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(−L) with a branch length exponent of  = 0.15. To evaluate the significance of this 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 . In simulation, the γ was maximized at 0.15 <  < 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.     

Why is the number of primary tunnels of the formosan subterranean termite,Coptotermes formosanus Shiraki (Isoptera: Rhinotermidae), restricted during foraging?

Subterranean termites forage by digging a network of tunnels to come into contact with food sources. When 1000 termites (Coptotermes formosanus Shiraki) were placed in a laboratory arena, 6.7 primary tunnels were constructed. The aim of this study was to explain the empirical observation in which termites restrict the number of primary tunnels. To this end, we constructed a model to simulate termite tunnel patterns based on empirical data and to calculate food transportation efficiency, γ, for the tunnel patterns. The efficiency was defined as the ratio of the number of encountered food particles to the sum of the shortest length from the location of encountered food particles to the initial position of growth of the tunnel. The γ was maximized when the number of primary tunnels was 5 or 6, which was fairly consistent with the empirical number of primary tunnels. This result indicated that termites may restrict the number of their primary tunnels to improve the transportation efficiency, which is directly related to their survival.     

Tunneling response of termites to a pre-formed tunnel

Subterranean termites move from place to place while foraging by tunneling through soil. During a period of foraging, they are likely to encounter a number of pre-formed tunnels created by, for example, tree roots or the breaking up of a zone of hard or compacted soil. We systematically observed the behavioral response of tunneling termites to such pre-formed, artificially constructed tunnels at widths, W, of 0.5, 1.0, 1.5, and 2.0mm, which mimicked pre-formed tunnels in the field. The two tunnels intersected at an angle, theta (=0 degrees , 10 degrees , 20 degrees , 30 degrees , 40 degrees , 50 degrees , and 60 degrees ) formed between the advance direction of a termite tunnel and the perpendicular direction of a pre-formed tunnel. For W=Wc (=0.5mm) and theta相似文献   

Estimating termite population size using spatial statistics for termite tunnel patterns

Subterranean termites build underground tunnels for foraging. The obtained food is transported to the nest through these tunnels, and consumed to maintain the termite colony. In this process, termites can cause damage to wooden structures. To develop effective control strategies to reduce termite damage, it is important to know the sizes of the termite populations in the tunnels. In this study, we proposed a method for estimating the termite population size using the spatial statistic indices including fractal dimension (FD), local density (LD), and join count statistic (JCS) for the tunnel patterns. However, the method needs further improvement to be applied in field conditions. For the method, we generated 8,000 tunnel pattern images (1,000 images for each N) using an agent-based model based on experimental data. Here, N (= 3, 4, ..., 10) represents the number of termites participating in tunnel construction in the simulation. Subsequently, we calculated the FD, LD and JCS values of the tunnel pattern and trained and verified the k-nearest neighbors (KNN) algorithm, using 5,600 and 2,400 images, respectively. The population size (N) was estimated based on the FD, LD and JCS using the KNN algorithm. The estimated accuracy for all N was 60% to 97% in the range of k = 1 to 300. If the model for tunnel pattern generation includes heterogeneous environmental conditions, the proposed method could be used to effectively estimate the actual number of termite populations. Finally, we briefly discuss the challenges affecting our model, and how these could be overcome.     

Food encounter rate of simulated termite tunnels in heterogeneous landscapes

The aim of this study was to explore how a heterogeneous landscape affects food encounter rate in the Formosan subterranean termite, Coptotermes formosanus Shiraki. To do this, a lattice model was formulated to simulate the tunneling structure of the termite. The model made use of minimized local rules derived from empirical data. In addition, a landscape structure was generated on a lattice space by using a neutral landscape model. Each lattice cell has a value h, representing spatially distributed property of the landscape (e.g., temperature or moisture). The heterogeneity of the landscape was characterized by a parameter, H controlling aggregation of lattice cells with higher values of h. Higher H values correspond to higher aggregation levels. The effect of the landscape heterogeneity on the encounter rate was clear in the presence of higher food density than in lower density. The effect was also enhanced by the increase of the number of primary tunnels.     

Movement efficiency and behavior of termites in tunnels with changing width

Subterranean termites build extensive underground galleries that consist of elaborate tunnels and channels to forage for food resources. The changes in tunnel width along the length of the tunnel are related to both biotic (e.g., termite activity) and abiotic factors (e.g., soil density). Termites transport food through the tunnels from food sources to their nest. Thus, understanding the relationship between traveling behavior in the tunnels and changing width is important to comprehend the stability of the termite ecosystem. In the present study, we explored the traveling behavior of termites in terms of movement efficiency, where the movement efficiency was defined as the time (τ) needed for a termite to pass through a tunnel. To do so, we designed artificial tunnels with linearly changing width in a two-dimensional arena. The tunnel widths, W ₁ (for the entrance) and W ₂ (for the exit), were 2, 3, 4, 5, and 6 mm. We systematically observed the traveling behavior of the termites Reticulitermes speratus kyushuensis Morimoto (Isoptera: Rhinotermitidae) in the artificial tunnels and measured τ. The value of τ increased with the increase of W ₂, regardless of W ₁. τ was longer in the case of W ₁ < W ₂ than that of W ₁ > W ₂. The experimental results can be explained by behavioral differences observed in each case. The implications of the findings are briefly discussed in relation to termite foraging efficiency and the development of individual-based models for the construction of termite tunnels.     

Prior knowledge about spatial pattern affects patch assessment rather than movement between patches in tactile-feeding mallard

1. Heterogeneity in food abundance allows a forager to concentrate foraging effort in patches that are rich in food. This might be problematic when food is cryptic, as the content of patches is unknown prior to foraging. In such case knowledge about the spatial pattern in the distribution of food might be beneficial as this enables a forager to estimate the content of surrounding patches. A forager can benefit from this pre-harvest information about the food distribution by regulating time in patches and/or movement between patches. 2. We conducted an experiment with mallard Anas platyrhynchos foraging in environments with random, regular, and clumped spatial configurations of full and empty patches. An assessment model was used to predict the time in patches for different spatial distributions, in which a mallard is predicted to remain in a patch until its potential intake rate drops to the average intake rate that can be achieved in the environment. A movement model was used to predict lengths of interpatch movements for different spatial distributions, in which a mallard is predicted to travel to the patch where it expects the highest intake rate. 3. Consistent with predictions, in the clumped distribution mallard spent less time in an empty patch when the previously visited neighbouring patch had been empty than when it had been full. This effect was not observed for the random distribution. This shows that mallard use pre-harvest information on spatial pattern to improve patch assessment. Patch assessment could not be evaluated for the regular distribution. 4. Movements that started in an empty patch were longer than movements that started in a full patch. Contrary to model predictions this effect was observed for all spatial distributions, rather than for the clumped distribution only. In this experiment mallard did not regulate movement in relation to pattern. 5. An explanation for the result that pre-harvest information on spatial pattern affected patch assessment rather than movement is that mallard move to the nearest patch where the expected intake rate is higher than the critical value, rather than to the patch where the highest intake rate is expected.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.     

Analysis of the responses of termites to tunnel irregularity

Subterranean termites build extensive underground galleries consisting of elaborate tunnels and channels to forage food resources. Diverse soil conditions surrounding the tunnels, such as soil density, may cause irregularities in the size and shape of the tunnels, and termites are likely to encounter a number of tunnel irregularities while traveling. Considering the tunnel length, how termites respond to an irregularity is likely to affect their movement efficiency, and this in turn is directly correlated to their foraging efficiency. To understand the response of termites, we designed an artificial linear tunnel with rectangular irregularities in a 2-D arena. The tunnel widths, W, were 3 and 4?mm. The rectangular irregularities were 2?mm in width and of varying heights H (2, 1, 0, ?1, and ?2?mm). The positive and negative sign of H represents a convex and concave structure, respectively. We systematically observed the movement of termites, Coptotermes formosanus Shiraki, at the irregularity and quantified the time needed, τ, for a termite to pass the irregularity. The time τ was shorter for (W, H)?=?(3, 0) and (3, ?1) than for (W, H)?=?(3, 1), (3, 2), and (3, ?2). The time τ was longer for (W, H)?=?(4, ?1), and (4, ?2), than for (W, H)?=?(4, 0), (4, 1) and (4, 2). Four types of behaviors explained the response to the irregularity. The implications of these findings are briefly discussed in relation to termite foraging efficiency.     

Tunnel orientation and search pattern sequence of the formosan subterranean termite (Isoptera: Rhinotermitidae).

Foraging behavior of the Formosan subterranean termite, Coptotermes formosanus Shiraki, was studied in the laboratory by using two-dimensional foraging arenas containing multiple foraging sites. Within each arena, 16 foraging sites were arranged in a uniform grid pattern and foragers were introduced into the arena through a central initiation site. Chi-square analysis determined the frequency of tunnels was uniformly distributed around the perimeter of the initiation site but became significantly skewed toward the foraging sites at a distance where the foraging sites could be encountered. Tunnel distribution was similar whether wood was present or absent at the foraging sites, suggesting that foragers respond to structural anomalies in the substrate rather than simply to the presence of food. Also described is the generalized sequence of events as foragers tunnel throughout the arenas.     

Quantifying the effect of colony size and food distribution on harvester ant foraging

Desert seed-harvester ants, genus Pogonomyrmex, are central place foragers that search for resources collectively. We quantify how seed harvesters exploit the spatial distribution of seeds to improve their rate of seed collection. We find that foraging rates are significantly influenced by the clumpiness of experimental seed baits. Colonies collected seeds from larger piles faster than randomly distributed seeds. We developed a method to compare foraging rates on clumped versus random seeds across three Pogonomyrmex species that differ substantially in forager population size. The increase in foraging rate when food was clumped in larger piles was indistinguishable across the three species, suggesting that species with larger colonies are no better than species with smaller colonies at collecting clumped seeds. These findings contradict the theoretical expectation that larger groups are more efficient at exploiting clumped resources, thus contributing to our understanding of the importance of the spatial distribution of food sources and colony size for communication and organization in social insects.     

Tunnel formation by Reticulitermes flavipes and Coptotermes formosanus (Isoptera: Rhinotermitidae) in response to wood in sand.

The tunneling responses of two subterranean termite species, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), to the presence of sound wood in laboratory arenas were studied. Branching pattern and the speed of tunnel construction between R. flavipes and C. formosanus also were compared. Patlak's residence index (rho) was generated using the length, width, speed of construction, and area of the primary tunnels built by termites. In the same allotted time, C. formosanus built wider and shorter primary tunnels, whereas R. flavipes built thinner and longer primary tunnels. The presence of wood did not affect termite tunnel formation. This lack of variation in tunnel formation parameters was evidenced by the inability of the termites to locate wood sources over distance, even as short as 2.5 mm, and by the similar tunneling behaviors in areas of the arena with or without wood. Patlak's model predicted the densities of tunnels with an error between 9 and 28%. in experiments with R. flavipes exposed to a range of 0-8,000 g of wood, and between 61 and 87% in experiments with C. formosanus. These results indicated that the residence index can provide a qualitative measure of the effect of habitat heterogeneity on the individual termite tunnels. The tunneling constructions strategy of these subterranean termites is discussed.     

Intake rate at differently scaled heterogeneous food distributions explained by the ability of tactile-foraging mallard to concentrate foraging effort within profitable areas

The ability to respond to spatial heterogeneity in food abundance depends on the scale of the food distribution and the foraging scale of the forager. The aim of this study is to illustrate that a foraging scale exists, and that at larger scaled food distributions foragers benefit from the ability to subdivide a continuous (non-discrete) heterogeneous environment into profitable and non-profitable areas. We recorded search patterns of mallards Anas plathyrhynchos foraging in shallow water on cryptic prey items (millet seeds), distributed at different scales. A small magnet attached to the lower mandible allowed us to record in great detail the position and movements of the bill tip within a feeding tray underlain by magnet sensors. Instantaneous intake rate was determined in a subsequent experiment. We successfully determined the foraging scale (about 2×2 cm), defined as the scale above which foragers do respond (coarse scaled distribution) and below which foragers do not respond (fine scaled distribution) to spatial heterogeneity, by concentrating foraging effort within areas of high food density. A response resulted in a significantly higher intake rate, compared to a homogeneous distribution with an equal overall density. Unlike systematic search cell revisitation was common in trials, and at coarse scaled food distributions even slightly (but significantly) more frequently observed than predicted for random search. Mallards respond to food capture by restricting displacement (area restricted search) at food distributions that are considered to be clumped for the forager (large scaled coarse distributions). We argue that partitioning the environment at the foraging scale in itself could be a mechanism to concentrate foraging efforts within profitable areas, because mallard were able to respond to heterogeneity at coarse scaled food distributions even when non-clumped (i.e. without conducting area restricted search).     

Minimizing moving distance in deposition behavior of the subterranean termite

Subterranean termite nests are located underground and termites forage out by constructing tunnels to reach food resources, and tunneling behavior is critical in order to maximize the foraging efficiency. Excavation, transportation, and deposition behavior are involved in the tunneling, and termites have to move back and forth to do this. Although there are three sequential behaviors, excavation has been the focus of most previous studies. In this study, we investigated the deposition behavior of the Formosan subterranean termite, Coptotermes formosanus Shiraki, in experimental arenas having different widths (2, 3, and 4 mm), and characterized the function of deposited particles. We also simulated moving distance of the termites in different functions. Our results showed that total amounts of deposited particles were significantly higher in broad (4 mm width) than narrow (2 mm) tunnels and most deposited particles were observed near the tip of the tunnel regardless of tunnel widths. In addition, we found that deposited particles followed a quadratic decrease function, and simulation results showed that moving distance of termites in this function was the shortest. The quadratic decrease function of deposited particles in both experiment and simulation suggested that short moving distance in the decrease quadratic function is a strategy to minimize moving distance during the deposition behavior.     

Simulation study on the tunnel networks of subterranean termites and the foraging behavior

Most subterranean termites forage for food by creating tunnel galleries underground. These tunnel networks reflect a compromise between foraging efficiency and other environmental constraints, such as soil hardness and moisture content. Thus, understanding tunnel networks is important for understanding foraging behavior. Due to the difficulties in direct observation of tunneling patterns in the field, we used a theoretical approach for this analysis. We first constructed a lattice model to simulate the tunnel networks of Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar) on the basis of the experimental data provided by Su et al. (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 (3), 471–483.). Using this model and two of its modified versions, we explored the relationship between the food encounter rate and food distributions and analyzed how this relationship is influenced by changes in the tunnel characteristic constituents, such as the branching tunnel length and frequency. Additionally, we investigated the effects of landscape heterogeneity on the foraging efficiency. In the discussion, we briefly introduced our novel individual-based model comprising individual termites and their surroundings, and we addressed the necessity of this model in the functioning of the network and the formation of the network in relation to foraging behavior.     

Effects of concentration,distance, and application methods of Altriset (Chlorantraniliprole) on eastern subterranean termite (Isoptera: Rhinotermitidae)

The effects of various concentrations, distance, and application methods of Altriset (Chlorantraniliprole) were investigated against one of the most destructive termites, the eastern subterranean termite, Reticulitermes flavipes Kollar. Three laboratory experiments were conducted. First, we examined the concentration effect of treating the soil contiguously to established foraging tunnels at a fixed 1 m distance. The results demonstrated 100% termite control in 19 d posttreatment at 100 and 50 μg/g and 27% termite mortality at 25 μg/g. Second, we tested the distance effect of the soil treatment (2 and 4 m) on the efficacy of Altriset to the satellite termite populations at a fixed 50 μg/g concentration. This resulted in 100% termite control in 22 d posttreatment at both 2 and 4 m. Third, we examined the effect of differing application methods using 12.5 and 25 μg/g prior to the establishment of foraging tunnels at a fixed 1m distance. This illustrated 100% termite control in 9 d posttreatment at 25 μg/g and 12 d posttreatment at 12.5 μg/g. The third experiment demonstrated soil treatments that were applied prior to termite tunnel establishment had greater efficacy than applications made post tunnel construction. Our results provide a comprehensive understanding about the efficacy of Altriset treatments on eastern subterranean termites.     

Measurement of the time required for termites to pass each other in tunnels of different curvatures

Subterranean termites construct complex tunnel networks for foraging. During travel in the tunnels, termites often encounter one another when passing in opposite directions. Such encounters are likely to affect the “movement efficiency,” which is the time required for a termite to travel a certain distance in a tunnel. In this study, we explored how individual–individual encounters affect movement efficiency in tunnels by measuring the time (τ) taken by two termites to pass one another in tunnels of different curvatures. Artificial tunnels of 5 cm in length and variable widths (W) of 2, 3, or 4 mm were made. Tunnel distance (D) was 2, 3, 4, or 5 cm. When D had a higher value, curvature was lower. When W = 2, τ was significantly shorter in the tunnel with D = 5 than in tunnels of D = 2, 3, or 4, whereas τ was statistically the same for D = 2, 3 and 4. When W = 3, τ was shorter in the tunnel with D = 5 than for D = 3 and 4, while τ was longer in the tunnel with D = 2 than for D = 3 and 4. When W = 4, τ was longer in the tunnels with D = 2 and 3 than for D = 4 and 5. Based on these observations, 3 types of termite behavior were identified: biased walking, backward walking, and zigzag walking. We considered these results in relation to foraging efficiency.     

基于Ripley的K(r)函数和分形维数的梭梭种群空间格局

应用Ripley的K(r)函数和分形维数,研究了古尔班通古特沙漠土质、沙质、盐土和石砾质4种生态类型梭梭在不同发育阶段的分布格局和分形特征.结果表明:沙质、盐土和石砾质生态类型中的梭梭种群呈显著聚集分布,而土质生态类型梭梭种群仅在1～18m范围内呈聚集分布,说明荒漠植物群落通过聚集分布适应其生存的环境;梭梭不同发育阶段的分布格局不同,幼苗和幼树呈聚集分布,成年树呈随机分布.与Ripley的K(r)函数相比,关联维数能反映种群的个体对空间占据能力的强弱,但不能直接反映干旱区种群的个体聚集/非聚集.此外,3种分形维数对样地内梭梭种群个体数量和植株大小较为敏感.     

Simulation study to determine why only some termites are active during tunneling activity

It has been known that some termites are responsible for tunnel excavation for foraging, while others are not involved in the excavation. The biological reason for this is that the resting termites are a backup for the termites that have used up their energy in the tunneling activity. In this study, we build an agent‐based model (ABM) wherein agents (simulated termites) follow simple rules that govern their behavior. In this model, the agents are endowed with a directional vector that has been shown to exist in real termites, but they do not communicate through pheromonal or physical marking of excavation sites. They move toward the tunnel tips, tunnel when their progress in that direction is blocked, and transport the excavated soil. Using the model, we investigated the work efficiency of termites in constructing tunnels and transporting food; the efficiency was defined as the inverse value of tunnel connectivity plus tunnel expansion speed. Biologically, the connectivity is related to the energy to be used for termites to transport food through tunnels, and the tunnel expansion speed is related to the energy required for constructing tunnels. Simulation results showed that the efficiency was maximized at an intermediate number of termites. This means that termites were better to be inactive to maintain the high efficiency when too many workers are present in the colony. We briefly discuss the strength and weakness of the ABM and the values of this study in relation to termite foraging strategy.