High-speed locomotion in the Saharan silver ant, Cataglyphis bombycina

Cataglyphis bombycina, better known as the silver ant of the Saharan desert, the Sinai and the deserts of the Arabian Peninsula, occupies the niche of a thermophilic scavenger. This implies foraging activity during the midday sun, when most other desert ants, and indeed desert animals, stop foraging, and preying on the carcasses of arthropods that have succumbed to heat stress. Because of the high midday temperatures, arthropod carcasses accumulate, although at low densities, while predators and competitors have retreated into their burrows (Wehner and Wehner, 2011; Wehner et al., 1992; Wehner, 1987).

To exploit this foraging niche, silver ants need to withstand the extremely hot and dry desert environment. During the hottest hours of the day, the surface temperature of the Saharan sand may easily exceed 60°C (Wehner et al., 1992) and desiccation stress reaches its maximum with very high water vapour saturation deficits (Lighton and Wehner, 1993). Food density is low and long distances may have to be covered during foraging, with shady resting places absent or far apart because of sparse vegetation and mostly blue sky. Moreover, the fluid granular sand medium may impede locomotion and demands considerable energy to cross. To survive such harsh desert conditions, silver ants have evolved a suite of (i) morphological, (ii) physiological and (iii) behavioural traits, as discussed below.

Morphologically, C. bombycina is well adapted through a number of features characteristic of the genus Cataglyphis. These include special epicuticular hydrocarbons, a favourable volume-to-surface relationship (at least for an insect), a slender alitrunk, powerful muscles and long legs (relative to other ants of more temperate climates) (Sommer and Wehner, 2012; Wehner and Wehner, 2011; Lenoir et al., 2009). Another feature, producing C. bombycina’s typical silvery appearance, is triangularly shaped hairs with thermoregulatory effects (Shi et al., 2015; Willot et al., 2016).

Physiologically, the silver ants are adapted to their hot environment through a discontinuous ventilation cycle that reduces respiratory water loss (Lighton and Wehner, 1993; Sommer and Wehner, 2012) and through special properties of heat-shock protein synthesis. It seems that these proteins accumulate prior to heat exposure, enabling C. bombycina to tolerate a critical thermal maximum of a body temperature of 53.6±0.8°C (Gehring and Wehner, 1995).

Behaviourally, the ants take advantage of thermal refuges like elevated pebbles or grass blades where available (Wehner and Wehner, 2011) (Fig. 1A). Foraging under just-sublethal heat conditions requires minimization of outdoor activities and a return to the moderate underground temperatures inside the nest to discharge excess heat regularly. Delays in homing may have serious consequences, making an excellent navigation ability and fast and efficient locomotion for straight and rapid homing important survival skills.

In the present study, we examined the silver ants' walking behaviour and walking kinematics across a large speed range to understand how this species achieves its remarkably high walking speeds, particularly in comparison to the longer-legged but slower C. fortis. Cataglyphis fortis is a thermophilic scavenger (Wehner, 2016), much like C. bombycina, although it lives in North African salt pan habitats that typically exhibit baked salty clay substrates in the summer months, as opposed to the sand dune habitat of C. bombycina. Are there different strategies in desert ants, and perhaps in animals more generally, to achieve high running speeds?

We expanded the range of recorded walking speeds in C. bombycina beyond the known limits (Wehner, 1983; Zollikofer, 1994), to more than 800 mm s⁻¹, and assessed the contribution of different spatial and temporal walking parameters to achieve such speeds and examined in detail gait and leg coordination patterns to gain a deeper understanding of the silver ant's walking behaviour. Cataglyphis bombycina combines high stride frequencies, short stance phases and fast swing movements to achieve high running speeds, together with the high synchrony of the legs in a tripod.

To analyse the characteristics of silver ant (Cataglyphis bombycina Roger 1859) locomotion, we compared its morphometry and walking behaviour with that of another desert ant species, Cataglyphis fortis (Forel 1902). For morphometric measurements, both ant species were obtained from colonies in their natural habitats. Walking behaviour of C. bombycina (Fig. 1C) was recorded near Douz, Tunisia (33.44°N, 9.04°S), and at Ulm University, Germany (48.42°N, 9.95°S), under laboratory conditions. Note that, although walking speeds tended to be higher in the Tunisian desert than under laboratory conditions in Germany, the two datasets overlap and merge smoothly regarding all recorded parameters. All data (n=177 runs) were obtained during the summer months of 2015 and 2016. For comparative purposes, the same procedures were followed for C. fortis (n=305 runs) (Fig. 1B). Parts of the latter dataset and corresponding analyses have been published previously (Wahl et al., 2015). The experiments were conducted in compliance with current laws, regulations an ethical guidelines of the University of Ulm and of the country where they were performed.

Lengths of the alitrunk (fused thorax and first abdominal segment, or propodeum) and leg pairs in C. bombycina (n=87) and C. fortis (n=100) were obtained for morphometric comparison (see Fig. 2). All measurements in C. bombycina were performed under a dissection microscope (Stemi SV 6, Zeiss Microskopy GmbH, Jena, Germany) with a measurement eyepiece calibrated with a stage micrometre. All six legs were severed in the coxa–thorax joints before measurement. Lengths of femur, tibia and basitarsus were determined for front, middle and hind legs. The respective leg lengths were taken as the sum of femur, tibia and basitarsus measurements (e.g. fig. 4 in Zollikofer, 1988; see also Sommer and Wehner, 2012). Alitrunk length was used to characterize body size (see fig. 11 in Agosti, 1990). Most morphological data for C. fortis were kindly provided by S. Sommer and R. Wehner.

High-speed video equipment (Mikroton MotionBlitz Mini1 high-speed camera, Mikroton, Unterschleissheim, Germany) allowed sampling rates of 500–1000 images s⁻¹. Example videos are available from ResearchGate (doi:10.13140/RG.2.2.21093.45282 and doi:10.13140/RG.2.2.12704.84488) and an extracted single image for each video is shown in the supplementary information (Fig. S2A,B). The ants walked through a linear aluminium channel with a width of 7 cm and a wall height of 7 cm. The floor was coated with fine sand (0.1–0.4 mm particle size) to provide a slip-free substrate for normal walking behaviour. Channel walls were painted with matt grey varnish to avoid distracting reflections. Video recordings were made by mounting the camera above the channel, providing a top view of the walking animals (see Fig. 1C). The highest walking speeds were recorded around noon (11:00 h to 15:00 h) in Douz, Tunisia, with air temperatures of around 45°C. In the laboratory, ants were filmed at different controlled room temperatures (10–30°C) to assess the complete speed range down to 57 mm s⁻¹. For indoor illumination, fibre optic cold light sources (Schott KL 1500LCD, 150 W, Schott AG, Mainz, Germany) were used, while outdoor conditions in Tunisia provided sufficient light for video recordings.

For discrimination, ants were marked individually with car paint (Motip Lackstift Acryl, MOTIP DUPLI GmbH, Haßmersheim, Germany). Ants were usually recorded up to 5 times at different temperatures in order to obtain different walking speeds. Only straight and linear running trajectories with regular stride patterns were used for analyses. That is, walking sequences with abrupt stops, decelerations or accelerations, or curve walking were disregarded. Further, each evaluated recording had to consist of at least three complete step cycles per leg. A piece of millimetre grid paper was used for calibration before a set of videos was recorded. All measurements were digitized with ImageJ (National Institutes of Health, Bethesda, MD, USA) in a frame-by-frame video analysis.

To quantify footfall geometry, we measured the x and y coordinates of tarsal touch-down (just after the end of a swing phase; AEP, anterior extreme position) and tarsal lift-off (just before the start of a swing phase; PEP, posterior extreme position) for each leg with respect to the petiole (Fig. 3A; cf. Seidl and Wehner, 2008; Mendes et al., 2013). The petiole can be regarded as the centre of mass (COM) of an ant (see Reinhardt and Blickhan, 2014). The footprint positions relative to the petiole were normalized to body size; that is, alitrunk length. Standard deviations of footfall positions were used to quantify the spread of footprint positions (footprint clustering in Fig. 3B). Tracks of leg movements and footfall geometry measurements were performed in ImageJ (National Institutes of Health). Movement of the COM was tracked to analyse its horizontal velocity and acceleration (see Figs S4 and S5). Forward velocity (walking speed along the longitudinal axis) was calculated by measuring the distance between the petiole images in two consecutive video frames, and dividing that distance by 1 ms, the frame rate. Forward acceleration is the respective change of forward speed within a 1 ms time interval (see Figs S4 and S5A,B). To determine lateral velocity (along the transverse axis, perpendicular to longitudinal movement), a regression line was first calculated, running through the petiole images in five consecutive video frames. The deviation of the petiole from this regression line was measured in the middle frame. This was done for all video frames (except the initial and final two frames, which did not allow calculation of a regression line). The differences in the lateral deviations in consecutive frames were used to calculate lateral velocity. Lateral acceleration is the respective change of lateral velocity in a 1 ms time interval (see Figs S4 and S5C).

Different walking parameters were analysed to obtain an overview of the silver ant's locomotor behaviour. We covered a range of 15-fold increase in walking speed, from about 57 to 855 mm s⁻¹, to provide a basis for comprehensive analysis. For all evaluated recordings, the mean walking speed was calculated as the distance covered from the start of the first step cycle to the end of the last step cycle in a given video sequence, divided by the time needed to cover that distance. Further, the timing of each lift-off and touch-down event of the six tarsal tips was measured. The swing phase was considered to be the time between tarsal touch-down and lift-off; that is, the time of tarsal tip movement. A leg was defined to be in stance phase as long as the tarsal tip touched the ground, and as long as it did not move relative to the ground. Stride length was calculated for each leg as the distance between lift-off and touch-down positions on the ground (‘SL’ in Fig. 1C). To calculate stride frequency, we divided walking speed by stride length. Different from stride length, stride amplitude was defined as the distance covered by a swing movement of the leg in body coordinates (Wosnitza et al., 2013). Stride amplitude was estimated by subtracting body displacement (swing phase duration × walking speed) from stride length (see also Fig. 1C and Wahl et al., 2015). Swing speed was determined as stride length divided by the duration of the respective swing phase. Angular velocity (deg s⁻¹) was calculated for representative sample steps as the angular deviation of the femur (with respect to body axis) during one swing movement.

We averaged the values recorded in all six legs of an ant to obtain mean values that illustrate general relationships (see Fig. 4A–D), particularly in cases where no significant differences were observed between leg pairs. To illustrate parameters that differed between leg pairs, we calculated mean values for a given pair of legs (L1 and R1; L2 and R2; L3 and R3; Fig. 4E–H; stride amplitude, swing speed and angular velocity).

To assess the quality of tripod coordination, we calculated tripod coordination strength (TCS) (e.g. Wosnitza et al., 2013). TCS is the ratio of two time periods, t₁/t₂, where t₁ is the time period where all three legs of a given tripod group are simultaneously in swing phase, and t₂ is the time period where at least one of the three legs of the respective tripod group is in swing phase. A TCS value of 1.0 indicates perfect tripod coordination, with all legs in a tripod taking off and touching down simultaneously. The more the TCS value approaches 0, the less synchronous are the swing movements in a tripod group. Phase plots analyse the phase coordination of the six legs in a circular step cycle diagram. The onset of swing (Fig. 5Bi) or stance (Fig. 5Bii) phase in the left hind leg was taken as a reference for the timing of the other five legs. Phase plots were calculated in a MATLAB environment (MathWorks, Inc., Natick, MA, USA) using the ‘CircStat’ toolbox (Berens, 2009). The duty factor is often used to characterize the transition from walking to running; that is, the introduction of aerial phases into the gait pattern, regarding one leg pair (Alexander, 2003). Duty factor is the duration of the stance phase of a leg divided by the entire duration of the respective step cycle, stance and swing phase together.

The sequence of swing and stance movements of the six legs was visualized by podograms (Fig. 6A,C). We further quantified the ant's inter-leg coordination by assigning each video frame an index number and a respective index colour, corresponding to the momentary leg coordination observed in that particular video frame (cf. Mendes et al., 2013; Pfeffer and Wittlinger, 2016). Besides the classical gait categories – pentapod, tetrapod, tripod – we also noted the remaining combinations of legs touching the substrate: hexapod, bipod, monopod, aerial phases. For example, in a given video frame, L1, R2, L3 may be in swing phase, and R1, L2, R3 in stance phase. The frame thus shows a typical tripod situation and is assigned index number ‘3’ and colour ‘dark green’ (see Fig. 6 legend). For a more detailed description of the different categories, see Fig. S3. For the calculation of podograms and frame-by-frame indexing, we used a MATLAB environment (MathWorks).

The generation of box-and-whisker plots, normality tests and statistical pairwise and multiple comparisons were performed in SigmaPlot 11.0 (Systat Software Inc., San Jose, CA, USA). Box-and-whisker plots show the median as the box centre, the 25th and 75th percentiles as box margins and the and 90th percentiles as whiskers. Datasets were tested for normal distribution with the Shapiro–Wilk normality test. For pairwise comparisons of normally distributed data, we used the t-test; for non-normally distributed data, we used the Mann–Whitney U-test (U-test). For multiple comparisons of normally distributed data, we used a one-way ANOVA (with Holm–Šidák method as post hoc test); for non-normally distributed data, we used an ANOVA on ranks (with Dunn's method as post hoc test). Levene's test, realized with Excel (Microsoft Corporation, Remond, WA, USA), was used to compare the variances in footprint positions. For statistical comparisons of circular data, the CircStat toolbox (Berens, 2009) was used. In our figures, a significance level of 0.01 to 0.05 is marked with one asterisk (*), a significance level of 0.001 to <0.01 with two asterisks (**) and a significance level of <0.001 with three asterisks (***).

Cataglyphis desert ants occupy the niche of a thermophilic scavenger that demands a fast and efficient locomotion while foraging. The question of how C. bombycina silver ants – renowned for their high speeds – walk across a large range of speeds will be addressed below. To emphasize and explicate particularities of the silver ants' locomotion, we compared their walking behaviour with that of another fast (though not quite as fast) running desert ant species, C. fortis.

For morphometric analyses (Fig. 2) we measured alitrunk length (as proxy of body size; Agosti, 1990) and the length of the different leg pairs for C. bombycina and C. fortis. The relationships of the different parameters within a species were close to isometry for both species (Fig. S1 and Table S1), as has been demonstrated previously for several desert ants (Sommer and Wehner, 2012). Cataglyphis bombycina was statistically significantly smaller than C. fortis, regarding all the absolute length measurements. Alitrunk length in C. bombycina was 2.5±0.37 mm (12%) shorter, on average, than in C. fortis. Leg lengths in C. bombycina were even smaller compared with those of C. fortis. The first leg pair averaged 4.3 mm (19% shorter), the second leg pair averaged 5.2 mm (18% shorter) and the third leg pair averaged 6.8 mm (18% shorter) than the respective leg pair of C. fortis.

Within both species, alitrunk length and leg length showed isometric size relationships. That is, larger individuals had proportionately longer legs, and vice versa. However, C. bombycina had shorter legs relative to body size compared with C. fortis, despite isometric relationships within the species (Fig. S1 and Table S1).

We next analysed the spatial properties of locomotion in C. bombycina regarding footfall patterns (Fig. 3). We analysed the footfall patterns of the legs in the PEP, just before lift-off at the end of stance, and in the AEP, just after touch-down at the beginning of stance (Fig. 3A). Cataglyphis bombycina showed footfall positions closer to the body when compared with C. fortis, consistently in AEPs and PEPs of all legs. This observation is indicative of the relatively shorter legs and the slightly more flexed leg conformation in the C. bombycina ants (see example videos: doi:10.13140/RG.2.2.21093.45282 and doi:10.13140/RG.2.2.12704.84488). The tarsal contact areas showed no significantly larger variability in C. bombycina than in C. fortis, indicated by the separate evaluation of footfall clustering in Fig. 3B. Intriguingly, COM movement can be described by a steady walking path with no apparent variation in speed or acceleration in the rhythm of the step cycle, either for longitudinal or for transverse horizontal COM movements (see Figs S4 and S5).

In comparison to C. fortis, C. bombycina thus have their tarsal ground contacts closer to the body. This is true not only in absolute terms but also explicitly for measurements normalized to body dimensions.

General walking parameters were analysed in the natural range of locomotor speeds, from 57 to 855 mm s⁻¹ for C. bombycina and from 30 to 620 mm s⁻¹ for C. fortis. The results presented below are summarized in Fig. 4, and the corresponding regression line equations with slope and intercept values are stated in the figure legend.

With increasing walking speed, stride length (Fig. 4A) increased from 4.7 mm (at 73 mm s⁻¹) to 20.8 mm (at 618 mm s⁻¹) in C. bombycina; that is, stride length more than quadrupled. Not surprisingly, because of their longer legs, C. fortis showed larger stride lengths at the respective walking speeds. However, the slopes of the linear regression lines (C. bombycina: y=0.02x+4.72; C. fortis: y=0.02x+6.04) and the range of stride lengths (4.5−21 mm) were quite comparable between the two species. Note that in both ant species the natural limit of stride length was further increased by the insertion of aerial phases that started to emerge in C. fortis at around 350 mm s⁻¹, and in C. bombycina at around 150 mm s⁻¹ (compare Fig. 6, ‘aerial phase’ category in gait analysis; and Fig. 5C,D graphs intersecting 0.5 duty factor line).

With increasing walking speed, stride frequency (Fig. 4B) increased following a power function, although with different slopes in the two species (power functions for C. bombycina: y=1.43x^0.52; C. fortis: y=0.81x^0.59). In silver ants, stride frequency levelled off beyond speeds of 150–200 mm s⁻¹ towards a value of 40 Hz. The highest stride frequencies of up to 47 Hz observed in C. bombycina (at 855 mm s⁻¹), exceeded the frequency plateau recorded in C. fortis at about 30 Hz. The highest measured frequency in C. fortis was 36 Hz at 596 mm s⁻¹.

Swing and stance phase durations (Fig. 4C,D) shortened with increasing walking speed in both ant species. At low walking speeds, stance phase duration was longer than swing phase duration; at medium and high walking speeds, this relationship reversed – that is, swing phase was longer than stance phase. The reversal point, with phase durations being about equal, was at a walking speed of about 100 mm s⁻¹ in C. bombycina and about 180 mm s⁻¹ in C. fortis. Notably, at high walking speeds, the silver ants' stance and swing phase durations decreased below those observed in C. fortis. Swing phase in C. bombycina exhibited a minimum duration of 17 ms and thus was just slightly shorter than the 19 ms recorded in C. fortis. Stance phase duration was as short as 7 ms in C. bombycina, while the minimum duration in C. fortis was almost twice as long, at 12 ms.

Stride amplitude (Fig. 4E,F) represents the size of a swing movement relative to body coordinates (see Materials and Methods). It thus indicates by how much a leg's swing movement exceeds the respective body movement during the swing. Stride amplitude increased linearly with walking speed, from 2.5 mm at 73 mm s⁻¹ to 8 mm at 742 mm s⁻¹ in C. bombycina, and from 2.0 mm at 74 mm s⁻¹ to 10.4 mm at 433 mm s⁻¹ in C. fortis. The shorter leg lengths of C. bombycina (cf. Fig. 2) are reflected in the smaller maximum stride amplitude. The similar slopes of the stride amplitude versus walking speed regression lines (Fig. 4E) indicate correspondingly similar performance of the three leg pairs in C. bombycina. In C. fortis, by contrast, a special role of the middle legs (Fig. 4F), probably related to propulsion and perhaps steering, has been discussed previously (Wahl et al., 2015).

The velocity of leg movements rose with increasing walking speed in an almost linear fashion, indicated by swing speed (Fig. 4G,H) and by corresponding angular velocities of the femur (table below Fig. 4G,H). Regression lines of the swing speed versus walking speed graphs tended to exhibit slightly lower slopes in C. bombycina. The fastest absolute swing speeds of 1.3 m s⁻¹ were not reached by C. fortis, however. A striking characteristic of desert ant locomotion appears to be the middle legs performing the fastest swing movements, spending less time in the air than the front and hind legs, and therefore showing the highest duty factor (see Fig. 5B–D).

In summary, C. bombycina apparently reaches high running speeds by having high stride frequencies of more than 40 Hz. These high frequencies are achieved by very short stance phases and fast swing speeds. The shorter legs, and resulting smaller stride lengths, of C. bombycina appear to be compensated for in this way.

TCS (Fig. 5A) captures the synchrony of leg swing movements in a tripod group; that is, one middle leg and the contralateral front and hind legs. TCS thus provides a measure of tripod gait quality (Wosnitza et al., 2013), with values of 1.0 characterizing exact synchrony in the movements of the legs in a tripod. In C. bombycina, TCS values were remarkably constant across the whole walking speed range. Observed values were mostly between 0.7 and 0.9, clustering around 0.8. These values were higher than TCS values recorded in C. fortis, especially at slow walking speeds.

Stance and swing movements are repetitive events in the step cycle. A circular illustration is thus an adequate means to analyse variability of inter-leg coordination. Phase plots show the onsets of swing (Fig. 5Bi) and stance (Fig. 5Bii) during the step cycle, with the left hind leg (L3) serving as reference (and thus without data point scatter in the diagrams). Considering the TCS values reported above, it was not surprising to observe a clear anti-phase relationship between the two tripod groups, L1, R2, L3 and R1, L2, R3. Swing and stance phase onset of the three legs in a tripod group occurred almost simultaneously. Although clear tripod coordination was obvious in both ant species, there were small differences regarding the relative timing of the different legs within the step cycle. In C. bombycina, all three legs were lifted off (onset of swing phase) and put down on the ground (onset of stance phase) in almost perfect synchrony, except for the stance phase onset of the middle legs. The middle legs were lifted together with the front and hind legs of their tripod group, but they started the transition towards stance phase slightly earlier (1.7 ms) than the front and hind legs.

Cataglyphis fortis, by comparison, showed larger relative phase shifts regarding all leg movements during the step cycle, as indicated by lower TCS values. This resulted in a not quite synchronous transition between swing and stance phases of the legs in one tripod group. There was a clear tendency for the hind leg in a tripod to be lifted off the ground first, followed by the front leg and the middle leg performing stance–swing transition last. For the swing–stance transition, the front and middle legs touched down in near synchrony, while the hind leg was the last to terminate its swing phase.

The duty factor represents that fraction of step cycle duration that is occupied by the stance phase, when the body is supported by a given leg. When the duty factor drops below 0.5, the swing phases of a given leg pair overlap as the stance phases of the two legs cannot cover the whole step cycle period. This is the reason why the duty factor is often used to characterize the transition from walking to running, especially for bipedal runners (see Discussion).

With increasing walking speed, duty factor decreased in all three leg pairs, although in a somewhat different manner in the two ant species (Fig. 5C,D). In C. bombycina, the front and hind leg duty factor dropped below 0.5 at rather low walking speeds, below 100 mm s⁻¹. The middle legs assumed a duty factor below 0.5 last, indicative of the final transition from walking to running, at about 120 mm s⁻¹. In C. fortis, these transitions occurred at much higher speeds, at about 170 mm s⁻¹ for front and hind legs, and at a remarkable speed of about 370 mm s⁻¹ for the middle legs.

In summary, leg movements in a tripod group are well synchronized in C. bombycina, even at low walking speeds, and aerial phases occur at remarkably low walking speeds of about 120 mm s⁻¹.

We characterized the silver ants' walking behaviour by further gait analyses. Fig. 6A shows an example of a podogram and corresponding gait indexing for C. bombycina; Fig. 6C provides an example for C. fortis, recorded at similar walking speeds (about 350 mm s⁻¹). Podograms present the alternation between swing and stance phases over time as black (swing) and white (stance) bars. For a quantitative analysis, each frame of the video was assigned an index number and a colour code marking the leg coordination in the particular video frame (see Fig. 6 legend; Fig. S3). Cataglyphis bombycina showed a consistent use of aerial phase (Fig. 6B, number code ‘6’, colour code ‘dark blue’) above walking speeds of 250 mm s⁻¹, while this was an altogether rarer event in C. fortis, except at the very highest speeds (Fig. 6D).

The method of gait indexing was used to quantify gait patterns across the observed range of walking speeds in both C. bombycina (Fig. 6B) and C. fortis (Fig. 6D). Gait indexing does not consider a continuous gait, such as a tripod gait, but rather assigns each frame in a video recording an index number according to the momentary leg coordination in that frame (see Fig. 6 legend). In C. fortis, there was a continuous change in gait pattern composition across the entire walking speed range, from the <50 mm s⁻¹ bin to the <650 mm s⁻¹ bin (Fig. 6Bi). Statistically significant changes in gait representation occurred between all adjacent speed bins except one (see Fig. 6 legend). In C. bombycina, by contrast, there were changes in gait pattern composition only from the lowest walking speeds up to the 250 to <350 mm s⁻¹ speed bin (Fig. 6Bi). For higher walking speeds, no statistically significant changes in the relative frequency of gait patterns were observed, with the silver ants exhibiting rather constant proportions of gait patterns. Aerial phases accounted for about 30%, periods with more than three legs in swing phase and monopod or bipod coordination for about 15% each, and tripod coordination for about 40%.

This was also indicated by a consistently high mean index number of about 4.3 (Fig. 6Bii, index number of 4, marking bipod coordination, and 5, indicating monopod coordination). In C. fortis, by comparison (Fig. 6Dii), there was a large proportion of gait patterns with more than three legs in stance phase at the lowest speeds (<50 mm s⁻¹): hexapod 15%, pentapod 26%, tetrapod 14%, with a mean index number of 1.7. The gait composition changed gradually towards patterns with at least three legs in swing phase: tripod 43%, bipod 14%, monopod 20%, aerial phases 23%, with a mean index number of 4.2 in the highest speed bin (550 to <650 mm s⁻¹). Thus, only at the highest speeds was the gait pattern composition similar to that of C. bombycina.

In summary, C. bombycina consistently employs gait patterns with at least three legs in the air, i.e. tripod, bipod, monopod or aerial phases, across most of its walking speed range. Aerial phases occur at intriguingly low walking speeds, with almost 15% at 150 mm s⁻¹ and about 30% above that speed. This is achieved by overlapping swing movements of the two tripod groups, partly as a result of the high synchrony of the leg movements within a tripod.

Cataglyphis bombycina (Wehner et al., 1992) and Cataglyphis fortis are sister desert ant species that inhabit North African sand dune and salt pan habitats, respectively, but are quite similar otherwise. An intriguing difference concerns relative leg length, which is shorter in C. bombycina despite the fact that this species achieves higher walking speeds. This was the initial incentive for the present analysis, where we observed a number of distinct differences in the details of the two species' walking behaviour.

We were able to measure top absolute walking speeds of 855 mm s⁻¹ in C. bombycina, a value that comes close to the maximum running speeds of 1 m s⁻¹ recorded previously (Wehner, 1983) with different methods. Calculating relative walking speed, typically in body lengths per second, appears more adequate when analysing parameters related to body size such as stride length or stride amplitude. Cataglyphis bombycina achieves maximum relative speeds of about 108 body lengths per second (which is around 157 leg lengths per second), one of the highest values documented for running animals. It is outperformed according to our present knowledge by very few species, most notably a Californian coastal mite (Paratarsotomus macropalpis) and an Australian tiger beetle (Cicindela sp.), with relative speeds of up to 377 and 171 body lengths per second, respectively (Rubin et al., 2016; Kamoun and Hogenhout, 1996).

From an evolutionary perspective, low food density and a hot climate in the North African deserts exert selective pressures that make fast and efficient foraging a crucial feat for the scavenging silver ants (Wehner and Wehner, 2011). To achieve high walking speeds, virtually all legged animals optimize spatial and temporal parameters (Heglund et al., 1974; Heglund and Taylor, 1988) that we have addressed in the present study. Although one might expect that the two examined ant species, C. bombycina and C. fortis, use the same strategies to reach high walking speeds, our analysis revealed distinct differences in the way the two species use those spatial and temporal parameters, as discussed below.

Absolute leg length per se would appear to limit stride length in C. bombycina, unless stride length is increased by inserting aerial phases into the walk. Maximum absolute stride length is quite similar at 20.81 mm in C. bombycina (at 618 mm s⁻¹) and 20.84 mm in C. fortis (at 592 mm s⁻¹). Interestingly, this holds true when calculating maximum relative stride length (stride length/alitrunk length), resulting in 2.34 and 2.41 for C. bombycina and C. fortis, respectively. This means that silver ants, with their shorter bodies and even shorter legs, enlarge their range of stride lengths by inserting aerial phases. They do this to a larger extent than C. fortis, a fact that was further demonstrated by measuring stride amplitude. Cataglyphis fortis ants exhibited larger stride amplitudes than C. bombycina, suggesting that they exploit their leg span without inserting aerial phases up to larger stride lengths and walking speeds than C. bombycina.

To achieve high stride frequencies, C. bombycina ants reduce step cycle period by shortening primarily stance phase duration, to a minimum of 7 ms. This is almost half the minimum stance phase duration in C. fortis of 12 ms. Swing phase duration is reduced relatively less, to a minimum of 17 ms in C. bombycina. This is slightly below the minimum of 19 ms in C. fortis. A steeper decline of stance phase duration compared with swing phase duration with increasing walking speed is commonly observed in walking animals (e.g. in stick insects: Wendler, 1964). This is due to the fact that swing phases are performed without mechanical load that relates to walking speed.

As noted above, only a few animals are known to achieve higher stride frequencies than C. bombycina, including the mite Paratarsotomus macropalpis (Rubin et al., 2016). These animals are much smaller than ants, about 0.7 mm in body length, and stride frequencies are correspondingly faster, ranging above 100 Hz. Together, this results in the mites moving at very low Reynolds numbers, between 4 and 5. Depending on body length, walking speed and ambient temperature, Reynolds numbers for C. bombycina range from about 140 (for an 8 mm ant walking at a medium speed of 300 mm s⁻¹ at 45°C) to 570 (for an 11 mm ant walking at the maximum speed of 840 mm s⁻¹ and a moderate temperature of 30°C). These Reynolds numbers are typically relevant for small flying insects, such as small Drosophila species. Viscous forces, rather than inertial momentums of the legs, would thus appear to impose speed limits.

Stride frequency is restricted by muscle contraction and relaxation kinetics (Rubin et al., 2016). In this context, the short legs of C. bombycina – by long-legged Cataglyphis standards – may be significant for reaching high leg movement speeds and high stride frequencies, as reported here. After all, long legs have high momentums of inertia, in small arthropods as well as in large mammals (Heglund et al., 1974; Heglund and Taylor, 1988). The relatively short legs may thus contribute to C. bombycina reaching a 40 Hz stride frequency, while the longer-legged C. fortis achieves just about 30 Hz.

Notably, this result is in accordance with the model of the spring-loaded inverted pendulum (SLIP), which abstracts the alternating movement of two coupled tripod leg groups as a spring-mass monopod (Blickhan and Full, 1993). The SLIP model nicely shows that smaller individuals change gait at lower walking speeds and show generally higher stride frequencies. Both aspects were observed in the present comparison of ant species. The smaller ant, C. bombycina, introduces aerial phases at lower walking speeds and reaches higher stride frequencies than its larger sister, C. fortis.

Leg coordination parameters are of secondary importance for speed production, but they are of course essential for static and dynamic stability (e.g. Ting et al., 1994). Several idealized gaits are known in insects – pentapod, tetrapod, tripod – merging into one another in a speed-dependent gait continuum (Wilson, 1966; Schilling et al., 2013; Dürr et al., 2018). A typical low-speed walking pattern is pentapod coordination, also termed wave gait, with one leg in swing and five legs on the ground. At intermediate walking speeds, tetrapod coordination is often observed, with two diagonally arranged legs in the air and four legs, supporting the body. For fast walking speeds, tripod coordination is typically observed, with three legs simultaneously in swing and three legs in stance phase, coupling the front and hind legs of one body side and the middle leg of the other body side into a tripod group.

Stick insects are textbook examples demonstrating the entire spectrum of the gait continuum from pentapod to tetrapod to tripod coordination with increasing walking speed (Wilson, 1966; Graham, 1972). The concept of gait continuum has been linked to several coordination rules derived from behavioural experiments (Cruse, 1990; Dürr et al., 2018) that were verified by successful implementation in hexapod walking models and machines (Schilling et al., 2013). Many insects, and especially faster walking species, apparently occupy just the upper end of the gait continuum, including cockroaches, beetles and ants (Hughes, 1952; Bender et al., 2011; Zollikofer, 1994). In these animals, the gait continuum is extended beyond the tripod by insertion of aerial phases (via bipod and monopod situations as tripod pattern variations), allowing higher walking speeds.

Note, however, that the definition of traditional walking patterns (pentapod, tetrapod, tripod) is based on the coupling of particular legs in the step cycle, while the extension of the gait continuum beyond the tripod gait that has been applied here (bipod, monopod, aerial phases) is the result of the continuous (and increasing) overlap of the swing phases of the two tripod groups. For strict and fast-walking tripod walkers, it would appear favourable to extend the gait continuum from exact tripod coordination (three legs in the air, three legs on the ground), via bipod (four legs in swing, two legs in stance) and monopod (five legs in swing and one leg in stance) coordination to aerial phases (all six legs in the air, with one tripod just after lift-off, the other just before touch-down; see also Fig. S3). This characterization appears to be a useful way to achieve a quantitative temporal analysis for the description of fast locomotion in hexapods.

A striking characteristic of the silver ant's locomotion is the high synchrony of the step cycles in the legs within a tripod group. This is illustrated by the rather constant TCS values of around 0.8 (Fig. 5A) and clearly revealed in phase plot analyses (Fig. 5B). All three legs of a tripod commence swing phase virtually simultaneously, and the middle legs are the first legs to touch down again, with the front and hind legs of the contralateral body side following immediately after. This near synchrony in combination with short stance phase durations leads to the occurrence of aerial phases at remarkably low walking speeds. This is also apparent in the analysis of gait index (Fig. 6) and duty factor (Fig. 5C,D). The middle leg is the last one to decrease its duty factor below 0.5, as an indicator for the occurrence of aerial phases, and it does so at speeds as low as 120 mm s⁻¹, i.e. far lower than in C. fortis, where aerial phases occur at about 370 mm s⁻¹ and above. In the silver ant, aerial phases thus occur well before maximum stride lengths or stride frequencies are reached. Duty factor is an indirect indicator of the occurrence of aerial phase, compared with gait indexing, for example. Regarding a single pair of legs, a duty factor below 0.5 implies that swing phase accounts for more than half of step cycle duration, resulting in swing phase overlap in that particular leg pair. However, in hexapods, and even quadrupeds, this does not imply the simultaneous occurrence of swing phase overlap in all leg pairs. High synchrony of the legs in a tripod results in a walking pattern in C. bombycina that is strongly reminiscent of bipedal locomotion, though, with the alternating tripods representing the two legs. This makes the duty factor a quite useful concept for the present study.

Synchronization of legs can lead to aerial phases (as a classical definition for the walk–run transition; Hildebrand, 1985), appropriate to several arthropods such as Periplaneta americana (Full and Tu, 1991), ghost crabs (Burrows and Hoyle, 1973) or Hololena spiders (Spagna et al., 2011). Other fast running arthropods do not show such high synchronization [e.g. the cockroach Blaberus discoidalis (Full and Tu, 1991), Formica wood ants (Reinhardt and Blickhan, 2014)]. To determine the walk–run transition in these cases, in the absence of aerial phases, further analysis is required such as ground reaction force patterns, energy transfer between the legs and body, and energy fluctuation patterns of the COM. These criteria have never been applied to desert ant locomotion, to our knowledge, but they exceed the scope of the present study and our current dataset.

As for the two Cataglyphis species, different arthropod taxa appear to behave differently at high speeds, with some tending towards more metachronal patterns and some species strengthening the synchronization of leg swings (which might require specific features for elastic energy storage in the legs; Weihmann et al., 2017; Weihmann, 2018). In line with the SLIP model (Blickhan and Full, 1993), leg synchronization in C. bombycina increases vertical forces and vertical amplitudes of the COM which might lead to increased elastic energy storage in the legs. Pronounced synchronization would appear favourable as all three tripod legs contribute equally to acceleration on the sand substrate. Movement of the COM in this context appears to be restricted to the vertical plane. Our high-speed videos taken in top view demonstrate movement of the alitrunk along a remarkably straight path at similarly remarkable constant speed (see Figs S4 and S5).

In the present study, we demonstrated that two closely related desert ants, namely C. bombycina and C. fortis, exhibit intriguing differences regarding their walking behaviour. One reason why silver ants may have evolved their peculiar locomotor behaviour is the Saharan dune habitat, as opposed to the hard-baked clay in salt pans habitat of C. fortis. This concerns in particular C. bombycina’s combination of high stride frequencies, short stance phases and fast swing movements in achieving high running speeds, together with the high synchrony of the legs in a tripod. There are two related potential advantages of this leg movement pattern.

First, this coordination results in brief, synchronous and forceful impacts of three legs on the sand substrate, which may serve to minimize sinking into the yielding dune sand (Li et al., 2009). After all, brief and fast movements in these small animals should occur at low Reynolds numbers and high substrate viscosity. The smaller body size, and thus body mass, of C. bombycina compared with C. fortis may further help to reduce the ants' subsidence into the soft granular medium.

Second, the high synchrony in the leg movements of a tripod should distribute body mass rather evenly across the tripod. A rather even distribution of body mass among the three legs of a tripod should be advantageous for both touch-down and lift-off. Both transitions will require relatively high acceleration forces when considering the brief stance phase durations (cf. Zollikofer, 1988).

We thank Annette Christine Janssen, Tanja Kaiser and Alexander Schaarmann for their most dedicated help with the field work, laboratory experiments and high-speed video analysis. Wolfgang Mader deserves sincere thanks for his help with statistical evaluations, and Alexander Lindt and Andrea Kubitz for their support in animal care. Ursula Seifert helped with editing and correcting the English in the manuscript. We thank Rüdiger Wehner and Stefan Sommer for providing morphological data for C. fortis.