A continuous‐time random encounter and staying time ( <scp>REST</scp> ) model: Moving beyond temporal aggregation in camera‐trap density estimation

Abstract Estimating wildlife population density is fundamental to ecology and conservation. While camera traps have revolutionized the monitoring of medium‐ to large‐sized mammals, estimating the density of unmarked populations remains a major challenge. Current models rely on a critical and often‐violated synchronized activity assumption. This assumption posits that all individuals in a sampled population are simultaneously active at the peak of their daily activity cycle. In natural settings, however, animal activity is highly plastic, shifting in response to environmental conditions. We develop a continuous‐time random encounter and staying time (REST) model that treats animal detections as a temporal point process, enabling explicit tracking of temporal changes in active population density —the density of individuals available for detection. Our model links detection intensity to active population density by reformulating the original REST model. We model temporal dynamics using periodic components for diel activity patterns and spatio‐temporal components for other variations. We evaluate model performance through simulations across scenarios with different densities and temporal patterns (static, linear trend, and pulse‐like fluctuations) and apply the model to Japanese badger ( Meles anakuma ) data from Japan. Simulations demonstrated that the continuous‐time REST model accurately recovered temporal fluctuations in active population density and yielded unbiased estimates across all scenarios. In contrast, conventional methods underestimated density under temporal variation because they averaged out these fluctuations, obscuring peak active population density. Application to badger data revealed seasonal declines in active population density, with daily maximum decreasing to approximately 30% of its initial value, consistent with the species' known behavioural ecology. The continuous‐time REST model relaxes the conventional assumption that all individuals must be active simultaneously each day, requiring only that all individuals are active simultaneously at least once during the survey period. Under this weaker assumption, the maximum of active population density provides a more accurate estimate of true population density. More fundamentally, by moving beyond temporal aggregation to continuous‐time modelling of active population density, this framework enables direct quantification of fine‐scale population changes. This provides richer ecological insights into population dynamics and responses to environmental change, opening avenues for studying fine‐scale ecological processes.