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First published online August 17, 2006
Journal of Experimental Biology 209, 3301-3308 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02370
Integrating two-dimensional paths: do desert ants process distance information in the absence of celestial compass cues?
1 Department of Biology, Humboldt University, Invalidenstr. 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 June 2006
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Summary |
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Key words: path integration, odometer, polarization compass, desert ant, Cataglyphis
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Wehner,
2003). Individual foragers perform large scale excursions from
which they return to their nest on the shortest route. This navigational feat
is accomplished with remarkable precision by a path integrator, which allows
for an approximate form of dead reckoning
(Wehner and Wehner, 1986;
Wehner and Wehner, 1990;
Müller and Wehner, 1988;
Wehner and Labhart, 2006). To
perform path integration the animals need two types of essential information,
that is, directional information (with reference to an external compass cue),
and information about the distances travelled in a particular direction
[(Müller and Wehner,
1988; Wehner,
1994); for a discussion of the necessity of distance information,
however (see Biegler, 2000)].
It is well established that ants as well as other insects rely on
polarizational (and, to a lesser degree, on intensity and spectral) sky-light
cues, for determining their travelling direction (e.g.
Wehner, 1982;
Wehner, 1997;
Dacke et al., 2003). Concerning
the measurement of travelling distances, evidence is accumulating that
Cataglyphis uses idiothetic cues, their odometer seems to be based on
a kind of step counter or an efference copy of a locomotor central pattern
generator (Wohlgemuth et al.,
2001; Wohlgemuth et al.,
2002; Thiélin-Bescond
and Beugnon, 2005; Wittlinger
et al., 2006). Idiothetic information can be used also by some
arthropods to identify changes in walking directions
(Seyfarth et al., 1982;
Mittelstaedt, 1985;
Moller and Görner, 1994)
(cf. Chittka et al., 1999).
However, these two pieces of information, about distance and direction,
must be processed in a meaningful way, in order to yield a correct home
vector. On the basis of a detailed analysis of directional errors produced by
Cataglyphis, when trained in a channel with sharp bends, Müller
and Wehner proposed that the ants use an approximate iterative algorithm to
continuously update their home vector on the basis of compass and odometric
information (Müller and Wehner,
1988). The aim of the present study was to further investigate the
interplay of these two essential inputs to the path integrator. In particular,
we asked how travelling distance is processed in a two-dimensional path if the
ants are deprived of any sky-light-based compass information during parts of
their path. Ants were trained in a Z-shaped channel system, the middle part of
which was covered with orange Perspex that excluded any short-wavelength
light, and therefore prevented the perception of polarization patterns, as
these are received by UV receptors in the dorsal rim region
(Wehner, 1994;
Labhart, 2000;
Labhart and Meyer, 2002). The
parcours in the channel maze was designed in a way that any change in the
ant's processing of walking distances while travelling in the Perspex covered
part of the maze should translate into a change of homing direction when the
animals returned to the estimated (fictive) nest position on a test field. The
main message from our data is that the odometric information about travelling
distance is largely ignored for path integration, if there is no simultaneous
input from the sky-view-based compass. This paper extends and confirms a
recent study (Sommer and Wehner,
2005), which explored the influence of celestial cues on the
processing of distance information in a linear channel array.
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Materials and methods |
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). A PVC
wall surrounded the nest entrance and guided foraging ants into the attached
training channel.
Straight control
In a control experiment, a 4-m channel leading from the nest to the feeder
was laid out in a straight line, pointing southward (see inset in
Fig. 1C).
|
)]. The dimensions were chosen to yield the same total lengths
in the N-S segments and the E-W segment. Hence, the expected homing directions
in the `open' controls were 315° and 45°, respectively. In the crucial
experiments, the compass information based on sky-light cues was completely
withheld for the middle segment (see Fig.
2). This was achieved by covering the channel with orange Perspex
that was completely non-transparent to UV radiation, and thereby precluded the
perception of polarization patterns which depends on UV receptors
[(Duelli and Wehner, 1973;
Labhart, 2000); the Perspex,
no. 478, Röhm and Haas, Darmstadt, excluded all wavelengths below 540 nm
- see curve e in fig. 43 in Wehner
(Wehner, 1982)]. In addition,
wooden plates of 60 cm width were arranged above the channels at a height of
approximately 80 cm above ground. These screens prevented the direct view of
the sky and in particular of the sun's position. In the experiment shown in
Fig. 2, the Perspex cover
extended by 15 cm into the N-S segments, so that an ant entering the middle
segment had to perform its 90° turn without sky view. However, in a
modification of this experiment the bends were left open (open section
extending 15 cm into the middle segment of the `Z'; see
Fig. 3). Hence, in this set-up
the ants could perform their 90° turns while still relying on sky compass
information.
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;
Wehner, 1994) works well under
natural conditions but induces systematic navigational errors if an ant is
trained in a straight channel, which restricts its view of the sky, and is
later released on a test field
(Müller, 1989). Such
errors may have been relevant also in our experimental set-up, although the
design of the Z-shaped maze with its perpendicularly oriented segments should
minimize this influence, as the opposite deviations caused by the N-S segments
and those caused in the E-W segment should largely cancel out (see
Fig. 1A,B). However, if the sky
view in the middle segment was occluded, then the errors induced by the
remaining open segments should be unveiled. The sign and size of this type of
directional errors depend on the orientation of the channel and the time of
day. For a N-S direction of the channel, Müller found that the deviations
were maximal, up to 20°, between 10:00 and 11:30 h, and, in the opposite
direction, between 13:00 and 14:30 h
[(Müller, 1989), fig. 10
therein]. Provided that the tests are evenly distributed over the whole day,
positive and negative deviations, although increasing the standard deviations,
should roughly cancel out. This held true for the straight control
(Fig. 1C), but in the
experiments shown in Fig. 2B
and Fig. 3B, the sampling times
were biased towards the afternoon (see Results).
Second `Z' experiment
We therefore decided to repeat the experiment of
Fig. 2 by choosing those times
of day (14:30 to 17:30 h) and an orientation of the uncovered channels (E-W)
that should result in only small errors [of less than 5°, see fig. 10 in
Müller (Müller,
1989)]. In this second experiment the channel segments were chosen
somewhat longer (2.65 m, 4.85 m and 2.20 m), and only the N-S direction of the
middle segment was used (see inset in Fig.
4), since the results of the first experiment [and those of others
(see Grah et al., 2005)],
revealed no influence of the compass direction in the mirror symmetric
arrangements. For the crucial experiment, the middle leg of the Z was covered
with orange Perspex, including the bends, and as before the direct view of the
sky and the sun was prevented (in this experiment 20 cm wide wooden plates
were arranged above the channels at a height of 15-20 cm above the
ground).
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Animals that had performed at least three successful foraging trips between
the feeder and the nest, as indicated by their unhesitating passage of the
covered segment 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 it was ascertained that it had a food item between
its mandibles and therefore intending to return to the nest. The ant's path
across the test field was recorded on squared paper until it switched to
search spirals (cf. Wehner and Srinivasan,
1981).
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, 2 m, 3 m,
and, if possible, 4 m around the animal's release point and measured the
azimuth of the ant path's intersection with these 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
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).
The directionality of intersection points of a treatment was examined using
the Rayleigh test, and the agreement with a theoretical value was checked by
calculating the 99% confidence intervals [chapter 5 in Batschelet
(Batschelet, 1981)].
Differences between mean angles obtained in different treatments were checked
using the Watson-Williams test, with a Bonferroni correction for multiple
comparisons if appropriate. All statistical parameters were calculated using
Oriana circular statistics software
(Kovach, 2004).
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Results |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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This picture changed drastically when the compass information was withheld in the middle segment of the Z (Fig. 2). Now the mean homing directions at 2 m were 350.3°±26.0° and 15.0°±23.7°, respectively (N=23, 20). In Fig. 2A the mean homing directions were not significantly different from the zero direction (i.e. north) at all distances, nor from the straight control (P>0.05, Watson-Williams test), but significantly different from the respective Z controls with an open sky view (compare Fig. 1A, P<0.01, after Bonferroni correction). In Fig. 2B the mean at 1 m was not significantly different from 0°, whereas those at 2 m and 3 m were significantly different from the theoretical value of 0°, according to the 99% confidence intervals (see Materials and methods). However, at all distances the mean homing directions shown in Fig. 2B were not significantly different from the straight control (Fig. 1C; Watson-Williams test P>0.10), but significantly different from the open controls at all distances (compare Fig. 1B; all P<0.001).
There are several possible reasons for this result. For the moment let us
focus on only one of them, i.e. that the ants were unable to perceive, or
simply ignored, the 90° turns when entering the occluded channel segment
(the channel was covered for up to 15 cm from the bends; see Materials and
methods). If the ants did not take into account these 90° turns, they
should have `added' the 4 m of the mid-segment to their north-bound home
vector at a rather small angle. (In the last leg the ants had an open sky view
again, so that this travelling distance must also have been assigned to the
north-bound vector.) Hence, under this assumption, the path lengths should
have been much larger than in the straight and open controls - which was not
observed. The lengths of the straight homing path segments, before the ant
switched to its typical search loops, were 3,43±1.11 m and
3.36±1.08 m for the data in Fig.
2A,B [difference to the open controls: not significant (n.s.) and
P<0.01, for a, b, respectively]. Although this was 27% and 24%
larger than the mean path length in the straight control (2.70±0.77 m,
Fig. 1C; differences n.s.;
t-test with Bonferroni correction), these homing distances were much
smaller than the 8-m prediction from the above hypothesis, but, most
importantly, still smaller than the distances observed in the open controls
(4.04±1.32 m and 4.46±1.11 m for
Fig. 1A,B). The path lengths
observed in the experiment shown in Fig.
3 were 3.9±1.97 m and 3.18±1.03 m (both n.s.
different from those of Fig.
2). Hence, the estimated nest distances are by no means compatible
with the assumption mentioned above. Note that the path lengths observed in
the controls were also distinctly smaller than the expected values of 4 m and
5.66 m (P<0.001). A similar undershooting of walking distances,
however, has been frequently found if training and testing conditions were
rather different, as in the present experiments (e.g.
Grah et al., 2005).
There is an additional result which makes the above interpretation of a misperception of the 90° turns very unlikely. We ran a control experiment in which the bends were left uncovered so that the ants could perform their 90° turn still with an open view of the sky (Fig. 3). If, in the situation with covered 90° bends (Fig. 2), the ants had wrongly perceived only the turning angle, while the distance estimate was unaffected, the experiment shown in Fig. 3 should yield a clearly different picture, as the ants now performed their 90° turn under open sky. But the path directions shown in Fig. 3 closely resemble those of Fig. 2 (data of Fig. 3A and Fig. 2A not significantly different at all radii, P>0.3; data of Fig. 3B and Fig. 2B not significantly different at 1 m and 2 m radii, only at 3 m: P<0.02; Watson-Williams test with Bonferroni correction).
Hence, the shift of homing path directions seen in
Fig. 2 (compared with
Fig. 1) cannot be solely
explained by an incorrect perception of the 90° turns. Rather, it must be
the processing of distance information within the path integration module that
has been affected by the exclusion of compass information. A puzzling result,
however, is the remaining angular deviation from a purely northern direction,
of 10° and 15° (Fig.
2A,B). In this context the directional errors induced by a partial
versus complete view of the sky must be considered
[(Müller, 1989); see also
Materials and methods]. Indeed, the 10-15° deviations found in
Fig. 2 are in the range of the
sizes of errors observed by Müller
(Müller, 1989). As in the
experiments shown in Fig. 2B
and Fig. 3B the sampling times
were biased towards the afternoon, this bias could have contributed to the
observed `deviation' from a pure northern direction. For the `left' condition
(E-W orientation of the mid-segment; Fig.
2A, Fig. 3A), there
was a smaller bias towards testing in the morning. We tentatively corrected
for these effects by subtracting the values reported in fig. 10 of Müller
(Müller, 1989) from
individual data points, according to the time of day of testing. Although this
procedure did shift the mean angles towards the expected 0° value (in
Fig. 2A from 350.3° to
352.5°, and in Fig. 2B from
15° to 11.5°), it could not completely account for the deviations from
0° seen in Fig. 2 (for
Fig. 3B this correction shifted
the mean angle from 27.1° to 23.1°, at 2-m distance, whereas that of
Fig. 3A was unaffected).
In order to reduce the possible confounding influence of angular errors caused by the different sky views when ants walked within the channel and on the test field, we repeated the experiment of Fig. 2 at times of day that minimized potential systematic errors to less than 5° (see Materials and methods). The paths of the ants in the control situation (middle leg open) and in the crucial test (middle leg covered) were in the mean directed towards NW and to W (not significantly different from the expectations of 315° and 270° in Fig. 4A,B at all distances). These results confirm those of Fig. 2. Although for the crucial experiment (Fig. 4B), the deviations from the expected point in the same direction as those of Fig. 2 (i.e. towards the direction of the first turn in the channel), these deviations were now only 6.1°, 3.8°, 2.2° and 0.2° for the 1-m, 2-m, 3-m and 4-m distance (mean values not significantly different from the expectation of 270°). Deviations of a similar size also occurred in the control situation (4.1°, 1.9°, 2.1° and -3.0°; Fig. 4A).
In Fig. 5 the data of all individual runs obtained in the control situations, with an open view of the sky, are plotted against the time of day (data of 2002 and 2005 combined). As predicted, the systematic errors induced by the two rectangularly oriented channel segments seem to largely cancel out. There is no systematic trend visible as a gliding average yielded only small deviations from the expected 45° value, and also a linear regression yielded no significant trend (r2=0.0144 and 0.0139, P=0.18 and P=0.29, for the 3 m and 4 m data, respectively). The mean angles correspond well to the expectation of 45° (the data of Fig. 1A and Fig. 4A were mirrored): 44.8°±13.3° (N=125), 44.3°±11.4° (N=122), and 47.7°±10.8° (N=81) for the 2-m, 3-m and 4-m circles, respectively.
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Discussion |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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;
Mittelstaedt, 1985;
Moller and Görner, 1994)
and Cataglyphis cursor
(Thiélin-Bescond and Beugnon,
2005). It seemed quite conceivable that the large turns involved
in our experiments could also be measured by proprioceptors, e.g. by means of
hair plates located on the leg joints. Hence, idiothetic information by itself
could still provide sufficient directional information for path integration -
at least with the comparatively small distances involved in the present
experiments. The main result was a dramatic change in homing directions induced by covering the middle segment of the Z-shaped maze to exclude UV radiation (Fig. 2, Fig. 4B). There are several conceivable explanations of this result: (1) An incorrect interpretation of only the turning angle when entering and leaving the covered channel segment - whereas the distance was measured and processed correctly. (2) A malfunction of the odometer within the covered channel. (3) A combination of 1 and 2. (4) A different weighting of odometric information if the path integrator is deprived of compass information.
;
Ronacher et al., 2000).
Walking bumble bees can measure distances in total darkness
(Chittka et al., 1999), and
recently Cataglyphis cursor has been reported to measure small
distances correctly when walking in darkness, though only after intensive
training (Thiélin-Bescond and
Beugnon, 2005). Hence, a malfunction of the odometer seems
unlikely, and also a combination of 1 and 2 (explanation 3) seems to be an
unrealistic assumption.
We therefore favour explanation 4: that it is not the (peripheral)
measurement of walking distance per se that has been affected by the
exclusion of sky compass cues but rather the processing of this input
within the path integration module. A still open question is whether the ants
completely omitted the distance information obtained within the occluded
channel segment, or whether it has been fed into the path integration module
with a reduced weight. A small weighting factor, e.g. of about 0.1, could
result from the sky compass input persisting with a certain decay time. Such
an after effect would have led to a noticeable, though reduced, input into the
path integrator of the distance travelled in the covered maze segment. Note
that by this assumption it is still necessary that the 90° turns have been
perceived idiothetically in the experiment shown in
Fig. 2. In the experiment in
Fig. 3, the somewhat larger
deviations from 0° could also have been caused by such a lagging decay
function. however, the rather close agreement between mean vector and expected
direction (270° in Fig.
4B), as well as the data of Sommer and Wehner
(Sommer and Wehner, 2005), do
not favour of this assumption of persisting sky compass information. As the
direct view of the sky and the sun was prevented by additional screens (see
Materials and methods), it is highly unlikely that the ants could have relied
on intensity or spectral gradients as compass information (see also
Wehner, 1982). Further
experiments will be necessary to explore whether there is a decay function of
the compass input that has lead to the deviations from a purely northern
course in Fig. 2, and if so,
what its time course may be.
However, irrespective of this possibility of a very small weighting factor
the clear message from our data is that the odometric information about
travelling distance is nearly completely ignored for two-dimensional path
integration, if there is no simultaneous input from the celestial compass.
This conclusion is in accord with the one drawn from experiments with
Cataglyphis trained in linear channels
(Sommer and Wehner, 2005).
Most importantly, the data presented here for the two-dimensional paradigm
rule out that Cataglyphis can maintain the path integration process
solely on the basis of idiothetic information. The latter possibility would
have been a rather likely hypothesis, since earlier as well as recent
experiments strongly suggest that (i) the ant's odometer operates on the basis
of a step counter (Ronacher et al.,
2000; Wohlgemuth et al.,
2001; Wohlgemuth et al.,
2002; Wittlinger et al.,
2006), and (ii) idiothetic information can be used by other
arthropods to infer changes in walking directions (see Introduction).
Remarkably, while using different aspects of visual information [polarization,
intensity and spectral cues (Wehner,
1982; Wehner,
1997)], the compass module of Cataglyphis apparently is
not able to substitute visual cues by idiothetic information.
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Acknowledgments |
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Footnotes |
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Present address: American Museum of Natural History, Department of
Mammalogy, Central Park West at 79th Street, New York, NY 10024, USA 
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References |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
|---|
Batschelet, E. (1981). Circular Statistics in Biology. London: Academic Press.
Biegler, R. (2000). Possible uses of path integration in animal navigation. Anim. Learn. Behav. 28,257 -277.
Chittka, L., Williams, N. M., Rasmussen, H. and Thomson, J. D. (1999). Navigation without vision: bumblebee orientation in complete darkness. Proc. R. Soc. Lond. B Biol. Sci. 266, 45-50.
Dacke, M., Nilsson, D.-E., Scholtz, C. H., Byrne, M. and Warrant, E. J. (2003). Insect orientation to polarized moonlight. Nature 424,33 .[Medline]
Duelli, P. and Wehner, R. (1973). The spectral sensitivity of polarized light orientation in Cataglyphis bicolor (Formicidae, Hymenoptera). J. Comp. Physiol. 86, 37-53.[CrossRef]
Grah, G., Wehner, R. and Ronacher, B. (2005).
Path integration in a three-dimensional maze: ground distance estimation keeps
desert ants (Cataglyphis fortis) on course. J. Exp.
Biol. 208,4005
-4011.
Kovach, W. (2004). Oriana v. 2. 02a. Anglesey: Kovach Compiling Services.
Labhart, T. (2000). Polarization-sensitive interneurons in the optic lobe of the desert ant Cataglyphis bicolor.Naturwissenschaften 87,133 -136.[CrossRef][Medline]
Labhart, T. and Meyer, E. P. (2002). Neural mechanisms in insect navigation: polarization compass and odometer. Curr. Opin. Neurobiol. 12,707 -714.[CrossRef][Medline]
Mittelstaedt, H. (1985). Analytical cybernetics of spider navigation. In Neurobiology of Arachnids (ed. F. G. Barth), pp. 298-316. Berlin, Heidelberg, New York: Springer.
Moller, P. and Görner, P. (1994). Homing by path integration in the spider Agelena labyrinthica Clerck. J. Comp. Physiol. A 174,221 -229.
Müller, M. (1989). Mechanismus der Wegintegration bei Cataglyphis fortis (Hymenoptera, Insecta). PhD thesis, University of Zürich.
Müller, M. and Wehner, R. (1988). Path
integration in desert ants, Cataglyphis fortis. Proc. Natl. Acad.
Sci. USA 85,5287
-5290.
Müller, M. and Wehner, R. (1994). The hidden spiral: systematic search and path integration in desert ants, Cataglyphis fortis. J. Comp. Physiol. A 175,525 -530.
Ronacher, B. and Wehner, R. (1995). Desert ants Cataglyphis fortis use self-induced optic flow to measure distances travelled. J. Comp. Physiol. A 177, 21-27.
Ronacher, B., Gallizzi, K., Wohlgemuth, S. and Wehner, R. (2000). Lateral optic flow does not influence distance estimation in the desert ant Cataglyphis fortis. J. Exp. Biol. 203,1113 -1121.[Abstract]
Seyfarth, E.-A., Hergenröder, R., Ebbes, H. and Barth, F. G. (1982). Idiothetic orientation of a wandering spider: Compensation of detours and estimates of goal distance. Behav. Ecol. Sociobiol. 11,139 -148.
Sommer, S. and Wehner, R. (2005). Vector navigation in desert ants, Cataglyphis fortis: celestial compass cues are essential for the proper use of distance information. Naturwissenschaften 92,468 -471.[CrossRef][Medline]
Thiélin-Bescond, M. and Beugnon, G. (2005). Vision-independent odometry in the ant Cataglyphis cursor. Naturwissenschaften 92,193 -197.[CrossRef][Medline]
Wehner, R. (1968). Optische Orientierungsmechanismen im Heimkehrverhalten von Cataglyphis bicolor (Formicidae, Hymenoptera). Rev. Suisse Zool. 75,1076 -1085.
Wehner, R. (1982). Himmelsnavigation bei Insekten. Neurophysiologie und verhalten. Neujahrsbl. Naturforsch. Ges. Zürich 184,1 -132.
Wehner, R. (1994). Himmelsbild und Kompaßauge - Neurobiologie eines Navigationssystems. Verh. Dtsch. Zool. Ges. 87,9 -37.
Wehner, R. (1997). The ant's celestial compass system: spectral and polarization channels. In Orientation and Communication in Arthropods (ed. M. Lehrer), pp.145 -185. Basel: Birkhäuser Verlag.
Wehner, R. (2003). Desert ant navigation: how miniature brains solve complex tasks. J. Comp. Physiol. A 189,579 -588.[CrossRef][Medline]
Wehner, R. and Labhart, T. (2006). Polarization vision. In Invertebrate Vision (ed. E. Warrant and D.-E. Nilsson), pp. Cambridge: Cambridge University Press. In Press.
Wehner, R. and Srinivasan, M. V. (1981). Searching behaviour of desert ants, genus Cataglyphis (Formicidae, Hymenoptera). J. Comp. Physiol. A 142,315 -338.
Wehner, R. and Wehner, S. (1986). Path integration in desert ants. Approaching a long-standing puzzle in insect navigation. Monitore Zool. Ital. 20,309 -331.
Wehner, R. and Wehner, S. (1990). Insect navigation: use of maps or Ariadne's thread? Ethol. Ecol. Evol. 2,27 -48.
Wittlinger, M., Wehner, R. and Wolf, H. (2006).
The ant odometer: stepping on stilts and stumps.
Science 312,1965
-1967.
Wohlgemuth, S., Ronacher, B. and Wehner, R. (2001). Ant odometry in the third dimension. Nature 411,795 -798.[CrossRef][Medline]
Wohlgemuth, S., Ronacher, B. and Wehner, R. (2002). Distance estimation in the third dimension in desert ants. J. Comp. Physiol. A 188,273 -281.[CrossRef][Medline]
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