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Remote detectors are being used increasingly often to study aquatic and aerial species, which move significantly differently from terrestrial species. Camera‐trapping studies have used frameworks based on animal movement patterns to show that a species' detection frequency, along with movement speed and detector specifications, can be used to estimate absolute population density. This approach, however, has not yet been adapted to cases where movement is three‐dimensional. Here we adapt one such framework to three‐dimensional movement, to characterize the relationship between population density, animal speed, characteristics of a remote sensor's 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 violations 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. [ABSTRACT FROM AUTHOR]

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species. [ABSTRACT FROM AUTHOR]