Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella)

Thinking about order: a review of common processing of magnitude and learned orders in animals

Rich behavioral and neurobiological evidence suggests cognitive and neural overlap in how quantitatively comparable dimensions such as quantity, time, and space are processed in humans and animals. While magnitude domains such as physical magnitude, time, and space represent information that can be quantitatively compared (4 "is half of" 8), they also represent information that can be organized ordinally (1→2→3→4). Recent evidence suggests that the common representations seen across physical magnitude, time, and space domains in humans may be due to their common ordinal features rather than their common quantitative features, as these common representations appear to extend beyond magnitude domains to include learned orders. In this review, we bring together separate lines of research on multiple ordinal domains including magnitude-based and learned orders in animals to explore the extent to which there is support for a common cognitive process underlying ordinal processing. Animals show similarities in performance patterns across natural quantitatively comparable ordered domains (physical magnitude, time, space, dominance) and learned orders (acquired through transitive inference or simultaneous chaining). Additionally, they show transfer and interference across tasks within and between ordinal domains that support the theory of a common ordinal representation across domains. This review provides some support for the development of a unified theory of ordinality and suggests areas for future research to better characterize the extent to which there are commonalities in cognitive processing of ordinal information generally.

Numerical cognition in black-handed spider monkeys (Ateles geoffroyi)

We assessed two aspects of numerical cognition in a group of nine captive spider monkeys (Ateles geoffroyi). Petri dishes with varying amounts of food were used to assess relative quantity discrimination, and boxes fitted with dotted cards were used to assess discrete number discrimination with equally-sized dots and various-sized dots, respectively. We found that all animals succeeded in all three tasks and, as a group, reached the learning criterion of 70% correct responses within 110 trials in the quantity discrimination task, 160 trials in the numerosity task with equally-sized dots, and 30 trials in the numerosity task with various-sized dots. In all three tasks, the animals displayed a significant correlation between performance in terms of success rate and task difficulty in terms of numerical similarity of the stimuli and thus a ratio effect. The spider monkeys performed clearly better compared to strepsirrhine, catarrhine, and other platyrrhine primates tested previously on both types of numerical cognition tasks and at the same level as chimpanzees, bonobos, and orangutans. Our results support the notion that ecological traits such as a high degree of frugivory and/or social traits such as a high degree of fission-fusion dynamics may underlie between-species differences in cognitive abilities.

Cichlids and stingrays can add and subtract 'one' in the number space from one to five

The numerical understanding of cichlids and stingrays was examined regarding addition and subtraction abilities within the number space of one to five. Experiments were conducted as two-alternative forced-choice experiments, using a delayed matching to sample technique. On each trial, fish had to perform either an addition or subtraction, based on the presentation of two-dimensional objects in two distinct colors, with the color signaling a particular arithmetic process. Six cichlids and four stingrays successfully completed training and recognized specific colors as symbols for addition and subtraction. Cichlids needed more sessions than stingrays to reach the learning criterion. Transfer tests showed that learning was independent of straightforward symbol memorization. Individuals did not just learn to pick the highest or lowest number presented based on the respective color; instead, learning was specific to adding or subtracting ‘one’. Although group results were significant for both species in all tests, individual results varied. Addition was learned more easily than subtraction by both species. While cichlids learned faster than stingrays, and more cichlids than stingrays learned the task, individual performance of stingrays exceeded that of cichlids. Previous studies have provided ample evidence that fish have numerical abilities on par with those of other vertebrate and invertebrate species tested, a result that is further supported by the findings of the current study.

The Sense of Number in Fish, with Particular Reference to Its Neurobiological Bases

Simple Summary

The ability to deal with quantity, both discrete (numerosities) and continuous (spatial or temporal extent) developed from an evolutionarily conserved system for approximating numerical magnitude. Non-symbolic number cognition based on an approximate sense of magnitude has been documented in a variety of vertebrate species, including fish. Fish, in particular zebrafish, are widely used as models for the investigation of the genetics and molecular mechanisms of behavior, and thus may be instrumental to development of a neurobiology of number cognition. We review here the behavioural studies that have permitted to identify numerical abilities in fish, and the current status of the research related to the neurobiological bases of these abilities with special reference to zebrafish. Combining behavioural tasks with molecular genetics, molecular biology and confocal microscopy, a role of the retina and optic tectum in the encoding of continuous magnitude in larval zebrafish has been reported, while the thalamus and the dorso-central subdivision of pallium in the encoding of discrete magnitude (number) has been documented in adult zebrafish. Research in fish, in particular zebrafish, may reveal instrumental for identifying and characterizing the molecular signature of neurons involved in quantity discrimination processes of all vertebrates, including humans.

Abstract

It is widely acknowledged that vertebrates can discriminate non-symbolic numerosity using an evolutionarily conserved system dubbed Approximate Number System (ANS). Two main approaches have been used to assess behaviourally numerosity in fish: spontaneous choice tests and operant training procedures. In the first, animals spontaneously choose between sets of biologically-relevant stimuli (e.g., conspecifics, food) differing in quantities (smaller or larger). In the second, animals are trained to associate a numerosity with a reward. Although the ability of fish to discriminate numerosity has been widely documented with these methods, the molecular bases of quantities estimation and ANS are largely unknown. Recently, we combined behavioral tasks with molecular biology assays (e.g c-fos and egr1 and other early genes expression) showing that the thalamus and the caudal region of dorso-central part of the telencephalon seem to be activated upon change in numerousness in visual stimuli. In contrast, the retina and the optic tectum mainly responded to changes in continuous magnitude such as stimulus size. We here provide a review and synthesis of these findings.

Neuroethology of number sense across the animal kingdom

Many species from diverse and often distantly related animal groups (e.g. monkeys, crows, fish and bees) have a sense of number. This means that they can assess the number of items in a set - its 'numerosity'. The brains of these phylogenetically distant species are markedly diverse. This Review examines the fundamentally different types of brains and neural mechanisms that give rise to numerical competence across the animal tree of life. Neural correlates of the number sense so far exist only for specific vertebrate species: the richest data concerning explicit and abstract number representations have been collected from the cerebral cortex of mammals, most notably human and nonhuman primates, but also from the pallium of corvid songbirds, which evolved independently of the mammalian cortex. In contrast, the neural data relating to implicit and reflexive numerical representations in amphibians and fish is limited. The neural basis of a number sense has not been explored in any protostome so far. However, promising candidate regions in the brains of insects, spiders and cephalopods - all of which are known to have number skills - are identified in this Review. A comparative neuroscientific approach will be indispensable for identifying evolutionarily stable neuronal circuits and deciphering codes that give rise to a sense of number across phylogeny.

Use of numerical and spatial information in ordinal counting by zebrafish

The use of non-symbolic numerical information is widespread throughout the animal kingdom, providing adaptive benefits in several ecological contexts. Here we provide the possible evidence of ordinal numerical skills in zebrafish (Danio rerio). Zebrafish were trained to identify the second exit in a series of five identically-spaced exits along a corridor. When at test the total length of the corridor (Exp. 1) or the distance between exits (Exp. 2) was changed, zebrafish appeared not to use the absolute spatial distance. However, zebrafish relied both on ordinal as well as spatial cues when the number of exits was increased (from 5 to 9) and the inter-exit distance was reduced (Exp. 3), suggesting that they also take into account relative spatial information. These results highlight that zebrafish may provide a useful model organism for the study of the genetic bases of non-symbolic numerical and spatial cognition, and of their interaction.

Precise relative-quantity judgement in the striped field mouse Apodemus agrarius Pallas

Applying the classical experimental scheme of training animals with food rewards to discriminate between quantities of visual stimuli, we demonstrated that not only can striped field mice Apodemus agrarius discriminate between clearly distinctive quantities such as 5 and 10, but some of these mice also exhibit high accuracy in discriminating between quantities that differ only by one. The latter include both small (such as 2 versus 3) and relatively large (such as 5 versus 6, and 8 versus 9) quantities of elements. This is the first evidence of precise relative-quantity judgement in wild rodents. We found striking individual variation in cognitive performance among striped field mice, which possibly reflects individual cognitive variation in natural populations. We speculate that high accuracy in differentiating large quantities is based on the adaptive ability of wild rodents to capture subtle changes in their environment. We suggest that the striped field mouse may be a powerful model species to develop advanced cognitive tests for comparative studies of numerical competence in animals and for understanding evolutionary roots of quantity processing.

Impact of stimulus format and reward value on quantity discrimination in capuchin and squirrel monkeys

Quantity discrimination abilities are seen in a diverse range of species with similarities in performance patterns, suggesting common underlying cognitive mechanisms. However, methodological factors that impact performance make it difficult to draw broad phylogenetic comparisons of numerical cognition across studies. For example, some Old World monkeys selected a higher quantity stimulus more frequently when choosing between inedible (pebbles) than edible (food) stimuli. In Experiment 1 we presented brown capuchin (Cebus [Sapajus] paella) and squirrel monkeys (Saimiri sciureus) with the same two-choice quantity discrimination task in three different stimulus conditions: edible, inedible, and edible replaced (in which choice stimuli were food items that stood in for the same quantity of food items that were given as a reward). Unlike Old World monkeys, capuchins selected the higher quantity stimulus more in the edible condition and squirrel monkeys showed generally poor performance across all stimulus types. Performance patterns suggested that differences in subjective reward value might motivate differences in choice behavior between and within species. In Experiment 2 we manipulated the subjective reinforcement value of the reward by varying reward type and delay to reinforcement and found that delay to reinforcement had no impact on choice behavior, while increasing the value of the reward significantly improved performance by both species. The results of this study indicate that species presented with identical tasks may respond differently to methodological factors such as stimulus and reward types, resulting in significant differences in choice behavior that may lead to spurious suggestions of species differences in cognitive abilities.

Capuchin monkeys (Cebus apella) treat small and large numbers of items similarly during a relative quantity judgment task

A key issue in understanding the evolutionary and developmental emergence of numerical cognition is to learn what mechanism(s) support perception and representation of quantitative information. Two such systems have been proposed, one for dealing with approximate representation of sets of items across an extended numerical range and another for highly precise representation of only small numbers of items. Evidence for the first system is abundant across species and in many tests with human adults and children, whereas the second system is primarily evident in research with children and in some tests with non-human animals. A recent paper (Choo & Franconeri, Psychonomic Bulletin & Review, 21, 93-99, 2014) with adult humans also reported "superprecise" representation of small sets of items in comparison to large sets of items, which would provide more support for the presence of a second system in human adults. We first presented capuchin monkeys with a test similar to that of Choo and Franconeri in which small or large sets with the same ratios had to be discriminated. We then presented the same monkeys with an expanded range of comparisons in the small number range (all comparisons of 1-9 items) and the large number range (all comparisons of 10-90 items in 10-item increments). Capuchin monkeys showed no increased precision for small over large sets in making these discriminations in either experiment. These data indicate a difference in the performance of monkeys to that of adult humans, and specifically that monkeys do not show improved discrimination performance for small sets relative to large sets when the relative numerical differences are held constant.

Numerical abilities in fish: A methodological review

The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish-spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied.

Intuitive probabilistic inference in capuchin monkeys

The ability to reason about probabilities has ecological relevance for many species. Recent research has shown that both preverbal infants and non-human great apes can make predictions about single-item samples randomly drawn from populations by reasoning about proportions. To further explore the evolutionary origins of this ability, we conducted the first investigation of probabilistic inference in a monkey species (capuchins; Sapajus spp.). Across four experiments, capuchins (N = 19) were presented with two populations of food items that differed in their relative distribution of preferred and non-preferred items, such that one population was more likely to yield a preferred item. In each trial, capuchins had to select between hidden single-item samples randomly drawn from each population. In Experiment 1 each population was homogeneous so reasoning about proportions was not required; Experiments 2-3 replicated previous probabilistic reasoning research with infants and apes; and Experiment 4 was a novel condition untested in other species, providing an important extension to previous work. Results revealed that at least some capuchins were able to make probabilistic inferences via reasoning about proportions as opposed to simpler quantity heuristics. Performance was relatively poor in Experiment 4, so the possibility remains that capuchins may use quantity-based heuristics in some situations, though further work is required to confirm this. Interestingly, performance was not at ceiling in Experiment 1, which did not involve reasoning about proportions, but did involve sampling. This suggests that the sampling task posed demands in addition to reasoning about proportions, possibly related to inhibitory control, working memory, and/or knowledge of object permanence.

Self-control assessments of capuchin monkeys with the rotating tray task and the accumulation task

Recent studies of delay of gratification in capuchin monkeys using a rotating tray (RT) task have shown improved self-control performance in these animals in comparison to the accumulation (AC) task. In this study, we investigated whether this improvement resulted from the difference in methods between the rotating tray task and previous tests, or whether it was the result of greater overall experience with delay of gratification tasks. Experiment 1 produced similar performance levels by capuchins monkeys in the RT and AC tasks when identical reward and temporal parameters were used. Experiment 2 demonstrated a similar result using reward amounts that were more similar to previous AC experiments with these monkeys. In Experiment 3, monkeys performed multiple versions of the AC task with varied reward and temporal parameters. Their self-control behavior was found to be dependent on the overall delay to reward consumption, rather than the overall reward amount ultimately consumed. These findings indicate that these capuchin monkeys' self-control capacities were more likely to have improved across studies because of the greater experience they had with delay of gratification tasks. Experiment 4 and Experiment 5 tested new, task-naïve monkeys on both tasks, finding more limited evidence of self-control, and no evidence that one task was more beneficial than the other in promoting self-control. The results of this study suggest that future testing of this kind should focus on temporal parameters and reward magnitude parameters to establish accurate measures of delay of gratification capacity and development in this species and perhaps others.

Abstract numerical discrimination learning in rats

In this study, we examined rats' discrimination learning of the numerical ordering positions of objects. In Experiments 1 and 2, five out of seven rats successfully learned to respond to the third of six identical objects in a row and showed reliable transfer of this discrimination to novel stimuli after being trained with three different training stimuli. In Experiment 3, the three rats from Experiment 2 continued to be trained to respond to the third object in an object array, which included an odd object that needed to be excluded when identifying the target third object. All three rats acquired this selective-counting task of specific stimuli, and two rats showed reliable transfer of this selective-counting performance to test sets of novel stimuli. In Experiment 4, the three rats from Experiment 3 quickly learned to respond to the third stimulus in object rows consisting of either six identical or six different objects. These results offer strong evidence for abstract numerical discrimination learning in rats.

Use of ordinal information by fish

Mammals and birds can process ordinal numerical information which can be used, for instance, for recognising an object on the basis of its position in a sequence of similar objects. Recent studies have shown that teleost fish possess numerical abilities comparable to those of other vertebrates, but it is unknown if they can also learn ordinal numerical relations. Guppies (Poecilia reticulata) learned to recognise the 3^rd feeder in a row of 8 identical ones even when inter-feeder distance and feeder positions were varied among trials to prevent the use of any spatial information. To assess whether guppies spontaneously use ordinal or spatial information when both are simultaneously available, fish were then trained with constant feeder positions and inter-feeder distance. In probe trials where these two sources of information were contrasted, the subjects selected the correct ordinal position significantly more often than the original spatial position, indicating that the former was preferentially encoded during training. Finally, a comparison between subjects trained on the 3^rd and the 5^th position revealed that guppies can also learn the latter discrimination, but the larger error rate observed in this case suggests that 5 is close to the upper limit of discrimination in guppies.

Non-visual numerical discrimination in a blind cavefish (Phreatichthys andruzzii)

Over a decade of comparative studies, researchers have found that rudimentary numerical abilities are widespread among vertebrates. While experiments in mammals and birds have employed a variety of stimuli (visual, auditory and tactile), all fish studies involved visual stimuli and it is unknown whether fish can process numbers in other sensory modalities. To fill this gap, we studied numerical abilities in Phreatichthys andruzzii, a blind cave-dwelling species that evolved in the phreatic layer of the Somalia desert. Fish were trained to receive a food reward to discriminate between two groups of objects placed in opposite positions of their home tank. In Experiment 1, subjects learned to discriminate between two and six objects, with stimuli not controlled for non-numerical continuous variables that co-vary with numbers, such as total area occupied by stimuli or density. In Experiment 2, the discrimination was two versus four, with half of the stimuli controlled for continuous quantities and half not controlled for continuous quantities. The subjects discriminated only the latter condition, indicating that they spontaneously used non-numerical information, as other vertebrates tested in similar experiments. In Experiments 3 and 4, cavefish trained from the beginning only with stimuli controlled for continuous quantities proved able to learn the discrimination of quantities based on the sole numerical information. However, their numerical acuity was lower than that reported in other teleost fish tested with visual stimuli.

The use of proportion by young domestic chicks (Gallus gallus)

We investigated whether 4-day-old domestic chicks can discriminate proportions. Chicks were trained to respond, via food reinforcement, to one of the two stimuli, each characterized by different proportions of red and green areas (¼ vs. ¾). In Experiment 1, chicks approached the proportion associated with food, even if at test the spatial dispositions of the two areas were novel. In Experiment 2, chicks responded on the basis of proportion even when the testing stimuli were of enlarged dimensions, creating a conflict between the absolute positive area experienced during training and the relative proportion of the two areas. However, chicks could have responded on the basis of the overall colour (red or green) of the figures rather than proportion per se. To control for this objection, in Experiment 3, we used new pairs of testing stimuli, each depicting a different number of small squares on a white background (i.e. 1 green and 3 red vs. 3 green and 1 red or 5 green and 15 red vs. 5 red and 15 green). Chicks were again able to respond to the correct proportion, showing they discriminated on the basis of proportion of continuous quantities and not on the basis of the prevalent colour or on the absolute amount of it. Data indicate that chicks can track continuous quantities through various manipulations, suggesting that proportions are information that can be processed by very young animals.

Numerical discrimination by frogs (Bombina orientalis)

Evidence has been reported for quantity discrimination in mammals and birds and, to a lesser extent, fish and amphibians. For the latter species, however, whether quantity discrimination would reflect sensitivity to number or to the continuous physical variables that covary with number is unclear. Here we reported a series of experiments with frogs (Bombina orientalis) tested in free-choice experiments for their preferences for different amounts of preys (Tenebrio molitor larvae) with systematic controls for variables such as surface area, volume, weight, and movement. Frogs showed quantity discrimination in the range of both small (1 vs. 2, 2 vs. 3, but not 3 vs. 4) and large numerousness (3 vs. 6, 4 vs. 8, but not 4 vs. 6), with clear evidence of being able to discriminate numerousness even when continuous physical variables were controlled for in the case of small numerousness (i.e., 1 vs. 2), whereas in the case of large numerousness it remains unclear whether the number or surface areas were dominant. We suggested that task demands are likely to be responsible for the activation of different systems for small and large numerousness and for their relative susceptibility to quantitative stimulus variables.

Lateralized mechanisms for encoding of object. Behavioral evidence from an animal model: the domestic chick (Gallus gallus)

In our previous research we reported a leftward-asymmetry in domestic chicks required to identify a target element, on the basis of its ordinal position, in a series of identical elements. Here we re-coded behavioral data collected in previous studies from chicks tested in a task involving a different kind of numerical ability, to study lateralization in dealing with an arithmetic task. Chicks were reared with a set of identical objects representing artificial social companions. On day 4, chicks underwent a free-choice test in which two sets, each composed of a different number of identical objects (5 vs.10 or 6 vs. 9, Experiment 1), were hidden behind two opaque screens placed in front of the chick, one on the left and one on the right side. Objects disappeared, one by one, behind either screen, so that, for example, one screen occluded 5 objects and the other 10 objects. The left-right position of the larger set was counterbalanced between trials. Results show that chicks, in the attempt to rejoin the set with the higher number of social companions, performed better when this was located to the right. However, when the number of elements in the two sets was identical (2 vs. 2, in Experiment 2) and they differed only in the coloration of the objects, this bias was not observed, suggesting a predisposition to map the numerical magnitude from left to right. Future studies should be devoted to the direct investigation of this phenomenon, possibly employing an identical number of mono-chromatic imprinting stimuli in both conditions involving a numerical discrimination and conditions not involving any numerosity difference.

Transfer of a serial representation between two distinct tasks by rhesus macaques

Do animals form task-specific representations, or do those representations take a general form that can be applied to qualitatively different tasks? Rhesus monkeys (Macaca mulatta) learned the ordering of stimulus lists using two different serial tasks, in order to test whether prior experience in each task could be transfered to the other, enhancing performance. The simultaneous chaining paradigm delivered rewards only after subjects responded in the correct order to all stimuli displayed on a touch sensitive video monitor. The transitive inference paradigm presented pairs of items and delivered rewards when subjects selected the item with the lower ordinal rank. After learning a list in one paradigm, subjects' knowledge of that list was tested using the other paradigm. Performance was enhanced from the very start of transfer training. Transitive inference performance was characterized by 'symbolic distance effects,' whereby the ordinal distance between stimuli in the implied list ordering was strongly predictive of the probability of a correct response. The patterns of error displayed by subjects in both tasks were best explained by a spatially coded representation of list items, regardless of which task was used to learn the list. Our analysis permits properties of this representation to be investigated without the confound of verbal reasoning.

Numerical abstraction in young domestic chicks (Gallus gallus)

In a variety of circumstances animals can represent numerical values per se, although it is unclear how salient numbers are relative to non-numerical properties. The question is then: are numbers intrinsically distinguished or are they processed as a last resort only when no other properties differentiate stimuli? The last resort hypothesis is supported by findings pertaining to animal studies characterized by extensive training procedures. Animals may, nevertheless, spontaneously and routinely discriminate numerical attributes in their natural habitat, but data available on spontaneous numerical competence usually emerge from studies not disentangling numerical from quantitative cues. In the study being outlined here, we tested animals' discrimination of a large number of elements utilizing a paradigm that did not require any training procedures. During rearing, newborn chicks were presented with two stimuli, each characterized by a different number of heterogeneous (for colour, size and shape) elements and food was found in proximity of one of the two stimuli. At testing 3 day-old chicks were presented with stimuli depicting novel elements (for colour, size and shape) representing either the numerosity associated or not associated with food. The chicks approached the number associated with food in the 5vs.10 and 10vs.20 comparisons both when quantitative cues were unavailable (stimuli were of random sizes) or being controlled. The findings emerging from the study support the hypothesis that numbers are salient information promptly processed even by very young animals.

Inherently Analog Quantity Representations in Olive Baboons (Papio anubis)

Strong evidence indicates that non-human primates possess a numerical representation system, but the inherent nature of that system is still debated. Two cognitive mechanisms have been proposed to account for non-human primate numerical performance: (1) a discrete object-file system limited to quantities <4, and (2) an analog system which represents quantities comparatively but is limited by the ratio between two quantities. To test the underlying nature of non-human primate quantification, we asked eight experiment-naive olive baboons (Papio anubis) to discriminate between number pairs containing small (<4), large (>4), or span (small vs. large) numbers of food items presented simultaneously or sequentially. The prediction from the object-file hypothesis is that baboons will only accurately choose the larger quantity in small pairs, but not large or span pairs. Conversely, the analog system predicts that baboons will be successful with all numbers, and that success will be dependent on numerical ratio. We found that baboons successfully discriminated all pair types at above chance levels. In addition, performance significantly correlated with the ratio between the numerical values. Although performance was better for simultaneous trials than sequential trials, evidence favoring analog numerical representation emerged from both conditions, and was present even in the first exposure to number pairs. Together, these data favor the interpretation that a single, coherent analog representation system underlies spontaneous quantitative abilities in primates.

1 < 2 and 2 < 3: non-linguistic appreciations of numerical order

Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

Implicit and explicit categorization: a tale of four species

Categorization is essential for survival, and it is a widely studied cognitive adaptation in humans and animals. An influential neuroscience perspective differentiates in humans an explicit, rule-based categorization system from an implicit system that slowly associates response outputs to different regions of perceptual space. This perspective is being extended to study categorization in other vertebrate species, using category tasks that have a one-dimensional, rule-based solution or a two-dimensional, information-integration solution. Humans, macaques, and capuchin monkeys strongly dimensionalize perceptual stimuli and learn rule-based tasks more quickly. In sharp contrast, pigeons learn these two tasks equally quickly. Pigeons represent a cognitive system in which the commitment to dimensional analysis and category rules was not strongly made. Their results may reveal the character of the ancestral vertebrate categorization system from which that of primates emerged. The primate results establish continuity with human cognition, suggesting that nonhuman primates share aspects of humans' capacity for explicit cognition. The emergence of dimensional analysis and rule learning could have been an important step in primates' cognitive evolution.

Sequential responding and planning in capuchin monkeys (Cebus apella)

Previous experiments have assessed planning during sequential responding to computer generated stimuli by Old World nonhuman primates including chimpanzees and rhesus macaques. However, no such assessment has been made with a New World primate species. Capuchin monkeys (Cebus apella) are an interesting test case for assessing the distribution of cognitive processes in the Order Primates because they sometimes show proficiency in tasks also mastered by apes and Old World monkeys, but in other cases fail to match the proficiency of those other species. In two experiments, eight capuchin monkeys selected five arbitrary stimuli in distinct locations on a computer monitor in a learned sequence. In Experiment 1, shift trials occurred in which the second and third stimuli were transposed when the first stimulus was selected by the animal. In Experiment 2, mask trials occurred in which all remaining stimuli were masked after the monkey selected the first stimulus. Monkeys made more mistakes on trials in which the locations of the second and third stimuli were interchanged than on trials in which locations were not interchanged, suggesting they had already planned to select a location that no longer contained the correct stimulus. When mask trials occurred, monkeys performed at levels significantly better than chance, but their performance exceeded chance levels only for the first and the second selections on a trial. These data indicate that capuchin monkeys performed very similarly to chimpanzees and rhesus monkeys and appeared to plan their selection sequences during the computerized task, but only to a limited degree.

Bears "Count" Too: Quantity Estimation and Comparison in Black Bears (Ursus Americanus)

Studies of bear cognition are notably missing from the comparative record despite bears' large relative brain size and interesting status as generalist carnivores facing complex foraging challenges, but lacking complex social structures. We investigated the numerical abilities of three American black bears (Ursus Americanus) by presenting discrimination tasks on a touch-screen computer. One bear chose the larger of two arrays of dot stimuli, while two bears chose the smaller array of dots. On some trials the relative number of dots was congruent with the relative total area of the two arrays. On other trials number of dots was incongruent with area. All of the bears were above chance on trials of both types with static dots. Despite encountering greater difficulty with dots that moved within the arrays, one bear was able to discriminate numerically larger arrays of moving dots, and a subset of moving dots from within the larger array, even when area and number were incongruent. Thus, although the bears used area as a cue to guide responding, they were also able to use number as a cue. The pattern of performance was similar to that found previously with monkeys, and suggests that bears may also show other forms of sophisticated quantitative abilities.

Monkeys (macaca mulatta and cebus apella) and human adults and children (homo sapiens) compare subsets of moving stimuli based on numerosity

Two monkey species (Macaca mulatta and Cebus apella) and human children and adults judged the numerousness of two subsets of moving stimuli on a computer screen. Two sets of colored dots that varied in number and size were intermixed in an array in which all dots moved in random directions and speeds. Participants had to indicate which dot color was more numerous within the array. All species performed at high and comparable levels, including on trials in which the subset with the larger number of items had a smaller total area of coloration. This indicated a similarity across species to use the number of items in the subsets, and not dimensions such as area or volume, to guide decision making. Discrimination performance was constrained by the ratio between the subsets, consistent with other reports of numerousness judgments of stationary stimuli. These results indicate a similarity in numerical estimation ability for moving stimuli across primate species, and this capacity may be necessary for naturally occurring experiences in which moving stimuli must be summed.

Can nonhuman primates use tokens to represent and sum quantities?

It is unclear whether nonhuman animals can use physical tokens to flexibly represent various quantities by combining token values. Previous studies showed that chimpanzees (Pan troglodytes) and a macaque (Macaca mulatta) were only partly successful in tests involving sets of different-looking food containers representing different food quantities, while some capuchin monkeys (Cebus apella) have shown greater success in tests involving sets of various concrete objects representing different food quantities. Some of the discrepancy in results between these studies may be attributed to the different methods used. In an effort to reconcile these discrepancies, we presented two primates species, chimpanzees and capuchin monkeys, with two token tasks. The critical test in each task involved summing the value of multiple tokens of different types to make accurate quantity judgments. We found that, using either method, individuals of both species learned to associate individual tokens with specific quantities, as well as successfully compare individual tokens to one another or to sets of visible food items. However, regardless of method, only a few individuals exhibited the capacity to sum multiple tokens of different types and then use those summed values to make an optimal response. This suggests that flexible combination of symbolic stimuli in quantity judgments tasks is within the abilities of chimpanzees and capuchins but does not characterize the majority of individuals. Furthermore, the results suggest the need to carefully examine specific methodological details that may promote or hinder such possible representation.

Information seeking by rhesus monkeys (Macaca mulatta) and capuchin monkeys (Cebus apella)

Animal metacognition is an active, growing research area, and one part of metacognition is flexible information-seeking behavior. In Roberts et al. (2009), pigeons failed an intuitive information-seeking task. They basically refused, despite multiple fostering experiments, to view a sample image before attempting to find its match. Roberts et al. concluded that pigeons' lack of an information-seeking capacity reflected their broader lack of metacognition. We report a striking species contrast to pigeons. Eight rhesus macaques and seven capuchin monkeys passed the Roberts et al. test of information seeking-often in their first testing session. Members of both primate species appreciated immediately the lack of information signaled by an occluded sample, and the need for an information-seeking response to manage the situation. In subsequent testing, macaques demonstrated flexible/varied forms of information management. Capuchins did not. The research findings bear on the phylogenetic distribution of metacognition across the vertebrates, and on the underlying psychological requirements for metacognitive and information-seeking performances.

Can monkeys make investments based on maximized pay-off?

Animals can maximize benefits but it is not known if they adjust their investment according to expected pay-offs. We investigated whether monkeys can use different investment strategies in an exchange task. We tested eight capuchin monkeys (Cebus apella) and thirteen macaques (Macaca fascicularis, Macaca tonkeana) in an experiment where they could adapt their investment to the food amounts proposed by two different experimenters. One, the doubling partner, returned a reward that was twice the amount given by the subject, whereas the other, the fixed partner, always returned a constant amount regardless of the amount given. To maximize pay-offs, subjects should invest a maximal amount with the first partner and a minimal amount with the second. When tested with the fixed partner only, one third of monkeys learned to remove a maximal amount of food for immediate consumption before investing a minimal one. With both partners, most subjects failed to maximize pay-offs by using different decision rules with each partner' quality. A single Tonkean macaque succeeded in investing a maximal amount to one experimenter and a minimal amount to the other. The fact that only one of over 21 subjects learned to maximize benefits in adapting investment according to experimenters' quality indicates that such a task is difficult for monkeys, albeit not impossible.

Numerical rule-learning in ring-tailed lemurs (lemur catta)

We investigated numerical discrimination and numerical rule-learning in ring-tailed lemurs (Lemur catta). Two ring-tailed lemurs were trained to respond to two visual arrays, each of which contained between one and four elements, in numerically ascending order. In Experiment 1, lemurs were trained with 36 exemplars of each of the numerosities 1-4 and then showed positive transfer to trial-unique novel exemplars of the values 1-4. In Experiments 2A and 2B, lemurs were tested on their ability to transfer an ascending numerical rule from the values 1-4 to novel values 5-9. Both lemurs successfully ordered the novel values with above chance accuracy. Accuracy was modulated by the ratio between the two numerical values suggesting that lemurs accessed the approximate number system when performing the task.

The psychological organization of "uncertainty" responses and "middle" responses: a dissociation in capuchin monkeys (Cebus apella)

Some studies of nonhuman animals' metacognitive capacity encourage competing low-level, behavioral descriptions of trial-decline responses by animals in uncertainty-monitoring tasks. To evaluate the force of these behavioral descriptions, the authors presented 6 capuchin monkeys (Cebus apella) with 2 density discrimination tasks between sparse and dense stimuli. In one task, difficult trials with stimuli near the middle of the density continuum could be declined through an "uncertainty" response. In the other task, making a "middle" response to the same stimuli was rewarded. In Experiment 1, capuchins essentially did not use the uncertainty response, but they did use the middle response. In Experiment 2, the authors replicated this result with 5 of 6 monkeys while equating the overall pace and reinforcement structure of the 2 tasks, although 1 monkey also showed appropriate use of the uncertainty response. These results challenge a purely associative interpretation of some uncertainty-monitoring performances by monkeys while sharpening the theoretical question concerning the nature of the psychological signal that occasions uncertainty responses.

Arithmetic in newborn chicks

Newly hatched domestic chicks were reared with five identical objects. On days 3 or 4, chicks underwent free-choice tests in which sets of three and two of the five original objects disappeared (either simultaneously or one by one), each behind one of two opaque identical screens. Chicks spontaneously inspected the screen occluding the larger set (experiment 1). Results were confirmed under conditions controlling for continuous variables (total surface area or contour length; experiment 2). In the third experiment, after the initial disappearance of the two sets (first event, FE), some of the objects were visibly transferred, one by one, from one screen to the other (second event, SE). Thus, computation of a series of subsequent additions or subtractions of elements that appeared and disappeared, one by one, was needed in order to perform the task successfully. Chicks spontaneously chose the screen, hiding the larger number of elements at the end of the SE, irrespective of the directional cues provided by the initial (FE) and final (SE) displacements. Results suggest impressive proto-arithmetic capacities in the young and relatively inexperienced chicks of this precocial species.

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.

When in doubt, chimpanzees rely on estimates of past reward amounts

Many animals can repeatedly judge the larger of two sets of food items. However, it remains unclear as to what information might accrue regarding the relative rates of return from these repeated responses. Information about overall rates of return is, in fact, unnecessary to perform well at the task itself. However, if an uncertain situation arose, such as when the quantity in one set was unknown, that information would be useful in determining whether to select a known quantity or an unknown quantity. We gave chimpanzees this test. First, they made multiple judgements between two visible food sets that varied in the number of items across trials. Then, they were faced with the same combinations of set sizes, but only one set was revealed while the other remained unknown. Rather than using a specific quantity as a threshold for choosing the known or the unknown set, the chimpanzees' choice of the unknown set varied in relation to the rate of return from responses in the first phase (when both sets were known). This indicated that the chimpanzees' decisions in the face of uncertainty were guided by a sense of how well they were rewarded overall during the session.

Monkeys match and tally quantities across senses

We report here that monkeys can actively match the number of sounds they hear to the number of shapes they see and present the first evidence that monkeys sum over sounds and sights. In Experiment 1, two monkeys were trained to choose a simultaneous array of 1-9 squares that numerically matched a sample sequence of shapes or sounds. Monkeys numerically matched across (audio-visual) and within (visual-visual) modalities with equal accuracy and transferred to novel numerical values. In Experiment 2, monkeys presented with sample sequences of randomly ordered shapes or tones were able to choose an array of 2-9 squares that was the numerical sum of the shapes and sounds in the sample sequence. In both experiments, accuracy and reaction time depended on the ratio between the correct numerical match and incorrect choice. These findings suggest monkeys and humans share an abstract numerical code that can be divorced from the modality in which stimuli are first experienced.

Perception of Food Amounts by Chimpanzees Based on the Number, Size, Contour Length and Visibility of Items

Nonhuman animals reliably select the largest of two or more sets of discrete items, particularly if those items are food items. However, many studies of these numerousness judgments fail to control for confounds between amount of food e.g., mass or volume) and number of food items. Stimulus dimensions other than number of items also may play a role in how animals perceive sets and make choices. Four chimpanzees (Pan troglodytes) completed a variety of tasks that involved comparisons of food items (graham crackers) that varied in terms of their number, size, and orientation. In Experiment 1, chimpanzees chose between two alternative sets of visible cracker pieces. In Experiment 2, the experimenters presented one set of crackers in a vertical orientation (stacked) and the other in a horizontal orientation. In Experiment 3, the experimenters presented all food items one-at-a-time by dropping them into opaque containers. Chimpanzees succeeded overall in choosing the largest amount of food. They did not rely on number or contour length as cues when making these judgments but instead primarily responded to the total amount of food in the sets. However, some errors reflected choices of the set with the smaller total amount of food but the individually largest single food item. Thus, responses were not optimal because of biases that were not related to the total amount of food in the sets.

Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella)

Capuchin monkeys (Cebus apella) were presented with two sets of food items, identical in food type but differing in number. Animals selected one set and were permitted to consume their choice. Set sizes ranged from 1 to 6 items. In experiment 1, each set was uncovered and recovered before a response was made, and the monkeys selected the larger set at high levels. Experiment 2 presented sets that had both visible and nonvisible food items in them at the time of the response, thus requiring the monkeys to sum the total amount of food that was available. The monkeys again selected the larger set with no decrement in performance. Overall, the data indicate that capuchins, like other more extensively studied primate species in this area of research, are responsive to quantitative differences between sets. Capuchins succeed in making these quantity judgments when sets are nonvisible at choice time and when summation of items must be performed, thus demonstrating coordination of quantification skills and memory. Capuchins also inhibit responses to visible food items when those items are only part of an overall smaller quantity of food compared with a completely nonvisible set.

Quantity representation in children and rhesus monkeys: linear versus logarithmic scales

The performances of 4- and 5-year-olds and rhesus monkeys were compared using a computerized task for quantity assessment. Participants first learned two quantity anchor values and then responded to intermediate values by classifying them as similar to either the large anchor or the small anchor. Of primary interest was an assessment of where the point of subjective equality (PSE) occurred for each species across four different sets of anchors to determine whether the PSE occurred at the arithmetic mean or the geometric mean. Both species produced PSEs that were closer to the geometric mean for three of four anchor sets. This indicates that monkeys and children access either a logarithmic scale for quantity representation or a linear scale that is subject to scalar variability, both of which are consistent with Weber's law and representation of quantity that takes the form of analog magnitudes.

Food and token quantity discrimination in capuchin monkeys (Cebus apella)

Quantity discrimination is adaptive in a variety of ecological contexts and different taxa discriminate stimuli differing in numerousness, both in the wild and in laboratory settings. Quantity discrimination between object arrays has been suggested to be more demanding than between food arrays but, to our knowledge, the same paradigm has never been used to directly compare them. We investigated to what extent capuchin monkeys' relative numerousness judgments (RNJs) with food and token are alike. Tokens are inherently non-valuable objects that acquire an associative value upon exchange with the experimenter. Our aims were (1) to assess capuchins' RNJs with food (Experiment 1) and with tokens (Experiment 2) by presenting all the possible pair-wise choices between one to five items, and (2) to evaluate on which of the two proposed non-verbal mechanisms underlying quantity discrimination (analogue magnitude and object file system) capuchins relied upon. In both conditions capuchins reliably selected the larger amount of items, although their performance was higher with food than with tokens. The influence of the ratio between arrays on performance indicates that capuchins relied on the same system for numerical representation, namely analogue magnitude, regardless of the type of stimuli (food or tokens) and across both the small and large number ranges.

Capuchin monkeys (Cebus apella) succeed in a test of quantity conservation

Nonhuman animals demonstrate a number of impressive quantitative skills such as counting sets of items, comparing sets on the basis of the number of items or amount of material, and even responding to simple arithmetic manipulations. In this experiment, capuchin monkeys were presented with a computerized task designed to assess conservation of discrete quantity. Monkeys first were trained to select from two horizontal arrays of stimuli the one with the larger number of items. On some trials, after a correct selection there was no feedback but instead an additional manipulation of one of those arrays. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array but not the quantity of items in the array. In other cases, additional items were added to the initially smaller array so that it became quantitatively larger. Monkeys then made a second selection from the two arrays of items. Previous research had shown that rhesus monkeys (Macaca mulatta) succeeded with this task. However, there was no condition in that study in which items were added to the smaller array without increasing its quantity to a point where it became the new larger array. This new condition was added in the present experiment. Capuchin monkeys were sensitive to all of these manipulations, changing their selections when the manipulations changed which array contained the larger number of items but not when the manipulations changed the physical arrangement of items or increased the quantity in one array without also reversing which of the two arrays had more items. Therefore, capuchin monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the arrays. The data indicate that capuchins are sensitive to simply arithmetic manipulations that involve addition of items to arrays and also that they can conserve quantity.

Nonverbal estimation during numerosity judgements by adult humans

On an automated task, humans selected the larger of two sets of items, each created through the one-by-one addition of items. Participants repeated the alphabet out loud during trials so that they could not count the items. This manipulation disrupted counting without producing major effects on other cognitive capacities such as memory or attention, and performance of this experimental group was poorer than that of participants who counted the items. In Experiment 2, the size of individual items was varied, and performance remained stable when the larger numerical set contained a smaller total amount than the smaller numerical set (i.e., participants used numerical rather than nonnumerical quantity cues in making judgements). In Experiment 3, reports of the number of items in a single set showed scalar variability as accuracy decreased, and variability in responses increased with increases in true set size. These data indicate a mechanism for the approximate representation of numerosity in adult humans that might be shared with nonhuman animals.

The role of reference points in ordinal numerical comparisons by rhesus macaques (Macaca mulatta)

Two experiments examined ordinal numerical knowledge in rhesus macaques (Macaca mulatta). Experiment 1 replicated the finding (E. M. Brannon & H. S. Terrace, 2000) that monkeys trained to respond in descending numerical order (4-->3-->2-->1) did not generalize the descending rule to the novel values 5-9 in contrast to monkeys trained to respond in ascending order. Experiment 2 examined whether the failure to generalize a descending rule was due to the direction of the training sequence or to the specific values used in the training sequence. Results implicated 3 factors that characterize a monkey's numerical comparison process: Weber's law, knowledge of ordinal direction, and a comparison of each value in a test pair with the reference point established by the first value of the training sequence.

Grey Parrot (Psittacus erithacus) numerical abilities: addition and further experiments on a zero-like concept

A Grey parrot (Psittacus erithacus), able to quantify 6 or fewer item sets (including heterogeneous subsets) by using English labels (I. M. Pepperberg, 1994), was tested on addition of quantities involving 0-6. He was, without explicit training, asked, "How many total X?" for 2 sequentially presented collections (e.g., of variously sized jelly beans or nuts) and required to answer with a vocal English number label. His accuracy suggested (a) that his addition abilities are comparable to those of nonhuman primates and young children, (b) some limits as to his correlation of "none" and the concept of zero, and (c) a possible counting-like strategy for the quantity 5.

Rhesus monkeys (Macaca mulatta) succeed on a computerized test designed to assess conservation of discrete quantity

Conservation of quantity occurs through recognition that changes in the physical arrangement of a set of items do not change the quantity of items in that set. Rhesus monkeys (Macaca mulatta) were presented with a computerized quantity judgment task. Monkeys were rewarded for selecting the greater quantity of items in one of two horizontal arrays of items on the screen. On some trials, after a correct selection, no reward was given but one of the arrays was manipulated. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array without changing the quantity of items in the array. In other cases, additional items were added to the initially smaller array so that it became quantitatively larger. Monkeys then made another selection from the two rows of items. Monkeys were sensitive to these manipulations, changing their selections when the number of items in the rows changed but not when the arrangement only was changed. Therefore, monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the sets.

A common representational system governed by Weber's law: nonverbal numerical similarity judgments in 6-year-olds and rhesus macaques

This study compared nonverbal numerical processing in 6-year-olds with that in nonhuman animals using a numerical bisection task. In the study, 16 children were trained on a delayed match-to-sample paradigm to match exemplars of two anchor numerosities. Children were then required to indicate whether a sample intermediate to the anchor values was closer to the small anchor value or the large anchor value. For two sets of anchor values with the same ratio, the probability of choosing the larger anchor value increased systematically with sample number, and the psychometric functions superimposed when plotted on a logarithmic scale. The psychometric functions produced by the children also superimposed with the psychometric functions produced by rhesus monkeys in an analogous previous experiment. These examples of superimposition demonstrate that nonverbal number representations, even in children who have acquired the verbal counting system, are modulated by Weber's law.