Toward developing a direct relation between gross volume increment and stand density

Abstract

A general form for expressing gross volume increment in terms of stand density is derived and tested with data from spacing trials in red alder (Alnus rubra Bong.), eastern white pine (Pinus strobus L.), longleaf pine (Pinus palustris Mill.), and loblolly pine (Pinus taeda L.). The equation relates the stand sum of individual-tree volume increment per metre height increment to a power function of quadratic mean diameter times tree density. The proposed equation fit the data best when the model included an intercept. Within each species, the fits were unbiased with respect to the independent variables, plantation age, and site height, and with the exception of the youngest ages for red alder and loblolly pine, they were unbiased with respect to the plot sums of individual-tree volume increment divided by individual height increment. Exponents estimated for quadratic mean diameter for each species ranged from 1.58 to 1.80. The resulting equations indicate a linear relationship between the stand sum of individual-tree volume increment per metre height increment and stand density. Scattergrams of gross-volume increment per hectare per year and stand density can be recovered by multiplying the predicted values of the regressions by Lorey’s height. The regressions support the hypothesis that each metre of height growth produces consistent changes in stem size, regardless of initial tree size, age, or site quality, and implies that the change in stem size is a predictable power function of stem diameter for an individual tree or quadratic mean diameter for a stand.