Reply to comment on Howard et al. (2019): ‘Nothing to dance about: unclear evidence for symbolic representations and numerical competence in honeybees'

We respond to the Comment by Shaki & Fischer [1] regarding their criticisms on three of our recent publications presenting the evidence of numerical abilities in honeybees [2–4]. Our work is part of a novel ‘cognitive revolution' in which ‘cognitive-like' behaviours are now observed in organisms evolutionarily separated from humans, for example bees, wasps [5], spiders [6], ants [7–9] and even slime moulds [10].

Shaki & Fischer [1] first criticise our recent paper demonstrating that honeybees could learn to match an abstract character/sign (an N-shape or inverted T-shape) to a small quantity (two or three) of elements [4]. Shaki & Fischer [1] do raise an interesting idea for an additional transfer test of testing numerosities outside of the training set. However, the absence of this suggested experiment does not invalidate our results, and such an experiment would extend our understanding of the capacity for insect brains to extrapolate information [11].

The key issue which Shaki & Fischer [1] raise, i.e. that bees may not be matching a specific sign with a respective numerosity but rather generalizing similar numerosities with signs, is controlled for within our study. Two groups of bees were trained in the study. One group was trained to match a sign to a numerosity, and a separate group was trained to match a numerosity to a sign. Both groups succeeded in learning their respective tasks. While the group matching a sign to a numerosity may potentially learn, as suggested by Shaki & Fischer [1], that N ≠ 3 or N = 1 or 2, the other group controls for this possibility. The second group only views a precise numerosity which was successfully matched to a sign. This counter-balanced experimental design was specifically implemented to control for the question posed by Shaki & Fischer [1]. Even without our experimental control, we note that Shaki & Fischer's suggestion still implies numerical understanding, albeit of a more complicated form than our work shows. Additionally, it is also known that honeybees can learn numerosity tasks in either an absolute [12] or relative [2] way depending upon conditioning; recent work shows that bees can transfer information between processing methods (i.e. larger/smaller rules from numerosity to size) [13]. Furthermore, if the position of Shaki & Fischer [1] is true this means bees are using the acquired symbol ‘N' as an inequality operator. Bees are able to learn relational rules such as ‘smaller than' and ‘greater than' [11]; however, this requires extended training on the specific relational concept, which was not provided in the symbol study [4]. Thus, while future work could explore such possibilities, we currently conclude that bees were implementing the simpler matching principle in their use of the symbols, rather than the suggested more complex relational comparison use of a symbol.

Shaki & Fischer [1] state that the failure of bees to reverse the sign and numerosity matching tasks supports their claim above, i.e. that bees may not have learnt a direct matching of sign to numerosity (e.g. N = 2), but a relative rule (e.g. N ≤ 2). The results of the reversal tests do not support Shaki & Fischer's [1] hypothesis, as the authors do not explain why bees would fail the reversal tests if they had learnt a relative rule instead of a direct association between two stimuli. It seems that if bees had learnt N ≤ 2 and an inverted T ≥ 3, then they should have no problem in reversing the task; in fact it may have been easier to reverse the task owing to such a generalization. Moreover, in our previous study [4], we discuss how the results of the reversal tests are consistent with Piaget's Theory on ‘operations' or ‘reversible actions’, which support the conclusion that bees learnt a direct association between a numerosity and a sign in Howard et al. [4].

Shaki & Fischer [1] next discuss our study on the ability of bees to perform simple addition and subtraction [3,14]. They state that bees were reinforced on a mean of 3.33 for addition and 2.66 for subtraction. Shaki & Fischer [1] provide a table in which they claim to present all training conditions; however, their table is an incomplete summary of all conditions. We provide the correct table above (table 1; also see methods section of [4]). During the training phase, the correct mean for the rewarded option in the addition trials would be 3.33 and the incorrect mean would be 2.93. Then during testing, the options have a mean of 4.00 for the correct option and a mean of 3.50 for an incorrect option (table 2). Thus, the reinforced mean of 3.33 is closer to the incorrect test option of 3.50. However, bees still prefer the correct option of 4.00 despite this. Similarly, for subtraction, the correct training mean is 2.67 and the incorrect mean is 3.08. During testing, the correct mean is 2.00 and the incorrect mean is 2.50. Therefore, the reinforced mean of 2.67 is closer to the incorrect option than the correct option. However, bees still prefer the correct option of 2 (table 2). Our careful planning of the stimuli options and procedure demonstrates that despite an easier low-level mechanism available for bees to use (see [14]), they prefer to choose the correct option in tests. The bees thus demonstrate simple arithmetic under conditioning. In regard to the suggestion of foil aversion, if bees had learnt foil aversion then they would fail in two of the tests (addition: sample = 3, correct = 2, incorrect = 1; subtraction: sample = 3, correct = 2, incorrect = 4) as both the correct and incorrect options are equidistant from 3; however, bees were successful in all transfer tests. Additionally, there is currently no evidence suggesting that bees can solve the different steps required to use the mean numerosities of previous training trials to drive future choices. Even if not explicitly written in our paper [3], we are conscious that bees add and subtract only after having been conditioned to do so. This is in agreement with what occurs in ants: they add and subtract only when having perceived the result of the operation during training [7,15,16].

Table 1.

Summary of numerosities used throughout the training phase of the study testing the ability of bees to match signs and numerosities [4].

addition			subtraction
sample	correct	incorrect	sample	correct	incorrect
1	2	1	2	1	2
1	2	3	2	1	3
1	2	4	2	1	4
1	2	5	2	1	5
2	3	1	4	3	1
2	3	2	4	3	2
2	3	4	4	3	4
2	3	5	4	3	5
4	5	1	5	4	1
4	5	2	5	4	2
4	5	3	5	4	3
4	5	4	5	4	5
mean (addition)	3.33	2.92	mean (subtraction)	2.67	3.08

Table 2.

Summary of numerosities used throughout the testing phase of the study testing the ability of bees to match signs and numerosities [4].

addition			subtraction
sample	correct	incorrect	sample	correct	incorrect
3	4	2	3	2	1
3	4	2	3	2	1
3	4	5	3	2	4
3	4	5	3	2	4
mean (addition)	4.00	3.50	mean (subtraction)	2.00	2.50

The criticism raised for Howard et al. [2], i.e. that ‘bees underwent a flawed training procedure where selecting the highest numerosity had always been punished while the lowest numerosity had never been punished', is an incorrect statement. In our study [2], bees were able to demonstrate, through a range of different experiments, that they could value an empty set as lower than other whole numerosities, sets containing elements with or without training on the position of the empty set itself. While this training procedure was implemented for some of the experiments to show that the concept of zero involves a quantitative understanding, other key control experiments were conducted to validate the results (see experiment 2 in [2]). Importantly, in Howard et al. (2018), experiment 2 demonstrated that bees trained on the numerosities 2–6 were able to correctly choose ‘0' as lower than ‘1', despite having never been reinforced on these numerosities prior to the tests [2]. A simple mechanism would predict that bees should choose ‘1' as it is closest to the rewarded numerosity of ‘2'; however, in this key experiment, bees chose ‘0' as predicted by concept acquisition [2]. In addition, the option of ‘1' was far more perceptually similar to the training set, and Shaki & Fischer propose that the ‘Miniature brains of insects are powerful pattern associators'. However, in this additional control experiment, the bees preferred the empty set stimulus. This portfolio of experiments enabled us to confirm that bees understand zero numerosity at a level consistent with available evidence for several animal species [17,18].

In summary, with careful methodological planning and appropriate transfer tests, we have been able to demonstrate the evidence of sign and numerosity matching, simple arithmetic, and abstract concept acquisition [2–4]. Abstract concept acquisition in honeybees has been previously shown in other studies under different experimental paradigms [11,19–23]. Importantly, recent independent studies have also confirmed that other insects (ants: Myrmica sabuleti) can add [7] and have the notion of zero numerosity [8,9].

An interesting take on the narrative of ‘nothing to dance about' [1] is that indeed bees do perceive when there are sufficient rewards present in an environment to communicate a signal to hive-mates [24], and if there is low or zero rewards bees elect not to dance. Thus, in the framework proposed by Nieder [17,18], i.e. that perceiving the absence of a stimulus to inform a decision requires a level of neural processing, it is of value for research to explore how bees process quantities in natural environments. The cognitive revolution has important implications for understanding the neuronal framework required to solve complex tasks [25,26]. By evaluating the importance of demanding cognitive tasks in miniature brains, we are starting to better understand why bees have a reason to dance.

Data accessibility

There is no additional data. All data is available within the manuscript.

Authors' contributions

All authors were involved in writing the manuscript and gave final approval for submission.

Competing interests

We declare we have no competing interests.

Funding

S.R.H. acknowledges the Fyssen Foundation.