A new empirical approach for estimation in k-tree sampling

• Published in: Forest ecology and management Vol. 237; no. 1; pp. 522 - 533
• Main Authors: Kleinn, Christoph, Vilčko, František
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.12.2006; Elsevier
• Subjects: Animal and plant ecology; Animal, plant and microbial ecology; Bias; Biological and medical sciences; Dendrometry. Forest inventory; Ecological surveys; Fixed area plot sampling; Forest inventory; Forestry; Fundamental and applied biological sciences. Psychology; Plot design; Point-to-tree distance sampling; Precision; Relascope sampling; Synecology; Terrestrial ecosystems; Plot design; Point-to-tree distance sampling; Precision; Fixed area plot sampling; Bias; Relascope sampling; Ecological surveys; Forest inventory; Tree; Ecology; Sampling; Distance
• ISSN: 0378-1127; 1872-7042
• DOI: 10.1016/j.foreco.2006.09.072

Point-to-tree distance techniques (also known as k-tree or fixed count sampling) are a practical field sampling method for forest inventories and ecological surveys, but statistical estimation remains a problem. Various approximation techniques have been proposed, partly on an empirical basis, partly under model assumptions about the underlying point processes. In this paper we present a brief history of k-tree sampling in forestry and introduce a new and simple empirical approximation method. This method builds on calculating the variable sample plot area from the distance not only to the k tree but averaging the distance to the k and to the ( k + 1) tree. Simulation studies were done on a tree map from the Miombo woodlands in northern Zambia and five artificially generated tree maps with different point patterns. In terms of bias, our techniques are superior to Prodan's approach; however, Eberhardt's estimator produces consistently the smallest bias for the studied clustered patterns, and is unbiased for random patterns. For the two uniform patterns studied, bias was smallest on average for our new estimators. A comparison with relascope sampling and fixed area sample plots sized to yield k trees per sample plot indicated that the k-tree sampling estimators studies produced higher standard errors for the estimation of basal area and number of stems than fixed area plots for the clustered and random maps. For the two uniform patterns, k-tree sampling with our mean-area estimator produces smallest errors, in particular for small values of k. It is concluded that it is mainly the simplicity of the method that makes point-to-tree distance sampling interesting for forest and ecological sampling, but its statistical performance remains somewhat uncertain.