Statistical analysis of spatial pattern: a comparison of grid and hierarchical sampling approaches

Previous studies have combined random-site hierarchical sampling designs with analysis of variance techniques, and grid sampling with spatial autocorrelation analysis. We illustrate that analysis techniques and sampling designs are interchangeable using densities of an infaunal bivalve from a study in Poverty Bay, New Zealand. Hierarchical designs allow the estimation of variances associated with each level, but high-level factors are imprecisely estimated, and they are inefficient for describing spatial pattern. Grid designs are efficient for describing spatial pattern, and are amenable to conventional analysis. Our example deals with a continuous spatial habitat, but our conclusions also apply in disjunct or patchy habitats. The influence of errors in positioning is also assessed. The advantages of systematic sampling are reviewed, and more efficient hierarchical approaches are identified. The distinction between biological and statistical significance in all analyses is emphasised.