|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online May 2, 2008
Journal of Experimental Biology 211, 1635-1644 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.013425
Variability in the encoding of spatial information by dancing bees
Freie Universität Berlin, Fachbereich Biologie/Chemie/Pharmazie, Institut für Biologie–Neurobiologie, Königin-Luise-Strasse 28-30, D-14195 Berlin, Germany
* Author for correspondence (e-mail: demarco{at}neurobiologie.fu-berlin.de)
Accepted 10 March 2008
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: Apis mellifera, communication, spatial information, waggle dance, variability
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
) discovered that a highly stereotyped, still variable motion
pattern that honeybees perform on the comb surface conveys to bees and human
observers the circular coordinates of relatively well-defined locations. The
term `waggle dance' denotes a form of this pattern, which conveys information
about targets located fairly far from the hive
(von Frisch, 1967). Compelling
evidence indicates that the waggle dance is at the core of a series of
communication systems enabling a honeybee colony to coordinate the activity of
its members during foraging and nest-site selection (e.g.
Lindauer, 1961;
Seeley, 1995;
Dyer, 2002;
Sherman and Visscher, 2002).
This is possible because those colony members that keep close contact with a
dancing bee, usually called dance followers, appear to detect a variety of
signals emitted by the dancer, and process them in such a way that their
ensuing behaviours may greatly depend upon the content of these signals
(von Frisch, 1967). In the
waggle dance, a returned, successful forager moves forward on the comb surface
while wagging its body from side to side at about fifteen times per second.
This straight portion of the dance is called a `waggle phase'. Typically
without interruption, it then moves on along a rather semicircular trajectory,
and returns to a position close to the starting point of the recent waggle
phase; this portion is called a `return phase', and tends to be alternatively
performed clockwise and counter-clockwise along the dance. Once at this
position, the dancing bee repeats the forward, wagging portion of the dance.
The number of waggle phases can vary significantly across dances, thereby
revealing regulatory responses and amplification phenomena on the signal
production side of the communication process (e.g.
Seeley, 1986;
De Marco et al., 2005).
Intriguingly, a dancer's motion pattern is strongly linked to its recent
navigation experience. Flying honeybees use the sun as a reference to maintain
a course, and the average orientation of a dancer's successive waggle phases
relative to the direction of gravity approximates the angle between the
direction toward the goal and the sun (von
Frisch, 1967). Honeybees also gauge the distance they travel
toward their various goals [most likely by integrating self-induced optic flow
during flight, i.e. the net amount of image motion over the retina accumulated
during movement (e.g. Esch and Burns,
1996; Srinivasan et al.,
1996)], and the average duration of a dancer's successive waggle
phases correlates well with the amount of visual flow experienced on the way
to the goal (Srinivasan et al., 2000;
Tautz et al., 2004;
De Marco and Menzel, 2005),
and, consequently, also with the travelled distance
(von Frisch and Jander, 1957).
These two correlations convey to a human observer the position of a relatively
well-defined area surrounding the endpoint of an average vector in a
two-dimensional system of coordinates. The waggle dance is thus an intriguing
example of multisensory convergence, central processing, motor coordination,
and symbolic information transfer.
Six decades after von Frisch's original discovery
(von Frisch, 1946), however,
the process of decoding information in the dance still remains elusive [see
Michelsen (Michelsen, 1999)
for a comprehensive account of the current hypotheses]. One reason is probably
to be found in the striking variability of the multiple dance signals. The
body contacts between dancers and followers most likely convey meaningful
stimulation to potential recruits (e.g.
von Frisch, 1967;
Bozic and Valentincic, 1991;
Rohrseitz and Tautz, 1999),
and the same can be said about chemical cues, both environmental
(von Frisch, 1967) and
semiochemicals (Thom et al.,
2007), coupled to a dancer's wagging movements. Three dimensional
fields of particle oscillations produced by the dancers' vibrating wings
(Michelsen et al., 1987;
Kirchner and Towne, 1994;
Michelsen, 2003) and
substrate-borne vibrations caused by their wagging movements
(Tautz, 1996) also appear to
be a source of meaningful stimulation. However, the question of how a dancer's
behaviour is mapped to that of its followers remains open, most probably as a
result of the use of sub-optimal methods to trace the behaviour of dancers and
followers, both inside and outside the hive. Furthermore, the study of a
dancer's manoeuvres and a follower's response to the dance have long been
addressed either independently (e.g. Towne
and Gould, 1988; Riley et al.,
2005) or without pondering the relative influence of simultaneous,
guiding cues (e.g. von Frisch and
Lindauer, 1961), e.g. olfactory cues that followers use to
pinpoint their targets. [An exception here is the work by Esch (Esch, 2001)
and colleagues, which simultaneously addressed the encoding of distance
information in the dance and the distribution of field searches by recruits.]
In addition, the influence of a follower's experience on the process of
decoding information in the dance remains obscure. Currently, unemployed
foragers appear to follow no more than a few waggle phases before resuming
their flights to natural goals, and they do so by following those seemingly
indicating familiar sites (Biesmeijer and
Seeley, 2005). Such a small number of dancing events provides
spatial information only roughly to a human observer
(De Marco and Menzel, 2008),
thereby posing the question of how informative
(Haldane and Spurway, 1954)
such a `sample' can be to the followers. This is probably the reason why a
distinction between experienced and novice foragers would prove fruitful for a
deeper understanding of the dance communication system.
Dance studies typically focus on an average vector whose endpoint roughly
corresponds to the location of a goal, and such a vector is often computed
from a variable – and usually small – collection of waggle phases,
from the same or different individuals. With only a few exceptions (e.g.
Haldane and Spurway, 1954;
Esch, 1978;
Weidenmüller and Seeley,
1999; Beekman et al.,
2005; Tanner and Visscher,
2006), variations in a dancer's manoeuvres are rarely discussed in
the context of information transfer, even when it is unclear whether and to
what extend followers average information from multiple waggle phases.
Certainly, it is the variability of a dancer's motion display that initially
defines the boundaries of the stimulation that followers must cope with if
they are to successfully decode information in the dance. Such variability
also defines the level of uncertainty that a human observer must cope with
while dealing with samples of limited size. Hence, a first and utterly
important step in the elucidation of how a dancer's behaviour is eventually
mapped to that of its followers relies on the analysis of the accuracy and
precision with which foragers map the position of a goal. Since the waggle
phase is the main source of spatial information for both bees and human
observers (von Frisch and Jander,
1957; von Frisch,
1967; Michelsen,
1999) our study is based upon thousands of waggle phases from
hundreds of dances recorded through high-speed video techniques, and presents
an analysis of the accuracy and precision with which an increasing number of
waggle phases conveys to a human observer the direction of and distance
towards a desirable goal.
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
;
Sokal and Rohlf, 1969).
The second experimental series focused on the variability in the encoding
of both distance and direction information. Bees foraged on an outdoor feeder
placed at 215 m from the hive along a single flight direction: 82°SW. The
feeder offered unscented 1.46 mol l–1 sucrose solution. This
sucrose concentration, slightly lower than that of the first series, was
chosen to attenuate recruitment and to carry out our recordings more
efficiently. The bees were individually marked and their dances filmed at 87
frames per second under red illumination. We used 87 frames per second because
it provided us with a favourable temporal resolution for our subsequent
analyses, and also with optimal values for the rate of information transfer
from the camera to the computer in which the digital videos were stored. The
time of day of each video recording was also noted. Owing to an apparent lack
of differences between the dances of trained and newly recruited bees, we
recorded dances from both groups of bees, provided that all of them had
already been individually marked; this helped us to enhance our rate of data
collection. In addition, several bees were repeatedly recorded. Next, we
analysed the digital videos frame by frame by means of specially designed
software, allowing precise measurements of a dancer's movements and body
orientation in space. In order to quantify the direction of each waggle phase,
we measured the angle formed by the direction of gravity and a line connecting
the centre of the dancer's head, the junction between its thorax and abdomen,
and the tip of the wagging abdomen when it was in the middle of its trajectory
from one side to the other. We recorded this angle twice for each waggle
phase, within its first and third portion, as calculated from the total number
of wagging movements involved in such a phase. Next, the mean from these two
measurements was computed as the waggle-phase orientation relative to gravity.
In doing our measurements, we recorded 38 waggle phases (out of 1452) with no
apparent wagging movements of the dancer's body; in all these cases, the
waggle-phase orientation was calculated based on a dancer's straight and
forward motion occurring between consecutive return phases. Bees tend to
regularly alternate between left and right turns when dancing, and the waggle
phases made after one type of turn (either to the left or to the right) tend
to have a different direction than the waggle phases made after the other one,
particularly when the duration of the waggle phase is short. Hence, we
separately analysed the waggle phases made after either left or right turns,
and calculated the mean angle of left and right waggle phases. The mean angle
of the entire dance was computed as the average between left and right mean
angles. In all cases, means were computed only when the dance consisted of at
least four left and four right waggle phases. For each side, either left or
right, the angular dispersion was defined as the average magnitude of the
differences between the angles of the single waggle phases and the mean from
all the waggle phases of the respective side. The angular divergence, in
addition, was defined as the difference between the angles of alternation
(i.e. left vs right) in consecutive waggle phases. We also calculated
the `Missweisung' (von Frisch and
Lindauer, 1961), or misdirection of the dance, as the difference
between the direction encoded in the dance and the actual direction toward the
goal. In addition, we counted the number of wagging movements occurring during
the waggle phase, as well as any interruption in a dancer's manoeuvres
occurring during the dance. For each side, either left or right, the
dispersion of the number of wagging movements was defined as the average
magnitude of the differences between the number of wagging movements of the
single waggle phases and the mean from all the waggle phases of the respective
side. In evaluating the encoding of distance information, we excluded the 38
dancing events (see above) lacking a dancer's characteristic wagging
movements. Overall, 1452 waggle phases were recorded throughout 145 dances
performed by 29 individuals. All angles are indicated clockwise with respect
to either north or upward vertical, and their means were calculated using
rectangular coordinates (Batschelet,
1981). To confirm some of the results of the first series, we
repeated the analysis of the relationship between the flown distance and the
duration of the waggle phase with a new group of bees. The slope of the
ensuing linear regression gave 0.038 wagging movements per meter of travelled
distance, thus matching our previous results (see below). With this new
calibration curve, we computed the locations encoded in the single waggle
phases of all dances for 215 m. Next, we estimated the level of uncertainty
associated with the mean direction and the mean number of wagging movements as
a function of the number of observed waggle phases. To this end, for each
chosen number of observed waggle phases, we randomly resampled 50 000 times
all waggle phases from dances with at least four left and four right waggle
phases, and calculated the proportion of those resamples for which the means
fell within each of a series of intervals around the overall mean.
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
), the
waggle-phase duration increased linearly with the flown distance (82°SW:
r2=0.78, P<0.0001; 3°NW:
r2=0.80, P<0.0001; linear regression). Neither
the slopes (F(1,56)=2.72, P=0.11; linear
regression) nor the elevations (F(1,57)=0.03,
P=0.86; linear regression) of the two regression lines were
statistically different, and the pooled slope gave 1.61 ms of waggle-phase
duration per meter of travelled distance; this result matches published data
obtained in our particular outdoor landscape
(De Marco and Menzel, 2005).
Next, we repeated the analysis with dances recorded at 125 frames
s–1, and found no statistical differences in either the
slopes (F(1,56)=0.01, P=0.91; ANCOVA) or in the
intercepts (F(1,57)=0.60, P=0.44; ANCOVA) of the
regression lines obtained with either 25 or 125 frames s–1.
Owing to a greater sample size, we focused on the former video-recordings (25
frames s–1) in order to analyze the frequency distribution of
the within-individual variations associated with the encoding of distance
information. To compare information from different bees and distances, the
data from each waggle phase was incorporated into a frequency distribution
using the difference between the duration of that waggle phase and the mean
duration from all the waggle phases of a dancer, and dividing this difference
by the individual mean. Each of these values is referred to as the
`divergence' between the distance information encoded in a single waggle phase
and that from all of a dancer's waggle phases.
Fig. 1A–C shows the
relationship between the flown distance and the frequency distribution of
these divergences (as percentages). The distributions of the different
distances were not normal (137 m: P=0.043; 248 m: P=0.011;
360 m: P=0.004; K–S goodness-of-fit test), although those
corresponding to 248 and 360 m did not deviate from a Gaussian model (248 m:
R2=0.97, P=0.064; 360 m: R2=0.91, P=0.568; runs test).
Skewness and Kurtosis were 1.0 and –0.2, 1.7 and 1.5, and 2.0 and 3.2
for 137, 248 and 360 m, respectively. The percentage of waggle phases (from
different dances and individuals) for which the duration differed less than
10% with respect to that of the mean was 14.4%
(Fig. 1A), 20.5%
(Fig. 1B) and 25.4%
(Fig. 1C) for 137, 248 and 360
m, respectively. Thus, the scatter of the distribution decreases as the flown
distance increases (Fig.
1A–C).
|
The number of wagging movements does not vary between right and left waggle phases, but changes with the overall dance orientation
Bees tend to regularly alternate between left and right turns when dancing,
and the waggle phases made after one type of turn (either to the left or to
the right) tend to have a different direction than the waggle phases made
after the other one. Hence, we asked if the duration of the waggle phase
changes depending on whether it follows a right or left turn. Moreover, it has
long been reported that the misdirection associated with the encoding of the
direction of a goal varies together with a dancer's orientation in space
(von Frisch and Lindauer,
1961; Lindauer,
1963). As described by von Frisch
(von Frisch, 1967): "One
sees that the `direction' indications are quite precise when the dances are
directed upward or downward or approximately horizontally to left or
right." It has remained unknown, however, whether the distance
indication also varies together with the overall dance orientation. We asked,
therefore, whether the encoding of distance information also varies together
with a dancer's orientation in space. In the second experimental series, the
scatter of WMs around the mean was asymmetrical in the waggle phases following
right turns (P<0.001), and symmetrical in those following left
turns (P=0.091). We found similar scatters when the data from both
sides were compared, with variances of 6.75 and 6.34 WMs for waggle phases
following left or right turns, respectively (Pearson's 
2=9.68,
P=0.64); 90% of the divergences fell within 4.5 WMs around the mean
(Fig. 2A), thereby matching the
results of the first series (Fig.
1B). Furthermore, the mean number of WMs changed together with the
overall dance orientation: it was smaller in horizontal
(
60–90°) than in downward dances
(Fig. 2B,C).
|
2=22.68, P=0.091;
Fig. 3A). The variance from
waggle phases following left and right turns was 126° and 133°,
respectively. Overall, 90% of the single directions were within 17° around
the mean. The scatter also changed with the overall dance orientation, meaning
that the angular dispersion was greater in horizontal (90°) than in
downward dances (Fig. 3B,E,F),
irrespective of whether the waggle phases followed right or left turns. The
misdirection gave an average of 3°, with higher and more variable values
in the early afternoon (14:00–16:00 h;
Fig. 3C), when the direction
toward the sun was perpendicular to that of the dancers' flights. The latter
result is in agreement with previous reports
(von Frisch, 1967).
|
90°) and downward (180°) dances, respectively
(Fig. 3D, white circles), but
the distributions of these divergences were independent of the overall dance
orientation (Fig. 3D). The mean
and distribution of divergences were intermediate in upward (0°)
dances. These variations could only be partially explained on the basis of
simultaneous variations in the scatter of the single waggle phases
(Fig. 3B), because there was a
notable increase in the mean angular divergence in horizontal dances
(Fig. 3D, white circles), and a
simultaneous, much smaller increase in the corresponding scatter of the waggle
phases following either left or right turns
(Fig. 3E,F, respectively).
Accuracy and precision in the encoding of spatial information
We examined the accuracy and precision of the encoding of spatial
information in the dance, as related to the field locations indicated by the
single waggle phases of all dances from our second series
(Fig. 4). Of the endpoints of
the vectors indicated by the single waggle phases, 15% corresponded to field
locations that fell well within an area centred at the feeder of a radius of
50 m, and 90% fell within an area of a radius of 180 m. The totality of the
indicated locations fell within a circular surface of 101.800 m2
(Fig. 4). The mode of the
signalled locations was slightly closer to the hive, and 3°S from the
actual position of the feeder (Fig.
4). This agreed with both the asymmetry found in the scatter of
the dancers' wagging movements (Fig.
2A) and the average misdirection
(Fig. 3C).
|
The relationship between the accuracy and precision of the dance and the number of waggle phases
We conducted a random resampling analysis based on an increasing number of
waggle phases to examine the relationship between a given number of waggle
phases and the precision of its corresponding mean angle and duration, thereby
gauging the level of uncertainty associated with the encoding of both
direction and distance information (Fig.
5). We used data from dances with at least four waggle phases per
side (i.e. following either left or right turns), and calculated the precision
of the mean from each resample as the average of the modules of the
differences between either the angle or duration (i.e. number of WMs) of the
single waggle phases and the mean angle or duration from all resamples with
the same number of waggle phases. For each given number of waggle phases, we
used 50 000 random resamples and computed the proportion of those resamples
yielding a certain level of precision. This gave us an estimate of the level
of uncertainty arising from a variable collection of waggle phases.
|
20 m with respect to the mean distance encoded in
the dance can simply not be `read' out of a dancer's wagging movements,
irrespective of the number of observed dancing events
(Fig. 5B,D).
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
;
Seeley et al., 2000;
Michelsen, 2003). For a human
observer, the spatial information is encoded in the direction relative to
gravity and the number of wagging movements of the waggle phase
(von Frisch, 1967). If these
two measures correlate well with a follower's estimate of the direction of and
distance towards the goal, our results then reflect the amount of variability
that a follower must cope with while decoding information in the dance.
Is there a built-in `noise' in the encoding of distance?
We measured the overall duration and the number of wagging movements of
waggle phases for different distances, thereby quantifying within-individual
variations in the encoding of distance information. We recorded dances from
the early morning until the evening for all the three different distances,
meaning that the different orientations of the dancers' bodies with respect to
the direction of gravity were equally represented in the different groups. We
also measured the duration of each of the pendulum-like wagging movements of
the waggle phases, and found that this measure did not change either across
distances (see Results) or throughout each of the single waggle phases (data
not shown). We show that the precision of the distance indication increases
with the flown distance (Fig.
1A–F), a result that is in close agreement with published
data (Esch, 1978;
Beekman et al., 2005). This
happens because the scatter of a dancer's wagging movements around the mean
from its various waggle phases remains constant across distances
(Fig. 1G,H), which means, in
turn, that the number of wagging movements above and below the mean can be
relatively large in dances for close (<300 m) goals. Such variations
account for more than 25% of the mean number of wagging movements in waggle
phases for goals located well within the foraging range of a colony. The
former result indicates that within-individual variations in the encoding of
distance information are scale-invariant, and do not depend upon a stored
estimate used by a dancer as a reference to set an average waggle phase
duration. We also found a regular dispersion of wagging movements around the
mean (Fig. 2A). This finding is
in agreement with previous reports (Beekman
et al., 2005), and fits predictions from the tuned-error
hypothesis (Haldane and Spurway,
1954; Towne and Gould,
1988). According to that hypothesis, the scatter of signalled
locations roughly corresponds to a circular distribution. We found such a
distribution, although twice the magnitude of that reported by Towne and Gould
(Towne and Gould, 1988) for a
similar distance. Comparisons are not straightforward, however, because we
measured the scatter of the signalled locations, instead of that of the
followers' searches.
The duration and direction of a waggle phase co-vary with the overall dance orientation
The number of wagging movements (Fig.
2B,C), the directional scatter of the single waggle phases
(Fig. 3B,E,F) and the angular
divergence between successive waggle phases
(Fig. 3D) co-vary with the
overall dance orientation. In contrast to horizontal (90°) dances,
downward (180°) dances had more wagging movements
(Fig. 2C) and showed smaller
directional scatter (Fig. 3B)
and angular divergence (Fig.
3D), whereas upward (0°) dances gave intermediate values
for these measures. The distribution of the angular divergences between
successive waggle phases was independent of the overall dance orientation
(Fig. 3D, colours), and the
greater mean divergence found in horizontal dances
(Fig. 3D, white circles) was
accompanied by a simultaneous, much smaller increase in the scatter of the
single waggle phases (Fig.
3B,E,F). This means that variations in the directional scatter of
the single waggle phases (Fig.
3B) can account only partially for the divergences found in
horizontal and downward dances (Fig.
3D, white circles). The `residual misdirection' of the dance also
co-varies with a dancer's orientation relative to gravity, as well as with its
previous flight direction relative to the azimuth of the sun
(von Frisch and Lindauer,
1961; von Frisch,
1967). Since Apis mellifera dancers transfer visual
information gathered during their foraging flights to a reference system
defined by propioceptory input, a process called `transposition'
(von Frisch, 1967), their
residual misdirection was initially thought of as being reliant on a `built-in
error' in the transposition system (von
Frisch, 1967). Evidence indicates, however, that its magnitude can
systematically be changed by manipulating the strength and direction of the
earth's magnetic field (Lindauer and
Martin, 1968), suggesting that it also depends upon the bees'
magnetoreception system (Kirschvink et
al., 2001).
As the distance to a goal increases, the average angular divergence
decreases and the duration of the waggle-phase increases
(von Frisch, 1967). We found
that horizontal dances have greater divergences and signal closer locations
than downward dances. This suggests that a common pathway underlies the
circuitry controlling these two tightly connected features of the dance.
Little is known of the mechanisms controlling the direction and duration of
the waggle phase, and our results help in describing features to be modelled
while addressing the regulation of a dancer's manoeuvres. However, the source
of the dance variations described above still remains unknown. They may arise
from (1) `built-in' variations in the processing of propioceptory input that
depend upon a dancer's orientation in space
(von Frisch, 1967), (2)
self-promoted variations in the strength and direction of the earth's magnetic
field, derived from a dancer's own motion
(Lindauer and Martin, 1968),
and (3) variations in the processing of navigation information prior to the
dance, depending on a dancer's recent flight direction relative to the azimuth
of the sun and the pattern of polarized skylight
(Rossel and Wehner, 1982).
Further experiments based upon manipulation of the orientation of the comb
surface, the position of the goal, and the navigation information available to
dancers are necessary to distinguish between these alternatives.
Gathering information from variable dances
The transfer of spatial information from dancers to followers seemingly
depends upon input derived from the dancers' wagging movements and wing
vibrations. A dancer's vibrating wings produce near field air flows
(Michelsen et al., 1987;
Michelsen, 1999) and narrow
jet air flows (Michelsen,
2003) oscillating with the frequency of its wagging body.
Moreover, a wagging dancer repeatedly deflects the followers' antennae, either
directly, by contact between its body and the follower's antennae
(Rohrseitz and Tautz, 1999),
or indirectly, via the air flows produced by its vibrating wings. It
has recently been shown that air-born antennal deflections, as those caused by
the 250–300 Hz dance sounds, can elicit signals conveyed by the
Johnston's organ (Tsujiuchi et al.,
2007). In addition, the number of a dancer's wagging movements is
mapped to the number of a follower's antennal deflections (R.J.DeM.,
unpublished observations). These observations suggest that followers rely on
mechanosensory input to compute estimates of the direction and duration of the
waggle phase, and it would be interesting to examine how the variability
described above is actually mapped to that of a follower's mechanosensory
input during the waggle phase, especially when dancers and followers have
different orientations relative to gravity.
It is not yet clear whether and how followers average stimulation from
multiple waggle phases. Several studies reported that bees tend to follow just
a few dancing events before resuming their flights to a goal
(von Frisch and Jander, 1957;
Esch and Bastian, 1970;
Mautz, 1971;
Bozic and Valentincic, 1991;
Judd, 1995;
Biesmeijer and Seeley, 2005),
although bees can also follow tens of waggle phases during dances for
artificial sources of sugar solution (R.J.DeM., unpublished observations).
Gathering information from only a few dancing events can lead a human observer
to experience a relatively large discrepancy between the virtual and the
actual position of a goal (Fig.
5), and it seems reasonable to ask whether followers may also
experience such a discrepancy. Moreover, if followers average information from
several waggle phases, including left and right waggle phases, variations in
the average angular divergence of the dance might have minor effects on the
scatter of recruits. However, it remains to be determined whether followers
tend to follow mainly right or left waggle phases during dances with
considerable angular divergences; if this were the case, the angular
divergence might have a significant, measurable effect on the scatter of
recruits. It also remains unknown whether and to what degree the number of
waggle phases followed by potential recruits depends upon their foraging
experience within the area of the goal.
Encoding and decoding spatial information in the dance
Our findings raise the question of how a dancer's behaviour is ultimately
mapped to that of its followers. By using harmonic radar techniques, Riley et
al. (Riley et al., 2005)
traced the flight paths of displaced bees seemingly recruited through dances
for a feeder placed 200 m from the hive. Based on the direction of and
distance to a virtual goal, the displaced bees exhibited well-directed flights
of an average – and not so variable – distance of 188 m, only 12 m
less than the initial hive-to-feeder distance
(Riley et al., 2005). Their
post-displacement flights in the absence of additional guiding cues were thus
remarkably accurate and precise. Yet, our resampling analysis shows that such
levels of accuracy and precision can simply not be `read' out of the number of
a dancer's wagging movements (Fig.
5B,D). Two different views might help to explain these
contradictory results. On the one hand, the accuracy of the followers' traced
flights (Riley et al., 2005)
could be accounted for by two separate, but still complementary concepts. The
first one is based upon the idea that the dance conveys highly accurate, still
unknown signals allowing followers to gather accurate and precise distance
information, whereas the second relies on multiple `built-in' compensatory
mechanisms embedded in a follower's response to the dance. That is, prior to
its flight, a follower may correct deviations arising from waggle phases with
systematically variable angles and durations. Thus, a follower may be able to
counterbalance (1) the residual misdirection of the dance
(Fig. 3C), as long as it is the
subject of the same source of variation that influences a dancer's
performance; (2) the differences across the angles of left and right waggle
phases, if it can reliably distinguish between both types of waggle phases,
and then compensate for their variable
(Fig. 3B) deviations from the
mean direction of the dance; (3) variations in the angular divergence of the
dance (Fig. 3D), if it is able
to average the angles of left and right waggle phases, and resolve the angular
divergence that correlates well with the overall dance orientation; and (4)
variations in the number of wagging movements that depend upon a dancer's
orientation relative to gravity (Fig.
2B,C), if a form of template allows it to correct its estimate of
the duration of a waggle phase based on propioceptory input. These concepts
are plausible, and constitute a reasonable basis for future research,
especially if one were to study the neural basis of dance communication.
On the other hand, an interaction may exist between two sources of spatial
information that a follower might access simultaneously, namely, the dance
signals and its own navigational memories
(Menzel et al., 2005;
Menzel et al., 2006;
De Marco and Menzel, 2008).
Such an interaction is a fundamental feature of any communication process.
Communication depends upon reproducing a symbolic entity selected and
transmitted by a sender, but the entity that a receiver finally reproduces
depends upon stored variants of it, which the receiver computes together with
the transmitted signals. One needs to ask whether a follower also recollects
stored information while decoding information in the dance. Biesmeijer and
Seeley (Biesmeijer and Seeley,
2005) reported that no more than a quarter of the lifetime field
excursions of a bee are preceded by dance following, and that bees tend to
follow dances seemingly indicating familiar goals. These findings match
previous results by von Frisch (von
Frisch, 1968), who reported that dances for familiar goals lead to
more effective recruitment. Biesmeijer and Seeley
(Biesmeijer and Seeley, 2005)
also found that experienced bees follow only a few waggle phases before
resuming their foraging flights, a `sample' that provides spatial information
only roughly to a human observer (Fig.
5).
A possible interaction between dance information and a follower's spatial
memory may seem inappropriate at first glance to account for the discrepancy
between the accuracy and precision of the followers' post-displacement flights
described above (Riley et al.,
2005) and that of a dancer's performance, as revealed by our data,
simply because the bees whose flights were traced by harmonic radar had never
foraged on the advertised goal. Flying honeybees, however, mark and pinpoint
the position of desirable sources of food and water by releasing volatiles
produced by their Nasonov glands (e.g. von
Frisch, 1967; Pflumm,
1969; Núñez,
1971; Free and Williams,
1972; Free, 1987).
They also use the flights of conspecifics as a source of visual cues to
pinpoint their targets (Tautz and
Sandeman, 2002), a phenomenon also found in stingless bees
(Nieh, 2004). Moreover,
stingless bees visually track the piloting flights of experienced
conspecifics, and these movements can guide them for at least part of the
distance to a food source (Esch et al.,
1965; Esch, 1967;
Kerr, 1969). Stingless bees do
not exhibit waggle dances, however, meaning that recruits would more strongly
rely on signals and cues that are different from those used by honeybees.
Nevertheless, several species of highly social insects exhibit local
enhancement and orient toward the visual presence of foraging conspecifics
(Slaa et al., 2003), which
suggests, in turn, that outdoor interactions with conspecifics may constitute
a robust strategy in the context of collective foraging. Furthermore, dance
followers fly out and return to the dance floor several times before reaching
their goals, and the duration of these interruptions increases together with
the number of followed waggle phases (R.J.DeM., unpublished observations).
Consequently, it is reasonable to ask to what degree a follower experiences a
given hive-to-goal trajectory before finding its foraging target. It might do
this in between its dance following performance, by using semiochemicals and
visual cues derived from the flights of conspecifics, and then use the spatial
information gathered through dances as well as that derived from its recent,
`truncated' flight excursions in order to pinpoint the goal. The wonder might
arise on the number and frequency of the pre-displacement excursions of the
bees whose post-displacements flights were later traced by radar techniques
(Riley et al., 2005).
Unfortunately, neither their dance-following behaviour nor their
pre-displacement excursions have been reported. Clearly, if one ignores the
possibility that bees are able to use this form of `outdoor' information from
conspecifics in conjunction with information gathered through dances, then the
hypothesis described above does not apply to the experiments reported by Riley
(Riley et al., 2005) and
colleagues. However, direct evidence stresses the synchronicity of the flights
of bees foraging on the same goal, as well as the role of semiochemicals and
visual cues in the context of recruitment
(Tautz and Sandeman,
2002).
Open questions
Studying the variability of the waggle dance may prove fruitful for
improving our understanding of the honeybee dance communication system. We
suggest that such a system has at least two functional levels that are
hierarchically organized. Thus, an active follower may first fly towards a
recently experienced goal, especially if goal-related cues are coupled to
current dances for the same or a different goal. This primary level would thus
rely on the interplay between a follower's past experience and the presence of
`arousing' cues associated with such dances, which eventually trigger the
recollection of specific route memories allowing the follower to resume its
flights to previously visited locations. Semiochemicals emitted by dancing
bees (Thom et al., 2007) and
olfactory cues associated with the nectar brought into the colony
(von Frisch, 1967;
Ribbands, 1954) are examples
of such arousing cues; the role of `taste' still remains elusive in this
context. Next, depending on both the availability of resources at these past
locations and the strength and duration of the current dances for a different
goal, a follower might also gather further stimulation from these dances, and
focus its subsequent searches within the area of a currently advertised goal.
This second level would involve gathering repetitive stimulation from waggle
phases, as well as several flight excursions and returns to the dance floor
before reaching the goal. On the basis of these two levels, the efficiency of
the honeybee dance communication system would largely depend upon the spatial
knowledge shared by dancers and followers. Future work should examine to what
extend the dance system depends upon a follower's ability to acquire, store
and recall navigational memories; it would be interesting, for example, to
manipulate a follower's experience with single or multiple goals, and to
evaluate its subsequent responses to dances for a different one. Combining
high-speed video recordings and harmonic radar techniques in such a context
would prove useful not only to distinguish dance variability from actual
noise, but also to reveal the functional structure of the honeybee dance
communication system.
|
Acknowledgments |
|---|
|
Footnotes |
|---|
Present address: Universidad de Buenos Aires, Facultad de Ciencias Exactas
y Naturales, Departamento de Ecología, Genética y
Evolución, Laboratorio de Eco-Epidemiología, Ciudad
Universitaria, C1428EHA, Buenos Aires, Argentina 
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Batschelet, E. (1981). Circular Statistics in Biology. New York: Academic Press.
Beekman, M., Doyen, L. and Oldroyd, B. P. (2005). Increase in dance precision with decreasing foraging distance in the honeybee Apis mellifera L. is partly explained by physical constraints. J. Comp. Physiol. A 191,1107 -1113.[CrossRef][Medline]
Biesmeijer, J. C. and Seeley, T. D. (2005). The use of waggle dance information by honey bees throughout their foraging careers. Behav. Ecol. Sociobiol. 59,133 -142.[CrossRef]
Bozic, J. and Valentincic, T. (1991). Attendants and followers of honeybee waggle dances. J. Apic. Res. 30,125 -131.
De Marco, R. J. and Menzel, R. (2005). Encoding
spatial information in the waggle dance. J. Exp. Biol.
208,3885
-3894.
De Marco, R. J. and Menzel, R. (2008). Learning and memory in communication and navigation in insects. In Learning and Memory: A Comprehensive Reference (ed. R. Menzel and J. Byrne), pp. 477-498. New York: Elsevier.
De Marco, R. J., Gil, M. and Farina, W. M. (2005). Does an increase in reward affect the precision of the encoding of directional information in the honeybee waggle dance? J. Comp. Physiol. A 191,413 -419.[CrossRef][Medline]
Dyer, F. C. (2002). The biology of the dance language. Annu. Rev. Entomol. 47,917 -949.[CrossRef][Medline]
Esch, H. (1967). The sounds produced by swarming honey bees. Z. Vergl. Physiol. 56,408 -411.[CrossRef]
Esch, H. (1978). On the accuracy of the distance message in the dance of honey bees. J. Comp. Physiol. A 123,339 -347.[CrossRef]
Esch, H. and Bastian, J. A. (1970). How do newly recruited honey bees approach a food site? Z. Vergl. Physiol. 68,175 -181.[CrossRef]
Esch, H. E. and Burns, J. E. (1996). Distance estimation by foraging honeybees. J. Exp. Biol. 199,155 -162.[Abstract]
Esch, H., Esch, I. and Kerr, W. E. (1965).
Sound: an element common to communication of stingless bees and to dances of
the honey bee. Science
149,320
-321.
Esch, H. E., Zhang, S., Srinivasan, M. V. and Tautz, J. (2001). Honeybee dances communicate distances measured by optic flow. Nature 411,581 -583.[CrossRef][Medline]
Free, J. B. (1987). Pheromones of Social Bees. London: Chapman & Hall.
Free, J. B. and Williams, I. H. (1972). The role of the Nasonov gland pheromone in crop communication by honeybees (Apis mellifera L.). Behaviour 41,314 -318.[CrossRef]
Haldane, J. B. S. and Spurway, H. (1954). A statistical analysis of communication in `Apis mellifera' and comparison with communication in other animals. Insectes Soc. 1,247 -283.[CrossRef]
Judd, T. M. (1995). The waggle dance of the honey bee: which bees following a dancer successfully acquire the information? J. Insect Behav. 8,342 -355.
Kerr, W. E. (1969). Some aspects of the evolution of social bees (Apidae). Evol. Biol. 3, 119-175.
Kirchner, W. H. and Towne, W. F. (1994). The sensory basis of the honeybee's dance language. Sci. Am. 270,52 -59.[Medline]
Kirschvink, J. L., Walker, M. M. and Diebel, C. E. (2001). Magnetite-based magnetoreception. Curr. Opin. Neurobiol. 11,462 -467.[CrossRef][Medline]
Lindauer, M. (1961). Foraging and homing flight of the honeybee (Apis mellifera): some general problems of orientation. R. Entomol. Soc. Lond. 7, 199-216.
Lindauer, M. (1963). Allgemeine Sinnesphysiologie. Orientierungim Raum. Fortschr. Zool. 16,58 -140.[Medline]
Lindauer, M. and Martin, H. (1968). Die Schwereorientierung der Bienen unter dem Einfluß des Erdmagnetfeldes. Z. Vergl. Physiol. 60,219 -243.[CrossRef]
Mautz, D. (1971). Der Kommunikationseffekt der Schwänzeltänze bei Apis mellifera carnica (Pollm.). Z. Vergl. Physiol. 72,197 -220.[CrossRef]
Menzel, R., Greggers, U., Smith, A., Berger, S., Brandt, R.,
Brunke, S., Bundrock, G., Hülse, S., Plümpe, T., Schaupp, F. et
al. (2005). Honeybees navigate according to a map-like
spatial memory. Proc. Natl. Acad. Sci. USA
102,3040
-3045.
Menzel, R., De Marco, R. J. and Greggers, U. (2006). Spatial memory, navigation and dance behaviour in Apis mellifera. J. Comp. Physiol. A 192,889 -903.[CrossRef][Medline]
Michelsen, A. (1999). The dance language of honeybees: recent findings and problems. In The Design of Animal Communication (ed. M. D. Hauser and M. Konishi), pp.111 -131. Cambridge, MA, London, UK: MIT Press.
Michelsen, A. (2003). Signals and flexibility in the dance communication of honeybees. J. Comp. Physiol. 189,165 -174.
Michelsen, A., Towne, W. F., Kirchner, W. H. and Kryger, P. (1987). The acoustic near field of a dancing honeybee. J. Comp. Physiol. 161,633 -643.[CrossRef]
Nieh, J. C. (2004). Recruitment communication in stingless bees (Hymenoptera, Apidae, Meliponinae). Apidologie 35,159 -182.[CrossRef]
Núñez, J. A. (1971). Beobachtungen an sozialbezogenen Verhaltensweisen von Sammelbienen. Z. Tierpsychol. 28,1 -18.
Pflumm, W. (1969). Beziehungen zwischen Putzverhalten und Sammelbereitschaft bei der Honigbiene. Z. Vergl. Physiol. 64,1 -36.[CrossRef]
Ribbands, C. R. (1954). Communication between honey bees. I. The response of crop-attached bees to the scent of their crop. Proc. R. Entomol. Soc. Lond. A 29,141 -144.
Riley, J. R., Greggers, U., Smith, A. D., Reynolds, D. R. and Menzel, R. (2005). The flight paths of honeybees recruited by the waggle dance. Nature 435,205 -207.[CrossRef][Medline]
Rohrseitz, K. and Tautz, J. (1999). Honey bee dance communication: waggle run direction coded in antennal contacts? J. Comp. Physiol. A 184,463 -470.[CrossRef]
Rossel, S. and Wehner, R. (1982). The bee's map
of the e-vector pattern in the sky. Proc. Natl. Acad. Sci.
USA 79,4451
-4455.
Seeley, T. D. (1986). Social foraging by honeybees: how colonies allocate foragers among patches of flowers. Behav. Ecol. Sociobiol. 19,343 -354.[CrossRef]
Seeley, T. D. (1995). The Wisdom of the Hive-the Social Physiology of Honey Bee Colonies. London: Harvard University Press.
Seeley, T. D., Mikheyev, A. S. and Pagano, G. J. (2000). Dancing bees tune both duration and rate of waggle-run production in relation to nectar-source profitability. J. Comp. Physiol. A 186,813 -819.[CrossRef][Medline]
Sherman, G. and Visscher, P. K. (2002). Honeybee colonies achieve fitness through dancing. Nature 419,920 -922.[CrossRef][Medline]
Slaa, E. J., Wassenberg, J. and Biesmeijer, J. C. (2003). The use of field-based social information in eusocial foragers: local enhancement among nestmates and heterospecifics in stingless bees. Ecol. Entomol. 28,369 -379.[CrossRef]
Sokal, R. S. and Rohlf, F. J. (1969). Biometry. San Francisco: W. H. Freeman.
Srinivasan, M. V., Zhang, S. W., Lehrer, M. and Collett, T. S. (1996). Honeybee navigation en route to the goal: visual flight control and odometry. J. Exp. Biol. 199,237 -244.[Abstract]
Tanner, D. A. and Visscher, K. (2006). Do honey bees tune error in their dances in nectar-foraging and house-hunting? Behav. Ecol. Sociobiol. 59,571 -576.[CrossRef]
Tautz, J. (1996). Honey bee waggle dance: recruitment success depends on the dance floor. J. Exp. Biol. 199,1375 -1381.[Abstract]
Tautz, J. and Sandeman, D. C. (2002). Recruitment of honeybees to non-scented food sources. J. Comp. Physiol. A 189,293 -300.
Tautz, J., Zhang, S., Spaethe, J., Brockmann, A., Aung, S. and Srinivasan, M. V. (2004). Honeybee odometry: performance in varying natural terrain. PloS 2, doi:10.1371/Journal.pbio.0020211.
Thom, C., Gilley, D. C., Hooper, J. and Esch, H. E. (2007). The scent of the waggle dance. PLoS Biol. 5,e228 .[CrossRef][Medline]
Towne, W. F. and Gould, J. L. (1988). The spatial precision of the honey bees' dance communication. J. Insect Behav. 1,129 -154.[CrossRef]
Tsujiuchi, S., Sivan-Loukianova, E., Eberl, D. F., Kitagawa, Y. and Kadowaki, T. (2007). Dynamic range compression in the honey bee auditory system toward waggle dance sounds. PLoS ONE 2,e234 .[CrossRef]
von Frisch, K. (1946). Die Tänze der Bienen. Österr. Zool. Z. 1, 1-48.
von Frisch, K. (1967). The Dance Language and Orientation of Bees. Cambridge, MA: Harvard University Press.
von Frisch, K. (1968). The role of dances in recruiting bees to familiar sites. Anim. Behav. 16,531 -533.[Medline]
von Frisch, K. and Jander, R. (1957). Über den Schwanzeltanz der Bienen. Z. Vergl. Physiol. 4, 1-21.
von Frisch, K. and Lindauer, M. (1961). Über die `Mißweisung' bei den richtungsweisenden Tänzen der Bienen. Naturwissenschaften 4, 585-594.
Weidenmüller, A. and Seeley, T. D. (1999). Imprecision in waggle dances of the honeybee (Apis mellifera) for nearby food sources: error or adaptation? Behav. Ecol. Sociobiol. 46,190 -199.[CrossRef]
Zar, J. H. (1984). Biostatistical Analysis (3rd edn). New Jersey: Prentice-Hall.
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
