Can angelfish (<Emphasis Type="Italic">Pterophyllum scalare</Emphasis>) count? Discrimination between different shoal sizes follows Weber’s law

The ability to discriminate between larger and smaller quantities has been demonstrated in several mammalian and avian species suggesting the possibility of evolutionary conservation of this characteristic. Preference for the larger of two groups has also been shown in fish species, although this ability has rarely been systematically studied in lower order vertebrates, and thus the mechanisms of such ability are not understood. Here, we exploit the tendency of angelfish to seek protection in an unfamiliar environment by joining a group of conspecifics, a behaviour called shoaling. Test fish were given a simultaneous choice between shoals varying both in terms of numerical ratios and absolute numbers of fish. Our results provide evidence for quantity discrimination in angelfish. In general, experimental subjects chose the larger of two shoals. Furthermore, in agreement with Weber’s law, which holds that discrimination between two quantities depends on their ratio, the discrimination between shoals of different quantities of fish was more difficult when the shoal sizes became more similar. The limit of discrimination ratio was found to be below 2:1. Briefly, angelfish are able to discriminate between different quantities of conspecifics subject to a ratio limit, a finding that implies a fitness component in this behaviour similar to what has been demonstrated in higher order vertebrates.     

Quantification abilities in angelfish (Pterophyllum scalare): the influence of continuous variables

Previous studies investigating quantity discrimination have shown that angelfish are able to select the larger of two groups of conspecifics (shoals). The discrimination limits shown by angelfish were similar to those found for other vertebrates when large (≥4) and small quantities (<4) were presented. However, in these studies, no attempt was made to control for non-numerical features of the stimulus shoals and thus the question whether numerical or some quantitative attributes of the shoals were utilized for making the choices could not be answered. Here, we investigate whether angelfish can discriminate between shoals differing in numerical size using non-numerical attributes. We systematically manipulate density, inter-fish distance, and overall space occupied by the shoals, one factor at a time, and analyse the choices angelfish made between the contrasting stimulus shoals. The stimulus shoals consisted of contrasts between large (10 vs. 5) and small (3 vs. 2) number of conspecifics. We found density to be a sufficient condition for discrimination between large shoals as the test subjects preferred the more dense shoal. Manipulation of inter-fish distance indicated that this variable is not a necessary factor in discrimination at either shoal size contrast. Likewise, we found that the size of space occupied by the contrasted shoals also did not significantly influence discrimination. Sensitivity to the density of large shoals indicates that angelfish can discriminate shoal size using this non-numerical cue. Nevertheless, the factors we examined may represent only a subset of all possible non-numerical features upon which angelfish may base their discrimination. Thus, we suggest that further research is required to clarify whether and under what circumstances angelfish may use numerical or non-numerical features when discriminating between shoals of differing size.     

Quantity discrimination in angelfish (<Emphasis Type="Italic">Pterophyllum scalare</Emphasis>) is maintained after a 30-s retention interval in the large but not in the small number range

The ability to discriminate between sets that differ in the number of elements can be useful in different contexts and may have survival and fitness consequences. As such, numerical/quantity discrimination has been demonstrated in a diversity of animal species. In the laboratory, this ability has been analyzed, for example, using binary choice tests. Furthermore, when the different number of items first presented to the subjects are subsequently obscured, i.e., are not visible at the moment of making a choice, the task requires memory for the size of the sets. In previous work, angelfish (Pterophyllum scalare) have been found to be able to discriminate shoals differing in the number of shoal members both in the small (less than 4) and the large (4 or more) number range, and they were able to perform well even when a short memory retention interval (2–15 s) was imposed. In the current study, we increased the retention interval to 30 s during which the shoals to choose between were obscured, and investigated whether angelfish could show preference for the larger shoal they saw before this interval. Subjects were faced with a discrimination between numerically small shoals (≤4 fish) and also between numerically large (≥4 fish) shoals of conspecifics. We found angelfish not to be able to remember the location of larger versus smaller shoals in the small number range, but to exhibit significant memory for the larger shoal in the large number range as long as the ratio between these shoals was at least 2:1. These results, together with prior findings, suggest the existence of two separate quantity estimation systems, the object file system for small number of items that does not work with the longer retention interval and the analogue magnitude system for larger number of items that does.     

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.     

Development and testing of a rapid method for measuring shoal size discrimination

The shoal-choice test is a popular method to investigate quantity discrimination in social fish based on their spontaneous preference for the larger of two shoals. The shoal-choice test usually requires a long observation time (20–30 min), mainly because fish switch between the two shoals with low frequency, thus reducing the possibilities of comparison. This duration limits the use of the shoal-choice test for large-scale screenings. Here, we developed a new version of the shoal-choice test in which the subject was confined in a large transparent cylinder in the middle of the tank throughout the experiment to bound the minimum distance from the stimulus shoals and favour switching. We tested the new method by observing guppies (Poecilia reticulata) in a 4 versus 6 fish discrimination (experiment 1). The new method allowed for a faster assessment of the preference for the larger shoal (<5 min), resulting in potential application for large population screenings. Guppies switched five times more frequently between the two shoals and remained close to the first chosen shoal ten times less compared to experiments with the old method. In experiment 2, we found that with the new method guppies were able to discriminate up to 5 versus 6 fish, a discrimination that was not achieved with the classical method. This last result indicates that minor methodological modifications can lead to very different findings in the same species and suggests that caution should be exercised when interpreting inter-specific differences in quantitative abilities.     

Quantity discrimination in fish species: fish use non-numerical continuous quantity traits to select shoals

Fish typically prefer to live in big shoals due to the associated ecological benefits. Shoaling is a behavior that depends on the ability to quantitatively discriminate. The fundamental mechanism involved in quantity discrimination determines whether fish can discriminate a shoal using numerical discrete cues (e.g., number of shoal members), non-numerical continuous traits (e.g., total body surface area) or both; however, the mechanism is currently a controversial topic. In the present study, we used a spontaneous choice experiment to test whether guppy (Poecilia reticulata), zebrafish (Danio rerio), Chinese crucian carp (Carassius auratus) and qingbo (Spinibarbus sinensis) rely on continuous (i.e., body surface area) or discrete (i.e., number of shoal members) information for shoal selection by altering the body surface area (cumulative body surface area ratio of 3:2 or 1:1) between two stimulus shoals with a different number of members (2 individuals vs 3 individuals). All four fish species preferred to shoal with the stimulus shoal with the larger cumulative surface area even if the shoal had fewer members; however, fish showed no shoal preference when the cumulative surface body areas of both stimulus shoals were equal. Furthermore, qingbo did not numerically discriminate between a shoal with 1 individual and a shoal with 3 individuals when the cumulative surface areas of both stimulus shoals were equal; however, qingbo showed a preference for the shoal with the larger cumulative surface area when the two stimulus shoals each had 3 individuals. In conclusion, the present study demonstrated that all four fish species relied only on non-numerical continuous quantity information for shoal selection, at least under a difficult task (i.e., 2 vs 3).     

Discrimination of small quantities by fish (redtail splitfin, Xenotoca eiseni)

Discrimination of quantity has been argued to rely on two non-verbal representational systems: an object file system (OFS) for representing small values (≤3–4) and an analog magnitude system (AMS) for representing large magnitudes (>4). Infants’ ability to discriminate 1 versus 2, 1 versus 3, 2 versus 3, but not 1 versus 4 or 2 versus 4 seems to prove the independence of such systems. Here, we show that redtail splitfin fish (Xenotoca eiseni) performed relative quantity estimations preferring to approach the location previously occupied by the larger in number between two groups of conspecifics (no longer visible at test) in sets of 1 versus 2 and 2 versus 3 items, but failed at 3 versus 4 items, thus showing the same set-size limit as infants for discrimination of small quantities. However, when tested with quantities that spanned the boundary of the two systems, that is, 1 versus 4 and 2 versus 4, fish succeeded. These results thus point to either the use of continuous physical variables and/or the use of the AMS also for small numerousness in fish in this task.     

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.     

Zebrafish prefer larger to smaller shoals: analysis of quantity estimation in a genetically tractable model organism

Numerical abilities have been demonstrated in a variety of non-human vertebrates. However, underlying biological mechanisms have been difficult to study due to a paucity of experimental tools. Powerful genetic and neurobiological tools already exist for the zebrafish, but numerical abilities remain scarcely explored with this species. Here, we investigate the choice made by single experimental zebrafish between numerically different shoals of conspecifics presented concurrently on opposite sides of the experimental tank. We examined this choice using the AB strain and pet store zebrafish. We found zebrafish of both populations to generally prefer the numerically larger shoal to the smaller one. This preference was significant for contrasted ratios above or equalling 2:1 (i.e. 4 vs. 0, 4 vs. 1, 8 vs. 2, 6 vs. 2 and 6 vs. 3). Interestingly, zebrafish showed no significant preference when each of the two contrasted shoals had at least 4 members, e.g. in a contrast 8 versus 4. These results confirm that zebrafish possess the ability to distinguish larger numbers of items from smaller number of items, in a shoaling context, with a potential limit above 4. Our findings confirm the utility of the zebrafish for the exploration of both the behavioural and the biological mechanisms underlying numerical abilities in vertebrates.     

When quantity trumps number: discrimination experiments in cotton-top tamarins (<Emphasis Type="Italic">Saguinus oedipus</Emphasis>) and common marmosets (<Emphasis Type="Italic">Callithrix jacchus</Emphasis>)

The capacity for non-linguistic, numerical discrimination has been well characterized in non-human animals, with recent studies providing careful controls for non-numerical confounds such as continuous extent, density, and quantity. More poorly understood are the conditions under which animals use numerical versus non-numerical quantification, and the nature of the relation between these two systems. Here we test whether cotton-top tamarins and common marmosets can discriminate between two quantities on the basis of the amount of food rather than on number. In three experiments, we show that when choosing between arrays containing different numbers and sizes of food objects, both species based their decisions on the amount of food with only minor influences of numerical information. Further, we find that subjects successfully discriminated between two quantities differing by a 2:3 or greater ratio, which is consistent with the ratio limits found for numerical discrimination with this species. These studies demonstrate that non-human primates possess mechanisms that enable quantification of total amount, in addition to the numerical representations demonstrated in previous studies, with both types of quantification subject to similar processing limits.     

Spontaneous number representation in mosquitofish

While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated that in fish the same set of signature limits that characterize non-verbal numerical systems in primates is present but yet to provide any demonstration that fish can really represent number rather than basing their discrimination on continuous attributes that co-vary with number. In the present work, using the method of ‘item by item’ presentation, we provide the first evidence that fish are capable of selecting the larger group of social companions relying exclusively on numerical information. In our tests subjects could choose between one large and one small group of companions when permitted to see only one fish at a time. Fish were successful when both small (3 vs. 2) and large numbers (8 vs. 4) were involved and their performance was not affected by the density of the fish or by the overall space occupied by the group.     

Number sense in human infants

Four experiments used a preferential looking method to investigate 6-month-old infants' capacity to represent numerosity in visual-spatial displays. Building on previous findings that such infants discriminate between arrays of eight versus 16 discs, but not eight versus 12 discs (Xu & Spelke, 2000), Experiments 1 and 2 investigated whether infants' numerosity discrimination depends on the ratio of the two set sizes with even larger numerosities. Infants successfully discriminated between arrays of 16 versus 32 discs, but not 16 versus 24 discs, providing evidence that their discrimination shows the set-size ratio signature of numerosity discrimination in human adults, children and many non-human animals. Experiments 3 and 4 addressed a controversy concerning infants' ability to discriminate large numerosities (observed under conditions that control for total filled area, array size and density, item size and correlated properties such as brightness: Brannon, 2002; Xu, 2003b; Xu & Spelke, 2000) versus small numerosities (not observed under conditions that control for total contour length: Clearfield & Mix, 1999). To investigate the sources of these differing findings, Experiment 3 tested infants' large-number discrimination with controls for contour length, and Experiment 4 tested small-number discrimination with controls for total filled area. Infants successfully discriminated the large-number displays but showed no evidence of discriminating the small-number displays. These findings provide evidence that infants have robust abilities to represent large numerosities. In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large versus small numerosities.     

Experimental setting affects the performance of guppies in a numerical discrimination task

A recent study found that guppies (Poecilia reticulata) can be trained to discriminate 4 versus 5 objects, a numerical discrimination typically achieved only by some mammals and birds. In that study, guppies were required to discriminate between two patches of small objects on the bottom of the tank that they could remove to find a food reward. It is not clear whether this species possesses exceptional numerical accuracy compared with the other ectothermic vertebrates or whether its remarkable performance was due to a specific predisposition to discriminate between differences in the quality of patches while foraging. To disentangle these possibilities, we trained guppies to the same numerical discriminations with a more conventional two-choice discrimination task. Stimuli were sets of dots presented on a computer screen, and the subjects received a food reward upon approaching the set with the larger numerosity. Though the cognitive problem was identical in the two experiments, the change in the experimental setting led to a much poorer performance as most fish failed even the 2 versus 3 discrimination. In four additional experiments, we varied the duration of the decision time, the type of stimuli, the length of training, and whether correction was allowed in order to identify the factors responsible for the difference. None of these parameters succeeded in increasing the performance to the level of the previous study, although the group trained with three-dimensional stimuli learned the easiest numerical task. We suggest that the different results with the two experimental settings might be due to constraints on learning and that guppies might be prepared to accurately estimate patch quality during foraging but not to learn an abstract stimulus–reward association.     

人类数能力的演化基础——数能力比较研究的启示

人类的数能力可以发展到很高的抽象水平,但大量研究表明,人类婴儿和非人灵长类也具有基本的数表征和数推理能力。文章从表征内容和表征形式两个方面系统地比较了人类婴儿和非人灵长类的数能力,并对比了成人和非人灵长类数表征的生理基础。人类和非人灵长类在这三方面存在的相似性揭示了他们可能享有相同的数表征系统。在今后的研究中,进一步探讨这两者相似的数表征核心系统,可以加深我们对人类数能力起源和本质的理解     

Small and large number processing in infants and toddlers with Williams syndrome

Previous studies have suggested that typically developing 6‐month‐old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination is successful even when variables continuous with number are systematically controlled for. These findings suggest the existence of different systems underlying small and large number processing in infancy. How do these develop in atypical syndromes? Williams syndrome (WS) is a rare neurocognitive developmental disorder in which numerical cognition has been found to be impaired in older children and adults. Do impairments of number processing have their origins in infancy? Here this question is investigated by testing the small and large number discrimination abilities of infants and toddlers with WS. While infants with WS were able to discriminate between 2 and 3 elements when total area was confounded with numerosity, the same infants did not discriminate between 8 and 16 elements, when number was not confounded with continuous variables. These findings suggest that a system for tracking the features of small numbers of object (object‐file representation) may be functional in WS, while large number discrimination is impaired from an early age onwards. Finally, we argue that individual differences in large number processing in infancy are more likely than small number processing to be predictive of later development of numerical cognition.     

Numerical acuity of fish is improved in the presence of moving targets,but only in the subitizing range

There is controversy in comparative psychology about whether on the one hand non-symbolic number estimation of small (≤4) and large numbers involves a single mechanism (an approximate number system), or whether on the other hand enumeration of the numbers 1–4 is accomplished by a separate mechanism, an object tracking system. To date, support for the latter hypothesis has come only from the different ratio-dependency of performance seen in the two numerical ranges, a reading that has been criticized on several grounds. In humans, the two-system hypothesis is supported by evidence showing that manipulation of the physical properties of the stimuli (e.g., the motion of the items) has dissimilar effects on small- and large-number discrimination. In this research, we studied this effect on guppies. Initially, fish were trained to simultaneously discriminate two numerical contrasts having the same easy ratio (0.50): one in the small-number (2 vs. 4) range and one in the large-number (6 vs. 12) range. Half of the fish were presented with moving items; the other half were shown the same stimuli without motion. Fish were then subjected to non-reinforced probe trials in the presence of a more difficult ratio (0.75: 3 vs. 4 and 9 vs. 12). Under both static and moving conditions, the fish significantly discriminated 6 versus 12, but not 9 versus 12 items. As regards small numbers, both groups learned to discriminate a 0.50 ratio, but only fish tested with moving stimuli also discriminated 3 and 4 items. This differential effect suggests that fish may possess two separate systems for small- and large-number discrimination.     

Pigeons can discriminate “good” and “bad” paintings by children

Humans have the unique ability to create art, but non-human animals may be able to discriminate “good” art from “bad” art. In this study, I investigated whether pigeons could be trained to discriminate between paintings that had been judged by humans as either “bad” or “good”. To do this, adult human observers first classified several children’s paintings as either “good” (beautiful) or “bad” (ugly). Using operant conditioning procedures, pigeons were then reinforced for pecking at “good” paintings. After the pigeons learned the discrimination task, they were presented with novel pictures of both “good” and “bad” children’s paintings to test whether they had successfully learned to discriminate between these two stimulus categories. The results showed that pigeons could discriminate novel “good” and “bad” paintings. Then, to determine which cues the subjects used for the discrimination, I conducted tests of the stimuli when the paintings were of reduced size or grayscale. In addition, I tested their ability to discriminate when the painting stimuli were mosaic and partial occluded. The pigeons maintained discrimination performance when the paintings were reduced in size. However, discrimination performance decreased when stimuli were presented as grayscale images or when a mosaic effect was applied to the original stimuli in order to disrupt spatial frequency. Thus, the pigeons used both color and pattern cues for their discrimination. The partial occlusion did not disrupt the discriminative behavior suggesting that the pigeons did not attend to particular parts, namely upper, lower, left or right half, of the paintings. These results suggest that the pigeons are capable of learning the concept of a stimulus class that humans name “good” pictures. The second experiment showed that pigeons learned to discriminate watercolor paintings from pastel paintings. The subjects showed generalization to novel paintings. Then, as the first experiment, size reduction test, grayscale test, mosaic processing test and partial occlusion test were carried out. The results suggest that the pigeons used both color and pattern cues for the discrimination and show that non-human animals, such as pigeons, can be trained to discriminate abstract visual stimuli, such as pictures and may also have the ability to learn the concept of “beauty” as defined by humans.     

Visual discrimination of normal and drug induced behavior in quails (<Emphasis Type="Italic">Coturnix coturnix japonica</Emphasis>)

The ability to discriminate the physical states of others could be an adaptive behavior, especially for social animals. For example, the ability to discriminate illness behavior would be helpful for avoiding spoiled foods. We report on an experiment with Japanese quails testing whether these birds can discriminate the physical states of conspecifics. The quails were trained to discriminate between moving video images of quails injected with psychoactive drugs and those in a normal (not injected) condition. Methamphetamine (stimulant) or ketamine (anesthetic) were used to produce drug-induced behaviors in conspecifics. The former induced hyperactive behavior and the latter hypoactive behavior. The subject quails could learn the discrimination and showed generalization to novel images of the drug-induced behaviors. They did not, however, show discriminative behavior according to the type and dosage of the drugs. Thus, they categorized the behavior not on the basis of degree of activity, but on the basis of abnormality.     

Infants’ auditory enumeration: Evidence for analog magnitudes in the small number range

Vigorous debate surrounds the issue of whether infants use different representational mechanisms to discriminate small and large numbers. We report evidence for ratio-dependent performance in infants’ discrimination of small numbers of auditory events, suggesting that infants can use analog magnitudes to represent small values, at least in the auditory domain. Seven-month-old infants in the present study reliably discriminated two from four tones (a 1:2 ratio) in Experiment 1, when melodic and continuous temporal properties of the sequences were controlled, but failed to discriminate two from three tones (a 2:3 ratio) under the same conditions in Experiment 2. A third experiment ruled out the possibility that infants in Experiment 1 were responding to greater melodic variety in the four-tone sequences. The discrimination function obtained here is the same as that found for infants’ discrimination of large numbers of visual and auditory items at a similar age, as well as for that obtained for similar-aged infants’ duration discriminations, and thus adds to a growing body of evidence suggesting that human infants may share with adults and nonhuman animals a mechanism for representing quantities as “noisy” mental magnitudes.     

Shetland ponies (Equus caballus) show quantity discrimination in a matching-to-sample design

Numerical competence is one of the aspects of animal cognition with a long history of research interest, but few results are available for the horse. In the present study, we investigated the ability of three Shetland ponies to discriminate between different quantities of geometric symbols presented on a computer screen in a matching-to-sample arrangement. In Experiment 1, the ponies had to relate two similar quantities to another, paired in contrasts (1 vs. 2, 3 vs. 4 and 4 vs. 5) of the same stimulus (dot). Specific pairs of quantities (all differing by one) of up to five different geometrical symbols were displayed in Experiment 2. In each session, both quantities (more and less) were used as sample in such a way that each of the two quantities presented in one test served as positive and as negative stimulus, respectively. The three Shetland ponies were able to discriminate between the given quantities of dots by showing more than 80 % correct responses in two consecutive sessions. Only one of the ponies distinguished different shapes of geometric symbols at a level of 4 versus 5 items. The results show that all ponies were capable of visual quantity discrimination in the present matching-to-sample design, but task solving seemed more difficult when quantities were composed of heterogeneous stimuli. The present results confirm our hypothesis that the ponies based their decision on the matching concept of sameness and were not biased by a spontaneous preference for higher quantities.