Characterising menotactic behaviours in movement data using hidden Markov models

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. 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. 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. 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.