Honeybee navigation: properties of the visually driven `odometer'
Centre for Visual Science, Research School of Biological Sciences, Australian National University, PO Box 475, Canberra, ACT 2601, Australia
* Author for correspondence (e-mail: M.Srinivasan{at}anu.edu.au)
Accepted 13 January 2003
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Summary |
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Key words: visual pattern, odometric signal, honeybee, navigation, optic flow
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Introduction |
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Early studies concluded that bees estimate distance flown by gauging the
amount of energy they expend to reach the destination (for a review, see
von Frisch, 1993). More recent
studies, however, are providing increasing evidence that this `energy
hypothesis' is incorrect, at least for moderate distances of a few hundred
meters (Neese, 1988
; Esch et
al., 1994
,
2001
;
Esch and Burns, 1995
;
Srinivasan et al., 1996
,
1997
,
2000
). Over these distances,
bees appear to gauge distance flown in terms of the extent to which the image
of the environment moves in the eye (Esch and Burns,
1995
,
1996
; Srinivasan et al.,
1996
,
1997
,
2000
;
Esch et al., 2001
). In other
words, the optic flow experienced by the eye (that is, the speed of motion of
the image of the environment) is integrated over time to obtain an estimate of
distance traveled. The most compelling evidence for this was obtained in a
study in which bees were trained to fly to a feeder placed inside a short,
narrow tunnel, the walls and floor of which were lined with a random visual
texture. When bees returned to the hive from the tunnel, they performed a
waggle dance in which they indicated a feeder distance as large as 200 m,
despite the fact that they had only flown a distance of 6 m
(Srinivasan et al., 2000
).
Evidently, the proximity of the walls and floor of the tunnel greatly
amplified the magnitude of the optic flow that they experienced, in comparison
with the situation during outdoor flight in a natural environment. On the
other hand, when the same tunnel was lined with axial stripes so that
a bee flying through it would experience very little optic flow, because the
stripes were parallel to the flight direction the bees signaled a very
small distance, even though they had flown the same physical distance as in
the previous condition (Srinivasan et al.,
2000
). This experiment indicated that distance flown was being
measured in terms of integrated optic flow, and not in terms of physical
distance flown or energy consumed.
If bees do indeed gauge distance traveled by measuring optic flow and integrating it over time, it is pertinent to enquire into the properties of their visually driven `odometer'. Given that the environment through which a bee flies can vary substantially in terms of its visual properties, such as contrast, texture and the distribution of objects, it is important to know whether, and to what extent, the bee's perception of distance flown is affected by these environmental variables. In other words, how `robust' is the honeybee's odometer?
The tunnel experiment described above
(Srinivasan et al., 2000)
offers a convenient means of exploring this question under controlled
laboratory conditions, since outdoor flights of a few hundred meters can be
simulated in the laboratory by flying bees through narrow tunnels a few meters
long. Thus, one can investigate the effects of varying the contrast, texture
or other attributes of the environment by varying the properties of the visual
patterns that line the walls and floor of the tunnel, and analysing the
resulting dances.
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Materials and methods |
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Tunnel patterns
The side walls and floor of the tunnel were lined with various
black-and-white patterns and gratings. In the first series of experiments, the
walls and floor of the tunnel were lined with a checkerboard pattern of
squares 3.2 cm2, or with axial stripes at 8 cm intervals. In the
second series, a randomly textured Julesz pattern with a pixel size of 1 cm
and a pattern of axial stripes were used in various combinations. As controls,
bees were made to fly to feeders placed at either 35 m or 41 m from the hive
entrance. In a third experimental series, the side walls and floor of the
tunnel were lined with vertical square-wave gratings at 3.6 cm intervals and
contrasts ranging from 20% to 92%. In a fourth series, the patterns were
sinusoidal gratings of medium contrast and varying spatial periods (values
given in Results).
In the latter two series of experiments the checkerboard pattern was used to provide a baseline against which to compare data obtained from the other experimental conditions. The axial pattern was used to create a condition in which the optic flow experienced by bees flying through the tunnel was very weak, because flight in the direction of the stripes produced very little apparent motion of the images of the walls and floor in the eyes.
The patterns were printed on a laser printer using a computer running a graphics program. The contrasts of the patterns were measured by using a photodiode that had a linear intensityresponse function and a visual field considerably narrower than the smallest pixel or stripe width that was used.
Dance analysis
For each experimental condition, we analysed the dances performed by the
marked bees upon their return to the hive. A dance typically consisted of a
number of loops, alternating between the clockwise and counterclockwise
senses. Some of these loops displayed a waggle component, whereas others did
not. For each dance, we measured three parameters: (i) the percentage of
waggle loops; (ii) the mean duration of the `pure' waggle component
(considering only the waggle loops and disregarding loops that contained no
waggle) and (iii) the mean duration of the waggle component over the entire
dance, assigning a waggle duration of zero to each loop that had no waggle.
The Fisher's Least-Significant-Difference Test was used to test for
statistically significant differences between the mean waggle durations
obtained for different conditions.
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Results |
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The dances observed (see Materials and methods) were typically somewhat
different from the dances that are elicited by long flights in natural outdoor
environments, where almost every loop contains a waggle (A. Si, M. V.
Srinivasan and S. Zhang, unpublished observations). Both measurements of
waggle duration increased systematically with distance flown
(Fig. 1), as did the percentage
of waggle loops (Fig. 2). At a
distance of 8 m into the tunnel, the mean waggle duration was approx. 250 ms
(Fig. 1). This waggle duration
is comparable to that exhibited by bees that return from distances as large as
100-200 m in a natural outdoor environment
(Srinivasan et al., 2000;
Esch et al., 2001
). Evidently,
the proximity of the walls and the floor of the tunnel greatly amplify the
magnitude of the optic flow in comparison with what the bees would normally
experience during outdoor flight in a natural environment. On the other hand,
when the tunnel was lined with axial stripes, the mean waggle duration was
very low (approx. 80 ms) regardless of whether the tunnel was 4 m or 8 m long
(Fig. 1). Under these
conditions the percentage of waggle loops was also at its lowest level,
approximately 40% (Fig. 2).
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These data support the conclusions of earlier studies
(Srinivasan et al., 2000;
Esch et al., 2001
) that
honeybees gauge distance flown in terms of the amount of image motion that is
experienced by the eyes en route to the food source. The present
results extend those findings by showing that the odometric signal increases
with distance flown in the tunnel, just as it does in the case of outdoor
flight in a natural environment. The difference is that in the tunnel the
odometric signal increases at a higher rate than during outdoor flight. The
tunnel can thus be used as a convenient experimental device in which to
`simulate', for the bee, outdoor flights of a few hundred meters, and to study
the effects of varying the contrast, texture and other properties of the
visual environment on the odometric signal.
We did not experiment with tunnels longer than 8 m, because it is difficult to coax bees to fly through long, narrow tunnels and dance upon their return. However, there is every indication that the mean waggle duration would have continued to increase with tunnels longer than 8 m, because other experiments in our laboratory have revealed that mean waggle duration can be increased beyond that at maximum tunnel length by moving the pattern on the wall backwards, against the bee's flight, thereby increasing the magnitude of the integrated optic flow (H. Esch, S. Zhang and M. V. Srinivasan, unpublished observations).
In another set of experiments we examined the effect of varying tunnel width. For a tunnel of a fixed length, increasing the width should decrease the magnitude of the integrated optic flow that is experienced by the bees, because the walls are then more distant from them. In an 8 m long, 11 cm wide tunnel lined with the checkerboard pattern, the mean waggle duration was 373 ms and the mean pure waggle duration was 401 ms (33 dances, 406 total loops). (These figures are higher than those shown in Fig. 1 because the new set of experiments was performed in a different year, using a different colony of bees). When the width of the tunnel was increased to 22 cm, the corresponding figures were 260 ms and 295 ms, respectively (30 dances, 366 total loops). Both mean waggle duration and mean pure waggle duration were significantly lower when the tunnel was wider (P<0.001). Thus, the dances show a clear dependence on tunnel width, as one might expect if travel distance were gauged in terms of the optic flow experienced en route.
Contribution of lateral and ventral visual fields to odometry
We next asked which region or regions of the eye are involved in the
measurement of the optic flow that is used by bees to assess distance
traveled, and how sensitive the calibration of the honeybee's visual odometer
is to deprivation of optic flow in specific regions of the visual field.
Bees were made to fly through a tunnel whose floor, or side walls, or all surfaces, were lined with a random black-and-white Julesz pattern to provide motion cues. The remaining surface(s) were lined with an axial striped pattern, and thus provided very weak optic flow cues.
The results revealed that when the tunnel provided optic flow on all surfaces (walls as well as floor), the mean waggle duration was approx. 210 ms (Fig. 3). This was the experimental condition that elicited the largest mean waggle duration and the largest mean pure waggle duration (Fig. 3), as well as the largest percentage of waggle loops (82%, Fig. 4). When the walls of the tunnel provided optic flow, but not the floor, the mean waggle duration and the mean pure waggle duration decreased slightly (Fig. 3). The percentage of waggle loops also displayed a slight decrease (Fig. 4). When the floor contributed optic flow, but not the walls, both measures of waggle duration decreased by further, small amounts (Fig. 3), which was mirrored by a further, small decrease in the percentage of waggle loops (Fig. 4). Comparing the data in the second and third columns of Fig. 3, we see that the walls of the tunnel make a slightly, but significantly greater contribution to the odometric signal than does the floor. The striking feature of the dances that were elicited by these three conditions, however, lies not in their slight differences, but in their similarity. Thus, even when optic flow cues were restricted to the floor (and the floor comprised only 20% of the tunnel's interior surface area), the mean waggle duration and the mean pure waggle duration were still approximately 70% of the value that was observed when all of the surfaces provided optic flow. The percentage of waggle loops also exhibited a relatively modest variation between these two rather extreme conditions. These findings indicate that the honeybee's odometer is remarkably robust to deprivation of optic flow information in large sections of the visual field, regardless of whether this deprivation occurs in the lateral or the ventral field of the eyes.
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When all of the interior surfaces of the tunnel were lined with axial stripes, both measurements of waggle duration dropped further (Fig. 3), as did the percentage of waggle loops (to 38%, Fig. 4). However, even under this highly impoverished condition, the bees signaled a distance that was greater than that corresponding to the outdoor flight of 35 m to the tunnel entrance (which elicited 18% waggle loops and a mean waggle duration of 40 ms). Evidently, small imperfections in the construction and laying of the axial stripe pattern in the tunnel (and, possibly, stray shadow edges) produced small, residual optic flow cues that were registered by the odometer.
Finally, when the bees returned from an outdoor feeder positioned 41 m from the tunnel entrance, they exhibited 55% waggle loops and a mean waggle duration of 80 ms. These values represent a flight distance that is slightly larger than that corresponding to an outdoor flight of 35 m, but lower than the distances that were signaled after flights within the tunnel when some or all of the surfaces provided optic flow cues. This is despite the fact that the bees flew the same distance from the hive to the feeder in the tunnel (35 m + 6 m) as they did when they flew to the outdoor feeder at 41 m. Clearly, then, the larger magnitude of the optic flow that bees experience in the tunnel due to the proximity of the walls and the floor compared to outdoor flight in a natural environment caused the bees to signal a greater distance when they flew in the tunnel, provided at least one of the surfaces generated optic flow cues.
Effect of contrast on the odometric signal
Next, we investigated the influence of the contrast of the visual
environment on the perception of distance flown. In a series of experiments,
bees were made to fly a constant distance (6 m) into a tunnel in which the
walls and floors were lined with square-wave gratings of constant period, but
with contrasts ranging from 20% to 92%.
Analysis of the dances of bees returning from this tunnel revealed that the odometric signal is rather insensitive to variation of contrast (Fig. 5). When the contrast was decreased from 92% to 20% (a 78% reduction), the mean waggle duration decreased from 270 ms to 180 ms (a reduction of only 33%). The 180 ms waggle duration elicited by the 20% contrast grating was more than twice as large as the waggle duration elicited by a tunnel lined with axial stripes (compare with Fig. 1). Evidently, even small contrasts generate sufficient optic flow information to produce an odometric signal of nearly normal strength. There was no significant decrease in the mean waggle duration when the contrast was reduced from 85% to 66%, or from 47% to 20% (P>0.05). The mean pure waggle duration exhibited a similar insensitivity to variation of contrast (Fig. 5), as did the percentage of waggle loops in the dances (Fig. 6). These findings indicate that the odometric signal is rather insensitive to variations of contrast in the environment.
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Effect of spatial frequency content of the environment on the
odometric signal
In another series of experiments, bees were made to fly a constant distance
(6 m) into a tunnel in which the walls and floor were lined with sinusoidal
gratings of fixed contrast (mean contrast, 58%) but with varying spatial
periods of 1.8 cm, 3.6 cm and 7.2 cm. (For a bee flying along the axis of the
tunnel, the spatial frequencies of these gratings as seen by the lateral field
of the eye would range from 0.03 to 0.10 cycles deg-1). The results
(Fig. 7) revealed that the mean
waggle duration does not vary significantly with a twofold increase in spatial
period from 1.8 cm to 3.6 cm. There was only a slight, but significant
decrease in mean waggle duration with an increase in spatial period from 3.6
cm to 7.2 cm. There was, however, no significant difference between the mean
waggle durations for any of the spatial periods and those obtained in the
conditions in which the walls and floor of the tunnel were lined with a
checkerboard pattern (Fig. 7; P>0.05), but all of these mean waggle durations were significantly
higher than that corresponding to the axial-stripe condition, in which there
was very weak optic flow (Fig.
7). The mean pure waggle duration showed a similar behaviour
(Fig. 7). Overall, these
results indicate that the calibration of the odometer is quite insensitive to
variations in the spatial texture of the environment through which the bee
flies, provided that the texture is capable of generating optic flow
information. A similar conclusion is reached when the waggle loop percentages
are analysed for these various conditions
(Fig. 8). There were no
statistically significant differences between the waggle loop percentages for
the three different spatial periods (P>0.05).
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Discussion |
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Our findings also indicate that the odometric signal is rather insensitive
to variations of scene contrast. The dances elicited by visual contrasts in
the range 66-92% are remarkably similar in their properties (Figs
5,
6), although with 92% contrast
the mean waggle duration and waggle loop percentage elicited by the grating
(Figs 5,
6) were slightly, but
significantly greater than those elicited by the checkerboard (Figs
5,
7) or the random texture (Figs
1,2,3,4;
P<0.05). When the contrast is reduced to below 50%, there is a
slight decrease in the mean waggle duration, mean pure waggle duration and
waggle loop percentage, but these values continue to be high even at a
contrast as low as 20%. This robustness to contrast variations should be of
considerable advantage, since the contrast of natural scenes can vary widely
and it would be important to have access to a strong and reliable odometric
signal even when the contrast in the environment is low. von Frisch noted that
bees returning from a feeder on a lake signaled almost the same distance in
their dances as bees that had flown a comparable distance on land
(von Frisch, 1993, pp.
111-113). Given that the surface of the lake offered very low optical
contrast, he concluded (from this and other evidence) that bees use energy
consumption, rather than visual information, to estimate how far they have
flown. Recently, however, considerable evidence has been mounting against this
so-called `energy' hypothesis, and in favour of a visually driven odometer
(Neese, 1988
; Esch et al.,
1994
,
2001
; Esch and Burns,
1995
,
1996
; Srinivasan et al.,
1996
,
1997
,
2000
; and our present
results). In the light of these recent findings, we reinterpret von Frisch's
results as implying that the odometer is indeed visually driven, and that it
generates a substantial signal even at the low contrasts that are
characteristic of water surfaces. Indeed, our finding that there is a
measurable odometric signal even in the axial-striped tunnel suggests that
very weak motion cues are sufficient to drive the odometer.
Substantial sensitivity to motion of low-contrast images has also been
observed in the so-called `centring response' another visually
mediated behaviour in honeybees
(Srinivasan et al., 1991).
Bees fly through the centre of narrow gaps or corridors by balancing the speed
of image motion in the lateral fields of the two eyes. The visual subsystem
that mediates this behaviour appears to measure image speed accurately even at
low contrasts: bees will fly through the middle of a corridor even when one
wall carries a 60% contrast pattern and the other a pattern with a contrast as
low as 15% (Srinivasan et al.,
1991
). Exactly how the visual system accurately registers motion
of very low contrast images remains to be unraveled. It is clear, however,
that neurons in the peripheral stages of the insect visual pathway display
some degree of contrast invariance and show substantial responses to low
contrast images (Laughlin,
1981
,
1989
).
Our findings indicate that the odometer is also robust to variation in the
spatial texture of the visual environment through which the bee flies,
provided the texture is capable of providing optic flow information. When the
tunnel is lined with vertical gratings, a fourfold change in spatial period
produces only modest variations in either measurement of waggle duration, and
no variation at all in the waggle loop percentage (Figs
7,
8). A similar insensitivity to
variations in spatial period was observed in an earlier study, which
investigated the ability of bees to use odometric information to locate a
feeder placed at a fixed position inside a tunnel
(Srinivasan et al., 1997).
There, the bees' accuracy in pinpointing the feeder location was unaffected
when the spatial period of the gratings lining the tunnel walls and floor was
varied over a fourfold range (Srinivasan
et al., 1997
). This robustness to variation of spatial texture is
also mirrored in the centring response: bees will fly down the middle of a
corridor even when the spatial periods of the gratings on the two walls differ
by a factor of four (Srinivasan et al.,
1991
).
It is interesting, however, to note that the dances elicited by the tunnel are somewhat different from those performed by bees flying in a natural environment to a distant feeder/food source. The proportion of non-waggle loops, when compared to the tunnel dances, is often much reduced or completely absent in dances performed by bees flying in the open (A. Si, M. V. Srinivasan and S. Zhang, unpublished data). This suggests that the dance performed by the tunnel bees is actually a modified form of the classical waggle dance, possibly arising from the result of a conflict between the bees' normal odometric signal derived from optic flow, and the `true' distance based on the bees' previously acquired knowledge of the environment external to the tunnel. These bees were likely to have a very good knowledge of the environment in the vicinity of the hive. Thus, when they were made to fly into the tunnel with a clear ceiling through which the outside environment was partly visible, there was likely to have been a strong conflict between their position as gauged by external landmarks, as opposed to optic flow.
Our results reveal that, while both the mean and pure waggle durations
increase with distance flown in the tunnel
(Fig. 1), the variability in
these durations (neasured as standard deviation) remains rather constant, and
independent of this distance. This finding is at some variance with the study
of Srinivasan et al. (1997),
where it was observed that the accuracy with which bees search for a feeder in
a tunnel deteriorates with increasing distance. While there could be many
reasons for the discrepancy, one possibility may be that the variability in
the dance behaviour is much larger than the errors associated with odomerty,
and swamps the latter. Indeed, detailed examination of our dance data reveals
considerable variability, not only across bees, but also across dances of a
given individual, as has been observed in classical studies of the waggle
dance (von Frisch, 1993
, pp.
70-74). Further investigation is needed, however, to test this hypothesis.
Our present study, a well as the others mentioned above, indicate that
there are pathways in the honeybee visual system that are capable of measuring
image speed rather independently of contrast and spatial texture. Most
motion-detecting neurons that have been studied so far in the insect visual
system (Egelhaaf and Borst,
1993), and the well-known model of visual motion detection in
insects the autocorrelation model
(Hassenstein and Reichardt,
1956
) do not exhibit this property. However, there are
several neurophysiologically realistic ways in which robust measurement of
image speed can be carried out, at least in principle (for a review of such
models, see, for example, Srinivasan et
al., 1999
). A recent study has reported the existence of
velocity-sensitive motion-detecting neurons in the honeybee
(Ibbotson, 2001
). More studies
at the neurophysiological level are required to explore how image velocity is
computed in a robust fashion.
The honeybees' odometer does not appear to be robust to variations in the
height at which the bee flies above the ground (Esch and Burns,
1995,
1996
), or to variations in the
distances to vertical surfaces (Srinivasan et al.,
1996
,
1997
; note also the data in
the present paper investigating the effect of tunnel width). This is what
causes the bees to signal an aberrantly large distance when they fly in our
narrow experimental tunnels. Thus, outdoor flight at a low altitude, for
example, would increase the magnitude of the optic flow that is experienced by
the ventral field of view, and therefore generate a larger odometric signal,
than flight at a high altitude. Indeed, studies of bees flying in outdoor
environments indicate that the mean waggle duration in the dance is shorter
when bees are forced to fly a given distance at a greater altitude (Esch and
Brown, 1996). It would therefore be of interest to investigate whether bees
foraging under natural conditions tend to fly at a more or less constant
height, or to correct the odometric signal for height variations in some as
yet unknown way.
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Acknowledgments |
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