Large number discrimination by mosquitofish

Abstract

Background: Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4) were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish.

Methodology/principal findings: Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance). Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1:2 or 2:3 but not when the ratio was 3:4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish.

Conclusions/significance: Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all vertebrates.

Figure 1. Results of Experiment 1a.

Accuracy when luminance, density, overall space and cumulative surface area were controlled. Fish performance dropped to chance level only when cumulative surface area was paired (*  =  p < 0.05; **  =  p < 0.01).

Figure 2. Results of Experiments 2 and 3.

Fish performance is not affected by total numerosity when the numerical ratio is kept constant. On the contrary, numerical ratio does affect fish performance when total numerosity is controlled (*  =  p<0.05).

Figure 3. Results of Experiment 4.

Adult humans were required to make numerical judgements with the same stimuli used in experiment 2. Both accuracy (graph a) and reaction time (ms, graph b) were not affected by total numerosity (Circles: stimuli controlled for continuous variables; squares: number and continuous variables available).

Figure 4. Results of Experiment 4.

Adult humans were required to make numerical judgements with the same stimuli used in experiment 3. Both accuracy (graph a) and reaction time (ms, graph b) showed a significant sensitivity to numerical ratio (Circles: stimuli controlled for continuous variables; squares: number and continuous variables available).

Figure 5. Schematic representation of the apparatus used in the pre-training phase.

The tank was divided into four equal sectors by plastic partitions (a). Each partition contained two potential doors (b): only the door below the reinforced quantity permitted fish to pass from one sector to the other.

Figure 6. Apparatus used to train fish in experiment 1.

Subjects were placed in the middle of a test chamber provided with two doors placed at opposite corners, one associated with 4 (a) and the other associated with 8 (b) figures. Only the door associated with the reinforced quantity could be opened by the fish in order to rejoin shoal mates in the outer tank.