Introduction: With the rapid growth of the global population and increasing concerns about future food security, reducing the yield gap in strategic crops has become a major priority in agricultural research. Soybean (Glycine max L.), one of the most important sources of high-quality protein and edible oil, plays a vital role in global food and feed supply, as well as in various industrial applications. However, under rainfed conditions, actual soybean yields achieved by farmers are often substantially lower than the attainable yield due to suboptimal management practices. Accurate estimation of yield gaps and identification of the main limiting factors require robust analytical methods. Boundary line analysis is a powerful statistical approach that quantifies the response of crop yield to individual management or environmental variables, even when other factors are not controlled. This method identifies the upper boundary of yield response by fitting a line to the scatter plot of yield data against a specific input, thereby determining the optimal range of that factor and estimating the associated yield gap. The objective of this study was to determine the optimal ranges of key management factors affecting soybean yield under rainfed conditions in Babolsar County, Mazandaran Province, Iran, using boundary line analysis. The study also aimed to estimate attainable yield and quantify the yield gap to identify the most important constraints on soybean production in farmer-managed fields.
Materials and Methods: This research was conducted during the 2018–2019 and 2019–2020 growing seasons in Babolsar, northern Iran. In each year, 60 soybean fields were selected to represent the diversity of soil types, field sizes, and prevailing management practices in the region. Weekly field monitoring was carried out throughout the growing season, complemented by structured face-to-face interviews with farmers and soil sampling. Data were collected on farmers’ experience (years), application rates of nitrogen (N), phosphorus (P₂O₅), and potassium (K₂O) fertilizers, seed rate (kg.ha⁻¹), and final plant density (plants.m⁻²). Grain yield was measured at harvest in each field. Boundary line analysis was applied to each management variable by plotting grain yield against the respective factor and fitting the upper boundary line (usually segmented linear functions). All statistical analyses and model fittings were performed using SAS software.
Results and Discussion: The average farming experience was 19.5 years. Mean application rates of potassium, phosphorus, nitrogen, and seed were 54.15, 56.75, 25.7, and 76 kg ha⁻¹, respectively, while the average plant density was 47.34 plants m⁻². The attainable yield under near-optimal management for most factors ranged between 3000 and 3500 kg ha⁻¹. The largest yield gap was associated with seed rate, reaching 1186 kg ha⁻¹ (33.89% of attainable yield). Notably, 79.49% of the fields used seed rates below the optimal level (>70.5 kg.ha⁻¹). Phosphorus and potassium applications also caused considerable yield losses of 727 kg.ha⁻¹ (24.23%) and 719 kg.ha⁻¹ (23.97%), respectively. More than 63% of the fields had phosphorus application rates below the optimal minimum of approximately 46 kg P₂O₅ ha⁻¹. Nitrogen application fell outside the optimal range (23–45 kg N ha⁻¹) in 38% of the fields. In contrast, plant density was within the optimal range (45–52.45 plants m⁻²) in 81.9% of the fields and contributed a smaller yield gap of 629 kg.ha⁻¹ (21.45%). These results indicate that deviations from optimal input levels—particularly insufficient seed rate and suboptimal macronutrient management—rather than the absolute quantities of inputs, were the primary causes of the yield gap in rainfed soybean production in Babolsar. The study confirms that boundary line analysis is an effective and practical tool for diagnosing management constraints under real on-farm conditions.
Conclusion: This study demonstrated that suboptimal nutrient management, especially phosphorus and potassium deficiencies, along with inadequate seed rates, are the main limiting factors responsible for the soybean yield gap in rainfed fields of Babolsar County. Boundary line analysis successfully quantified these limitations under actual farmer-managed conditions. Optimizing fertilizer application based on soil test recommendations, adjusting seed rates to approximately 70–75 kg.ha⁻¹, maintaining proper plant density, and enhancing farmers’ knowledge through extension programs can substantially reduce the existing yield gap. The findings provide a scientific basis for improving soybean productivity, increasing input-use efficiency, and promoting sustainable soybean production in the region.