Quantitative Silviculture and Growth &Yield

Board-foot volume estimation functions proposed by Grosenbaugh (1952) will be used with concepts from Monte Carlo integration to estimate board-foot contents of trees and logs. This approach can also be used to estimate board-foot volumes with critical height sampling, which can be understood as a form of Monte Carlo integration. Based on the work of Clark (1906) Grosenbaugh (1952) proposed the following function for estimation of board-foot volume for logs:

VBF = b1VCF + b2S + b3L

Where VBF is board-foot volume, VCF is cubic foot volume, S is surface area, L is length, and b1, b2, b3 are constants. Volume according to log rules such as International, Doyle, Scribner can be obtained by using the appropriate constants. The function could also be used as a regression model in mill studies.

Estimators of tree and log volume and surface area based on Monte Carlo integration have been proposed (Gregoire et al. 1986, 1993). These estimators are based on sampling of tree and log diameters at randomly selected points on the tree stem or log. Usually, variance reduction techniques such as importance sampling, control variates or antithetic variates are used. If it can be assumed that trees or logs are circular in cross-section, Monte Carlo integration provides unbiased estimates of tree or log surface area or volume. To estimate board-foot volumes for logs and standing trees, Monte Carlo integration could be used to estimate cubic foot volume and surface area in the board-foot volume function given above.

^*Presented by Thomas B. Lynch.

Preliminary Evaluation Of Age-Independent Diameter Growth Models Of Individual Hardwoods In The Southern Appalachian Mountains

W. Henry McNab and F. Thomas Lloyd

Southern Research Station

USDA Forest Service

1577 Brevard Road Asheville 28806 USA

Abstract

The relationship of tree size, competition, and topographic site variables affecting periodic diameter increment was determined for 1393 individual trees representing 12 species in thinned, even-aged stands of mixed hardwoods in the southern Appalachian Mountains. Site index- and age-independent model formulations were evaluated that had been previously developed for western conifers. Parsimonious regression models of strongly significant variables (p<0.05) explained from 46 to 80 percent of variation in diameter increment among species and always included tree size (dbh), usually a measure of competition (stand basal area), and differing sets of site variables (elevation, aspect, gradient, etc.). Size, competition, and site variables accounted for an average of 37%, 14%, and 8% respectively of total variation associated with increment. A yellow-poplar (Liriodendron tulipifera) model based on 146 samples was examined in detail; residuals were not correlated with tree size, stand age, or site index. Validation testing of the yellow-poplar model derived from mixed stands with a larger (n=967 samples) independent data set from pure stands indicated that residuals were homogeneously distributed, but biased. Evaluation of similarly formulated yellow-poplar models using the development and validation data sets indicated stable coefficients for size and competition variables, but not for the intercept or site variables. Comparison of the two data sets suggests that the models are estimating different sample tree populations (p<0.001). Reasons for these results are discussed. Equations from this study are generally comparable with age-dependent individual tree basal area increment models previously developed for the same species.

^*Presented by Henry McNab.

Pine height, stand basal area, and stand volume response to level of hardwood control and age of release

Dwight K. Lauer, Bruce R. Zutter, and Glenn R. Glover

School of Forestry and Wildlife Sci.

Auburn University

109 M. White Smith Hall Auburn 36849-5418 USA

Abstract

The analysis of a multi-location trial to estimate response from control of hardwoods (release) in young (ages 0-5) loblolly pine (Pinus taeda L.) plantations in the Southeastern United States is discussed. Two approaches were used to relate response to age of release and level of hardwood control. A Schumacher type yield model without an age term but with an additional term to account for hardwood basal area was used in the first approach. Location intercepts were included in the model to account for variation among locations. Height was modeled separately and then combined with this yield model to predict response from hardwood control with and without herbaceous weed control. This approach could not be used for stands released past year 2 because pre-treatment level of hardwood affected the height-diameter relationship. Pine height alone was sufficient to account for pre-treatment hardwood level and herbaceous weed control in stands released at ages 0-2. The second approach estimates yield loss from site potential for all ages of release using a model in which pine height and density are not explicitly included. Both methods provide a study-wide average response to herbaceous weed control but do not relate this response to site factors.

Keywords: Release, hardwood competition, loblolly pine, hardwood basal area, herbaceous weed control, multi-location trial.

^*Presented by Dwight Lauer.

Predicting The Time To Onset Of Intertree Competition In Loblolly Pine Plantations

Philip J. Radtke

Forest Resources

University of Minnesota

115 Green Hall, 1530 Cleveland Av. North St.Paul 55108-1027 USA

Harold E. Burkhart

Department of Forestry, Virginia Tech

Blacksburg, Virginia 24061

Abstract

A model was developed to predict the number of years remaining until the inflection of cumulative basal growth in loblolly pine (Pinus taeda L.) plantations. The inflection age may be useful as a proxy for the onset of intertree competition since it marks the start of a period of declining annual basal area increment. Existing models of the onset of competition typically depend on single measures of basal area or crown closure, but do not incorporate both measures. Further, existing models do not predict the time to competition onset based on measurements made at a pre-competitive age. The predictor variables here are crown closure, surviving number of trees, rectangularity of spacing and site index. The expected application of the model involves obtaining inputs from a large-scale aerial photograph at a young age, e.g., 2 years after planting, since inflection ages occur between ages 3 and 9 years. The data used to develop this model were collected over a relatively narrow range of site index, so the role of site index as a predictor could not be fully assessed. The importance of site index as a predictor can best be addressed by the collection of additional data.

^*Presented by Phil Radtke.

Ptaeda2v - An Establishment Model For The South - Should The Method Of Modeling Seedling Size Be Changed?

David B. South

School of Forestry and Wildlife Sci.

Auburn University

Auburn University 36849-5418 USA

Abstract

PTAEDA2V is a stand establishment model that allows the user to vary the size of loblolly pine (Pinus taeda) seedlings at time of planting. An Establishment Quality Boost (EQB) technique is used to model the gains from planting large-diameter seedlings (average root-collar of 6-7 mm). Predicted yields from using this method are provided for a single stand. The simulation suggests the EQB method is very different from the "age-shift" method of predicting potential gains from increasing seedling quality. The EQB method appears to underestimate early seedling-size gains (10 to 18 years) while overestimating gains at later ages (35 to 50 years). The EQB method also predicts a strong synergistic interaction between seedling size and herbaceous weed control (which most empirical studies do not support). It is recommended that the EQB method be replaced with a more appropriate technique.

^*Presented by David South.

Predicting Yearly Mortality From Data Collected At Longer Time Intervals

Mike R. Strub

Weyerhaeuser Company

P.O. Box 1060 Hot Springs 71902 USA

Abstract

Simulation of loblolly pine (Pinus taeda) plantations requires estimation of yearly mortality. Data from these plantations are often collected at longer time intervals. Using beginning and average values for growth periods results in biased estimates of yearly mortality. Estimates from measurements taken at the beginning of the growth period result in overestimation of mortality. Estimates from the average of measurements at the beginning and end of the growth period result in underestimation of mortality. Maximum likelihood estimators that eliminate this bias are presented. These estimates require complex specialized computer programs. An alternative method that utilizes the SAS CATMOD procedure and results in low bias of mortality estimates is presented as an alternative to maximum likelihood estimation. A large data set is used to illustrate the properties of the mortality estimates.

^*Presented by Mike Strub.

Last revised: April 6, 2000

Quantitative Silviculture and Growth &Yield

(Moderated by Harold Burkhart)

Contents