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Anim Cogn (2008) 11:683–689
DOI 10.1007/s10071-008-0159-y
123
ORIGINAL PAPER
Evidence for counting in insects
Marie Dacke · Mandyam V. Srinivasan
Received: 22 November 2007 / Revised: 29 April 2008 / Accepted: 13 May 2008 / Published online: 27 May 2008
© Springer-Verlag 2008
Abstract Here we investigate the counting ability in hon-
eybees by training them to receive a food reward after they
have passed a speciWc number of landmarks. The distance
to the food reward is varied frequently and randomly,
whilst keeping the number of intervening landmarks con-
stant. Thus, the bees cannot identify the food reward in
terms of its distance from the hive. We Wnd that bees can
count up to four objects, when they are encountered
sequentially during Xight. Furthermore, bees trained in this
way are able count novel objects, which they have never
previously encountered, thus demonstrating that they are
capable of object-independent counting. A further experi-
ment reveals that the counting ability that the bees display
in our experiments is primarily sequential in nature. It
appears that bees can navigate to food sources by maintain-
ing a running count of prominent landmarks that are passed
en route, provided this number does not exceed four.
Keywords Counting · Honeybee · Cognition
Introduction
One of the popular measures of the cognitive capacity of
animals is the ability to count objects (Hauser 2000). Stud-
ies of numerical cognition have over the last decades
extended from a focus on humans and non-human primates
to include other mammals (Gallistel 1990; West and Young
2002; Killian et al. 2003), as well as birds (Pepperberg
2006; Roberts et al. 2002; Rugani et al. 2007), Wsh (Agrillo
et al. 2007) and salamanders (Uller et al. 2003). Little is
known about the numerical abilities of invertebrates. To
date, only two studies suggest a counting ability in insects
(Chittka and Geiger 1995; Karban et al. 2000), but a recent
study questions the generality of these claims (Franks et al.
2006).
The process of counting, or estimation of numerosity,
can be carried out in a number of diVerent ways: ‘Subitiz-
ing’ refers to the ability to rapidly recognize the cardinality
of a small set of objects at a single glance, without register-
ing them sequentially. Subitizing appears to be possible
with small numbers of objects, typically four or fewer
(Wiese 2003, Gallistel and Gelman 2000), although the
exact nature of the underlying process is unclear and
controversial (Gallistel 1990). Sequential counting is the
ability to count objects or events that are encountered one
after another. This requires the ability to maintain a running
tally of the number of events, incrementing the tally by one
each time an event occurs (Dehaene 1999). A related pro-
cess is that of summation, or integration, which involves
accumulating, over time or space, some attribute of the
objects that are to be counted. For example, if the task is to
count the number of blue discs that are visible simulta-
neously on a display screen, this would mean estimating the
total area of blue that is present in the screen; or if the discs
are presented sequentially, it would involve accumulating
M. Dacke · M. V. Srinivasan
ARC Centre for Excellence in Vision Science,
Research School of Biological Sciences,
Australian National University,
P. O. Box 475, Canberra, ACT 2601, Australia
Present Address:
M. Dacke (&)
Department of Cell and Organism Biology,
Lund University, Lund, Sweden
e-mail: marie.dacke@cob.lu.se
Present Address:
M. V. Srinivasan
Queensland Brain Institute, University of Queensland,
Brisbane, Australia
684 Anim Cogn (2008) 11:683–689
123
the total area of blue that is observed through the succes-
sion of presentations (Davis and Pérusse 1988; Franks et al.
2006). According to Gallistel and Gelman (2000), summa-
tion (or accumulation) could, under certain circumstances,
constitute a form of counting, and perform a function that is
equivalent to the counting of integers. However, if an ani-
mal that uses this technique is trained to count to a certain
number by using objects of a Wxed size, it could potentially
overcount when it is subsequently tested with smaller
objects, and undercount when tested with larger objects.
True counting involves assigning successive numbers to
objects, irrespective of item size (Davis and Pérusse 1988).
Apart from humans, this ability has been demonstrated, or
been claimed to exist, in a relatively small number of ani-
mal species that includes chimpanzees, dolphins, raccoons,
chicks, rats and parrots (Davis and Pérusse 1988; Dehaene
1999; Pepperberg 2006; Rugani et al. 2007). The existence
of a counting ability has also been suggested in bees (Chit-
tka and Geiger 1995) and cicadas (Karban et al. 2000).
Chittka and Geiger (1995) explored whether honeybees
could learn to Xy along a row of yellow tents in a Weld to
Wnd a food reward placed half way between the third and
the fourth tent on the route. When the bees were subse-
quently tested for their ability to locate the feeder, a propor-
tion of the bees did indeed land on a control feeder after
they had Xown over the three tents, whether or not the land-
marks were closer together or further apart than during
training. Thus, while these Wndings provide evidence in
favour of a counting ability in honeybees, they do not prove
it. This is because the study, using the same size and shape
of the landmarks throughout, did not demonstrate a capac-
ity of the bee to learn and use numbers in an object-inde-
pendent way. In addition, the overwhelming majority of the
bees landed on a control feeder that was located approxi-
mately at the same distance from the nest as during train-
ing. This is probably because the training paradigm, which
used a constant separation between landmarks—and hence
a constant distance to the food reward—was such that it
encouraged the bees to attend primarily to the distance they
had Xown, rather than to the number of landmarks they had
passed.
Here we re-examine the ability of bees to count by using
an experimental design that encourages them to Wnd a food
source by counting landmarks, rather than by relying on
their odometer.
Methods
Experimental set-up
Bees (Apis mellifera L.) were trained to forage from a tun-
nel placed outdoors under a homogenous veranda roof. The
tunnel was 4 m long, 20 cm wide and 20 cm high, and was
placed with its entrance 7 m from the hive. The walls and
Xoor of the tunnel were lined with light grey paper, and the
tunnel was covered with clear Perspex sheets. The tunnel
carried a series of prominent landmarks, described below.
For each experiment, up to 30 individually marked bees
were trained to enter the tunnel and receive a food reward at
one of the landmarks. The food was provided by Wve incon-
spicuous small cylindrical containers, each 1 cm dia and
0.5 cm tall, placed in the base of the rewarded landmark.
The reward-bearing landmark was thus identical in appear-
ance to the other landmarks, which carried no reward.
Procedure
In the Wrst series of experiments, each landmark consisted if
a yellow strip of paper, 3.5 cm wide and 60 cm long, deco-
rating the walls and Xoor of the tunnel as shown in Fig. 1a.
Depending upon the particular experiment, the reward was
placed at the Wrst, second, third, fourth or Wfth landmark. A
separate group of bees was trained for each experiment.
The landmarks were always spaced at regular intervals.
During training, the separation between the landmarks—
and consequently the position of the rewarded landmark in
the tunnel—was varied every 5 min. This was done to elim-
inate any tendency of the bees to otherwise learn to identify
the correct landmark in terms of its distance from the tunnel
entrance, rather than in terms of its numerical position in
the landmark sequence. During training, the position of the
landmarks varied randomly over a set of eight diVerent sep-
arations, carefully chosen to ensure that the average posi-
tion of the rewarded landmark did not coincide with the
expected position of search in the subsequent test situation
(see below). Each of the eight separations was an integer
multiple of the smallest separation. This ensured that the
position of the rewarded landmark was uniformly distrib-
uted over a large range of distances during the training. The
position of the rewarded landmark from the tunnel entrance
varied between 120 and 320 cm, to ensure that the bees
were trained within the same section of the tunnel in all of
the experiments. The bees were trained for a minimum of 3
and a maximum of 5 days. The training was considered to
be complete when no improvement in the bees’ perfor-
mance could be recorded during the tests.
After training, the bees were tested individually in a tun-
nel that carried no reward. Prior to each test, the last posi-
tion of the rewarded landmark was recorded to cheque for
any possible inXuence of this position on the performance
in the test.
In the Wrst experimental series, the tests carried the same
landmarks as in the training (Fig. 1a). The separation
between landmarks was 70 cm for all tests, except for two
tests in which the bees were initially trained to landmark 3,
Anim Cogn (2008) 11:683–689 685
123
and then tested with the landmarks spaced regularly at
40 cm (Fig. 3a) or irregularly (Fig. 3b).
In a second experiment, the bees were trained as before
on stripe landmarks, with the reward oVered at landmark 3.
The trained bees were then tested on a novel set of land-
marks, each consisting of three yellow discs, 7 cm in diam-
eter, one placed on the Xoor and one on each wall (Fig. 1b).
In the tests, the landmarks were separated by 70 cm.
In a third experiment, the landmarks were designed to
ensure that the bees saw only one landmark at a time as
they Xew through the tunnel (Fig. 1c). Here each landmark
consisted of a baZe, with slightly overlapping left and right
partitions, separated by 4 cm. Each partition was 20 cm tall
and 10.5 cm wide. When viewed from the front, the left
partition was yellow and the right partition was grey; when
viewed from behind, both partitions were grey. The overlap
between the partitions ensured that a bee could not see
beyond one landmark, at any location in the tunnel.
Analysis of counting performance
The test data were analysed by subdividing the tunnel into
40 units, each 10 cm long. In their search for food, the bees
typically Xew back and forth along the tunnel, making a
number of U-turns as they searched for the reward. This
searching behaviour was quantiWed by recording visually
the positions in the tunnel in which the bee made the Wrst
six turns. By measuring the number of times the bee
entered each unit during these six turns, we could estimate
the spatial distribution of each search. To ascertain the
maximum number of landmarks that could be counted, we
used a ‘Counting Performance Index’ (CPI) deWned as the
ratio of the frequency of search in the three units surround-
ing the position of the correct landmark, to the mean of the
equivalent frequencies of search at the other landmarks.
The larger this ratio, the better is the discrimination of the
correct landmark from the others. A CPI of 1 represents
uniform searching at all landmarks, i.e. a breakdown of the
counting process.
Results
We began by asking whether bees can learn to ‘count’ the
number of landmarks that they encounter on the way to a
food source. Individually marked bees were trained to
receive a reward of sugar solution after they had Xown past
a speciWc number of regularly spaced yellow stripes during
their Xight through a narrow tunnel. Depending upon the
experiment, this number was 1, 2, 3, 4 or 5. After training,
the bees were individually tested by removing the food
reward, and observing their searching behaviour in the tun-
nel to determine which landmark they had associated most
strongly with the reward during the training.
We see from Fig. 2a that bees trained to landmark 1
show a strong preference to search in the vicinity of land-
mark 1. Bees trained to landmark 2 similarly prefer to
search near landmark 2 (Fig. 2b); and so on (Fig. 2c–e).
Even when trained on landmark 5, bees spend the greatest
time searching in the vicinity of this landmark, although
clearly discernible peaks now appear at all landmarks. One
interpretation of this data is that the bees were learning to
count the number of landmarks passed en route to the
feeder, and using this learned number to guide their search
in the tests.
A hallmark of the ability to truly ‘count’ landmarks is
the capacity to count accurately, irrespective of how these
landmarks are arranged spatially. To investigate this, we
conducted two further tests in which bees were trained to
receive a reward at landmark 3. The trained bees were then
tested with a conWguration in which the landmarks were
separated by 40 cm rather than 70 cm (Fig. 3a), and with
another conWguration in which the landmarks were spaced
irregularly (Fig. 3b). The bees always showed a clear pref-
erence for searching in the vicinity of the third landmark,
regardless of the position of this particular landmark in the
tunnel, and irrespective of the layout of the other land-
marks. A similar ability has been demonstrated recently in
young chicks (Rugani et al. 2007).
The experiments so far do not indicate whether the bees
were truly ‘counting’ the landmarks, or whether they were
simply performing a cumulative integration of the areas of
the landmarks as they went by. For example, could the bees
have been summing the area of yellow that they had Xown
past, stopping when the appropriate area had been accumu-
lated? To test for this possibility, we again trained bees to
Fig. 1 Illustration of the experimental tunnels with landmarks consist-
ing of stripes (a), circles (b) and baZes (c) spaced at regular intervals
a
b
c
686 Anim Cogn (2008) 11:683–689
123
Wnd a reward on a given stripe, exactly as in the Wrst series
of experiments. In the test conWguration each stripe was
replaced by a yellow disc, with an area of only 55% of the
area of the stripe in the training situation. The results are
shown in Fig. 4. The bees showed a clear preference for
searching at the correct landmark in four out of the Wve
experiments. Thus, bees trained on landmark 1 searched
preferentially at landmark 1 in the test even though the
landmark was now of a diVerent size and shape (Fig. 4a).
The same was true when the bees were tested after training
on landmark 2, 3 or 4 (Fig. 4b–d). Thus, the bees were not
locating the goal by summing target areas: they were truly
‘counting’, in the sense that they were assigning a number
to each individual landmark, regardless of its shape or size.
This conclusion of course relies on the assumption that
the bees were able to distinguish between the two shapes.
We conWrmed the validity of this assumption by examining
whether bees could be trained to distinguish between the
disc and the stripe in a Y-maze (for set-up and method, see
Srinivasan and Lehrer 1988). After training by reward on
the disc, bees displayed a choice frequency of 72% for the
disc. After training by reward on the stripe, bees displayed
Fig. 2 Pinpointing the correct landmark in a series of landmarks.
Search distributions of bees that are tested after being trained to receive
a reward at landmark 1 (a), landmark 2 (b), landmark 3 (c), landmar
k
4 (d) and landmark 5 (e). Bees trained to landmark 1 show a strong
preference to search in the vicinity of landmark 1 (a). Bees trained to
landmark 2 similarly prefer to search near landmark 2 (b); and so on
(c–e). The arrows mark the position of the rewarded landmark in the
training, just prior to each test. f Variation of CPI with the number o
f
the rewarded landmark. The CPI is greater than 1 when the bees are re-
warded at landmark 1, 2, 3 or 4 and is equal to 1 at landmark 5. This
indicates that bees can count up to four landmarks, but no more
Frequency of search
0
0.04
0.08
0.12
0.16
Frequency of search
Frequency of search
0.04
0.08
0.12
0.16
0
0.1
0.2
0.3
0
0.02
0.04
0.06
0.08
Position in tunnel (cm)
L1L1 L2L2 L3L3 L4L4
L5L5
Frequency of search
Frequency of search
0
0
0.02
0.04
0.06
0.08
n=23
n=18
n=19
n=19
n=14
0
1
2
3
4
40
12345
Stripe #
CPI
f
50 100 150 200 250 300 350 400
a
b
c
d
e
Fig. 3 Pinpointing the correct landmark irrespective of spatial
arrangement along the tunnel. Searching distributions of bees trained
to landmark 3 as in Fig. 1c, and then tested on their ability to count
landmarks that are spaced regularly at 40 cm (a), or irregularly (b). In
each case, the bees show a clear preference for searching in the vicinity
of the third landmark (*). The CPI is 3.1 in a and 3.4 in b
0
0.02
0.04
0.06
0.08
0
0.04
0.08
0.12
50 100 150 200 250 300 350 400
50 100 150 200 250 300 350 400
Position in tunnel (cm)
L1 L2 L3
L4 L5
Frequency of search
Frequency of search
*
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10
*
n=17
Position in tunnel (cm)
n=23
b
a
Anim Cogn (2008) 11:683–689 687
123
a choice frequency of 70% for the stripe. A binominal test
(Zar 1999) revealed a signiWcant diVerence from the ran-
dom choice level of 50%, (P < 0.001, n = 100) for both
results, indicating that the bees must have generalized their
capacity from counting stripes to counting discs.
Can bees continue to count items if they are forced to
encounter them in a truly sequential fashion? To examine
this question, bees were trained in a tunnel in which each
landmark now consisted of a baZe, with slightly overlap-
ping left and right partitions. The overlap between the parti-
tions ensured that a bee could not see beyond one landmark
at any time. Thus, in order to identify the correct landmark,
the bee would have to count the landmarks in a sequential
fashion. In this experiment, bees were trained to Wnd a food
reward at the base of landmark 3. Again, the landmarks
were regularly spaced, but their separation was varied ran-
domly during training. The trained bees were then tested
with the same set of landmarks, spaced regularly at 70 cm.
The results of this test (Fig. 5) show a clear preference for
landmark 3, revealing that bees are indeed capable of
counting landmarks when they are presented sequentially.
Discussion
Our Wndings provide evidence that bees are capable of
counting objects that are encountered on the way to a food
source. In all probability, this counting is performed
sequentially, and requires the ability to maintain a running
tally of the number of events, incrementing the tally by one
each time an event occurs. The number of landmarks that
can be counted in this way appears to be four. When trained
to landmark 4 the CPI is still greater than 2, indicating that
the bees still spend more than twice the time searching in
the vicinity of that landmark, compared with the other
Fig. 4 Pinpointing landmarks of novel shape. Searching distribution
of bees trained to count stripes, and then tested on their ability to count
landmarks of a diVerent size and shape (circles). Bees trained on land-
mark 1 (stripe) search preferentially at landmark 1 (L1) (circle) in the
test (a). Bees also pinpoint the correct landmark when tested after
training on landmark 2 (L2), 3 (L3) and 4 (L4) (b–d). After training on
landmark 5 (L5), the bees no longer search preferentially at this land-
mark in the test (e), but rather show a strong preference to search in the
vicinity of landmarks 2 and 3. f Variation of CPI with the number o
f
the rewarded landmark. The CPI is greater than 1 when the bees are re-
warded at landmark 1, 2, 3 or 4, and is less than 1 at landmark 5. This
indicates that bees can count up to four landmarks, but no more
0
0.02
0.04
0.06
0.08
0.1
Frequency of search
Frequency of search
Frequency of search
0
0.02
0.04
0.06
0.08
L1L1 L2L2 L3L3 L4L4
L5L5
Frequency of search
Frequency of search
0
0.02
0.04
0.06
0.08
n=18
n=19
n=18
n=21
n=12
0
0.04
0.08
0.12
0.16
0
1
2
3
4
12345
Circle #
F
CPI
0
0.02
0.04
0.06
0.08
50 100 150 200 250 300 350 400
Position in tunnel (cm)
a
c
b
d
e
Fig. 5 Pinpointing the correct landmark in a series of sequentially pre-
sented landmarks. Searching distribution of bees trained in an experi-
ment in which they are forced to count landmarks sequentially. Bees
trained to feed from landmark 3 (L3), show a clear preference for
searching in the vicinity of the third landmark (*) in subsequent tests.
The CPI is 4.8
0
0.04
0.08
0.12
50 100 150 200 250 300 350 400
Frequency of search
n=10
Position in tunnel (cm)
L1 L2 L3
L4 L5
*
688 Anim Cogn (2008) 11:683–689
123
landmarks (Figs. 1f, 2f). When rewarded at landmark 5 the
CPI falls below 1, and the bees no longer show a clear pref-
erence to search in the vicinity of the correct landmark.
Could the bees’ ability to count be mediated by a visu-
ally driven ‘odometer’, of the kind proposed by Esch and
Burns (1996) and Srinivasan et al. (2000) for estimating
distances to food sources? It has been shown that, when
landmarks are close together and appear in rapid succes-
sion along the journey the odometer integrates the per-
ceived optic Xow (image motion) and measures the total
angular motion of the image of the environment over the
journey, irrespective of the number of landmarks passed
(Si et al. 2003). However, when the landmarks are few and
far between—as they are in some of the present experi-
ments—one could consider whether the odometer plays a
‘counting’ role. If the odometer is to keep track of the
number of sparse landmarks encountered during a journey,
it must operate in a diVerent mode in which the visual
pathway produces a signal (e.g. a pulse) of a constant mag-
nitude every time a landmark is passed, irrespective of the
size or shape of the landmark. These pulses must then be
accumulated at a subsequent stage of processing. While it
is conceivable that the odometer could operate in this way
under these conditions, it is unlikely because, in the initial
phases of the training in our experiments, the bees tend to
learn the (most recent) distance of the feeder from the
entrance, rather than the number of landmarks passed. This
suggests that the odometer operates in its normal, distance-
measuring mode even when the landmarks are sparse.
Indeed, our informal observations of the bees’ perfor-
mance during the course of the training suggest that bees
have to be trained to disregard information on the distance
actually traveled and to learn to attend to a diVerent signal,
namely, one that represents the number of landmarks
passed. In other words, it is necessary to ‘de-emphasize’
the importance of the odometric signal before the counting
ability can be revealed. This was the basis of our training
paradigm, in which the distance to the goal was varied fre-
quently and randomly, whilst keeping the number of inter-
vening landmarks constant. The training protocol was
further arranged such that, just prior to each test, the
rewarded landmark was always at a Wxed distance from the
tunnel entrance, as indicated by the arrow in each panel of
Fig. 1. In none of the tests is there a peak in the searching
distribution at the position of the arrow. Thus, the bees
could not have pinpointed the correct landmark in the tests
by memorizing the most recent distance that they had
Xown to reach the reward.
Could the bees’ ability to count be mediated by sum-
ming the amount of yellow they had Xown past? To address
this question, we conducted an experiment in which the
bees were trained to count stripes, and then tested in a tun-
nel in which each stripe was replaced by a yellow disc, with
an area of only 55% of the area of the stripe in the training
situation. During the training the inter-stripe distance was
varied frequently, as before. If the bees had simply been
summing target areas to locate the correct landmark, we
would expect bees trained to the second stripe to search at
the fourth disc in the tests, and bees trained to the third
stripe to search for the sixth disc in the tests—that is, they
should have searched at the end of the tunnel. Clearly, this
did not occur. Furthermore, this Wnding reveals that the
bees were treating the novel landmarks (discs) in the tests
in exactly the same way as the familiar landmarks (stripes)
in the training, thus demonstrating a capacity to learn and
use numbers in an abstract and object-independent way.
The data from this second set of experiments suggest that
bees are able to acquire a representation of a number, learnt
from counting landmarks of one kind, and then to apply it
to count a sequence of novel, unfamiliar objects. It is
unlikely that this ability is mediated by any simple process
of accumulation, because it functions even when the novel
landmarks are of a diVerent size and shape.
The third experiment in this study, where the overlap
between the partitions ensured that a bee could not see
beyond one landmark at any time, clearly shows that the
counting performance in bees is not limited to situations in
which the objects to be counted are viewed simultaneously.
Subitizing has been studied extensively in human infants,
and it would be of interest to enquire whether similar pro-
cesses also underlie counting performance in bees.
The ability to count landmarks sequentially on the way
to a food source, as we have shown here, should beneWt an
animal that visits a food source repeatedly. A running count
of the number of prominent and recognizable landmarks
encountered en route, e.g. trees, bushes or buildings, can be
used to monitor progress and to indicate when the navigator
is approaching the vicinity of its destination. This informa-
tion could be supplemented by odometry, which serves to
pinpoint the Wnal destination. Indeed, landmarks can inter-
act with odometric information to enhance the accuracy of
navigation (Chittka et al.
1995; Srinivasan et al. 1997;
Vladusich et al. 2005).
Acknowledgments We thank Hong Zhu for assistance. Financial
support was provided by the Royal Physiographic Society, the Swedish
Research council (623-2004-2903) and the ARC Centre of Excellence
in Vision Science (CE0561903).
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