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 meaningful. With simulations, we demonstrate that our lasso method effectively shrinks spurious threshold effects towards zero. When applied to narwhal $\textit{(Monodon monoceros)}$ movement data, our analysis suggests that narwhal react to vessels up to 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.

翻译：理解野生动物对干扰的行为反应对于物种保护至关重要。例如，在北极地区，海冰减少开辟了新的航运路线，从而增加了量化海洋哺乳动物对船舶存在产生反应距离的需求。此类信息可指导制定针对性缓解政策，如船舶减速规定和规避区域划定。利用遥测数据确定与正常行为偏离相关的距离需要先进的统计模型，例如阈值隐马尔可夫模型。尽管这些是强大的工具，但它们无法评估估计的阈值是否反映有意义的行为转变。我们提出了一种套索惩罚阈值隐马尔可夫模型，该模型基于计算高效的方法对隐马尔可夫模型施加惩罚，并提出了一种新的高效惩罚拟限制最大似然估计器。我们的框架能够估计阈值并评估干扰效应是否具有实际意义。通过模拟实验，我们证明套索方法能有效将虚假阈值效应收缩至零。将模型应用于独角鲸（Monodon monocros）运动数据时，分析表明独角鲸对4公里内的船舶会产生反应，表现为运动持续性降低并更多时间停留在深水区（平均最大深度356米）。总体而言，我们提出了一个广泛适用的量化生物对刺激行为反应的框架，其应用范围涵盖从确定干扰反应阈值到估算陆地物种（如大象）探测水源的距离。