Stigmergic construction and topochemical information shape ant nest architecture.

The nests of social insects are not only impressive because of their sheer complexity but also because they are built from individuals whose work is not centrally coordinated. A key question is how groups of insects coordinate their building actions. Here, we use a combination of experimental and modeling approaches to investigate nest construction in the ant Lasius niger. We quantify the construction dynamics and the 3D structures built by ants. Then, we characterize individual behaviors and the interactions of ants with the structures they build. We show that two main interactions are involved in the coordination of building actions: (i) a stigmergic-based interaction that controls the amplification of depositions at some locations and is attributable to a pheromone added by ants to the building material; and (ii) a template-based interaction in which ants use their body size as a cue to control the height at which they start to build a roof from existing pillars. We then develop a 3D stochastic model based on these individual behaviors to analyze the effect of pheromone presence and strength on construction dynamics. We show that the model can quantitatively reproduce key features of construction dynamics, including a large-scale pattern of regularly spaced pillars, the formation and merging of caps over the pillars, and the remodeling of built structures. Finally, our model suggests that the lifetime of the pheromone is a highly influential parameter that controls the growth and form of nest architecture.

The role of colony size on tunnel branching morphogenesis in ant nests.

Many ant species excavate nests that are made up of chambers and interconnecting tunnels. There is a general trend of an increase in nest complexity with increasing population size. This complexity reflects a higher ramification and anastomosis of tunnels that can be estimated by the meshedness coefficient of the tunnelling networks. It has long been observed that meshedness increases with colony size within and across species, but no explanation has been provided so far. Since colony size is a strong factor controlling collective digging, a high value of the meshedness could simply be a side effect of a larger number of workers. To test this hypothesis, we study the digging dynamics in different group size of ants Messor sancta. We build a model of collective digging that is calibrated from the experimental data. Model's predictions successfully reproduce the topological properties of tunnelling networks observed in experiments, including the increase of the meshedness with group size. We then use the model to investigate situations in which collective digging progresses outward from a centre corresponding to the way tunnelling behaviour occurs in field conditions. Our model predicts that, when all other parameters are kept constant, an increase of the number of workers leads to a higher value of the meshedness and a transition from tree-like structures to highly meshed networks. Therefore we conclude that colony size is a key factor determining tunnelling network complexity in ant colonies.

Characterization of spatial networklike patterns from junction geometry.

We propose a method for quantitative characterization of spatial networklike patterns with loops, such as surface fracture patterns, leaf vein networks, and patterns of urban streets. Such patterns are not well characterized by purely topological estimators: also patterns that both look different and result from different morphogenetic processes can have similar topology. A local geometric cue--the angles formed by the different branches at junctions--can complement topological information and allow the quantification of the large scale spatial coherence of the pattern. For patterns that grow over time, such as fracture lines on the surface of ceramics, the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment. We apply the method to various networklike patterns and find a continuous but sharp dichotomy between two classes of spatial networks: hierarchical and homogeneous. The former class results from a sequential growth process and presents large scale organization, and the latter presents local, but not global, organization.

Percolation in insect nest networks: evidence for optimal wiring.

Optimization has been shown to be a driving force for the evolution of some biological structures, such as neural maps in the brain or transport networks. Here we show that insect networks also display characteristic traits of optimality. By using a graph representation of the chamber organization of termite nests and a disordered lattice model, it is found that these spatial nests are close to a percolation threshold. This suggests that termites build efficient systems of galleries spanning most of the nest volume at low cost. The evolutionary consequences are outlined.

The growth and form of tunnelling networks in ants.

Many biological networks grow under strong spatial constraints, where the large-scale structure emerges from the extension, the branching and intersection of growing parts of the network. One example is provided by ant tunnelling networks, which represent the most common nest architecture in ants. Our goal was to understand how these network structures emerge from the tunnel growth dynamics. We used a standardized two-dimensional set-up shaped as a disk and studied the characteristics of tunnel growth in terms of initiation, propagation and termination of new digging sites and found that they can be described with simple probabilistic laws. We show that a model based on these simple laws and for which parameters were measured from the sand disks experiments can account for the emergence of several topological properties that were observed in experimental networks. In particular, the model accurately reproduced an allometric relation between the number of edges and the number of nodes, as well as an invariance of the node degree distribution. The model was then used to make predictions about the resulting networks' topology when the geometry of the sand substrate was shaped as a square. Experiments aimed at testing the model's predictions showed that the predictions were indeed validated. Both in the model and in the experiments, there was a similar trend for the node degree distribution tail to be steeper in the square sand patch than in the disk sand patch, while other characteristics such as the meshedness (i.e. how densely the network is internally connected) remained constant. Because network growth based on branching/fusion events is widespread in biological systems, this general model might provide useful insights for the study of other systems and, more generally, the evolution of spatial networks in biological systems.