Spatial pattern corrections and sample sizes for forest density estimates of historical tree surveys

The U. S. General Land Office land surveys document trees present during European settlement. However, use of these surveys for calculating historical forest density and other derived metrics is limited by uncertainty about the performance of plotless density estimators under a range of conditions. Therefore, we tested two plotless density estimators, developed by Morisita and Pollard, for two, three, and four trees per survey point under simulated ranges of tree densities, non-uniform densities, and different tree spatial distributions. Based on these results, we developed estimator corrections and determined number of survey points needed for reliable density estimates. The Morisita estimator was accurate for densities ranging from 5 to 1,000 trees per unit area, non-uniform densities, random and regular spatial distribution, and outperformed the Pollard estimator. Estimators using points with two or three trees did need a simple correction to account for overestimation. Likewise, for clustered distributions, depending on the number of trees per survey point and the amount of clustering, there should be adjustment for a range of under and overestimation. Sample sizes for survey points with three or four trees should be at least 200 survey points, and 1,000 survey points will have density estimates within ±10% tolerance range of actual density. For survey points with two trees, the minimum sample size should be 600 survey points, and 2,000 survey points should be the target value. These results provide guidelines for researchers to improve density estimates of historical forests.