Achieving spatial balance in environmental surveys under constant inclusion probabilities or inclusion density functions

In environmental and ecological surveys, well spread samples can be easily obtained via widely adopted tessellation schemes, which yield equal first-order inclusion probabilities in the case of finite populations of areas or constant inclusion density functions in the case of continuous populations. In the literature, many alternative schemes that are explicitly tailored to select well spread samples have been proposed, but owing to their complexity, their use should be preferred only if they allow us to achieve a valuable gain in precision with respect to the tessellation schemes. Therefore, by means of an extensive simulation study, the performances of tessellation schemes and several specifically tailored schemes are compared under constant first-order inclusion probabilities or constant inclusion density functions.