Modelling the relationship of tree-level product value with tree characteristics in black spruce

The establishment of the relationship between tree-level product value and tree characteristics will allow for predicting the potential value of individual trees and a stand directly using tree characteristics. Using statistical and elasticity analysis methods this study examined the relationship of tree-level product value with selected tree characteristics in black spruce (Picea mariana). The study was based a sample of 139 trees from 48-year-old black spruce plantations grown in Ontario,Canada. The sample trees showed large variation in tree characteristics and tree-level product value. Models were developed and compared on the basis of statistics of the estimated and predicted criteria. Results show that the model, including only tree DBH, tree height and stem taper, is the best in describing the relationship of the tree-level product value with tree characteristics. Furthermore, relationships including input-output and interaction factors in the model were analyzed by calculating the elasticity of production and scale and the cross partial derivative of output with respect to the inputs. The analyses indicate that tree DBH has the largest and positive influence on tree-level product value, followed by tree height; however, stem taper has a negative effect on tree-level product value. When tree DBH, tree height and stem taper each increase by 1%, the quantities of output elasticity show 2.53%, 0.64% and -0.37% changes in the product value, respectively; while the scale elasticity shows a 2.81% increase in tree-level product value with a simultaneous 1% change in tree DBH, tree height and stem taper. Results indicate that the model is suitable for predicting tree-level product value using those tree characteristics from forest inventory and also reflects biological behaviour.