A new test of random walks in heterogeneous environments

Environmental heterogeneities can change animal movement in two different manners. First, they can modify movement characteristics (move lengths or turning angles), in which case the movement remains of the diffusive kind. Second, they can bias displacement towards a particular direction in which case it becomes non-diffusive. We propose in this paper a simple method that only requires computing the mean length of a sample of trajectories in some bounded area to distinguish between these two kinds of movement. We show through simulations that the method allows to detect the presence of heterogeneities that orient animal movement. We apply it to experimental trajectories of Messor sancta ants engaged in corpse aggregation to show that their displacement is oriented at the contact of the formed corpse piles and that their trajectories become non-diffusive.