Scaling and Intermittency in Animal Behavior

Scale-invariant spatial or temporal patterns and Lévy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform Lévy flight motion with power law distribution of times between two changes of the direction of motion. Here we study the temporal behaviour of nesting gilts. The time spent by a gilt in a given form of activity has power law probability distribution without finite average. Further analysis reveals intermittent eruption of certain periodic behavioural sequences which are responsible for the scaling behaviour and indicates the existence of a critical state. We show that this behaviour is in close analogy with temporal sequences of velocity found in turbulent flows, where random and regular sequences alternate and form an intermittent sequence. Scale-invariant spatial and temporal patterns have been observed in a large variety of biological systems [1]. It has been demonstrated that ants [2], Drosohyla [3] and the wandering albatross, Diomedea exulants [4] perform motion with power law distribution of times between two changes of the direction of motion. The power law distribution of times then leads to an anomalous Lévy type diffusion in space. In the last few years an increasing interest has been devoted to these superdiffusive processes in physics [5–7]. and in econophysics [8–11]. Inspite of the extensive experimental studies the detailed mechanism responsible for the creation of the underlying power law distributions is not well understood. In this letter we demonstrate the first time that the power law and scaling observed in the behaviour of certain animals is related to intermittency, a phenomenon familiar from the theory of dynamical systems and turbulence. It is well known that non-hyperbolic dynamical systems show superdiffusive behaviour. In dissipative systems it is caused by the trapping of trajectories in the neighborhood of marginally unstable periodic orbits [12]. The paradigmatic system showing such behaviour is Manneville’s one dimensional map [13]