Applying Liebig’s law of the minimum for variable rate soybean seeding based on CEC-nutrient fertility index

Abstract This study investigated the impact of spatial variability in soil Cation Exchange Capacity and key macronutrients on soybean (Glycine max (L.) Merril) population establishment and yield across two distinct fields. Field A presented Magnesium as the primary concern due to low inherent levels and potential antagonism from high Calcium and Potassium concentrations. Field B was characterized by a significant Calcium deficiency. Recognizing these site-specific limiting nutrients, a variable rate seeding approach was implemented in both fields. A fertility index, derived by multiplying soil CEC values by either Mg content (Field A) or Ca content (Field B), guided the delineation of five management units per field. Higher soybean populations were sown in areas with lower fertility indices, while lower populations were used in higher fertility zones. This approach, applying Liebig’s Law, not only significantly increased soybean yields compared to conventional fixed rate seeding but also increased net revenue. The key take-home message is that an effective fertility index (CEC × limiting nutrient) successfully delineated management zones that addressed soil limitations. This strategy optimized resource use by revealing that maximum grain output is not achieved at maximum plant density; contrary to expectations, the highest yields were harvested from low to medium-low population zones. Plants in these lower-density zones compensated by producing more pods per plant, confirming the economic and agronomic viability of the methodology. The increase in productivity of crops A and B translated directly into better economic returns. For crop A, net income increased by 11.3% (from USD 1369.25 ha−1 to USD 1524.49 ha−1), even with a slight increase in seed cost (2.7%). For crop B, net income increased by 6.9% (from USD 1516.41 ha−1 to USD 1651.03 ha−1), with a significant reduction in seed costs (5.4%). This success was attributed to an optimized plant arrangement, incorporating spatial variations in CEC (Cation Exchange Capacity) and the limiting nutrient. Additional profits, ranging from USD 5 to USD 57 per hectare, can be obtained by farmers adjusting seeding rates based on field productivity variability, as opposed to using fixed seeding rates.