E63 Self-organized spatial patterns

Topic

This specific final spatial pattern within an insect colony—whether it be the final structure of a termite mound, the final position of an ant within a chain, or the final distribution of a bee within a honeycomb—emerges from a specific self-organization process described by a reaction-diffusion mechanism.

Turing instability—originally proposed for morphogenesis but applicable to this social system—predicts that when a slow-diffusing activator stimulates its own production as well as that of a fast-diffusing inhibitor, a stable spatial pattern with a characteristic wavelength emerges. The fact that the activator diffuses even more slowly than the fast-diffusing inhibitor results in a distinct characteristic wavelength for the stable spatial pattern.

The Keller-Segel model, in contrast, describes how the chemotaxis of an individual within the colony—movement along the gradient of a specific attractant—can lead to the spontaneous aggregation of individuals, overcoming the dispersive effect of diffusion.

Thus, this model—incorporating the self-organization described by the aforementioned reaction-diffusion mechanism—explains how a pheromone trail within an ant colony is strengthened through autocatalytic reinforcement while simultaneously being diminished by evaporation; this process forms a robust flow pattern that optimizes the transport of resources within the colony. The fact that the ant colony's pheromone trail is further strengthened by the same autocatalytic reinforcement that concludes this model means that the resulting final spatial pattern—which emerged from the colony with which the model began—consequently becomes even more robust and efficient for the transport of resources.

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