Non-numerical strategies used by bees to solve numerical cognition tasks

Abstract

We examined how bees solve a visual discrimination task with stimuli commonly used in numerical cognition studies. Bees performed well on the task, but additional tests showed that they had learned continuous (non-numerical) cues. A network model using biologically plausible visual feature filtering and a simple associative rule was capable of learning the task using only continuous cues inherent in the training stimuli, with no numerical processing. This model was also able to reproduce behaviours that have been considered in other studies indicative of numerical cognition. Our results support the idea that a sense of magnitude may be more primitive and basic than a sense of number. Our findings highlight how problematic inadvertent continuous cues can be for studies of numerical cognition. This remains a deep issue within the field that requires increased vigilance and cleverness from the experimenter. We suggest ways of better assessing numerical cognition in non-speaking animals, including assessing the use of all alternative cues in one test, using cross-modal cues, analysing behavioural responses to detect underlying strategies, and finding the neural substrate.

Keywords: accumulator model; animal cognition; inhibition of return; magnitude; spatial frequency.

Figure 1.

Number of elements naturally covaries with non-numerical cues. (a–d) Examples of two-dimensional stimuli used in numerical cognition studies and how different continuous cues normally covary with numerosity. Note that illusory contour does not covary with numerosity but can still be learned and used to solve numerical cognition tasks, especially with lower numbers of elements. (e) Spatial frequency (the amount of alternating dark and light regions in a given area) also normally covaries with numerosity. The more changes from black to white across an image in all directions, the greater spatial frequency. The right images of each pair in (e) all have higher spatial frequency than the left images. (f–h) For all stimuli in [28], from which our stimulus set was borrowed, area (amount of total black) was kept constant (f), but edge length (total boundary length; g) and convex hull (the minimum convex region covering all elements; h) covaried with numerosity. (i,j) Spatial frequency is calculated by obtaining a power spectrum (Methods) and measuring the area under the power spectrum's curve. The power spectrum plots (i and zoomed-in inset) for all stimuli in [28], from which our stimulus set was borrowed, averaged for each number of elements from one to six, shows that spatial frequency increases with numerosity (j). Note that for all covarying continuous cues, a zero-set stimulus will have zero measurement and thereby be placed naturally at the lower end of the spectrum for each of these non-numerical cues. (Online version in colour.)

Figure 2.

Bees can use non-numerical strategies to discriminate numerical stimuli. (a) Experiment setup. Honeybees were trained to find 50% sucrose solution at one of two pairs of displays showing different numbers of elements, and aversive quinine solution on the other display pair (Methods). (b) Once honeybees reached 80% performance, they were tested using displays with novel shapes. In the learning test, honeybees more often chose stimuli following the numerical rule on which they had been trained (71.3 ± 3.3%; more-than: 70.3 ± 4.7%; less-than: 72.4 ± 4.8%). However, when tested on stimuli that differed in continuous cues but not number of elements (equal/incongruent test; middle bar; 32.5 ± 2.6; more-than: 30.7 ± 4.2%; less-than: 34.2 ± 3.4%) and separately on two pairs of stimuli where numerosity and continuous cues were set in opposition (incongruent/opposite test; right bar; 36.7 ± 1.8; more-than: 35.1 ± 2.4%; less-than: 38.2 ± 2.8%), honeybees chose stimuli based on continuous cues over numerosity. Data shown are combined from the two groups trained with different numerical rules as no difference in performance was found between groups (electronic supplementary material, table S1; Methods). Dotted line = 0.5 chance level. Bars = mean. Vertical lines = s.e.m. Circles = individual bees' data points (filled circles: bees trained to more-than rule; empty circles: bees trained to less-than rule). (c–f) Stimuli used in tests with corresponding continuous variable measurements (Methods).

Figure 3.

A simple computational model using only non-numerical cues reproduces honeybees’ performance in a numerosity tasks. (a) The model uses seven sensory neurons that are activated by the output of visual receptors. Each sensory neuron responds to multiple levels of a single continuous cue with different sensitivities. Firing of each sensory neuron is specific and selective to the preference level modelled by a Gaussian tuning curve. Information from all sensory neurons converges at a single decision neuron. Synaptic connectivity (W) between sensory neurons and the decision neuron are modified by an associative learning rule for encoding appetitive and aversive valences. Performance of the model is evaluated by a simple subtraction of the responses of the decision neuron to the test stimuli. (b–e) Our model is able to reproduce behaviours claimed to be indicative of numerical cognition [28], without any reference to numerosity. (b) Our model can transfer a ‘more/less-than' rule to novel shapes in a ‘conflict test' examining preference for zero numerosity (Wilcoxon signed-rank test, z-value > 6.22 and p < 3.50 × 10⁻⁹) and a ‘transfer test' using displays with more shapes than in training (Wilcoxon signed-rank test, z-value > 7.99 and p < 3.17 × 10⁻¹⁴). Compare to fig. 1c in [28]. (c) Our model can transfer a ‘more/less-than' rule to stimuli containing a number of elements outside the training stimuli range, in a learning test (Wilcoxon signed-rank test, z-value = 3.89 and p = 9.98 × 10⁻⁵), conflict test (z-value = 3.23 and p = 0.0012) and transfer test (z-value = 2.40 and p = 0.016). Compare to fig. 1d in [28]. (d) Our model can transfer a ‘more/less-than’ rule to novel pairs of stimuli, including stimuli with zero elements, in a learning test (Wilcoxon signed-rank test, z-values > 5.27 and p < 1.35 × 10⁻⁶), and conflict test (Wilcoxon signed-rank test, z-values > 5.51 and p < 3.49 × 10⁻⁷). Compare to the electronic supplementary material, fig. S4 in [28]. (e) Our model can recognize stimuli with zero elements as the lower end of a continuum (Wilcoxon signed-rank test for comparing each pair with the chance level 50%, z-values > 2.24 and p < 0.024; Kruskal–Wallis test, χ²₂₉₉ = 183.94 and p = 7.71 × 10⁻³⁷. Compare to fig. 2b in [28]. Light grey, less-than; dark grey, more-than; insets, test stimuli; bars, mean; vertical lines, s.e.m. calculated from the firing rate of the decision neuron for 50 different initial parameters that simulated 50 different model bees.