Stem profile models for loblolly pine (Pinustaeda L.) that allow for both taper and form changes were constructed and evaluated. In 1956, H. R. Gray defined form to be the basic shape of the tree (e.g., cone or paraboloid) and taper to be the rate of narrowing in diameter given a tree form. D. W. 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 a 10–20% gain can be made in predicting stem diameters using the variable-taper and variable-form stem profile models.
The distribution of within-stand basal area growth following silvicultural treatments was investigated using a relative size–relative growth (RSG) function. The effects of thinning on the distribution of tree basal area, including changes in location or scale, can be incorporated into the estimation of the RSG function parameters. Additional stand growth due to fertilization can also be allocated to individual trees using the same RSG function, since the contribution of a tree's response to total stand treatment response depends on its relative size in the stand. Statistical tests and validation of the RSG function indicated that thinning and fertilization do not alter the characteristic relationships between tree size, stand density, stand structure, and the relative distribution of growth across size classes within a stand. Therefore, silvicultural treatment growth responses predicted at a whole-stand level of resolution can be disaggregated to a list of individual trees using the RSG function developed from untreated plots.
This is one paper of a series investigating the effects of extended training and multiple succesSve reward shifts. Four groups were run in a straight alley. The control groups received either 75% or 25% reinforcement throughout training. Each experimental group was given 40 acquisition trials at either 75% or 25% reinforcement followed by three shifts of 24 trials each. All groups were given 24 extinction trials. There were initial significant differences betMen the 75% and 25% groups. These differences disappeared after about 40 trials. The only significant shift effect was a NCE on the third shift. Ext;inction results were a function of the initial acquisition series. Together with earlier studies, these results indicate that extended training effects are often different from early stages of training.
Diameter-increment models for nitrogen-fertilized stands were developed using data from permanent research plots in northern Idaho. The equations partially resembled PROGNOSIS model diameter growth formulations. Results indicated that both initial tree size and initial stand density produced significant interactions with treatment to explain an individual tree's response to fertilization. Larger trees in a stand showed more fertilization response than smaller trees. Furthermore, individual trees in low-density stands showed more fertilization response than those growing in high-density stands. These diameter increment predictive equations were formulated to be compatible with individual-tree distance-independent simulation models.
An approach for estimating asymptotic forest stand yield, basal area, and tree density (number of stems per unit of area) is proposed. Available forest stand growth data are used to establish the reciprocal equation of Competition-Density (C-D) effect and develop equations relating the coefficients of C-D effect to stand top height. Asymptotic stand yield, basal area, and tree density are derived based on bio-mathematical rationales and expressed as functions of asymptotic top height. Asymptotic top height can be obtained for different site qualities and/or habitat types by evaluating a height growth model in the limit as age approaches infinity. Estimated asymptotes can be utilized to parameterize sigmoid-shaped growth functions (e.g., Richards growth model) for developing forest growth and yield models.
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