【目的】构建黑龙江省红松(Pinus koraiensis)人工林的林分生长和径阶分配模型系统,从而优化林分经营策略,为制定经营方案和提升森林质量提供模型支持。【方法】基于1980—2023年黑龙江省218块红松人工林固定样地的复测数据,构建包含枯损模型、优势高生长方程、断面积模型以及Weibull径阶分配模型的生长预测系统。运用高斯-牛顿法和似乎不相关回归求解生长模型参数,并且采用矩解法恢复径阶分配模型中的直径分布参数。为验证模型组的适用性,采用差分进化(differential evolution,DE)算法,针对处于3个地位指数梯度(11.2、14.2、16.0 m)的红松人工林林分,开展以数量成熟龄为目标的经营优化,模拟不同经营措施对林分生长的影响。【结果】生长模型中的各组分解释了超过90%的变异性。采用似乎不相关回归最终得到的林分枯损模型和林分断面积模型的临界误差分别为16.769%和17.685%;利用矩解法对Weibull方程进行参数恢复时,Kolmogorov-Smirnov (KS)检验的通过率为96.946%;当应用生长和径阶分配模型系统进行林分蓄积预测时,临界误差为14.612%。优化结果表明,地位指数每提升2 m,间伐时间提前1~3 a,主伐时间为72~75 a。【结论】本研究构建的生长模型满足经营模拟过程中路径不变性、一致性和因果性的基本假设,提高了林分生长预测的可靠性。模型组和DE算法相结合能够提供有效的森林经营方案。

【Objective】A system of stand-level growth models with diameter-class disaggregation was developed for Korean pine (Pinus koraiensis) plantations in Heilongjiang Province to optimize stand management strategies, providing model support for developing management schedules and enhancing forest quality.【Method】Based on the remeasurement data from 218 permanent plots in Korean pine plantations in Heilongjiang Province during 1980—2023, a model system consisting of models for mortality, dominant height, stand basal area and diameter-class disaggregation was constructed. The Weibull function was used to disaggregate the predictions over diameter classes. The parameters of the growth models were estimated using the Gauss-Newton method and seemingly unrelated regression. The method of moments was used to recover the diameter distribution parameters for the diameter-class disaggregation. To verify the applicability of the model system, the study used the differential evolution (DE) algorithm with a model system to perform stand-level management optimization to find the rotation length that maximized wood production in different site indices (11.2, 14.2, 16.0 m).【Result】The components of the dynamic growth model explained over 90% of the variation in the modelling data. The final critical errors for stand mortality and basal area model obtained using seemingly unrelated regression were 16.769% and 17.685%, respectively. When applying the method of moments for parameter estimation of the Weibull equation, the pass rate of the Kolmogorov-Smirnov test was 96.946%. When using the growth with diameter-class disaggregation for predicting stand volume, using an existing taper model, the critical error was 14.612%. The optimization results indicated that, for the three stands, the thinning is by 1-3 years later as site index improves by 2 m, with the final harvest age ranging from 72 to 75 years.【Conclusion】The growth model constructed in this study satisfies the basic assumptions of path-invariance, consistency, and causality during management simulations, thereby allowing reliable growth simulations. Integrating the model with the DE algorithm provides effective forest management prescriptions, offering useful advise for the management decisions of Korean pine plantations.