Understanding of the concept of numerically "less" by bottlenose dolphins (Tursiops truncatus)

The relative contribution of acoustic signals versus movement cues in group coordination and collective decision-making

To benefit from group living, individuals need to maintain cohesion and coordinate their activities. Effective communication thus becomes critical, facilitating rapid coordination of behaviours and reducing consensus costs when group members have differing needs and information. In many bird and mammal species, collective decisions rely on acoustic signals in some contexts but on movement cues in others. Yet, to date, there is no clear conceptual framework that predicts when decisions should evolve to be based on acoustic signals versus movement cues. Here, we first review how acoustic signals and movement cues are used for coordinating activities. We then outline how information masking, discrimination ability (Weber's Law) and encoding limitations, as well as trade-offs between these, can identify which types of collective behaviours likely rely on acoustic signals or movement cues. Specifically, our framework proposes that behaviours involving the timing of events or expression of specific actions should rely more on acoustic signals, whereas decisions involving complex choices with multiple options (e.g. direction and destination) should generally use movement cues because sounds are more vulnerable to information masking and Weber's Law effects. We then discuss potential future avenues of enquiry, including multimodal communication and collective decision-making by mixed-species animal groups. This article is part of the theme issue 'The power of sound: unravelling how acoustic communication shapes group dynamic'.

Zebrafish excel in number discrimination under an operant conditioning paradigm

Numerical discrimination is widespread in vertebrates, but this capacity varies enormously between the different species examined. The guppy (Poecilia reticulata), the only teleost examined following procedures that allow a comparison with the other vertebrates, outperforms amphibians, reptiles and many warm-blooded vertebrates, but it is unclear whether this is a feature shared with the other teleosts or represents a peculiarity of this species. We trained zebrafish (Danio rerio) to discriminate between numbers differing by one unit, varying task difficulty from 2 versus 3 to 5 versus 6 items. Non-numerical variables that covary with number, such as density or area, did not affect performance. Most fish reached learning criterion on all tasks up to 4 versus 5 discrimination with no sex difference in accuracy. Although no individual reached learning criterion in the 5 versus 6 task, performance was significant at the group level, suggesting that this may represent the discrimination threshold for zebrafish. Numerosity discrimination abilities of zebrafish compare to those of guppy, being higher than in some warm-blooded vertebrates, such as dogs, horses and domestic fowl, though lower than in parrots, corvids and primates. Learning rate was similar in a control group trained to discriminate between different-sized shapes, but zebrafish were slightly more accurate when discriminating areas than numbers and males were more accurate than females. At the end of the experiment, fish trained on numbers and controls trained on areas generalized to the reciprocal set of stimuli, indicating they had used a relational strategy to solve these tasks.

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.

Automated Operant Conditioning Devices for Fish. Do They Work?

Simple Summary

Automated training devices are commonly used for investigating learning, memory, and other cognitive functions in warm-blood vertebrates, whereas manual training procedures are the standard in fish and other lower vertebrates, thus limiting comparison among species. Here, we directly compared the two different approaches to training in guppies (Poecilia reticulata) by administering numerical discrimination tasks of increasing difficulty. The automated device group showed a much lower performance compared to the traditionally-trained group. We modified some features of the automated device in order to improve its efficiency. Increasing the decision time or inter-trial interval was ineffective, while reducing the cognitive load and allowing subjects to reside in the test tank improved numerical performance. Yet, in no case did subjects match the performance of traditionally-trained subjects, suggesting that small teleosts may be limited in their capacity to cope with operant conditioning devices.

Abstract

The growing use of teleosts in comparative cognition and in neurobiological research has prompted many researchers to develop automated conditioning devices for fish. These techniques can make research less expensive and fully comparable with research on warm-blooded species, in which automated devices have been used for more than a century. Tested with a recently developed automated device, guppies (Poecilia reticulata) easily performed 80 reinforced trials per session, exceeding 80% accuracy in color or shape discrimination tasks after only 3–4 training session, though they exhibit unexpectedly poor performance in numerical discrimination tasks. As several pieces of evidence indicate, guppies possess excellent numerical abilities. In the first part of this study, we benchmarked the automated training device with a standard manual training procedure by administering the same set of tasks, which consisted of numerical discriminations of increasing difficulty. All manually-trained guppies quickly learned the easiest discriminations and a substantial percentage learned the more difficult ones, such as 4 vs. 5 items. No fish trained with the automated conditioning device reached the learning criterion for even the easiest discriminations. In the second part of the study, we introduced a series of modifications to the conditioning chamber and to the procedure in an attempt to improve its efficiency. Increasing the decision time, inter-trial interval, or visibility of the stimuli did not produce an appreciable improvement. Reducing the cognitive load of the task by training subjects first to use the device with shape and color discriminations, significantly improved their numerical performance. Allowing the subjects to reside in the test chamber, which likely reduced the amount of attentional resources subtracted to task execution, also led to an improvement, although in no case did subjects match the performance of fish trained with the standard procedure. Our results highlight limitations in the capacity of small laboratory teleosts to cope with operant conditioning automation that was not observed in laboratory mammals and birds and that currently prevent an easy and straightforward comparison with other vertebrates.

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.

Surpassing the subitizing threshold: appetitive–aversive conditioning improves discrimination of numerosities in honeybees

Animals including humans, fish and honeybees have demonstrated a quantity discrimination threshold at four objects, often known as subitizing elements. Discrimination between numerosities at or above the subitizing range is considered a complex capacity. In the current study, we trained and tested two groups of bees on their ability to differentiate between quantities (4 versus 5 through to 4 versus 8) when trained with different conditioning procedures. Bees trained with appetitive (reward) differential conditioning demonstrated no significant learning of this task, and limited discrimination above the subitizing range. In contrast, bees trained using appetitive–aversive (reward–aversion) differential conditioning demonstrated significant learning and subsequent discrimination of all tested comparisons from 4 versus 5 to 4 versus 8. Our results show conditioning procedure is vital to performance on numerically challenging tasks, and may inform future research on numerical abilities in other animals.

An assessment of touchscreens for testing primate food preferences and valuations

Typically, animals' food preferences are tested manually, which can be both time-consuming and vulnerable to experimenter biases. Given the utility of ascertaining animals' food preferences for research and husbandry protocols, developing a quick, reliable, and flexible paradigm would be valuable for expediting many research protocols. Therefore, we evaluated the efficacy of using a touchscreen interface to test nonhuman primates' food preferences and valuations, adapting previously validated manual methods. We tested a nonhuman primate subject with four foods (carrot, cucumber, grape, and turnip). Preference testing followed a pairwise forced choice protocol with pairs of food images presented on a touchscreen: The subject was rewarded with whichever food was selected. All six possible pairwise combinations were presented, with 90 trials per pairing. Second, we measured how hard the subject was willing to work to obtain each of the four foods, allowing us to generate demand curves. For this phase, a single image of a food item was presented on the touchscreen that the subject had to select in order to receive the food, and the number of selections required increased following a quarter-log scale, with ten trials per cost level (1, 2, 3, 6, 10, and 18). These methods allowed us to ascertain the subject's relative preferences and valuations of the four foods. The success of this touchscreen protocol for testing the subject's food preferences, from both a practical and a theoretical standpoint, suggests that the protocol should be further validated with other foods with this subject, with other subjects, and with other test items.

Inference by exclusion in the red-tailed black cockatoo (Calyptorhynchus banksii)

Inference by exclusion is the ability to select a given option by excluding the others. When designed appropriately, tests of this ability can reveal choices that cannot be explained by associative processes. Over the past decade, exclusion reasoning has been explored in several non-human taxonomic groups, including birds, mainly in Corvids and Parrots. To increase our understanding of the taxonomic distribution of exclusion reasoning and, therefore, its evolution, we investigated exclusion performances in red-tailed black cockatoos (Calyptorhynchus banksii), an Australian relative of the Goffin cockatoo (Cacatua goffini), using a food-finding task. Cockatoos were required to find a food item hidden in 1 of the 2 experimenter's hands. Following training sessions in which they reliably selected the closed baited hand they had just been shown open, each individual was tested on 4 different conditions. Critical to demonstrating exclusion reasoning was the condition in which they were shown the empty hand and then offered a choice of both closed hands. The performance of all birds was above chance on all experimental conditions but not on an olfactory and/or cuing control condition. The results suggest that the birds might be able to infer by exclusion, although an explanation based on rule learning cannot be excluded. This first experiment in red-tailed black cockatoo highlights the potential of this species as a model to study avian cognition and paves the pathway for future investigations.

Numerical ordering of zero in honey bees

Some vertebrates demonstrate complex numerosity concepts-including addition, sequential ordering of numbers, or even the concept of zero-but whether an insect can develop an understanding for such concepts remains unknown. We trained individual honey bees to the numerical concepts of "greater than" or "less than" using stimuli containing one to six elemental features. Bees could subsequently extrapolate the concept of less than to order zero numerosity at the lower end of the numerical continuum. Bees demonstrated an understanding that parallels animals such as the African grey parrot, nonhuman primates, and even preschool children.

Is There Really an Evolved Capacity for Number?

Humans and other species have biologically endowed abilities for discriminating quantities. A widely accepted view sees such abilities as an evolved capacity specific for number and arithmetic. This view, however, is based on an implicit teleological rationale, builds on inaccurate conceptions of biological evolution, downplays human data from non-industrialized cultures, overinterprets results from trained animals, and is enabled by loose terminology that facilitates teleological argumentation. A distinction between quantical (e.g., quantity discrimination) and numerical (exact, symbolic) cognition is needed: quantical cognition provides biologically evolved preconditions for numerical cognition but it does not scale up to number and arithmetic, which require cultural mediation. The argument has implications for debates about the origins of other special capacities - geometry, music, art, and language.

Thinking chickens: a review of cognition, emotion, and behavior in the domestic chicken

Domestic chickens are members of an order, Aves, which has been the focus of a revolution in our understanding of neuroanatomical, cognitive, and social complexity. At least some birds are now known to be on par with many mammals in terms of their level of intelligence, emotional sophistication, and social interaction. Yet, views of chickens have largely remained unrevised by this new evidence. In this paper, I examine the peer-reviewed scientific data on the leading edge of cognition, emotions, personality, and sociality in chickens, exploring such areas as self-awareness, cognitive bias, social learning and self-control, and comparing their abilities in these areas with other birds and other vertebrates, particularly mammals. My overall conclusion is that chickens are just as cognitively, emotionally and socially complex as most other birds and mammals in many areas, and that there is a need for further noninvasive comparative behavioral research with chickens as well as a re-framing of current views about their intelligence.

An emergentist perspective on the origin of number sense

The finding that human infants and many other animal species are sensitive to numerical quantity has been widely interpreted as evidence for evolved, biologically determined numerical capacities across unrelated species, thereby supporting a 'nativist' stance on the origin of number sense. Here, we tackle this issue within the 'emergentist' perspective provided by artificial neural network models, and we build on computer simulations to discuss two different approaches to think about the innateness of number sense. The first, illustrated by artificial life simulations, shows that numerical abilities can be supported by domain-specific representations emerging from evolutionary pressure. The second assumes that numerical representations need not be genetically pre-determined but can emerge from the interplay between innate architectural constraints and domain-general learning mechanisms, instantiated in deep learning simulations. We show that deep neural networks endowed with basic visuospatial processing exhibit a remarkable performance in numerosity discrimination before any experience-dependent learning, whereas unsupervised sensory experience with visual sets leads to subsequent improvement of number acuity and reduces the influence of continuous visual cues. The emergent neuronal code for numbers in the model includes both numerosity-sensitive (summation coding) and numerosity-selective response profiles, closely mirroring those found in monkey intraparietal neurons. We conclude that a form of innatism based on architectural and learning biases is a fruitful approach to understanding the origin and development of number sense.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

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.

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.

Genomic and expression analyses of Tursiops truncatus T cell receptor gamma (TRG) and alpha/delta (TRA/TRD) loci reveal a similar basic public γδ repertoire in dolphin and human

BACKGROUND

The bottlenose dolphin (Tursiops truncatus) is a mammal that belongs to the Cetartiodactyla and have lived in marine ecosystems for nearly 60 millions years. Despite its popularity, our knowledge about its adaptive immunity and evolution is very limited. Furthermore, nothing is known about the genomics and evolution of dolphin antigen receptor immunity.

RESULTS

Here we report a evolutionary and expression study of Tursiops truncatus T cell receptor gamma (TRG) and alpha/delta (TRA/TRD) genes. We have identified in silico the TRG and TRA/TRD genes and analyzed the relevant mature transcripts in blood and in skin from four subjects. The dolphin TRG locus is the smallest and simplest of all mammalian loci as yet studied. It shows a genomic organization comprising two variable (V1 and V2), three joining (J1, J2 and J3) and a single constant (C), genes. Despite the fragmented nature of the genome assemblies, we deduced the TRA/TRD locus organization, with the recent TRDV1 subgroup genes duplications, as it is expected in artiodactyls. Expression analysis from blood of a subject allowed us to assign unambiguously eight TRAV genes to those annotated in the genomic sequence and to twelve new genes, belonging to five different subgroups. All transcripts were productive and no relevant biases towards TRAV-J rearrangements are observed. Blood and skin from four unrelated subjects expression data provide evidence for an unusual ratio of productive/unproductive transcripts which arise from the TRG V-J gene rearrangement and for a "public" gamma delta TR repertoire. The productive cDNA sequences, shared both in the same and in different individuals, include biases of the TRGV1 and TRGJ2 genes. The high frequency of TRGV1-J2/TRDV1- D1-J4 productive rearrangements in dolphins may represent an interesting oligo-clonal population comparable to that found in human with the TRGV9- JP/TRDV2-D-J T cells and in primates.

CONCLUSIONS

Although the features of the TRG and TRA/TRD loci organization reflect those of the so far examined artiodactyls, genomic results highlight in dolphin an unusually simple TRG locus. The cDNA analysis reveal productive TRA/TRD transcripts and unusual ratios of productive/unproductive TRG transcripts. Comparing multiple different individuals, evidence is found for a "public" gamma delta TCR repertoire thus suggesting that in dolphins as in human the gamma delta TCR repertoire is accompanied by selection for public gamma chain.

Quantification acuity in spontaneous shoaling decisions of three-spined sticklebacks

The ability to discriminate between different quantities is widespread throughout the animal kingdom, and the underlying mechanisms of quantity discrimination are currently intensely discussed. In contrast, questions elucidating the limits of quantity estimation received rather little attention so far. Here, we examined fine-tuned quantity estimation in the three-spined stickleback (Gasterosteus aculeatus) in a natural context, i.e. during shoaling decisions. Wild-caught focal fish were given the spontaneous choice between two shoals which differed in group size by 1 fish (0 vs. 1, 1 vs. 2, 2 vs. 3, 3 vs. 4, 4 vs. 5, 5 vs. 6 and 6 vs. 7), based on visual assessment. The results show that sticklebacks generally prefer to shoal with the larger group. They discriminated numerical contrasts up to 6 versus 7, equalling a numerical ratio of 0.86. Preference patterns followed Weber's law, i.e. decreased with increasing numerical ratio. This pattern was found across all numerical conditions as well as within the small number range (ranging from 1 vs. 2 to 3 vs. 4). The results suggest that wild-caught three-spined sticklebacks are spontaneously able (i.e. without prior learning) to detect subtle differences in shoal sizes. Further, they confirm findings of previous studies highlighting the contribution of the analogue magnitude system to quantity estimation in fishes.

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.

Quantitative relationships in delphinid neocortex

Possessing large brains and complex behavioral patterns, cetaceans are believed to be highly intelligent. Their brains, which are the largest in the Animal Kingdom and have enormous gyrification compared with terrestrial mammals, have long been of scientific interest. Few studies, however, report total number of brain cells in cetaceans, and even fewer have used unbiased counting methods. In this study, using stereological methods, we estimated the total number of cells in the neocortex of the long-finned pilot whale (Globicephala melas) brain. For the first time, we show that a species of dolphin has more neocortical neurons than any mammal studied to date including humans. These cell numbers are compared across various mammals with different brain sizes, and the function of possessing many neurons is discussed. We found that the long-finned pilot whale neocortex has approximately 37.2 × 10⁹ neurons, which is almost twice as many as humans, and 127 × 10⁹ glial cells. Thus, the absolute number of neurons in the human neocortex is not correlated with the superior cognitive abilities of humans (at least compared to cetaceans) as has previously been hypothesized. However, as neuron density in long-finned pilot whales is lower than that in humans, their higher cell number appears to be due to their larger brain. Accordingly, our findings make an important contribution to the ongoing debate over quantitative relationships in the mammalian brain.

Visual nesting of stimuli affects rhesus monkeys' (Macaca mulatta) quantity judgments in a bisection task

Nonhuman animals are highly proficient at judging relative quantities presented in a variety of formats, including visual, auditory, and even cross-modal formats. Performance typically is constrained by the ratio between sets, as would be expected under Weber's law and as is described in the approximate number system (ANS) hypothesis. In most cases, tests are designed to avoid any perceptual confusion for animals regarding the stimulus sets, but despite this, animals show some of the perceptual biases that humans show based on organization of stimuli. Here, we demonstrate an additional perceptual bias that emerges from the illusion of nested sets. When arrays of circles were presented on a computer screen and were to be classified as larger than or smaller than an established central value, rhesus monkeys (Macaca mulatta) underestimated quantities when circles were nested within each other. This matched a previous report with adult humans (Chesney & Gelman, Attention, Perception, & Psychophysics 24:1104-1113, 2012), indicating that macaques, like humans, show the pattern of biased perception predicted by ANS estimation. Although some macaques overcame this perceptual bias, demonstrating that they could come to view nested stimuli as individual elements to be included in the estimates of quantity used for classifying arrays, the majority of the monkeys showed the bias of underestimating nested arrays throughout the experiment.

Extensive training extends numerical abilities of guppies

Recent studies on animal mathematical abilities suggest that all vertebrates show comparable abilities when they are given spontaneous preference tests, such as selecting the larger number of food items, but that mammals and birds generally achieve much better performance than fish when tested with training procedures. At least part of these differences might be due to the fact that fish are usually trained with only one or two dozen trials while extensive training, sometimes with thousands of trials, is normally performed in studies of mammals and birds. To test this hypothesis, female guppies were trained on four consecutive numerical discriminations of increasing difficulty (from 2 vs. 3 to 5 vs. 6 items), with up to 120 trials with each discrimination. Five out of eight subjects discriminated all contrasts up to 4 versus 5 objects at levels significantly better than chance, a much higher limit than the 2 versus 3 limit previously reported in studies that provided fish with only short training sequences. Our findings indicate that the difference in numerical cognition between teleosts and warm-blooded vertebrates might be smaller than previously supposed.

Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals

A large body of experimental evidence shows that animals as diverse as mammals, birds, and fish are capable of processing numerical information. Considerable differences have been reported in some cases among species and a wide debate currently surrounds the issue of whether all vertebrates share the same numerical systems or not. Part of the problem is due to the fact that these studies often use different methods, a circumstance that potentially introduces confounding factors in a comparative analysis. In most studies, two main methodological approaches have been used: spontaneous choice tests and training procedures. The former approach consists of presenting to the subjects two groups of biologically-relevant stimuli (e.g., food items or social companions) differing in numerosity with the assumption that if they are able to discriminate between the two quantities, they are expected to spontaneously select the larger/smaller quantity. In the latter approach, subjects undergo extensive training in which some neutral stimuli (e.g., a quantity of dots) are associated with a reward and the capacity to learn a numerical rule is taken as evidence of numerical abilities. We review the literature on this topic, highlighting the relevance, and potential weaknesses in controlling confounding factors obtained with either approach.

Rhesus monkeys (Macaca mulatta) map number onto space

Humans map number onto space. However, the origins of this association, and particularly the degree to which it depends upon cultural experience, are not fully understood. Here we provide the first demonstration of a number-space mapping in a non-human primate. We trained four adult male rhesus macaques (Macaca mulatta) to select the fourth position from the bottom of a five-element vertical array. Monkeys maintained a preference to choose the fourth position through changes in the appearance, location, and spacing of the vertical array. We next asked whether monkeys show a spatially-oriented number mapping by testing their responses to the same five-element stimulus array rotated ninety degrees into a horizontal line. In these horizontal probe trials, monkeys preferentially selected the fourth position from the left, but not the fourth position from the right. Our results indicate that rhesus macaques map number onto space, suggesting that the association between number and space in human cognition is not purely a result of cultural experience and instead has deep evolutionary roots.

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.

What counts for 'counting'? Chimpanzees, Pan troglodytes, respond appropriately to relevant and irrelevant information in a quantity judgment task

Nonhuman animals quantify all manner of things, and the way in which this is done is fairly well understood. However, little research has been conducted to determine how they know what is or is not relevant in the instances in which they quantify stimuli. We assessed how four chimpanzees chose between two sets of food items when the items were distributed across separate spatial arrays. Each item was covered by a container, and then was revealed in sequence so that neither whole set was visible at one time. After all containers were revealed, some were revealed again. The chimpanzees should have ignored items that were seen a second time and instead enumerated each item only once. In another test, some of the items were transposed in location and then uncovered again. Here, the chimpanzees needed to recognize that the newly shown food items were ones they already had seen. Overall, the chimpanzees were successful in selecting the truly larger array of items despite these potential distracting re-presentations of items. Discrimination performance also reflected analogue magnitude estimation because comparisons of sets that differed by larger amounts were easier than comparisons that differed by smaller amounts. Thus, chimpanzee quantity judgments for nonvisible sets of items are inexact, but they include an aspect of control for determining when items are uniquely presented versus re-presented.

Large number discrimination in newborn fish

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

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.

Do Social Conditions Affect Capuchin Monkeys' (Cebus apella) Choices in a Quantity Judgment Task?

Beran et al. (2012) reported that capuchin monkeys closely matched the performance of humans in a quantity judgment test in which information was incomplete but a judgment still had to be made. In each test session, subjects first made quantity judgments between two known options. Then, they made choices where only one option was visible. Both humans and capuchin monkeys were guided by past outcomes, as they shifted from selecting a known option to selecting an unknown option at the point at which the known option went from being more than the average rate of return to less than the average rate of return from earlier choices in the test session. Here, we expanded this assessment of what guides quantity judgment choice behavior in the face of incomplete information to include manipulations to the unselected quantity. We manipulated the unchosen set in two ways: first, we showed the monkeys what they did not get (the unchosen set), anticipating that "losses" would weigh heavily on subsequent trials in which the same known quantity was presented. Second, we sometimes gave the unchosen set to another monkey, anticipating that this social manipulation might influence the risk-taking responses of the focal monkey when faced with incomplete information. However, neither manipulation caused difficulty for the monkeys who instead continued to use the rational strategy of choosing known sets when they were as large as or larger than the average rate of return in the session, and choosing the unknown (riskier) set when the known set was not sufficiently large. As in past experiments, this was true across a variety of daily ranges of quantities, indicating that monkeys were not using some absolute quantity as a threshold for selecting (or not) the known set, but instead continued to use the daily average rate of return to determine when to choose the known versus the unknown quantity.

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.

A new training procedure for studying discrimination learning in fish

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

Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes)

Many species can choose between two visual sets of stimuli on the basis of quantity. This is true when sets are both visible, or are presented one set at a time or even one item at a time. However, we know comparatively little about how well nonhuman animals can compare auditory quantities. Here, three chimpanzees (Pan troglodytes) chose between two sets of food items when they only heard each item fall into different containers rather than seeing those items. This method prevented the chimpanzees from summing the amount of visible food they saw because there were no visual cues. Chimpanzees performed well, and their performance matched that of previous experiments with regard to obeying Weber's law. They also performed well with comparisons between a sequentially presented auditory set and a fully visible set, demonstrating that duration of presentation was not being used as a cue. In addition, they accommodated empty sets into these judgments, although not perfectly. Thus, chimpanzees can judge auditory quantities in flexible ways that show many similarities to how they compare visual quantities.

Relative quantity judgments in South American sea lions (Otaria flavescens)

There is accumulating evidence that a variety of species possess quantitative abilities although their cognitive substrate is still unclear. This study is the first to investigate whether sea lions (Otaria flavescens), in the absence of training, are able to assess and select the larger of two sets of quantities. In Experiment 1, the two sets of quantities were presented simultaneously as whole sets, that is, the subjects could compare them directly. In Experiment 2, the two sets of quantities were presented item-by-item, and the totality of items was never visually available at the time of choice. For each type of presentation, we analysed the effect of the ratio between quantities, the difference between quantities and the total number of items presented. The results showed that (1) sea lions can make relative quantity judgments successfully and (2) there is a predominant influence of the ratio between quantities on the subjects' performance. The latter supports the idea that an analogue representational mechanism is responsible for sea lions' relative quantities judgments. These findings are consistent with previous reports of relative quantities judgments in other species such as monkeys and apes and suggest that sea lions might share a similar mechanism to compare and represent quantities.

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.

A claim in search of evidence: reply to Manger's thermogenesis hypothesis of cetacean brain structure

In a recent publication in Biological Reviews, Manger (2006) made the controversial claim that the large brains of cetaceans evolved to generate heat during oceanic cooling in the Oligocene epoch and not, as is the currently accepted view, as a basis for an increase in cognitive or information-processing capabilities in response to ecological or social pressures. Manger further argued that dolphins and other cetaceans are considerably less intelligent than generally thought. In this review we challenge Manger's arguments and provide abundant evidence that modern cetacean brains are large in order to support complex cognitive abilities driven by social and ecological forces.

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.