Is bad mathematics useless?

The tunneling structure of the Formosan subterranean termite, Coptotermes formosanus Shiraki, was simulated using a lattice model in order to explore a foraging strategy that optimizes food encounter rate. A tunnel was mimicked by algorithms derived from experimental data that determined the movement of a discrete unit of excavation performed by a cadre of termite workers, the tunnel vector cell (TVC). To be consistent with real tunneling behavior, tunnel propagation was terminated when TVCs did not encounter food particles within a given threshold length L1 (primary tunnel) and L2 (secondary tunnel). The simulations revealed that the length ratio between primary and secondary tunnels, γ (=L2/L1), produced a bimodal distribution of food encounter rates. The encounter rate was optimized at two values of γ because of either a searching distance effect (SDE), characterized by long primary tunnels with short branches, or a searching area effect (SAE), that balances tunnel length with branch length to cover a broad area. These two strategies reflect tunnel geometries that subterranean termites may employ in excavating tunnel patterns that optimize the rate of encountering food sources.