Measuring the probability of patch detection for four spatial sampling designs

In this paper, we derive the probabilities that four chosen sampling schemes will detect a circular patch of organisms whose location is at some random location in the study area. We also describe simulations which indicate the variation of patch detection probabilities for different realizations of the sampling design. We comment briefly on how probabilities would be affected by multiple and different shaped patches. Our results are a useful guide for practitioners when choosing a design and an appropriate sampling intensity.