- Email: [email protected]
Rounding a corner of a bent termite tunnel and tunnel traffic efficiency
Available online at www.sciencedirect.com
Behavioural Processes 77 (2008) 135–138
Rapid report
Rounding a corner of a bent termite tunnel and tunnel traffic efficiency Sang-Hee Lee ∗ , Paul Bardunias, Nan-Yao Su Department of Entomology and Nematology, Ft. Lauderdale Research and Education Center, University of Florida, Ft. Lauderdale, FL 33314, USA Received 2 March 2007; received in revised form 22 June 2007; accepted 26 June 2007
Abstract Subterranean termites construct underground tunnels, tens to hundreds of feet, to reach feeding sites and to transport food items to their nest. To ensure a high rate food return to the nest, an optimized tunnel should be constructed. We found that termites (Coptotermes formosanus Shiraki) fill the corner of a bent tunnel with soil particles excavated from tunnel tip where their digging behavior is activated. The corner-filling behavior, eventually, made a sharp corner smooth-rounded. In the present study, we showed that the corner-filling behavior could play an important role in improving the tunnel traffic efficiency. To do this, we compared the termites’ time spent for passing corners between with a right-angled flat tip (RA-corner), corresponding to the sharp corner, and with a rounded tip (R-corner) corresponding to the smooth-rounded corner. As a result, the passing time in the R-corner was significantly shorter than in the RA-corner. In addition, tunnel width effect was discussed in terms of individual movement. © 2007 Elsevier B.V. All rights reserved. Keywords: Termite foraging; Termite tunnel network; Tunneling behavior; Traffic efficiency
1. Introduction Subterranean termites and ants are social insects that live in colonies that may contain hundreds of thousands to millions of individuals. The colony members disperse throughout the soil, constructing underground tunnel network, tens to hundreds of meters, to reach feeding sites (Mikheyev and Tschinkel, 2004; Tschinkel, 2004). They should build tunnels that allow for efficient traffic flow or they risk a loss of fitness because energy that could be allocated to reproduction may be used to transporting food. Experimental evidence indirectly supports the existence of evolved structures tailored for efficiency. For instance, tunnel geometry of subterranean termites exhibited branching angle (between the primary and the secondary tunnel) of 50◦ on the average (Su et al., 2004). This appears to have converged on the branching angles of ant paths (Acosta et al., 1993). Buhl et al. (2004a) also found that when the tunnel networks of ants were mapped onto planar graphs composed of the vertices corresponding intersections between tunnels, and the edges
∗ Corresponding author at: Ft. Lauderdale Research and Education Center, University of Florida, 3205 College Ave, Ft. Lauderdale, FL 33314, USA. Tel.: +1 954 577 6351; fax: +1 954 475 4125. E-mail address: [email protected] (S.-H. Lee).
0376-6357/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2007.06.012
representing tunnels, the networks belonged to a same topological family and showed several striking invariants such as the distribution of vertex degree that follows a power law. The length of secondary tunnels of subterranean termites was characterized by the frequency distribution of branch length P(L)∼ exp(−αL) with a branch length exponent, α = 0.15 as obtained from empirical tunnel patterns (Lee et al., 2006). From these studies, we conjecture that the efficient tunnels may be established through two means; one is the regulation of structural properties such as tunnel branch length and branching angle (Su et al., 2004; Puche and Su, 2001), and the other is the adjustment of topological properties such as tunnel volume and its connectivity (Buhl et al., 2004a,b; Campora1 and Grace, 2004; Rasse and Deneubourg, 2001). Combinational optimization of the two means is most likely to be a solution for constructing traffic efficient tunnels. However, inferring from the flow of vehicles in a highway (Smeed, 1967, 1968), we hypothesize that the smoothness (or curvature) of tunnel may be another mechanism to improve the traffic efficiency so as to cope with individual flow delay resulting from the congested traffics in the tunnels. In the present study with the Formosan subterranean termite (Coptotermes formosanus Shiraki) in two-dimensional arenas, we carried out an experiment to examine if termites construct a tunnel without sharp corners and investigated the effect of the tunnel width and geometry on tunnel traffic. We compared the
136
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Fig. 1. A two-dimensional arena consisted of three layers (13 cm × 13 cm) of clear acryl (2.0 mm in thickness) with the middle layer to create a circular space (10 cm in diameter and 2 mm in height) between two outer layers.
termites’ time spent for passing corners between with a rightangled flat tip (RA-corner), corresponding to the sharp corner, and with a rounded tip (R-corner) corresponding to the smoothrounded corner. In addition, tunnel width effect was discussed in relation to the spent time. 2. Materials and methods Termites were collected from a C. formosanus colony with underground monitoring stations as described by Su and Scheffrahn (1986) in the spring of 2006. Each station contained spruce blocks of wood inside a 3.78-l plastic bucket with a removable lid installed approximately 30 cm in the soil with 3 cm of the bottom cut-off. Termites were separated from these
blocks and processed immediately in the laboratory. They were stored at 27 ± 2 ◦ C in plastic boxes with thin moist wood chips before use. The experimental arena consisted of three layers (13 cm × 13 cm) of clear acryl (2.0 mm in thickness) with the middle layer to create a circular space (10 cm in diameter and 2 mm in height) between two outer layers. The top and middle layers of the arena had a hole (1.5 cm in diameter) drilled through them to act as an introduction site for the termites. Blue or yellow Sand (0.3–0.35 mm sieved) moistened by deionized water (≈7% by sand weight) was added respectively to two parts of the middle space, which separated to two domains, being contiguous with each other, to serve as the foraging substrate. The sand in the middle layer was compacted to a bulk density (≈1.3 g/cm3 ). After this, various bent tunnels were artificially excavated in sand substrates by using templates. The bent tunnels had one of two types of corner, a right-angled (RAcorner) or a rounded (R-corner), and had four different widths W = 2, 3, 4 and 5 mm. The tunnel tips were located at the interface line between the two domains in order to observe the position of sand deposition that resulted from new excavation (Fig. 1). The arena was placed in the horizontal position at the room temperature (26 ◦ C) and 30 termites, including three soldiers, were introduced into the arena via the hole in the top two layers. Above the arena a video camera (Sony GR-D22U) was installed, which enabled the recording of the termite behavior for 2 h. Using an A/D-converter (Samsung DVD-120), the videotape was digitized in real time (30 frames/sec). The corner-passing time of a termite defined as the traveling time between the two 8 mm stretches of tunnel and around the corner between them was measured in the R-corner and in the RA-corner. For the R-corner, sample size for W = 2, 3, 4 and 5 mm were 71, 85, 47, and 31, respectively. For the RA-corner, sample size for W = 2, 3, 4 and 5 mm were 45, 62, 36, and 34,
Fig. 2. (a) Termites digging behavior at the tunnel tip, (b) the region of blue sand growing up along tunnel walls, (c) the RA-corner filled with the blue sand and (d) the back-lighted tunnel image confirming the fully-filled space.
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Fig. 3. The average passing time for the RA- and the R-corner where W = 2, 3, 4 and 5 mm. Each error bar represents the standard deviation of individuals.
respectively. Five repetitions were performed for each corner and each tunnel width.
137
subsequent heading. Perhaps a R-corner, displaying no disparity in width with the flanking tunnels, does not elicit this delaying response. As the tunnel width W increased from 2 to 3 mm, the difference of the passing time between RA- and R-corner was significantly decreased, while for W > 3 mm, the difference was changed only slightly. This was attributed to the fact that as W increased the number of termites stopping at the RA-corner decreased because they had enough space to turn their body without encountering the right-angled wall near the corner. The wider tunnel width diluted the influence of the RA-corner on the corner-passing movement. But too wide a width caused an increase in the passing time due to their zig-zag walking. The balance of the two effects resulted in little change in passing time for W = 2, 3 and 4 mm. This implies that to construct a tunnel for efficient traffic flow, termites need to not only smooth a sharp-angled corner but also select an appropriate tunnel width in relation to the balance of the two effects. In this study, we measured only individual corner-passing time but in many cases, some termites competed with each other to pass the same corner at the same time. High traffic flow and inter-individual interference may alter the efficiency of these structures further and will be addressed in future studies.
3. Results Termites were introduced into the hole connected to the bent tunnel with the RA-corner, passed through the pre-formed tunnel until reaching the tunnel tip and initiating digging behavior (Fig. 2(a)). Termites transported the blue sand particles and pasted them on both sides of tunnel wall (Fig. 2(b)). When termites were presented with a pre-formed tunnel with a RAcorner, they deposited sand in the outer corner of the bend so as to make the RA-corner smoothly rounded (Fig. 2(c)). To ensure that soil was being uniformly deposited to fill the space caused by the RA-corner rather than simply being plastered on the top and bottom plane of the arena we photographed the arena with strong back-lighting, and the beam did not penetrate the filled corner indicating that the space was fully filled (Fig. 2(d)). Significant difference in the passing time between RA- and R-corner was found (t-test, t = 8.05, p < 0.05). Termites passed the R-corner more quickly than RA-corner (Fig. 3). In the RAcorner, the corner-passing time was longer at W = 2 mm than at W = 3, 4, and 5 mm. In the R-corner, the passing time was much less influenced by the tunnel width W. 4. Discussion In the present study, we showed that termites passed the R-corner (smooth-rounded corner) more quickly than the RAcorner (sharp-corner). This was due to the fact that when termites were faced with the RA-corner, many stopped walking and antennated laterally to touch the tunnel wall momentarily (∼1–2 s). This pause accompanied by antennation may be the result of termites reacting to their perception of the unusual geometry of the RA-corner and having to actively orient their
Acknowledgments We would like to thank P. Ban and R. Pepin (Univ. of Florida) and for technical assistance. This research was supported by the Florida Agricultural Experiment Station and a grant from USDA-ARS under the grant agreement No. 58-6435-30075. References Acosta, F.J., Lopez, F., Serrano, J.M., 1993. Branching angles of ant trunk trails as an optimization cue. J. Theor. Biol. 160, 297–310. Buhl, J., Gautrais, J., Sole, R.V., Kuntz, P., Valverde, S., Deneuborug, J.L., Theraulaz, G., 2004a. Efficiency and robustness in ant networks of galleries. Eur. Phys. J. B. 42, 123–129. Buhl, J., Gautrais, J., Deneubourg, J.-L., Theraulaz, G., 2004b. Nest excavation in ants: group size effects on the size and structure of tunneling networks. Natuwissenschaften 91, 602–606. Campora1, C.E., Grace, J.K., 2004. Effect of average worker size on tunneling behavior of formosan subterranean termite colonies. J. Insect Behav. 17, 777–791. Lee, S.-H., Bardunias, P., Su, N.-Y., 2006. Food encounter rates of simulated termite tunnels with variable food size/distribution pattern and tunnel branch length. J. Theor. Biol. 243, 493–500. Mikheyev, A.S., Tschinkel, W.R., 2004. Nest architecture of the ant Formica pallidefulva: strucutre, costs and rules of excavation. Insect. Soc. 51, 30– 36. Puche, H., Su, N.-Y., 2001. Tunnel formation by Reticulitermes flavipes and Coptotermes formosanus (Isoptera: Rhinotermitidae) in response to wood in sand. J. Econ. Entomol. 94, 1398–1404. Rasse, P., Deneubourg, J.L., 2001. Dynamics of nest excavation and nest size regulation of Lasius niger (Hymenoptera: Formicidae). J. Insect Behav. 14, 433–449. Smeed, R.J., 1967. The road capacity of city centers. High-way Res. Record 169, 22–29.
138
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Smeed, R.J., 1968. Traffic studies and urban congestion. J. Trans. Econ. Policy 2, 33–70. Su, N.-Y., Scheffrahn, R.H., 1986. A method to access, trap, and monitor field populations of the Formosan subterranean termite (Isoptera: Rhinotermitidae) in the urban environment. Sociobiology 12, 299–304.
Su, N.-Y., Stith, B.M., Puche, H., Bardunias, P., 2004. Characterization of tunneling geometry of subterranean termites (Isoptera: Rhinotermitidae) by computer simulation. Sociobiology 44, 471–483. Tschinkel, W.R., 2004. The nest architecture of the Florida harvester ant, Pogonomyrmex badius. J. Insect. Sci. 4, 21.
Behavioural Processes 77 (2008) 135–138
Rapid report
Rounding a corner of a bent termite tunnel and tunnel traffic efficiency Sang-Hee Lee ∗ , Paul Bardunias, Nan-Yao Su Department of Entomology and Nematology, Ft. Lauderdale Research and Education Center, University of Florida, Ft. Lauderdale, FL 33314, USA Received 2 March 2007; received in revised form 22 June 2007; accepted 26 June 2007
Abstract Subterranean termites construct underground tunnels, tens to hundreds of feet, to reach feeding sites and to transport food items to their nest. To ensure a high rate food return to the nest, an optimized tunnel should be constructed. We found that termites (Coptotermes formosanus Shiraki) fill the corner of a bent tunnel with soil particles excavated from tunnel tip where their digging behavior is activated. The corner-filling behavior, eventually, made a sharp corner smooth-rounded. In the present study, we showed that the corner-filling behavior could play an important role in improving the tunnel traffic efficiency. To do this, we compared the termites’ time spent for passing corners between with a right-angled flat tip (RA-corner), corresponding to the sharp corner, and with a rounded tip (R-corner) corresponding to the smooth-rounded corner. As a result, the passing time in the R-corner was significantly shorter than in the RA-corner. In addition, tunnel width effect was discussed in terms of individual movement. © 2007 Elsevier B.V. All rights reserved. Keywords: Termite foraging; Termite tunnel network; Tunneling behavior; Traffic efficiency
1. Introduction Subterranean termites and ants are social insects that live in colonies that may contain hundreds of thousands to millions of individuals. The colony members disperse throughout the soil, constructing underground tunnel network, tens to hundreds of meters, to reach feeding sites (Mikheyev and Tschinkel, 2004; Tschinkel, 2004). They should build tunnels that allow for efficient traffic flow or they risk a loss of fitness because energy that could be allocated to reproduction may be used to transporting food. Experimental evidence indirectly supports the existence of evolved structures tailored for efficiency. For instance, tunnel geometry of subterranean termites exhibited branching angle (between the primary and the secondary tunnel) of 50◦ on the average (Su et al., 2004). This appears to have converged on the branching angles of ant paths (Acosta et al., 1993). Buhl et al. (2004a) also found that when the tunnel networks of ants were mapped onto planar graphs composed of the vertices corresponding intersections between tunnels, and the edges
∗ Corresponding author at: Ft. Lauderdale Research and Education Center, University of Florida, 3205 College Ave, Ft. Lauderdale, FL 33314, USA. Tel.: +1 954 577 6351; fax: +1 954 475 4125. E-mail address: [email protected] (S.-H. Lee).
0376-6357/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.beproc.2007.06.012
representing tunnels, the networks belonged to a same topological family and showed several striking invariants such as the distribution of vertex degree that follows a power law. The length of secondary tunnels of subterranean termites was characterized by the frequency distribution of branch length P(L)∼ exp(−αL) with a branch length exponent, α = 0.15 as obtained from empirical tunnel patterns (Lee et al., 2006). From these studies, we conjecture that the efficient tunnels may be established through two means; one is the regulation of structural properties such as tunnel branch length and branching angle (Su et al., 2004; Puche and Su, 2001), and the other is the adjustment of topological properties such as tunnel volume and its connectivity (Buhl et al., 2004a,b; Campora1 and Grace, 2004; Rasse and Deneubourg, 2001). Combinational optimization of the two means is most likely to be a solution for constructing traffic efficient tunnels. However, inferring from the flow of vehicles in a highway (Smeed, 1967, 1968), we hypothesize that the smoothness (or curvature) of tunnel may be another mechanism to improve the traffic efficiency so as to cope with individual flow delay resulting from the congested traffics in the tunnels. In the present study with the Formosan subterranean termite (Coptotermes formosanus Shiraki) in two-dimensional arenas, we carried out an experiment to examine if termites construct a tunnel without sharp corners and investigated the effect of the tunnel width and geometry on tunnel traffic. We compared the
136
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Fig. 1. A two-dimensional arena consisted of three layers (13 cm × 13 cm) of clear acryl (2.0 mm in thickness) with the middle layer to create a circular space (10 cm in diameter and 2 mm in height) between two outer layers.
termites’ time spent for passing corners between with a rightangled flat tip (RA-corner), corresponding to the sharp corner, and with a rounded tip (R-corner) corresponding to the smoothrounded corner. In addition, tunnel width effect was discussed in relation to the spent time. 2. Materials and methods Termites were collected from a C. formosanus colony with underground monitoring stations as described by Su and Scheffrahn (1986) in the spring of 2006. Each station contained spruce blocks of wood inside a 3.78-l plastic bucket with a removable lid installed approximately 30 cm in the soil with 3 cm of the bottom cut-off. Termites were separated from these
blocks and processed immediately in the laboratory. They were stored at 27 ± 2 ◦ C in plastic boxes with thin moist wood chips before use. The experimental arena consisted of three layers (13 cm × 13 cm) of clear acryl (2.0 mm in thickness) with the middle layer to create a circular space (10 cm in diameter and 2 mm in height) between two outer layers. The top and middle layers of the arena had a hole (1.5 cm in diameter) drilled through them to act as an introduction site for the termites. Blue or yellow Sand (0.3–0.35 mm sieved) moistened by deionized water (≈7% by sand weight) was added respectively to two parts of the middle space, which separated to two domains, being contiguous with each other, to serve as the foraging substrate. The sand in the middle layer was compacted to a bulk density (≈1.3 g/cm3 ). After this, various bent tunnels were artificially excavated in sand substrates by using templates. The bent tunnels had one of two types of corner, a right-angled (RAcorner) or a rounded (R-corner), and had four different widths W = 2, 3, 4 and 5 mm. The tunnel tips were located at the interface line between the two domains in order to observe the position of sand deposition that resulted from new excavation (Fig. 1). The arena was placed in the horizontal position at the room temperature (26 ◦ C) and 30 termites, including three soldiers, were introduced into the arena via the hole in the top two layers. Above the arena a video camera (Sony GR-D22U) was installed, which enabled the recording of the termite behavior for 2 h. Using an A/D-converter (Samsung DVD-120), the videotape was digitized in real time (30 frames/sec). The corner-passing time of a termite defined as the traveling time between the two 8 mm stretches of tunnel and around the corner between them was measured in the R-corner and in the RA-corner. For the R-corner, sample size for W = 2, 3, 4 and 5 mm were 71, 85, 47, and 31, respectively. For the RA-corner, sample size for W = 2, 3, 4 and 5 mm were 45, 62, 36, and 34,
Fig. 2. (a) Termites digging behavior at the tunnel tip, (b) the region of blue sand growing up along tunnel walls, (c) the RA-corner filled with the blue sand and (d) the back-lighted tunnel image confirming the fully-filled space.
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Fig. 3. The average passing time for the RA- and the R-corner where W = 2, 3, 4 and 5 mm. Each error bar represents the standard deviation of individuals.
respectively. Five repetitions were performed for each corner and each tunnel width.
137
subsequent heading. Perhaps a R-corner, displaying no disparity in width with the flanking tunnels, does not elicit this delaying response. As the tunnel width W increased from 2 to 3 mm, the difference of the passing time between RA- and R-corner was significantly decreased, while for W > 3 mm, the difference was changed only slightly. This was attributed to the fact that as W increased the number of termites stopping at the RA-corner decreased because they had enough space to turn their body without encountering the right-angled wall near the corner. The wider tunnel width diluted the influence of the RA-corner on the corner-passing movement. But too wide a width caused an increase in the passing time due to their zig-zag walking. The balance of the two effects resulted in little change in passing time for W = 2, 3 and 4 mm. This implies that to construct a tunnel for efficient traffic flow, termites need to not only smooth a sharp-angled corner but also select an appropriate tunnel width in relation to the balance of the two effects. In this study, we measured only individual corner-passing time but in many cases, some termites competed with each other to pass the same corner at the same time. High traffic flow and inter-individual interference may alter the efficiency of these structures further and will be addressed in future studies.
3. Results Termites were introduced into the hole connected to the bent tunnel with the RA-corner, passed through the pre-formed tunnel until reaching the tunnel tip and initiating digging behavior (Fig. 2(a)). Termites transported the blue sand particles and pasted them on both sides of tunnel wall (Fig. 2(b)). When termites were presented with a pre-formed tunnel with a RAcorner, they deposited sand in the outer corner of the bend so as to make the RA-corner smoothly rounded (Fig. 2(c)). To ensure that soil was being uniformly deposited to fill the space caused by the RA-corner rather than simply being plastered on the top and bottom plane of the arena we photographed the arena with strong back-lighting, and the beam did not penetrate the filled corner indicating that the space was fully filled (Fig. 2(d)). Significant difference in the passing time between RA- and R-corner was found (t-test, t = 8.05, p < 0.05). Termites passed the R-corner more quickly than RA-corner (Fig. 3). In the RAcorner, the corner-passing time was longer at W = 2 mm than at W = 3, 4, and 5 mm. In the R-corner, the passing time was much less influenced by the tunnel width W. 4. Discussion In the present study, we showed that termites passed the R-corner (smooth-rounded corner) more quickly than the RAcorner (sharp-corner). This was due to the fact that when termites were faced with the RA-corner, many stopped walking and antennated laterally to touch the tunnel wall momentarily (∼1–2 s). This pause accompanied by antennation may be the result of termites reacting to their perception of the unusual geometry of the RA-corner and having to actively orient their
Acknowledgments We would like to thank P. Ban and R. Pepin (Univ. of Florida) and for technical assistance. This research was supported by the Florida Agricultural Experiment Station and a grant from USDA-ARS under the grant agreement No. 58-6435-30075. References Acosta, F.J., Lopez, F., Serrano, J.M., 1993. Branching angles of ant trunk trails as an optimization cue. J. Theor. Biol. 160, 297–310. Buhl, J., Gautrais, J., Sole, R.V., Kuntz, P., Valverde, S., Deneuborug, J.L., Theraulaz, G., 2004a. Efficiency and robustness in ant networks of galleries. Eur. Phys. J. B. 42, 123–129. Buhl, J., Gautrais, J., Deneubourg, J.-L., Theraulaz, G., 2004b. Nest excavation in ants: group size effects on the size and structure of tunneling networks. Natuwissenschaften 91, 602–606. Campora1, C.E., Grace, J.K., 2004. Effect of average worker size on tunneling behavior of formosan subterranean termite colonies. J. Insect Behav. 17, 777–791. Lee, S.-H., Bardunias, P., Su, N.-Y., 2006. Food encounter rates of simulated termite tunnels with variable food size/distribution pattern and tunnel branch length. J. Theor. Biol. 243, 493–500. Mikheyev, A.S., Tschinkel, W.R., 2004. Nest architecture of the ant Formica pallidefulva: strucutre, costs and rules of excavation. Insect. Soc. 51, 30– 36. Puche, H., Su, N.-Y., 2001. Tunnel formation by Reticulitermes flavipes and Coptotermes formosanus (Isoptera: Rhinotermitidae) in response to wood in sand. J. Econ. Entomol. 94, 1398–1404. Rasse, P., Deneubourg, J.L., 2001. Dynamics of nest excavation and nest size regulation of Lasius niger (Hymenoptera: Formicidae). J. Insect Behav. 14, 433–449. Smeed, R.J., 1967. The road capacity of city centers. High-way Res. Record 169, 22–29.
138
S.-H. Lee et al. / Behavioural Processes 77 (2008) 135–138
Smeed, R.J., 1968. Traffic studies and urban congestion. J. Trans. Econ. Policy 2, 33–70. Su, N.-Y., Scheffrahn, R.H., 1986. A method to access, trap, and monitor field populations of the Formosan subterranean termite (Isoptera: Rhinotermitidae) in the urban environment. Sociobiology 12, 299–304.
Su, N.-Y., Stith, B.M., Puche, H., Bardunias, P., 2004. Characterization of tunneling geometry of subterranean termites (Isoptera: Rhinotermitidae) by computer simulation. Sociobiology 44, 471–483. Tschinkel, W.R., 2004. The nest architecture of the Florida harvester ant, Pogonomyrmex badius. J. Insect. Sci. 4, 21.