Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting

Abstract

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties –including Lévy flights– in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.

Stationary superstatistics distributions of trapped run-and-tumble particles

“…Notoriously, the stationary distribution of the particle positions shows an accumulation of particles around the boundaries of con-Typeset by REVT E X finement (see, for instance, Ref. [26] for trajectories of worker termites in a circular arena, Ref. [27] for confined colloidal rollers in a circular disk, or Ref.…”

Inverse Square Lévy Walks are not Optimal Search Strategies for d≥2

“…strategies maximising the capture rate η = lim t→∞ n t /t with respect to α, where n t is the mean number of targets detected at time t) are studied. (a) In the first case of "revisitable targets", meaning that, as soon as detected, a target reappears and stays immobile at the same location, the authors claim that in the small density limit the encounter rate is optimized for a Lévy exponent α → 1 , the so called inverse square Lévy walk, and independently of the small scale characteristics of p(l) or space dimension d. (b) In the second case of "destructive search" where each target can be found only once, the optimal strategy is not of Lévy type, but reduces to a simple lin-ear ballistic motion for all d.The optimality of inverse square Lévy walks claimed in [7] is at the core of the Lévy hypothesis, which has been the reference theoretical framework for the analysis of trajectories of broad classes of living systems, from molecular motors [8] to cells [9] and foraging animals [6,7,[10][11][12][13] ; many studies have indeed interpreted field data as Lévy walks, thereby concluding that their observation was the result of a selection process based on the optimality claimed in [7]. In fact, since then the relevance to field data of the condition (a) of revisitable targets has been questioned [14][15][16][17], and the identification of Lévy patterns from real data has been debated [18,19].…”

Suitable Light Regimes for Filming Termites in Laboratory Bioassays

“…Being easily captured from conspicuous and populous nests, this species large individuals allow video recording without macro lenses, and are hence an obvious choice for lab bioassays footage. Miramontes et al (2014), for instance, studying patterns of spatial exploratory behavior in individual termites, video-recorded the movement of C. cumulans workers continuously for 5-6 hours. In order to accurately track every termite cartesian location during the assay, the arena was constantly illuminated by a cold white fluorescent lamp.…”