Foraging grass-cutting ants (Atta vollenweideri) maintain stability by balancing their loads with controlled head movements

Abstract

Grass-cutting ants (Atta vollenweideri) carry leaf fragments several times heavier and longer than the workers themselves over considerable distances back to their nest. Workers transport fragments in an upright, slightly backwards-tilted position. To investigate how they maintain stability and control the carried fragment’s position, we measured head and fragment positions from video recordings. Load-transporting ants often fell over, demonstrating the biomechanical difficulty of this behavior. Long fragments were carried at a significantly steeper angle than short fragments of the same mass. Workers did not hold fragments differently between the mandibles, but performed controlled up and down head movements at the neck joint. By attaching additional mass at the fragment’s tip to load-carrying ants, we demonstrated that they are able to adjust the fragment angle. When we forced ants to transport loads across inclines, workers walking uphill carried fragments at a significantly steeper angle, and downhill at a shallower angle than ants walking horizontally. However, we observed similar head movements in unladen workers, indicating a generalized reaction to slopes that may have other functions in addition to maintaining stability. Our results underline the importance of proximate, biomechanical factors for the understanding of the foraging process in leaf-cutting ants.

Appendix

We used simplified two-dimensional models to calculate the fragment angle that a load-carrying ant should keep to avoid any forward or backward shift of the total center of mass (Figs. 7, 8).

Fig. 7

Calculation of the angle α‘ at which the ants would have to hold long fragments to keep the projected position of the total center of mass constant. α Fragment angle for short fragments, l _f length of short fragment, l′_f length of long fragment, COM _a: ant center of mass, COM _f fragment center of mass, COM _t total center of mass, c _f (c _t) distance between mandibles and the projection of COM_f (COM_t)

Fig. 8

Calculation of the fragment angle α′ required to keep the distance c _t between the mandibles and the total center of mass (projected onto the body axis) constant when walking on slopes: a uphill (ω = 20°), b horizontal and c downhill (ω = −20°). α Fragment angle when walking horizontally, c _f distance between the mandibles and the projected fragment center of mass, l _f length of the fragment, COM _a ant center of mass, COM _f fragment center of mass, COM _t total center of mass

Fragments of different length

When carrying short and long fragments, ants have to change the fragment angle to avoid any forward or backward shift of the total center of mass (COM_t, ant + fragment). Thus, the anterior–posterior position of the center of mass (i.e. the vertical projection of COM_t onto the body axis) has to remain unchanged. This implies that

$$ c_{\text{t}} = c^{\prime}_{\text{t}} $$

(2)

where c _t is the distance between the mandibles and the total center of mass (both projected onto the body axis, see Fig. 7) for the short fragment, and c _t ’ the corresponding distance for the long fragment. As the fragment mass and the ant’s body mass are the same in both cases, the projected position of the fragment’s center of mass along the body axis remains also constant:

$$ c_{\text{f}} = c^{\prime}_{{_{\text{f}} }} $$

(3)

where c _f is the projected distance between the mandibles and the fragment center of mass. As the ants hold the fragment very near the end, c _f can be expressed in terms of the fragment’s length l _f and angle α for short fragments

$$ c_{\text{f}} = {\frac{{l_{\text{f}} }}{2}}\cos \alpha $$

(4)

and accordingly for long fragments:

$$ c^{\prime}_{\text{f}} = {\frac{{l^{\prime}_{\text{f}} }}{2}}\cos \alpha^{\prime} $$

(5)

Combination of Eqs. 3, 4 and 5 gives a prediction for the fragment angle when carrying long fragments:

$$ \alpha^{\prime} = \arccos \left( {{\frac{{l_{\text{f}} }}{{l^{\prime}_{\text{f}} }}}\cos \alpha } \right) $$

(6)

As the mean angle for short fragments (l _f = 15 mm) was α = 39°, we would therefore expect ants to carry long fragments ($l'_{\text{f}}$=30 mm) at an angle of α′=67° to keep the projected position of the total center of mass constant.

Carrying fragments on slopes

As for fragments of different length, ants carrying the same fragment on different slopes should adjust the fragment angle to keep the distance between the mandibles and the projected total center of mass constant (see Eq. 2). We use the projection of COM_t onto the body axis here; the small distance between the body and the surface is ignored here for simplicity. To predict the angle α′ at which ants would have to carry fragments on different slopes ω to avoid any forward or backward shift of COM_t, we used a similar model as above (Fig. 8). As both the ant’s mass and the fragment mass do not change when walking on slopes, Eq. 3 is valid. For an ant carrying a fragment horizontally the distance between the mandibles and the projected fragment center of mass is given by Eq. 4. The corresponding distance for ants walking uphill and downhill is

$$ c^{\prime}_{\text{f}} = {\frac{{l_{\text{f}} }}{2}}{\frac{{\cos (\alpha^{\prime} - \omega )}}{\cos \omega }} $$

(7)

Combination of Eqs. 3, 4 and 7 gives the prediction for the fragment angle required to keep the distance between the mandibles and the projected total center of mass constant:

$$ \alpha^{\prime} = \arccos \left( {\cos \alpha \cos \omega } \right) + \omega $$

(8)

Ants carrying the fragment at an angle of α = 45° when walking horizontally, should hold it at α′=68° when walking uphill (ω = +20°) to keep c _t constant. Correspondingly, when walking downhill (ω = −20°), they should carry the fragment at an angle of α′=28°. Equation 8 shows that ants walking uphill would have to hold fragments in a forward orientation (α′ > 90°) already for slopes of ω > arctan(cosα) = 35.3° (for α = 45°). For even steeper slopes, the contribution of the small distance between body and substrate will become important, making it increasingly difficult even for unloaded ants to keep their center of mass within the supporting leg tripod.