Objective Based on the Hegyi intraspecific and interspecific competition indexes related to distance, the prediction model of DBH increment of natural spruce-fir forest was constructed based on initial DBH and Hegyi competition index.

Method In order to explore the effects of competition and growth on DBH growth of individual trees, the measured data of three permanent sample plots (each of 1 ha) of spruce-fir in Jingouling Forest Farm, Jilin Province of northeastern China in 2013 were utilized. Based on the nonlinear Logistics model, initial DBH, intraspecific and interspecific competition indexes were gradually added. The nonlinear mixed-effect model was utilized to improve the model accuracy.

Result The results of model fitting showed that the model had the best fitting effect when initial DBH, intraspecific and interspecific Hegyi competition indexes were used as predictive variables, the best fitting efficiency occurred based on the species-level of random effect worked on parameters a₀, a₂, a₃, and without heteroscedasticity. The R_\rmadj^2 , root mean squared error (RMSE) and total relative error (TRE) of modeling data were 0.512 6, 0.607 1, 3.651 9%, respectively. The R_\rmadj^2 , RMSE and TRE of validation data were 0.509 8, 0.624 2, 3.883 1%, respectively. The residual distribution of validation data did not show obvious heteroscedasticity.

Conclusion The factors affect the diameter growth of target trees in natural spruce-fir forest, including self-growth factors and competition factors. Among the self-growth factors, initial DBH is the main factor and plays a positive role to promote DBH increment. Among the competition factors, interspecific competition and intraspecific competition have obvious inhibition effects on the growth of individual tree DBH increment. The nonlinear mixed effect model based on species-level can provide a theoretical basis and technical reference for the DBH growth of target trees in natural spruce-fir forest in the study area.