Laura Piffer

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.

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.

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.

Early differences in epithalamic left-right asymmetry influence lateralization and personality of adult zebrafish

The habenulae are part of an evolutionary conserved conduction system that connects the limbic forebrain areas with midbrain structures and is implicated in important functions such as feeding, mating, avoidance learning, and hormonal response to stress. Very early during zebrafish neurogenesis the parapineal organ migrates near to one habenula, commonly the left, inducing wide left-right habenular asymmetries in gene expression and connectivity. It was posited that this initial symmetry-breaking event determines the development of lateralized brain functions and early differences in epithalamic left-right asymmetry give rise to individual variation in coping styles and personality. We tested these two hypotheses by sorting zebrafish with left or right parapineal at birth using a foxD3:GFP marker and by measuring visual and motor laterality and three personality dimensions as they become adults. Significant differences between fish with opposite parapineal position were found in all laterality tests while the influence of asymmetry of the habenulae on personality was more complex. Fish with atypical right parapineal position, tended to be bolder when inspecting a predator, spent less time in the peripheral portion of an open field and covered a shorter distance when released in the dark. Activity in the open field was not associated to anatomical asymmetry but correlated with laterality of predator inspection that in turn was influenced by parapineal position. One personality dimension, sociality, appeared uncorrelated to both anatomical and functional asymmetries and was instead influenced by the sex of the fish, thus suggesting that other factors, i.e. hormonal, may be implicated in its development.

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.

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.

Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM

BackgroundA significant debate surrounds the nature of the cognitive mechanisms involved in non-symbolic number estimation. Several studies have suggested the existence of the same cognitive system for estimation of time, space, and number, called “a theory of magnitude” (ATOM). In addition, researchers have proposed the theory that non-symbolic number abilities might support our mathematical skills. Despite the large number of studies carried out, no firm conclusions can be drawn on either topic.MethodsIn the present study, we correlated the performance of adults on non-symbolic magnitude estimations and symbolic numerical tasks. Non-symbolic magnitude abilities were assessed by asking participants to estimate which auditory tone lasted longer (time), which line was longer (space), and which group of dots was more numerous (number). To assess symbolic numerical abilities, participants were required to perform mental calculations and mathematical reasoning.ResultsWe found a positive correlation between non-symbolic and symbolic numerical abilities. On the other hand, no correlation was found among non-symbolic estimations of time, space, and number.ConclusionsOur study supports the idea that mathematical abilities rely on rudimentary numerical skills that predate verbal language. By contrast, the lack of correlation among non-symbolic estimations of time, space, and number is incompatible with the idea that these magnitudes are entirely processed by the same cognitive system.

Large Number Discrimination in Newborn Fish

Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata) can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14) in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density), three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.

A new training procedure for studying discrimination learning in fish

The study of animal cognition and its neurobiological bases often requires the adoption of associative learning procedures. Though fish are increasingly being used as a model system in behavioral neuroscience, the availability of adequate learning protocols can be a limiting factor in this field of research. This study describes a novel training procedure to explore visual discrimination in fish. Subjects were singly housed in rectangular tanks. At intervals, two stimuli were introduced at opposite ends of the tank and food was delivered near the stimulus to be reinforced. Time spent near positive stimulus in probe trials was taken as a measure of discrimination performance. To validate the method, we replicated two published studies that used operant conditioning to investigate the mechanisms of numerical discrimination in mosquitofish. Our data indicate a complete overlap of the results obtained using the two different methods. The pros and cons of the new procedure are discussed in respect of traditional associative learning paradigms.

Musicians outperform nonmusicians in magnitude estimation: Evidence of a common processing mechanism for time, space and numbers

It has been proposed that time, space, and numbers may be computed by a common magnitude system. Even though several behavioural and neuroanatomical studies have focused on this topic, the debate is still open. To date, nobody has used the individual differences for one of these domains to investigate the existence of a shared cognitive system. Musicians are known to outperform nonmusicians in temporal discrimination tasks. We therefore observed professional musicians and nonmusicians undertaking three different tasks: temporal (participants were required to estimate which of two tones lasted longer), spatial (which line was longer), and numerical discrimination (which group of dots was more numerous). If time, space, and numbers are processed by the same mechanism, it is expected that musicians will have a greater ability, even in nontemporal dimensions. As expected, musicians were more accurate with regard to temporal discrimination. They also gave better performances in both the spatial and the numerical tasks, but only outside the subitizing range. Our data are in accordance with the existence of a common magnitude system. We suggest, however, that this mechanism may not involve the whole numerical range.