1. Movement is the primary means by which animals obtain resources and avoid hazards. Most movement exhibits directional bias that is related to environmental features (defined as taxis when biased orientation is voluntary), such as the location of food patches, predators, ocean currents or wind. Numerous behaviours with directional bias can be characterised by maintaining orientation at an angle relative to the environmental stimuli (menotaxis), including navigation relative to sunlight or magnetic fields and energy-conserving flight across wind. However, new methods are needed to flexibly classify and characterise such directional bias.
2. We propose a biased correlated random walk model that can identify menotactic behaviours by predicting turning angle as a trade-off between directional persistence and directional bias relative to environmental stimuli without making a priori assumptions about the angle of bias. We apply the model within the framework of a multi-state hidden Markov model (HMM) and describe methods to remedy information loss associated with coarse environmental data to improve the classification and parameterisation of directional bias.
3. Using simulation studies, we illustrate how our method more accurately classifies behavioural states compared to conventional correlated random walk HMMs that do not incorporate directional bias. We illustrate the application of these methods by identifying cross wind olfactory foraging and drifting behaviour mediated by wind-driven sea ice drift in polar bears (Ursus maritimus) from movement data collected by satellite telemetry.
4. The extensions we propose can be readily applied to movement data to identify and characterise behaviours with directional bias towards any angle, and open up new avenues to investigate more mechanistic relationships between animal movement and the environment.

中文翻译：

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使用隐马尔可夫模型表征运动数据中的趋向行为

1. 运动是动物获取资源和避免危险的主要手段。大多数运动表现出与环境特征相关的方向偏差（当偏差方向是自愿时定义为出租车），例如食物斑块、捕食者、洋流或风的位置。许多具有方向偏差的行为的特征在于保持相对于环境刺激（趋向性）成一定角度的方向，包括相对于阳光或磁场的导航以及跨越风的节能飞行。然而，需要新的方法来灵活地分类和表征这种方向性偏差。
2. 我们提出了一种有偏相关随机游走模型，该模型可以通过预测转向角作为相对于环境刺激的方向持久性和方向偏差之间的权衡来识别趋向行为，而无需对偏差角度做出先验假设。我们在多状态隐马尔可夫模型 (HMM) 的框架内应用该模型，并描述了补救与粗略环境数据相关的信息丢失的方法，以改进方向偏差的分类和参数化。
3. 使用模拟研究，我们说明了与不包含方向偏差的传统相关随机游走 HMM 相比，我们的方法如何更准确地对行为状态进行分类。我们通过从卫星遥测收集的运动数据中识别北极熊（Ursus maritimus）的风驱动海冰漂移介导的侧风嗅觉觅食和漂移行为来说明这些方法的应用。
4. 我们提出的扩展可以很容易地应用于运动数据，以识别和表征具有朝向任何角度的方向偏差的行为，并开辟新的途径来研究动物运动与环境之间的更多机械关系。