The effect of surface topography on the ball-rolling ability of Kheper lamarcki (Scarabaeidae)

Dung beetles and other coprophagous insects are attracted to dung and compete for this food source. In response to the intense inter- and intraspecific competition at the dung pat in combination with quick desiccation, various strategies have evolved to secure nutrition (Halffter and Matthews, 1966; Bernon, 1981). While most species live directly in or below the dung pile and share the same space, the telecoprids have evolved the ability to mould and roll dung balls away from the dung pile and their competitors (Matthews, 1963; Halffter and Matthews, 1966; Cambefort and Hanski, 1991; Ybarrondo and Heinrich, 1996; Scholtz, 2009).

The most effective way to maximize the distance to the dung pile in the shortest time period and thus protect the dung ball from competitors, is to escape with the ball along a straight path. The initial bearing direction is ‘reset’ every time a (new) dung ball is formed (Baird et al., 2012), which could be a strategy to avoid clustering of competitors. On flat surfaces, dung beetles are able to roll a ball along a nearly perfect straight path (Dacke et al., 2013). This requires a reliable orientation mechanism (Byrne et al., 2003; Dacke et al., 2003, 2011, 2021). Natural surfaces, however, are rarely flat and as locomotion is the result of a complex interaction between the beetle and the substrate structure, it is reasonable to assume that the surface topography will impact the trajectories of the ball-rolling beetles. Since telecoprid dung beetles are found in a wide range of habitats, from deserts to tropical rainforests (Cambefort, 1991), they also encounter a wide range of characteristic surface features. It has been observed that the apparently effortless, quick and straight rolling behavior on a smooth and sandy surface becomes tortuous and ungainly on rough terrain (Baird et al., 2012; Khaldy et al., 2019). In complex environments, the beetles are frequently confronted with obstacles that result in deviations from a straight-line course.

To date, little attention has been paid to the effect of surface topography on the ball-rolling ability of dung beetles. While most studies were conducted on flat terrain, some insight has been gained on the effect of individual obstacles on the rolling trajectory. Those studies have shown that a dung beetle maintained its initial bearing and continued along its straight path after overcoming or siding the obstacle that has forced the beetle to deviate from its straight path. (Matthews, 1963; Byrne et al., 2003). To include the full complexity of natural surface topographies, Bijma et al. (2021) numerically modelled the transportation of a spherical object on complex terrain with varying characteristic scales of surface roughness. In this study, natural perturbations were simulated by a characteristic scale of a wave vector. By decoupling the motion of the sphere from the externally generated force of the beetle, only the effect of surface topography on the shape of the trajectory was studied. According to these simulations, there is a strong correlation between effective ball transportation (time, distance, work) and the ratio of the size of the ball relative to the size of the terrain roughness. Furthermore, there is a negative correlation between surface irregularities of a size comparable to the ball diameter and the efficiency of ball transportation (Bijma et al., 2021). Frantsevich et al. (1993) previously studied the behavior of two dung beetle species on inclines, but as the beetle species they used do not roll balls, their study rather addressed posture adaptations during locomotion on slopes.

The aim of the present study was to experimentally investigate the effect of surface topography and inclination on the efficiency of ball transportation by telecoprid dung beetles. We specifically studied the influence of the surface topography on the ability of the African species Kheper lamarcki to transport a dung ball in a straight line on four different surface topographies that were generated according to a numerical model previously used by Bijma et al. (2021). The effect of four surface slopes (2.5, 5.0, 7.5 and 10.0 deg) on ball-rolling ability was also assessed. By comparing the experimental data with the modelled trajectories on identical surfaces (Bijma et al., 2021), we are able to quantify the passive influence of the surface topography on the ball/beetle trajectories. This allowed us to draw conclusions about optimal ball size in relation to the surface topography and incline.

For the experiments, adult individuals of the species Kheper lamarcki MacLeay 1821 (Coleoptera, Scarabaeidae) were collected at the game farm ‘Stonehenge’, 70 km northwest of Vryburg, South Africa (24.32°E, 26.39°S). After collection, the beetles were kept outdoors at Thornwood Lodge (28.02°E, 24.77°S) in the shade in soil-filled plastic boxes (30×22×22 cm), each containing about 20 individuals and fed daily with fresh cow dung. Prior to experiments, several specimens were placed in large plastic containers and provided with fresh cow dung. Beetles that were actively moulding dung balls were used for the experiments.

Three experimental surfaces were made using a 3D printer reproducing the same surfaces as previously used in the study of Bijma et al. (2021). We used MATLAB (v. R2013 A) to produce surfaces, which have a semi-fractal structure with a well-defined Fourier spectrum and amplitude of roughness. Details of the numerically generated surfaces have been described in Bijma et al. (2021). The maximum amplitude of the surface roughness was set to a constant value of 17.7 mm. This value corresponds to the average radius of a naturally moulded dung ball of K. lamarcki (Khaldy et al., 2019). To study the interaction between the ball and the surface topography, the average wave vector q₀, was scaled in relation to the ball diameter to be smaller, larger and much larger than the average dung ball (0.5×, 1.8× and 6.6× ball diameter on the surface with the small, intermediate and large average wave vector, respectively). A flat surface with a corresponding infinitely high average wavelength was used as reference (Fig. 1).

For production, the surface models were divided into 16 segments (10×10 cm) using the open-source software Blender (v.2.8 Blender Foundation; www.blender.org), which made it possible to manufacture them using a Prusa i3 MK2 3D printer (Prusa Research, Prague, Czech Republic) with heat-resistant acrylonitrile–butadiene–styrene (ABS) filament (Filamentworld, Neu-Ulm, Germany). The layer height was set to 0.2 mm to minimize steps in the surface model. Once printed, the surfaces of the segments were additionally covered with a thin layer of fine-grained sand using Uhu all-purpose adhesive (Bolton Adhesives, Rotterdam, Netherlands). This step was necessary to generate some natural microroughness of the surface, to enable mechanical interlocking with the claws and spines of the beetle tarsi and tibiae, respectively (Dai et al., 2002; Bußhardt et al., 2014). The segments were assembled and fixed with additional connectors to form the three experimental ‘arenas’ for beetles.

The tracks of 20 individual beetles were recorded during ball rolling from a top view at 30 frames s⁻¹ (Sony DSC-RX10, Sony Imaging Products & Solutions Inc., Tokyo, Japan). While transporting their dung balls, the beetles walk backwards, head facing the ground (Fig. 2A). The forelegs are used for propulsion while the middle and hind legs steer and stabilize the ball. The beetles were placed in the centre of a horizontally aligned arena alongside or on top of their dung balls (diameter, 3.59±0.12 cm; mass, 24.37±1.74 g; mean±s.d.) (Fig. 2B).

The beetles immediately climbed on the balls and rotated about their vertical axis before they started rolling their dung balls across the surface in an individually selected direction. Once they reached a linear distance of 20 cm from the starting point, the individual was picked up and the trial was terminated. Before the procedure was repeated and the dung beetles were again placed with their dung ball in the centre of the arena, the surface was rotated clockwise by an angle of 90 deg. Since K. lamarcki maintains its initial rolling direction until it moulds a new dung ball (Baird et al., 2010), rotating the surface underneath the beetle produces a quasi-new surface topography with the same characteristic wave vector. Hence, each beetle was placed on the same topography four times before the surface was replaced. The order in which the beetles were confronted with the four different surface topographies (hereafter referred to as: flat, small, intermediate and large) was randomized. In total, 20 individuals were recorded.

The flat surface topography was also used to investigate the effect of inclination on the ball-rolling ability (Fig. 2C). Again, the beetles were placed alongside their ball in the centre of the inclined flat surface (0, 2.5, 5, 7.5 and 10±0.1 deg) in a randomized order. Each condition was repeated three times before the inclination was changed. The exit bearings and failures – where the dung beetle lost contact with the surface – were recorded for 18 individuals (Movie 1). To ensure optimal conditions for straight-line orientation (Dacke et al., 2014), all field experiments were performed under a clear sky at medium sun elevations (45–60 deg)

Most of the data were at least partially not normally distributed. A Friedman one-way repeated-measure ANOVA by ranks test was therefore performed to evaluate the influence of surface characteristics on the ball-rolling efficiency. If significant differences were found, a Dunn′s post hoc test with Bonferroni correction was performed. As the speed on the different surfaces was normally distributed, a one-way repeated measures ANOVA test was performed. For the frequency data, a χ² test was performed. If frequencies below 5 were observed, a Fisher's exact test was done. A Rayleigh's test of Uniformity was used to ascertain whether the distributions of exit angles differed from uniformity. If not stated otherwise, reported values are median±median absolute deviation (MAD).

Even though all surfaces were successfully mastered by K. lamarcki, the surface topographies had a strong impact on both the shapes and distributions of the trajectories. On a flat surface (Fig. 3A), the trajectories were evenly distributed (Rayleigh′s test, =0.04, P=0.89) and the initial bearing was roughly maintained throughout the path.

On surfaces with intermediate to large average wave vectors (AWVs), the trajectories were strongly influenced by the surface topography (Movie 2). The tracks were no longer randomly distributed and a clustering of tracks became visible (Fig. 3B,C). Preferred path directions were observed in the depressions, whereas higher elevations were avoided. Converting the height profile to a slope profile (Fig. S1) allowed for the determination of corresponding slopes. On surfaces with the large and medium AWVs (Fig. S1A,B), beetles are unable to roll their dung ball through the steepest sloping areas (highlighted in yellow), demonstrating slopes or slope regions that are nearly inaccessible. Only when the dung beetles encountered local surface inclines at an almost right angle, were they able to overcome the slope and reach the summit of the elevation, rather than being forced around it. However, even in this scenario, a significant number of trajectories aimed for the hill with the steep gradient but finally bypassed the hill right or left. On the surfaces with large AWV, dung beetles were observed to traverse slopes only up to approximately 22 deg. Steeper inclines were consistently avoided by the beetles and thus remained unexplored.

As the ratio of the height and the average distance between maxima of the surface structures (aspect ratio) increased from ‘intermediate’ (Fig. 3C) to ‘small’ (Fig. 3D), the distribution of the trajectories became more random again. The tracks became comparable to the flat surface but areas with slightly higher track density were still observed. At a higher magnification, the tracks were less straight compared with the flat surface (Fig. S2A,B). Owing to the irregularities resulting from the small AWV, slight directional changes occurred more frequently where the ball was forced in a different direction. The inclination on this surface was the most extreme and reached up to 70 deg. Interestingly, despite the steep inclination, the beetles traversed these regions.

The qualitatively different shapes of trajectories on the four topographies resulted in significant differences in the detour (⁠=107.76, P<0.001, Friedman), time (⁠=117.59, P<0.001, Friedman), speed (F_df=3,312=7.547, P<0.001, repeated measures ANOVA) and curvature (⁠=84.828, P<0.001, Friedman). When comparing the four consecutive runs, no significant differences were observed (detour: =7.605, P=0.055, Friedman; time: =4.504, P=0.212, Friedman; speed: F_df=3,312=0.202, P=0.895, Repeated measures ANOVA; curvature: =5.914, P=0.116, Friedman). Hence, there did not appear to be any ‘learning effect’ during the four runs.

The small directional changes on the surface with the small AWV resulted in significantly longer detour values (119.59±55.75 mm), compared with the flat surface (50.05±30.36 mm) (P<0.001) (Fig. 4A). The detour length increased (50.05±30.36 mm, 77.75±47.7 mm, 141.45±57.69 mm) with a decreasing AWV [infinitely high (corresponds to the flat surface), large, intermediate AWVs, respectively]. The slight decrease towards the smallest AWV (119.59±55.75 mm) was not significant (P=0.06) but seems to point towards a decrease with continuing decrease of the AWVs. Because both the time (Fig. 4B) and curvature (Fig. 4D) are related to the detour, similar trends were also observed for these parameters.

The average speed is defined as the distance covered by the dung ball to traverse a linear distance of 20 cm, divided by the time needed to cover it. Naturally, detours affect the time required to reach the perimeter at 20 cm linear distance. It is interesting to note that a minimum speed of 5.55±2.02 cm s⁻¹ was found at an intermediate AWV, which approximates the diameter of the average size of a naturally moulded dung ball. Whether the differences in speed are related to the surface characteristics alone or to a combination of these and the consequences of lost control of the ball remains unclear. To investigate this, we analysed the rolling speed, which is defined as the distance covered by the dung ball during a specific time interval, excluding the distance and time corresponding to the loss of control over the ball. No significant difference was found between the average speed and the rolling speed on identical surfaces (Fig. S3B). This means that the difference in the average speed is related to the different surface topographies and is not the result of the ball control loss by the beetle.

Loss of control (where either both front legs or both hind legs lost contact with the ground or with the ball for more than 0.1 s) on the flat surface rarely happened (four times out of 80 runs only). However, there was a sharp increase in the total number of losses of control, when the surfaces became rough and challenging to traverse (85, 171 and 75 times during 80 runs on the surfaces with the large, intermediate and small AWVs, respectively). We found a correlation between the number of times the beetles lost control and the AWV of the surface topography. Again, a clear maximum was found at the intermediate AWV where the AWV and ball diameter are similar. On those surfaces the ball was able to fully enter the valleys of the surface topography. We did not observe any significant difference between the number of losses of control during the four consecutive runs (⁠=1.609, P=0.657, Pearson).

In the rare cases (n=4) that control was lost on the flat surface, the median time required to regain control was rather long (2.1±1.1 s) compared to the other AWVs (Fig. S3A). The reason for this is that, due to our definition of loss of control, cases in which control was regained after 0.1 s were also included in the analysis. While on surfaces with small, intermediate and large AWVs, in most cases of loss of control both hind legs were still in contact with the ball and thus control was regained almost immediately. In the few cases where the beetle lost control of the ball on the flat surface, contact with the ball was completely lost and consequently the time needed for reorientation was much longer. On the structured surfaces, the time of loss of control seemed to be independent of the AWV (⁠5.275, P=0.509, time binned in: 0.10–0.39 s; 0.40–0.69 s; 0.70–0.99 s and >1.0 s). In contrast, the distance of tumbling seemed to be roughly positively correlated to the AWV, i.e. the distance of tumbling decreased with decreasing AWV (19.3±9.1 mm, 24.2±8.4 mm, 44.3±25.1 mm on the surface with the small, intermediate and large AWVs, respectively). Although the surfaces with small and large AWVs did not differ greatly with respect to the number of losses of control (75 and 85, respectively), the events were significantly different with respect to the distance covered before control was regained (⁠=42.307, P<0.001, Pearson; distance binned in 1–20 mm, 20–40 mm 40–60 mm and >60 mm; Fig. S3C). It should be noted that the recording was terminated as soon as the dung ball and the beetle passed the perimeter. The dung beetle and its ball, however, often rolled completely off the experimental surface having the large AWV. Therefore, the distance after which control was regained is underestimated for that surface.

The maximum number of orientation dances (n=24) were carried out on the surface topography with the intermediate AWV. In addition, a significant difference in the number of losses of control that resulted in an orientation dance was found between the different surfaces (⁠=7.799, P=0.020, Pearson; because of the small sample size of only four losses of control, the flat surface was not considered for statistical analysis) but not between the four consecutive runs (⁠=1.75, P=0.626, Pearson). On the surface with the intermediate AWV, 14% of the losses of control resulted in an orientation dance, whereas on surfaces with the small and large AWVs, only 4% and 6% resulted in an orientation dance, respectively. It should be noted that, on the surface with the largest AWV, this number was most likely underestimated, as in case of control loss, when the dung ball with the beetle passed the arena perimeter further actions were not experimentally recorded. It is possible that subsequent orientation dances followed outside the experimental arena.

The exit angles and success rates of rolling trajectories on inclined surfaces were recorded. The trajectories were divided into two categories: successful (black dots) and unsuccessful (red dots) (Fig. 5). In successful trials, the beetles managed to roll the dung ball to the periphery of the arena without losing control of the ball. The number of successful trials was significantly different between inclinations (⁠=75.538, P<0.001, Pearson) and decreased with increasing inclination from 91% (49 out of 54) at an inclination of 0 deg to 19% (10 out of 54) on 10 deg inclined surfaces.

The exit angles on the flat surface were relatively uniformly distributed in space with only a slightly higher frequency observed in the western quadrant (19 out of 54). A clustering of exit angles was observed with an increasing inclination of the surface (⁠50.605, P<0.001, Pearson). The frequency of exits per quadrant (Fig. 5F) decreased significantly with an increasing inclination angle in the quadrants facing west (19 to 2, P=0.007), while the frequency in the southern quadrant increased (13 to 39, P<0.001). However, the slight decreases in frequency in the quadrants facing east (10 to 3) and north (12 to 10) were not significant (⁠=6.148, P=0.18, Pearson; =2.033, P=0.73, Pearson, respectively).

The increase in exit angles in the southern quadrant is the result of a clustering of unsuccessful trails at the lowest quadrant of the arena. A critical inclination of 7.5 deg was observed, at which successful trails were no longer independent of the initial bearing direction. Successful trajectories were almost exclusively (with the exception of one trail in the eastern quadrant) in the upward (northern quadrant) or downward (southern quadrant) direction. With an additional increase of slope by 2.5 deg (to 10 deg), K. lamarcki was exclusively able to successfully roll balls upwards. However, the frequency of upward rolling did not change with increasing inclination, suggesting that the beetles do not adapt their initial bearing in response to the inclination. Additionally, when comparing the three consecutive runs (Fig. S3D), no significant difference in success rate was observed (⁠=1.108, P=0.575, Pearson). Hence, there did not appear to be any learning effect during the three runs.

Telecoprid dung beetles traverse a variety of different environments. It is known that the straight ball-rolling behaviour on flat and sandy surface becomes more tortuous as soon as the surface becomes challenging (Baird et al., 2012). Here, we show that the surface topography strongly influences the distribution and the kinematic properties of the ball-rolling trajectories of K. lamarcki. We observed a maximum in terms of time, detour and curvature of the trajectories and, at the same time, a minimum in terms of the average speed for those surfaces where the mean wavelength of the surface topography approaches the diameter of the dung ball (Fig. 4). In light of these results, we propose that there is a correlation between the kinematic properties of the trajectories and the ratio between the ball diameter and the mean wavelength of the surface topography. We assume that when the wavelength approaches the size of the dung ball (i.e. it fits perfectly into the troughs of the surface topography), the harder it will become for the dung beetle to transport its ball without significant interruptions. This is also supported by the high degree of loss of control and subsequent orientation dances on the surfaces with the intermediate AWV (Fig. 4), where the ball often gets caught briefly (Fig. S3A). If the mean wavelength becomes infinitely large or small, which in principle is the same, ball rolling will most likely become easier, resulting in straighter paths again.

Previously, trajectories of a ball that was pushed in a fixed direction on surfaces with similar surface characteristics were numerically simulated (Bijma et al., 2021). With regard to the kinematic parameters, such as detour, time and speed, these simulations revealed a similar correlation between ball diameter and average distance between the surface irregularities [cf. fig. 5B,D in Bijma et al. (2021) with Fig. 4 herein]. As the AWV approaches the ball radius, both time and detour increases. Once the AWV becomes either very large or small, both parameters decrease again. Although the dung beetle experiment did not reveal a significant difference in time and detour between the intermediate and small AVWs, we propose that a further reduction in AWV will likely lead to a continued decrease in both time and detour.

The comparison of the experimental data with the modelled trajectories enabled us to assess the question whether the real trajectories of live dung beetles are passively affected by surface topography and/or to which extend they actively counteract the course of the ball. On a flat surface, the most effective way is to maintain a straight path, maximizing distance over time. The distribution of the trajectories (simulated and real) shows similar characteristics [cf. fig. 2 in Bijma et al. (2021) with Fig. 3 herein]. In both cases, the tracks are relatively straight and have little detours compared with the other topographies. The trajectories on the surfaces with an AWV that is comparable or a bit larger with respect to the ball diameter, strongly deviate from a straight line and run along the valleys [cf. fig. 2 in Bijma et al. (2021) with Fig. 3C herein]. This supports the conclusion that the trajectories are strongly influenced by the surface topography and especially by the slopes (Fig. 5).

Matthews (1963) noticed that slopes pose challenges for dung beetles. He concluded that it might be difficult to roll a ball sideways or downward on a slope without losing control. Some additional challenges for the sensory system of the dung beetle during their locomotion on slopes are also discussed by Frantsevich et al. (1993). Our results support these observations and indicate a threshold of 10 deg at which K. lamarcki is no longer able to successfully transport its dung ball over a distance of 20 cm while maintaining continuous contact with the surface (no tumbling or rolling of the surface together with the dung ball) in an arbitrary direction. The only successful runs are upward and restricted within the upper quadrant of the circle (with one exception). At the same time, the probability of a successful run also decreases to below 19%.

The analysis of the slope map reveals fascinating insights into dung beetles' behaviour concerning various slope conditions. Our findings demonstrate a distinct avoidance of areas with steep slopes on the surface with large and intermediate AWV. However, this pattern is not observed on the surface with the small AWV, despite the actual maximum slope reaching up to 70 deg, noticeably higher than on the other two surfaces with maximum slopes of 55 deg and 25 deg (intermediate and large AWV, respectively). It is noteworthy that on all surfaces, some dung beetles were at least for a very short distance capable of overcoming slopes much steeper than the maximum 10 deg slope used in the slope experiment. On the surface with the large AVW, we occasionally observed instances where beetles successfully rolled their balls over inclines of 22 deg (see Fig. S1A). This is consistent with the observations of Leung et al. (2021), who observed K. lamarcki rolling a ball uphill on slopes of 20 deg. However, Leung et al. (2021) did not specify the distance covered or the frequency of failures. In our experiment, the distance was relatively short (<5 cm), and only a few beetles that initially aimed for an elevation managed to traverse over the hill. Instead, most beetles deviated to the right or left of the elevation. In their natural environment, dung beetles are likely to encounter inclined terrain over longer distances, potentially causing difficulties for many dung beetles. Hence, steep slopes per se are no obstacle. The addition of the distance they have to travel is what makes it problematic. As the AWV decreases, as seen on the surface with the intermediate and small AWV, dung beetles are occasionally able to traverse slopes of up to 50 deg (intermediate AWV) or even 70 deg (small AWV). Since the distances with such high inclinations are short, approximately 1 cm on the intermediate AWV, the beetle can simply roll the ball over the slope without having to walk with it. However, even in such cases, the ball is usually guided around the hills.

The ball only appeared to move in a straight line over the surface and the hills across the surface with the small AWV. It is noteworthy that the sinking depth of the dung ball on the surface with the small AWV is limited to an average of only 2.3 mm. As a result, these slopes are likely perceived as small bumps rather than significant inclines and can presumably be easily overcome. Calculating the actual slopes helps us to understand why the trajectories accumulate in the troughs on the surfaces with an intermediate and large AWV and reveal regions that are hardly accessible.

It is still difficult to determine to what extent the beetles try to counteract the passive meandering of the ball generated by the topography or to what extent they actively follow the path of least resistance in the troughs of the surface topography. There is evidence that dung beetles rigidly adhere to their initial bearing. In previous studies, it has been observed that they do not seem to modify their trajectory to avoid obstacles but rather keep pushing in the initial set direction, trying to go over the obstacle rather than around it (Matthews, 1963; Baird et al., 2012). In addition, we did not observe a significant improvement in the ability to walk on slopes in three consecutive runs (Fig. S3D), or a significantly higher frequency of the beetles running into the upper quadrant which would presumably be the case if the beetles are able to adapt their trajectory to the slope of the surface. The ability to perceive changes in the gravitational field is demonstrated in the geotropic reactions of several insect species such as flies, ants and stick insects by adapting their head, body and leg positions according to the slopes (Markl, 1962; Horn and Lang, 1978; Frantsevich et al., 1993; Diederich et al., 2002). Although Matthews (1963) observed a notable effect of inclination when the dung beetle species Canthon pilularius initiated rolling, K. lamarcki, however, appears to disregard slopes when it has already established its initial bearing prior to encountering the incline. Kheper lamarcki continues locomotion and ball transport in its initially set direction, even if this may cause loss of ball control. Hence, we propose that dung beetles try to maintain their initially chosen direction but are simply not powerful enough to overcome the disruptive impact of the surface topography on their locomotion with a ball, leading to a directional impulse away from the initial bearing. The impact of the surface topography is strongest when the diameter of the ball approaches the AWV of the surface structures but is large enough that the ball is still able to fully enter the valleys of surface topography.

Considering that the main objective of the beetle is to quickly escape with their dung ball from the zone of heavy competition, where the risk of having their ball stolen is highest (Matthews, 1963; Halffter and Matthews, 1966; Cambefort and Hanski, 1991; Ybarrondo and Heinrich, 1996; Scholtz, 2009), it seems reasonable to assume that speed is the more important parameter of this behaviour than direction. In contrast to many other navigating insects, such as desert ants (Wehner, 2003), bees (Giurfa and Capaldi, 1999; Collett and Collett, 2000) or even some other dung beetle species (Halffter and Matthews, 1966; Scholtz, 1989; Dacke et al., 2020), who aim to navigate to a known target, K. lamarcki does not need to return to a stationary nest at the end of their foraging journey. Instead, they seem to follow a straight course until they find a suitable patch of ground to bury their ball at an average distance of 12.4±1.28 m (Khaldy et al., 2019). Even though walking along a straight path prevents them from returning to the starting point and ensures that the largest distance is covered in the shortest time, maintaining a straight path on rough terrain might not be worth the additional energy cost and time loss to overcome an obstacle. Instead, it may be better to follow the path of least resistance, similar to the flow of water. It would be of interest to investigate how the behavior of K. lamarcki differs from other dung beetle species, such as e.g. the homing Scarabaeus galenus, that does repeat foraging trips between its home and burrow with a small dung pellet (Dacke et al., 2020).

In challenging environments, it could be advantageous to have a ball that is larger or much smaller than the AWV of the surface topography. On the one hand, this may help to overcome surface irregularities more easily, but on the other hand, there may be a limit to: (1) the capacities of a dung beetle to handle the ball in terms of power and momentum or (2) the amount of transported food material. A larger ball may roll more smoothly over surface irregularities and allow for more food to be transported but might also increase the chance of kleptoparasitism and hence a complete loss of the ball. Also, parameters other than the surface topography, such as beetle size, might be important in determining ball size and hence the rolling efficiency. Ybarrondo and Heinrich (1996) observed a reduction in ball size and ball construction time as a response to inter- and intraspecific competition in Kheper nigroaeneus, which might be another strategy for minimizing the effect of competition at the dung pile.

As our test surfaces were always less variable than natural surfaces, it remains difficult to project our results into real environments. However, our conclusion that dung balls with a particular diameter are more critical on certain surfaces of the terrain remains valid. As a result, a broad range of different optimization strategies can appear during the course of biological evolution, which is the topic of our follow up studies.

Ball-rolling dung beetles live in a huge variety of environments including deserts, grasslands, savannas and tropical forests and thus encounter extremely different surface topographies in various terrains. Here, we propose that, even though dung beetles are able to roll balls in almost every environment, the surface topography still strongly influences their ball-rolling trajectory. If the AWV of the surface is comparable with the size of the dung ball, the influence of the surface topography on detour, trajectory curvature, the clustering of trajectories, and even on speed is the highest. This implies that dung beetles exhibit sensitivity to substrate topography and there is a critical size of terrain roughness when dung ball transport is ineffective. On such substrates energetic cost to profit ratio will be small and dung beetles might be pushed away from such habitat by other species.

We thank Julius Kuhn for the assistance with the tracking of the ball movement.