Using hidden Markov models to characterize termite traveling behavior in tunnels with different curvatures

Subterranean termites live underground and build tunnel networks to obtain food and nesting space. After obtaining food, termites return to their nests to transfer it. The efficiency of termite movement through the tunnels is directly connected to their survival. Tunnels should therefore be optimized to ensure highly efficient returns. An optimization factor that strongly affects movement efficiency is tunnel curvature. In the present study, we investigated traveling behavior in tunnels with different curvatures. We then characterized traveling behavior at the level of the individual using hidden Markov models (HMMs) constructed from the experimental data. To observe traveling behavior, we designed 5-cm long artificial tunnels that had different curvatures. The tunnels had widths (W) of 2, 3, or 4 mm, and the linear distances between the two ends of the tunnels were (D) 20, 30, 40, or 50 mm. High values of D indicate low curvature. We systematically observed the traveling behavior of Coptotermes formosanus shiraki and Reticulitermes speratus kyushuensis and measured the time (τ) required for a termite to pass through the tunnel. Using HMM models, we calculated τ for different tunnels and compared the results with the τ of real termites. We characterized the traveling behavior in terms of transition probability matrices (TPM) and emission probability matrices (EPM) of HMMs. We briefly discussed the construction of a sinusoidal-like tunnels in relation to the energy required for termites to pass through tunnels and provided suggestions for the development of more sophisticated HMMs to better understand termite foraging behavior.