Network-based model of the growth of termite nests

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.

Figure 1

Empirical network description in the case of nest C9 (Cubitermes sp., Central African Republic; see Fig. 1B in [28]). (a) Each tunnel or edge is represented as a vector in spherical coordinates, (b) tunnel lengths ($r$) distribution, (c) distribution of the vertical component ($\theta$, 0 points upwards and $\pi$ points downwards), and (d) distribution of the horizontal component ($\varphi$). (c) and (d) are symmetric and periodic respectively because both ${\vec{c}}_1-{\vec{c}}_2$ and ${\vec{c}}_2-{\vec{c}}_1$ are used.

Figure 2

Degree distribution of the real networks (data: red line) and the networks generated by the BBP model (BBP: black line), by the RGG model (RGG: blue line), and RP model (RP: magenta line). $P\left(k\right)$ are relative frequencies (summing to 1).

Figure 3

Analyzed Thoracotermes nest T29 with its network representation (middle) and a simulated network (right) by the BBP model. The pink node (lower right) indicates the initial node of the simulated network. Note that while there are isolated chambers in the original network, isolated chambers are more prevalent in the simulated nests. See the Discussion for further comments.

Figure 4

Comparison between the real networks (data: red bar) and the networks generated by the BBP model (BBP: gray bar), by the RGG model (RGG: blue bar), and RP model (RP: magenta bar). (a) Size of the largest connected components (LCC). (b) Average topological distance between any two nodes in the LCC. (c) The backbone link ratio. (d) Local graph redundancy. The error bars represent standard deviations computed from 1000 model generated networks.

Figure 5

Sensitivity analysis of the BBP model. The sizes of largest connected components (LCC) are depicted in (a), (e), (i), and (m). LCC is shown as the fraction of the original network size. The average distances are depicted in (b), (f), (j), and (n). The backbone link ratios are depicted in (c), (g), (k), and (o). The local graph redundancies are depicted in (d), (h), (l), and (p). Note that nest P79b with $\xi =0.451$ and nest T29 with $\xi =0.551$ lie outside the range of simulated $\xi$ values; they therefore do not appear in figures (e) to (h) and (a) to (d), respectively. The spatial information of Nest C9 was considered as physical constraints for the analysis.