Quantifying size-dependent developmental trajectories of commercial-relevant fibre attributes within maturing black spruce plantations employing hierarchical linear models

Abstract

The primary objective of this study was to quantitatively describe size-dependent developmental trajectories of commercially-relevant fibre attributes within maturing black spruce (Picea marina (Mill.) B.S.P.) plantations employing hierarchical linear models. A stratified random sample design was deployed within 5 density-stressed semi-mature plantations to obtain transverse breast-height radial xylem sequences from 47 trees representing 5 basal area size classes (quintiles). The cumulative annual ring-area-weighted moving average proceeding from the pith to the ith cambial age was calculated for density, microfibril angle, modulus of elasticity, fibre coarseness, tracheid wall thickness, tracheid dimensions (radial and tangential diameters) and specific surface area. Hierarchical linear regression models were used to quantify size-dependent effects on these developmental trajectories: (1) at the first hierarchical level, compound exponential models were specified following the assessment of a set of candidate functional forms; and (2) given (1), at the second hierarchical level, linear model specifications under fixed and random error structures were used to account for potential size-dependent effects on the first-level parameter estimates. In order to ensure statistically valid inferences regarding size-dependence by employing radial sequences devoid of serial correlation, and provide an independent data set for evaluating the parameterized models in terms of goodness-of-fit, lack-of-fit and predictive ability, the data set consisting of 1566 observations per attribute was systematically stratified into parameterization and valuation subsets. The results revealed that the parameters of the Hoerl-based compound exponential model varied by tree-size indicating the presence of significant (p⩽0.05) size-dependence in fibre attribute developmental trajectories. Statistical measures of model performance and associated graphical analysis of the final specifications indicated that the models performed well in terms of accounting for a relatively large proportion of variation (61–88%), unbiasedness and predictive ability (e.g., temporal invariant patterns in absolute and relative prediction errors). These results and related inferences demonstrated the utility of quantifying size-dependent fibre developmental trajectories employing hierarchical linear models.