2.1. Site Description
This research utilized six loblolly pine installations of the South Atlantic Gulf Slope (SAGS) Culture Density study managed by the University of Georgia Plantation Management Research Cooperative (PMRC). Four of these installations are located in the Georgia Piedmont, one is in the Alabama Piedmont, and one is in the Georgia Upper Coastal Plain (
Figure 1). All installations were on upland, well-drained sites common to this region. Standard tree measurements were taken at age 15, and tree quality assessments were completed during the 16th growing season. The expressed site index ranged from 21 to 27.1 m (
Table 1) for stands planted at 1482 trees per hectare and which received operational culture.
Three planting densities that have been used in commercial plantations were evaluated: 741, 1482, and 2223 trees per hectare. Two management intensities were tested: operational and intensive. The operational treatment consisted of early competition control and several fertilization treatments; the intensive treatment consisted of complete competition control throughout the entire rotation and numerous fertilization events (
Table 2).
At each installation, one replication was established using a split-plot design. The main plots consisted of the two management intensities while the subplots consisted of the planting densities. Planting on each site occurred in 1998 with seedlings sourced by the PMRC cooperator controlling the installation. Genetically improved open pollinated stock was the common choice for plantations established in the late 1990’s. At each planting location, seedlings were double planted and were reduced to one seedling after the first growing season. This ensured adequate survival for each installation. Plot size varied by planting density (
Table 3), and each plot contained a measurement plot surrounded by a buffer approximately 7.9 m wide.
2.2. Measurements
Diameter at breast height (DBH) was measured on every tree in the measurement plots to the nearest 0.254 of a centimeter (1/10th of an inch). Total height and height to live crown were measured on every other tree to the nearest 0.3 of a meter (1 foot). Those trees without measured heights were estimated using the following linear regression model (Equation (1)) with data collected from trees with measured heights for each plot. This linear regression model was fit to trees at different densities separately to avoid the possibility of a density effect on dominant height [
32]. In this equation,
is the
y-intercept,
is the slope, ε represents the unknown error,
H represents total height in meters and D represents diameter at breast height in centimeters:
During the age 16 growing season, assessments of tree quality were made on all trees in the measurement plots. Trees were assigned a crown class as dominant/co-dominant, intermediate, or suppressed. Height to the lowest product-defining defect (stem fork, crook, broken top, disease, large branch whorl) was measured with a laser hypsometer to the nearest 0.3 m. Each tree was assigned a tree quality index (TQI). This is a partially subjective tree quality assessment that assigns trees a score on a 1 to 4 scale without 2 as an option (
Table 4). Some versions of this method use a TQI 2 for stems with solid wood product potential but with moderate defects; however, this score is not used in this study for simplification.
The TQI score is a total tree evaluation that incorporates stem sinuosity, branching, product-defining defects, and disease. A score of 1 indicates that the tree has solid wood product potential and is free of any major defects including disease, crook, sweep, large knots and branches (approximately 7.5 cm or larger through ocular estimation), forks, or broken tops below 5 m. A tree was assigned a TQI 1 if there were none of the listed defections that would eliminate 5-m length solid wood product potential. A tree assigned a TQI 3 has major defects that eliminate all solid wood product potential. Once a tree has been assigned a TQI 3, the given tree is assumed to be pulpwood for the remainder of the rotation. A tree assigned a TQI 4 has major defects that will preclude any merchantability and is classified as cull. The same individual (observer) scored every tree. It is important to note that the TQI system scores tree product potential, not necessarily current product. Recording the reason for each tree assessment would have provided valuable information but was not done due to time constraints. An example would be a tree downgraded from a TQI 1 to a 3 because of large or excessive branching. Assessing how branches influence product potential is difficult with the TQI method and is its main limitation. This is due to the difficulty in assessing an individual tree’s potential to self prune and grow over knots. While efforts have been made to model branching and knots in loblolly pine [
33], further data on branching are needed to understand how specific management decisions affect the branching dynamics. Solid wood product potential is not limited to sawtimber. Log length (≥5 m) product potential for “super-pulp”, chip-and-saw, or sawtimber qualify a tree as having solid wood product potential. If a defect was present in the lower 3 m of the stem that did not seriously affect the product potential, the height of the defect was measured and recorded (results not shown). An example of such a defect would be a fusiform rust gall at the base of the stem. Such a defect would commonly be removed in a harvest, and the remainder of the stem would be merchandized accordingly.
2.3. Analysis
TQI is an ordinal-based categorical measure rendering traditional methods like analysis of variance (ANOVA) inappropriate for analysis. TQI scores were transformed into a binary yes/no for solid wood product potential. A TQI score of 1 indicated yes and a 3 or 4 indicated no. The proportion of stems in each plot that exhibited solid wood product potential was analyzed using Equation (2) where: y represents the vector of the observed proportion of stems with solid wood product potential with link function , X represents the known design matrix for the fixed effects, β represents the vector of unknown fixed effects parameters, Z represents the known design matrix for the random effects, and u represents the vector of unknown random effects parameters.
Equation (2) is a generalized linear mixed effects model (GLMEM) in which the management level and planted trees per hectare were designated as the fixed effects. The interaction terms that were found to be non-significant were not included in the final model specification. Installation, interaction of installation and management level, and interaction of planted trees per hectare and the interaction of installation and management were designated as the random effects through random intercepts. Although random slopes were evaluated, they did not improve the fit of the model when included and hence were removed. In this GLMEM, the response distribution is assumed to be binomial with a logit link function. Planted trees per hectare was designated as a factor to ensure convergence of the model.
Analysis of product-defining defects was considered for both the proportion of stems with these defects as well as the average height at which the defects occurred. The proportion of stems that exhibited a product-defining defect in each plot was also analyzed using a GLMEM (Equation (3)) in which y represents the vector of the observed proportion of stems with product-defining defects, and all other terms are as described for Equation (2).
The management level and planted trees per hectare were designated as the fixed effects. The interaction terms that were found to be non-significant were not included in the final model. Random effects were designated in the same manner as in the analysis of solid wood product potential. Planted trees per hectare was again designated as a factor to ensure model convergence. In this GLMEM, the response distribution is assumed to be binomial with a logit link function.
The average height of the product-defining defects in each plot was analyzed using a linear mixed effects model (LMEM), with management level and planted trees per hectare designated as the fixed effects (Equation (4)), in which y represents the vector of observed plot product-defining defect heights, and ε represents the vector of unknown random errors. All other terms are as described in Equation (2).
The interaction terms that were found to be non-significant were not included in the final model. Random effects were designated in the same manner as in previously described models. Due to large differences in the number of defects per plot, frequency weights were utilized in the model. Plots with more defects have a greater influence on the model than plots with much smaller numbers of defects.
To help demonstrate the impact of the effects of management intensity and planting density on product potential, pulpwood, top-wood, chip and saw, and sawtimber, green kilograms per hectare were calculated for each combination of management intensity and planting density. Two evaluations were performed, one including the TQI and product-defining defect values and one without these values. Product specifications can be found in
Table 5. Total green weight, green weight to a specific diameter, and green weight to a specific height were determined using allometric weight equations (Equations (1), (7) and (8), respectively, in the original publication) proposed by [
34]. These equations predict green weight in Imperial green tons. Allometric measurements including total height and diameter at breast height were not available at age 16; thus, age 15 measurements were utilized in conjunction with age 16 quality information. Green weight was converted to metric tons after estimation.
Once age 16 product weights were calculated, a generalized stand table projection procedure was utilized to project the tree list to age 30. The FASTLOB mortality function [
35] was utilized to model plot mortality.
Using the FASTLOB mortality function, the stand table was carried from age 16 to rotation age using the generalized stand table projection (GSTP) procedure described in the PMRC Technical Report 2004-4 [
36]. The same allometric weight equations proposed by [
34] were utilized to compute product metric tons per hectare after the projection. In the GSTP, the TQI and product-defining defects were carried through the projection. No thinning or additional management activities were assumed.
Analysis was conducted using the R statistical package [
37]. Graphics were developed using the package ggplot2 [
38]. All mixed effects models were fitted using the lme4 package [
39]. All green weight calculations and growth projections, using equations previously described, were conducted using the proprietary “SMART” software from Smarter Forestry LLC, Bogart, GA, USA.