Modelling group movement with behaviour switching in continuous time

This article presents a new method for modelling collective movement in continuous time with behavioural switching, motivated by simultaneous tracking of wild or semi-domesticated animals. Each individual in the group is at times attracted to a unobserved leading point. However, the behavioural state of each individual can switch between 'following' and 'independent'. The 'following' movement is modelled through a linear stochastic differential equation, while the 'independent' movement is modelled as Brownian motion. The movement of the leading point is modelled either as an Ornstein-Uhlenbeck (OU) process or as Brownian motion (BM), which makes the whole system a higher-dimensional Ornstein-Uhlenbeck process, possibly an intrinsic non-stationary version. An inhomogeneous Kalman filter Markov chain Monte Carlo algorithm is developed to estimate the diffusion and switching parameters and the behaviour states of each individual at a given time point. The method successfully recovers the true behavioural states in simulated data sets , and is also applied to model a group of simultaneously tracked reindeer (Rangifer tarandus).