Screening optimum population density in response to soil water availability in dryland wheat: From laboratory to field

The rational close planting in agricultural production is an old topic, yet it is so far unclear whether the optimum population density (Nopd) is dependent on soil water availability and its mechanism in dryland crops. To address this issue, we established a mathematical model of Nopd dynamics under soil moisture gradients and performed a modeling verification from laboratory to field using wheat as testing material. In pot-culture experiment with 3 moisture gradients and 9 planting densities, the quadratic function fitting of yield-density relation indicated that old landrace and modern cultivar shared a similar increasing trend of Nopd in response to soil water availability. The biomass-density relation displayed a typical mode of asymptotical line, and conformed to the law of constant final yield. We therefore established a classic equation of Nopd=k/(α-1) via adopting the scaling exponent (α) between grain yield and body size (aboveground biomass), and the density producing half of maximum biomass (k). With the increasing drought stress, the increasing extent of k was evidently lower than α-1, suggesting that the Nopd decreased along with increasing drought stress. To verify the above model, we therefore performed a field experiment and found that the Nopd under the rain-fed condition (no irrigation) was lowered by 32.4% in 2017 and 16.7% in 2018 respectively, compared to that of supplemental irrigation. Interestingly, the biomass-density relationship was parabolic under field condition, which could be well fitted by quadratic function. We thus established an improved model of Nopd= 2 A/(α + 1), where A referred to the symmetrical axis of biomass-density quadratic function and remained relatively stable regardless of soil moisture. Since the α became significantly greater under the rain-fed condition (P < 0.05), the Nopd was lowered by drought stress. Our findings highlighted a critical role of the plastic allometric relations to affect the Nopd dynamics, suggesting that lower seeding density would be more favorable for field production of wheats in dry environment.