Abstract
Protected species bycatch can be rare, making it difficult for fishery managers to develop unbiased estimates of fishing-induced mortality. To address this problem, we use Bayesian time-series models to estimate the bycatch of humpback whales ( Megaptera novaeangliae ), which have been documented only twice since 2002 by fishery observers in the United States West Coast sablefish pot fishery, once in 2014 and once in 2016. This model-based approach minimizes under- and over-estimation associated with using ratio estimators based only on intra-annual data. Other opportunistic observations of humpback whale entanglements have been reported in United States waters, but, because of spatio-temporal biases in these observations, they cannot be directly incorporated into the models. Notably, the Bayesian framework generates posterior predictive distributions for unobserved entanglements in addition to estimates and associated uncertainty for observed entanglements. The United States National Marine Fisheries Service began using Bayesian time-series to estimate humpback whale bycatch in the United States West Coast sablefish pot fishery in 2019. That analysis resulted in estimates of humpback whale bycatch in the fishery that exceeded the previously anticipated bycatch limits. Those results, in part, contributed to a review of humpback whale entanglements in this fishery under the United States Endangered Species Act. Building on the humpback whale example, we illustrate how the Bayesian framework allows for a wide range of commonly used distributions for generalized linear models, making it applicable to a variety of data and problems. We present sensitivity analyses to test model assumptions, and we report on covariate approaches that could be used when sample sizes are larger. Fishery managers anywhere can use these models to analyze potential outcomes for management actions, develop bycatch estimates in data-limited contexts, and guide mitigation strategies.