Integrating multiple datasets to align biological and statistical populations for abundance estimation

Ideally, a statistical population is the same as, or accurately represents its corresponding biological population. However, in practice, they rarely align in space and time, which can lead to variable exposure to sampling and biased inference. We often view a population mismatch as a temporary emigration process and resolve it with replicate and/or repeat sampling, though this approach is not feasible for all species and habitats. We developed a hierarchical Bayesian integrated model to estimate abundance of a biological population of the Kittlitz’s murrelet (Brachyramphus brevirostris), a highly mobile, non-territorial, ice-associated seabird of conservation concern in Alaska and eastern Russia. Our model combines datasets from boat and telemetry surveys to account for all components of detection probability, specifically using telemetry locations to estimate probability of presence (pp) and line transect distance sampling to estimate probability of detection (pd). By estimating pp directly, we were able to account for temporary emigration from the sampled area, which changed with shifting icefloes between sampling occasions. Between 2007 and 2012, annual pp was highly variable, ranging from 0.33 to 0.75 (median=0.50, SE=0.02), but was not predictable using five environmental covariates. In years when two boat surveys were conducted, our model reduced the coefficient of variation (CV) of abundance estimates by 13–35%, yet in the year with only one boat survey (2009), the CV skyrocketed about 10-fold, emphasizing the importance of a second survey if pp varies. Although we increased the precision of annual abundance estimates by accounting for pp, we did not see the same improvement in the estimate of mean r, or trend, indicating that while we reduced within-year variance, we failed to account for a source(s) of variation across years, which we suspect is related to the propensity for murrelets to skip breeding in some years. Our integrated model to resolve a population mismatch is simple, flexible, and scalable for generating unbiased and precise abundance estimates of highly mobile species that occupy dynamic habitats where other open population models are not feasible. Importantly, it improves inference of the biological population, which is the true population of interest. We urge ecologists to think critically about the population in which they want to draw inference, especially as tracking technology improves and model complexity increases.