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