Estimating the distance at which narwhal respond to disturbance: a penalized threshold hidden Markov model

Abstract

Understanding behavioural responses to disturbances is vital for wildlife conservation. For example, in the Arctic, the decrease in sea ice has opened new shipping routes, increasing the need for impact assessments that quantify the distance at which marine mammals react to vessel presence. This information can then guide targeted mitigation policies, such as vessel slow-down regulations and delineation of avoidance areas. Using telemetry data to determine distances linked to deviations from normal behaviour requires advanced statistical models, such as threshold hidden Markov models (THMMs). While these are powerful tools, they do not assess whether the estimated threshold reflects a meaningful behavioural shift. We introduce a lasso-penalized THMM that builds on computationally efficient methods to impose penalties on HMMs and present a new, efficient penalized quasi-restricted maximum-likelihood estimator. Our framework is capable of estimating thresholds and assessing whether the disturbance effects are distinguishable from baseline behaviour. With simulations, we demonstrate that our lasso method effectively shrinks spurious threshold effects towards zero. When applied to narwhal movement data, our analysis suggests that narwhal react to vessels up to 3.4 kilometres away by decreasing movement persistence and spending more time in deeper waters (average maximum depth of 356m). Overall, we provide a broadly applicable framework for quantifying behavioural responses to stimuli, with applications ranging from determining reaction thresholds to disturbance to estimating the distances at which terrestrial species, such as elephants, detect water. We also provide a tutorial and an open-source implementation to facilitate the application of our framework.