Comparison of taper functions applied to eucalypts of varying genetics in Brazil: application and evaluation of the penalized mixed spline approach

Abstract

Taper functions have been widely used with an existing array of model forms and methods; however, comparisons of contrasting statistical methods have been more limited. This study aimed to assess contrasting statistical approaches for achieving accurate stem taper and individual-tree volume predictions, with a focus on the novel penalized mixed spline (PMS) approach. The approaches were tested using four different eucalyptus genetic families planted in Brazil. For comparison, the predictions of diameter outside bark (dob) and volume using a 5th-degree polynomial, the polynomial of integer and fractional powers, a segmented taper function, a variable exponent taper function, and a semi-parametric PMS were conducted. Comparisons using the generalized functions of every stem taper function with genetic family as an extra random component were also conducted. Data splitting was used to test the accuracy of each taper function. PMS and the generalized PMS were the most accurate for both dob and volume, while the generalized PMS approach displayed more stable volume predictions along the stem. The other approaches were more variable across the tree size classes examined. Overall, this study highlights the applicability of the PMS methodology for predicting tree taper and volume that warrants future assessment and application.