Horvitz–Thompson whale abundance estimation adjusting for uncertain recapture, temporal availability variation, and intermittent effort

A Horvitz–Thompson-type estimator is introduced to estimate total abundance of the Bering–Chukchi–Beaufort Seas population of bowhead whales using combined visual and acoustic location data. The estimator divides sightings counts by three correction factors that are themselves estimated from various portions of the data. The first correction models how detection probabilities depend on covariates like offshore distance and visibility. The second correction adjusts for availability using the acoustic location data to estimate a time-varying smooth function of the probability that animals pass within visual range of the observation stations. The third correction accounts for whales passing during periods when one or both sighting stations were temporarily closed down. We derive an asymptotically unbiased estimator of abundance incorporating all these components and a corresponding variance estimate. Correcting the count of 4011 observed whales yields a 2011 abundance estimate of 16,820 with a 95% confidence interval of (15,176, 18,643) and an estimated annual rate of population increase of 3.7% (2.9%, 4.6%). These results are indicative of very low conservation risk for this population under the current low levels of aboriginal hunting permitted by the International Whaling Commission. Although few other capture–recapture surveys will confront exactly the same set of challenges addressed here, many studies face one or more issues that could be resolved by adapting portions of our approach or relevant underlying concepts thereof. Moreover, the generic estimator we derive represents an improved way to handle random correction factors rather than assuming fixed values. Copyright © 2016 John Wiley & Sons, Ltd.