The study dealt with developing methodologies for predicting basal area distributions and individual tree basal areas. Data for the study was from the Hill Farm Experiment Station at Homer, Louisiana.

Five height-diameter (basal area) curves were examined to determine which was most appropriate for the data set utilized. The model H = a + b log(BA), where H denotes height and BA denotes basal area, was chosen as best, based on several fit and prediction oriented statistics.

A stochastic basal area distribution model, called the parameter distribution model, was developed. The model was based on the Chapman-Richards growth curve. This curve was fit to all stems on approximately 3/4 of the data set. Two parameters of the curve were fixed a priori, leaving two parameters to be estimated. A sampling distribution was fit to the estimates of the rate parameter, k. Models were developed to predict the parameters of this distribution from stand variables. A model was then derived to predict m, the shape parameter of the C-R curve, from k and stand variables. Finally, an existing survival function was modified. The overall model was implemented as follows: first, the number of surviving stems was predicted. Then k and m values were predicted for each predicted stem. Substitution of these two values into the C-R curve yielded a predicted basal area for each stem. The previously mentioned height diameter curve was employed to predict a height for each predicted basal area. Stochastic elements were built into the prediction model for m and the height-diameter curve. Predicted basal area and height distributions were compared to observed on the remaining 1/4 of the data set. Although the two--sample K-S test was statistically significant, the observed and predicted distributions did appear to be close, in general, from a practical standpoint. This approach appears promising as a stochastic method of predicting size distributions.

The Chapman-Richards curve was also modified for use as an individual tree basal area growth model. Two parameters of the curve were fixed, and the remaining two were modelled as functions of tree- and stand-level variables. The modified growth function fit the data well, but on an independent data set, a simpler linear model of basal area growth performed better in terms of mean difference and mean absolute difference between observed and predicted basal areas. Thus, the only anticipated use of the modified C-R model is in situations where extrapolation beyond the range of observed data is required, since this model has desirable long-term characteristics, whereas the linear model does not.