Abstract
Branch structure is the fundamental component of an individual tree crown and has an important effect on tree growth and wood quality. A number of studies have focused on the primary branch attributes, but only a few research has been conducted on secondary branch size distribution and models. To analyze the secondary branch structure, we selected 54 Korean pine sample trees from Northeast China and measured a total of 24,053 secondary branches on 717 primary branches. The length and diameter for all the secondary branches and the current-year shoot of the secondary branch distribution were quantified. The allometric relationship between the length and diameter for the primary and secondary branches of the same age and the scaling factor variation within the tree crown were quantified. The nonlinear mixed-effects secondary branch diameter and length model were finally developed. The results indicated that the secondary branches showed an increase in length and diameter, then a decline as they reached deeper into the base of the primary branch. Secondary branch structure varies slightly among trees of varying ages and sizes. The Roeecp function was selected as the basic model to explore the relationship between different variables and the length and diameter of the secondary branches. Absolute distance from the tree tip to the primary branch base and the diameter of the primary branch significantly impacted the branch model, while the individual tree variables and competitive variables had minimal influence on the model. Ultimately, we developed two-level nonlinear mixed-effects models incorporating branch variables for secondary branch length and diameter.