Modeling the Diameter Distribution in Juvenile Loblolly Pine (Pinus taeda L.) from Diverse Genetic Provenances under Deficient and Optimum Nutrition Regimes.

Abstract

The ability to predict diameter distributions is an important tool for the forest manager. By accurately predicting the diameter distribution, the manager may make better-informed decisions regarding the silvicultural treatments for a stand, such as when and how to conduct a thinning operation. This study compares the suitability of the gamma, lognormal, and two-parameter Weibull distributions for modeling diameter distributions in juvenile loblolly pine from ages 5 to 11. Using the most appropriate distribution as determined by the Anderson-Darling goodness-of-fit statistic, the two-parameter Weibull distribution, the study also determines the most suitable method for estimating distributional parameters from stand level characteristics such as mean basal area, relative spacing, quadratic mean diameter, and age. The methods tested were a parameter prediction method (PPM), a parameter recovery method (PRM), and a percentiles-based method (PCT). Comparisons were made from ages 5 to 10 using a modification of the Reynold's error index, weighted by basal area. Final parameter estimation equations were developed from data from ages 5 to 11.

The parameter recovery method of parameter estimation proved to be most appropriate for modeling these data. Although the PPM had a slightly lower Reynold's error index than the PRM, the shape parameter was predicted within a very narrow range about the mean, while the distribution of shape parameters recovered by the PRM was much closer to the empirical distribution. In addition, the PRM required fewer inputs into the model, and as such was more desirable for modeling purposes. An application is presented to demonstrate the construction of stand tables from the output parameters.

A second study examined the relationships among the maximum likelihood fitted parameters of the two-parameter Weibull distribution and the treatment effects due to fertilization, genetic provenances, and open-pollinated genetic families. Both the scale and shape parameters differed significantly between the non-fertilized control treatment and the optimally fertilized treatment. Further research utilizing the three-parameter Weibull might lead to significant differences among the location parameter instead of the scale and shape parameters. No significant differences were observed in the shape parameters between genetic provenances, but significant differences did exist in the younger ages between provenances in the scale parameters.

Family means tended to increase over time for the scale parameter, and family mean rankings were relatively stable within and across fertilization treatments. The shape parameter family mean rankings were less stable over time, with the means tending to increase in the non-fertilized treatment and decrease in the fertilized treatment, reflecting the differences in stand development. As stand development progressed, year to year rank changes were minor, but less stable family mean rankings over time were observed.