Evaluation of sampling methods for the estimation of structural indices in forest stands

The paper is about the accurate (i.e. unbiased and precise) and efficient estimation of structural indices in forest stands. We present SIAFOR, a computer programme for the calculation of four nearest-neighbour indices, which describe the spatial arrangement of tree positions, the distribution pattern of species, and the size differentiation between trees. The study uses SIAFOR as a sampling simulator in eight completely stem-mapped forest stands of varying area and structural complexity. We statistically evaluate two sample types (distance and plot sampling), comparing sampling error, bias and minimum sample size for index estimation. We introduce the concepts of measurement expansion factor (MEF) and design expansion factor (DEF) for the technical evaluation of sample type efficiency (optimal sample type). Results indicate that sampling error can reach high levels and that minimum sample sizes for index estimation often amply exceed the limit of 20% of tree density or 20 trees per species per hectare, that we set as the highest feasible sample size in normal situations. We found clear feasibility limits (in terms of minimal tree densities and reachable accuracy levels) for the estimation of all investigated indices. Generally, equal or higher sample sizes are needed for plot sampling than for distance sampling to reach equal accuracy levels. Nevertheless, plot sampling resulted more efficient for the estimation of tree size differentiation at low to medium accuracy levels. For all other investigated indices distance sampling resulted more efficient than plot sampling. Minimum sample size increases with accuracy and is negatively correlated with tree density. At a given accuracy level minimum sample size is highest for the estimation of relative mingling and lowest for tree size differentiation; furthermore it is generally lower in large stands than in small ones. Because of the consistency of our conclusions in all of the investigated stands, we think they apply in most stands of similar area (between 1 and 10 ha) and species diversity (not more than four species).