Assessment of the Winter Wheat Yield Gap for Smallholder Farmers in the Loess Plateau via Boundary Line Analysis

Closing the yield gap in smallholder farming systems requires precise identification of key limiting factors. This study addresses this need by applying boundary line analysis (BLA) to diagnose primary soil constraints to winter wheat (Triticum aestivum L.) yield across 95 smallholder farms in the Loess Plateau of China. The BLA approach effectively delineates optimum nutrient ranges amidst inherent field variability, offering a novel methodological advantage for heterogeneous agricultural landscapes. The results showed that, regarding variability, the coefficients of variation for productive spike number and grain yield were considerably greater than those for kernels per spike and thousand-kernel weight. Soil available phosphorus showed the highest coefficient of variation (67.1%), 1.8-2.2 times greater than that of soil organic matter, alkali-hydrolyzed nitrogen, and available potassium. Boundary line models identified significant (p < 0.05) parabolic relationships, defining optimal ranges of 18.5-21.7 g kg^-1 for soil organic matter, 10.4-49.0 mg kg^-1 for alkali-hydrolyzed nitrogen, 40.5-61.6 mg kg^-1 for available phosphorus, and 218.3-284.1 mg kg^-1 for available potassium. Crucially, maintaining soil organic matter and available phosphorus within their respective optimal ranges was fundamental for maximizing yield. These findings provide a scientific basis for site-specific nutrient management and offer direct implications for designing targeted agricultural extension services and fertilization policies to enhance productivity in smallholder systems.