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Biomathematical Growth Equations for Natural Longleaf Pine Stands

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Abstract:

Simultaneous stand level basal area projection and survival prediction equations with useful extrapolative properties are derived from assumptions that reflect many of the currently accepted concepts about stand development. Both equations are modifications of the Chapman-Richard's growth curve which has parameters for the asymptote and the annual rate of growth towards the asymptote. The original form is modified by defining the asymptote and annual growth rate as functions of changing stand conditions. For basal area projection the asymptote is a function of number of trees which approaches zero as density declines. The rate of approach to the asymptote is a function of growth in average dominant and codominant trees and change in average stand age. The survival equation is a reverse Chapman-Richard's curve that approaches zero over time. The asymptotic value is a decreasing function of basal area in accordance with the self-thinning rule. Additional terms controlling the rate of movement away from the asymptote are a minimum mortality rate for low density stands and ingrowth of new trees into the smallest diameter class for young stands with vigorous basal area growth. Nonlinear three-stage least squares procedures are used to simultaneously fit both equations to a natural longleaf pine (Pinus palustris Mill.) permanent plot data set. Predictions are verified using cross-validation procedures, and long-range extrapolations are demonstrated and discussed. For. Sci. 37(1):227-244.

Keywords: Chapman-Richards; basal area prediction; survival

Document Type: Journal Article

Affiliations: Principal Silviculturist, Southern Forest Experiment Station, USDA Forest Service, Mississippi State University, Starkville, MS. 39762

Publication date: March 1, 1991

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