Assessment of the Bering-Chukchi-Beaufort Seas stock of bowhead whales using Bayesian model averaging

Abstract

Bayesian estimation methods are used to fit an age- and sex-structured population model to available data on abundance and stageproportions (i.e. calves/mature animals in the population) for the Bering-Chukchi-Beaufort Seas stock of bowhead whales (Balaena mysticetus). The analyses consider three alternative population modelling approaches: (1) modelling the entire population trajectory from 1848, using the ‘backwards’ method where the trajectory is back-calculated based on assigning a prior distribution to recent abundance; (2) modelling only the recent population trajectory, using the ‘forwards from recent abundance’ method, where the population is projected forwards from a recent year and the abundance in that year is not assumed to be at carrying capacity; and (3) a version of (2) that ignores density-dependence. The ‘backwards’ method leads to more precise estimates of depletion level. In contrast, the ‘forwards from recent abundance’ method provides an alternative way of calculating catch-related quantities without having to assume that the catch record is known exactly from 1848 to the present, or having to assume that carrying capacity has not changed since 1848. Not only are all three models able to fit the abundance data well, but each is also able to remain consistent with available estimates of adult survival and age of sexual maturity. Sensitivity to the stage-proportion data and the prior distributions for the life history parameters indicates that use of the 1985 stage-proportion data has the greatest effect on the results, and that those data are less consistent with data on trends in abundance and age of sexual maturity. The analyses indicate that the population has approximately doubled in size since 1978, and the ‘backwards’ analyses suggest that the population may be approaching carrying capacity, although there is no obvious sign in the data that the population growth rate has slowed. Bayes factors are calculated to compare model fits to the data. However, there is no evidence for selecting one model over another, and furthermore, the models considered in this study result in different posterior distributions for quantities of interest to management. Posterior model probabilities are therefore calculated and used as weights to construct Bayesian model-averaged posterior distributions for outputs shared among models to take this ambiguity into account. This study represents the first attempt to explicitly quantify model uncertainty when conducting a stock assessment of bowhead whales.