Effects of sample size and tree selection criteria on the performance of taper equations

Abstract

Accuracy of a taper equation is affected by the quality of calibration data. We evaluated the effects of eight tree selection protocols, originating from two sample sizes and four tree selection criteria (randomly selected trees, trees with diameter at breast height (DBH) closest to quadratic mean diameter, dominant/ co-dominant trees, and trees randomly selected from each class of stratified basal area [BA]), on the accuracy of taper equations by Sharma and Zhang and Kozak by comparing resulting predictions of diameters inside bark and cumulative volumes of tree stems. Evaluations were performed using the data collected via stem analysis from 1098 jack pine (Pinus banksiana Lamb.), and 1122 black spruce (Picea mariana Mill. BSP) trees sampled across the boreal forest of Northern Ontario. About half of the trees were randomly selected for model calibration and the remainder was used for model evaluation. Prediction accuracy, here defined as bias, depended on the tree species, the tree selection protocol including sample size and tree selection criteria, and the model form of the taper equation. A protocol that involved selecting trees from five stratified BA classes (one randomly selected tree from each BA class) was more efficient than other protocols in representing the mean taper function of jack pine and black spruce trees for both taper equations for small sample sizes (five trees per plot). The minimum number of trees required to model taper equations without compromising model accuracy depended on tree species and the model form used to describe tree taper.

Keywords:

• Stem profile model
• tree selection protocol
• model calibration
• bootstrapping

Acknowledgements

The authors thankfully acknowledge staff of the Ontario Ministry of Natural Resources for facilitating data collection, the Forestry Futures Trust Ontario for financial support (Project No. EFPS 028-2-RI), and Lisa Buse, Ontario Forest Research Institute for editing an earlier version of the manuscript. The authors also thank the associate editor and two anonymous reviewers for their valuable suggestions and helpful comments to improve the manuscript.