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) approximately exp(-alphaL) with a branch length exponent of alpha=0.15. To evaluate the significance of this alpha 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, gamma for various simulated tunnel patterns with the different values of alpha. In simulation, the gamma was maximized at 0.15