Using quantile regression and relative entropy to assess the period of anomalous behavior of marine mammals following tagging

Tagging of animals induces a variable stress response which following release will obscure behavior. It is of scientific relevance to establish methods that assess recovery from such behavioral perturbation and generalize well to a broad range of animals, while maintaining model transparency. We propose two methods that allow for subdivision of animals based on covariates, and illustrate their use on narwhals () and bowhead whales (), captured and instrumented with Acousonde™ behavioral tags, but with a framework that easily generalizes to other marine animals and sampling units. The narwhals were divided into two groups based on handling time, ( min) and ( min), to measure the effect on recovery. Proxies for energy expenditure (VeDBA) and rapid movement (jerk) were derived from accelerometer data. Diving profiles were characterized using two metrics (target depth and dive duration) derived from depth data. For accelerometer data, recovery was estimated using quantile regression (QR) on the log-transformed response, whereas depth data were addressed using relative entropy (RE) between hourly distributions of dive duration (partitioned into three target depth ranges) and the long-term average distribution. Quantile regression was used to address location-based behavior to accommodate distributional shifts anticipated in aquatic locomotion. For all narwhals, we found fast recovery in the tail of the distribution (<3 h) compared with a variable recovery at the median (∼1-10 h) and with a significant difference between groups separated by handling time. Estimates of bowhead whale recovery times showed fast median recovery (<3 h) and slow recovery at the tail (>6 h), but were affected by substantial uncertainty. For the diving profiles, as characterized by the component pair (target depth, dive duration), the recovery was slower (narwhals-: h; narwhals-: h; bowhead whales: <9 h) and with a difference between narwhals with short vs long handling times. Using simple statistical concepts, we have presented two transparent and general methods for analyzing high-resolution time series data from marine animals, addressing energy expenditure, activity, and diving behavior, and which allows for comparison between groups of animals based on well-defined covariates.