Transfer from number to size reveals abstract coding of magnitude in honeybees

Number discrimination has been documented in honeybees. It is not known, however, whether it reflects, as in vertebrates, the operating of an underlying general magnitude system that estimates quantities irrespective of dimensions (e.g., number, space, time) and format (discrete, continuous). We investigated whether bees spontaneously transfer discrete discrimination of number to continuous discrimination of size. Bees were trained to discriminate between different numerical comparisons having either a 0.5 (2 vs. 4 and 4 vs. 8) or 0.67 ratio (2 vs. 3 and 4 vs. 6). Half of the subjects learnt to choose the smaller quantity and the other half the larger quantity. Bees were then tested for spontaneous choice (in the absence of reward) using comparisons with identical numbers but different sizes. Irrespective of the ratio of the stimuli, bees trained to select the smaller numerical quantity chose the congruent smaller size; bees trained to choose the larger numerical quantity chose the congruent larger size. This finding provides the first evidence for a cross-dimensional transfer between discrete (numerical) and continuous (spatial) dimensions in an invertebrate species and supports the hypothesis of a cognitive universality of a coding for general magnitude.

Constructing and model-fitting receiver operator characteristics using continuous data.

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.