Surveyor and analyst biases in forest density estimation from United States Public Land Surveys

Abstract

Accurate forest density estimates based on United States Public Land Surveys have long been questioned because of doubts about randomness of both the surveyors' selection of witness trees and the underlying tree dispersion. This study analyzes the surveyor sampling of witness trees in six Midwestern states in the mid‐1800s. It develops universal methods for identification, quantification, and correction of bias, and then calculation of unbiased density. Applying these techniques produces unbiased site‐specific densities before Euro‐American settlement, which are the essential baseline for determining historic changes in forest structure. Previous analysts used untested assumptions, inaccurate estimators, unknown or unrealistic sampling designs, and omitted or poorly corrected surveyor bias, resulting in hundreds of unreliable density estimates. The surveyors' recording of the empirical distance, bearing, and diameter of witness trees documented the exact sampling design. The intended design and deviation from it are investigated with a combination of descriptive statistics, probability theory, computer simulations, analogue geometric models, and modern stand conditions. Herein, analyst bias is eliminated using the robust Morisita II density estimator matching the predominant sampling design of two trees in opposing semicircles. Six widespread surveyor biases deviating from the nearest tree to the corner are evaluated. Quadrant bias and diameter bias for medium‐sized trees are subsumed under newly framed design and small tree biases. Two novel surveyor positional biases (pair angle and near‐post) are introduced here. Previously recognized azimuthal and species biases are analyzed with new techniques. Widely postulated surveyor bias for certain species was found to be minimal. Bias correction and density estimation are applied in detail over 68 townships in northern Wisconsin. The estimated historical forest density in northern Wisconsin, corrected for bias and small tree truncation, averaged 323 trees/ha ≥20 cm. Over 80 Midwestern subregions, surveyors bypassed an estimated 17% of the nearest trees due to their position, resulting in an average bias correction of +24% over the base density. If censored trees below a 20‐cm “veil‐line” are considered, the surveyors bypassed 48% of the nearest trees >12.7 cm in diameter. This study resolves a 70‐year‐old conundrum of surveyor and analyst biases in historical density estimation.