Modelling number, vertical distribution, and size of live branches on coniferous tree species in British Columbia

Abstract

A compound, nonhomogeneous Poisson process was used to model the number, vertical distribution, and size of branches on four coniferous tree species: 134 western hemlock ( Tsuga heterophylla (Raf.) Sarg.) on six sites, 45 amabilis fir ( Abies amabilis Douglas ex J. Forbes) (three sites), 60 lodgepole pine ( Pinus contorta var. latifolia Engelm. ex S. Watson) (six sites), and 60 white spruce ( Picea glauca (Moench) Voss) trees (five sites) and two varieties: 66 coastal Douglas-fir ( Pseudotsuga menziesii var. menziesii (Mirb.) Franco) (five sites) and 50 interior Douglas-fir ( Pseudotsuga menziesii var. glauca (Mayr) Franco) (four sites). Branches of these species are typically more or less clustered and have a characteristic, nonuniform vertical distribution along annual shoots. Total number and relative positions of clusters varied with shoot age. Clustering patterns in three of four species and two varieties appeared to scale proportionally with shoot length. However, in lodgepole pine, which has fewer clusters per metre and more branches per cluster, the vertical distribution of clusters along shoots ≤5 years old was consistent with a gamma-Poisson model but converged to a nonhomogeneous Poisson process model in shoots >5 years old. Separate mixed-effect regression models were developed for each species relating length and diameter of live branches to tree (crown), shoot, and branch (cluster) predictor variables.