Discrete-space continuous-time models of marine mammal exposure to Navy sonar

Assessing the patterns of wildlife attendance to specific areas is relevant across many fundamental and applied ecological studies, particularly when animals are at risk of being exposed to stressors within or outside the boundaries of those areas. Marine mammals are increasingly being exposed to human activities that may cause behavioural and physiological changes, including military exercises using active sonars. Assessment of the population-level consequences of anthropogenic disturbance requires robust and efficient tools to quantify the levels of aggregate exposure for individuals in a population over biologically relevant time frames. We propose a discrete-space, continuous-time approach to estimate individual transition rates across the boundaries of an area of interest, informed by telemetry data collected with uncertainty. The approach allows inferring the effect of stressors on transition rates, the progressive return to baseline movement patterns, and any difference among individuals. We apply the modelling framework to telemetry data from Blainville's beaked whale (Mesoplodon densirostris) tagged in the Bahamas at the Atlantic Undersea Test and Evaluation Center (AUTEC), an area used by the US Navy for fleet readiness training. We show that transition rates changed as a result of exposure to sonar exercises in the area, reflecting an avoidance response. Our approach will support the assessment of the aggregate exposure of individuals to sonar and the resulting population-level consequences. The approach has potential applications across many applied and fundamental problems where telemetry data are used to characterise animal occurrence within specific areas.,Data are satellite telemetry data from seven Blainville's beaked whales (Mesoplodon densirostris) tagged between 2009 and 2015 within or near the Atlantic Undersea Test and Evaluation Center (AUTEC), in the Bahamas. This region is regularly used by the U.S. Navy to carry out military exercises with active sonar. Tagging was carried out in advance of large-scale exercises (Submarine Command Courses) to monitor resulting changes in the animals' movement behavior. Animals were fitted with Wildlife Computers SPLASH transmitters (n = 2, Mk-10; Wildlife Computers Inc., Redmond, WA, USA) and SPOT model tags (n = 5, AM‐S240A‐C; Wildlife Computers Inc.) in the Low Impact Minimally Percutaneous External-electronics Transmitter (LIMPET) configuration. Tags were attached on or near the dorsal fin from distances of 5-25 m using a crossbow or black powder gun. Location estimates of tagged whales were provided by the Argos system based on the Kalman filtering method. See manuscript for further details.