Use of growth curve derivatives to illustrate acceleration and deceleration of growth in young plantations under variable competition

Abstract

Deceleration of growth rates can give an indication of competition and the need for thinning in early years but can be difficult to detect. We computed the first and second derivatives of the von Bertalanffy – Richards equation to assess impacts of density and vegetation control in young plantations in western Oregon. The first derivative describes the response in growth and the second derivative describes the change in growth over time. Three sets of density experiments were used: (i) pure Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), (ii) mixed Douglas-fir and grand fir (Abies grandis (Dougl. ex D. Don) Lindl.), and (iii) mixed western hemlock (Tsuga heterophylla (Raf.) Sarg.) and red alder (Alnus rubra Bong.). Original planting densities ranged from 475 to 85 470 trees·ha–1 (4.6 m × 4.6 m to 0.34 m × 0.34 m spacing); western hemlock and red alder plots were weeded and unweeded. For the highest densities, the second derivative was rarely above zero for any of the time periods, indicating that the planting densities were too high for tree growth to enter an exponential phase. As expected, the lower the density, the greater and later the peak in growth for both the first and second derivatives. Weeding increased the growth peaks, and peaks were reached earlier in weeded than in unweeded plots. Calculations of this sort may help modelers identify when modifiers for competition and density are needed in growth equations. Specific applications help define onset of competition, precise determining of timing of peak growth, period of acceleration of growth, and interaction of spacing and age in determination of peaks of increment or acceleration or deceleration.