n-tree distance sampling for per-tree estimates with application to unequal-sized cluster sampling of increment core data

Samples from the n trees nearest to a point or plot center are sometimes used to estimate per-tree values such as age or growth from increment cores. Clutter et al. (J.L. Clutter, J.C. Fortson, L.V. Pienaar, G.H. Brister, and R.L. Bailey. 1983. Timber management: a quantitative approach. John Wiley & Sons, New York) indicated that this procedure can be biased because it is more likely to sample large trees occupying large amounts of space. This sampling procedure falls into the category of n-tree distance sampling in which the nth closest tree to a point defines a plot radius that can be used to estimate number of trees or amount of volume per hectare. When a ratio of n-tree perhectare estimates is used to estimate per-tree attributes, the resulting estimator is a weighted average in which weights are the inverse of the n-tree sampling plot size. Since this ratio estimator essentially weights observations inversely with plot size, it is not subject to the objections of Clutter et al. (1983). This estimator is used to estimate age by diameter at breast height class for eastern cottonwood (Populus deltoides Bartr. ex Marsh.) on the Cimarron National Grassland.