Varying coefficients correlated velocity models in complex landscapes with boundaries applied to narwhal responses to noise exposure
Alexandre Delporte, Susanne Ditlevsen, Adeline Samson
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 4
Abstract
Narwhals in the Arctic are increasingly exposed to human activities that can temporarily or permanently threaten their survival by modifying their behaviour. We examine GPS data from a population of narwhals exposed to ship and seismic airgun noise during a controlled experiment in 2018 in the Scoresby Sound fjord system in Southeast Greenland. The fjord system has a complex shore line, restricting the behavioural response options for the narwhals to escape the threats. We propose a new continuous-time correlated velocity model with varying coefficients that includes an attractive and a repulsive term, which imply spatial constraints by adjusting the direction of the movement to the boundary of the domain. To our knowledge, this is the first model that includes spatial constraints and also captures a propensity to move close to the shoreline and along the shoreline. To assess the sound exposure effect, we compare a baseline model for the movement before exposure to a response model for the movement during exposure. Our model, applied to the narwhal data, indicates that sound exposure can disturb motion up to a couple of tens of kilometres. Specifically, we found an increase in velocity and a decrease in persistence. We give estimates and confidence intervals of threshold distances to the sound source for medium and strong shifts in the whales’ motion.
Keywords
behavioural response study; constrained movement model; mixed effect model; Stochastic differential equations;
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