzania and 150 from Zanzibar, selected using a Probability Proportional to Size (PPS) approach. This technique assigns greater weight to areas with higher agricultural activity, thereby enhancing the precision and relevance of the collected data. Additional details regarding the sampling framework and execution are available in the official NSCA report (URT, 2021). 2.3. Data Processing and Simulation 2.3.1 Data Processing The first thing was to sort the bean yield data from the dataset and categorize it into six AEZs. The sorted data were categorized into two farming practices for more straightforward analysis and comparison for the two different seasons (short and long rainy seasons). Farms that used local seeds in the short rainy season were marked with SRS1, and those that used improved seed varieties were marked with SRS2. Farms using local seed during the long rainy season were marked as LRS1, while those using improved seeds were marked as LRS2. Table 1 summarizes the observed data sorted from the NSCA for each AEZ. These data included only farms that were already harvested. The yield distribution for each farming system (local and improved users) per agro-ecological zones is summarized in Appendix A. Table 1 Number of observations for Bean farms using local vs improved seeds per AEZ Agroecological Zone Farming Using Local Seed Farming Using Improved Seed Short Rain Season (SRS1) Long Rain Season (LRS1) Short Rain Season (SRS2) Long Rain Season (LRS2) Central Zone (CZ) 5 99 0 13 Eastern Zone (EZ) 268 307 35 31 Lake Zone (LZ) 1,358 591 93 29 Northern Zone (NZ) 595 814 81 137 Southern Highlands (SHZ) 213 1,548 39 103 Western Zone (WZ) 125 880 0 13 All Farms (AllTZ) 2564 4,231 248 326 2.3.2 Data Simulation The data analysis for this study utilizes a Stochastic Simulation Model (SSM) that follows a non-parametric Monte Carlo simulation approach, as detailed by Richardson et al. ( 2000 , 2003 , 2007 ) and Kadigi et al. ( 2020 ; 2025 ). Monte Carlo simulations are well-regarded for their ability to model stochastic variables, such as yields or output and input prices, and generate estimated distributions for these variables. This technique robustly quantifies the risks and variabilities tied to crop profitability in Tanzania. In the initial phase of the simulation, we define and parameterize the stochastic (risky) yields for each farming system, grounded in actual observed data. The yields are then converted into a stochastic format using standard Monte Carlo protocols, which allow for the simulation and validation of yield distributions tailored to each seed type and farming setup. The study further categorizes data across agroecological zones to address Tanzania's geographical and climatic diversity. For the analysis of these varied yields, the study employs a Multivariate Empirical (MVE) distribution method, as also detailed in the work by Kadigi et al. ( 2020 ; 2025 ). This approach effectively handles multiple variables simultaneously and ensures that the simulated values remain within realistic limits, such as avoiding the generation of implausible negative yields. To facilitate this, residuals defined as percentage deviations of observed yields from their mean are used to estimate the parameters of the MVE yield distribution. This method captures the variability in historical yield data and underscores the probabilistic nature of bean yield variability across the two farming systems per AEZ, providing a comprehensive view of potential production outcomes (Kadigi et al., 2025 ). The following equation was used to develop the stochastic yield: $$\:{\stackrel{\sim}{y}}_{i,\omega\:}={\stackrel{̄}{y}}_{c,i,\omega\:}*\left(1+EMP\left({S}_{y,i,\omega\:},P\left({S}_{y,i,\omega\:}\right),CUS{D}_{y,i,\omega\:}\right)\right)*{\beta\:}_{{\stackrel{\sim}{y}}_{0}}$$ 1 Where: ~ = A tilde represents a random (stochastic) variable. i = Type of farming practices used ( local seeds, improved seeds ). \(\:\omega\:\) = Represents farms in six agroecological zones a i = Hectares (ha) allocated for farming practice i = Stochastic mean yield per ha for farming practice i \(\:{\stackrel{-}{y}}_{i}\) = Deterministic (mean) yield per ha for farming practice i \(\:{\beta\:}_{{\stackrel{\sim}{y}}_{0}}\) = The normalization factor, which is given by \(\:\frac{{\stackrel{\sim}{y}}_{c,i}}{{\stackrel{\sim}{y}}_{h,i}}\:\) and it is used to scale/adjust the 2019/20 NCSA mean yield. \(\:{\stackrel{\sim}{y}}_{c}\) = Stochastic yield for the current survey (2019/20 NCSA) \(\:{\stackrel{\sim}{y}}_{h}\) = Stochastic yield for the historical or previous survey (2007/08 NCSA) S y = Fraction deviations from the mean or sorted array of random yields for farming practice i P(S y ) = Cumulative probability function for the S y values CUSD y = Simetar function to simulate the correlated uniform standard deviation of random variables. EMP() = Simetar function used to simulate a stochastic variable (yield) The subsequent phase of the analysis involved simulating the SSM for a minimum of 500 iterations for each farming practice using the Latin Hypercube Sampling (LHC) method, as detailed by Richardson et al. ( 2008 ) and Kadigi et al. ( 2025 ). The LHC technique was selected for its efficiency, allowing for a comprehensive replication of the parent yield distributions despite the relatively modest number of iterations. This efficiency is crucial because it ensures that the sample size of 500 iterations is sufficient to accurately capture the underlying characteristics of the yield distributions. This simulation considered 26 random variables (yields) represented by two farming systems: local seed users in the short and long rainy seasons, and improved seed users in the short and long seasons across six agroecological zones, resulting in a total simulated sample size of 13,000 (500 × 26). This extensive dataset enhances the robustness of our analysis, enabling a more precise evaluation of how various farming practices affect bean yields. To validate the accuracy of these simulations, the final step of the analysis involved comparing the simulated yield distributions against historical yield data. This validation step is crucial to ensure that the stochastic model accurately reflects observed data while incorporating the inherent variability of SSM. By aligning the simulation outputs with historical distributions, the study ensures that its findings are both reliable and relevant for assessing the impact of different farming practices within Tanzania's diverse agroecological landscapes. Results from this validation are detailed in the Results section, which utilizes probability distribution functions (PDFs). 2.4 Ranking of Target Probabilities Using the Stoplight Function The Stoplight Chart function was used to rank the probabilities of bean farms achieving the maximum yield thresholds and the probabilities of falling below the minimum values per unit area (which is hectares, or ha, in this study). The stoplight function calculates the probabilities of (a) exceeding the upper target ( green ), (b) being less than the lower target ( red ), and (c) falling between the targets ( yellow ). The views from various bean actors, particularly farmers, and literature review including the current National Sample Census of Agriculture (NSCA) URT (2021) revealed that the average yield in Tanzania ranges between 0.6–1.2 t/ha; hence, we set our minimum threshold to be 0.60 t/ha and the maximum being 1.50 t/ha (Fig. 2 ). The maximum was set to meet most national initiatives, such as the ASDP-II (URT, 2016) and the Tanzania Seed Sector Development Strategy – 2030 (Minde et al., 2024 ), which aims to double the productivity of major crops, including beans, by 2030. 3.0 Results and Discussion 3.1. Model Validation The stochastic model used in this analysis was validated to ensure it accurately simulated the farming practices under investigation. The stochastic model was validated using probability density function (PDF) charts to compare observed and simulated yield distributions. These comparisons were made across various farming scenarios in Tanzania, including: Yield of farms using local seeds in the short rainy season Yield of farms using improved seeds in the short rainy season Yield of farms using local seeds in the long rainy season Yield of farms using improved seeds in the long rainy season Figure 3 presents the model validation results by comparing the observed and simulated probability distribution functions (PDFs) of bean yield across all farms in Tanzania. The visual alignment across the subplots demonstrates the model's effectiveness in replicating real-world yield distributions under different seed types and seasonal conditions. Specifically, panels (a) and (b) depict yield distributions for farms using local seed varieties and improved seed varieties, respectively, during the long rainy season (LRS), while panels (c) and (d) show the same comparisons for the short rainy season (SRS). In each subplot, the observed distribution is shown in black, and the simulated distribution is shown in red. The close match between the two curves in all cases highlights the simulation model’s robustness and accuracy in capturing the statistical behavior of actual farm yields. These results provide strong empirical support for the model’s reliability, validating its use in analyzing the impact of improved seed adoption on bean productivity across varying agroecological and seasonal contexts in Tanzania. 3.1. Beans Productivity Across All Agroecological Zones of Tanzania in the Long Rainy Season for Farms Using Local vs. Improved Seed Varieties 3.1.1 Beans yield distribution during the long and short rainy seasons The results presented in Table 2 demonstrate notable differences in bean productivity across Tanzania based on seed type and seasonal conditions. On average, farms using improved seed varieties achieved relatively higher yields in both the short and long rain seasons compared to those using local seed. Specifically, during the short rain season (TZ_SRS2), improved seeds yielded an average of 1.40 t/ha, surpassing the 1.32 t/ha from local seeds (TZ_SRS1). Similarly, during the long rainy season (TZ_LRS2), improved seed users recorded a mean yield of 0.70 t/ha, slightly higher than the 0.63 t/ha achieved with local seed (TZ_LRS1). While these differences in means may appear modest, they suggest that improved seed varieties consistently offer an advantage across seasons. The observed higher maximum yields, 3.06 t/ha for improved seed versus 3.16 t/ha for local seed in the short rain season, highlight variability in performance. However, the yield gap is more evident during the long rainy season, where local seeds reached a maximum of 1.65 t/ha compared to only 1.52 t/ha for improved seeds. Additionally, the coefficient of variation (CV) values indicate higher yield variability among farms using improved seeds, particularly during the long rain season (CV = 38.40%), as compared to farms using local seeds (CV = 24.42% for TZ_LRS1). This suggests that while improved seeds can increase productivity, their performance may be more sensitive to management practices or agroecological conditions. The relatively higher standard deviation and broader range of yields observed in improved seed plots (e.g., a minimum of 0.26 t/ha and a maximum of 1.52 t/ha in the long rains) also support the presence of more pronounced production risk or heterogeneity. These findings underscore the importance of complementary inputs and localized extension support to realize the full potential of improved varieties. Overall, the data affirm that improved seeds offer a yield advantage, albeit with variability that needs to be carefully managed, especially under changing climatic conditions. The yield distribution (in t/ha) per agroecological zone and seasons are summarized in Appendix A Table 2 Summary Statistics on Bean Productivity Across all Tanzania Farms Using Local vs Improved Seed Types Yield Distribution (t/ha) Farming Using Local Seed Farming Using Improved Seed Short Rain Season (TZ_SRS1) Long Rain Season (TZ_LRS1) Short Rain Season (TZ_SRS2) Long Rain Season (TZ_LRS2) Mean 1.32 0.63 1.40 0.70 STD 0.37 0.15 0.42 0.27 CV 27.00 24.42 30.08 38.40 Min 0.59 0.30 0.55 0.26 Max 3.16 1.65 3.06 1.52 Figure 4 presents probability density function (PDF) approximations for bean productivity across all Tanzanian farms using local (black line) and improved seed varieties (red line), disaggregated by season. In panel (a), representing the short rain season, both distributions appear slightly right-skewed with peaks around the 1.2–1.4 t/ha range. However, the red curve (improved seeds, TZ_SRS2) demonstrates a marginally broader distribution, with a rightward shift in the peak compared to the black curve (local seeds, TZ_SRS1), indicating a general yield advantage. The improved seed distribution also exhibits a longer tail, suggesting that a subset of farmers achieved substantially higher yields, up to approximately 3.0 t/ha. The black curve, while more concentrated, peaks at a slightly lower yield level and declines more steeply, indicating lower variability but a less frequent occurrence of high yields. Panel (b), which illustrates the long rain season, shows more pronounced differences. The PDF for improved seed users (red line, TZ_LRS2) is flatter and more dispersed, with multiple minor peaks, indicating a more heterogeneous yield response. While the peak of the improved seed distribution is slightly right of the local seed distribution (black line, TZ_LRS1), it is less sharply defined, suggesting greater variability in outcomes. Conversely, the local seed curve is narrower and more concentrated, peaking near 0.60–0.70 t/ha. The presence of higher-density tails in the improved seed curve implies that, despite the variability, more farmers were able to achieve yields above 1.0 t/ha compared to those using local seeds. Collectively, these PDFs reinforce the interpretation that improved seeds tend to increase average productivity and expand yield possibilities, especially in the short rain season, but may also introduce greater variability that necessitates supportive agronomic practices for consistent gains. 3.1.2 Beans yield distribution across the agroecological zones during the short rainy season Figure 5 presents probability density function (PDF) approximations of bean productivity across four major producing agroecological zones of Tanzania, Lake Zone (LZ), Eastern Zone (EZ), Northern Zone (NZ), and Southern Highlands Zone (SHZ), during the short rain season (SRS), comparing farmers using local seeds (black curves) with those using improved seeds (red curves). In the Lake Zone (Fig. 5 a), the distribution for improved seeds (LZ_SRS2) is flatter and broader than that of local seeds (LZ_SRS1), with a rightward shift in the peak. This indicates that while the majority of improved seed users achieved moderate yields (~ 1.2–1.6 t/ha), a notable number of them attained higher productivity (up to 3.0 t/ha), suggesting a performance edge with improved seeds. The Eastern Zone (Fig. 5 b) exhibits overlapping PDFs, with the red curve for improved seeds slightly exceeding the black curve in density around 1.4–1.8 t/ha, indicating modest gains in productivity among users of improved seeds in this zone. In the Northern Zone (Fig. 5 c), both seed types exhibit similar peak locations around 1.1–1.3 t/ha; however, the red curve (NZ_SRS2) has a heavier right tail, indicating that more farmers using improved seeds were able to surpass 2.0 t/ha, albeit with greater variability. This suggests potential for higher yield ceilings when improved seeds are effectively managed. The Southern Highlands Zone (Fig. 5 d) exhibits the most pronounced divergence, with improved seeds yielding a broader distribution and a noticeable secondary peak near 2.0–2.5 t/ha, which is absent in the local seed curve. This indicates substantial productivity gains and heterogeneity in yield outcomes among users of improved seeds in this high-altitude zone. Overall, these patterns suggest that improved seed varieties generally enhance yield potential across zones. However, the magnitude and consistency of their impact vary by agroecological context, underscoring the need for localized seed system strategies and agronomic support. 3.1.3 Beans yield distribution across the agroecological zones during the Long rainy season Figure 6 illustrates the PDF approximations of bean productivity across six agroecological zones in Tanzania during the Long Rainy Season (LRS), comparing farmers who use local seeds (black lines) with those who use improved seeds (red lines). In the Central Zone (Fig. 6 a), improved seed users (CZ_LRS2) demonstrate a slightly broader and flatter distribution than local seed users (CZ_LRS1), with the red curve exhibiting a wider tail and density beyond 1.0 t/ha. This indicates that while many improved seed users achieved yields similar to those of local seed users (~ 0.60–0.80 t/ha), a notable portion achieved higher-than-average yields, albeit with increased variability. In the Eastern Zone (Fig. 6 b), the red curve is marginally right-shifted compared to the black curve, suggesting improved seeds offered slight productivity gains in the 0.60–0.90 t/ha range. However, the presence of multiple peaks suggests inconsistent performance across farms, possibly due to variations in management practices or climatic influences. In the Lake Zone (Fig. 6 c), the improved seed PDF (LZ_LRS2) closely overlaps with that of local seeds, with both reaching a peak near 0.60 t/ha. Nonetheless, the improved seed distribution has a broader tail, showing that more farmers achieve yields over 1.0 t/ha, albeit with reduced density. This suggests only marginal yield gains with improved seeds in this zone during the long rainy season. In the Northern Zone (Fig. 6 d), a more pronounced shift is observed. Both local and improved seed PDFs (NZ_LRS1 & NZ_LRS2) are highly concentrated around 0.40 t/ha – 0.80 t/ha, with the improved seed curve spreading more evenly, with visible density extending beyond 1.2 t/ha, indicating potential for significant productivity improvements with better agronomic support and input use. Moving to the Southern Highlands Zone (Fig. 6 e), the black curve for local seeds peaks at a higher value (around 0.5 t/ha) and is more narrowly defined, lying to the left. In contrast, the red curve for improved seeds is broader and flatter, extending further into higher yield ranges, which lie more to the right. This suggests that a larger proportion of improved seed users achieved relatively higher peak yields compared to their counterparts. Finally, the Western Zone (Fig. 6 f) exhibits considerable rightward spread in the red curve, with improved seed users showing greater yield variability and the potential to exceed 1.2 t/ha. However, the flatter distribution also points to inconsistency in realizing yield advantages across farms. Overall, these patterns suggest that improved seeds generally increase yield potential across agroecological zones during the long rainy season; however, the magnitude and consistency of impact vary widely, underscoring the importance of targeted support for input access, extension, and climate adaptation. 3.2. Probability of Bean Yield Falling Below 0.6 t/ha and Above 1.5 t/ha During Short Rains: Local vs. Improved Seeds 3.2.1 Yield Probability for Local Seed under SRS Figure 6 presents the probabilities of bean yields falling below 0.6 t/ha (low productivity) and exceeding 1.5 t/ha (high productivity) across different agroecological zones in Tanzania during the short rainy season (SRS), specifically for farms using local seed varieties. The chart clearly shows that across all zones, Central Zone (CZ), Eastern Zone (EZ), Lake Zone (LZ), Northern Zone (NZ), Southern Highlands Zone (SHZ), Western Zone (WZ), and the national aggregate (AllTZ), there is zero probability of bean yields falling below 0.6 t/ha. This finding indicates that, despite the use of local seeds, extreme yield failure is unlikely during the SRS, and most farms can at least reach the minimum productivity threshold. However, the probability of attaining high yields (above 1.5 t/ha) remains modest, ranging from 29–34% across zones. The Eastern Zone (EZ_SRS1) has the highest probability (34%), while the Northern Zone (NZ_SRS1) and Southern Highlands Zone (SHZ_SRS1) record the lowest probabilities at 29%. However, the majority of farmers using local seeds consistently fall within the middle productivity band (0.6–1.5 t/ha), with proportions ranging from 66–71%. The national average for high productivity stands at 33%, suggesting that only about one-third of farmers using local seeds can exceed the global yield benchmark. These results underscore the limitations of local seed varieties in achieving optimal productivity levels, even under favorable seasonal conditions, and highlight the need for interventions that promote improved seed technologies and complementary inputs to close the yield gap. 3.2.2 Yield Probability for Improved Seed Under SRS Figure 8 illustrates the probabilities of bean yields falling below 0.6 t/ha (red segment) and exceeding 1.5 t/ha (green segment) during the short rainy season across selected agroecological zones in Tanzania for farms using improved seeds. In contrast to Fig. 7 , which depicted outcomes for local seed users, Fig. 8 reveals a more diversified distribution of yield probabilities, with slightly higher risk but also notably increased chances of high productivity. The probability of achieving yields above 1.5 t/ha ranges from 32% in the Southern Highlands Zone (SHZ_SRS2) to 49% in the Eastern Zone (EZ_SRS2), with the national average (TZ_SRS2) at 40%. These figures are consistently higher than those in Fig. 7 , where the maximum was 34% (EZ_SRS1) and the national average was 33%. This confirms that improved seeds offer a statistically significant yield advantage, increasing the likelihood of surpassing the global benchmark of 1.5 t/ha in all observed zones. On the downside, a small probability of yield falling below 0.6 t/ha re-emerges in Fig. 8 for some regions, specifically 2% in LZ_SRS2 and 1% in SHZ_SRS2 and TZ_SRS2, compared to 0% in all zones in Fig. 7 for local seeds. This suggests that while improved seeds increase average and upper-bound yields, they may also introduce greater production risk for a small subset of farmers, possibly due to inadequate agronomic management or environmental mismatches. Nevertheless, the majority of farmers using improved seeds consistently fall within the middle productivity band (0.6–1.5 t/ha), with proportions ranging from 51–67%, which is similar to or slightly higher than those of local seed users. Overall, the results demonstrate that improved seeds enhance the probability of high yields, justifying their promotion. However, they should be coupled with agronomic support and input packages to minimize downside risk. 3.3. Probability of Bean Yield Falling Below 0.6 t/ha and Above 1.5 t/ha During Long Rains: Local vs. Improved Seeds3.3.1 Yield Probability for Local Seed under LRS 3.2.1 Yield Probability for Local Seed under LRS Figure 9 presents the probability distribution of bean yields during the long rainy season (LRS) for farmers using local seeds across various agroecological zones in Tanzania. The red segments represent the probability of low productivity (below 0.6 t/ha), yellow indicates moderate yields (0.6–1.5 t/ha), and green shows high yields (above 1.5 t/ha). The findings are concerning: low yields dominate, with probabilities ranging from 45–60%, and the national average (TZ_LRS1) at 53%. This suggests that more than half of the farmers using local seeds during the long rainy season are likely to achieve suboptimal yields, significantly limiting food security and income generation. Conversely, the probability of achieving high yields above 1.5 t/ha is almost negligible, with most zones registering yields of only 0.00–0.01 t/ha, reaffirming the inability of local seeds to meet global productivity standards under long-rain conditions. When compared to Fig. 6 (short rainy season with local seeds), the contrast is stark. In Fig. 7 , the probability of low yields was 0% across all zones, and the chances of exceeding 1.5 t/ha ranged from 29–34%. This demonstrates that the short rainy season (SRS) is more favorable for bean production, even with local seed varieties. Similarly, in Fig. 8 , improved seeds during the SRS showed increased likelihood of high productivity (up to 49%) and minimal yield failures. The findings from Fig. 9 thus reinforce the seasonal advantage of the SRS over the LRS for bean cultivation in Tanzania. This could be attributed to better rainfall distribution, reduced pest/disease pressure, or more suitable temperature patterns during the SRS. The implication is that policy and investment strategies should prioritize improved seed access and agronomic interventions during the short rains, as the potential for achieving optimal yields is higher, regardless of seed type. Moreover, transitioning from local to improved varieties could significantly mitigate the high yield risks associated with the long rainy season, especially in vulnerable zones such as the Central and Southern Highlands. 3.3.2 Yield Probability for Improved Seed under LRS Figure 10 provides critical insights into the probability distribution of bean yields for farms using improved seeds during the long rainy season (LRS) across different agroecological zones in Tanzania. Compared to local seed performance during the same season (Fig. 9 ), improved seeds yield slightly better results but with limited breakthrough. Notably, the probability of low yields (below 0.6 t/ha) remains high, ranging from 35% in WZ_LRS2 to 56% in LZ_LRS2, with the national average (TZ_LRS2) at 51%, which is barely different from the local seed average of 53%. This implies that improved seeds alone are insufficient to eliminate the substantial risk of yield shortfall under long rain conditions without complementary inputs or agronomic practices. The probability of high yield attainment (above 1.5 t/ha) remains extremely low, except in the Western Zone (WZ_LRS2), where it reaches 12%, indicating a zone-specific opportunity for maximizing productivity with improved seeds. In other zones, high yield probabilities are negligible (0–1%). These patterns reflect that the long rainy season presents less favorable growing conditions for beans, even with the use of improved varieties, likely due to factors such as excessive rainfall, poor soil drainage, increased disease pressure, or lower seed responsiveness in these months. When compared with results from the short rainy season (Fig. 9 ), where improved seeds resulted in high yield probabilities of 32–49%, the data in Fig. 10 affirm that the short rainy season is significantly more productive and stable for bean cultivation in Tanzania. Therefore, policies promoting seasonal targeting, such as prioritizing SRS planting with improved seeds and providing location-specific agronomic packages, could offer more substantial gains in productivity and profitability than blanket promotion across both seasons. 4. Discussion This study offers valuable insights into the probabilistic distribution of bean productivity under varying seed technologies and seasonal conditions across Tanzania's agroecological zones. The stochastic simulations revealed clear distinctions in yield performance between farms using local and improved seed varieties, particularly across the short and long rainy seasons. 4.1 Yield Distribution Patterns: Seasonality and Seed Type Figures 4 , 5 , and 6 demonstrate that improved seed varieties consistently outperformed local seeds in terms of mean yield across most agroecological zones during the short rainy season (SRS). For instance, the probability density functions (PDFs) indicate that improved seeds achieved higher peak densities and extended right tails, signifying an increased likelihood of attaining yields above 1.5 t/ha, especially in zones such as the Lake Zone (LZ) and the Southern Highlands Zone (SHZ). This observation is consistent with previous findings, which highlight that improved varieties bred for drought tolerance and disease resistance can yield significantly higher than local landraces under favorable management and seasonal conditions (Terán & Singh, 2002 ; Beebe et al., 2008 ; Rubyogo et al., 2010 ; Buruchara et al., 2011 ; Rao et al., 2013 ). The long rainy season (LRS) results, shown in Fig. 6 , contrast sharply with those of the short rains (Fig. 5 ). Despite the use of improved seeds, the PDFs indicate compressed and left-skewed distributions with higher densities in the low-yield region (0.3–0.8 t/ha). This suggests that the LRS is generally less favorable for bean cultivation across most agroecological zones, which may be attributed to excess rainfall, increased disease pressure, and suboptimal physiological response of bean crops during prolonged wet conditions (Hillocks et al., 2006 ; Ndakidemi et al., 2006 ; Tryphone et al., 2013 ; Hummel et al., 2018 ; Katungi et al., 2009 ). The sharper peaks and lack of right-tail extension in many zones reflect constrained yield potential during the LRS, even when improved seeds are used. 4.2 Probabilities of Achieving or Falling Short of Yield Thresholds Figures 7 and 8 quantify the probability of yields falling below 0.6 t/ha (indicating low productivity) and exceeding 1.5 t/ha (indicating high productivity) during the short rainy season. Farms using local seeds (Fig. 7 ) showed a zero probability of falling below 0.6 t/ha, indicating resilience against complete yield failure; however, they had limited potential for high productivity, with a national average of only 33% probability of exceeding 1.5 t/ha. On the other hand, farms using improved seeds (Fig. 8 ) during the SRS exhibited slightly higher risk, with up to 2% probability of yields below 0.6 t/ha in some zones (e.g., LZ_SRS2), yet they showed marked improvement in high yield attainment, with probabilities reaching 49% in the Eastern Zone (EZ_SRS2) and a national average of 40%. These results suggest that improved seeds increase both the mean and variance of yield distributions, offering higher upside potential but with some exposure to downside risk, especially in areas where complementary agronomic practices (e.g., pest control, optimal planting time, and soil fertility management) may be inadequate (Antle & Valdivia, 2006 ; Antle, 2006 ; Jiménez, 2019 ; Parker et al., 2022 ). Nevertheless, the substantially higher probability of achieving yields above 1.5 t/ha with improved seeds supports their promotion as a critical strategy for meeting global productivity benchmarks of 1.3–1.5 t/ha (Beebe et al., 2012 ; Jansa et al., 2011 ). 4.3 Seasonal Disadvantage of the Long Rains Figures 9 and 10 underscore the productivity constraints associated with the long rainy season. Among farmers using local seeds (Fig. 9 ), the probability of low yields (< 0.6 t/ha) was disturbingly high, averaging 53% nationally and reaching up to 60% in the Central Zone (CZ_LRS1). The probability of achieving yields above 1.5 t/ha was negligible (0–1%) in all zones. Even for farms using improved seeds (Fig. 10 ), the probability of high productivity remained low, with only the Western Zone (WZ_LRS2) showing a notable 12% chance of yields above 1.5 t/ha. The probabilities of low yields remained around 50% in most zones, indicating that seed improvements alone may not be sufficient to counteract the agronomic limitations of the LRS. The results highlight that seasonality plays a more significant role than seed type in determining yield outcomes. This aligns with prior studies, which suggest that beans perform best under moderate moisture conditions typical of the short rains, while prolonged wet conditions during the long rains exacerbate diseases such as root rot and angular leaf spot, which severely curtail productivity (Assefa et al., 2006 ; Muthoni & Nyamongo, 2009 ; Katungi et al., 2010 ; Wortmann & Allen, 1994 ; Rubyogo et al., 2010 ). 4.4 Implications for Policy and Practice These findings carry important policy implications. First, the short rainy season offers a more reliable opportunity for achieving optimal bean yields using improved seed varieties. With proper input support, extension services, and climate-resilient agronomic packages, the SRS could serve as the main window for maximizing bean productivity in Tanzania. Second, the promotion of improved seeds must be paired with localized agroecological support, especially in zones such as the SHZ and LZ, where potential gains are greatest. Finally, in the LRS, efforts should focus more on climate adaptation strategies, such as drainage management, disease-tolerant varieties, and seasonal forecasts, to mitigate the heightened yield risks even with improved genetics. The application of stochastic modeling in this study further provides a nuanced understanding of yield distribution, risk exposure, and probability-based planning, which are essential for designing smart seed policies and investment strategies (Antle et al., 2017 ; Vanlauwe et al., 2014 ; Sommer et al., 2014 ; Giller et al., 2009 ). 5. Conclusions This study modeled the impact of improved seed varieties on bean productivity across Tanzania’s agroecological zones using a stochastic simulation approach. By analyzing yield probability distributions and thresholds across both short and long rainy seasons, the research revealed substantial seasonal and spatial variation in the productivity outcomes of local versus improved seed users. Notably, the findings underscore the importance of seed technology and seasonal targeting as key determinants of yield performance, with significant implications for food security, nutritional well-being, and agricultural resilience. The simulation results clearly show that improved seed varieties consistently outperform local seeds in terms of mean yield and probability of attaining global yield standards (1.3–1.5 t/ha), especially during the short rainy season (SRS). In this season, improved seeds increased the probability of achieving yields above 1.5 t/ha by up to 42% and 49% in certain zones (e.g., Lake Zones and Eastern), compared to a maximum of 34% with local seeds. These gains, however, were accompanied by a modest increase in variability and risk of yield failure (i.e., falling below 0.6 t/ha), indicating that while improved varieties enhance potential, they must be coupled with good agronomic practices and institutional support systems to ensure consistent performance. Conversely, the long rainy season (LRS) exhibited less favorable conditions for bean production. Both local and improved seed users faced high probabilities (often above 50%) of producing yields below 0.6 t/ha, and negligible chances of exceeding 1.5 t/ha. This seasonal disparity underscores that climate-smart seasonal planning, focusing on the SRS for bean cultivation, could be a strategic entry point for enhancing national productivity and reducing vulnerability among smallholder farmers. Moreover, the Western Zone emerged as a unique exception during the LRS, where improved seeds enabled up to 12% of farmers to exceed 1.5 tonnes per hectare, highlighting the need for region-specific recommendations. From a broader development perspective, these findings contribute to the evidence base supporting Sustainable Development Goal 2 (Zero Hunger). Beans are not only a major source of calories but also provide essential proteins, iron, and zinc, especially for rural and low-income households. Increasing bean yields through improved seed adoption directly enhances household food availability, dietary diversity, and income, thereby tackling both chronic and hidden hunger. When smallholder farmers achieve productivity above subsistence levels, they are better positioned to market their surplus, save, and reinvest, further contributing to rural economic transformation and resilience. Furthermore, the study has direct relevance to Sustainable Development Goal 3 (Good Health and Well-being). As an affordable and accessible source of high-quality protein and micronutrients, common beans play a crucial role in combating malnutrition, stunting, and anemia conditions that remain prevalent in many Tanzanian regions. Improving bean productivity can therefore have downstream health benefits, particularly for children and women of reproductive age. By enabling farmers to produce more nutritious food reliably, the promotion of improved seed varieties contributes to both preventive health care and the strengthening of food systems as determinants of well-being. In conclusion, this study reinforces the importance of deploying context-specific, climate-smart agricultural technologies such as improved bean varieties, especially during the short rains, to increase productivity and meet global yield standards sustainably. The integration of stochastic simulation has been demonstrated to be a powerful tool for capturing yield variability, informing policymakers and development actors about the probability of success under various scenarios. However, achieving full benefits will require more than just seed dissemination. Supportive measures, such as access to credit, extension services, disease control, and weather forecasting, must be scaled alongside seed interventions to achieve widespread transformation. Future research should further explore the interaction between improved seeds and other production inputs (e.g., fertilizers, irrigation) under climate stress, to better inform investment and policy priorities. Ultimately, aligning agricultural development strategies with the principles of SDG 2 and SDG 3 will ensure that Tanzania’s bean sector makes a meaningful contribution to ending hunger, improving nutrition, and enhancing the health and resilience of its population. Declarations Authors' contributions: ILK conceptualized the research, collected data, performed the data analysis, developed all figures and tables, and wrote the article. Funding The author declares that no financial support or funding was received for the preparation of this manuscript Data availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. Acknowledgment I am grateful to the Simetar© team (www.simetar.com), particularly Dr. James W. Richardson, former Regents Professor at Texas A&M University, and Dr. Jean-Claude Bizimana, for their endless, invaluable guidance on the Monte Carlo Simulation Protocols. Ethics approval and consent to participate This study is based on secondary data obtained from the 2019/2020 National Sample Census of Agriculture (NSCA), which was conducted by the National Bureau of Statistics (NBS) of Tanzania in collaboration with the Ministry of Agriculture and the World Bank. The data are anonymized and publicly available for research and policy analysis purposes. 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Atlas of common bean (Phaseolus vulgaris L.) production in Africa. CIAT; 1998. p. 297. Wortmann CS, Allen DJ. African bean production environments: their definition. characteristics and constraints; 1994. Additional Declarations No competing interests reported. Supplementary Files AppendixA.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7237495","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":503760406,"identity":"35e77bbf-acb7-407f-a53e-64d185b36bdc","order_by":0,"name":"Ibrahim L. Kadigi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYBACCWYGAxDNw8DAfADElyFeCw8DWwKIz0NYCwNEC9AaHph1BIBkO/PGBz933JGxZ+/5/OpGjQUPA/vhoxvwaZFmZis27D3zjIeH5+w265xjQIfxpKXdwKdFjpnHTIK37TAPj0TuNuMcNqAWCR4zQlrMf/4Fa8l5Zpzzjwgt0kBbmCG25DA/zm0jQotkM1uxtCxIy5ljZsy5fRI8bIT8InH+8MaPb9sO27O3Nz/+nPOtTo6f/fAxvFqQAZsEmCRWOQgwfyBF9SgYBaNgFIwcAABRJT5n6r6ChgAAAABJRU5ErkJggg==","orcid":"","institution":"Mbeya University of Science and Technology (MUST)","correspondingAuthor":true,"prefix":"","firstName":"Ibrahim","middleName":"L.","lastName":"Kadigi","suffix":""}],"badges":[],"createdAt":"2025-07-28 22:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7237495/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7237495/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89649939,"identity":"1ea79a68-087e-4afd-82e4-71630f1a86ca","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":75316,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProduction of Bean in Tanzania by Region During the 2019/20 Agricultural Year (URT, 2021)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/93196e147d8cf886952647f2.jpg"},{"id":89651212,"identity":"1b3dff6d-c130-4e8f-8b73-a6a2a2d1e085","added_by":"auto","created_at":"2025-08-22 09:44:09","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":120235,"visible":true,"origin":"","legend":"\u003cp\u003eStoplight Chart for ranking of target probabilities\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/bd6027353e7089cf04f74bc8.jpg"},{"id":89651211,"identity":"fba72037-3b16-48d3-ba4b-772e7a79deb1","added_by":"auto","created_at":"2025-08-22 09:44:09","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":116097,"visible":true,"origin":"","legend":"\u003cp\u003ePDF charts compare observed and simulated distributions for common bean yields across all farms in Tanzania using local seed varieties (Figures 3a, 3c), and farms using improved varieties (Figures 3b, 3d) under both the long rainy season (Figures 3a, 3b) and short rainy season (Figures 3c, 3d).\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/cbc9a165367474a3dc3de32d.jpg"},{"id":89649944,"identity":"28ee42f6-d311-4b4b-82b5-b25810f859f2","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":59813,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePDF Approximation of Beans Productivity (t/ha) across all farms in Tanzania during the Short Rainy Season (a) and Long Rainy Season (b) for farmers using local seeds (in black) and those using improved seeds (in red).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/6f8e71475cce9172f79c2d34.jpg"},{"id":89649947,"identity":"fe4a9be0-e852-4c89-b2db-1bce2123d5cb","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":113187,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePDF Approximation of Beans Productivity (t/ha) Across Different Agroecological Zones of Tanzania during Short Rainy Season (_SRS) categorized by farmers using local seeds (in black) and those using improved seeds (in Red). LZ_ = Lake Zone (a), EZ_ = Eastern Zone (b), NZ _ = Northern Zone (c); SHZ_ = Southern Highlands Zone (d).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/62dba1542f87a313d10b0605.jpg"},{"id":89651635,"identity":"1bd5e96c-0b20-466d-ba9b-0d8777e9303c","added_by":"auto","created_at":"2025-08-22 09:52:09","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":111527,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePDF Approximation of Beans Productivity (t/ha) Across Different Agroecological Zones of Tanzania during Long Rainy Season (_LRS) categorized by farmers using local seeds (in black) and those using improved seeds (in Red). LZ_ = Lake Zone (a), EZ_ = Eastern Zone (b), NZ_= Northern Zone (c); SHZ_ = Southern Highlands Zone (d).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/24a71b7a5301a09b4880e589.jpg"},{"id":89649945,"identity":"7b62a118-2237-4828-8c44-2015563163eb","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":348965,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProbability of bean yield falling below 0.6 t/ha and above 1.5 t/ha in the short rainy season for farms using local seeds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/662ee79a9f0dfb1b59f01d26.jpg"},{"id":89649953,"identity":"513e4f34-cc56-4ca1-ad77-aae1f9f0ced2","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":389250,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProbability of bean yield falling below 0.6 t/ha and above 1.5 t/ha in the short rainy season for farms using improved seeds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/4f36fcb5a3abde7636ee9334.jpg"},{"id":89651217,"identity":"b5752f94-7229-4a81-a3b5-c90f888d62ed","added_by":"auto","created_at":"2025-08-22 09:44:09","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":370039,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProbability of bean yield falling below 0.6 t/ha and above 1.5 t/ha in the long rainy season for farms using local seeds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/f989195bf3e5796ea8ee1e98.jpg"},{"id":89649954,"identity":"70638cdd-1696-41b3-8da3-2918105647b8","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":384273,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProbability of bean yield falling below 0.6 t/ha and above 1.5 t/ha in the long rainy season for farms using improved seeds\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Picture10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/3f4c8d86d6298e432262c7a4.jpg"},{"id":105880826,"identity":"da58e3fd-fde6-4890-b39f-12ab92f1db0d","added_by":"auto","created_at":"2026-04-01 06:43:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4026059,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/b757eb44-791b-4150-ac11-9f632b5c9810.pdf"},{"id":89649941,"identity":"8c227d0e-2733-4b30-8c96-77ded5c053f8","added_by":"auto","created_at":"2025-08-22 09:36:09","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":19453,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixA.docx","url":"https://assets-eu.researchsquare.com/files/rs-7237495/v1/c377d222ba334dba89efd2d8.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling the impact of improved seed varieties on common beans productivity in agroecological zones of Tanzania: A stochastic simulation approach","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eCommon beans (\u003cem\u003ePhaseolus vulgaris L.\u003c/em\u003e) constitute a vital component of the daily diet for millions of households in developing countries, serving as both a staple food and a crucial source of protein, micronutrients, and cash crop legumes (Mkuna, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Globally, beans are recognized for their role in enhancing food and nutritional security, particularly among low-income populations who rely heavily on plant-based protein sources (Beebe et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Paredes et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Assefa et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Blair et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Mukankusi et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Rich in iron, zinc, fiber, and essential amino acids, beans significantly contribute to reducing micronutrient deficiencies and combating undernutrition, particularly among children and women of reproductive age (Petry et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Huertas et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Muthoni \u0026amp; Nyamongo, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Katungi et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wortmann \u0026amp; Allen, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Globally, common bean production covers approximately 30\u0026nbsp;million hectares, with an annual production of over 28\u0026nbsp;million metric tons. Latin America and Sub-Saharan Africa (SSA) are the largest producers and consumers, with countries such as Brazil, Mexico, Kenya, and Tanzania among the top contributors (Beebe et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Jansa et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In SSA alone, beans occupy a central position in both rainfed agriculture and local diets, providing up to 20% of daily protein intake in some rural communities (Wortmann et al., 1998; Buruchara et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Farrow \u0026amp; Muthoni-Andriatsitohaina, 2020). Despite this critical role, bean productivity remains substantially below global standards in most SSA countries, averaging between 0.6 and 0.8 t/ha, compared to the global potential yield range of 1.3\u0026ndash;1.5 t/ha (Ter\u0026aacute;n \u0026amp; Singh, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Buruchara et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Farrow \u0026amp; Muthoni-Andriatsitohaina, 2020; Rubyogo et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Hummel et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Katungi et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Beebe et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Rao et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn East Africa (EA), common beans are among the top five most widely cultivated food crops, grown by over 30\u0026nbsp;million smallholder farmers, largely under low-input, rainfed systems (Asfaw, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Asfaw et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Bruno et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Tanzania stands as one of the leading producers in the region, with over 1.2\u0026nbsp;million hectares dedicated to bean farming, yielding more than 900,000 metric tons annually (URT, 2021). The crop is cultivated across diverse agroecological zones, including the Northern Highlands, Southern Highlands, Lake Zone, and the Western Zone, where it supports both household food security and market-oriented farming (Justus et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hamazakaza et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Letaa et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Hillocks et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Ndakidemi et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Tryphone et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). However, despite its significance, bean production in Tanzania continues to face myriad challenges that constrain productivity. These include low adoption of improved seed varieties, recurrent droughts, erratic rainfall, pest and disease outbreaks (notably angular leaf spot, root rots, and bean fly), soil fertility depletion, and limited access to extension services and inputs such as certified seeds and fertilizers (David \u0026amp; Sperling, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Rubyogo et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Assefa et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Beebe et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Jansa et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Jim\u0026eacute;nez, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Parker et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Furthermore, much of Tanzania's bean production is conducted using local landraces, which, although well-adapted to local conditions, have lower yield potential and poor resistance to biotic and abiotic stresses compared to improved varieties (Lunze et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Birnholz et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Barasa, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eOver the past two decades, several initiatives have been introduced by governments and development partners in SSA to address these constraints and boost bean productivity. These include regional programs such as the Pan-Africa Bean Research Alliance (PABRA) and the Eastern Africa Agricultural Productivity Project (EAAPP), as well as national interventions like Tanzania\u0026rsquo;s Agricultural Sector Development Programme (ASDP I \u0026amp; II). These programs have promoted the dissemination of improved bean varieties, capacity building in seed systems, and participatory breeding to align varieties with farmer preferences and local agroecological realities (Buruchara et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Rubyogo et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Monyo \u0026amp; Varshney, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Daudi et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite these interventions, adoption of improved bean varieties remains patchy, and their impacts on farm-level productivity have not been rigorously quantified, particularly across Tanzania's varied agroecological zones. Many existing studies tend to generalize productivity outcomes without accounting for ecological heterogeneity or input interaction effects (Mwongera et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Moreover, most empirical assessments rely on cross-sectional data or linear regressions that fail to capture stochastic variation in productivity, limiting their relevance for risk-based decision-making in smallholder farming systems (Antle, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Antle \u0026amp; Valdivia, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). There is a critical need for robust, simulation-based models that can evaluate the probability of achieving target yields under various seed adoption scenarios across ecological gradients. Specifically, quantifying whether improved seed adoption can enable smallholders to attain the global benchmark of 1.3\u0026ndash;1.5 t/ha is essential for guiding evidence-based investment in seed systems, policy design, and agricultural research targeting (Ter\u0026aacute;n \u0026amp; Singh, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Beebe et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Giller et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Rao et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Vanlauwe et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Sommer et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Nevertheless, such assessments remain limited in the literature, particularly those that incorporate stochastic elements to reflect real-world production risk and uncertainty.\u003c/p\u003e\u003cp\u003eThis study seeks to fill this critical gap by employing a stochastic simulation approach to model the potential impact of improved bean varieties on productivity across Tanzania\u0026rsquo;s major agroecological zones. Using nationally representative data and yield probability distributions, the simulation assesses whether the adoption of improved seed varieties, either alone or in combination with other inputs, can enable smallholders to reach or exceed the global productivity threshold. The stochastic framework also facilitates estimation of risk-adjusted yield outcomes and policy-relevant probability metrics, thereby supporting more informed investment decisions in Tanzania\u0026rsquo;s bean sector. The primary objective of this study is to determine whether the adoption of improved bean seed varieties can enable farmers in Tanzania\u0026rsquo;s diverse agroecological zones to achieve or surpass the global yield standard of 1.3\u0026ndash;1.5 t/ha. This work not only contributes to the academic discourse on productivity modeling and input adoption but also provides critical insights for stakeholders in Tanzania\u0026rsquo;s agricultural policy, seed systems development, and climate-resilient farming initiatives.\u003c/p\u003e"},{"header":"2.0 Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Study Area\u003c/h2\u003e\u003cp\u003eThis research focuses on the impacts of improved seed on common bean yield across all regions of Tanzania (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), which are categorized into six agroecological zones (AEZs). The AEZs include the Central Zone (CZ), Eastern Zone (EZ), Lake Zone (LZ), Northern Zone (NZ), the Southern Highlands Zone (SHZ), and Western Zone (WZ).\u003c/p\u003e\u003cp\u003eThe composition of each zone includes:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe Central Zone (CZ) covers the central regions of Tanzania (Dodoma and Singida).\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe Eastern Zone (EZ) covers Morogoro, Dar es Salaam, Tanga, and the Coastal region.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe Western Zone (WZ) covers the Kigoma and Tabora regions.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eLake Zone (LZ) includes Mara, Shinyanga, Simiyu, Geita, Mwanza, and Kagera.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe Northern zone (NZ) covers the Arusha, Kilimanjaro, and Manyara regions.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe Southern Highlands zone (SHZ) includes the Mbeya, Iringa, Songwe, Njombe, Ruvuma, Katavi, and Rukwa regions.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eTanzania\u0026rsquo;s AEZs are characterized by distinct environmental features, including rainfall patterns, temperature, altitude, soil types, and seasonal moisture distribution, all of which significantly influence crop productivity (URT, 2021). These biophysical conditions and variations in farming systems and land use practices contribute to differences in crop responses across regions. By grouping bean farms according to these AEZs, the study assesses how improved common bean varieties influence yields under different agro-environmental settings. This approach ensures that the results reflect national diversity while remaining applicable to localized planning and extension services (Tittonell \u0026amp; Giller, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDisaggregating the analysis by AEZs enables a more detailed comparison of the performance of improved varieties across diverse production landscapes. Such spatially explicit evaluation is crucial for formulating region-specific strategies that address unique agronomic constraints and potential (Sheahan \u0026amp; Barrett, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Kadigi et al, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Furthermore, this zonal analysis sheds light on how different regions respond to climatic variability, soil fertility limitations, and resource availability, key factors in building resilient and adaptive farming systems (Vanlauwe et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Acknowledging Tanzania\u0026rsquo;s ecological heterogeneity provides a robust foundation for targeting productivity-enhancing interventions and tailoring input recommendations. Ultimately, this spatial classification helps identify priority zones for improved variety support, contributing to evidence-based decision-making that improves bean yields and promotes sustainable agricultural development (Pretty \u0026amp; Bharucha, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Struik \u0026amp; Kuyper, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Overview of Beans Production in Tanzania\u003c/h2\u003e\u003cp\u003eBeans are the most widely cultivated pulses in Tanzania, grown extensively during both the short and long rainy seasons. According to the 2019/20 National Sample Census of Agriculture (NSCA), over 1.04\u0026nbsp;million households in the short rainy season and 1.52\u0026nbsp;million households in the long rainy season were engaged in bean production, predominantly in Mainland Tanzania. During the same agricultural year, the total planted area under beans was 826,685 hectares, with 99.6% of this land managed by smallholder farmers. Kagera, Kigoma, and Manyara regions recorded the largest planted areas, while Mtwara had the least (URT, 2021).\u003c/p\u003e\u003cp\u003eOut of the total planted area, approximately 86.1% was eventually harvested, resulting in 661,699 tons of beans, with 659,497 tons by smallholders and 2,202 tons by large-scale farms. Kagera contributed the most to national output, followed by Manyara and Kigoma. Productivity levels varied across regions, with an average yield of 0.9 tons/ha nationwide. Notably, Zanzibar achieved higher productivity (1.6 tons/ha) compared to Mainland Tanzania, with Mwanza and Geita reporting the highest yields on the mainland (1.3 tons/ha). These statistics reflect the significance of beans as a food security and income crop, particularly among smallholder farmers in Tanzania (URT, 2021).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Data Sources\u003c/h2\u003e\u003cp\u003eTanzania has undertaken multiple rounds of the National Sample Census of Agriculture (NSCA), with the most recent being conducted in 2019/2020. This follows earlier rounds completed in 1971/72, 1994/95, 2002/03, and 2007/08. The present study primarily draws on data from the 2019/20 NSCA while also incorporating information from the 2007/08 census to adjust historical comparisons and contextualize the latest figures. The NSCA is managed by the National Bureau of Statistics (NBS) and serves as a key source of agricultural data in Tanzania. It offers comprehensive coverage of rural farming households, documenting aspects such as landholding size, types and levels of crop production, livestock ownership, and the application of agricultural inputs like fertilizers and improved seeds. Additionally, the survey gathers insights into rural infrastructure, livelihood conditions, and household living standards, providing a critical basis for evaluating agricultural performance and the outcomes of development initiatives (URT, 2021).\u003c/p\u003e\u003cp\u003eTo ensure national representativeness, the NSCA applies a rigorous two-stage sampling strategy. In the first phase, Census Enumeration Areas (CEAs) are selected using the 2012 Population and Housing Census as a sampling frame. These CEAs serve as Primary Sampling Units (PSUs) and are strategically selected from various regions and districts to ensure comprehensive geographical coverage. In the second phase, agricultural households within these selected PSUs are randomly sampled, with an emphasis on those involved in crop and livestock production. The final survey sample comprises 2,820 PSUs, consisting of 2,670 from Mainland Tanzania and 150 from Zanzibar, selected using a Probability Proportional to Size (PPS) approach. This technique assigns greater weight to areas with higher agricultural activity, thereby enhancing the precision and relevance of the collected data. Additional details regarding the sampling framework and execution are available in the official NSCA report (URT, 2021).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Data Processing and Simulation\u003c/h2\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1 Data Processing\u003c/h2\u003e\u003cp\u003eThe first thing was to sort the bean yield data from the dataset and categorize it into six AEZs. The sorted data were categorized into two farming practices for more straightforward analysis and comparison for the two different seasons (short and long rainy seasons). Farms that used local seeds in the short rainy season were marked with SRS1, and those that used improved seed varieties were marked with SRS2. Farms using local seed during the long rainy season were marked as LRS1, while those using improved seeds were marked as LRS2. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the observed data sorted from the NSCA for each AEZ. These data included only farms that were already harvested. The yield distribution for each farming system (local and improved users) per agro-ecological zones is summarized in Appendix A.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eNumber of observations for Bean farms using local vs improved seeds per AEZ\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAgroecological Zone\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eFarming Using Local Seed\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eFarming Using Improved Seed\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eShort Rain Season (SRS1)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLong Rain Season (LRS1)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eShort Rain Season\u003c/p\u003e\u003cp\u003e(SRS2)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLong Rain Season\u003c/p\u003e\u003cp\u003e(LRS2)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCentral Zone (CZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEastern Zone (EZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e268\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e307\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLake Zone (LZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1,358\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e591\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e29\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNorthern Zone (NZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e595\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e814\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e137\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSouthern Highlands (SHZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e213\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1,548\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e103\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWestern Zone (WZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e880\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eAll Farms (AllTZ)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e2564\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e4,231\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e248\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e326\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.3.2 Data Simulation\u003c/h2\u003e\u003cp\u003eThe data analysis for this study utilizes a Stochastic Simulation Model (SSM) that follows a non-parametric Monte Carlo simulation approach, as detailed by Richardson et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2000\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2003\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) and Kadigi et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Monte Carlo simulations are well-regarded for their ability to model stochastic variables, such as yields or output and input prices, and generate estimated distributions for these variables. This technique robustly quantifies the risks and variabilities tied to crop profitability in Tanzania. In the initial phase of the simulation, we define and parameterize the stochastic (risky) yields for each farming system, grounded in actual observed data. The yields are then converted into a stochastic format using standard Monte Carlo protocols, which allow for the simulation and validation of yield distributions tailored to each seed type and farming setup. The study further categorizes data across agroecological zones to address Tanzania's geographical and climatic diversity.\u003c/p\u003e\u003cp\u003eFor the analysis of these varied yields, the study employs a Multivariate Empirical (MVE) distribution method, as also detailed in the work by Kadigi et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). This approach effectively handles multiple variables simultaneously and ensures that the simulated values remain within realistic limits, such as avoiding the generation of implausible negative yields. To facilitate this, residuals defined as percentage deviations of observed yields from their mean are used to estimate the parameters of the MVE yield distribution. This method captures the variability in historical yield data and underscores the probabilistic nature of bean yield variability across the two farming systems per AEZ, providing a comprehensive view of potential production outcomes (Kadigi et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe following equation was used to develop the stochastic yield:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\stackrel{\\sim}{y}}_{i,\\omega\\:}={\\stackrel{̄}{y}}_{c,i,\\omega\\:}*\\left(1+EMP\\left({S}_{y,i,\\omega\\:},P\\left({S}_{y,i,\\omega\\:}\\right),CUS{D}_{y,i,\\omega\\:}\\right)\\right)*{\\beta\\:}_{{\\stackrel{\\sim}{y}}_{0}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e~\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eA tilde represents a random (stochastic) variable.\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eType of farming practices used (\u003cem\u003elocal seeds, improved seeds\u003c/em\u003e).\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRepresents farms in six agroecological zones\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eHectares (ha) allocated for farming practice \u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStochastic mean yield per ha for farming practice \u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{y}}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDeterministic (mean) yield per ha for farming practice \u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{{\\stackrel{\\sim}{y}}_{0}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eThe normalization factor, which is given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{\\stackrel{\\sim}{y}}_{c,i}}{{\\stackrel{\\sim}{y}}_{h,i}}\\:\\)\u003c/span\u003e\u003c/span\u003eand it is used to scale/adjust the 2019/20 NCSA mean yield.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\sim}{y}}_{c}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStochastic yield for the current survey (2019/20 NCSA)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\sim}{y}}_{h}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStochastic yield for the historical or previous survey (2007/08 NCSA)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFraction deviations from the mean or sorted array of random yields for farming practice \u003cem\u003ei\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eP(S\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCumulative probability function for the \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e values\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eCUSD\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSimetar function to simulate the correlated uniform standard deviation of random variables.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cem\u003eEMP()\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e=\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSimetar function used to simulate a stochastic variable (yield)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe subsequent phase of the analysis involved simulating the SSM for a minimum of 500 iterations for each farming practice using the Latin Hypercube Sampling (LHC) method, as detailed by Richardson et al. (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) and Kadigi et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The LHC technique was selected for its efficiency, allowing for a comprehensive replication of the parent yield distributions despite the relatively modest number of iterations. This efficiency is crucial because it ensures that the sample size of 500 iterations is sufficient to accurately capture the underlying characteristics of the yield distributions. This simulation considered 26 random variables (yields) represented by two farming systems: local seed users in the short and long rainy seasons, and improved seed users in the short and long seasons across six agroecological zones, resulting in a total simulated sample size of 13,000 (500 \u0026times; 26). This extensive dataset enhances the robustness of our analysis, enabling a more precise evaluation of how various farming practices affect bean yields.\u003c/p\u003e\u003cp\u003eTo validate the accuracy of these simulations, the final step of the analysis involved comparing the simulated yield distributions against historical yield data. This validation step is crucial to ensure that the stochastic model accurately reflects observed data while incorporating the inherent variability of SSM. By aligning the simulation outputs with historical distributions, the study ensures that its findings are both reliable and relevant for assessing the impact of different farming practices within Tanzania's diverse agroecological landscapes. Results from this validation are detailed in the Results section, which utilizes probability distribution functions (PDFs).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Ranking of Target Probabilities Using the Stoplight Function\u003c/h2\u003e\u003cp\u003eThe Stoplight Chart function was used to rank the probabilities of bean farms achieving the maximum yield thresholds and the probabilities of falling below the minimum values per unit area (which is hectares, or ha, in this study). The stoplight function calculates the probabilities of (a) exceeding the upper target (\u003cem\u003egreen\u003c/em\u003e), (b) being less than the lower target (\u003cem\u003ered\u003c/em\u003e), and (c) falling between the targets (\u003cem\u003eyellow\u003c/em\u003e). The views from various bean actors, particularly farmers, and literature review including the current National Sample Census of Agriculture (NSCA) URT (2021) revealed that the average yield in Tanzania ranges between 0.6\u0026ndash;1.2 t/ha; hence, we set our minimum threshold to be 0.60 t/ha and the maximum being 1.50 t/ha (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The maximum was set to meet most national initiatives, such as the ASDP-II (URT, 2016) and the Tanzania Seed Sector Development Strategy \u0026ndash; 2030 (Minde et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which aims to double the productivity of major crops, including beans, by 2030.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3.0 Results and Discussion","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Model Validation\u003c/h2\u003e\n \u003cp\u003eThe stochastic model used in this analysis was validated to ensure it accurately simulated the farming practices under investigation. The stochastic model was validated using probability density function (PDF) charts to compare observed and simulated yield distributions. These comparisons were made across various farming scenarios in Tanzania, including:\u003c/p\u003e\n \u003col\u003e\n \u003cli\u003e\u003cspan\u003eYield of farms using local seeds in the short rainy season\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eYield of farms using improved seeds in the short rainy season\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eYield of farms using local seeds in the long rainy season\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eYield of farms using improved seeds in the long rainy season\u003cbr\u003e\u003c/span\u003e\u003c/li\u003e\n \u003c/ol\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e presents the model validation results by comparing the observed and simulated probability distribution functions (PDFs) of bean yield across all farms in Tanzania. The visual alignment across the subplots demonstrates the model\u0026apos;s effectiveness in replicating real-world yield distributions under different seed types and seasonal conditions. Specifically, panels (a) and (b) depict yield distributions for farms using local seed varieties and improved seed varieties, respectively, during the long rainy season (LRS), while panels (c) and (d) show the same comparisons for the short rainy season (SRS).\u003c/p\u003e\n \u003cp\u003eIn each subplot, the observed distribution is shown in black, and the simulated distribution is shown in red. The close match between the two curves in all cases highlights the simulation model\u0026rsquo;s robustness and accuracy in capturing the statistical behavior of actual farm yields. These results provide strong empirical support for the model\u0026rsquo;s reliability, validating its use in analyzing the impact of improved seed adoption on bean productivity across varying agroecological and seasonal contexts in Tanzania.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e3.1. Beans Productivity Across All Agroecological Zones of Tanzania in the Long Rainy Season for Farms Using Local vs. Improved Seed Varieties\u003c/strong\u003e\u003c/p\u003e\n \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.1 Beans yield distribution during the long and short rainy seasons\u003c/h2\u003e\n \u003cp\u003eThe results presented in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e demonstrate notable differences in bean productivity across Tanzania based on seed type and seasonal conditions. On average, farms using improved seed varieties achieved relatively higher yields in both the short and long rain seasons compared to those using local seed. Specifically, during the short rain season (TZ_SRS2), improved seeds yielded an average of 1.40 t/ha, surpassing the 1.32 t/ha from local seeds (TZ_SRS1). Similarly, during the long rainy season (TZ_LRS2), improved seed users recorded a mean yield of 0.70 t/ha, slightly higher than the 0.63 t/ha achieved with local seed (TZ_LRS1). While these differences in means may appear modest, they suggest that improved seed varieties consistently offer an advantage across seasons. The observed higher maximum yields, 3.06 t/ha for improved seed versus 3.16 t/ha for local seed in the short rain season, highlight variability in performance. However, the yield gap is more evident during the long rainy season, where local seeds reached a maximum of 1.65 t/ha compared to only 1.52 t/ha for improved seeds.\u003c/p\u003e\n \u003cp\u003eAdditionally, the coefficient of variation (CV) values indicate higher yield variability among farms using improved seeds, particularly during the long rain season (CV\u0026thinsp;=\u0026thinsp;38.40%), as compared to farms using local seeds (CV\u0026thinsp;=\u0026thinsp;24.42% for TZ_LRS1). This suggests that while improved seeds can increase productivity, their performance may be more sensitive to management practices or agroecological conditions. The relatively higher standard deviation and broader range of yields observed in improved seed plots (e.g., a minimum of 0.26 t/ha and a maximum of 1.52 t/ha in the long rains) also support the presence of more pronounced production risk or heterogeneity. These findings underscore the importance of complementary inputs and localized extension support to realize the full potential of improved varieties. Overall, the data affirm that improved seeds offer a yield advantage, albeit with variability that needs to be carefully managed, especially under changing climatic conditions. The yield distribution (in t/ha) per agroecological zone and seasons are summarized in Appendix A\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSummary Statistics on Bean Productivity Across all Tanzania Farms Using Local vs Improved Seed Types\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eYield Distribution\u003c/p\u003e\n \u003cp\u003e(t/ha)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eFarming Using Local Seed\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eFarming Using Improved Seed\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eShort Rain Season (TZ_SRS1)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLong Rain Season (TZ_LRS1)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eShort Rain Season\u003c/p\u003e\n \u003cp\u003e(TZ_SRS2)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLong Rain Season\u003c/p\u003e\n \u003cp\u003e(TZ_LRS2)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSTD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCV\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents probability density function (PDF) approximations for bean productivity across all Tanzanian farms using local (black line) and improved seed varieties (red line), disaggregated by season. In panel (a), representing the short rain season, both distributions appear slightly right-skewed with peaks around the 1.2\u0026ndash;1.4 t/ha range. However, the red curve (improved seeds, TZ_SRS2) demonstrates a marginally broader distribution, with a rightward shift in the peak compared to the black curve (local seeds, TZ_SRS1), indicating a general yield advantage. The improved seed distribution also exhibits a longer tail, suggesting that a subset of farmers achieved substantially higher yields, up to approximately 3.0 t/ha. The black curve, while more concentrated, peaks at a slightly lower yield level and declines more steeply, indicating lower variability but a less frequent occurrence of high yields.\u003c/p\u003e\n \u003cp\u003ePanel (b), which illustrates the long rain season, shows more pronounced differences. The PDF for improved seed users (red line, TZ_LRS2) is flatter and more dispersed, with multiple minor peaks, indicating a more heterogeneous yield response. While the peak of the improved seed distribution is slightly right of the local seed distribution (black line, TZ_LRS1), it is less sharply defined, suggesting greater variability in outcomes. Conversely, the local seed curve is narrower and more concentrated, peaking near 0.60\u0026ndash;0.70 t/ha. The presence of higher-density tails in the improved seed curve implies that, despite the variability, more farmers were able to achieve yields above 1.0 t/ha compared to those using local seeds. Collectively, these PDFs reinforce the interpretation that improved seeds tend to increase average productivity and expand yield possibilities, especially in the short rain season, but may also introduce greater variability that necessitates supportive agronomic practices for consistent gains.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.2 Beans yield distribution across the agroecological zones during the short rainy season\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e presents probability density function (PDF) approximations of bean productivity across four major producing agroecological zones of Tanzania, Lake Zone (LZ), Eastern Zone (EZ), Northern Zone (NZ), and Southern Highlands Zone (SHZ), during the short rain season (SRS), comparing farmers using local seeds (black curves) with those using improved seeds (red curves). In the Lake Zone (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea), the distribution for improved seeds (LZ_SRS2) is flatter and broader than that of local seeds (LZ_SRS1), with a rightward shift in the peak. This indicates that while the majority of improved seed users achieved moderate yields (~\u0026thinsp;1.2\u0026ndash;1.6 t/ha), a notable number of them attained higher productivity (up to 3.0 t/ha), suggesting a performance edge with improved seeds. The Eastern Zone (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb) exhibits overlapping PDFs, with the red curve for improved seeds slightly exceeding the black curve in density around 1.4\u0026ndash;1.8 t/ha, indicating modest gains in productivity among users of improved seeds in this zone.\u003c/p\u003e\n \u003cp\u003eIn the Northern Zone (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec), both seed types exhibit similar peak locations around 1.1\u0026ndash;1.3 t/ha; however, the red curve (NZ_SRS2) has a heavier right tail, indicating that more farmers using improved seeds were able to surpass 2.0 t/ha, albeit with greater variability. This suggests potential for higher yield ceilings when improved seeds are effectively managed. The Southern Highlands Zone (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed) exhibits the most pronounced divergence, with improved seeds yielding a broader distribution and a noticeable secondary peak near 2.0\u0026ndash;2.5 t/ha, which is absent in the local seed curve. This indicates substantial productivity gains and heterogeneity in yield outcomes among users of improved seeds in this high-altitude zone. Overall, these patterns suggest that improved seed varieties generally enhance yield potential across zones. However, the magnitude and consistency of their impact vary by agroecological context, underscoring the need for localized seed system strategies and agronomic support.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.3 Beans yield distribution across the agroecological zones during the Long rainy season\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the PDF approximations of bean productivity across six agroecological zones in Tanzania during the Long Rainy Season (LRS), comparing farmers who use local seeds (black lines) with those who use improved seeds (red lines). In the Central Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea), improved seed users (CZ_LRS2) demonstrate a slightly broader and flatter distribution than local seed users (CZ_LRS1), with the red curve exhibiting a wider tail and density beyond 1.0 t/ha. This indicates that while many improved seed users achieved yields similar to those of local seed users (~\u0026thinsp;0.60\u0026ndash;0.80 t/ha), a notable portion achieved higher-than-average yields, albeit with increased variability. In the Eastern Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003eb), the red curve is marginally right-shifted compared to the black curve, suggesting improved seeds offered slight productivity gains in the 0.60\u0026ndash;0.90 t/ha range. However, the presence of multiple peaks suggests inconsistent performance across farms, possibly due to variations in management practices or climatic influences.\u003c/p\u003e\n \u003cp\u003eIn the Lake Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ec), the improved seed PDF (LZ_LRS2) closely overlaps with that of local seeds, with both reaching a peak near 0.60 t/ha. Nonetheless, the improved seed distribution has a broader tail, showing that more farmers achieve yields over 1.0 t/ha, albeit with reduced density. This suggests only marginal yield gains with improved seeds in this zone during the long rainy season. In the Northern Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ed), a more pronounced shift is observed. Both local and improved seed PDFs (NZ_LRS1 \u0026amp; NZ_LRS2) are highly concentrated around 0.40 t/ha \u0026ndash; 0.80 t/ha, with the improved seed curve spreading more evenly, with visible density extending beyond 1.2 t/ha, indicating potential for significant productivity improvements with better agronomic support and input use.\u003c/p\u003e\n \u003cp\u003eMoving to the Southern Highlands Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ee), the black curve for local seeds peaks at a higher value (around 0.5 t/ha) and is more narrowly defined, lying to the left. In contrast, the red curve for improved seeds is broader and flatter, extending further into higher yield ranges, which lie more to the right. This suggests that a larger proportion of improved seed users achieved relatively higher peak yields compared to their counterparts. Finally, the Western Zone (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ef) exhibits considerable rightward spread in the red curve, with improved seed users showing greater yield variability and the potential to exceed 1.2 t/ha. However, the flatter distribution also points to inconsistency in realizing yield advantages across farms. Overall, these patterns suggest that improved seeds generally increase yield potential across agroecological zones during the long rainy season; however, the magnitude and consistency of impact vary widely, underscoring the importance of targeted support for input access, extension, and climate adaptation.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e3.2. Probability of Bean Yield Falling Below 0.6 t/ha and Above 1.5 t/ha During Short Rains: Local vs. Improved Seeds\u003c/strong\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.1 Yield Probability for Local Seed under SRS\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents the probabilities of bean yields falling below 0.6 t/ha (low productivity) and exceeding 1.5 t/ha (high productivity) across different agroecological zones in Tanzania during the short rainy season (SRS), specifically for farms using local seed varieties. The chart clearly shows that across all zones, Central Zone (CZ), Eastern Zone (EZ), Lake Zone (LZ), Northern Zone (NZ), Southern Highlands Zone (SHZ), Western Zone (WZ), and the national aggregate (AllTZ), there is zero probability of bean yields falling below 0.6 t/ha. This finding indicates that, despite the use of local seeds, extreme yield failure is unlikely during the SRS, and most farms can at least reach the minimum productivity threshold.\u003c/p\u003e\n \u003cp\u003eHowever, the probability of attaining high yields (above 1.5 t/ha) remains modest, ranging from 29\u0026ndash;34% across zones. The Eastern Zone (EZ_SRS1) has the highest probability (34%), while the Northern Zone (NZ_SRS1) and Southern Highlands Zone (SHZ_SRS1) record the lowest probabilities at 29%. However, the majority of farmers using local seeds consistently fall within the middle productivity band (0.6\u0026ndash;1.5 t/ha), with proportions ranging from 66\u0026ndash;71%. The national average for high productivity stands at 33%, suggesting that only about one-third of farmers using local seeds can exceed the global yield benchmark. These results underscore the limitations of local seed varieties in achieving optimal productivity levels, even under favorable seasonal conditions, and highlight the need for interventions that promote improved seed technologies and complementary inputs to close the yield gap.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.2 Yield Probability for Improved Seed Under SRS\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates the probabilities of bean yields falling below 0.6 t/ha (red segment) and exceeding 1.5 t/ha (green segment) during the short rainy season across selected agroecological zones in Tanzania for farms using improved seeds. In contrast to Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, which depicted outcomes for local seed users, Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e reveals a more diversified distribution of yield probabilities, with slightly higher risk but also notably increased chances of high productivity. The probability of achieving yields above 1.5 t/ha ranges from 32% in the Southern Highlands Zone (SHZ_SRS2) to 49% in the Eastern Zone (EZ_SRS2), with the national average (TZ_SRS2) at 40%. These figures are consistently higher than those in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, where the maximum was 34% (EZ_SRS1) and the national average was 33%. This confirms that improved seeds offer a statistically significant yield advantage, increasing the likelihood of surpassing the global benchmark of 1.5 t/ha in all observed zones.\u003c/p\u003e\n \u003cp\u003eOn the downside, a small probability of yield falling below 0.6 t/ha re-emerges in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e for some regions, specifically 2% in LZ_SRS2 and 1% in SHZ_SRS2 and TZ_SRS2, compared to 0% in all zones in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e for local seeds. This suggests that while improved seeds increase average and upper-bound yields, they may also introduce greater production risk for a small subset of farmers, possibly due to inadequate agronomic management or environmental mismatches. Nevertheless, the majority of farmers using improved seeds consistently fall within the middle productivity band (0.6\u0026ndash;1.5 t/ha), with proportions ranging from 51\u0026ndash;67%, which is similar to or slightly higher than those of local seed users. Overall, the results demonstrate that improved seeds enhance the probability of high yields, justifying their promotion. However, they should be coupled with agronomic support and input packages to minimize downside risk.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e3.3. Probability of Bean Yield Falling Below 0.6 t/ha and Above 1.5 t/ha During Long Rains: Local vs. Improved Seeds3.3.1 Yield Probability for Local Seed under LRS\u003c/strong\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.1 Yield Probability for Local Seed under LRS\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e presents the probability distribution of bean yields during the long rainy season (LRS) for farmers using local seeds across various agroecological zones in Tanzania. The red segments represent the probability of low productivity (below 0.6 t/ha), yellow indicates moderate yields (0.6\u0026ndash;1.5 t/ha), and green shows high yields (above 1.5 t/ha). The findings are concerning: low yields dominate, with probabilities ranging from 45\u0026ndash;60%, and the national average (TZ_LRS1) at 53%. This suggests that more than half of the farmers using local seeds during the long rainy season are likely to achieve suboptimal yields, significantly limiting food security and income generation. Conversely, the probability of achieving high yields above 1.5 t/ha is almost negligible, with most zones registering yields of only 0.00\u0026ndash;0.01 t/ha, reaffirming the inability of local seeds to meet global productivity standards under long-rain conditions.\u003c/p\u003e\n \u003cp\u003eWhen compared to Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e (short rainy season with local seeds), the contrast is stark. In Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, the probability of low yields was 0% across all zones, and the chances of exceeding 1.5 t/ha ranged from 29\u0026ndash;34%. This demonstrates that the short rainy season (SRS) is more favorable for bean production, even with local seed varieties. Similarly, in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, improved seeds during the SRS showed increased likelihood of high productivity (up to 49%) and minimal yield failures. The findings from Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e thus reinforce the seasonal advantage of the SRS over the LRS for bean cultivation in Tanzania. This could be attributed to better rainfall distribution, reduced pest/disease pressure, or more suitable temperature patterns during the SRS. The implication is that policy and investment strategies should prioritize improved seed access and agronomic interventions during the short rains, as the potential for achieving optimal yields is higher, regardless of seed type. Moreover, transitioning from local to improved varieties could significantly mitigate the high yield risks associated with the long rainy season, especially in vulnerable zones such as the Central and Southern Highlands.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n \u003ch2\u003e3.3.2 Yield Probability for Improved Seed under LRS\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e provides critical insights into the probability distribution of bean yields for farms using improved seeds during the long rainy season (LRS) across different agroecological zones in Tanzania. Compared to local seed performance during the same season (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e), improved seeds yield slightly better results but with limited breakthrough. Notably, the probability of low yields (below 0.6 t/ha) remains high, ranging from 35% in WZ_LRS2 to 56% in LZ_LRS2, with the national average (TZ_LRS2) at 51%, which is barely different from the local seed average of 53%. This implies that improved seeds alone are insufficient to eliminate the substantial risk of yield shortfall under long rain conditions without complementary inputs or agronomic practices.\u003c/p\u003e\n \u003cp\u003eThe probability of high yield attainment (above 1.5 t/ha) remains extremely low, except in the Western Zone (WZ_LRS2), where it reaches 12%, indicating a zone-specific opportunity for maximizing productivity with improved seeds. In other zones, high yield probabilities are negligible (0\u0026ndash;1%). These patterns reflect that the long rainy season presents less favorable growing conditions for beans, even with the use of improved varieties, likely due to factors such as excessive rainfall, poor soil drainage, increased disease pressure, or lower seed responsiveness in these months. When compared with results from the short rainy season (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e), where improved seeds resulted in high yield probabilities of 32\u0026ndash;49%, the data in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e affirm that the short rainy season is significantly more productive and stable for bean cultivation in Tanzania. Therefore, policies promoting seasonal targeting, such as prioritizing SRS planting with improved seeds and providing location-specific agronomic packages, could offer more substantial gains in productivity and profitability than blanket promotion across both seasons.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study offers valuable insights into the probabilistic distribution of bean productivity under varying seed technologies and seasonal conditions across Tanzania's agroecological zones. The stochastic simulations revealed clear distinctions in yield performance between farms using local and improved seed varieties, particularly across the short and long rainy seasons.\u003c/p\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Yield Distribution Patterns: Seasonality and Seed Type\u003c/h2\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e demonstrate that improved seed varieties consistently outperformed local seeds in terms of mean yield across most agroecological zones during the short rainy season (SRS). For instance, the probability density functions (PDFs) indicate that improved seeds achieved higher peak densities and extended right tails, signifying an increased likelihood of attaining yields above 1.5 t/ha, especially in zones such as the Lake Zone (LZ) and the Southern Highlands Zone (SHZ). This observation is consistent with previous findings, which highlight that improved varieties bred for drought tolerance and disease resistance can yield significantly higher than local landraces under favorable management and seasonal conditions (Ter\u0026aacute;n \u0026amp; Singh, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Beebe et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Rubyogo et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Buruchara et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Rao et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe long rainy season (LRS) results, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, contrast sharply with those of the short rains (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Despite the use of improved seeds, the PDFs indicate compressed and left-skewed distributions with higher densities in the low-yield region (0.3\u0026ndash;0.8 t/ha). This suggests that the LRS is generally less favorable for bean cultivation across most agroecological zones, which may be attributed to excess rainfall, increased disease pressure, and suboptimal physiological response of bean crops during prolonged wet conditions (Hillocks et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Ndakidemi et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Tryphone et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Hummel et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Katungi et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). The sharper peaks and lack of right-tail extension in many zones reflect constrained yield potential during the LRS, even when improved seeds are used.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Probabilities of Achieving or Falling Short of Yield Thresholds\u003c/h2\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e quantify the probability of yields falling below 0.6 t/ha (indicating low productivity) and exceeding 1.5 t/ha (indicating high productivity) during the short rainy season. Farms using local seeds (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) showed a zero probability of falling below 0.6 t/ha, indicating resilience against complete yield failure; however, they had limited potential for high productivity, with a national average of only 33% probability of exceeding 1.5 t/ha. On the other hand, farms using improved seeds (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) during the SRS exhibited slightly higher risk, with up to 2% probability of yields below 0.6 t/ha in some zones (e.g., LZ_SRS2), yet they showed marked improvement in high yield attainment, with probabilities reaching 49% in the Eastern Zone (EZ_SRS2) and a national average of 40%.\u003c/p\u003e\u003cp\u003eThese results suggest that improved seeds increase both the mean and variance of yield distributions, offering higher upside potential but with some exposure to downside risk, especially in areas where complementary agronomic practices (e.g., pest control, optimal planting time, and soil fertility management) may be inadequate (Antle \u0026amp; Valdivia, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Antle, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Jim\u0026eacute;nez, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Parker et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Nevertheless, the substantially higher probability of achieving yields above 1.5 t/ha with improved seeds supports their promotion as a critical strategy for meeting global productivity benchmarks of 1.3\u0026ndash;1.5 t/ha (Beebe et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Jansa et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Seasonal Disadvantage of the Long Rains\u003c/h2\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e underscore the productivity constraints associated with the long rainy season. Among farmers using local seeds (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e), the probability of low yields (\u0026lt;\u0026thinsp;0.6 t/ha) was disturbingly high, averaging 53% nationally and reaching up to 60% in the Central Zone (CZ_LRS1). The probability of achieving yields above 1.5 t/ha was negligible (0\u0026ndash;1%) in all zones. Even for farms using improved seeds (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e), the probability of high productivity remained low, with only the Western Zone (WZ_LRS2) showing a notable 12% chance of yields above 1.5 t/ha. The probabilities of low yields remained around 50% in most zones, indicating that seed improvements alone may not be sufficient to counteract the agronomic limitations of the LRS. The results highlight that seasonality plays a more significant role than seed type in determining yield outcomes. This aligns with prior studies, which suggest that beans perform best under moderate moisture conditions typical of the short rains, while prolonged wet conditions during the long rains exacerbate diseases such as root rot and angular leaf spot, which severely curtail productivity (Assefa et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Muthoni \u0026amp; Nyamongo, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Katungi et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wortmann \u0026amp; Allen, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Rubyogo et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Implications for Policy and Practice\u003c/h2\u003e\u003cp\u003eThese findings carry important policy implications. First, the short rainy season offers a more reliable opportunity for achieving optimal bean yields using improved seed varieties. With proper input support, extension services, and climate-resilient agronomic packages, the SRS could serve as the main window for maximizing bean productivity in Tanzania. Second, the promotion of improved seeds must be paired with localized agroecological support, especially in zones such as the SHZ and LZ, where potential gains are greatest. Finally, in the LRS, efforts should focus more on climate adaptation strategies, such as drainage management, disease-tolerant varieties, and seasonal forecasts, to mitigate the heightened yield risks even with improved genetics. The application of stochastic modeling in this study further provides a nuanced understanding of yield distribution, risk exposure, and probability-based planning, which are essential for designing smart seed policies and investment strategies (Antle et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Vanlauwe et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Sommer et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Giller et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study modeled the impact of improved seed varieties on bean productivity across Tanzania\u0026rsquo;s agroecological zones using a stochastic simulation approach. By analyzing yield probability distributions and thresholds across both short and long rainy seasons, the research revealed substantial seasonal and spatial variation in the productivity outcomes of local versus improved seed users. Notably, the findings underscore the importance of seed technology and seasonal targeting as key determinants of yield performance, with significant implications for food security, nutritional well-being, and agricultural resilience. The simulation results clearly show that improved seed varieties consistently outperform local seeds in terms of mean yield and probability of attaining global yield standards (1.3\u0026ndash;1.5 t/ha), especially during the short rainy season (SRS). In this season, improved seeds increased the probability of achieving yields above 1.5 t/ha by up to 42% and 49% in certain zones (e.g., Lake Zones and Eastern), compared to a maximum of 34% with local seeds. These gains, however, were accompanied by a modest increase in variability and risk of yield failure (i.e., falling below 0.6 t/ha), indicating that while improved varieties enhance potential, they must be coupled with good agronomic practices and institutional support systems to ensure consistent performance.\u003c/p\u003e\u003cp\u003eConversely, the long rainy season (LRS) exhibited less favorable conditions for bean production. Both local and improved seed users faced high probabilities (often above 50%) of producing yields below 0.6 t/ha, and negligible chances of exceeding 1.5 t/ha. This seasonal disparity underscores that climate-smart seasonal planning, focusing on the SRS for bean cultivation, could be a strategic entry point for enhancing national productivity and reducing vulnerability among smallholder farmers. Moreover, the Western Zone emerged as a unique exception during the LRS, where improved seeds enabled up to 12% of farmers to exceed 1.5 tonnes per hectare, highlighting the need for region-specific recommendations.\u003c/p\u003e\u003cp\u003eFrom a broader development perspective, these findings contribute to the evidence base supporting Sustainable Development Goal 2 (Zero Hunger). Beans are not only a major source of calories but also provide essential proteins, iron, and zinc, especially for rural and low-income households. Increasing bean yields through improved seed adoption directly enhances household food availability, dietary diversity, and income, thereby tackling both chronic and hidden hunger. When smallholder farmers achieve productivity above subsistence levels, they are better positioned to market their surplus, save, and reinvest, further contributing to rural economic transformation and resilience.\u003c/p\u003e\u003cp\u003eFurthermore, the study has direct relevance to Sustainable Development Goal 3 (Good Health and Well-being). As an affordable and accessible source of high-quality protein and micronutrients, common beans play a crucial role in combating malnutrition, stunting, and anemia conditions that remain prevalent in many Tanzanian regions. Improving bean productivity can therefore have downstream health benefits, particularly for children and women of reproductive age. By enabling farmers to produce more nutritious food reliably, the promotion of improved seed varieties contributes to both preventive health care and the strengthening of food systems as determinants of well-being.\u003c/p\u003e\u003cp\u003eIn conclusion, this study reinforces the importance of deploying context-specific, climate-smart agricultural technologies such as improved bean varieties, especially during the short rains, to increase productivity and meet global yield standards sustainably. The integration of stochastic simulation has been demonstrated to be a powerful tool for capturing yield variability, informing policymakers and development actors about the probability of success under various scenarios. However, achieving full benefits will require more than just seed dissemination. Supportive measures, such as access to credit, extension services, disease control, and weather forecasting, must be scaled alongside seed interventions to achieve widespread transformation. Future research should further explore the interaction between improved seeds and other production inputs (e.g., fertilizers, irrigation) under climate stress, to better inform investment and policy priorities. Ultimately, aligning agricultural development strategies with the principles of SDG 2 and SDG 3 will ensure that Tanzania\u0026rsquo;s bean sector makes a meaningful contribution to ending hunger, improving nutrition, and enhancing the health and resilience of its population.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthors' contributions:\u003c/strong\u003e ILK conceptualized the research, collected data, performed the data analysis, developed all figures and tables, and wrote the article.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares that no financial support or funding was received for the preparation of this manuscript\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability \u0026nbsp; \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment \u0026nbsp; \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI am grateful to the Simetar© team (www.simetar.com), particularly Dr. James W. Richardson, former Regents Professor at Texas A\u0026amp;M University, and Dr. Jean-Claude Bizimana, for their endless, invaluable guidance on the Monte Carlo Simulation Protocols.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study is based on secondary data obtained from the 2019/2020 National Sample Census of Agriculture (NSCA), which was conducted by the National Bureau of Statistics (NBS) of Tanzania in collaboration with the Ministry of Agriculture and the World Bank. The data are anonymized and publicly available for research and policy analysis purposes. Therefore, ethical approval and individual consent to participate were not required for this study. The use of the data complies with the terms and conditions set by the NBS for secondary data analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests \u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares no conflicts of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAntle JM. Predicting the supply of ecosystem services from agriculture. Am J Agric Econ. 2006;88(5):1174\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAntle JM, Valdivia RO. Modelling the supply of ecosystem services from agriculture: A minimum-data approach. Australian J Agricultural Resource Econ. 2006;50(1):1\u0026ndash;15.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAntle JM, Jones JW, Rosenzweig C. 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Field Crops Res. 2014;155:10\u0026ndash;3.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWortmann CS. Atlas of common bean (Phaseolus vulgaris L.) production in Africa. CIAT; 1998. p. 297.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWortmann CS, Allen DJ. African bean production environments: their definition. characteristics and constraints; 1994.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"stochastic simulation, local seeds, improved seeds, bean productivity, agroecological zones, Tanzanian","lastPublishedDoi":"10.21203/rs.3.rs-7237495/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7237495/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBeans are a critical source of food and income for smallholder farmers in Tanzania; yet, their productivity remains low due to a reliance on traditional varieties and limited adoption of inputs. This study evaluates the impact of improved seed varieties on bean productivity across diverse agroecological zones (AEZs) in Tanzania, employing a stochastic simulation approach. Drawing on nationally representative data from the 2019/20 National Sample Census of Agriculture (NSCA), we compared yield distributions for farms using local versus improved seeds. Monte Carlo simulations assessed the probabilities of achieving productivity thresholds of 0.6 t/ha (low) and 1.5 t/ha (high) during both long and short rainy seasons. Findings reveal that improved seeds significantly increase the likelihood of higher yields, particularly in the short rainy season. In zones such as the Lake and Eastern regions, improved seed users had a 42\u0026ndash;49% probability of surpassing the global standard of 1.5 t/ha, compared to only 34% for local seed users. However, this yield gain was accompanied by slightly higher variability and risk of yield failure. The long rainy season presented less favorable conditions, with over 50% of farms, regardless of seed type, yielding less than 0.6 t/ha and minimal chances of exceeding 1.5 t/ha. Spatial variability was evident, with improved seeds showing stronger effects in the Lake, Eastern, and Northern zones. Notably, local seeds continued to demonstrate profitability during the short rainy season. The study recommends improving access to improved seeds, enhancing extension services, and implementing input subsidies for marginalized AEZs. These findings support policy interventions that boost resilience, productivity, and food security, aligning with Sustainable Development Goal 2 (Zero Hunger). The study also highlights the need for spatially differentiated strategies and provides empirical evidence to inform adaptive agricultural policy and investment planning.\u003c/p\u003e","manuscriptTitle":"Modeling the impact of improved seed varieties on common beans productivity in agroecological zones of Tanzania: A stochastic simulation approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-22 09:36:04","doi":"10.21203/rs.3.rs-7237495/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0146b457-fb4d-4afe-817b-ae58e261d8d7","owner":[],"postedDate":"August 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-01T06:41:21+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-22 09:36:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7237495","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7237495","identity":"rs-7237495","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}