Spatial modeling, parameter uncertainty, and precision of density estimates from line-transect surveys: a case study with Western Arctic bowhead whales

Abstract

Spatially-explicit models of animal density, such as density surface models (DSMs), are diverse, flexible, and powerful tools for investigating spatial patterns in animal density, examining associations between animal density and environmental covariates, and estimating abundance. Advances in spatial modeling methods and subsequent incorporation into widely accessible software allow the non-specialist to add these tools to their analytical toolbox. However, limitations in some software may prevent a thorough treatment of uncertainty. I expanded the functionality of tools for constructing DSMs from line-transect survey data to derive a population abundance estimate that honestly accounts for multiple sources of detection bias and associated uncertainty. As an illustrative case study, I used data collected during an aerial line-transect survey for Western Arctic bowhead whales (\textit{Balaena mysticetus}) over their summering grounds in the Beaufort Sea and Amundsen Gulf during August 2019. Using spatially explicit hierarchical generalized additive models that incorporated correction factors and associated uncertainty for perception and availability bias, I estimated the abundance of the Western Arctic bowhead whale population to be 17,175 whales (CV($\hat{N}$)= 0.237; 95\% confidence interval = [10,793, 27,330]). This model-based abundance estimate is similar in magnitude to the two most recent estimates for this population based on data from ice-based surveys in 2011 and 2019. Additionally, my abundance estimate is sufficiently precise to inform management decisions for this protected species. The enhanced precision of my abundance estimate over the estimate derived using design-based analytical methods applied to the same data is due to explicit modeling of the spatial correlation in whale density. Applying the power of DSMs to the aerial line-transect survey data made this survey methodology a viable alternative to ice-based surveys, which are facing obstacles due to climate change, for updating abundance estimates for Western Arctic bowhead whales in the future. My analytical developments can easily be applied to other line-transect datasets with similar and common challenges due to multiple survey platforms, spatial heterogeneity in animal density and environmental conditions, and habitat partitioning among groups (e.g., defined by age, sex, activity state) in the target population.