Generalizing systematic adaptive cluster sampling for forest ecosystem inventory

Reliable statistical inference is central to forest ecology and management, much of which seeks to estimate population parameters for forest attributes and ecological indicators for biodiversity, functions and services in forest ecosystems. Many populations in nature such as plants or animals are characterized by aggregation of tendencies, introducing a big challenge to sampling. Regardless, a biased or imprecise inference would mislead analysis, hence the conclusion and policymaking. Systematic adaptive cluster sampling (SACS) is design-unbiased and particularly efficient for inventorying spatially clustered populations. However, (1) oversampling is common for nonrare variables, making SACS a difficult choice for inventorying common forest attributes or ecological indicators; (2) a SACS sample is not completely specified until the field campaign is completed, making advance budgeting and logistics difficult; (3) even for rare variables, uncertainty regarding the final sample still persists; and (4) a SACS sample may be variable-specific as its formation can be adapted to a particular attribute or indicator, thus risking imbalance or non-representativeness for other jointly observed variables. Consequently, to solve these challenges, we aim to develop a generalized SACS (GSACS) with respect to the design and estimators, and to illustrate its connections with systematic sampling (SS) as has been widely employed by national forest inventories and ecological observation networks around the world. In addition to theoretical derivations, empirical sampling distributions were validated and compared for GSACS and SS using sampling simulations that incorporated a comprehensive set of forest populations exhibiting different spatial patterns. Five conclusions are relevant: (1) in contrast to SACS, GSACS explicitly supports inventorying forest attributes and ecological indicators that are nonrare, and solved SACS problems of oversampling, uncertain sample form, and sample imbalance for alternative attributes or indicators; (2) we demonstrated that SS is a special case of GSACS; (3) even with fewer sample plots, GSACS gives estimates identical to SS; (4) GSACS outperforms SS with respect to inventorying clustered populations and for making domain-specific estimates; and (5) the precision in design-based inference is negatively correlated with the prevalence of a spatial pattern, the range of spatial autocorrelation, and the sample plot size, in a descending order.