Dynamics of locomotion in the seed harvesting ant Messor barbarus: effect of individual body mass and transported load mass

Studied species

Experiments were carried out with a large colony of M. barbarus collected in April 2018 at St Hippolyte (Pyrénées Orientales), on the French Mediterranean coast. Workers in the colony ranged from 2 to 15 mm in length and from 1 to 40 mg in body mass. The colony was housed in glass tubes with a water reservoir at one end and kept in a room at 26 °C with a 12:12 L:D regime. The tubes were placed in a box (LxWxH: 0.50 × 0.30 × 0.15 m) whose walls were coated with Fluon^® to prevent ants from escaping. During the experimental period, ants were fed with a mixture of seeds of various species and had access ad libitum to water.

Experimental setup

Ants were tested on a setup designed and built by a private company (R&D Vision, France. http://www.rd-vision.com/). It consisted in a walking platform surrounded by five high speed cameras (JAI GO-5000M-PMCL: frequency: 250 Hz; resolution: 30 µm/px for the top camera, 20 µm/px for the others). One camera was placed above the platform and four were placed on its sides. The platform was 160 mm long and 25 mm wide and was covered with a piece of black paper (Canson^®, 160 g/m²). Four infrared spots (λ = 850 nm, pulse frequency= 250 Hz) synchronized with the cameras illuminated the scene from above. The mean temperature in the middle of the platform, measured with an infrared thermometer (MS pro, Optris, USA, http://www.optris.com) over the course of the experiment, was (mean ± SD) 28 ± 1.4 °C.

Experimental protocol

We performed all experiments between April and July 2018.

We wanted to make sure that the ants we tested were foraging workers. Therefore, the first day of an experimental session, we selected a random sample of workers returning to their nest with a seed on a foraging trail established between the box containing the colony and a seed patch. We then kept these ants in a separate box and used them in our experiments the following days.

Each ant was tested twice: the first time unloaded and the second time loaded with a fishing lead glued on its mandibles. Before being tested, unloaded ants were first weighed to the nearest 0.1 mg with a precision balance (NewClassic MS semi-micro, Mettler Toledo, United States). Individual ants were then gently placed at one end of the platform and we started recording their locomotion as soon as they entered the camera fields. The recording was retained only if ants walked straight for at least three full strides, a stride being defined as the interval of time elapsed between two consecutive lift off of the right mid leg. All videos were subsequently cropped to a whole number of strides. To stimulate the ants and to obtain a straighter path, an artificial pheromone trail was laid down along the middle axis of the platform by depositing every centimeter a small drop of a hexane solution of Dufour gland (1 gland/20µl), which is responsible for the production of trail pheromone in M. barbarus (Heredia & Detrain, 2000). This operation was renewed every 45 min in order to keep a fresh trail on the platform.

Once five ants were tested in unloaded condition, we proceeded with the test in loaded condition. First, each ant was anesthetized by putting it in a vial plunged in crushed ice. It was then fixed on its back, with its head maintained horizontally, and we glued a calibrated fishing lead on its mandibles with a droplet of superglue (Loctite, http://www.loctite.fr/). After letting the glue dry for 15 min and the ant recover for half an hour, the ant was placed again on the platform and its locomotion was recorded in loaded condition. We retained only the recordings in which the load did not touch the ground during the transport (see Merienne et al., 2020). At the end of the recording, the ant was captured and weighed a second time. It was then killed and each of its body parts (head, thorax, gaster) was weighed separately.

Data extraction and analysis

In order to compute the 3D displacement of the ants’ main body parts (head, thorax, gaster) and of its overall CoM, we tracked several anatomic points on the view of the top camera (Figs. 1A–1C) and on the view of one of the side cameras (Figs. 1B–1D) with the software Kinovea (version 0.8.15, https://www.kinovea.org).

We assumed a homogeneous distribution of the mass within each body parts and thus computed the (X, Y) coordinates of the CoM of the three main body parts (plus the load) as the mean of the (X, Y) coordinates of the two points tracked at their extremities on the top view and the vertical position (Z) as the mean of the vertical position of the two points tracked on each of these parts on the side view. For each frame we computed the position of the overall CoM of an ant as the barycenter of the CoM of its three main body parts (plus the load for loaded ants) weighted by their mass. For each ant tested, we delimited the different strides on the videos and then, for each stride, we calculated the positions (X, Y, Z) and velocity vectors of the overall CoM. Finally, we averaged the CoM speeds and positions across the multiple stride cycles in order to obtain a single mean trajectory of the CoM in each condition (unloaded and loaded).

In order to characterize the mean trajectories of the CoM for each ant and condition, we computed the peak-to-peak amplitude of the Z positions of the CoM and assessed the sinus-like behavior of the changes in Z position and in the norm of the velocity vector. In order to do so, we first normalized the Z positions and the values of the norm of the velocity vector by their respective peak-to-peak amplitude and fitted a sinus function to the resulting signals. We then computed the root-mean-square error (RMSE) between the fitted function and the normalized data.

In order to assess the general posture of the ants during locomotion, we also computed the mean Z position of their CoM in units of body length and the mean inclination angle of their body during locomotion (defined as the angle between the horizontal X axis and the line linking the gaster and head CoMs).

From the dynamic of the CoM, we then computed its kinetic E_k and gravitational potential E_p energies relative to the surroundings with the formulae (1)${\displaystyle E_k=0.5\ast m\ast v^2}$

and (2)${\displaystyle E_p=m\ast g\ast h}$ where m is the mass of the ant (plus the mass of the load if one is carried), v the speed of the CoM, g the gravitational constant and h the vertical position of the CoM above the walking platform. We then computed the external mechanical energy of the CoM as the sum of the kinetic and potential energies.

Finally, following Bastien et al. (2016), we computed the external mechanical work (W_ext) achieved to raise and accelerate the CoM as the sum of the positive increments of the external mechanical energy. Since ants did not walk the same distance or during the same amount of time, in order to compare the mechanical work they achieved, we divided W_ext by the distance travelled and thus obtained a “mechanical work per unit distance” W_ext,d. This makes sense if one considers that locomotion is a repetitive process and that we cropped our videos to a whole number of strides. We then computed the mean external power (P_ext) by dividing W_ext by the duration of locomotion. Finally, we computed the mass specific values of W_ext,d and P_ext by dividing both of these metrics by the ant mass for unloaded locomotion and the ant mass plus load mass for loaded locomotion.

Following Cavagna, Thys & Zamboni (1976) we then computed the energy recovered (R, expressed in percentage) through the pendulum-like oscillations of the CoM with the formula: (3)${\displaystyle R=100\mathrm{\ast }\frac{W_k+W_p-W_{ext}}{W_k+W_p}}$ where W_k is the sum of the positive increments of the kinetic energy versus time curve and W_p is the sum of the positive increments of the potential energy versus time curve. R is an indicator of the amount of energy transferred between the potential and the kinetic energy of the CoM due to its pendulum-like behavior: the closer the value of R to 100%, the more consistent the locomotor pattern is with the Inverted Pendulum System (IPS) model (Cavagna, Heglund & Taylor, 1977) in which the fluctuations of E_p and E_k are perfectly out of phase, i.e., all the kinetic energy of the CoM is transformed in potential energy, and vice versa, over a stride.

In order to further characterize the relationship between E_k and E_p, we computed the Pearson correlation coefficient between E_k and E_p, and, following Ahn, Furrow & Biewener (2004) and Vereecke, D’Août & Aerts (2006), the percentage congruity between E_k and E_p (defined as the percentage of time E_k and E_p changed in the same direction). We then fitted a sinus function to the variations of both E_k and E_p, extracted the phase of E_k and E_p from these sinus functions, and computed the difference between the two phases in order to access the phase lag between E_k and E_p (a positive value of this lag indicating that E_k is late compared to E_p).

For the unloaded condition, we expressed all variables Y as a power law function of ant mass M, i.e., Y = a∗M^b (Merienne et al., 2020). For each variable, the values of the coefficients a and b, as well as the value of the variable predicted by the statistical model for the mean mass of the tested ants (12.5 mg), are given in a table, along with their 95% confidence interval. For the loaded condition, we computed for each ant the ratio of the value of each variable between the loaded Y_l and unloaded Y_u condition. This ratio was then expressed as a power law function of both ant mass M and load ratio LR, defined as 1 + (load mass/ant body mass) (Bartholomew, Lighton & Feener Jr, 1988), i.e., $\frac{Y_l}{Y_u}=c\ast M^d\ast L{R}^e$ (Merienne et al., 2020). The value of the coefficients c, d for ant mass, e for load ratio for each variable, as well as the value of the variable predicted by the statistical model for the mean mass of tested ants and a load ratio of one, along with their 95% confidence interval, are given in a table. The coefficients d and e are positive when the response variable increases with increasing value of ant mass and load ratio, they are negative in the other case.

All data analyses were performed and graphics designed with R (v. 3.5.1) run under RStudio (v. 1.0.136). The confint() function was used to calculate the confidence intervals of the model coefficients.

Unloaded ants: influence of body mass

The analysis of the position of the CoM shows that there was no evidence of a periodic pattern on the Y axis. On the Z axis on the other hand, the position of the CoM (Fig. 3A), as well as its speed norm (Fig. 3B), followed a periodic pattern that was well approximated by a sinus function, as shown by the low value of the RMSE (Table 1, line 1 & 2). Interestingly, the amplitude of the oscillations of the CoM Z position seems to be approximately the same for small and big ants (Fig. 3A). Indeed, the relative amplitude (expressed in units of body length, Table 1, line 3) of the oscillations of the CoM Z position, as well as its mean relative position (Table 1, line 4), decreased significantly with increasing ant mass (F_1,52= 75.88, P < 0.001 and F_1,52 = 105.24, P < 0.001, respectively). The CoM of big ants was thus relatively lower and oscillated with a relatively smaller amplitude than that of small ants. The ant body angle was independent of ant mass (Table 1, line 5).

The variations of E_k and E_p were periodic and the amplitude of E_p was much greater than that of E_k in both small (Fig. 4A) and big ants (Fig. 4B). E_k and E_p were mostly in phase, as shown by the high values of both the correlation coefficient (Table 1, line 6) and the percentage congruity (Table 1, line 7). Nevertheless, E_k and E_p were more in phase for small ants than for big ants (Fig. 5A). The phase lag between the variation of potential and kinetic energies was positive (Fig. 5B) and increased with increasing ant mass (Table 1, line 8: F_1,52 = 11.51, P = 0.001). As a consequence, E_k and E_p were more out of phase for big ants compared to small ants and thus both the correlation coefficient (Table 1, line 6) and the percentage congruity (Table 1, line 7) decreased with increasing ant mass (F_1,52 = 5.79, P = 0.020 and F_1,52 = 4.75, P = 0.034, respectively).

The external mechanical work of the CoM per unit distance (W_ext,d) increased with increasing ant mass (Fig. 6A). However, there was no relationship between the mass-specific external mechanical work of the CoM per unit distance (W_ext,d/m) and ant mass (m) (Table 1, line 9). In the same way, the mean external mechanical power of the CoM (P_ext) increased with increasing ant mass (Fig. 6B) but there was no relationship between the mass-specific external mechanical power of the CoM (P_ext/m) and ant mass (Table 1, line 10).

The percentage of energy recovery was very low and did not depend on ant mass (Table 1, line 11).

Loaded ants: influence of ant mass and load ratio

In the same way as in unloaded condition, no periodicity was found in the CoM Y trajectory in the loaded condition. On the Z axis, independent of ant mass, the sinus-like periodicity of the Z position of the CoM (assessed by the Z position RMSE) decreased with increasing load ratio (Figs. 3C and 3E, Table 2, line2: F_1,52 = 3.87, P = 0.010). We found no significant changes in the relative amplitude of the oscillations of the CoM Z position (Table 2, line 3) and in the mean Z position of the CoM (Table 2, line 4) between the unloaded and loaded condition, whatever the ant mass and load ratio. The speed of the CoM in loaded condition followed a periodic pattern (Figs. 3D and 3F) that was well approximated by a sinus function, whatever the values of ant mass and load ratio (Table 2, line 1). Independent of ant mass and load ratio, the ant body angle did not change between the unloaded and loaded condition (Table 2, line 5).

In the same way as in unloaded condition, E_k and E_p were mostly in phase for low load ratio in small (Fig. 4C) and big ants (Fig. 4D), but less so for high load ratio (Figs. 4E and 4F). Independent of ant mass and load ratio, the correlation coefficient between E_k and E_p did not vary significantly between the unloaded and loaded condition (Fig. 5A, Table 2, line 6) and the phase lag only slightly decreased (Fig. 5B, Table 2, line 8). However, independent of ant mass, the percentage congruity decreased for ants carrying loads of increasing load ratio (Table 2, line 7: F_1,52 = 8.22, P<0.001). In the loaded condition, in the same way as in the unloaded condition, E_k and E_p were more in phase for small ants than for big ants (Fig. 5A). However, contrary to the unloaded condition, the phase lag was not statistically different between small and big ants in the loaded condition (Fig. 5B).

Independent of load ratio, the mass-specific W_ext,d increased with increasing ant mass (Table 2, line 9: F_2,51 = 12.47, P = 0.024) and, independent of ant mass, it also increased with increasing load ratio (F_2,51 = 12.47, P<0.001). However, there was no effect of the load on the mass-specific P_ext (Table 2, line 10). Finally, there was no significant change in percentage recovery between the unloaded and loaded condition (Table 2, line 11).

Unloaded ants

During unloaded locomotion, the mean of the absolute Z position of the CoM, as well as the amplitude of its variations, did not differ between small and big ants. Therefore, relative to their size, the body of small ants was higher over the ground than that of big ants and their CoM made greater vertical oscillations. This difference cannot be explained by a change in body inclination because this latter did not change between small and big ants. It thus seems that small ants are walking in a more erect posture than big ants. This could be related to a more excited state of small ants compared to big ants in response to manipulation, as also suggested by their higher locomotory speed relative to their size (Merienne et al., 2020). Such a difference between ants of different sizes in response to threat has already been found in other ant species, e.g., the leaf-cutting ant Atta capiguara (Hughes & Goulson, 2001), and this could be related to the division of labor within colonies. Further experiments should be performed to answer this question.

The kinetic and potential energies of the CoM were mainly in phase during unloaded locomotion, which led to very low energy recovery values (7–9%). These values are similar to those reported by Full & Tu (1991) in the cockroach Periplaneta americana and a bit below those reported in the cockroach Blaberus discoidalis (Full & Tu, 1990) and in the ant Formica polyctena (Reinhardt & Blickhan, 2014). These values are not consistent with the inverted pendulum model of Cavagna, Heglund & Taylor (1977). As walking ants never display aerial phases (Merienne et al., 2020), their locomotion is thus rather better characterized as a form of grounded running (Formica polyctena: Reinhardt & Blickhan, 2014).

No differences were observed in the mass specific external mechanical work nor in the mass specific external mechanical power between individuals of different sizes. This is in agreement with the literature, which shows that the mass specific external mechanical work is constant over a wide range of animal species ranging from 10g to 100 kg in body mass (Full & Tu, 1991; Alexander, 2005). The value we found in M. barbarus workers (mean ± SD: 1.082 ± 0.175 J m⁻¹ kg⁻¹) is very close to that reported in the literature for a wide variety of organisms, i.e., just above 1 J m⁻¹ kg⁻¹.

Loaded ants

Independent of ant mass, we did not observe any changes in the mean CoM Z position and in the amplitude of the oscillations of the CoM Z position in loaded ants. Even if the CoM mean speed decreased in loaded ants (Merienne et al., 2020), this decrease seems to have little impact on the sinus-like variation of the CoM speed (Figs. 3D and 3F). On the other hand, the pattern of variation of the CoM Z position was strongly affected by heavy loads. The locomotion was much more jerky and the variations in the CoM Z position could not be approximated by a sinus function, especially for big ants (Fig. 3E). Moreover, because of the decrease in locomotory speed due to carrying a load (Merienne et al., 2020) and the amplitude of the CoM Z position which remained unchanged, the amplitude of the variation of the CoM potential energy became much greater than that of the kinetic energy (Figs. 4C–4F). The mechanical energy required to raise the CoM in loaded ants is thus much greater than that required to accelerate it in the forward direction. Therefore, the variations in the CoM potential energy and in the CoM mechanical energy are nearly identical and the external mechanical work is mostly achieved for raising the CoM.

Independent of ant mass, the mass specific mechanical work increased with load ratio. This is an unexpected result as the mass specific mechanical work is independent of load ratio in humans (Bastien et al., 2016). It is thus mechanically more costly for ants to move one unit of mass on one unit of distance during loaded locomotion than during unloaded locomotion. Moreover, independent of load ratio, the mass specific mechanical work increased with ant mass, which means that the mechanical work big ants have to perform in order to raise one unit mass of their body on one unit of distance is greater than that of small ants.

Compared to unloaded locomotion, none of the gait parameters we studied was modified in a discrete way in loaded locomotion. We conclude that ants do not use a specific gait in order to carry a load. Rather, they adapt their locomotion to the mass of the load they transport.

In this study we focused only on the external mechanical work ants have to perform in order to raise and accelerate their CoM. Therefore, we did not take into account the movement of the leg segments in the determination of both the position of the overall CoM and the internal mechanical work that ants have to perform in order to accelerate their legs relative to their CoM. Kram, Wong & Full (1997) found in the cockroach Blaberus discoidalis that this internal work represents about 13% of the external mechanical work generated to lift and accelerate the CoM. Considering that the stride frequency of M. barbarus (mean ± SD: 4.8 ± 0.9 Hz, Merienne et al., 2020) is lower than that of B. discoidalis (mean ± SD: 6.8 ± 0.8 Hz, Kram, Wong & Full, 1997), if one assumes that the mass of the legs of M. barbarus workers represents the same percentage of total body mass as that of B. discoidalis, i.e., 10–12% (Kram, Wong & Full, 1997), we would expect the internal mechanical work to represent a smaller part of the total mechanical work in M. barbarus compared to B. discoidalis. Despite the technical difficulties for tracking the 3D displacement of insect legs (but see: Uhlmann et al., 2017), this aspect could constitute an interesting perspective for further studies.