The law of constant final yield and allometric theory have been seldom used to explore density-dependent yield formation and water use in rainfed farming systems, particularly in ridge-furrow mulching (RFM) system of maize. A two-year RFM field experiment was conducted using maize variety Yuyuan7879 in semiarid Kenya from 2015 to 2016, with four planting densities: 5.2 × 10⁴ (D52, conventional density), 6.0 × 10⁴ (D60), 6.9 × 10⁴ (D69) and 8.5 × 10⁴ (D85) plants per hectare. The grain yield and aboveground biomass per plant were significantly decreased with increasing density across two growing seasons. However, the population grain yield significantly was increased from D52 to D60 (from 3395.1–4471.7 kg ha⁻¹) but declined significantly from D60 to D69 and D85 (p < 0.05) in 2015 and 2016, respectively. Meanwhile, the population aboveground biomass was significantly promoted from D52 to D60 (p < 0.05) and then remained relatively stable in D69 and D85, achieving a state of constant final yield. Under the improved soil storage, the RFM system raised the rational planting density from conventional D52 to D60 with regard to population yield. Water use efficiency for population yield (WUE_G) was the highest at D52 and D60, followed by D69, and the lowest at D85. However, the WUE for the aboveground biomass (WUE_A) was significantly lower in D52 than D60 and D85. Principal component analysis suggested that the population grain yield and WUE_G were significantly positively associated with the reproductive allocation and leaf growth. This result was further affirmed by the allometric relationship between leaf biomass and body size, since the allometric exponent (<1) was raised with density. Allometric relationship between reproductive and vegetative mass demonstrated that the D60 treatment achieved a relatively balanced allocation of photosynthetic products into reproductive organs in comparison with other treatments. The RFM application significantly improved the availability of soil water, and the rational planting density of maize for better yield and WUE_G. Thus, this phenomenon mechanically resulted from relatively better trade-offs between reproductive and vegetative growth, together with moderately increased leaf growth.

很少使用恒定最终产量定律和异速生长理论来研究雨养耕作系统（特别是玉米的垄沟覆盖（RFM）系统）中密度相关的产量形成和用水情况。从2015年到2016年，在肯尼亚半干旱地区使用玉米品种Yuyuan7879进行了为期两年的RFM田间试验，种植密度为四个：5.2×10 ⁴（D52，常规密度），6.0×10 ⁴（D60），6.9×10 ⁴（ D69）和每公顷8.5×10 ⁴（D85）的植物。在两个生长季节中，随着密度的增加，每株植物的谷物产量和地上生物量显着下降。但是，人口粮食产量从D52显着提高到D60（从3395.1–4471.7 kg公顷^-1），但分别在2015年和2016年从D60分别降至D69和D85（p <0.05）。同时，地上生物量从D52显着提高到D60（p <0.05），然后在D69和D85保持相对稳定，达到恒定的最终产量状态。在改良的土壤储存条件下，RFM系统在人口产量方面将合理的种植密度从常规的D52提高到了D60。D52和D60最高的群体产量用水效率（WUE _G），其次是D69，最低的是D85。但是，D52中地上生物量的WUE（WUE _A）明显低于D60和D85。主成分分析表明，人口籽粒产量和水分利用效率_ģ与生殖分配和叶片生长显着正相关。叶片生物量与体重之间的异位关系进一步证实了这一结果，因为异位指数（<1）随着密度的增加而提高。生殖与营养质量之间的异形关系表明，与其他处理相比，D60处理可将光合产物分配到生殖器官中相对平衡。该RFM应用显著改善土壤水分的可用性和更好的产率和水分利用效率玉米的合理种植密度_ģ。因此，这种现象机械地是由于生殖和营养生长之间的相对较好的权衡，以及叶片生长的适度增加引起的。