Developing and assessing a density surface model in a Bayesian hierarchical framework with a focus on uncertainty: insights from simulations and an application to fin whales (Balaenoptera physalus)

Density surface models (DSMs) are an important tool in the conservation and management of cetaceans. Most previous applications of DSMs have adopted a two-step approach to model fitting (hereafter referred to as the Two-Stage Method), whereby detection probabilities are first estimated using distance sampling detection functions and subsequently used as an offset when fitting a density-habitat model. Although variance propagation techniques have recently become available for the Two-Stage Method, most previous applications have not propagated detection probability uncertainty into final density estimates. In this paper, we describe an alternative approach for fitting DSMs based on Bayesian hierarchical inference (hereafter referred to as the Bayesian Method), which is a natural framework for simultaneously propagating multiple sources of uncertainty into final estimates. Our framework includes (1) a mark-recapture distance sampling observation model that can accommodate two team line transect data, (2) an informed prior for the probability a group of animals is at the surface and available for detection (i.e. surface availability) (3) a density-habitat model incorporating spatial smoothers and (4) a flexible compound Poisson-gamma model for count data that incorporates overdispersion and zero-inflation. We evaluate our method and compare its performance to the Two-Stage Method with simulations and an application to line transect data of fin whales (Balaenoptera physalus) off the east coast of the USA. Simulations showed that both methods had low bias (<1.5%) and confidence interval coverage close to the nominal 95% rate when variance was propagated from the first step. Results from the fin whale analysis showed that density estimates and predicted distribution patterns were largely similar among methods; however, the coefficient of variation of the final abundance estimate more than doubled (0.14 vs 0.31) when detection variance was correctly propagated into final estimates. An analysis of the variance components demonstrated that overall detectability as well as surface availability contributed substantial amounts of variance in the final abundance estimates whereas uncertainty in mean group size contributed a negligible amount. Our method provides a Bayesian alternative to DSMs that incorporates much of the flexibility available in the Two-Stage Method. In addition, these results demonstrate the degree to which uncertainty can be underestimated if certain components of a DSM are assumed fixed.