A hierarchical modelling approach to estimating humpback whale abundance from sand lance abundance

The primary prey of humpback whales in the southwestern Gulf of Maine is sand lance. Despite this established relationship, we lack models to further understand the influence of sand lance on humpback whales or to predict humpback abundance or distribution in response to climate-related changes in sand lance abundance or distribution. We used a subset of long-term standardized survey data (2013–2019) from Stellwagen Bank National Marine Sanctuary and a Bayesian hierarchical modeling approach to explore the influence of sand lance on humpback whales at multiple spatial and temporal scales while accounting for sampling variability and propagating uncertainty. We developed zero-inflated Poisson mixed effects models for both sand lance and humpbacks, using modelled sand lance abundance as a predictor in the whale model. Results showed a statistically clear positive correlation between sand lance and humpback whales. Regional mean abundances of both species increased from north to south, though site-level variation within regions showed more variability. Results suggest annual variation in abundance of both species, with potentially different influences. We demonstrate one management application of our method by examining entanglement risk for humpback whales. Whale aggregations were more likely to occur in a high density area of fixed fishing gear that overlaps with an area of higher sand lance abundance. Our work suggests that humpback whale distribution in the larger Gulf of Maine may be impacted by climate-related fluctuations in sand lance abundance. Predicting future distributions of humpback whales is important for ecosystem-based management, including mitigation of human impacts, and our work serves as a foundation for further model development.