Thomas Collett
*Many decades ago, von Frisch (1) showed that honeybees are able to measure the distance that they fly from their hive to a foraging site. Knowing this distance helps bees to return to the site and also enables them to communicate the location of the site to other bees. A forager bee imparts this information on its return to the hive by performing a waggle dance (see the figure). A missing piece to this story is an understanding of the way in which bees measure this distance. Led by the bees' errors when flying with tail winds or against head winds, von Frisch supposed that the bees' estimate of distance was derived from the energy they expended during a flight--a curiously unreliable tape measure for bees to use.
Flight of the honeybee. The round and waggle dances are performed by foraging bees on an area of vertical comb close to the entrance of the hive to signal the availability of food. When food is close to the hive, foragers perform a round dance, which gives no indication of the direction in which the food is located. For sites more distant than about 50 m, the direction of food with respect to the sun's azimuth is signaled by the angle of the waggle component (S) relative to gravity, and the distance of the food from the hive is signaled by the duration of the waggle component. Duration increases nonlinearly with distance.
CREDIT: SCOTT CAMAZINE/PHOTO RESEARCHERS, INC.
The issue was reexamined by two groups in the mid-1990s, one in Notre Dame headed by Esch and another at the Australian National University led by Srinivasan, who reports his latest findings on page 851 of this issue (2). Both groups rejected the energy consumption hypothesis. They showed instead that bees monitor distance visually. Bees integrate over time the motion of images crossing the retina as they fly through a landscape. By this means they can both measure and control the distance that they travel. The experimental proofs of both groups depended on a fundamental limitation of the insect neural system that measures self-generated image motion (optic flow). This system is ignorant of the distance of features in the world that generate image motion on the retina. Consequently, flying a short distance close to the ground will generate the same integrated motion signal as flying a longer distance high above the ground.
Esch and Burns (3) trained bees to forage from the top of a 50-m-high building to a feeder placed on the roof of another tall building 230 m away. The waggle dances of these bees indicated a distance that was about half the length signaled by bees traveling the same distance from a hive to a feeder on the ground. Srinivasan et al. (4) took a different tack. They analyzed the search behavior of bees that were trained to fly several meters down a narrow, well-lit tunnel and to forage at a feeder partway along its length. When the feeder was absent, bees searched persistently at the expected location. Evidence for the use of optic flow came from testing these trained bees in tunnels of different widths. Making the tunnel narrower than the standard 22 cm caused bees to search closer to the entrance. When the tunnel was widened, bees searched further from the entrance. To maximize the perceived image motion, the tunnel was decorated with black and white vertical stripes on the walls (see the cover of this issue). But if the stripes were horizontal, so that there were no contrast changes to activate the motion detection system, bees did not know where to search when the feeder was missing and flew from one end of the tunnel to the other without stopping in the middle. Srinivasan and his colleagues have now woven these two strands of research together, and in this issue of Science they present an analysis of the dances that bees perform after flying through the tunnel (2).
The 11-cm-wide and 6.4-m-long tunnel was lit by skylight through the top. It was placed a few meters from the hive. Honeybees typically do not perform the waggle dance when the feeder is closer than 50 m from the hive. Instead, they signal through the round dance that food is nearby (see the figure). Bees returning from a feeder at the entrance to the tunnel performed the expected round dance. The feeder was then placed 6 m into the tunnel. When the tunnel had horizontal stripes that generated minimal image motion, bees continued to perform a round dance. In contrast, if the tunnel walls were covered with a random texture generating abundant image motion, bees performed a waggle dance that indicated a greatly magnified distance between hive and feeder of about 200 m. Flying a short distance through a narrow tunnel thus turns out to be equivalent to flying a distance 30 times further over open ground. Srinivasan et al. infer from these data that in the outdoor environment in which the bees were tested, features generating image motion were about 170 cm away from the bees' eyes. As the perceived image motion depends strongly on details of the terrain, the bees' measuring tape will be route dependent. This shortcoming does not matter if the principal use of the measuring tape is to gather and transmit information about a particular route.
The slope of the relation between waggle duration and distance becomes less steep with distances greater than about 500 m (see the figure). The shallower slope at greater distances might result either from saturation of the system that integrates optic flow, or because bees fly higher over longer journeys (5) and so are at a greater mean distance from objects generating optic flow. The great advantage of measuring the waggle dance of bees that have flown through the tunnel is that the optic flow in the tunnel is well defined. It thus becomes possible to test for the linearity of the integrator, provided, of course, that workshop and bees cooperate in building and flying the much longer tunnels that would be needed.
Different insects have to contend with different ecological problems so that image motion is unlikely to be the only cue that insects use for measuring distance. Because bees fly and are subject to unknown winds, ground speed and distance are most reliably controlled and measured through image motion. But insects that walk on the ground and are not subject to passive transport by wind can do better. Rather than relying on optic flow, with its unavoidable uncertainties, walking insects can, with advantage, use proprioceptive information or some kind of step counting to monitor the speeds and distances that they travel. Indeed, desert ants keep a precise record of the distance that they walk to and from their nest, and they seem to make little if any use of optic flow in monitoring these distances (6).
References
There are two theories about how honeybees estimate the distance to food sources. One theory proposes that distance flown is estimated in terms of energy consumption. The other suggests that the cue is visual, and is derived from the extent to which the image of the world has moved on the eye during the trip. Here the two theories are tested by observing dances of bees that have flown through a short, narrow tunnel to collect a food reward. The results show that the honeybee's "odometer" is visually driven. They also provide a calibration of the dance and the odometer in visual terms.
* To whom correspondence should be addressed.
E-mail: M.Srinivasan@anu.edu.au
It is well known that honeybees navigate accurately and repeatedly to a food source, as well as communicate to their nestmates the distance and direction in which to fly to reach it, through the "waggle dance" (1). However, the cues by which bees gauge the distance to the goal have been controversial. Early work suggested that flight distance is estimated in terms of energy consumption (2). More recent studies suggest that the primary cue is the integral, over time, of the image motion that is experienced en route (3-6). Here we put the two theories to a stringent test by recording dances of bees that have been trained to fly into a short, narrow tunnel to collect a food reward.
The experimental bees (Apis mellifera ligustica Spinola) were housed in a two-frame observation hive, with transparent walls on both sides. One frame was positioned above the other so that all comb faces were visible for observing and filming dances. The hive was located on the inside wall of a building, with an exit to the outside. Typically, six bees were individually marked and used for each experiment.
In one series of experiments, individually marked bees were trained to forage at a feeder carrying sugar solution placed in a wooden tunnel 6.4 m long, 11 cm wide, and 20 cm high. The tunnel was positioned outdoors near the hive. The far end was closed, and bees could enter and leave the tunnel only at the near end. The top of the tunnel was covered with black insect-screen cloth, which permitted observation and provided the bees with a view of the sky.
In experiment 1, the tunnel was positioned with its entrance 35 m from the hive, and was oriented along the direction to the hive (Fig. 1A). The walls and floor of the tunnel were lined with a random visual texture (7). The feeder was placed at the entrance to the tunnel. Bees returning from the feeder performed predominantly round dances: The probability of a round dance was 85.2% (Fig. 1B). This is consistent with the fact that A. mellifera ligustica performs mainly round dances when visiting food sources that are within 50 m of the hive (8). However, when the feeder was placed 6 m inside the tunnel (experiment 2), the bees performed primarily waggle dances: The probability of a waggle dance was 90.0% (Fig. 1B) (9). This change from round dances to waggle dances occurred while the distance flown by the bees had increased by a mere 6 m, from 35 m in experiment 1 to 41 m in experiment 2. Clearly, in experiment 2, the feeder was still at a distance at which bees normally perform round dances when flying outdoors.
Fig. 1. (A) Layout for experiments using
tunnels. Each tunnel represents a separate experiment (1, 2, 3, or 4). The
dot in the tunnel shows the position of the feeder in each case. (B) Probability of
waggle (W) round (R) dance for experiments 1 to 4. N and n
represent the numbers of bees and dances analyzed, respectively, in each experiment.
Why were the bees performing waggle dances in experiment 2? One possibility is that flight in the narrow tunnel generated a large integrated optic flow on the eye, mimicking the effect of a long flight in natural outdoor conditions. The distances to the walls and the floor would typically be much smaller than those to nearby objects or the ground during free flight in an open environment. Therefore, if the bee moves forward by, say, 1 cm, it would experience a greater angular motion of the image when flying in the tunnel than when flying outdoors. The magnified image motion in the tunnel might cause the bees to infer a journey considerably longer than 6 m.
The possibility that image motion is indeed the cue for estimating flight distance was tested in experiment 3 (Fig. 1A). Here the tunnel and the feeder were positioned as in experiment 2, but the walls and floor were lined with axially oriented stripes (10). This tunnel provided negligible image motion cues, because the stripes were parallel to the direction of flight. Bees returning from this tunnel produced predominantly round dances: The probability of a round dance was 86.7% (Fig. 1B), even though these bees had flown exactly the same physical distance--41 m--as those in experiment 2. Evidently, the lack of image motion in the axial-striped tunnel caused the bees to infer that they had flown a very short distance.
In a further experiment (experiment 4), the tunnel carried a random texture, as in experiments 1 and 2, but was positioned such that the entrance was only 6 m from the hive exit (Fig. 1A). The tunnel was pointed toward the hive, and the feeder was placed 6 m inside the tunnel. Bees returning from this tunnel performed mainly waggle dances: The probability of a waggle dance was 87.5% (Fig. 1B), even though the feeder was now only 12 m from the hive. We conclude from these experiments that distance flown is inferred on a visual basis, the primary cue being the extent of image motion experienced by the eye.
How is image motion translated into a percept of distance flown? To examine this question, we carried out another series of experiments in which we recorded the dances of marked bees returning to our hive from feeders placed at various locations in the outdoor environment of the campus of the Australian National University. The feeders were positioned at distances of 60, 110, 150, 190, 225, 340, and 350 m from the hive (11). Data were obtained from two different hives, H1 and H2, each at a different location on campus, to check for possible colony-specific or route-specific differences (12). Bees returning from these feeders performed primarily waggle dances at all of the distances tested. The mean durations of the waggle phases (13) of the dances for each of these feeder distances are plotted in Fig. 2 [see Table 1 and (14)]. The waggle duration increases approximately linearly with distance flown, as is well known for distances up to 1 km (15). Linear regression on the data yields a correlation coefficient of 0.998. The slope of the regression line is 1.88 ms of waggle duration per meter of distance traveled. This value is in close agreement with classical published data for comparable flight distances (15). For any given distance, there were no significant differences between the durations of the waggle phases recorded from the two colonies. We infer from this that the bees from the two hives flew through essentially similar outdoor environments (see below).
Fig. 2. Mean waggle durations of dances
elicited by outdoor feeders at various distances d. The straight line is a linear
regression on the data, defined by the expression 
= 95.91 + 1.88d. Also shown are the mean waggle
durations measured in the tunnel experiments (experiments 2 and 4) and their
equivalent outdoor flight distances as read off from the regression line. 
How do the dances of bees returning from the tunnels in experiments 2 and 4 compare with those of bees flying in the open outdoor environment? We found no qualitative differences. In either case, bees signaled the direction of the feeder in their waggle dances, regardless of the time of day: The direction of the waggle axis shifted in step with the sun's movement in the sky.
However, bees returning from the tunnels massively overestimated the distance that they had traveled. In experiment 2, the bees flew 35 m in a natural outdoor environment, followed by 6 m in the tunnel--a total of 41 m to the feeder. But analysis of their dances revealed a mean waggle duration as long as 529 ms. This corresponds to a flight of 230 m in an outdoor environment, as revealed by projection of this duration on the regression line of Fig. 2. Evidently, a flight of 6 m in the tunnel was perceived as equivalent to a flight of 195 m outdoors. In experiment 4, the bees flew 6 m outdoors, followed by 6 m in the tunnel. But this was signaled by a waggle dance of 441 ms, which, from the regression line, represents a distance of 184 m outdoors. In this case, the 6-m flight in the tunnel was perceived as equivalent to an outdoor flight of 178 m (see Table 1). Averaging the two results, we calculate that a 6-m flight in the tunnel is equivalent to a journey of 186 m in the outdoor environment. In other words, the tunnel magnifies the perception of distance flown by a factor of 31.
We can use the data from the tunnel experiments to calibrate the honeybee's odometer and the dance in terms of the visual input to the eye. This is because the dimensions of the tunnel are known and, unlike the situation in an open outdoor environment, flight in the tunnel is tightly constrained. In the tunnel, bees tend to fly along an axis roughly midway between the two walls (16) and halfway between the floor and the ceiling. The distance to each wall is therefore 5.5 cm, and the height above the floor is 10 cm. Assuming that distance flown in the tunnel is gauged primarily on the basis of the image motion that is experienced by the lateral fields of view of the eyes (6), we calculate that 1 cm of forward motion in the tunnel would cause the image of the wall to move backward by an angle of 10.3° in the lateral visual field. Therefore, 6 m of forward motion in the tunnel would generate 6180° of image motion. We have already shown that a 6-m flight in the tunnel corresponds to a flight of 186 m in a natural outdoor environment. From the slope of the regression line in Fig. 2, we calculate that 186 m of outdoor flight is encoded by a waggle duration of 350 ms. Therefore, 1 ms of waggle in the dance encodes (6180/350) = 17.7° of image motion in the eye (17).
Traditionally, the honeybee's odometer has been calibrated in terms of the waggle duration, the number of waggles, or the waggle length, per meter of distance flown (15). However, it is now clear that the distance flown is not perceived directly in distance units, but rather in terms of the amount of image motion that is experienced by the eye. The image motion that is generated during 1 m of forward flight would depend strongly on the average distance of foliage and the ground during the bee's journey, which could vary from one environment to another. Therefore, the traditional calibration cannot be an "absolute" one because it is environment-dependent. The correct way of specifying the calibration of the odometer would be in terms of the amount of image motion that is required to generate a given waggle duration. As derived above, this calibration is 17.7° of image motion per millisecond of waggle. We propose that this is the fundamental, absolute calibration of the honeybee's visual odometer. We surmise that, in nature, visual odometry of this kind is reliable because new recruits tend to take the same route as experienced foragers.
The total angular image motion that a bee experiences while flying a
particular route depends only on how far she flies, and not on the speed of
flight. The reason is as follows. Assume that the bee moves forward by a small
distance 
d cm at a speed of
V cm/s. The induced angular velocity of the image in the lateral field
of view of the eye, A (in degrees per second), would depend on the
distance of the scene being viewed. However, for a given scene, A would
be proportional to V. Thus, A = k·V, where k is
a scene-dependent constant. On the other hand, the time t taken to fly the distance d is inversely proportional to V.
That is, t = d/V. Therefore, during this
interval, the angular motion of the image on the eye (in degrees) would be 
= A·t = k·d, which depends only on the distance
traveled and is independent of flight speed. Thus, the total angular motion of
the image is a robust measure of the distance traveled along a particular
route. Indeed, there is some evidence that bees are able to estimate the
distance traveled to a goal fairly accurately, regardless of how rapidly they
fly to it (6), although this needs more careful examination.
If we assume that odometry in outdoor flights also relies primarily on image motion, then we can obtain from our data a rough estimate of the average distance of objects and the ground as experienced by the bees when they flew in the outdoor environment. Given that the tunnel amplifies the perception of distance flown by a factor of 31, and that the distance to each wall of the tunnel was 5.5 cm, we deduce that the average object distance outdoors was ~31 × 5.5 = 170 cm. Although this value is difficult to verify precisely, it is quite plausible for our environment. Thus, it is reasonable to infer that cues based on image motion play an important role even in outdoor flights of several hundred meters.
Bisetzky (18) elicited waggle dances from bees that were trained to walk through short tunnels. It is not clear what cues the bees were using in these experiments: The visual cues were not defined or controlled. Kirchner and Braun (19) were able to elicit waggle dances from tethered, flying bees that were exposed to moving visual patterns. They found that the duration of the waggle increased with flight duration. However, this finding does not distinguish between visual and energy-based cues, because both would increase with flight duration. The visual cues were not manipulated independently.
Our study suggests that honeybees use cues based primarily on image motion to monitor flight distances of hundreds of meters in natural outdoor environments. In the future it should be possible to study mechanisms of navigation and path integration conveniently, and under controlled conditions, by training bees to fly through short tunnels arranged in various configurations.
25 October 1999; accepted 15 December 1999