Some problems and solutions in density estimation from bearing tree data: a review and synthesis

Aim I detail several problems and solutions related to estimating pre-settlement forest density from land surveyors' bearing tree data. The data have a high value, so clarification of existing problems is needed in the development of a better theoretical framework in which to treat them. I focus on absolute density because it is the foundation for several other variables, e.g. basal area, timber volume and carbon content. Location The issues raised are relevant to the vast area encompassed by rectangular land surveys, including the General Land Office survey area of the United States (roughly, Ohio and Florida to the Pacific coast and Alaska), as well as significant areas in the eastern United States, and possibly elsewhere. Methods A literature review details the history and nature of density estimation from bearing tree data, and spatial simulations quantify the effects of certain identified problems on density estimates. The review focuses on methodological issues appearing in the ecological and biometrical literature. Results Problems encountered in the literature and addressed here include: (1) aggregated tree spatial patterns and their effect on density using traditional estimators; (2) the mis-designation of bearing tree labels in relation to definitions given in the estimators; (3) biases due to small sample size; and (4) surveyor-induced biases. Simulations of aggregated tree populations having a 44-fold density variation show that estimates ranging from 5 to 127 per cent of actual can result, depending on the estimator used, the scale at which it is calculated, and the error in tree distance rank assignments. The traditionally used estimator is accurate only when trees are spatially random throughout, and sample size is not small. More robust estimators exist that can accommodate a wider range of variation in spatial pattern, sampling design and sample size. One of these is discussed in detail. Main conclusions Data users should pay much closer attention to critical aspects of bearing tree data and analytical methods, provide basic but necessary descriptive data, and more accurately represent the inherent range of possible errors of estimate. They can narrow this range of uncertainty by using the methods and considerations discussed here and in other recent work.