EVOLUTIONARY COGNITION
Numerical ordering of zero in
honey bees
Scarlett R. Howard1
, Aurore Avarguès-Weber2
*, Jair E. Garcia1
*,
Andrew D. Greentree3
, Adrian G. Dyer1,4
†
Some vertebrates demonstrate complex numerosity concepts—including
addition, sequential ordering of numbers, or even the concept of zero—but whether
an insect can develop an understanding for such concepts remains unknown.
We trained individual honey bees to the numerical concepts of “greater than” or
“less than” using stimuli containing one to six elemental features. Bees could
subsequently extrapolate the concept of less than to order zero numerosity at the
lower end of the numerical continuum. Bees demonstrated an understanding that
parallels animals such as the African grey parrot, nonhuman primates, and even
preschool children.
F
our stages are used to describe the acquisition
of understanding zero in human history,
psychology, animal cognition, and
neurophysiology (1). The first is the ability
to define zero as nothing—the absence of a
stimulus. The second is the categorical classification
of zero as “nothing” versus “something.”
The third stage is understanding zero as a quantity
at the low end of the positive integer numerical
continuum. The fourth, and currently
designated as the most advanced stage of understanding
zero, is the symbolic representation of
zero, as with an Arabic number and as used in
modern mathematics and calculations (1).
Several ancient human civilizations lacked the
full understanding and importance of zero, leading
to constraints in their numeric systems (1).
Interestingly, some vertebrate animals have recently
demonstrated a capacity to acquire and
understand this numerical concept. Rhesus monkeys
learned that empty sets of objects occupy a
position on a numerical continuum (2, 3), vervet
monkeys used subtraction-like reasoning to determine
if food was present or absent (4), a
chimpanzee reached near-perfect performance
on zero-concept tasks with training (5), and an
African grey parrot spontaneously labeled absent
objects as “none” (6).
Honey bees have previously demonstrated the
capacity to count and discriminate up to four
objects (7–10) in experiments that use classic
conditioning techniques. Recent advancements
in conditioning protocols (11) reveal that bees can
acquire rule-based relational concepts (12, 13),
thus enabling remarkable plasticity to acquire
and apply seemingly advanced concepts such as
size ordering (14). In this study, we tested the
capacity of honey bees to extrapolate the acquired
concepts of “greater than” and “less than,” as
shown in primates (15, 16), and thus formally
demonstrate that an invertebrate can understand
the concept of zero numerosity.
We designed a set of experiments to test the
extent to which honey bees may understand the
concept of zero numerosity (17). In the first experiment,
we trained bees to understand the
concepts of less than and greater than using
appetitive-aversive differential conditioning (11).
Bees were trained to the respective concepts using
white square stimuli containing one to four black
elements (Fig. 1A, fig. S1, and table S1). After
reaching a criterion of ≥80% accuracy, bees demonstrated
in nonreinforced tests that they had
learned the concept of “numerically less” [75.0 ±
4.1% (mean ± SEM); logistic regression with
individual as random term tested differences between
observed proportion of bee choices and
chance level, y = 0.5, z score = 5.08, P < 0.001,
n = 10] and “numerically greater” (75.5 ± 3.3%;
z score = 6.556, P < 0.001, n = 10) when presented
with novel stimuli of one to four elements. Furthermore,
bees were able to apply these concepts
to determine that five elements were greater than
two or three elements (less-than group: 68.0 ±
5.0%, z score = 3.411, P < 0.001, n = 10; greaterthan
group: 75.0 ± 3.9%, z score = 5.333, P <
0.001, n = 10). Interestingly, bees demonstrated
an understanding that zero numerosity lies at
the lower end of the numerical continuum by
choosing an “empty set” stimulus containing
no elements if trained to less than (64.0 ± 5.4%;
z score = 2.795, P = 0.005, n = 10; Fig. 1C) or by
choosing unfamiliar stimuli containing elements
if trained to greater than (74.5 ± 2.6%; z score =
6.609, P < 0.001, n = 10; Fig. 1C).
In the second experiment, we tested the extent
to which bees may understand the quantitative
concept of zero in comparison with other animals.
As some animals find it challenging to
differentiate between the numbers zero and one
(5, 6, 18), we trained bees to less than using
stimuli containing two to five elements and then
tested their ability to differentiate between the
unfamiliar numerosities of one and zero (Fig. 1B).
After reaching a criterion of ≥80% accuracy,
bees demonstrated the learned concept of numerically
less when presented with the numbers
two to five (73.8 ± 1.9%; z score = 10.18, P < 0.001).
When presented with the unfamiliar numbers
of one versus zero, bees chose the lower number
of zero (63.0 ± 2.9%; z score = 4.23, P < 0.001;
Fig. 1D), showing an understanding that an
empty set is lower than one, which is challenging
for some other animals (5, 6, 18).
When bees were presented with two conflicting
pieces of information, two versus zero, where
the two-elementstimulihadalways beenrewarded
in training and zero was the correct lower number,
bees chose the empty set at a frequency level
that was not significant from chance (56.2 ±
3.4%; z score = 1.64, P = 0.101; Fig. 1D); thus, bees
perceived both plausible alternatives as consistent
with their conditioning experience. These
results demonstrate that bees were using both
an associative mechanism for choosing two
elements and a concept-based mechanism for
choosing zero numerosity. This phenomenon
was also observed in a dolphin trained to choose
the numerically less option by using white dots
on a black background. This result is explained
in terms of an artifact of training-set conditioning
causing a bias toward consistently rewarding
stimuli (19).
To test if bees understood an empty set quantitatively
along the numerical continuum, we
evaluated numerical-distance effects, where accuracy
of performance potentially improves
as the difference in magnitude between two
respective numbers increases (1). In the third experiment,
we trained and tested bees on the lessthan
concept using the numbers zero to six. If
bees considered zero numerosity as a number
along the numerical continuum, we would expect
accuracy of decisions to be the greatest with
zero versus six and poorer for lower numbers
versus zero numerosity (Fig. 2). After reaching a
criterion of ≥80% accuracy during training, bees
demonstrated in tests that they could discriminate
an empty set from numbers one to six accurately
(supplementary text S1 and Fig. 2B).
Although bees could accurately discriminate all
numbers from zero numerosity, there was a significant
effect of numerical distance on accuracy
(Fig. 2B). Bees were more accurate when numbers
were numerically more distant (zero versus
five and zero versus six) than when numerically
closer (zero versus one), showing that bees are
affected by number magnitude and thus exhibit
numerical-distance effects.
An alternative explanation for our results
could be that bees have a preference for the unfamiliar
presentation of an empty-set stimulus.
However, control experiments showed that the
bees’ understanding that zero belongs at the
lower end of the numerical continuum was rule
based and not driven by an unfamiliar preference
(supplementary text S2 and fig. S2). The spatial
RESEARCH
Howard et al., Science 360, 1124–1126 (2018) 8 June 2018 1 of 3
1
Bio-inspired Digital Sensing (BIDS) Lab, School of Media and
Communication, RMIT University, Melbourne, VIC, Australia.
2
Centre de Recherches sur la Cognition Animale, Centre de
Biologie Intégrative (CBI), Université de Toulouse, CNRS, UPS,
Toulouse, France. 3
ARC Centre of Excellence for Nanoscale
BioPhotonics, School of Science, RMIT University, Melbourne,
VIC, Australia. 4
Department of Physiology, Monash University,
Clayton, VIC, Australia.
*These authors contributed equally to this work.
†Corresponding author. Email: adrian.dyer@rmit.edu.au
onJune7,2018http://science.sciencemag.org/Downloadedfrom
frequencies of stimuli are also ruled out as a
potential explanation for results (supplementary
text S1 and table S1). We additionally conducted
further control experiments to exclude the possibility
that bees learn to match pairs of numbers
during training (supplementary text S3 and
fig. S2).
Our findings show that honey bees can learn
and apply the concepts of greater than and less
than to interpret a blank stimulus as representing
the conceptual number of zero and place zero
in relation to other numerical values. Bees thus
perform at a level consistent with that of nonhuman
primates by understanding that zero is
lower than one (5).
Howard et al., Science 360, 1124–1126 (2018) 8 June 2018 2 of 3
Fig. 1. Graphic representation of the method and results
of experiments 1 and 2. (A and B) Examples of possible
stimuli combinations during trials and tests in experiments
1 and 2. (C and D) Performance during the unreinforced
testing phases during experiments 1 and 2. Data shown are
means ± SEM for both treatment groups. Bees trained to less
than are shown in dark blue; bees trained to greater than
are shown in turquoise. Stimuli above the columns represent
the choices for those stimuli in the data. In experiment 1, in
the conflict test evaluating the bees’ concept of zero, data
shown for the less-than group (n = 10) are choices for zero,
and data shown for the greater-than group (n = 10) are
choices for stimuli containing elements. In the transfer test to
a higher number, data shown for bees trained to less than
are choices for a lower number, and data shown for bees
trained to greater than are choices for the higher number of
five. In experiment 2 (n = 25), the conflict and transfer tests
show the bees’ choices for zero. Dashed black line at 0.5
indicates chance-level performance. Significance from
chance-level performance is indicated by ** P ≥ 0.01 and
*** P ≥ 0.001. NS, not significant.
Fig. 2. Photographic representation of stimuli and results from experiment 3.
(A) Representation of honey bee spatial vision when viewing stimuli of either zero or
one (22). (B) Honey bee performance during experiment 3, testing the behavioral
effects of numerical distance of numerosity zero. Data shown are means ± SEM for the
choice of the zero stimuli. Dashed black line at 0.5 indicates chance-level
performance. Significance from chance-level performance and from other tests is
indicated by *P ≥ 0.05 and ***P ≥ 0.001. NS, not significant.
RESEARCH | REPORT
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An open question remains as to whether such
advanced numerical understandings may be widespread
across many animals that deal with complexity
in their environments or if our findings are
the result of independent evolution in honey bees.
Recent comparative studies of primate and crow
brains found that similar levels of numeric processing
are facilitated by very different brain structures,
suggesting independent evolution of numeric
processing (20, 21). Because it can be demonstrated
that an insect, with a different brain structure
from primates and birds, can understand the
concept of zero, it would be of high value to
consider such capacities in other animals.
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ACKNOWLEDGMENTS
We thank M. Giurfa, S. Zhang, and J. M. Devaud for suggestions.
Funding: S.R.H. acknowledges the Australian Government Research
Training Program (RTP) Scholarship and the Company of Biologists
JEB Travelling Fellowship. A.D.G. is funded by the Australian Research
Council through the Future Fellowship scheme, FT160100357.
Author contributions: S.R.H., A.A.-W., J.E.G., A.D.G., and A.G.D. were
involved in the design of the experiment, data interpretation, and
drafting of the manuscript. S.R.H., J.E.G., A.D.G., and A.G.D. analyzed
data. S.R.H. collected data. All authors gave final approval for
submission. Competing interests: None declared. Data and materials
availability: Additional data, including the individual choices of
all bees, are available in the supplementary materials, and raw data are
available in the Dryad Digital Repository at doi:10.5061/dryad.7187rf5.
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Materials and Methods
Supplementary Text
Figs. S1 to S4
Table S1
References (23–26)
14 November 2017; accepted 25 April 2018
10.1126/science.aar4975
Howard et al., Science 360, 1124–1126 (2018) 8 June 2018 3 of 3
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Numerical ordering of zero in honey bees
Scarlett R. Howard, Aurore Avarguès-Weber, Jair E. Garcia, Andrew D. Greentree and Adrian G. Dyer
DOI: 10.1126/science.aar4975
(6393), 1124-1126.360Science
, this issue p. 1124; see also p. 1069Science
that it may be more widespread than previously appreciated.
understanding has evolved independently in distantly related species that deal with complexity in their environments, and
concept is present in untrained honey bees (see the Perspective by Nieder). This finding suggests that such an
now show that an understanding of thiset al.some other vertebrates understand the concept of the ''empty set,'' Howard
in humans, and we have been thought to be unique in this understanding. Although recent research has shown that
It has been said that the development of an understanding of zero by society initiated a major intellectual advance
Understanding zero
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REFERENCES
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