Estimating animal density in three dimensions using capture‐frequency data from remote detectors

Remote detectors are being used increasingly often to study aquatic and aerial species, for which movement is significantly different from terrestrial species. While terrestrial camera-trapping studies have shown that capture frequency, along with the species9 movement speed and detector specifications can be used to estimate absolute densities, the approach has not yet been adapted to cases where movement occurs in three dimensions. Frameworks based on animal movement patterns allow estimating population density from camera-trapping data when animals are not individually distinguishable. Here we adapt one such framework to three-dimensional movement to characterize the relationship between population density, animal speed, characteristics of a remote sensor9s detection zone, and detection frequency. The derivation involves defining the detection zone mathematically and calculating the mean area of the profile it presents to approaching individuals. We developed two variants of the model - one assuming random movement of all individuals, and one allowing for different probabilities for each approach direction (e.g. that animals more often swim/fly horizontally than vertically). We used computer simulations to evaluate model performance for a wide range of animal and detector densities. Simulations show that in ideal conditions the method approximates true density well, and that estimates become increasingly accurate using more detectors, or sampling for longer. Moreover, the method is robust to invalidation of assumptions, accuracy is decreased only in extreme cases where all detectors are facing the same way. We provide equations for estimating population density from detection frequency and outline how to estimate the necessary parameters. We discuss how environmental variables and species-specific characteristics affect parameter estimates and how to account for these differences in density estimations. Our method can be applied to common remote detection methods (cameras and acoustic detectors), which are currently being used to study a diversity of species and environments. Therefore, our work may significantly expand the number and diversity of species for which density can be estimated.