|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online October 17, 2008
Journal of Experimental Biology 211, 3392-3400 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.017624
The response of the honeybee dance to uncertain rewards
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 1 September 2008
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: Apis mellifera, reward uncertainty, recruitment dances, risk-sensitive behaviour, reward learning
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
). Like
many other animals, honeybees have evolved strategies to face such
variability. Their famous dance communication system
(von Frisch, 1967) is an
example of that kind of strategies. A honeybee's dance consists of a series of
seemingly ritualized movements that foragers perform on the comb surface and
use to recruit conspecifics from the nest – or the swarm – to the
location of desirable resources. Compelling evidence indicates that it is part
and parcel of a series of communication systems enabling a colony to
coordinate the activity of its members during foraging and nest-site selection
(e.g. Seeley, 1995). 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 (e.g. Michelsen,
2003), and process them in such a way that their subsequent
behaviours can greatly depend upon the content of these signals.
The key stimulus for dancing is the presence of a sugar reward at a given
feeding place. Apparently, a dance is triggered when the amount and sugar
concentration of sugar reward exceeds a threshold that has previously been
established by a dancer's central nervous system according to several
properties of the feeding place (e.g.
Seeley, 1986;
De Marco and Farina, 2001), the
dancer's past experience with such a reward
(Raveret-Richter and Waddington,
1993; De Marco et al.,
2005) and various stimuli available within the colony (e.g.
Núñez, 1970;
Seeley, 1986;
Seeley, 1989;
De Marco, 2006). Thus, the
probability and the strength of the dance are presumably graded according to
both the dancer's estimate of the overall quality of the feeding place and the
current needs of the colony. Yet, what has remained elusive in the study of
the honeybee dance is whether and how a dancer responds to variations in the
level of uncertainty of reward, as one would reasonably expect from any
behaviour that has seemingly evolved to convey information about reward
opportunities. This is of considerable interest, given the fact that the dance
has long been quoted as an intriguing example of a complex behaviour serving
the transfer of such type of information (e.g.
von Frisch, 1967;
Seeley, 1995;
Dyer, 2002;
De Marco and Menzel, 2008). Is
the honeybee dance sensitive to uncertainty of reward, irrespective of the
costs and benefits of a dancer's foraging activities? Information has long
been described as an abstract quantity that removes or reduces our current
level of uncertainty. Clearly, uncertainty appears as the opposite of
information, and depends upon the relative proportion of at least two mutually
exclusive inputs (Shannon,
1948). In the present context, reward uncertainty translates into
the relative proportion of rewarding and non-rewarding flower inspections.
We present the results of two experimental series addressing the relationship between a honeybee's experience with uncertain rewards and its subsequent dance behaviour within the colony. We varied the distribution of a fixed amount of unscented sucrose solution among the several flowers of a patch, thereby manipulating the arithmetic mean and variance of the volume of sugar reward per flower, and recorded the foraging and dance behaviour of single honeybees. We found evidence supporting the view that a honeybee's dance involves a component that computes not only the energy balance during foraging, but also an estimate of the distribution of food resources among the several flowers recently visited by the dancer. As a consequence, the dance system appears as `risk averse'. We propose that `risk-averse' dances help to optimize a colony's energy balance during foraging by diminishing delayed rewards and the effects of competition with other flower visitors for limited resources.
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
100 m
away from the hive, either outdoors (covered by UV-transmitting Plexiglas) or
indoors, in the first and the second series, respectively. Each artificial
flower (hereafter referred to as a flower) consisted of a 75 mm wide, 20 mm
high plastic cylinder with the upper surface covered by a yellow paper disc
(diameter: 75 mm; HKS® 3N; K+E Druckfarben, Germany). We recorded foraging
and within-the-hive behaviours of single bees by means of digital video
cameras, webcams, and voice recorders. The experiments were conducted during
the late summer and the beginning of autumn, when natural resources are
scarce. The first experimental series (hereafter, S1) focused on the
relationship between the distribution of a fixed amount of unscented sucrose
solution among the 16 flowers of the arena and the foraging and subsequent
within-the-hive behaviours of the single foragers. The second series
(hereafter, S2) was an extension of S1, in that it focused on the same
question by means of a similar protocol, although we changed the presentation
of the different groups and incorporated additional variables into the
analysis.
The first experimental series (S1)
Marked bees were first trained to forage on a close feeder offering
unscented 50% (w/w) sucrose solution. Next, the feeder was gradually moved
away from the hive towards the vicinity of the arena. After all the marked
bees resumed at least five consecutive visits to the arena, a single bee was
randomly selected from the group. (The remaining foragers were captured, kept
inside small cages, fed with 20% w/w sucrose solution, and released at the end
of the experiment.) The selected bee was then allowed to resume six additional
visits to the arena. Throughout these visits it was presented with the
treatments described below (Table
1), in a semi-random fashion. This enabled us to establish
steady-state foraging conditions at the beginning of each session. The floor
of the arena provided the bees with a homogeneous grey background. The sixteen
flowers were regularly distributed inside the arena, placed at equal distances
of 20 cm (centre to centre), and their relative positions were randomly
interchanged in-between the single visits of the experimental bee. Each
rewarding flower offered unscented 20% w/w sucrose solution by means of a
small plastic receptacle (4 mm high) at the centre of the upper surface of the
plastic cylinder.
|
We defined our treatments (Table 1) according to the distribution of a fixed amount of sugar reward among the 16 flowers of the patch. In the first treatment (hereafter, T`4x8'), each of four flowers offered 8 µl of sucrose solution, while 12 flowers remained empty. In the second treatment (hereafter, T`8x4'), each of eight flowers offered 4µl of sucrose solution, while eight flowers remained empty. Finally, in the third treatment (hereafter, T`16x2'), each of the 16 flowers of the patch offered 2 µl of sucrose solution. Thus, the total amount of sugar reward was 32µl in all the treatments, and we varied the arithmetic mean and variance of the amount of sugar reward per flower, with reward distributions that included zero rewards in T`4x8' and T`8x4'. Each bee performed a total of 36 successive visits to the arena. Each treatment was assayed three times in `blocks' of four successive visits – a total of 12 visits (three blocks) per treatment per session. Blocks from different treatments were assayed in a semi-random fashion. We tested six bees under these conditions.
The second experimental series (S2)
In S2, we placed the arena indoors, and used 50% w/w sucrose solution as
sugar reward. An open window allowed the single bees to access the arena,
which had a homogeneous white floor as the background. This helped us to video
(using 25 frames per second) the bees' foraging behaviour by means of a video
camera placed above the arena. In addition, we did not use `blocks' of
successive, comparable visits in S2. All the treatments were assayed in a
semi-random fashion throughout the totality of the successive visits of the
bees, meaning that each bee could experience any of the treatments in a given
visit, with the exception of that experienced in the previous one. Each animal
undertook ten foraging visits per session. We tested ten bees under these
conditions.
Measurements
The following measurements were made. (1) The temperature, both inside and
outside the arena. (2) The time inside the arena (henceforth, visit time, in
seconds), defined as the time interval between when the bee entered the arena
and when it left the arena and flew towards the hive. (3) The cumulative
flight time and the cumulative non-flight time inside the arena (in seconds).
(We made these measurements only in S2.) (4) The cumulative volume of sugar
solution collected by the bee at the end of the visit time (henceforth, crop
load, in micolitres). This measure allowed us to compute an `average solution
intake rate' (henceforth, flow rate), as the ratio between the crop load and
the visit time. (5) The number of inspections to flowers offering sugar reward
(henceforth, number of rewarding inspections), defined as the number of times
a bee landed on a flower that offered sugar reward, searched for and drank the
offered sucrose solution. (6) The number of inspections to flowers that did
not offer sugar reward (henceforth, number of non-rewarding inspections),
defined as the number of times a bee landed on and searched for sucrose
solution inside an empty flower. (This last measure also includes those
inspections to the flowers that had initially offered sugar solution, but were
already empty at the time of landing.) (7) The total number of inspections to
the flowers, defined as the number of times a bee landed on any of the 16
flowers of the patch, irrespective of whether or not such flower offered sugar
solution. (8) The time outside the hive (in seconds), defined as the time
interval between departure from the hive and arrival at the hive after
visiting the arena. (9) The time that the bee stayed inside the hive
in-between its successive flights toward the arena (henceforth, hive time, in
seconds). (10) The probability of dancing (henceforth, dance probability),
computed as the proportion of foraging cycles in which a marked bee performed
either round circuits or waggle-phases
(von Frisch, 1967) or both,
calculated from the totality of the foraging cycles that the animal made under
a similar treatment. Each marked bee was considered as an experimental unit in
the analysis, and individual probabilities were averaged for the sake of
comparisons across treatments. (Upon entering the hive, bees transfer the
content of their crops to food-receivers by means of a common behaviour in
social insects called trophallaxis, i.e. the transfer of liquid food by mouth.
We separately analysed the dances occurring before and after the animals' food
unloading. In doing this, we took into account that bees may transfer the
content of their crops through more than one trophallaxis; each time a marked
bee performed more than one trophallaxis, we used the longest of such events
in order to discriminate between dances occurring before and after the food
unloading.) (11) The number of round circuits or waggle-phases recorded
throughout the hive time, which allowed us to compute an estimate of the
`dance strength'.
Statistics
Comparisons were made by means of one-way ANOVAs, LSD tests, Lilliefors and
Shapiro–Wilk tests, and Pearson correlations
(Zar, 1984).
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
|
We found significant differences among the three groups in the number of rewarding (Fig. 1C; F(2,15)=558.40, P<0.001; one-way ANOVA, after log transformation) and non-rewarding (Fig. 1D; F(2,15)=5.20, P=0.02; one-way ANOVA) flower inspections. As expected, the number of rewarding inspections was higher in T`16x2' than in T`4x8' (Fig. 1C; P<0.001; LSD test), and the number of non-rewarding inspections was higher in T`4x8' than in T`16x2' (Fig. 1D; P<0.01; LSD test). However, we did not find significant differences among the three groups in the total number of flower inspections (F(2,15)=1.54, P=0.23; one-way ANOVA). Next, we calculated a `relative inspection index' (henceforth, RI), defined as (axb–1)xc, where a and b are the number of rewarding and non-rewarding inspections to the flowers, respectively, and c is the total number of inspected flowers. This index reflects the proportions of an animal's encounters with rewarding and non-rewarding flowers during the visit time, and clearly changed across groups (Fig. 1E; F(2,15)=742.20, P<0.001, one-way ANOVA, after log transformation).
We also found group differences in the probability of dancing before the foragers' food unloading, i.e. immediately after they entered the hive (Fig. 1F; F(2,15)=4.96, P=0.02; one-way ANOVA): it was higher in T`16x2' than in T`8x4' and T`4x8' (Fig. 1F; P<0.05; LSD tests). Similarly, there were group differences in the probability of dancing after the food unloading (Fig. 1G; F(2,15)=2.45, P=0.12; one-way ANOVA): it was higher in T`16x2' than in T`4x8' (Fig. 1G; P=0.04; LSD test). By contrast, we did not find statistical differences among the three groups in the dance strength, either before (F(2,15)=0.25, P=0.78; one-way ANOVA) or after (F(2,15)=0.98, P=0.40; one-way ANOVA) the food unloading.
It is well-known that the regulation of a honeybee's dance threshold
partially depends upon a colony's nectar intake rate, and that returned
foragers sense such rate by computing how quickly
(Seeley, 1989) and eagerly
(De Marco, 2006) the
food-receivers unload their crops. Our treatments were assayed in blocks of
four successive visits to the arena, also presented in a semi-random fashion.
This means that any possible group difference regarding the bees' thresholds
for dancing could not be accounted for by changes in the colony's nectar
intake rate, simply because such rate cannot vary systematically within a
four-visit time window as to promote detectable differences in the likelihood
of the foragers' dances, particularly during the autumn, when natural sources
are scarce, and, therefore, variations of a colony's nectar intake rate are
typically small. In spite of this, we measured the speed and eagerness of the
foragers' food unloading by computing all the variables reported by De Marco
(De Marco, 2006). As expected,
we did not find group differences among these variables (data not shown).
Thus, in spite of having collected the same amount of sugar solution, the bees showed lower thresholds for dancing when all the sixteen flowers of the patch offered a small amount of sugar reward in T`16x2' (Fig. 1B,F,G). In principle, this might be accounted for by the slightly diminished visit time found in T`16x2' (Fig. 1A), which might have modified the bees' the energy gain during foraging. That is, a shorter visit time might have changed the bees' estimate of the net rate of energy intake, [(G–C)/t], or that of the net energy efficiency, [(G–C)/C], where G, C and t are the energy gain, energy cost and the time required to make a round trip to the arena, respectively. Yet, the bees' thresholds for dancing might also have changed because of the observed variations in the number of rewarding and/or non-rewarding inspections to the flowers (Fig. 1C–E), which might have modified the animals' estimate of the level of uncertainty associated with the offered reward.
We examined the correlations between the probability of dancing, both before and after the food unloading, and each of the following four measurements: The visit time, the number of rewarding and non-rewarding inspections of the flowers and the relative inspection index. We found no correlation between the visit time and both dance probabilities (before the food unloading: Pearson's r=–0.17, P=0.50, N=18; after the food unloading: Pearson's r=0.11, P=0.68, N=18). By contrast, we found a positive correlation between the number of rewarding flower inspections and the dance probability before (Pearson's r=0.54, P=0.02, N=18), but not after the food unloading (Pearson's r=0.42, P=0.09, N=18). We also found a negative correlation between the number of non-rewarding flower inspections and the probability of dancing, both before (Pearson's r=–0.75, P<0.001, N=18) and after the food unloading (Pearson's r=–0.72, P<0.001, N=18). Similarly, there was a negative correlation between the inspection index and both dance probabilities (before the food unloading: Pearson's r=–0.75, P<0.001, N=18; after the food unloading: Pearson's r=–0.72, P<0.001, N=18).
We also examined whether any possible correlation between the probability of dancing and the visit time, as well as between the probability of dancing and the number of non-rewarding flower inspections, changed within a series of four successive, comparable visits to the arena. (We focused on the number of non-rewarding flower inspections because this measure correlated well with the probability of dancing both before and after the food unloading.) After pooling data from all groups and four-visit series, we found that both the visit time (Pearson's r=–0.50, P=0.04, N=18) and the number of non-rewarding inspections to the flowers (Pearson's r=–0.67, P=0.003, N=18) correlated with the probability of dancing in the first visit of an average four-visit series. However, only the number of non-rewarding inspections, but not the visit time, correlated with the probability of dancing in the remaining three visits of such sequence (number of non-rewarding inspections vs dance probability, visit 2: r=–0.57, P=0.01, visit 3: r=–0.72, P<0.001, visit 4: r=–0.74, P<0.001, N=18; Pearson correlations; visit time vs dance probability, visit 2: r=0.11, P=0.66, visit 3: r=–0.21, P=0.40, visit 4: r=–0.37, P=0.19, N=18; Pearson correlations).
The second experimental series (S2)
In the present context, the visit time and the time outside the hive
provide only a rough estimate of a bee's foraging costs. As a result, it is
necessary to quantify a bee's cumulative flight time inside the arena –
a measure that co-varies with the number of flower inspections – in
order to estimate more accurately the net rate of energy intake, as well as
the net energy efficiency during foraging. This is why we conducted a new
series of experiments in which we measured the cumulative flight time inside
the arena. In this new series, in addition, we presented the animals with the
different treatments in a semi-random fashion throughout the totality of their
successive visits to the arena.
In S2, we did not find group differences in the visit time (F(2,27)=1.49, P=0.24; one-way ANOVA), which gave means (±s.e.m.) of 225.51 (±18.14), 227.93 (±25.52) and 271.86 (±19.79) s for T`16x2', T`8x4' and T`4x8', respectively. Likewise, we did not find significant differences among the different groups in the cumulative flight time (Fig. 2A; F(2,27)=2.22, P=0.13; one-way ANOVA) and the cumulative non-flight time (F(2,27)=0.51, P=0.61; one-way ANOVA). For the latter the means (±s.e.m.) were 152.6 (±9.2), 144.8 (±8.6) and 157.6 (±9.1) s for T`16x2', T`8x4' and T`4x8', respectively. Similarly, we did not find group differences in either the crop load attained by the foraging bees (Fig. 2B; F(2,27)=0.87, P=0.43; one-way ANOVA) or the flow rate that they experienced during the visit time (F(2,27)=1.34, P=0.28; one-way ANOVA). For the flow rates the means (±s.e.m.) were 0.12 (±0.01), 0.14 (±0.01) and 0.12 (±0.01) µls–1 for T`16x2', T`8x4' and T`4x8', respectively. Moreover, we did not find significant differences among the different groups in the time outside the hive (F(2,27)=1.64, P=0.21; one-way ANOVA) and in the hive time (F(2,27)=0.29, P=0.75; one-way ANOVA). The time outside the hive gave means (±s.e.m.) of 300.8 (±20.5), 325.9 (±32.2) and 367.5 (±24.9) s for T`16x2', T`8x4' and T`4x8', respectively, whereas the hive time gave means (±s.e.m.) of 155.6 (±23.9), 188.1 (±40.4) and 183.5 (±32.4) s for T`16x2', T`8x4' and T`4x8', respectively. The temperature, both outside and inside the arena, did not vary across the different groups (outside, F(2,27)=0.002, P=0.998; inside, F(2,27)=0.01, P=0.997; one way ANOVAs).
|
Multiple comparisons among all three groups gave no statistical differences for the probability of dancing. It did not change either before (Fig. 2F; F(2,27)=0.57, P=0.57; one-way ANOVA) or after (Fig. 2G; F(2,27)=2.29, P=0.12; one-way ANOVA) the foragers' food unloading. However, the probability of dancing after the food unloading was higher in T`16x2' than in T`4x8' (Fig. 2G; P=0.04; LSD test). Thus, the bees of S2 also showed lower thresholds for dancing when all the sixteen flowers of the patch offered a small amount of sugar reward in T`16x2' (Fig. 2B,G). This happened when the several variables (see above) defining the speed and eagerness of the foragers' food unloading did not change across groups (data not shown). As in S1, we did not find group differences in the dance strength either before (insufficient data prevents statistical analyses) or after (F(2,27)=0.30, P=0.74; one-way ANOVA) the food unloading.
Detecting the influence of the energy gain on a honeybee's threshold for dancing
The bees of S1 and S2 attained similar crop loads and experienced similar
flow rates. In S1, they showed lower dance thresholds in T`16x2', and
such thresholds were positively and negatively correlated with the number of
rewarding and non-rewarding flower inspections, respectively. The bees of S2
also showed lower thresholds for dancing in T`16x2', and such thresholds
were negatively correlated to the number of non-rewarding inspections. In S2,
in addition, neither the visit time nor the cumulative flight time varied
across groups (see above), suggesting that the observed variations in the
bees' dance thresholds may be accounted for, at least partially, by variations
in the animals' estimates of the level of reward uncertainty, as derived from
the computation of their rewarding and non-rewarding flower inspections.
However, both the visit time (Pearson's r=0.85, P<0.0001,
N=30) and the cumulative flight time (Pearson's r=0.88,
P<0.0001, N=30) co-vary with the number of non-rewarding
flower inspections. This is interesting because we know that these time-based
measures co-vary with a honeybee's estimate of its energy balance during
foraging [as derived from the net rate of energy intake or the net energy
efficiency, (G–C)/t or
(G–C)/C, respectively], and that such balance
influences, in turn, the animal's threshold for dancing: the higher the energy
gain the lower the threshold for dancing
(Seeley, 1986). Detection of
the latter relationship in the present context may prove fruitful to check
upon the robustness of the correlations reported above. To this end, we
followed an approach already described by Seeley
(Seeley, 1986), thereby
bringing together our own database and the work of other authors.
To estimate the energy gain G per trip first requires
quantification of the animals' crop loads, the mean values of which were found
to be 27.4, 27.9 and 29.6 µl in T`16x2', T`8x4' and
T`4x8', respectively (Fig.
2B). This value, together with the standard value for the
energetic equivalence of sucrose, 5.8 J µlmol
(Kleiber, 1961), gave us an
estimate of G, the gross energy gain per trip, using the equation:
 | (1) |
We directly measured the time outside the hive during the experiments (t), i.e. the time required to fly toward the arena, collect the offered solution and fly back to the hive. Since we also measured the time that the bees spent inside the arena, we also calculated the difference between the time outside the hive and the visit time, and divided this difference by 2, in order to approximate the average duration of the outbound and the inbound components of the foraging excursion, and to assign each of these two flight components with different costs based on the mass of the load: 13.7, 14.0 and 14.8 mg in T`16x2', T`8x4' and T`4x8', respectively.
To estimate the energy expended per trip, C, we used 484 W
Kg–1 for the metabolic rate of flying bees
(Heinrich, 1980;
Withers, 1981;
Louw and Hadley, 1986), and 80
W Kg–1 for the metabolic rate of walking or feeding bees
(Cahill and Lustick, 1976;
Withers, 1981;
Louw and Hadley, 1986;
Seeley, 1986). For the mass of
the bees during their outbound flight, we used an average mass of 80 mg
(Núñez, 1970).
For the mass of a bee flying back to the hive, we used the initial mass of 80
mg plus the mass of the load obtained for each treatment, i.e. 93.7, 94.0 and
94.8 mg in T`16x2', T`8x4', and T`4x8', respectively. Next,
we used the average between these two masses, 86.9, 87.0 and 87.4 in
T`16x2', T`8x4' and T`4x8', respectively, to estimate the
mass of a bee foraging inside the arena. We then calculated the cost per trip,
as the sum of the energy expended during the three phases of the foraging
trip, i.e. the outbound flight, the time inside the arena (including the
cumulative flight time) and the inbound flight:
 | (2) |
Both (G–C)/t (Pearson's r=0.43, P=0.02, N=29) and (G–C)/C (Pearson's r=0.47, P=0.01, N=29) positively correlated with the probability of dancing after the foragers' food unloading, and their corresponding coefficients of determination (rs) were 0.18 and 0.22, respectively. Thus, the influence of the energy gain during foraging on a honeybee's threshold for dancing can also be detected in the context of our experiments, where both the total amount of sugar reward and the foraging time remained stable. This suggests that any possible correlation between the probability of dancing and the number of flower inspections, being either rewarding or non-rewarding, will be at least as reliable as the correlation between the energy gain and the probability of dancing. We then focused on the relationship between the probability of dancing and the number of rewarding and non-rewarding inspections to the flowers. We found no correlation between the probability of dancing and the number of the rewarding flower inspections (Pearson's r=0.28, P=0.18, N=29). By contrast, we found a negative correlation between the probability of dancing and the number of non-rewarding flower inspections (Pearson's r=–0.61, P<0.001, N=29), whose coefficient of determination (rs) was 0.37.
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
). In our context, this translates into the relative
proportion of rewarding and non-rewarding flower inspections. Intriguingly, we
found group differences in the bees' thresholds for dancing when the total
amount of sugar reward, the cumulative flight time, and the total time
invested during foraging remained stable (see Results), meaning that the bees
tuned their dancing according to the distribution of sugar reward among the
several flowers of the patch. Additionally, the correlation between the number of non-rewarding flower inspections and the probability of dancing, as compared to the correlation between the bees' energy balance during foraging and the probability of dancing, appeared to be more salient in the first experimental series. It was in fact in the first series that the bees were repeatedly exposed to each of the different treatments throughout blocks of four successive visits to the arena. We found a correlation between the number of non-rewarding flower inspections and the probability of dancing in all four visits of such blocks in such a situation, but it was only in the first of those four successive visits that we found a correlation between the bees' energy balance during foraging and the probability of dancing (see Results). This is interesting because it is the level of reward uncertainty that, under comparable circumstances, presumably diminishes with increasing experience. If one assumes that a honeybee's dance actually conveys information, then it is a bee's prediction of such a level of uncertainty that is expected to be manifested through variations of the animal's threshold for dancing.
The question of whether the honeybee dance is sensitive to uncertainty of
reward is important because such sensitivity is a pre-requisite for the dance
to be communicative. In addressing such question, however, a very important
obstacle arises from the fact that sugar reward has modulatory effects on both
the probability and the strength of a dance
(von Frisch, 1967). Moreover,
a dancer's behaviour is also influenced by past experience with an offered
reward (Raveret-Richter and Waddington,
1993; De Marco et al.,
2005). This is why it is virtually impossible to isolate
completely any possible effect of uncertainty of reward on a dancer's
behaviour. In searching for such an effect, therefore, one needs to set
experimental circumstances in which the dance system, the outcome of which
depends upon various, mostly unknown parameters, appears to be highly
regulated, thereby exhibiting only slight oscillations in the probability and
the strength of a dance. For obvious reasons, minimizing the modulatory
effects of sugar reward on a dancer's performance also means maximizing the
effects of the energy expenditure during foraging on a honeybee's dance
behaviour: the higher the energy expenditure the lower the probability of
dancing. This happens because a honeybee's dance is finely tuned to the energy
gain during foraging (e.g. Seeley,
1986). In such context, in fact, one would also need to focus on
dances occurring before and after a dancer's food unloading, simply because
the process of food unloading itself conveys to dancers stimuli that partially
modify the probability and the strength of the dance (e.g.
Núñez, 1970;
Seeley, 1986;
Seeley, 1989;
De Marco, 2006). (Such stimuli
can only increase the variability associated with the dancer's performance,
thereby overshadowing any possible influence of uncertainty of reward on the
honeybee dance.) It becomes clear that asking whether the dance is sensitive
to uncertainty of reward is more of an entropy problem, rather than a problem
of energy gradients. In order to answer such a question, one needs to rely on
experimental conditions leading to virtually insignificant variations in a
dancer's performance. Eventually, one would benefit from simple patterns of
simultaneous variations to examine whether or not the energy balance during
foraging co-varies with a suitable, robust estimate of reward uncertainty. The
above comments are relevant to understanding the limitations and specificities
of our experiments. In particular because, due to our specific experimental
conditions and the ensuing complexity of our analysis, our interpretations
arise from a relatively small sample size and are based on assumptions and
statistical differences that reveal tendencies, rather than unambiguous
evidence for acceptance or rejection of null hypotheses. However, our focus is
on the well-known relationship between energy gain and dance performance, on
the one hand, and a, hitherto, `presumed' relationship between reward
uncertainty and dance performance, on the other. The question here is whether
these relationships show similar or dissimilar patterns of variation. The
former arises from inherent, scale-invariant properties of the dance system
(already supported by empirical evidence), meaning that the relationship
between energy gain and dance probability transcend unambiguously variations
across species. The later presumably arises from analogous properties based on
the system's information processing capacities. (Eventually, the question of
what is the actual equivalence between energy gain and uncertainty of reward
will still remain elusive.)
There has long been controversy regarding the fundamental measure
underlying a honeybee's estimate of the quality of a patch, particularly with
respect to the adaptive significance of energy efficiency at the individual
level (Schmid-Hempel et al.,
1985; Schmid-Hempel,
1993), as opposed to energy intake rate and information flow rate
at the individual and group level, respectively
(Varjú and Núñez,
1991; Varjú and
Núñez, 1993). We found that both the net energy
efficiency and the net rate of energy intake accounted for 20% of the
variance of a forager's dance threshold when the total amount of sugar reward
and the time invested during foraging remained stable. Under such
circumstances, we also found that the number, or the frequency, of the
foragers' non-rewarding flower inspections accounted for 40% of such
variance, suggesting that the honeybee dance system computes not only the
energy balance that a dancer has recently achieved during foraging, but also
an estimate of the level of uncertainty of reward derived from the
distribution of food resources across the several flowers that the animal
inspected prior to dancing. The latter computation, which unambiguously
relates to the level of reward uncertainty, might well be the subject of
adjustments depending on the overall flow rate of reward that the dancer
experiences during foraging.
In line with these findings, recent studies of choice behaviour in
harnessed honeybees (Shafir et al.,
1999; Drezner-Levy and Shafir,
2007) support the view that subjects on a positive energy budget
invariably prefer less variable reward magnitudes if the variable reward
distribution includes zero rewards, as it does in our experiments. The same
pattern has been reported by analyses of human studies
(Weber et al., 2004), where
the subjects strongly avoided reward variability if the variable distribution
included zero rewards and had a large coefficient of variation. Response to
reward variability has frequently been referred to as risk-sensitive behaviour
(Caraco, 1980;
Stephens, 1981;
Pyke, 1984;
Real, 1992;
McNamara and Houston, 1992;
Kacelnik and Bateson, 1996;
Kacelnik and Abreu, 1998).
Experimental studies of risk-sensitive behaviour typically focus on how
foraging choices depend upon reward variability (e.g.
Real and Caraco, 1986;
Stephens and Krebs, 1986). For
example, while foraging on two types of artificial flowers offering different
amounts of nectar, bumblebees rapidly switched their preference for a flower
type when reward contingencies were switched between the flowers
(Real, 1981). Bees also showed
a strong preference for landing on constant rewarding flowers, as opposed to
variably rewarding flowers offering the same mean reward
(Real, 1981;
Waddington, 1981). This type
of response, also found in other animals
(Kacelnik and Bateson, 1996),
is frequently referred to as risk-averse behaviour, in contrast to risk-prone
or risk-indifferent behaviour, and has traditionally been accounted for by
hypothesizing a nonlinear subjective `utility function' for reward
(von Neumann and Morganstern,
1944; Real, 1992;
Smallwood, 1996).
Analyses of other bee studies have shown no preferences for either nectar
constancy or variability (Banschbach and
Waddington, 1994; Waddington,
1995; Fülöp and
Menzel, 2000). For example, in studies with several bee species,
variance of nectar concentration had no influence on the animals' choice
behaviour (Banschbach and Waddington,
1994; Waddington,
1995; Perez and Waddington,
1996), although bumblebees showed preferences for constancy when
the variance of concentration was large and the arithmetic mean of reward was
low (Waddington, 2001). The
discrepancies among these and other studies (e.g.
Shapiro, 2000;
Shapiro et al., 2001), as it
has previously been stated by Perez and Waddington
(Perez and Waddington, 1996),
are most probably based on the identities of the targeted species, differences
in the size of the colonies and social conditions of the subjects, the
foraging arenas employed in the experiments, the manipulation of reward during
the experiments, and the presence or absence of non-rewarding flowers.
We support the view that testing risk-sensitive behaviours demands the
consideration of alternative hypotheses and predictions from additional
mechanisms (Cartar and Smallwood,
1996). One should also ask whether such sensitivity would be
relevant for an organism's survival and fitness. Intriguingly, a honeybee's
dance has long been described as a behavioural response evolved to convey
information on desirable resources (e.g.
Dyer, 2002;
De Marco and Menzel, 2008). If
it conveys information on desirable nectar, for example, then it should be
sensitive to the level of uncertainty of sugar reward, which depends, of
course, upon how variable such a reward actually is. It follows, therefore,
that a honeybee's dance for nectar should appear as `risk averse'. Our results
indeed suggest that honeybees foraging on several flowers are able to compute
an estimate of the variance of the volume of sugar reward per flower if the
variable volume distribution includes zero values, and subsequently adjust
their dance thresholds according to the ensuing level of uncertainty of
reward.
This is interesting because the foraging strategy of a honeybee colony
strongly relies on collective foraging, which is unambiguously enhanced by
dances (Seeley, 1995). In
addition, foraging is a form of reinforcement learning
(Sutton and Barto, 1998), i.e.
learning how to map situations to actions, so as to maximize a reward signal.
Thus, a forager's overall response to uncertain rewards might result from two
parallel maximization processes
(Varjú and Núñez,
1993). The first one, working at the individual level, would tend
to maximize a honeybee's energy gain during foraging
(Greggers and Menzel, 1993),
whereas the second, working at the social level, would tend to maximize a
colony's energy gain by mapping the probability of recruitment dances to the
distribution of food resources among the several flowers inspected by the
dancers. We hypothesize that the ultimate result of having `risk-averse'
dances is a colony's ability to diminish delayed rewards and the effects of
competition with other flower visitors for limited resources.
We suggest that theoretical accounts of `risk-sensitive' dances would prove
fruitful in further analyses of the honeybee dance system, particularly if one
were to examine how the overlap region of recruitment and risk-sensitive
behaviour eventually translates into fitness. Further experiments will be
aimed at elucidating the responses of dancing bees to variance of sugar
concentration, as well as the relationship between a forager's dance
performance and the coefficient of reward variance in relation to both volume
and concentration. This will allow further evaluations of the influence of
non-rewarding flower inspections on a honeybee's perception of reward
uncertainty. Experiments manipulating the contingency between different floral
signals and nectar concentrations might also provide an evaluation of the
influence of visual and olfactory signals on the foragers' perception of
reward uncertainty. It would also be interesting to compare the responses of
dancing bees of different lines to uncertain rewards. It has been documented
that the threshold for recruiting conspecifics is lower in African than in
European bees (Núñez,
1979). It follows that any possible relationship between the
probability of dancing and the level of reward uncertainty might well appear
to be shifted in African bees, as compared to that of European bees, in that
the same level of reward uncertainty may lead to a larger increase in the
animals' threshold for dancing. Eventually, our approach would also prove
fruitful in further analyses of the mechanisms underlying the regulation of a
honeybee's threshold for dancing. For example, octopamine (OA) release in the
honeybee brain is sucrose-responsive, and capable of modulating downstream
behaviours (Hammer, 1997). It
has recently been shown that a honeybee's dance threshold can be decreased
– thereby increasing dance likelihood – by applying controlled
doses of OA on the dancer's thorax prior to dancing
(Barron et al., 2007). It would
be interesting to re-examine the correlation between the probability of
dancing and the number of non-rewarding flower inspections in OA-treated bees.
This would help to further evaluate to what extent such correlation depends
upon an increased overall sensitivity to sugar reward, or, instead, a more
integrative variation of a honeybee's perception of uncertainty of reward.
|
Acknowledgments |
|---|
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Baker, H. G. and Baker, I. (1983). A brief historical review of the chemistry of floral nectar. In The Biology of Nectaries (ed. B. Bentley and T. Elias), pp.126 -152. New York: Columbia University Press.
Banschbach, V. S. and Waddington, K. D. (1994). Risk-sensitive foraging in honey bees: no consensus among individuals and no effect of colony honey stores. Anim. Behav. 47,933 -941.[CrossRef]
Barron, A. B., Maleszka, R., Vander Meer, R. K. and Robinson, G.
E. (2007). Octopamine modulates honey bee dance behavior.
Proc. Natl. Acad. Sci. USA
104,1703
-1707.
Cahill, K. and Lustick, S. (1976). Oxygen consumption and thermoregulation in Apis mellifera workers and drones. Comp. Biochem. Physiol. 55,355 -357.[Medline]
Caraco, T. (1980). On foraging time allocation in a stochastic environment. Ecology 61,119 -128.[CrossRef]
Cartar, R. V. and Smallwood, P. D. (1996). Risk sensitivity in behavior: where do we go from here? Am. Zool. 36,530 -531.
De Marco, R. J. (2006). How bees tune their
dancing according to their colony's nectar influx: re-examining the role of
the food-receivers' `eagerness'. J. Exp. Biol.
209,421
-432.
De Marco, R. J. and Farina, W. M. (2001). Changes in food source profitability affect the trophallactic and dance behavior of forager honeybees. Behav. Ecol. Sociobiol. 50,441 -449.[CrossRef]
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]
Drezner-Levy, T. and Shafir, S. (2007).
Parameters of variable reward distributions that affect risk sensitivity of
honey bees. J. Exp. Biol.
210,269
-277.
Dyer, F. (2002). The biology of the dance language. Annu. Rev. Entomol. 47,917 -949.[CrossRef][Medline]
Fülöp, A. and Menzel, R. (2000). Risk-indifferent foraging behaviour in honeybees. Anim. Behav. 60,657 -666.[CrossRef][Medline]
Greggers, U. and Menzel, R. (1993). Memory dynamics and foraging strategies of honeybees. Behav. Ecol. Sociobiol. 32,17 -29.
Hammer, M. (1997). The neural basis of associative reward learning in honeybees. Trends. Neurosci. 20,245 -252.[CrossRef][Medline]
Heinrich, B. (1980). Mechanisms of
body-temperature regulation in honeybees, Apis mellifera. II.
Regulation of thoracic temperature at high air temperatures. J.
Exp. Biol. 85,73
-87.
Kacelnik, A. and Abreu, F. B. E. (1998). Risky choice and Weber's law. J. Theor. Biol. 194,289 -298.[CrossRef][Medline]
Kacelnik, A. and Bateson, M. (1996). Risky theories: the effects of variance on foraging decisions. Am. Zool. 36,402 -434.
Kleiber, M. (1961). The Fire Of Life: An Introduction to Animal Energetics. New York: Wiley.
Louw, G. N. and Hadley, N. F. (1986). Water economy of the honeybee: a stoichiometric accounting. J. Exp. Zool. 235,147 -150.[CrossRef]
McNamara, J. M. and Houston, A. I. (1992). Risk-sensitive foraging: a review of the theory. Bull. Math. Biol. 54,355 -378.
Michelsen, A. (2003). Signals and flexibility in the dance communication of honeybees. J. Comp. Physiol. A 189,165 -174.[Medline]
Núñez, J. A. (1970). The relationship between sugar flow and foraging and recruiting behaviour of honey bees (Apis mellifera L.). Anim. Behav. 18,527 -538.[CrossRef]
Núñez, J. A. (1979). Time spent on various components of foraging activity: comparison between European and Africanized honeybees in Brazil. J. Apic. Res. 18,110 -115.
Perez, S. M. and Waddington, K. D. (1996). Carpenter bee (Xylocopa micans) risk indifference and a review of nectarivore risk-sensitivity studies. Am. Zool. 36,435 -446.
Pyke, G. H. (1984). Optimal foraging theory: a critical review. Annu. Rev. Ecol. Syst. 15,523 -575.[CrossRef]
Raveret-Richter, M. and Waddington, K. D. (1993). Past foraging experience influences honeybee dance behavior. Anim. Behav. 46,123 -128.[CrossRef]
Real, L. A. (1981). Uncertainty and plant pollinator interactions: the foraging behavior of bees and wasps on artificial flowers. Ecology 62,20 -26.[CrossRef]
Real, L. A. (1992). Information processing and the evolutionary ecology of cognitive architecture. Am. Nat. 140,108 -145.[CrossRef]
Real, L. A. and Caraco, T. (1986). Risk and foraging in stochastic environments. Annu. Rev. Ecol. Syst. 17,371 -390.[CrossRef]
Schmid-Hempel, P. (1993). On optimality, physiology and honeybees: a reply to Varjú and Núñez. J. Comp. Physiol A 172,251 -256.
Schmid-Hempel, P., Kacelnik, A. and Houston, A. I. (1985). Honeybees maximize efficiency by not filling their crop. Behav. Ecol. Sociobiol. 17, 61-66.[CrossRef]
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. (1989). Social foraging in honey bees: how nectar foragers assess their colony's nutritional status. Behav. Ecol. Sociobiol. 24,181 -199.[CrossRef]
Seeley, T. D. (1995). The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Cambridge, MA: Harvard University Press.
Shafir, S., Wiegmann, D. D., Smith, B. H. and Real, L. A. (1999). Risk-sensitive foraging: choice behaviour of honeybees in response to variability in volume of reward. Anim. Behav. 57,1055 -1061.[CrossRef][Medline]
Shannon, C. E. (1948). The mathematical theory of information. Bell Syst. Tech. J. 27, 379-423, 623-656.
Shapiro, M. S. (2000). Quantitative analysis of risk sensitivity in honeybees (Apis mellifera) with variability in concentration and amount of reward. J. Exp. Psychol. 26,196 -205.
Shapiro, M. S., Couvillon, P. A. and Bitterman, M. E. (2001). Quantitative tests of an associative theory of risk-sensitivity in honeybees. J. Exp. Biol. 204,565 -573.[Abstract]
Smallwood, P. D. (1996). An introduction to risk sensitivity: the use of Jensen's Inequality to clarify evolutionary arguments of adaptation and constraint. Am. Zool. 36,392 -401.
Stephens, D. W. (1981). The logic of risk-sensitive foraging preferences. Anim. Behav. 29,628 -629.[CrossRef]
Stephens, D. W. and Krebs, J. R. (1986). Foraging Theory. Princeton: Princeton University Press.
Sutton, R. S. and Barto, A. G. (1998). Reinforcement Learning: An Introduction. Cambridge, MA: MIT Press.
Varjú, D. and Núñez, J. A. (1991). What do foraging honeybees optimize? J. Comp. Physiol. A 169,729 -736.
Varjú, D. and Núñez, J. A. (1993). Energy balance versus information exchange in foraging Honeybees. J. Comp. Physiol. A 172,257 -261.
von Frisch, K. (1967). The Dance Language and Orientation of Bees. Cambridge, MA: Harvard University Press.
von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Waddington, K. D. (1981). Factors influencing pollen flow in bumblebee-pollinated Delphinium virescens. Oikos 37,153 -159.[CrossRef]
Waddington, K. D. (1995). Bumblebees do not respond to variance in nectar concentration. Ethology 101, 33-38.
Waddington, K. D. (2001). Subjective evaluation and choice behavior by nectar- and pollen-collecting bees. In Cognitive Ecology of Pollination: Animal Behavior and Floral Evolution (ed. L. Chittka and J. D. Thompson), pp.41 -60. Cambridge: Cambridge University Press.
Weber, E. U., Shafir, S. and Blais, A. R. (2004). Predicting risk sensitivity in humans and lower animals: risk as variance or coefficient of variation. Psychol. Rev. 111,430 -445.[CrossRef][Medline]
Withers, P. (1981). The effects of ambient air pressure on oxygen consumption of resting and hovering honeybees. J. Comp. Physiol. 141,433 -437.
Zar, J. H. (1984). Biostatistical Analysis. NJ: Prentice-Hall International.
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
