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 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：理解动物对干扰的行为反应对于野生动物保护至关重要。例如，在北极地区，海冰减少开辟了新的航道，这增加了对影响评估的需求，以量化海洋哺乳动物对船只存在产生反应的距离。这些信息随后可用于指导针对性的减缓政策，如船只减速法规和规避区域的划定。利用遥测数据来确定与正常行为偏离相关的距离，需要采用先进的统计模型，例如阈值隐马尔可夫模型（THMM）。尽管这些工具功能强大，但它们并未评估所估计的阈值是否反映了有意义的行为转变。我们引入了一种基于计算高效方法对HMM施加惩罚的lasso惩罚THMM，并提出了一种新的高效惩罚拟受限最大似然估计量。我们的框架能够估计阈值，并评估干扰效应是否与基线行为可区分。通过模拟，我们证明我们的lasso方法能有效地将虚假的阈值效应收缩至零。当应用于独角鲸运动数据时，我们的分析表明，独角鲸对最远4公里外的船只作出反应，表现为运动持续性降低并花费更多时间在更深水域（平均最大深度356米）。总体而言，我们提供了一个广泛适用的框架，用于量化对刺激的行为反应，其应用范围从确定对干扰的反应阈值，到估计陆地物种（例如大象）探测水源的距离。