Scale-free movement patterns in termites emerge from social interactions and preferential attachments

Abstract

As the number or density of interacting individuals in a social group increases, a transition can develop from uncorrelated and disordered behavior of the individuals to a collective coherent pattern. We expand this observation by exploring the fine details of termite movement patterns to demonstrate that the value of the scaling exponent μ of a power law describing the Lévy walk of an individual is modified collectively as the density of animals in the group changes. This effect is absent when termites interact with inert obstacles. We also show that the network of encounters and interactions among specific individuals is selective, resembling a preferential attachment mechanism that is important for social networking. Our data strongly suggest that preferential attachments, a phenomenon not reported previously, and favorite interactions with a limited number of acquaintances are responsible for the generation of Lévy movement patterns in these social insects.

Visibility graphs of animal foraging trajectories

“…This exponent is different from the one found for Brownian motion [41] and suggests the onset of long-range temporal correlations. Interpretation of these results is in agreement with by Paiva et al [29], where authors argue that Lévy-like trajectories are more likely to appear in termites with social interactions than in isolated ones.…”

“…Second, interpretation of these patterns in graph space suggests that the onset of strategies closer to the Levy walk hypothesis are notably enhanced when individuals interact. It seems plausible that this change in movement strategy would be a result of the information exchange and social trapping that is provided by social contacts [29]. Third, our visibility-graph analysis suggests the onset of collective effects at intermediate densities and unveils a non-monotonic trend that pinpoints an optimal density where collective effects -and complexityare maximized.…”

“…Using the visibility algorithm [30], we converted our time series containing termite displacements (with both segmentation methods) into networks and proceeded to compute specific topological properties of these. Following Paiva et al [29], we use this new approach to investigate how social interactions between termites modulate their movements and their foraging behavior.…”

“…Our results are well aligned to these works, as our visibility graph analysis suggests that the emergence of Lévy walks is indeed a densityinduced collective phenomenon. We wonder if, at least in the case of social insects, Lévy-like processes might thus emerge not only for foraging success and optimized biological encounters [29], but also perhaps driven by other biological mechanisms such as those mentioned above.…”

“…In these studies, the termite trajectories were analyzed by means of standard mean squared displacement, structure functions, autocorrelation functions, and probability functions histograms. Although these are valuable, well-established tools to identify normal and anomalous diffusion, it was only recently that more sophisticated studies established that indeed Lévy walks are common in the movements of termites [29]. Importantly, time series obtained from biological foraging and searching behavior usually involve nonlinear processes, so their analysis in principle needs the use of different techniques of increasing complexity, e.g.…”