When to switch from simple random to probability-based sampling in mapping and monitoring of rare habitats and species?

Many habitats and species of conservation concern are too rare to be adequately represented in a simple random sample of observation units, e.g., for monitoring purposes. Here, we explore possibilities and limitations of a promising alternative approach, probability-based sampling, by which the probability of being sampled is a function of the predicted probability of occurrence in a potential sampling unit. We compare probability-based vs. random sampling for rare and common target phenomena by simulating variables at three nested sample levels allowing investigation of, e.g., presence or absence of a habitat, presence or abundance of a species in the habitat, and properties of this species, and by deriving theoretical limits for the different sampling designs based on a priori knowledge of the properties of the system. We show that the lower limit for target prevalence, allowing for reliable estimation of its properties, can be expressed as a function of the acceptable precision, the sampling effort and variable parameters. The simulations confirm these theoretically derived lower prevalence limits. As expected, lower demands on precision and higher sampling effort allow investigation of rarer and less predictable phenomena. Probability-based sampling gives sufficiently precise estimates for phenomena with prevalence several orders of magnitude lower than simple random sampling, as well as more precise estimates for common phenomena. This suggests a substantial unrealized potential for the use of probability-based sampling in biodiversity and conservation studies. We demonstrate how our results can be applied in sampling design for veteran oaks with many rare and threatened beetles.