Sampling threatened and endangered species with non-constant occurrence and detectability: a sensitivity analysis of power when sampling low-occurrence populations with varying probability parameters

Detecting populations of low-abundance species has become increasingly important. The mathematics involved in a sampling design generally require that probability parameters be fixed numbers; whereas, the reality is that the parameters vary widely within time and space. This is an issue of great concern for biologists and is of particular importance when sampling endangered or threatened species. The power of a sampling design with varying probability values of the generalized binomial distribution model was investigated using computer simulations. These empirical estimates of power compare favorably to theoretical estimates which use fixed probabilities, indicating that the sampling design is robust against variability in actual probability parameters in situations with low levels of occurrence where detectability is low. Thus, theoretically calculated estimates of power using fixed probability values yield a good estimate of the actual power of such a sampling design.