Estimating population density of mobile species is a long-standing challenge in ecology. Precise and accurate density estimates are critical for testing ecological theory, and for management and conservation. The Random Encounter and Staying Time (REST) model takes advantage of camera traps’ continuous-time motion sensors to determine species population density. The REST model is currently derived from a verbal logical model underlying movement patterns. Here, however, we challenge this logic with mathematical reasoning to reconstruct the model from first principles.
Results/Conclusions
We construct a revised version of the REST model based on ideal gas law physics and use mathematical moments to derive mean and variance of the model’s density estimates. From this we show that the mean is a consistent estimator of population density, whereas the variance depends on four measurable ecological variables: species density, detection zone area, animal speed, and duration of the sampling period. We then use the derived variance to demonstrate the expected accuracy of REST estimates under a variety of ecologically realistic conditions. Ultimately, we confirm that the REST model is a functional tool for measuring large animal density and demonstrate how estimating model parameters using mathematical moments is a functional way to create precise and accurate density measurements for empirical data.