LAUSR

Phoebe bournei is a rare and endangered woody species and the success of its plantation development is dependent upon proper seedling cultivation. This study explored the regulation of N, P and K fertilizer and the interaction of these macronutrients on the growth of Phoebe bournei seedlings. To determine the optimum rate and ratio of N–P–K fertilizer in seedling cultivation, we used the unique “3414” incomplete orthogonal regression design to evaluate the effects of N–P–K fertilization on seedling morphological development. One-year-old Phoebe bournei bareroot seedlings were grown for one growing season under the defined fertilization regime, with their morphological development determined by measuring seedling attributes—root, stem, leaves and total biomass, root collar diameter and seedling height. These attributes were then combined to calculate the following indices: height-diameter ratio, shoot-root ratio and the seedling quality index (QI). Results showed that the N–P–K fertilizer had significant and beneficial effect on seedling cultivation. N effect was highest, followed by K and P. The three-way N×P×K interaction effect was strong, and the two-way interactions effect was highest for N×P, followed by P×K and N×K. At the “2” level of N (0.532 g·plant−1), P (P2O5, 0.133 g·plant−1), and K fertilizer (K2O, 0.356 g·plant−1), seedling growth and biomass accumulation were at their maximum. Unary, binary, and ternary quadratic fertilizer effect function equations of QI were established. Through comparative analysis, the ternary quadratic model was the optimal model and through a simulation–optimization, the optimal N–P–K fertilizer rates were 0.373~0.420 g·plant−1 (N), 0.086~0.106 g·plant−1 (P2O5), 0.243~0.280 g·plant−1 (K2O), with a N–P–K ratio of 1:0.20:0.43~1:0.65:0.75.