Self-organized biotectonics of termite nests

Abstract

The termite nest is one of the architectural wonders of the living world, built by the collective action of workers in a colony. Each nest has several characteristic structural motifs that allow for efficient ventilation, cooling, and traversal. We use tomography to quantify the nest architecture of the African termite Apicotermes lamani, consisting of regularly spaced floors connected by scattered linear and helicoidal ramps. To understand how these elaborate structures are built and arranged, we formulate a minimal model for the spatiotemporal evolution of three hydrodynamic fields-mud, termites, and pheromones-linking environmental physics to collective building behavior using simple local rules based on experimental observations. We find that floors and ramps emerge as solutions of the governing equations, with statistics consistent with observations of A. lamani nests. Our study demonstrates how a local self-reinforcing biotectonic scheme is capable of generating an architecture that is simultaneously adaptable and functional, and likely to be relevant for a range of other animal-built structures.

Keywords: collective animal behavior; ecophysiology; morphogenesis; stigmergy; termite nests.

Fig. 1.

Digital reconstruction of A. lamani nests reveals layered floors and chambers connected by linear and helicoidal ramps. (A and B) Cutaway view of two A. lamani nests, collected around Libreville (Gabon): MeMo14 (A) and MeMo13 (B). The nests were digitized with X-ray computer tomography and reconstructed in three dimensions (3D). (C) A large A. lamani nest (Left, MeMo80) collected in 2008 near Pointe Noire (Republic of the Congo) with examples of a linear ramp (C, i, red dots) and two helicoidal ramps with opposing chirality (C, ii, red and cyan dots).

Fig. 2.

Statistical analysis of A. lamani nests shows consistent floor and ramp spacing. (A–C, Top) Nest MeMo80. (A–C, Bottom) Nest MeMo14. (A) Representative vertical slices of nest structure with floors labeled in average height order. (B) Histograms for floor thickness (pink) and spacing between floors (cyan), measured in millimeters, corresponding to the nest depicted in A. Both the thickness of and spacing between floors tend to fall within a consistent band in each nest. (C) Density plot for the horizontal distance from a ramp to the nearest other ramp on the same floor (red) or on an adjacent floor above or below (blue), corresponding to the nest depicted in A. Ramps on the same floor tend to be spaced out, while ramps on adjacent floors often connect directly, resulting in minimal spacing.

Fig. 3.

Biotectonic model predicts floor spacing and ramp emergence in termite nests. (A) Model schematic of the feedback loop driving nest construction, highlighting the interactions between nest material $u$, termite workers $n$, and secreted pheromone $\rho$. (B) Illustration of a local region of a nest, showing the processes in our model. Termite workers migrate preferentially to low-density regions and cannot travel through very high-density regions. Workers remove dirt throughout the nest but are more likely to deposit dirt near pheromones which they release during deposition. Pheromones are assumed to have a low diffusivity and hence provide a local signal. (C) Diagrams of edge and screw dislocations in floor patterning. Edge dislocations that result from floor misalignment can give rise to linear ramps, while screw dislocations can lead to helicoidal ramps that pivot about a slip plane. (D) Three-dimensional reconstruction of a nest simulated according to our construction model, shown here at two angles. This simulated nest contains one linear ramp (i, blue) and two helicoidal ramps (ii and iii, red).

Fig. 4.

Simulated nests resemble natural A. lamani nests and produce helicoidal ramps across a range of parameters. (A) Time snapshots of helicoidal ramp emergence during simulated nest construction, from early (Top) to late (Bottom) in the building period. (B) Heatplot for the frequency of helicoidal ramps in a simulated nest as a function of the two model parameters governing pheromone dynamics. (C) Histograms for floor thickness (pink) and spacing between floors (cyan), as measured in millimeters, averaged over simulated nests. The histograms show a pattern similar to the natural nests in Fig. 2B. (D) Density plot for the horizontal distance from a ramp to the nearest other ramp on the same floor (red) or on an adjacent floor above or below (blue), averaged over simulated nests and resembling the natural patterns shown in Fig. 2C. (E) The power spectrum of nest density, averaged over horizontal slices, peaks sharply at a one-floor period for both simulated (gray) and natural (purple) nests, indicating regularly spaced floor structures.