Scale invariance in the dynamics of spontaneous behavior

Abstract

Typically one expects that the intervals between consecutive occurrences of a particular behavior will have a characteristic time scale around which most observations are centered. Surprisingly, the timing of many diverse behaviors from human communication to animal foraging form complex self-similar temporal patterns reproduced on multiple time scales. We present a general framework for understanding how such scale invariance may arise in nonequilibrium systems, including those that regulate mammalian behaviors. We then demonstrate that the predictions of this framework are in agreement with detailed analysis of spontaneous mouse behavior observed in a simple unchanging environment. Neural systems operate on a broad range of time scales, from milliseconds to hours. We analytically show that such a separation between time scales could lead to scale-invariant dynamics without any fine tuning of parameters or other model-specific constraints. Our analyses reveal that the specifics of the distribution of resources or competition among several tasks are not essential for the expression of scale-free dynamics. Rather, we show that scale invariance observed in the dynamics of behavior can arise from the dynamics intrinsic to the brain.power law | criticality

Experimental evidence for inherent Lévy search behaviour in foraging animals

“…Similar to most of those studies, the timing of ARS clustering in mud snails showed multi-scale search behaviour also in a homogeneous environment, implying intrinsic behavioural control [31,34,36]. Because of our novel experimental set-up, we could also demonstrate spatial multi-scale foraging behaviour in the absence of food encounter [15].…”

“…Timing of spontaneous behaviours, like flight turns in Drosophila [31], ambush waiting in marine predators [35] and activity dynamics of mice [36], as well as planned task cueing in humans [37], revealed Lévy walk characteristics without environmental feedback, indicating intrinsic control by the nervous system. In million-year-old fossil tracks, Lévy walks were suggested to have emerged from simple self-avoiding trails, again suggesting an intrinsic mechanism that has evolved as a natural adaptation [25].…”

Enhanced sensory sampling precedes self-initiated locomotion in an electric fish

“…The power spectrum of spontaneous up-transition events showed power at all frequencies (Fig. 8D), suggesting no clear periodicity features or characteristic time scale (Proekt et al, 2012).…”

Intrinsic Lévy behaviour in organisms – searching for a mechanism

“…To account for observed Lévy-like behaviour -by which I mean behaviour patterns well approximated by a truncated Lévy distribution -it has been hypothesized that (i) scale-free activities may arise from intrinsic processes [9,11,[13][14][15][16], (ii) that behavioural adaptations to changes in environmental resources may cue the switching between localized Brownian and Lévy random searching [5,7], or (iii) that sensory interactions with heterogeneous environments may give rise to Lévy movement patterns (an emergent phenomena) [17,18]. However, the origins of such potential mechanisms remain elusive.…”