A Monte Carlo Study of Distance Measures in Sampling for Spatial Distribution in Forest Stands

Two rules using distance measures are studied: (1) the measurement from a random point to the t th nearest tree and (2) the measurement to the t th nearest tree in each of 4 sectors. First a statistical framework was developed to determine their performance characteristics and both theoretical and intuitive estimators of the number of trees and basal area per acre to use with them. Three hypothetical but typical forest patterns of 100 trees each are examined. A computer program was used to produce the frequency distributions. For this paper t ranged from 1 to 4. Edge effect was discussed but only those sample points free of edge effect were used in the analysis. The frequency distributions generated were compared with 5 common mathematical distributions. No statistically significant fit was found. All estimators are shown to be biased. On the basis of this study it is possible to use these rules to separate areas based on pattern and density. The variance of the average distance from a random point to the t th nearest tree is an indicator of pattern and the average distance is an indicator of density. With either of these rules it seems unlikely that unbiased estimators of density or basal area can be developed for most nonrandom biological populations.