Wednesday , August 4 2021

Numerical cognition in honey bees allows for addition and subtraction


Many animals understand numbers at a basic level for use in important tasks such as foraging, shoaling and resource management. However, complex arithmetic operations, such as addition and subtraction, by symbols and / or labeling have only been detected in a limited number of non-human vertebrates. We show that honey bees with a miniature brain can learn to use blue and yellow as symbolic representations of addition or subtraction. In a free-flying environment, individual bees used this information to solve unfamiliar issues of adding or subtracting an element from a group of elements. This display of numerosity requires bees to acquire long-term rules and use short-term working memory. Given that honey bees and humans are separated by over 400 million years of development, our findings suggest that advanced numerical cognition may be more accessible to non-human animals than previously thought.


Currently, there is much debate on animal's ability to have or learn complex speech skills (15). A distinction is made between species which can use quantitative (eg quantity discrimination) and numerical (precise, symbolic) cognition (2). While many species are able to use quantitative cognition for feed, make decisions and solve problems, it is discussed whether non-human or nonprimate animals can reach the level of numerical cognition, such as exact numbers and arithmetic operations, eg, solution of addition and subtraction problems (1. 2). Such a capacity would require complex control of volumes in both work memory and long-term rule-based memory (6). There are studies that show that fetishes (6), chimpanzees (79), orangutans (10), Rhesus monkeys (11), an African gray parrot (12. 13), you are (14), spiders (15. 16) and human children (17. 18) has the ability to add and / or subtract. Some studies show very sophisticated addition and subtraction skills such as In the case of a chimpanzee and an African gray parrot, both could sense the result of an addition sum using Arabic symbols or an English label, which would constitute exact numerical cognition (7. 12. 13). Other studies show that some species are able to perform addition and subtraction problems spontaneously without training in a more naturalized task, such as spiders that can count swapping items and notice when prey is added or subtracted (15) and rhesus monkeys who choose to approach immersed food in nature when a subtraction sum should result in food being present (11).

Honey bees are a model for insect cognition and vision (19. 20). Bees have shown the ability to learn a number of rules and concepts to solve problems like "left / right" (21), "Over under" (22), "Same / Different" (23) and "larger / smaller" (2426). Honey bees have also shown some capacity to count and the number of discrimination when trained by an appetizing (reward) different conditioning frame (2730). Recent advances in educational protocols reveal that bees perform significantly better on perceptually difficult tasks when trained with an appetizing-aversive (reward-punishment) differentiation approach (31). This improved learning ability is associated with bee attention (31), and attention is a key aspect of advanced numerosity and spatial treatment capabilities in the human brain (32. 33). By this condition protocol, honeybees were recently shown to acquire the numerical rules of "greater than" and "less than" and then use these rules to show an understanding that an empty set, zero, is at the lower end of the numerical continuum (34). To inform the current debate on animal speech skills, research on miniature brain insects allows valuable comparisons of which brains of different sizes and architectures can be achieved.

Honeybee's ability to learn complex rules and concepts (20) along with evidence of their number sensation (29. 34) suggests that they are a good model for testing numerical cognition. We trained bees to identify a prominent color (blue or yellow) as a symbolic representation of whether to follow a rule based on addition (blue) or subtraction (yellow) and thus selecting the right result from an arithmetic operation.

In this study, honeybees were trained to enter a Y-maze and see a visual sample stimulus presented vertically containing a set of elements isolated (Figure 1). Bees then fly through an opening in a decision chamber and choose between two possible options (Figure 1). Sample stimulus may contain one, two, four or five elements (one, two or four elements if blue / add; two, four or five elements if yellow / subtraction). If the elements were blue, the bees would have to choose the stimulation option in the decision chamber, which was an element larger than the sample; But if the elements were yellow, the bees would have to choose the stimulus, which contained a smaller element than the sample number (Figure 1). The color of the elements and hence the arithmetic problem to be solved were randomly distributed. Bee for each experiment. Correct and incorrect choices during trials ranged from one to five elements, and the wrong setting could be higher or lower than the correct option (which also included the sample number as a possible incorrect setting). The sample number of three elements was never shown during training and was only used as a new test number during testing. See Materials and Methods below for more information.

FIG. 1 Experimental devices are used to train and test flying boars on their ability to learn to add and subtract.

Device setup for (ONE) subtraction and (B) add-on attempt. The diagram shows parts of the Y maze and the stimulus positions. When the bees see a yellow sample stimulus (A), they must extract an element from it, and when the bees see a blue sample stimulus (B), they must add an element to it. (Not visible in this diagram is the entrance wall of the first chamber).


Training Phase

During 100 appetite-aversive (reward-punishment) enhanced elections (31), honeybees were trained to add or subtract an element based on the color of a sample stimulus (Fig. S1). Bees were provided with a 10 μl drop of a 50% sucrose solution (CS +) or a 60 mM quinine solution (CS-), respectively, as giving or punishing results for correct or incorrect selection, respectively (see Materials and Methods). In this learning phase, there was a marked increase in the number of correct choices made over the 100 conditional elections (z = 8.14, P <0.001), showing that bees learned to simultaneously add or subtract one based on the color of sample stimulus (Figure 2A). Each bee seems to learn differently, possibly due to the random presentation of stimuli and by individual differences in cognitive abilities (Supplementary materials, methods and results, and Fig. S2).

FIG. 2 Results of learning and testing phases.

(ONE) Results during the learning phase. Dotted line of 0.5 indicates the performance level. Solid black line represents a function that describes the learning phase n = 14 bees modeled by a generalized linear mixed-effect model (GLMM). Points (closed circles) along the curve indicate the averages ± 95% confidence intervals (CIs) (purple) with the correct bees selection. Increasing performance in the learning phase was significant. (B) Performance in the test phase for addition and subtraction. Pink columns (left) show results when the wrong answer was in the same direction as the correct answer, and the blue column (right) shows results when the wrong answer was in the opposite direction as the correct answer. Numbers under columns (1, 2, 3 and 4) correspond to the operations of the main text. Dotted line of 0.5 indicates the performance level. The significance of the performance level is indicated by *P <0.05, **P <0.01 and ***P <0.001. Data shown means ± 95% CI limits for all tests.

Test Phase

We subsequently tested the bees during non-untested tests (no reward or punishment) on their ability to interpolate the learned concepts for addition and subtraction to the new three-element test stimulus (see Materials and Methods). We conducted four tests: two addition operations and two subtraction operations. Two of these four tests showed a wrong setting in the same numerical direction as the correct option, and the other two showed an incorrect setting in the opposite numerical direction of the correct option:

1) Addition: Incorrect setting in the same numerical direction as the correct option

Sample = 3, correct = 4, wrong = 5

2) Addition: Incorrect setting in opposite numeric direction as correct option

Sample = 3, correct = 4, wrong = 2

3) Subtraction: Incorrect setting in the same numerical direction as the correct option

Sample = 3, correct = 2, wrong = 1

4) Subtraction: Incorrect setting in opposite numeric direction as correct option

Sample = 3, correct = 2, wrong = 4

In each of the four tests, the bees performed at a level that was significantly different from randomness. In the addition (same direction) test, the bees selected the correct option for 4 in 72.1 ± 3.20% (mean ± SEM) of choice (z = 5.05, P <0.001; Figure 2B). In the second addition (opposite direction), the bees selected the correct option for 4 in 66.4 ± 2.69% of the options (z = 3.81, P <0.001; Figure 2B). In subtraction (same direction) the bees chose the correct option for 2 in 63.6 ± 2.89% of the options (z = 3.17, P = 0.002; Figure 2B). In the second subtraction (opposite direction) test, the bees selected the correct option for 2 in 67.9 ± 3.66% of the options (z = 4.13, P <0.001; Figure 2B). There was no significant difference between bees performance in any of the four tests (z = -0.887, P = 0.375), which shows that the bees performed just as well on all tests.


Honey bees could use color as a symbolic representation of the addition and subtraction signs and learned under 100 appetite-aversive attempts so as to add or subtract an element from different samples. In addition, the bees could successfully interpolate the learned operations of addition and subtraction to an unknown sample number and form during testing.

Arithmetic operations such as addition and subtraction problems are known to involve complex cognitive processes as they require two levels of information processing. The first is the representation of numerical attributes, and the second is the mental manipulation of these representations in working memory (6). In the present study, the bees not only succeeded in performing these processing tasks, but also performing the arithmetic operations in working memory, since the number to be added or subtracted (an element) was not visually present, but rather an abstract concept, such as bees. had to be resolved during the training. This important step in combining the arithmetic and symbolic learning abilities of an insect has identified many new areas of future research and also asks whether these complex numerical understandings may be available to other species without large brains, such as the honey bee (35). While the posterior parietal cortex and the prefrontal cortex are key areas for numerical treatment in primates (32), we have not yet determined where number representation and processing can occur in honeybee brain; However, we show that the relatively large and complex brain regions required in primates are not required for an insect to treat number problems.

While the specific task of addition / subtraction may not be directly evident in the natural environment of the honey bee, the skills and cognitive plasticity needed to perform the arithmetic task are likely to be ecologically beneficial. For example, the bees' ability to acquire and manipulate learned information to make decisions using multiple memory phases (23) is useful in foraging to remember which flower properties (eg, color, shape and size) can provide essential resources and which flower properties may not (35). Thus, learning involving linking visual features to the reward of quantification, as in the arithmetic task, is likely to be beneficial for a honeybee's foraging lifestyle.

Debates on the ability of a non-human animal to demonstrate numerical cognition have so far focused on arguments either that numerical skills are biologically developed traits (1) or that animals have only limited quantitative abilities, and human culture is needed for more complex numerical abilities (2. 4). But these debates have inspired a third important argument: Verguts and Chen (5) suggests that we should at least consider the rapid development of individual learning of numerical cognition that occurs during the life of an animal. Honeybee is in this context a skilled teacher of many tasks, including cohesion and discrimination (23), mazes (21. 36), face stimuli (37) and spatial relationships (38), and the results of the present study show that honey bees are able to learn and use numerical cognition as individuals. Our results suggest that honey bees and other non-human animals may be biologically tuned to complex numerical tasks. These opportunities have important implications for further exploration, especially in insects.

Human children without language for numbers have shown great addition and subtraction (18) and Mundurukú mother tongue members from Brazil, a language that does not have words for large numbers, can add large approximate numbers far beyond their naming range (39). While Munduruku language speakers demonstrated precise arithmetic with small numbers (<4 and 5), they failed at exact arithmetic for large numbers (>4 or 5), but could use approximation to calculate solutions. These studies show that human language is not necessary for arithmetic operations such as addition and subtraction. Combined with the results of our current study, we suggest that language and prior advanced numerical understanding are not a prerequisite for the ability to calculate addition and subtraction solutions. In the current study, bees were only tested in the range 1 to 5 for their ability to add and subtract; Thus, it would be valuable to investigate high-volume bi-performance to determine if they could use approximation or exact arithmetic to solve similar large numbers of arithmetic problems.


Study design

We aimed to determine if free flying honey bees could learn to add or subtract an element from a series of elements in a delayed matching to the test task. To solve this question, we trained bees to use different colors (blue or yellow) as a prompt to perform either addition or subtraction. Bees were trained to use a Y labyrinth (described below, Figure 1) to see a sample stimulus containing a certain number of colored elements on a gray background. Once they saw this stimulus, they could fly into a decision chamber to choose the correct option due to the arithmetic problem that arose (Figure 1).

Student species

We used 14 free-flying honey bees (Apis mellifera) Head to this experiment. All bees were labeled with a colored dot on the thorax to identify persons. An ad lib von Frisch type gravity feeder gives approx. 10 to 30% sucrose was created to maintain a regular number of bees.


Individual honey bees were trained to enter a Y-maze[Sombeskreveti([Asdescribedin([sombeskreveti([asdescribedin(22); Figure 1]. Bees had to fly through an initial entrance hole to enter a chamber where they would see the sample stimulation. This stimulus will contain either blue or yellow elements on a gray background. Each bee could then fly through another hole in the decision chamber, where it would be presented with two different options in each arm of the chamber. If the sample stimulus had been blue, the bee would have to select the stimulus with a number of elements, which was one more than the sample number; However, if the test stimulus had turned yellow, the bee would have to select the stimulus with a number of elements that were less than the sample number (Figure 1). This delayed matching-to-sample method using a Y labyrinth apparatus is the standard method for testing honeybee learning and specifically quantity matching in honeybees (30) and has been validated by producing uniform learning outcomes for alternative apparatus (20).

The stimuli were presented on gray backgrounds located 15 cm away from the decision lines. Two stimuli, one correct and one wrong, were presented simultaneously in each arm of the Y maze on the gray plastic background (Figure 1). A 10 μl drop of either a 50% sucrose solution (correct choice) or a 60 mM quinine solution (incorrect selection) was used as a reward and punishment during the training phase, respectively, as this promotes improved visual discrimination notions in flying honey bees. Each stimulus had a gray bar underneath the one holding the drop of either sucrose under the proper option or quinine under the wrong setting so that the bees would learn to associate stimuli with either a reward or punishment. The poles were replaced when stirred by a bee and cleaned with 20% ethanol to exclude closed signs. The pages of correct and wrong stimuli were randomly changed between choices (38). If a bee made an incorrect choice and began to recreate the quinine, it was allowed to fly to the rod in front of the correct stimulus to collect sucrose to maintain motivation, but only the first choice was recorded for statistical analysis (38). When the bee had finished tying the sucrose, it was allowed to fly back to the beehive if it was satiated or made another decision by entering the maze again. During the untested tests, a drop of water was placed on each of the poles located in front of stimuli. Ten selections (points of the poles) were recorded for each of the four tests to allow statistical comparisons.


Each stimulus was a 6 cm by 6 cm gray square with either blue (additions) or yellow (subtraction) elements presented on it (Fig. S1) and covered with 80 μm Lowell laminate. The colors selected were spectrally different and important in view of honeybee vision. Elements can be one of four forms: square, diamond, circle or triangle. Three of these forms were used in training, and the second new form was used for testing to ensure that patterns and shapes were unknown to the bees during testing. To check for surface area (SA), each pattern (cumulative SA of black elements) was 10 ± 0.3 cm2 regardless of shape, pattern or number of elements, and each element was above the minimum resolution limit of honeybee vision as based on previous psychophysical findings (SA area: circle, 1 cm2 to 9.95 cm2; square / diamond, 1 cm2 to 6.32 cm2; triangle, 1 cm2 to 10 cm2). There were a total of 216 stimuli, 108 for addition and 108 for subtraction (Fig. S1). Element size, line length, and convex hull for all stimuli were not consistently correlated with increasing or decreasing number of elements.

There were a total of 108 different patterns consisting of one to five elements of the four different shapes (square, diamond, circle and triangle) that could be presented throughout the experiment, and this was done to check for the potential use of a associating mechanism of the bees to learn the results of each stimulus. There were no low level signals that could be used to solve the problem as the correct answer could be lower or higher than the original number depending on sample color and the wrong answer could be the same number as the sample or any (not correct) numbers above or during the test. Thus, the correct answer was not predicted by visual similarity to the original sample number or numerical proximity to the sample number.

training procedure

Bees were incrementally trained to enter the Y-maze and both arms of the apparatus within 30 to 60 minutes. When each bee was able to fly into the entrance hole and the hole that led to the decision chamber and be able to find the poles in both Y-maze arms, the experiment began.

After entering the Y maze, bees would be in the initial chamber where they could see the sample number. To solve the task, the bees were required to either add or subtract the value of one to this sample number depending on the color of the elements (Figure 1). Bees would then fly through the next hole in the Y-labyrinth and into the decision chamber, where they could simultaneously see two stimuli in a double-choice test. If the sample number was blue, the bee would have to choose the option that was an element larger than the sample pulse to receive a reward, while if the sample number was yellow, the bee would choose the option that was an element less than the sample number to receive a reward. The incorrect option was randomly chosen and could be any number from 1 to 5, including the sample number itself, which controlled the bees, and the correct option was based on visual similarity, and incorrect choices were associated with a bitter tasting quinine solution.

Each bee thus ends 100 appetite-aversive (31) reinforced trials that present either addition or subtraction arithmetic problems. Whether a sample would involve adding or subtracting an element from the sample number was randomized.

During the training, the numbers that could be used for the test in the add-on attempts could be 1, 2, and 4. Thus, the correct answers could be 2, 3, and 5, and the wrong answers could be 1, 2, 3, 4, and 5 During the subtraction tests, the numbers that could be used for the sample number could be 2, 4, and 5. Thus, the correct answers could be 1, 3, and 4, and the incorrect answers could be 1, 2, 3, 4, and 5. never shown as a test number during training for a bee and was thus used as the sample number for all uncontrolled tests to ensure that the sample number was new during testing.

Test procedure

When bees had completed the training, there were four tests of 10 uncontrolled choices. Between each of the four tests there were 10 refresh enhancements to maintain bi motivation. The sequence of these tests was randomized. These tests were non-fortified (no reward or punishment) and used a 10 μl drop of water instead of quinine or sucrose to motivate the bees to land. We conducted four tests where two arithmetic operations were added and two were subtraction. Since the test stimulation of three elements had never been presented during the training, the bees had not previously received amplification at number four for addition or two for subtraction testing. Two of these four tests showed a wrong setting in the same direction as the correct option, and the other two showed a wrong setting in the opposite direction to the correct option. Two of the tests required addition and two necessary subtraction using the new sample number of three.

Two of the tests involved the incorrect answer in the same direction as the correct answer (addition: sample = 3, correct = 4, wrong = 5, subtraction: sample = 3, correct = 2, incorrect = 1). Two of the tests involved the incorrect answer to be in the opposite direction of the correct answer and thus also one element different from the sample (addition: sample = 3, correct = 4, wrong = 2; subtraction: sample = 3, correct = 2, incorrect = 4).

Statistical analysis

To test the effect of training on side effects (number of correct choices), data from the learning phase of 100 choices was analyzed with a generalized linear mixed-effect model (GLMM) with binomial distribution using the "glmer" package within R environment for statistical purposes. analysis. We mounted a full model with sample number as a continuous prediction and topic as a random factor to account for repeated selections of individual bees.

To determine if the bees could learn to follow further and subtraction rules, we analyzed the test data by using a GLMM that contained only the intercept as a fixed factor and subject as an arbitrary expression. The average proportion of "correct" selections (MPCC) recorded from the tests was used as the response variable in the model. Wald statistics (z) tested, if the MPCC recorded from the learning test, represented by the coefficient of the intercept period, was significantly different from the chance expectation, ie. H0: MPCC = 0.5.

A separate analysis was performed to determine if there were differences between the four tests on bee performance. We analyzed the test data using a GLMM, which contained only the intercept as a fixed factor and subject as an arbitrary expression. The MPCC during the tests and the test type (addition test 1, addition sample 2, subtraction test 1 and subtraction test 2) were used as a response variable in the model. The z statistically tested, if the MPCC recorded from the tests varied on the basis of test type. All assays were performed within the R environment for statistical analysis.


Additional material for this article is available at

Additional materials, methods and results

FIG. S1. The full set of stimuli used (n = 216) for the addition (blue; n = 108) and subtraction (yellow; n = 108) training and test phases.

FIG. S2. The Bayesian-specific bias for each of the bees, averaged over nt = 10 experiments (except for the first 10 experiments evaluated for all previous experiments).

Reference (40)

This is an open-access article distributed under the Creative Commons Attribution-Noncommercial License that allows use, distribution, and reproduction on any medium as long as the resulting use is does not for commercial benefit and provided that the original work is properly cited.

Thanks: financing: S.R.H. Recognizes the company for the biologists JEB Traveling Society (grant JEBTF-170217) and the Australian Government Research Training Program (RTP) scholarship. A.A.-W. Recognizes CNRS and Paul Sabatier University (Toulouse 3). A.D.G. acknowledges the support of an ARC Future Fellowship (Grant No FT160100357). Ethics statement: All animal care was consistent with institutional guidelines. Author Contributions: S. R. H., A. A. W., J. E. G., and A. G. D. designed the experiment. S.R.H. data collection. S.R.H., J.E.G., and A.D.G. analyzed data. All authors were involved in the interpretation of results and preparation of the manuscript. Competing interests: The authors state that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions of the paper is present in the paper and / or the supplementary materials. The raw selection data for individual bees supporting the results of this study are available in the Dryad Data Repository with the identification document: 10.5061 / dryad.56r4rv4. Additional information related to this paper may be requested from the authors.

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