Ants swimming in pitcher plants: kinematics of aquatic and terrestrial locomotion in Camponotus schmitzi

Abstract

Camponotus schmitzi ants live in symbiosis with the Bornean pitcher plant Nepenthes bicalcarata. Unique among ants, the workers regularly dive and swim in the pitcher’s digestive fluid to forage for food. High-speed motion analysis revealed that C. schmitzi ants swim at the surface with all legs submerged, with an alternating tripod pattern. Compared to running, swimming involves lower stepping frequencies and larger phase delays within the legs of each tripod. Swimming ants move front and middle legs faster and keep them more extended during the power stroke than during the return stroke. Thrust estimates calculated from three-dimensional leg kinematics using a blade-element approach confirmed that forward propulsion is mainly achieved by the front and middle legs. The hind legs move much less, suggesting that they mainly serve for steering. Experiments with tethered C. schmitzi ants showed that characteristic swimming movements can be triggered by submersion in water. This reaction was absent in another Camponotus species investigated. Our study demonstrates how insects can use the same locomotory system and similar gait patterns for moving on land and in water. We discuss insect adaptations for aquatic/amphibious lifestyles and the special adaptations of C. schmitzi to living on an insect-trapping pitcher plant.

Appendix: Blade element calculation of drag and thrust

As only the coxae and foot tips were digitised in the 3D recordings of swimming C. schmitzi ants, we made the simplifying assumption that the legs are straight cylinders of variable length (extending from the coxa to the foot tip) that move through the water. As the legs’ drag and thrust forces are dominated by the velocity of the foot, the error introduced by ignoring leg segmentation is probably small.

For each pair of consecutive video frames, we calculated the velocities v _c and v _t of the coxa and the tarsus, respectively, from the observed displacements

$$ \overrightarrow {{v_{c} }} = \left( {\begin{array}{*{20}c} {v_{cx} } \\ {v_{cy} } \\ {v_{cz} } \\ \end{array} } \right)\;\;,\;\;\overrightarrow {{v_{t} }} = \left( {\begin{array}{*{20}c} {v_{tx} } \\ {v_{ty} } \\ {v_{tz} } \\ \end{array} } \right) $$

where forward movements were defined as positive x displacements; upward movements as positive z displacements.

The corresponding leg length L and the leg direction were calculated from the vector $\overrightarrow {L}$ connecting the coxa and tarsus positions halfway between two consecutive video frames.

At a position l along the leg, the velocities in the x, y and z directions are:

$$ \overrightarrow {v\left( l \right)} = \left( {\begin{array}{*{20}c} {v_{cx} + \frac{l}{L}\left( {v_{tx} - v_{cx} } \right)} \\ {v_{cy} + \frac{l}{L}\left( {v_{ty} - v_{cy} } \right)} \\ {v_{cz} + \frac{l}{L}\left( {v_{tz} - v_{cz} } \right)} \\ \end{array} } \right) $$

The angle between the leg and the velocity vector is the “angle of attack”, α, which is calculated as:

$$ \alpha = \arccos \left( {\frac{{\overrightarrow {L} \cdot \overrightarrow {v\left( l \right)} }}{L \cdot v\left( l \right)}} \right) $$

The flow velocity normal to the leg is thus v(l) sin α, and the axial flow velocity is v(l) cos α.

We divided each leg into 100 short cylinders of length dl = L/100, each representing a blade element with a projected area of A = dl × w, where w is the width of the leg. The blade element experiences a drag in the normal direction of

$$ F_{\text{N}} = \frac{1}{2}C_{\text{DN}} \rho A\;\left[ {v\left( l \right)\sin \alpha } \right]^{2} $$

and in the axial direction of

$$ F_{\text{A}} = \frac{1}{2}C_{\text{DA}} \rho A\;\left[ {v\left( l \right)\cos \alpha } \right]^{2} $$

where ρ is the density of water at 25 °C and C _DN and C _DA are the drag coefficients in the normal and axial direction, respectively. The drag coefficients were estimated according to Ellington (1991) from the corresponding Reynolds numbers (Re) as

$$ C_{\text{DN}} = 1.1 + \frac{22}{{Re_{\text{N}} }}\, \text{ and } \,C_{\text{DA}} = \frac{1.33}{{\sqrt {Re_{\text{A}} } }} + \frac{2l}{{wRe_{\text{A}} }}$$

where Re _N = vwρ/η and Re _A = vlρ/η are the Reynolds numbers for normal and axial flow, where η is the dynamic viscosity.

For each leg and video frame, we summed up the normal and axial drag across all blade elements and calculated the total force along the body (x) axis.

Apart from drag, the swimming ant experiences a force due to the acceleration of fluid, the acceleration reaction (Daniel 1984). We estimated this force at each point in time as the product of the mass of the blade element, an added mass coefficient (≈1 for a cylinder normal to the direction of motion), the density of water and the acceleration of the blade element normal to its surface. We found the contribution of the acceleration reaction to be highly variable (positive or negative) and insignificant (ca. 10 times smaller than the drag force); we therefore excluded it from the analysis.