View-based navigation in insects: how wood ants (Formica rufa L.) look at and are guided by extended landmarks
School of Biological Sciences, University of Sussex, Brighton, BN1 9QG, UK
* e-mail: paulgr{at}cogs.susx.ac.uk
Accepted 18 May 2002
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Unlike many flying insects, an ant's direction of motion while walking is always along its longitudinal body axis and, perhaps for this reason, it favours its frontal retina for viewing discrete landmarks. We find that ants also use their frontal retina for viewing a laterally placed wall. On a coarse scale, the ant's path along the wall is straight, but on a finer scale it is roughly sinusoidal, allowing the ant to scan the surrounding landscape with its frontal retina. The ant's side-to-side scanning means that the wall is viewed with its frontal retina for phases of the scanning cycle throughout its trajectory. Details of the scanning pattern depend on the scene. Ants scan further to the side that is empty of the wall than to the side containing the wall, and they scan further into the wall side when the wall is of a lower apparent height. We conclude that frontal retina is employed for image storage and for path control.
Key words: view-based navigation, navigation, image matching, wood ant, Formica rufa, landmark
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The first advance underpinning this study is the finding that two species
of ant, Cataglyphis fortis
(Collett et al., 2001) and
Leptothorax albipennis (Pratt et
al., 2001
), will follow a path that is defined by an extended
landmark, such as a wall, that can be parallel or at an oblique angle to the
ant's path. For Cataglyphis fortis, when the barrier was rotated from
the training orientation, the ants' paths rotated by approximately the same
amount. This result implies that ants' paths can be governed entirely by
visual information derived from the wall independently of compass cues and
makes it possible to study landmark guidance in isolation, without
complications introduced by other navigational mechanisms. We examine here
what visual information the wood ant (Formica rufa) obtains from a
wall when using it for guidance, how the ant might gain this information, and
how this information might serve to correct the ants' path. By rotating the
wall on every trial and placing the start position and a sucrose reward at
constant positions relative to the wall, we have forced ants to rely
exclusively on the wall for guidance.
The second advance is technical. A tracking video camera recorded the paths
of individual ants as they walked parallel to the wall. This camera gives
images of the ant at high magnification over a large (3 mx2.5 m) indoor
arena so that not only the ant's position but also the orientation of its long
axis can be monitored throughout its path
(Fry et al., 2000). Unlike many
flying insects that can fly sideways or even backwards, walking ants are
limited to moving parallel to their long axis. This constrained pattern of
locomotion may be why they place particular emphasis on viewing features with
their frontal retina (Judd and Collett,
1998
; Nicholson et al.,
1999
; Fukushi,
2001
). We were particularly interested in the way in which ants
look at an object to the side of their route, whether they have a pattern of
movements that enables them to scan their environment with their frontal
retina and, if so, how their scanning pattern and overall path might be
controlled by visual features of the wall.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Experimental apparatus and training configurations
Experiments were performed in a 300 cmx250 cm arena surfaced with
white Perspex that was roughened to prevent the ants slipping. The arena was
surrounded by a Fluon-coated barrier to prevent escape and a 230 cm high
curtain to obscure external cues. The arena was lit from above by four
fluorescent strip lights. The walls used as landmarks were made from aluminium
sheet sprayed black and bent into an L-shape so as to be free-standing. For
all experiments except those with a stepped wall, the wall used in training
was 20 cm high. Ants were carried from the nest to the arena on a drinking
straw and were placed at the starting point on an upturned polystyrene cup,
from which they descended to the floor. A drop of sucrose solution was
provided on a microscope slide at a distance that was typically 80 cm from the
starting point. Ants were trained in two configurations in which the route
from the start to the food was parallel to the wall, either at 20 cm or 30 cm
from it. In a third configuration, the route was oblique to the wall, starting
20 cm from the wall and ending with the food 30 cm from the wall. In all three
cases, the wall, the start and the food were rotated en bloc between
each training trial. For comparison, we also trained ants in a fourth
situation, again with the start and the food placed 20 cm from the wall but
without rotating the wall.
Two-wall experiment
Some ants were trained to a route defined by two walls. The ants' routes
ran down the centre of a corridor composed of two walls 20 cm high and 160 cm
long and placed 60 cm apart. The end of the corridor towards which the ants
headed was blocked off by a semi-circular piece of card of the same height as
the walls. Ants started from a polystyrene cup and walked towards sucrose
solution on a microscope slide 100 cm away. Between each training trial, the
walls were rotated by 80° about the centre of the arena.
Training
In the early stages of training, 20-30 active ants from the colony were
placed on top of the start cup with the sucroseladen microscope slide placed
at the finish. The first 10 ants to reach the slide were caught and marked
individually with dots of enamel paint. They were then allowed to feed and to
return to the start cup, where they were caught again and returned to the
nest. Ants typically emerged from the nest mound a few minutes later and were
given another training trial with the wall in a new position. After 20-25 runs
(2-3 days), the ants' paths followed a direct line from the start cup to the
food, regardless of the wall position. Testing began when the ants had
performed three straight runs to the food, all of which had been tracked
successfully by the camera. During the testing phase, ants were given three
rewarded training runs between nonrewarded tests, with the wall rotated
between each training or test run. Between runs, the arena surface was wiped
down with ethanol to remove possible pheromone cues.
Tracking
During test runs, ants were tracked by a camera placed 3 m above the centre
of the arena. The camera (Sony EVI-D30) has movable optics allowing a
high-resolution image to be captured of any part of the arena. The camera is
controlled by a PC (Pentium II 233 MHz) running customized software
(Fry at al., 2000) that
maintains the ant at the centre of the camera's visual field and stores the
pan and tilt values of the camera at 50 frames s-1. The orientation
of the long axis of the ant is also calculated in real time, and the 180°
ambiguity is solved by assuming that the ant always walks forwards. Before
analysis, the output was converted to arena coordinates and smoothed by taking
a moving average with a window size of nine frames. Trajectories were lost on
occasions when the ant entered the shadow created by landmarks or if there
were additional high-contrast objects in the camera's field of view.
The Cartesian coordinate system used to superimpose trajectories took the start of the wall as the origin and the wall as the x-axis. For instance, in the 20 cm condition, the start was at (20,20) and the food was at (100,20). Throughout this paper, we follow this convention, with x distance and y distance referring to distance along and perpendicular to the wall respectively.
Finding endpoints
The endpoint of a trajectory was defined as the first major turn that the
ant made. This turn was found by heavily smoothing the tracks (moving average,
window size 100) and locating the first maximum in a trace of distance from
the start, indicating the point at which the ant first turned back. To make
sure that the algorithm picked out an event specific to the start of a search
process, rather than a characteristic of an ongoing trajectory, it was applied
to the middle 50 cm of 48 trajectories recorded from ants on the way to the
food during training. The algorithm found endpoints in only eight of these
trajectory sections. When applied to 50 control runs in which no food was
present, the algorithm found 39 endpoints clustered around the expected
position of the food slide (as in Table
2).
|
Measuring the wavelength and amplitude of path wiggles
On a fine scale, the ants' paths were roughly sinusoidal. The wavelength of
each cycle was taken to be twice the average distance between adjacent
zero-crossings, where zero-crossings are the points at which individual
trajectories crossed the direct line from the start to the goal. To calculate
amplitude, the maximum deviation from the line was measured every half-cycle
and summed over each cycle. Amplitude is the mean of these cyclical
deviations.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
How do ants measure and control their distance from the wall?
A simple means of controlling distance from the wall (y distance)
is to keep the top edge of the wall at the appropriate vertical position on
the retina (see also Pratt et al.,
2001). According to this hypothesis, ants trained to follow a
route 20 cm from a 20 cm high wall keep the top edge of the wall at an
elevation of 45°. The path of an ant trained under these conditions and
started at 40 cm from a 40 cm high wall should also be parallel to the wall
where the retinal elevation of the top of the wall is 45°. However, an ant
started at 20 cm from a 40 cm high wall should tend to move out from the wall,
and if started 40 cm from a 20 cm wall should head towards the wall. The
outcome of testing ants with these conditions is summarised in
Fig. 2 and
Table 1.
|
|
If the apparent height at the start of the path differs from that experienced during training, correction starts immediately, but progresses slowly (Fig. 2A,C). The mean path of ants displaced to a y distance of 40 cm from the normal 20 cm high wall is directed towards the wall and differs significantly from the straight-ahead course for all x distances greater than 20 cm. Starting at a y distance of 20 cm from a 40 cm high wall, the mean path heads away from the wall and differs significantly from the parallel course at all x distances along the wall greater than 10 cm. Ants tend to approach the wall when the elevation of the top edge is less than 45° and to veer away from the wall when the elevation is greater then 45°, moving in an appropriate direction to reduce the mismatch between the training and perceived elevation. Compensation for the mismatch (Fig. 2B,D) is rarely complete. Ants trained with a 120 cm long wall were also tested with a longer wall of 155 cm. The ants' starting position was either 20 cm from a 40 cm wall or 40 cm from a 20 cm high wall. The retinal elevation of the top of the wall versus distance travelled for individual runs is plotted in Fig. 2B,D. Ants slowly reduce the 20° discrepancy between the desired and actual elevation. But in only seven out of 21 cases does the elevation reach the 45° experienced in training.
When the vertical elevation of the wall matched that of the training condition, deviations from a parallel course were small. The resultant mean path of ants started at 20 cm y distance from a 20 cm high wall deviates by 1.5 cm at most from a line parallel to the wall. This deviation is, however, significant and comes from a small but consistent bowing of the trajectories towards the wall. When both starting y distance and wall height are set at 40 cm, the mean trajectory does not differ significantly from the parallel course over the first 50 cm. The mean path shows a small kink after 20 cm, which is corrected by 30 cm. After 40 cm, the mean path lies only 1.5 cm from the predicted parallel course. This parallel path suggests that other cues to y distance have at best a small effect on an ant's path. The gradual correction of errors in apparent height (Fig. 2B,D) is likely to occur because of the way that the correction process operates and not because of interference from other cues.
Where do ants look during trajectories?
Earlier studies (Judd and Collett,
1998; Nicholson et al.,
1999
; Fukushi,
2001
) suggested that wood ants tend to look at landmarks with
their frontal retina when storing information about the appearance of the
landmarks or using them for guidance. Ants need a scanning strategy if they
are to view an extended wall with their frontal retina while walking parallel
to it. A detailed analysis of the ants' trajectories reveals that their path
is sufficiently sinuous to place the wall on their frontal retina
approximately 30% of the time. Frequency distributions of where ants look
along the wall are shown in Figs
3A,C for the 20 cm and 30 cm training conditions respectively.
Ants spend most time looking at a point on the wall approximately 20-30 cm
ahead of their current x position. The mean looking points for the 20
and 30 cm conditions are not significantly different (20 cm, 27±6 cm,
N=132; 30 cm, 28±9 cm, N=65; means ± S.D.;
t-test, t=-0.7, d.f.=192, P>0.4).
|
Looking distances of similar lengths for the two conditions arise as a consequence of the ant turning further towards the wall when the route was 30 cm from the wall than when it was 20 cm. It can be seen in Fig. 3B,D that ants trained at 30 cm from the wall spend significantly more time at orientations further from the straight-ahead course when viewing the wall than do ants trained at 20 cm from the wall (Watson's F-test, F=13.69, d.f.=192, P<0.001). We suggest that this increased turning is generated by a scanning system that aims to put large stimuli on the frontal retina. However, the increase in turning is insufficient to equalise the retinal elevation of the top of the wall for the two conditions. At the mean looking points, the retinal elevation for the 20 cm training condition is 36° and that for the 30 cm training condition is 28°.
The conclusion that turning is controlled by what the ant sees on its frontal retina is supported by an asymmetry in the amplitude of the scan to the two sides (Fig. 3B,D). Ants turn significantly further from the direct path when they face away from the wall than when they face towards it. In the 20 cm training condition, this asymmetry occurs in 95 out of 132 runs, and it occurs in 55 out of 65 runs in the 30 cm training condition (binomial test, P<<0.01 in both cases). These asymmetries and looking patterns are constant along the length of the wall. The same asymmetry (Fig. 3E,F, 56 out of 74 runs, binomial test, P<<0.01) was found when ants were trained under more natural conditions with the wall always in the same position. However, the distribution of looking distances differed significantly from those of the 20 cm and 30 cm conditions, perhaps because the paths bowed more towards the wall.
Fine structure of trajectories
To analyse these looking patterns further, individual cycles were segmented
into four phases (Fig. 4A) on
the basis of the ants' looking direction (towards or away from the wall) and
turning direction (clockwise or counterclockwise). The mean amplitudes and
wavelengths of an average cycle for ants trained at a 20 cm y
distance from the wall differed significantly from those of ants trained with
a 30 cm y distance from the wall (mean amplitudes, 20 cm,
2.9±2.8 cm, N=132; 30 cm, 4.1±4.0 cm, N=65;
t-test, t=-2.0, d.f.=85, P<0.05; mean
wavelengths, 20 cm, 10.4±4.1 cm; 30 cm, 12.4±5.9 cm;
t-test, t=-2.745, d.f.=195, P<0.01; means
± S.D.). These differences must be a consequence of the visual input
received during the trajectory. If the amplitude of the `sinusoidal' component
of movement is transformed into changes in the apparent height of the wall
between the extremes of the sinusoid, the difference between groups ceases to
be significant (20 cm, 4.1±2.7°, N=132; 30 cm,
3.5±2.3°, N=65; t-test, t=1.552,
d.f.=179, P=0.1; mean ± S.D.). Ants at 30 cm from the wall
deviate more from their straight-ahead course to look at the wall at their
favoured point (Fig. 3C), and
the amplitude of trajectories in this condition is correspondingly greater.
The increased sinuosity in the 30 cm condition is also associated with a
slightly reduced velocity along the trajectory (20 cm, 2.9±0.7 cm
s-1, N=132; 30 cm, 2.5±0.5 cm s-1,
N=65; t-test, t=4.8, d.f.=168, P<0.05;
means ± S.D.).
|
The asymmetry in the looking patterns (Fig. 3) can be related to the significantly different amplitudes and angular velocities of the four (i-iv) phases of the cycle (Fig. 4D, i versus ii, i versus iii, i versus iv, ii versus iii and ii versus iv all differ in angular velocity, Watson's F-test, P<0.005; iii versus iv does not). Ants turn fastest in phase i (rotating clockwise whilst looking away from the wall) and slowest in phase ii (rotating clockwise and looking towards the wall). We suggest that the ant turns to one side until a visual feature that is captured on the frontal retina slows and brings the scan in that direction to a stop. Ants thus turn relatively slowly and less far in the direction of the wall, which increasingly fills their visual field. They turn faster and further when turning away from the wall with no significant visual object to slow them down.
Testing a scanning model of trajectory control
The ant's approximately sinusoidal path and the dependence of the form of
the sinusoid on visual input (Fig.
4) led us to test a simple model of course control. According to
this model, the ant scans along the wall and learns wall height using its
frontal retina at the most extreme position of its scan, when the wall's
retinal elevation (for a wall of uniform height) is at a maximum. If the ant
is too close to the wall, the learnt elevation will be reached earlier in the
scan. If the ant reverses its scan at this point, its trajectory will veer
away from the wall, gradually correcting the path over several scanning
cycles. Conversely, if the ant is too far from the wall and it scans a little
further in the same direction, its overall path will turn towards the wall.
The model implies that scanning and correction are a single process that is
adjusted by input to the frontal retina. Simulation of the model
(Fig. 5A) shows that correction
is slow, taking many cycles, corresponding to the ant's behaviour shown in
Fig. 2.
|
To test this model, ants were trained to run down the middle of a 60 cm wide, blindly ending corridor with 20 cm high walls (Fig. 5B). The scanning model predicts that the amplitude of the sinusoid will be smaller when both walls are raised and larger when both walls are lowered. With two walls of equal height, the amplitude of the sinusoid should increase or decrease by the same amount on both sides of the midline, and the ant's path should remain in the middle of the corridor. The data do not support the model. In tests with trained ants, the walls were either raised to 40 cm or lowered to 15 cm. Neither the amplitude of the sinusoid nor the angles through which the ants turned were altered significantly by these changes to wall height. Fig. 5C-E shows the distributions of orientations at the points where ants finish a scan phase. The distributions have a characteristic bimodal shape with a peak at 0° and another peak at approximately 60°. The peak at 0° may be a consequence of ants paying attention to the semi-circular end segment of the corridor. The position of the second peak does not vary significantly across conditions and certainly does not match the prediction of the scanning model (shown on the distributions as a grey bar).
Where along the wall is height measured?
Throughout their trajectory, ants scan the wall ahead with their frontal
retina. Is wall height measured continuously during this cycle or are
measurements restricted to particular phases? We have approached this question
with a test situation in which the height of the first part of the wall
matched the training condition, but the second part was higher than the ants
expected. We could then assess how far in advance the ants responded to the
unexpected increase in height. Two situations were used. In the first, ants
were trained with a wall of uniform height (20 cm) and tested with a wall that
was stepped to 40 cm in height after 60 cm
(Fig. 6A).
Fig. 6B shows mean trajectories
for test and training runs. The means of the difference between each
individual's test and training runs are shown in
Fig. 6C. Test and training runs
have diverged by the time the ant has walked 40 cm in the x
direction: i.e. 20 cm before the increase in wall height. In the second
situation, ants were trained with a wall that was stepped in height from 20 to
40 cm at 100 cm and then tested with a wall of a constant 40 cm height
(Fig. 6D). The second portion
of the test wall again gave an increased retinal elevation in comparison with
the training wall. The training and test trajectories diverge from the start
and are significantly different after 30 cm, even though the step in the wall
is still 50 cm ahead of the ant's current position. This early response
suggests that ants either integrate signals from the frontal retina over the
entire scanning cycle or measure wall height over a large area of the retina.
Weak evidence that the frontal retina may dominate in measuring wall height
comes from the increase in the rate of divergence between training and test
trajectories 20 cm before the two walls differ in height
(Fig. 6F), a distance that
matches the position of the peak in the distribution of looking distances
(Fig. 3).
|
What sets trajectory endpoints?
When ants are tested in a cleaned arena with no food present, their
trajectories stop at the expected food site
(Table 2;
Fig. 7A,B). The stopping point
could be controlled by visual cues from the wall or from other parts of the
room or by self-generated idiothetic cues. One likely cue from the wall is the
vertical edge at the food end. Since the rotation of the wall marks out an
annulus in the centre of the area, the lighting array and the surrounding
curtains may also provide a rough indication of the position of the food site.
Ants could also learn the distance that they travel between the start and food
from proprioceptive signals or monitors of their motor output
(Ronacher et al., 2000)
provided that they can abstract distance across training trials in which
trajectory direction is constantly changing.
|
Table 2 summarises the data from tests in which the signals from different stopping cues conflicted. In all conditions, the ants set a course parallel to the wall and maintained it until search behaviour began (e.g. Fig. 7E).
Visual cues versus distance cues
Ants were tested with walls that were 155 and 85 cm long (approximately 130
and 70 % of the length of the training wall). Walls were placed in the arena
so that the endpoints specified by the end of the wall and by room cues
coincided. In both cases, the mean length of the trajectory differed
significantly from the 80 cm travelled in training (mean ± S.D; 85 cm
wall, 56.9±6.66 cm; 155 cm wall, 117±21.6 cm). The stopping
points for the longer wall (Fig.
7D) cluster around the endpoint set by visual cues. With the 85 cm
wall (Fig. 7C), ants stop
significantly earlier than the normal 80 cm distance
(Table 2), but their paths are
significantly longer than the 45 cm predicted by visual cues (t-test,
t=6.7, d.f.=11, P<0.005).
What is the visual cue?
Table 2 shows that both room
cues and wall cues are significant, but the results cannot be summarised
neatly. If one of the cues is set at 80 cm and the other at 45 cm, ants stop
at an intermediate value, whether room or wall cues signal the longer
distance. The results are less clear if one cue is set at 80 cm and the other
set beyond the normal distance at 115 cm. When wall cues predict 115 cm and
room cues 80 cm, the mean endpoint is approximately 80 cm, but the scatter is
large. Some trajectories stop transiently at approximately 80 cm and then
continue parallel to the wall until the end, without any searching. When room
cues are set to 115 cm and the wall set to 80 cm, ants mostly continue beyond
the wall, again without searching. Table
2 gives the mean value for the seven out of a total of 16
trajectories for which endpoints could be measured. For this subset of
trajectories, room cues seem to dominate wall cues in controlling
stopping.
In conclusion, we see that room cues, wall cues and idiothetic cues all have a role in determining endpoints. Visual cues override idiothetic cues when the wall and room cues coincide in indicating a distance longer than 80 cm. However, ants are reluctant to stop before they have walked 80 cm and overshoot the 45 cm set by both visual cues. This result indicates that ants can abstract the distance that they travel in the absence of compass cues. It was surprising to find that room cues are as significant as the closer and seemingly better-defined wall cues.
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Since ants always move parallel to their long axis (unlike flying bees and wasps), they can change their direction of motion only by turning. Consequently, if ants relied on the lateral retina for wall-following and moved in a straight line, the wall's position on their retina would change whenever the ant corrected its path not a good recipe for a stable control system. One consequence of the ant's approximately sinusoidal track (Fig. 4) is that, for some part of the scanning cycle, the important part of the scene is guaranteed to be picked up by frontal retina.
We tested a simple scanning model of trajectory control in which the scan to one side ended when frontal retina encountered a part of the wall that subtended a desired retinal height. The suggestion was that this desired value is set when learning the route and that the value may be the outcome of two opposing tendencies: (i) the ant turning to maximise the informational content on its frontal retina and (ii) the ant's increasing tendency to reverse the direction of the scan as its orientation deviates further from its direct path. The ant would then turn further than usual if the wall were lower than expected and less far if it were higher. Visual control of the scan could then automatically correct the path. The greater turning amplitude found when the ant was trained at 30 cm rather than at 20 cm from the wall fits this model. However, in the two-wall experiment, raising or lowering the wall from the training value did not influence the amplitude of the scan. Consequently, a model that combines scanning and correction into one process must be rejected. Instead, the data suggest that the result of a mismatch between stored and perceived elevation causes the overall direction of the trajectory to shift. Separating the detection and correction of errors is possibly a more versatile way of using the variety of discrete and extended landmarks that may be encountered along a route. In this case, the gradual correction that is seen in Fig. 2 may be a consequence of an in-built preference to take a straight path, and it may prevent the ant from making large changes in direction that might cause a discrete landmark to fall outside the range of its scanning movements.
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Baerends, G. P. (1941) Fortpflanzungsverhalten und Orientierung der Grabwespe Ammophilia campestris Jur. Tijdschr. Entomol. 84,68 -275.
Batschelet, E. (1981). Circular Statistics in Biology. London: Academic Press.
Cartwright, B. A. and Collett, T. S. (1983). Landmark learning in bees: experiments and models. J. Comp. Physiol. 151,521 -543.
Collett, T. S., Collett, M. and Wehner, R.
(2001). The guidance of desert ants by extended landmarks.
J. Exp. Biol. 204,1635
-1639.
Collett, T. S., Dillmann, E., Giger, A. and Wehner, R. (1992). Visual landmarks and route following in desert ants. J. Comp. Physiol. A 170,435 -442.
Fry, S. N., Bichsel, M., Muller, P. and Robert, D. (2000). Tracking of flying insects using pan-tilt cameras. J. Neurosci. Meth. 101,59 -67.[Medline]
Fukushi, T. (2001). Homing in wood ants,
Formica japonica: use of the skyline panorama. J. Exp.
Biol. 204,2063
-2072.
Judd, P. D. and Collett, T. S. (1998). Multiple stored views and landmark guidance in ants. Nature 39,710 -714.
Nicholson, D. J., Judd, P. D., Cartwright, B. A. and Collett, T.
S. (1999). Learning walks and landmark guidance in wood ants
(Formica rufa). J. Exp. Biol.
202,1831
-1838.
Pratt, S., Brooks, S. E. and Franks, N. F. (2001). The use of edges in visual navigation by the ant Leptothorax albipennis. Ethology 107,1125 -1136.
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.
Rosengren, R. (1971). Route fidelity, visual memory and recruitment behaviour in foraging wood ants of genus Formica (Hymenopterus, Formicidae). Acta Zool. Fenn. 133, 1-106.
Santschi, F. (1913). Comment s'orientent les fourmis. Rev. Suisse Zool. 21,347 -425.
Tinbergen, N. (1932). Über die Orientierung des Bienenwolfes (Philanthus triangulum Fabr.). Z. Vergl. Physiol. 16,305 -334.
Wehner, R., Michel, B. and Antonsen, P. (1996).
Visual navigation in insects: coupling of egocentric and geocentric
information. J. Exp. Biol.
199,129
-140.
Wehner, R. and Raber, F. (1979). Visual spatial memory in desert ants. Cataglyphis bicolor (Hymenoptera: Formicidae). Experientia 35,1569 -1571.