Path integration in a three-dimensional maze: ground distance estimation keeps desert ants Cataglyphis fortis on course
1 Department of Biology, Humboldt-Universität zu Berlin,
Invalidenstrasse 43, D 10099 Berlin, Germany
2 Department of Zoology, University of Zürich, Winterthurerstrasse 190,
CH 8057 Zürich, Switzerland
* Author for correspondence (e-mail: Bernhard.Ronacher{at}Rz.Hu-Berlin.De)
Accepted 5 September 2005
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Summary |
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Key words: three-dimensional path integration, distance estimation, odometer, ant, Cataglyphis fortis
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Introduction |
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In the experiments of Wohlgemuth et al.
(2002), the ants were trained
and tested in a linear array of hills or in a linear horizontal channel. It
was, therefore, not evident whether the animals can integrate this measurement
of ground distances into their path integrator module in a more complex,
really three-dimensional (3D) task. We set out to investigate if this is, in
fact, the case. In order to do so, we employed the following experimental
paradigm. If ants are trained to visit a feeder via an L-shaped set
of channels, the azimuth steered by the animals on their way back from the
feeder to the nest will depend on the lengths of the channel segments. From
the angles steered, we can hence infer the relation of the lengths of both
segments, as they were gauged by the ants' odometer. If one section of the
L-shaped outbound route is not laid out on level ground but leads up to an
apex and back down again (Fig.
1A), and if the other, horizontal, section is of known length, we
can determine from the ants' homing direction the length by which the sloped
segment added to the state of the path integrator. We assume two possible
outcomes. Either, the `hill' segment is measured by the walking distance, or
alternatively, the animals could have integrated this segment only with the
(shorter) ground distance. In this paper, we show that sloped parts of an
ant's journey are correctly incorporated into the path integrator with their
corresponding ground distances. As a consequence, the home vector of desert
ants also maintains its accuracy in heavily undulating, 3D terrain.
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Materials and methods |
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Ants were trained from their nest entrance to visit a feeder, using pieces of watermelon and biscuit crumbs. Training took place in aluminium channels (dimensions: 7 cm wide, height of side walls: 7 cm). A PVC wall surrounded the nest entrance and guided foraging ants into the attached training channel (Fig. 1A). Fine grey sand was glued to the channel's bottom in order to facilitate the animals' walking. The inner side walls were painted grey to prevent possibly irritating reflections from the channel walls' metallic surfaces. The upper end of the walls was evenly covered with khaki-coloured adhesive tape in order to minimise, by its smooth surface, escape attempts. The channels provided no visual contrast cues that could be used to estimate distances.
3D experiment
The first leg of the channel system led away horizontally from the nest
entrance for 3 m in a southward direction. The second leg connected at a right
angle, leading either towards the east or the west in mirrored test set-ups
(in Fig. 1A, the westward
orientation is shown). This second leg led upwards at an inclination of
70° for 2 m. It was followed by a short horizontal channel (0.35 m) at a
height of 1.9 m above the ground, before a last channel segment led back down
to ground level (inclination: -70°, length: 2 m). The end of this downward
ramp marked the training location of the feeder, placed in a short channel
segment that was closed at its far end
(Fig. 1A).
Straight 3D control
In a first control experiment, the path from the nest to the feeder was
laid out in a straight line pointing southward, i.e. without leading around a
corner. The ascending and descending channel segments of this control followed
a level channel segment of 3 m length, and were identical to those of the 3D
experiment described above (not shown).
2D controls
In a second set of control experiments, the channels were laid horizontally
on the ground (Fig. 1B,C). The
first leg was identical with the 3D set-up. The second leg connected at a
right angle, but horizontally, pointing either east or west, and led to a
feeder at a distance from the bend of 1.4 m or 4.35 m. These distances
corresponded to the ground and walking distances, respectively, in the 3D
set-up. Thus, the homing azimuths from the critical, 3D test could be compared
with results of animals that had walked the corresponding ground distance or
walking distance in the horizontal plane.
Animals that had performed several successful foraging trips between the feeder and the nest, as indicated by their unhesitating climb and descent on the sloped parts of the channel, were captured and transferred in a lightproof container to a test field at some distance to the training site. The test field was a flat area devoid of any vegetation, with a grid (10 mx10 m; grid width: 1 m) consisting of thin white lines painted on the desert floor. An ant was released after ascertaining that it had a food item between its mandibles and was therefore intending to return to the nest. The ant's path across the test field was recorded for 3 min on squared paper.
In order to determine the compass directions of the ants' initial homebound
run, we drew a circle corresponding to a test field radius of 1 m and 2 m
around the animal's release point and measured the azimuth of the ant path's
intersection with both circles (as conventionally done in Cataglyphis
experiments; see Wehner,
1968). The length of the home vector was measured as the distance
between the release point and the position where the ant first made a distinct
turn, which usually indicates that the animal has run off its vector and begun
making search spirals in order to find the nest entrance
(Wehner and Srinivasan, 1981
).
Furthermore, the complete runs were digitised on a graphic tablet (Digikon 3,
Kontron, Eching, Germany) with GEDIT Graphics Editor & Run-Analyser
(Antonsen, 1995
). The paths of
all ants during the first 30 s after release were combined for each treatment,
respectively. Also, search densities were determined for each treatment by
calculating the animals' walking distance within a particular area (grid
width: 0.25 m) in relation to the total walking distance (measured over the 3
min period).
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Results |
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In each training situation, the intersection points of runs at 1 m and 2 m distance from the release point were highly clustered (Rayleigh test, P<0.001, Fig. 3), resulting in all cases in high mean vector strengths (for 1 m/2 m radius: 3D: 0.95/0.93; ground distance: 0.96/0.97; walking distance: 0.95/0.98). The mean vectors of the two control groups from L-shaped training (ground distance control and walking distance control) differed strongly from each other (MWW test, P<0.001, both at 1 m and 2 m radius). The mean azimuths of these control runs pointed into the expected direction with high accuracy (2 m meanazimuth vs expected azimuth: ground distance control, 25.1° vs 24.9°, Fig. 3B, outer black arrow; walking distance control: 64.7° vs 55.4°, Fig. 3C, outer white arrow).
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Three-dimensional training along a straight path (Fig. 3D, N=20, both radii) showed that climbing and descending did not shift an ant's homing direction: intersection points were highly clustered (Rayleigh test, P<0.001) and clearly oriented towards the expected nest position (Fig. 3D, outer grey arrow), located at due north (mean vector strength: 0.97/0.98; 2 m azimuth: 4.3°; Fig. 3D).
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The search density diagrams of the test and control experiments reveal for all training situations that search densities were highest between the release point and the expected nest position (Fig. 5). In 3D training, ground distance controls, and straight controls, the club-shaped area of high search densities just reaches the expected position of the nest according to its ground distance, with much lower densities in the sector beyond (Fig. 5A,B,D). This distance undershooting is even more pronounced in the case of walking distance controls, where only low search densities were found at the fictive position of the nest (Fig. 5C).
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Discussion |
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The mean home vectors in the two 2D controls differed distinctly and
corresponded closely to the expected directions (compare
Figs 3B,C and 1B,C). The mean
home vector of ants trained in the 3D set-up
(Fig. 1A) was indistinguishable
from that of the 2D control with the 1.4 m leg (compare
Fig. 3A,B), which corresponded
to the ground distance of the 3D maze. These results allow two conclusions:
first, that Cataglyphis fortis is indeed able to derive the ground
distance information when walking over hills and, second, that this
information is incorporated in a meaningful way into the path integration
process. Furthermore, these results provide independent support for and extend
the hypotheses developed in Wohlgemuth et al.
(2001,
2002
): The path integration
module is also fully functional in 3D tasks, enabling desert ants to navigate
accurately even in landscapes with strong vertical stratification.
The exact mechanism by which the ants determine the slope of a steep ascent
or descent remains to be unravelled. In Formica polyctena,
hair-plates at the joints of the coxae, and on the joints between head and
thorax, and between petiolus and gaster, play a role in the perception of
relative positions of body parts, which in turn may enable the ant to judge
its overall orientation within the gravity field
(Markl, 1962). Interestingly,
in Cataglyphis fortis, the manipulation of hair fields in the neck of
the ant, as well as hair fields located between petiolus and gaster, did not
yield any change in the distance estimation
(Wittlinger et al., 2005
).
A second important input source of the ant's path integrator is the pattern
of polarised skylight, which is used by Cataglyphis (and other
insects) as the main allothetic compass cue
(Fent, 1986;
Wehner, 1997
). However, under
the present training paradigm two systematic error sources could influence the
ant's perception of compass directions. Because of the limited view of the sky
within the channel on the way to the feeder, as opposed to a full view on the
return trip, a discrepancy exists between the perceived compass directions of
the outbound and inbound route
(Müller, 1989
). The
amount and direction of the navigational errors within both channels of the
L-shaped 2D control experiments depends on the walking direction (i.e. the
channel's compass bearing) and the channel's angle relative to the solar
azimuth. At present, a precise estimation of errors that may have been
introduced by different view sectors of the sky is not possible.
The straight controls aimed at estimating the extent of this possible error
in the ants' determination of the homing direction. The skylight compass can
be described as a detector for the orientation of the symmetry plane of the
E-vector pattern present in the sky (Rossel and Wehner,
1984,
1986
;
Wehner, 1998
). However, it
actually employs an averaging mechanism of polarisation orientations and
intensities over a large area of the visible sky
(Wehner, 1994
). If the sun's
azimuth is not aligned with the orientation of the channel in which the ant
walks, and if large parts of the sky become invisible for the ant while
climbing on a ramp, the axis of symmetry of the polarisation pattern appears
under a different azimuth. Hence, the ant may perceive a deviation of her
walking course while being on a slope. In the straight control, such an error
did not occur (Fig. 3D). We
suggest the reason is that the errors of the upward and downward slopes are in
mirrored orientation to each other and therefore cancel out, as long as the
orientation of upward and downward slopes is mirrored as well. This symmetry
is unaffected by the position of the sun and the resulting orientation of the
polarisation pattern.
In addition, we cannot decide to what extent the ants having been trained
over extended periods of time have derived the exact compass courses from the
sun and the spectral gradients in the sky (for the latter, see
Wehner, 1997). Finally, in
one-sided detour arrangements systematic errors are to be expected according
to what is known about the ant's path integration system
(Müller and Wehner, 1988
;
Müller, 1989
; cf. also
Hartmann and Wehner, 1995
). As
all these potential sources of systematic errors are superimposed in ways that
vary according to the time of day, it is nearly impossible to predict the
total effect these error sources might have on the ants' bearings in the
tests. In fact, the ants' bearings in all experiments with L-shaped channel
combinations correspond amazingly well with the expected ones
(Fig. 3A,B). Only in the
walking distance controls (Fig.
3C), ants exhibit a systematic error, turning too far inwards, by
9°, as was described first for Cataglyphis
(Müller and Wehner, 1988
;
Müller, 1989
), and found
in other insects and mammals in L-shaped training situations alike
(Etienne et al., 1996
;
Séguinot et al., 1998
).
We do not have a convincing explanation why this `Müller'-error did not
occur in the tests of Fig.
3A,B. One possible reason is that the second leg of the L was too
short to induce this kind of error. We also checked whether the day-time of
testing could have led to a shift that canceled this error (cf.
Müller, 1989
), but this
cause could be ruled out.
The accuracy of the ant's path integrator in a 3D environment can also be
estimated by the distance that an ant walks in a straight path before it
begins to search for the nest entrance in conspicuous search loops. The
results after a 3D outbound run did not differ from the ground distance
control, but differed significantly from the walking distance control
(Fig. 4, see also
Fig. 5). This also suggests
that the path integrator treats sloped sections of an itinerary in the same
way as their corresponding ground distances. It is worth noticing, however,
that the distances covered before the search behaviour started, were in all
cases too short. This `undershooting' is a phenomenon that has been repeatedly
observed in experimental set-ups where ants performed an outbound trip within
a channel and then were transferred to the open field for their return trip
(Burkhalter, 1972;
Müller, 1989
; Collett et
al., 1999
,
2003
). The most likely
explanation for the premature end of the vector run is the discrepancy between
the panoramic views that the ants expect in the nest's vicinity and the actual
imagery. The memorisation of landmarks in the vicinity of the nest and the
ability of actions associated with these `snapshots' to override the state of
the path integrator, could already be demonstrated
(Andel and Wehner, 2004
). The
search density diagrams (Fig.
5) show that the undershooting results in the ants spending most
time in an area that lies on the feeder's side of the expected position of the
nest. Hence, under natural conditions, the ants would start their search
within an area they are familiar with. They should be able to pick up visual
cues that they had passed numerous times just recently while shuttling back
and forth between the feeder and the nest, leading them to the nest entrance
(cf. Sommer and Wehner,
2004
).
One question that this study cannot yet answer is whether the ants possess
a 3D representation of their world, or if hills and valleys are only computed
with their correct ground distance, with any further information about the
position on the vertical dimension being discarded immediately. Recent,
preliminary findings suggest, however, that the notion of an elevated food
source as being `above the ground' is present in the ant's representation of
space (Grah et al., 2005).
Lastly, there remains the question of ecological relevance for the species examined. Cataglyphis fortis lives on salt pans and in the desert, i.e. in only slightly undulating terrain. It does not climb on trees or into bushes, where the third dimension takes on an important role in the definition of a point in space. Most probably, a path integrator that incorporates slopes with their walking distances (instead of their ground distances) would still work reasonably well for this species. But other cataglyphids, like C. bicolor, live in more uneven habitats and might very much have to rely on an orientation mechanism that also keeps fully functional in a heavily undulating, 3D environment.
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Acknowledgments |
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