Christian Agrillo

Do fish count? Spontaneous discrimination of quantity in female mosquitofish

The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.

Quantity discrimination in female mosquitofish

The ability in animals to count and represent different numbers of objects has received a great deal of attention in the past few decades. Cumulative evidence from comparative studies on number discriminations report obvious analogies among human babies, non-human primates and birds and are consistent with the hypothesis of two distinct and widespread mechanisms, one for counting small numbers (<4) precisely, and one for quantifying large numbers approximately. We investigated the ability to discriminate among different numerosities, in a distantly related species, the mosquitofish, by using the spontaneous choice of a gravid female to join large groups of females as protection from a sexually harassing male. In one experiment, we found that females were able to discriminate between two shoals with a 1:2 numerosity ratio (2 vs. 4, 4 vs. 8 and 8 vs. 16 fish) but failed to discriminate a 2:3 ratio (8 vs. 12 fish). In the second experiment, we studied the ability to discriminate between shoals that differed by one element; females were able to select the larger shoal when the paired numbers were 2 vs. 3 or 3 vs. 4 but not 4 vs. 5 or 5 vs. 6. Our study indicates that numerical abilities in fish are comparable with those of other non-verbal creatures studied; results are in agreement with the hypothesis of the existence of two distinct systems for quantity discrimination in vertebrates.

Evidence for Two Numerical Systems That Are Similar in Humans and Guppies

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.

Use of Number by Fish

Background Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. Methodology/Principal Findings Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. Conclusions/Significance Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a ‘last resort’ strategy in fish, when no other perceptual mechanism may suggest the quantity of the elements. However, our data suggest that, at least in fish, the priority of perceptual over numerical information is not related to a greater cognitive load imposed by direct numerical computation.

Number versus Continuous Quantity in Numerosity Judgments by Fish.

In quantity discrimination tasks, adults, infants and animals have been sometimes observed to process number only after all continuous variables, such as area or density, have been controlled for. This has been taken as evidence that processing number may be more cognitively demanding than processing continuous variables. We tested this hypothesis by training mosquitofish to discriminate two items from three in three different conditions. In one condition, continuous variables were controlled while numerical information was available; in another, the number was kept constant and information relating to continuous variables was available; in the third condition, stimuli differed for both number and continuous quantities. Fish learned to discriminate more quickly when both number and continuous information were available compared to when they could use continuous information only or number only; there was no difference in the learning rate between the two latter conditions. Our results do not support the hypothesis that processing numbers imposes a higher cognitive load than processing continuous variables. Rather, they suggest that availability of multiple information sources may facilitate discrimination learning.

Quantity discrimination in felines: a preliminary investigation of the domestic cat ( Felis silvestris catus )

A large body of studies has investigated the capacity of non-human primates, dogs, birds and lower vertebrates to estimate different quantities of objects or events. Little attention, however, has been devoted to felines, and no study has specifically concentrated on cats’ numerical cognition. The present study aims to investigate the capacity of domestic cats to distinguish between two and three dots in order to obtain food; results showed that cats can be trained to discriminate between the two quantities. Furthermore our research suggests that cats do not spontaneously use numerical information, but rather seem to make use of visual cues that co-vary with numerosity in order to solve the task.

Small and large number discrimination in guppies

Non-verbal numerical behavior in human infants, human adults, and non-human primates appears to be rooted in two distinct mechanisms: a precise system for tracking and comparing small numbers of items simultaneously (up to 3 or 4 items) and an approximate system for estimating numerical magnitude of a group of objects. The most striking evidence that these two mechanisms are distinct comes from the apparent inability of young human infants and non-human primates to compare quantites across the small (<3 or 4)/large (>4) number boundary. We ask whether this distinction is present in lower animal species more distantly related to humans, guppies (Poecilia reticulata). We found that, like human infants and non-human primates, fish succeed at comparisons between large numbers only (5 vs. 10), succeed at comparisons between small numbers only (3 vs. 4), but systematically fail at comparisons that closely span the small/large boundary (3 vs. 5). Furthermore, increasing the distance between the small and large number resulted in successful discriminations (3 vs. 6, 3 vs. 7, and 3 vs. 9). This pattern of successes and failures is similar to those observed in human infants and non-human primates to suggest that the two systems are present and functionally distinct across a wide variety of animal species.

Ontogeny of Numerical Abilities in Fish

Background It has been hypothesised that human adults, infants, and non-human primates share two non-verbal systems for enumerating objects, one for representing precisely small quantities (up to 3–4 items) and one for representing approximately larger quantities. Recent studies exploiting fishs spontaneous tendency to join the larger group showed that their ability in numerical discrimination closely resembles that of primates but little is known as to whether these capacities are innate or acquired. Methodology/Principal Findings We used the spontaneous tendency to join the larger shoal to study the limits of the quantity discrimination of newborn and juvenile guppies. One-day old fish chose the larger shoal when the choice was between numbers in the small quantity range, 2 vs. 3 fish, but not when they had to choose between large numbers, 4 vs. 8 or 4 vs. 12, although the numerical ratio was larger in the latter case. To investigate the relative role of maturation and experience in large number discrimination, fish were raised in pairs (with no numerical experience) or in large social groups and tested at three ages. Forty-day old guppies from both treatments were able to discriminate 4 vs. 8 fish while at 20 days this was only observed in fish grown in groups. Control experiments showed that these capacities were maintained after guppies were prevented from using non numerical perceptual variables that co-vary with numerosity. Conclusions/Significance Overall, our results suggest the ability of guppies to discriminate small numbers is innate and is displayed immediately at birth while discrimination of large numbers emerges later as a result of both maturation and social experience. This developmental dissociation suggests that fish like primates might have separate systems for small and large number representation.

The costs of hemispheric specialization in a fish

Laboratory and field studies have documented better cognitive performance associated with marked hemispheric specialization in organisms as diverse as chimpanzees, domestic chicks and topminnows. While providing an evolutionary explanation for the emergence of cerebral lateralization, this evidence represents a paradox because a large proportion of non-lateralized (NL) individuals is commonly observed in animal populations. Hemispheric specialization often determines large left–right differences in perceiving and responding to stimuli. Using topminnows selected for a high or low degree of lateralization, we tested the hypothesis that individuals with greater functional asymmetry pay a higher performance cost in situations requiring matching information from the two eyes. When trained to use the middle door in a row of a nine, NL fish correctly chose the central door in most cases, while lateralized fish showed systematic leftward or rightward biases. When choosing between two shoals, each seen with a different eye, NL fish chose the high-quality shoal significantly more often than the lateralized fish, whose performance was affected by eye preference for analysing social stimuli. These findings suggest the existence of a trade-off between computational advantages of hemispheric specialization and the ecological cost of making suboptimal decisions whenever relevant information is located on both sides of the body.

Large Number Discrimination by Mosquitofish

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.