An integrated data model to estimate abundance from counts with temporal dependence and imperfect detection

In the spirit of so-called "sightability models" for estimating population abundance, we developed a Bayesian hierarchical model that combines survey counts for animals (or plants) and a separate data set for detection to account for individuals that were missed during surveys. Our case study consisted of harbor seal (Phoca vitulina richardii) aerial survey counts from 1996 to 2023 for the Prince William Sound (PWS) stock in Alaska and haul-out data from bio-logged individuals. Detection (i.e., haul-out probability) was modeled using logistic regression with temporally autocorrelated latent random effects. The probability of detection informed binomial count models, where true abundances were temporally autocorrelated Poisson models, leading to a logistic-binomial-Poisson hierarchical model. To speed computations, we coupled a two-stage sampling with first-order autoregressive (AR1) and random walk models for autocorrelation. We found time-of-year and time-from-low-tide to be the most important predictors for detection, and our population abundance analysis showed a significant decline (1996-2001), followed by an increase (2001-2015), and then another decline (2015-2023) for the PWS stock. Our approach can be used for other organisms and surveys that have separate detection and count data sets, such as those commonly used in sightability models, as part of long-term population monitoring programs.