Integrating source-sink coordination and pod-setting optimization: A field study on plant density effects for soybean productivity enhancement in the Huang-Huai-Hai Plain

Increasing plant density (PD) has proven effective in maximizing yield worldwide, but the optimal PD for soybean production in the Huang-Huai-Hai Plain and its physiological mechanisms remain unclear. To address this gap, a two-year experiment was conducted to investigate the effects of six PDs (135,000, 180,000, 225,000, 270,000, 315,000, and 360,000 plants ha -1 ) on plant characteristics, source parameters (leaf area index (LAI) and light interception rate (LIR)), sink traits (seed number and weight), pod-setting characteristics (seeds per pod and pod spatial distribution), and productivity. Results showed that as PD increased, individual-level relative productivity variation (RPV) decreased by 2.1% per additional 10,000 plants ha -1 , while population-level RPV and seed yield peaked at 315,000 plants ha -1 . This indicates that higher densities can offset declines in individual productivity up to 315,000 plants ha -1 , boosting total yield by 2.6% per additional 10,000 plants ha -1 , driven by increases in LAI (1.9%) and LIR (1.1%). Beyond 315,000 plants ha -1 , however, seeds per m 2 and 100-seed weight declined despite continued increases in plant height, LAI, and LIR, signaling a shift in photoassimilate allocation to stems and leaves at the expense of yield sinks. These findings highlight a transition from source-limited to sink-limited yield constraints as PD rises. Additionally, higher PD improved yield by increasing the proportions of 3-seed pod, middle-node pod, and main stem pod. Overall, 270,000 and 315,000 plants ha -1 delivered the highest economic returns and seed yield, attributed to balanced individual and population productivity, optimized source-sink relationships, and improved pod-setting characteristics, making them the most suitable densities for regional soybean cultivation. This study offers new insights into the source-sink dynamics and pod-setting mechanisms under varying PDs and proposes a 22%-40% increase in PD over current standards (225,000 plants ha -1 ) as an effective high-yield strategy to address the region's soybean production shortfall. • Yield limitations shift from source-driven at low density to sink-driven at high density. • Optimal density optimizes pod-setting characteristics by increasing the proportions of 3-seed pod, middle-node pod, and main stem pod. • 270,000 to 315,000 plants ha -1 is the suitable density for high-yield soybean production in the HHHP.