Variable Density Grid-Based Sampling Designs for Continuous Spatial Populations

Many environmental resources, such as mineral resources or vegetation cover, or environmental attributes, such as chemical concentration in a stream or benthic community structure, are most appropriately sampled as continuous populations distributed over space, but most applied sampling theory and methodology is concerned with finite, discrete populations. This paper reports sampling methodology that explicitly recognizes the continuous nature of ecological resources. A family of designs are developed to permit control of the spatial dispersion of the sample, variable spatial density, and nested subsampling. The designs have non-zero joint inclusion probability densities, so that rigorous design-based inference and variance estimation are possible.