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. / Ph. D.

Stem profile models which allow for both taper and form changes (Gray 1956) were constructed and evaluated. Gray defined form to be the basic shape of the tree, e.g. cone or parabolid, and taper to be the rate of narrowing in diameter given a tree form. Ormerod's stem profile model was selected as the basic model since its parameters were readily interpretable in terms of Gray's taper and form definitions. Two stage modeling procedures were used to relate individual tree taper and form parameters to tree and stand characteristics. Two second-stage parameter estimation alternatives were evaluated. Parameter estimates for both techniques, ordinary least squares and random function analysis, were similar. Characteristics used to predict stem form were total tree height, crown ratio, height to the live crown, site index, and tree age. The taper parameter was related to diameter at breast height, crown ratio and site index. Error evaluations suggest that substantial gains in predicting stem diameters were not made using the variable taper and form stem profile models. Two methods were proposed for modeling whole stem inside-bark diameter or cross-sectional area increment. Whole stem increment models were derived from several stem profile models and Presseler's hypothesis on the vertical distribution of cross-sectional area growth. Stem profile models evaluated for constructing compatible increment models were Kozak and others (1969), Ormerod (1973), Goulding and Murray (1976), Max and Burkhart (1976), Cao and others (1980), and Amidon (1984). The increment model based on Presseler's hypothesis was derived as a generalization of the work of Mitchell (1975). Evaluations, with limited increment data, consistently showed that the models based on Presseler's hypothesis predict inside-bark diameter increment with less error than do the profile model compatible increment models. This may be due to the lack of crown information currently used in stem profile models. / Ph. D.