Estimating gray whale abundance from shore-based counts using a multilevel Bayesian model

Abstract

Counts of southbound migrating whales off California form the basis of abundance estimation for the eastern North Pacific stock of gray whales (Eschrichtius robustus). Previous assessments (1967–2007) have estimated detection probability (p) from the detection-non detection of pods by two independent observers. However, tracking distinct pods in the field can be difficult for single observers; resulting in biased estimates of pod sizes that needed correcting, and matching observations of the same pod by both observers involved key assumptions. Due to these limitations, a new observation approach has been adopted wherein a paired team of observers work together and use a computerised mapping application to better track and enumerate distinct pods and tally the number of whales passing during watch periods. This approach has produced consistent counts over four recently monitored migrations (2006/7, 2007/8, 2009/10 and 2010/11), with an apparent increase in p compared to the previous method. To evaluate p and estimate abundance in these four years, counts from two independent stations of paired observers operating simultaneously were compared using a hierarchical Bayesian ‘N-mixture’ model to jointly estimate p and abundance without the challenge of matching pods between stations. The baseline detectability po was estimated as 0.80 (95% Highest Posterior Density Interval [HPDI] = 0.75–0.85), which varied with observation conditions, observer effects and changes in whale abundance during the migration. Abundance changes were described using Bayesian model selection between a parametric model for a normally distributed common migration trend and a semi-parametric model that estimated the time trends independently for each year; the resultant migration curve was a weighted compromise between models, allowing for key departures from the common trend. The summed estimates of migration abundance ranged from 17,820 (95% HPDI = 16,150–19,920) in 2007/08 to 21,210 (95% HPDI = 19,420–23,230) in 2009/10, consistent with previous estimates and indicative of a stable population.