Validating the historical record: a relative distance test and correction formula for selection bias in presettlement land surveys

Presettlement land surveys have been used throughout North America to reconstruct forest characteristics prior to major Euro-American settlement. The bearing tree record derived from these surveys is an example of a distance-based ecological inventory lacking strict selection rules. Such inventories pose a problem of potential selection bias if the nearest individuals are not always selected. The possibility of bias presents a major impediment to compositional analysis from bearing tree proportions. This article presents a modification to distance-based tests and correction formulas that utilize the corner-to-tree distances recorded in the General Land Office (GLO) and similar surveys. The proposed modification consists of replacing absolute with relative corner-to-tree distances to remove the effects of density variation. Monte Carlo simulation is conducted to assess the validity, power and effectiveness of the modified test and correction formula. The modified test is found to be robust in most forests that vary in density and aggregation pattern, but exhibits some statistical bias when density and composition vary simultaneously at local scales. The correction formulas accurately reflect the direction of surveyor bias, and adjusted estimates are consistently closer to the true values than unadjusted estimates. Based on a range of simulation results, upper bound limits on the effects of selection bias can be estimated. Application to the GLO bearing tree records for the state of Minnesota indicates that Minnesota surveyors favored Pinus resinosa, P. strobus and Quercus spp. and avoided five taxa including Salix spp. and Alnus spp. The magnitude of bias appears to be small, however, with an estimated upper bound of 5-6% dissimilarity between biased and unbiased bearing tree selection, some of which may be explained by size differences among taxa.