Evidence for two numerical systems that are similar in humans and guppies

Abstract

Background: Humans and non-human animals share an approximate non-verbal system for representing and comparing numerosities that has no upper limit and for which accuracy is dependent on the numerical ratio. Current evidence indicates that the mechanism for keeping track of individual objects can also be used for numerical purposes; if so, its accuracy will be independent of numerical ratio, but its capacity is limited to the number of items that can be tracked, about four. There is, however, growing controversy as to whether two separate number systems are present in other vertebrate species.

Methodology/principal findings: In this study, we compared the ability of undergraduate students and guppies to discriminate the same numerical ratios, both within and beyond the small number range. In both students and fish the performance was ratio-independent for the numbers 1-4, while it steadily increased with numerical distance when larger numbers were presented.

Conclusions/significance: Our results suggest that two distinct systems underlie quantity discrimination in both humans and fish, implying that the building blocks of uniquely human mathematical abilities may be evolutionarily ancient, dating back to before the divergence of bony fish and tetrapod lineages.

Figure 1. The experimental design used in the undergraduate experiment.

The participants were sequentially presented with two groups of dots and had to estimate which group was more numerous.

Figure 2. The experimental apparatus used in the fish experiment.

Fish were individually placed into the middle of the apparatus where two shoals containing different numbers of fish were visible at the ends.

Figure 3. The results of the undergraduate experiment.

Accuracy (proportion of correct responses) and reaction time are plotted against the numerical ratio of the contrasts for both large and small number (1–4) ranges. The performance of the participants showed ratio sensitivity for large numbers and ratio insensitivity in the small number range. Bars represent the standard error.

Figure 4. The results of the fish experiment.

The proportion of time spent near the larger shoal is plotted against the numerical ratio of the contrasts for both large and small number (1–4) ranges. The performance of the fish (both experienced and inexperienced fish) adhered to the same patterns as for humans in the two numerical ranges, with ratio sensitivity only being shown in the large number range. Bars represent the standard error.