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A Direct Measure of Stand Density Based on Stand Growth

Formally Refereed
Authors: Thomas Dean, Anthony D’Amato, Brian Palik, Mike Battaglia, Constance A. Harrington
Year: 2020
Type: Scientific Journal
Station: Northern Research Station
Source: Forest Science


Standardizing gross volume increment on periodic height increment of the dominant trees is a means of minimizing the effects of site quality and age in growth–growingstock relations; however, volume increment per height increment contains more information than just a normalization method for fitting growth models. This study builds on previous work suggesting that the cumulative sum of the ratios between individual-tree volume increment and height increment may be a direct measure of stand density. We used data from several levels of growing-stock studies for Douglas-fir, ponderosa pine, and red pine to explore this hypothesis. Regression analysis indicated that the sum of the ratios is proportional to (Dqx · N), the underlying equation form of Reineke’s stand density index. Stem growth is a function of canopy dynamics, and additional analyses showed that volume added per unit of height growth was also related to canopy architecture, increasing with decreasing live-crown ratio and increasing foliage density. The linkages between growth, canopy architecture, intermediary canopy dynamics, and (Dqx · N) support the hypothesis that the sum of the tree ratios between volume increment and height increment is a direct measure of site occupancy due to its association between growth and corresponding resource use. Study Implications: Stand density indices are fundamental to managing the development of forest stands to achieve habitat and production goals, and advanced statistical techniques are providing silviculturists with more precise tools to manage density. However, the increased precision is only available with data from self-thinning stands, rare in managed forests. Furthermore, silviculturists must assume that constant fractions of relative stand density are parallel to fitted self-thinning trajectories. The results of this study show that the slope of the stand density gradient can be determined without data from self-thinning stands and the gradient in stand density runs parallel to the trajectory of self-thinning stands.


volume increment, height increment, canopy architecture, Reineke’s stand density index


Dean, Thomas J; D'Amato, Anthony W; Palik, Brian J; Battaglia, Mike A; Harrington, Constance A. 2020. A Direct Measure of Stand Density Based on Stand Growth. Forest Science. 67(1): 103-115.