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We present a simple three-dimensional model to describe the autonomous expansion of a substrate which grows driven by the local mean curvature of its surface. The model aims to reproduce the nest construction process in arboreal Nasutitermes termites, whose cooperation may similarly be mediated by the shape of the structure they are walking on, for example focusing the building activity of termites where local mean curvature is high. We adopt a phase-field model where the nest is described by one continuous scalar field and its growth is governed by a single nonlinear equation with one adjustable parameter d. When d is large enough the equation is linearly unstable and fairly reproduces a growth process where the initial walls expand, branch and merge, while progressively invading all the available space, which is consistent with the intricate structures of real nests. Interestingly, the linear problem associated to our growth equation is analogous to the buckling of a thin elastic plate under symmetric in-plane compression which is also known to produce rich pattern through non linear and secondary instabilities. We validated our model by collecting nests of two species of arboreal Nasutitermes from the field and imaging their structure with a micro-CT scanner. We found a strong resemblance between real and simulated nests, characterised by the emergence of a characteristic length-scale and by the abundance of saddle-shaped surfaces with zero-mean curvature which validates the choice of the driving mechanism of our growth model., Comment: 24 pages 6 figures + 9 pages supplementary material

Group living animals form aggregations and flocks that remain cohesive in spite of internal movements of individuals. This is possible because individual group members repeatedly adjust their position and motion in response to the position and motion of other group members. Here we develop a theoretical approach to address the question, what general features -- if any -- underlie the interaction rules that mediate group stability in animals of all species? We do so by considering how the spatial organisation of a group would change in the complete absence of interactions. Without interactions, a group would disperse in a way that can be easily characterised in terms of Fick's diffusion equations. We can hence address the inverse theoretical problem of finding the individual-level interaction responses that are required to counterbalance diffusion and to preserve group stability. We show that an individual-level response to neighbour densities in the form of Weber's law (a 'universal' law describing the functioning of the sensory systems of animals of all species) results in an 'anti-diffusion' term at the group level. On short time scales, this anti-diffusion restores the initial group configuration in a way which is reminiscent of methods for image deblurring in image processing. We also show that any non-homogeneous, spatial density distribution can be preserved over time if individual movement patterns have the form of a Weber's law response. Weber's law describes the fundamental functioning of perceptual systems. Our study indicates that it is also a necessary -- but not sufficient -- feature of collective interactions in stable animal groups.

We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general., Comment: 11 pages, 5 figures. Published in Phy. Rev. E. Supplement materials are available at http://journals.aps.org/pre/supplemental/10.1103/PhysRevE.92.062810/YHE-TermiteNestModel-SM-V1.2.pdf

Background: Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we address specifically the problem of what interaction responses support different nearest neighbour configurations in terms of mutual position and distance. Results: We find that the different interaction rules observed in different animal species may be a simple consequence of the relative positions that individuals assume when they move together, and of the noise inherent with the movement of animals, or associated with tracking inaccuracy. Conclusions: The anisotropic positioning of individuals with respect to their neighbours, in combination with noise, can explain several aspects of the movement responses observed in real animal groups, and should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, we provide a frame to discriminate movement interactions that signal directional conflict from those underlying consensual group motion.