Optimal length distribution of termite tunnel branches for efficient food search and resource transportation

Subterranean termites excavate branching tunnels for searching and transporting food in soil. Experimentally, the length distribution of the branch tunnels, P(L), was characterized by the exponentially decaying function, P(L) exp(−αL) with a branch length exponent of α = 0.15. To evaluate the significance of this α value, we used a lattice model to simulate tunnels of the Formosan subterranean termite, Coptotermes formosanus Shiraki in featureless soil and computed the ratio of energy gain for obtained food to loss for transporting food for a given time, γ for various simulated tunnel patterns with the different values of α. In simulation, the γ was maximized at 0.15 < α < 0.20 for the number of primary tunnels N = 6, 8, and 10. Our results indicate that tunnels with branch length distributions similar to those derived from empirical tunnel patterns result in tunnels made up of highly efficient paths to search and transport resources.