Understanding the origin of number sense: a review of fish studies

Analysis of visual discrimination in Japanese eel (Anguilla japonica)

Japanese eels were trained to discriminate between a checkerboard panel and a plain gray panel in a circular pool with three pipes. One of the pipes was open, whereas the others were closed. The correct choice of discriminative stimulus was reinforced by entering the pipe. When the panels were displayed vertically (on the wall), the eels successfully learned discrimination, but they were unable to acquire the task when the panels were presented horizontally (on the floor). Enucleation of the retina impaired discrimination, whereas ablation of the olfactory plates did not. In the second experiment, the eels underwent three tests after discriminative training with vertical stimuli displayed. When plain black or white panels were presented instead of a checkerboard panel, the eels could not discriminate. Thus, the discriminative stimulus must have both black and white components. The eels exhibited a generalization gradient along the fines of the checkerboard. Finally, the pallium was damaged by coagulation, and the eels did not maintain the discrimination after the lesions. The behavioral deficits were classified into successful relearning and no relearning. Damage to the dorso-lateral (DL) or dorso-central (DC) pallium was associated with severe impairment (no relearning), although it was not possible to isolate the particular brain area or combination of brain areas which was required. The DL damage probably causes memory deficits, but the deficits caused by the DC damage might be motor or motivational deficits.

Personality and cognition: shoal size discrimination performance is related to boldness and sociability among ten freshwater fish species

Several studies have reported that animals' personalities are often correlated with individual differences in cognition. Here, we tested whether personality is related to cognition across species, focusing on 10 freshwater fishes and a task relevant for fitness, the ability to discriminate shoal size. Bolder species exhibited more 'shuttle' behavior for information sampling during shoal selection and showed high performance (HP) in the numerical discrimination than shyer species, i.e., low performance (LP) species. Species at both the high and low ends of sociability showed LP, possibly due to loosened selection pressure because of either no need to perform shoal size discrimination tasks frequently in nature for very high sociability species or decreased willingness and motivation to join and stay within shoals for very low sociability species. Notably, the numerical discrimination was sensitive to the numerical contrast ratio in LP species but not in HP species, suggesting that the numerical system used for size discrimination also varied between species. Overall, we demonstrated the interspecies relationship between personality and shoal size discrimination across fish species, suggesting an evolutionary link between numerical abilities and behavior.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

Visual number sense for real-world scenes shared by deep neural networks and humans

Recently, visual number sense has been identified from deep neural networks (DNNs). However, whether DNNs have the same capacity for real-world scenes, rather than the simple geometric figures that are often tested, is unclear. In this study, we explore the number perception of scenes using AlexNet and find that numerosity can be represented by the pattern of group activation of the category layer units. The global activation of these units increases with the number of objects in the scene, and the variations in their activation decrease accordingly. By decoding the numerosity from this pattern, we reveal that the embedding coefficient of a scene determines the likelihood of potential objects to contribute to numerical perception. This was demonstrated by the more optimized performance for pictures with relatively high embedding coefficients in both DNNs and humans. This study for the first time shows that a distinct feature in visual environments, revealed by DNNs, can modulate human perception, supported by a group-coding mechanism.

Keep numbers in view: red-eared sliders (Trachemys scripta elegans) learn to discriminate relative quantities

The ability to discriminate relative quantities, one of the numerical competences, is considered an adaptive trait in uncertain environments. Besides humans, previous studies have reported this capacity in several non-human primates and birds. Here, we test whether red-eared sliders (Trachemys scripta elegans) can discriminate different relative quantities. Subjects were first trained to distinguish different stimuli with food reward. Then, they were tested with novel stimulus pairs to demonstrate how they distinguished the stimuli. The results show that most subjects can complete the initial training and use relative quantity rather than absolute quantity to make choices during the testing phase. This study provides behavioural evidence of relative quantity discrimination in a reptile species and suggests that such capacity may be widespread among vertebrates.

Quantity discrimination in newly hatched zebrafish suggests hardwired numerical abilities

An intriguing hypothesis to explain the ubiquity of numerical abilities is that all vertebrates are born with hardwired neuronal networks for processing numbers. To date, only studies on human foetuses have clearly supported this hypothesis. Zebrafish hatch 48-72 h after fertilisation with an embryonic nervous system, providing a unique opportunity for investigating this hypothesis. Here, we demonstrated that zebrafish larvae exposed to vertical bars at birth acquired an attraction for bar stimuli and we developed a numerical discrimination task based on this preference. When tested with a series of discriminations of increasing difficulty (1vs.4, 1vs.3, 1vs.2, and 2vs.4 bars), zebrafish larvae reliably selected the greater numerosity. The preference was significant when stimuli were matched for surface area, luminance, density, and convex hull, thereby suggesting a true capacity to process numerical information. Converging results from two phylogenetically distant species suggests that numerical abilities might be a hallmark feature of vertebrates' brains.

Large-scale study of the precision of the approximate number system: Differences between formats, heterogeneity and congruency effects

The study used a large sample of elementary schoolchildren in Russia (N = 3,448, 51.6% were girls, with a mean age of 8.70 years, ranging 6-11 years) to investigate the congruency, format and heterogeneity effects in a nonsymbolic comparison test and between-individual differences in these effects with generalized linear mixed effects models (GLMMs). The participants were asked to compare two arrays of figures of different colours in spatially separated or spatially intermixed formats. In addition, the figures could be similar or different for the two arrays. The results revealed that congruency (difference between congruent and incongruent items), format (difference between mixed and separated formats) and heterogeneity (difference between homogeneous and heterogeneous conditions) interacted. The heterogeneity effect was higher in the separated format, while the format effect was higher for the homogeneous condition. The separated format produced a greater congruency effect than the mixed format. In addition, the congruency effect was lower in the heterogeneous condition than in the homogeneous condition. Analysis of between-individual differences revealed that there was significant between-individual variance in the format and congruency effects. Analysis of between-grade differences revealed that accuracy improved from grade 1 to grade 4 only for congruent trials in separated formats. Consequently, the congruency effect increased in separated/homogeneous and separated/heterogeneous conditions. In general, the study demonstrated that the test format and heterogeneity affected accuracy and that this effect varied for congruent and incongruent items.

No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization

Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards number, or a general bias towards the more perceptually discriminable dimension (i.e., number). Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children's previously observed number bias may be due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role for area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed. RESEARCH HIGHLIGHTS: Previous work found that children and adults spontaneously categorized dot array stimuli by number, over other magnitudes (e.g., area), suggesting number is uniquely salient. However, here we found that when number and area were matched by ratio, as in prior work, number was significantly more perceptually discriminable than area. When number and area were made equally discriminable ('perceptually-matched'), children, contra adults, spontaneously categorized stimuli by area over number (and other non-numerical magnitudes). These findings suggest that area may be uniquely salient early in childhood, with the previously-observed number bias not emerging until later in development.

Quantity as a Fish Views It: Behavior and Neurobiology

An ability to estimate quantities, such as the number of conspecifics or the size of a predator, has been reported in vertebrates. Fish, in particular zebrafish, may be instrumental in advancing the understanding of magnitude cognition. We review here the behavioral studies that have described the ecological relevance of quantity estimation in fish and the current status of the research aimed at investigating the neurobiological bases of these abilities. By combining behavioral methods with molecular genetics and calcium imaging, the involvement of the retina and the optic tectum has been documented for the estimation of continuous quantities in the larval and adult zebrafish brain, and the contributions of the thalamus and the dorsal-central pallium for discrete magnitude estimation in the adult zebrafish brain. Evidence for basic circuitry can now be complemented and extended to research that make use of transgenic lines to deepen our understanding of quantity cognition at genetic and molecular levels.

How to behave when marooned: the behavioural component of the island syndrome remains underexplored

Animals on islands typically depart from their mainland relatives in assorted aspects of their biology. Because they seem to occur in concert, and to some extent evolve convergently in disparate taxa, these changes are referred to as the ‘island syndrome’. While morphological, physiological and life-history components of the island syndrome have received considerable attention, much less is known about how insularity affects behaviour. In this paper, we argue why changes in personality traits and cognitive abilities can be expected to form part of the island syndrome. We provide an overview of studies that have compared personality traits and cognitive abilities between island and mainland populations, or among islands. Overall, the pickings are remarkably slim. There is evidence that animals on islands tend to be bolder than on the mainland, but effects on other personality traits go either way. The evidence for effects of insularity on cognitive abilities or style is highly circumstantial and very mixed. Finally, we consider the ecological drivers that may induce such changes, and the mechanisms through which they might occur. We conclude that our knowledge of the behavioural and cognitive responses to island environments remains limited, and we encourage behavioural biologists to make more use of these ‘natural laboratories for evolution’.

Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation

Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.

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 evolution of quantitative sensitivity

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability.

This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.

Characterizing ontogeny of quantity discrimination in zebrafish

A sense of non-symbolic numerical magnitudes is widespread in the animal kingdom and has been documented in adult zebrafish. Here, we investigated the ontogeny of this ability using a group size preference (GSP) task in juvenile zebrafish. Fish showed GSP from 21 days post-fertilization and reliably chose the larger group when presented with discriminations of between 1 versus 3, 2 versus 5 and 2 versus 3 conspecifics but not 2 versus 4 conspecifics. When the ratio between the number of conspecifics in each group was maintained at 1 : 2, fish could discriminate between 1 versus 2 individuals and 3 versus 6, but again, not when given a choice between 2 versus 4 individuals. These findings are in agreement with studies in other species, suggesting the systems involved in quantity representation do not operate separately from other cognitive mechanisms. Rather they suggest quantity processing in fishes may be the result of an interplay between attentional, cognitive and memory-related mechanisms as in humans and other animals. Our results emphasize the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny and function of number cognition.

Video playback versus live stimuli to assess quantity discrimination in angelfish (Pterophyllum scalare)

Video playback is a widely used technique for presentation of visual stimuli in animal behavior research. In the analysis of behavioral responses to social cues, presentation of video recordings of live conspecifics represents a consistently reproducible stimulus. However, video-recordings do not interact with the experimental subject, and thus this stimulus may be inferior in the social context. Here, we evaluated how angelfish (Pterophyllum scalare) respond to a video playback of conspecifics versus a live shoal of conspecifics. Using binary choice tests, subjects were presented different stimuli. Time spent close to one versus the other stimulus was considered an index of preference. We found angelfish to prefer a live shoal of conspecifics to an empty tank, and also the video playback of a shoal of conspecifics to a blank screen, although the level of preference in the latter was lower than in the former. These results indicate that video-playback of live conspecifics may be appropriate in angelfish, thus allowing manipulation of specific cues that angelfish may use in quantity discrimination. However, when we directly contrasted a live and a video recorded shoal, both having the same number of members, experimental fish preferred the live shoal. When the choice consisted of a live shoal of four conspecifics versus a video playback of a shoal of nine conspecifics no clear preference emerged. These results imply that video-playback has disadvantages in quantity discrimination studies with angelfish. Exploring procedural and/or technological parameters will verify the suitability of video-recording-based stimulus presentation for future use in angelfish.

Dogs (canis familiaris) underestimate the quantity of connected items: first demonstration of susceptibility to the connectedness illusion in non-human animals

In humans, numerical estimation is affected by perceptual biases, such as those originating from the spatial arrangement of elements. Different animal species can also make relative quantity judgements. This includes dogs, who have been proposed as a good model for comparative neuroscience. However, dogs do not show the same perceptual biases observed in humans. Thus, the exact perceptual/cognitive mechanisms underlying quantity estimations in dogs and their degree of similarity with humans are still a matter of debate. Here we explored whether dogs are susceptible to the connectedness illusion, an illusion based on the tendency to underestimate the quantity of interconnected items. Dogs were first trained to choose the larger of two food arrays. Then, they were presented with two arrays containing the same quantity of food, of which one had items interconnected by lines. Dogs significantly selected the array with unconnected items, suggesting that, like in humans, connectedness determines underestimation biases, possibly disrupting the perceptual system's ability to segment the display into discrete objects. The similarity in dogs' and humans' susceptibility to the connectedness, but not to other numerical illusions, suggests that different mechanisms are involved in the estimation of quantity of stimuli with different characteristics.

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.

Boosting Numerical Cognition in Children and Adolescents with Mathematical Learning Disabilities by a Brain-Based Intervention: A Study Protocol for a Randomized, Sham-Controlled Clinical Trial

Numbers are everywhere, and supporting difficulties in numerical cognition (e.g., mathematical learning disability (MLD)) in a timely, effective manner is critical for their daily use. To date, only low-efficacy cognitive-based interventions are available. The extensive data on the neurobiology of MLD have increased interest in brain-directed approaches. The overarching goal of this study protocol is to provide the scientific foundation for devising brain-based and evidence-based treatments in children and adolescents with MLD. In this double-blind, between-subject, sham-controlled, randomized clinical trial, transcranial random noise stimulation (tRNS) plus cognitive training will be delivered to participants. Arithmetic, neuropsychological, psychological, and electrophysiological measures will be collected at baseline (T0), at the end of the interventions (T1), one week (T2) and three months later (T3). We expect that tRNS plus cognitive training will significantly improve arithmetic measures at T1 and at each follow-up (T2, T3) compared with placebo and that such improvements will correlate robustly and positively with changes in the neuropsychological, psychological, and electrophysiological measures. We firmly believe that this clinical trial will produce reliable and positive results to accelerate the validation of brain-based treatments for MLD that have the potential to impact quality of life.

Superior continuous quantity discrimination in a freshwater turtle

BACKGROUND

Quantity discrimination, the ability to discriminate a magnitude of difference or discrete numerical information, plays a key role in animal behavior. While quantitative ability has been well documented in fishes, birds, mammals, and even in previously unstudied invertebrates and amphibians, it is still poorly understood in reptiles and has never been tested in an aquatic turtle despite the fact that evidence is accumulating that reptiles possess cognitive skills and learning ability. To help address this deficiency in reptiles, we investigated the quantitative ability of an Asian freshwater turtle, Mauremys sinensis, using red cubes on a white background in a trained quantity discrimination task. While spontaneous quantity discrimination methods are thought to be more ecologically relevant, training animals on a quantity discrimination task allows more comparability across taxa.

RESULTS

We assessed the turtles' quantitative performance in a series of tests with increasing quantity ratios and numerosities. Surprisingly, the turtles were able to discriminate quantities of up to 9 versus 10 (ratio = 0.9), which shows a good quantitative ability that is comparable to some endotherms. Our results showed that the turtles' quantitative performance followed Weber's law, in which success rate decreased with increasing quantity ratio across a wide range of numerosities. Furthermore, the gradual improvement of their success rate across different experiments and phases suggested that the turtles possess learning ability.

CONCLUSIONS

Reptile quantitative ability has long been ignored and therefore is likely under-estimated. More comparative research on numerical cognition across a diversity of species will greatly contribute to a clearer understanding of quantitative ability in animals and whether it has evolved convergently in diverse taxa.

Counting on Numbers-Numerical Abilities in Grey Bamboo Sharks and Ocellate River Stingrays

Over the last decade, studies examining the cognitive abilities of fish have increased, using a broad range of approaches. One of the foci has been to test the ability of fish to discriminate quantities of items and to determine whether fish can solve tasks solely on the basis of numerical information. This study is the first to investigate this ability in two elasmobranch species. All animals were trained in two-alternative forced-choice visual experiments and then examined in transfer tests, to determine if previously gained knowledge could be applied to new tasks. Results show that the grey bamboo shark (Chiloscyllium griseum) and the ocellate river stingray (Potamotrygon motoro) can discriminate quantities based on numerical information alone, while continuous variables were controlled for. Furthermore, the data indicates that similar magnitudes and limits for quantity discrimination exist as in other animals. However, the high degree of intraspecific variation that was observed as well as the low rate of animals proving to be successful suggest that the ability to discriminate quantities may not be as important to these species as to some other vertebrate and invertebrate species tested so far.

Understanding behaviour to improve the welfare of an ornamental fish

Some common practices in aquaculture, ornamental trade and fish facilities may disturb the behavioural repertoire of fish and its natural adaptive value, reducing welfare and impairing fish production. Hence, it is necessary to understand fish behaviour, as well as the factors affecting it, to improve the quality of fish's life under artificial environment. Here, we reviewed the behaviour of the angelfish Pterophyllum scalare, an Amazonian cichlid used worldwide both as an ornamental fish and as a fish model in scientific research. We characterized social, reproductive and feeding behaviour, as well as the amazing cognitive ability of the angelfish. In addition, we reviewed the effects of environmental enrichment and suggested some important variables that need to be considered for rearing P. scalare. In this review, we show for the first time a synthesis on behaviour and a best practice overview to improve the welfare of angelfish as a target species. Nonetheless, most topics reviewed fit a broader set of fish species, particularly ornamental ones. This synthesis can therefore open a path for further behavioural research applied to the welfare of angelfish and bring insights to other fish species.

Quantity discrimination in a spontaneous task in a poison frog

The use of quantitative information underlies a range of animal behaviors. There are thought to be two parallel systems for judging quantity: a precise representation of small numbers of objects, typically less than 4, that can be tracked visually (object tracking system) and an imprecise system for larger quantities (approximate number system) governed by Weber's law. Using a spontaneous discrimination task with live prey, we examined the ability of the poison frog Dendrobates auratus to discriminate quantities of low (1-4) or high (4-16) numerosity over a range of ratio contrasts (0.33, 0.5, 0.67, 0.75). Similar to a previous study in treefrogs, we found that the poison frogs chose the larger quantity of flies when choosing between 1 and 3 and between 1 and 2. However, their performance was near chance when choosing between 2 and 3 and below chance when choosing between 3 and 4. When the numerosity of flies was higher, they did not discriminate between the larger and smaller quantity. Our findings are consistent with the ability of poison frogs to discriminate small quantities of objects using an object tracking system, but could also reflect a singular vs. plural discrimination. We did not find evidence of an approximate number system governed by Weber's law, nor evidence of a speed-accuracy tradeoff. However, total set size was associated with lower accuracy and longer latencies to choose. Future studies should explore quantity discrimination in additional contexts to better understand the limits of these abilities in poison frogs.

Behavioral and Neuronal Representation of Numerosity Zero in the Crow

Different species of animals can discriminate numerosity, the countable number of objects in a set. The representations of countable numerosities have been deciphered down to the level of single neurons. However, despite its importance for human number theory, a special numerical quantity, the empty set (numerosity zero), has remained largely unexplored. We explored the behavioral and neuronal representation of the empty set in carrion crows. Crows were trained to discriminate small numerosities including the empty set. Performance data showed a numerical distance effect for the empty set in one crow, suggesting that the empty set and countable numerosities are represented along the crows' "mental number line." Single-cell recordings in the endbrain region nidopallium caudolaterale (NCL) showed a considerable proportion of NCL neurons tuned to the preferred numerosity zero. As evidenced by neuronal distance and size effects, NCL neurons integrated the empty set in the neural number line. A subsequent neuronal population analysis using a statistical classifier approach showed that the neuronal numerical representations were predictive of the crows' success in the task. These behavioral and neuronal data suggests that the conception of the empty set as a cognitive precursor of a zero-like number concept is not an exclusive property of the cerebral cortex of primates. Zero as a quantitative category cannot only be implemented in the layered neocortex of primates, but also in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.SIGNIFICANCE STATEMENT The conception of "nothing" as number "zero" is celebrated as one of the greatest achievements in mathematics. To explore whether precursors of zero-like concepts can be found in vertebrates with a cerebrum that anatomically differs starkly from our primate brain, we investigated this in carrion crows. We show that crows can grasp the empty set as a null numerical quantity that is mentally represented next to number one. Moreover, we show that single neurons in an associative avian cerebral region specifically respond to the empty set and show the same physiological characteristics as for countable quantities. This suggests that zero as a quantitative category can also be implemented in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.

Tuned neural responses to haptic numerosity in the putamen

The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.

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.

Numerosity representation in a deep convolutional neural network

Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.

Spontaneous quantity discrimination in a family-living lizard

While foraging or during social interactions, animals may benefit from judging relative quantity. Individuals may select larger prey or a patch with more food and, likewise, it may pay to track the number and type of individuals and social interactions. We tested for spontaneous quantity discrimination in the gidgee skink (Egernia stokesii), a family-living lizard. Lizards were presented with food quantities differing in number or size and were able to select the larger quantity of food items when they differed in number but not when items differed in size. We show, for the first time, superior spontaneous discrimination of items differing in number over size in a lizard species, which contrasts with previous findings. Our simple method, however, did not include controls for the use of continuous quantities, and further tests are required to determine the role of such information during quantity discrimination. Our results provide support for the use of the parallel individuation system for the discrimination of small quantities (four or fewer items). Lizards might, however, still use the approximate number system if items in larger quantities (more than four) are presented. Overall, we uncovered evidence that species might possess specific cognitive abilities potentially adapted to their niche with respect to quantity information (discrete and/or continuous) and the processing system used when judging quantities. Importantly, our results highlight the need for testing multiple species using similar testing procedures to gain a better understanding of the underlying causes leading to differences across species.

Neural substrates involved in the cognitive information processing in teleost fish

Over the last few decades, it has been shown that fish, comprising the largest group of vertebrates and in many respects one of the least well studied, possess many cognitive abilities comparable to those of birds and mammals. Despite a plethora of behavioural studies assessing cognition abilities and an abundance of neuroanatomical studies, only few studies have aimed to or in fact identified the neural substrates involved in the processing of cognitive information. In this review, an overview of the currently available studies addressing the joint research topics of cognitive behaviour and neuroscience in teleosts (and elasmobranchs wherever possible) is provided, primarily focusing on two fundamentally different but complementary approaches, i.e. ablation studies and Immediate Early Gene (IEG) analyses. More recently, the latter technique has become one of the most promising methods to visualize neuronal populations activated in specific brain areas, both during a variety of cognitive as well as non-cognition-related tasks. While IEG studies may be more elegant and potentially easier to conduct, only lesion studies can help researchers find out what information animals can learn or recall prior to and following ablation of a particular brain area.

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.

Small-range numerical representations of linguistic sounds in 9- to 10-month-old infants

Coordinated studies provide evidence that very young infants, like human adults and nonhuman animals, readily discriminate small and large number of visual displays on the basis of numerical information. This capacity has been considerably less studied in the auditory modality. Surprisingly, the available studies yielded mixed evidence concerning whether numerical representations of auditory items in the small number range (1 to 3) are present early in human development. Specifically, while newborns discriminate 2- from 3-syllable sequences, older infants at 6 and 9 months of age fail to differentiate 2 from 3 tones. This study tested the hypothesis that infants can represent small sets more precisely when listening to ecologically relevant linguistic sounds. The aim was to probe 9- to 10-month-olds' (N = 74) ability to represent sound sets in a working memory test. In experiments 1 and 2, infants successfully discriminated 2- and 3-syllable sequences on the basis of their numerosity, when continuous variables, such as individual item duration, inter-stimulus duration, pitch, intensity, and total duration, were controlled for. In experiment 3, however, infants failed to discriminate 3- from 4-syllable sequences under similar conditions. Finally, in experiment 4, infants were tested on their ability to distinguish 2 and 3 tone sequences. The results showed no evidence that infants discriminated these non-linguistic stimuli. These findings indicate that, by means of linguistic sounds, infants can access a numerical system that yields precise auditory representations in the small number range.

Continuous versus discrete quantity discrimination in dune snail (Mollusca: Gastropoda) seeking thermal refuges

The ability of invertebrates to discriminate quantities is poorly studied, and it is unknown whether other phyla possess the same richness and sophistication of quantification mechanisms observed in vertebrates. The dune snail, Theba pisana, occupies a harsh habitat characterised by sparse vegetation and diurnal soil temperatures well above the thermal tolerance of this species. To survive, a snail must locate and climb one of the rare tall herbs each dawn and spend the daytime hours in an elevated refuge position. Based on their ecology, we predicted that dune snails would prefer larger to smaller groups of refuges. We simulated shelter choice under controlled laboratory conditions. Snails’ acuity in discriminating quantity of shelters was comparable to that of mammals and birds, reaching the 4 versus 5 item discrimination, suggesting that natural selection could drive the evolution of advanced cognitive abilities even in small-brained animals if these functions have a high survival value. In a subsequent series of experiments, we investigated whether snails used numerical information or based their decisions upon continuous quantities, such as cumulative surface, density or convex hull, which co-varies with number. Though our results tend to underplay the role of these continuous cues, behavioural data alone are insufficient to determine if dune snails were using numerical information, leaving open the question of whether gastropod molluscans possess elementary abilities for numerical processing.

Giraffes go for more: a quantity discrimination study in giraffes (Giraffa camelopardalis)

Many species, including humans, rely on an ability to differentiate between quantities to make decisions about social relationships, territories, and food. This study is the first to investigate whether giraffes (Giraffa camelopardalis) are able to select the larger of two sets of quantities in different conditions, and how size and density affect these decisions. In Task 1, we presented five captive giraffes with two sets containing a different quantity of identical foods items. In Tasks 2 and 3, we also modified the size and density of the food reward distribution. The results showed that giraffes (i) can successfully make quantity judgments following Weber's law, (ii) can reliably rely on size to maximize their food income, and (iii) are more successful when comparing sparser than denser distributions. More studies on different taxa are needed to understand whether specific selective pressures have favored the evolution of these skills in certain taxa.

Learning in non-avian reptiles 40 years on: advances and promising new directions

Recently, there has been a surge in cognition research using non-avian reptile systems. As a diverse group of animals, non-avian reptiles [turtles, the tuatara, crocodylians, and squamates (lizards, snakes and amphisbaenids)] are good model systems for answering questions related to cognitive ecology, from the role of the environment on the brain, behaviour and learning, to how social and life-history factors correlate with learning ability. Furthermore, given their variable social structure and degree of sociality, studies on reptiles have shown that group living is not a pre-condition for social learning. Past research has demonstrated that non-avian reptiles are capable of more than just instinctive reactions and basic cognition. Despite their ability to provide answers to fundamental questions in cognitive ecology, and a growing literature, there have been no recent systematic syntheses of research in this group. Here, we systematically, and comprehensively review studies on reptile learning. We identify 92 new studies investigating learning in reptiles not included in previous reviews on this topic - affording a unique opportunity to provide a more in-depth synthesis of existing work, its taxonomic distribution, the types of cognitive domains tested and methodologies that have been used. Our review therefore provides a major update on our current state of knowledge and ties the collective evidence together under nine umbrella research areas: (i) habituation of behaviour, (ii) animal training through conditioning, (iii) avoiding aversive stimuli, (iv) spatial learning and memory, (v) learning during foraging, (vi) quality and quantity discrimination, (vii) responding to change, (viii) solving novel problems, and (ix) social learning. Importantly, we identify knowledge gaps and propose themes which offer important future research opportunities including how cognitive ability might influence fitness and survival, testing cognition in ecologically relevant situations, comparing cognition in invasive and non-invasive populations of species, and social learning. To move the field forward, it will be immensely important to build upon the descriptive approach of testing whether a species can learn a task with experimental studies elucidating causal reasons for cognitive variation within and among species. With the appropriate methodology, this young but rapidly growing field of research should advance greatly in the coming years providing significant opportunities for addressing general questions in cognitive ecology and beyond.

Application of an abstract concept across magnitude dimensions by fish

Mastering relational concepts and applying them to different contexts presupposes abstraction capacities and implies a high level of cognitive sophistication. One way to investigate extrapolative abilities is to assess cross-dimensional application of an abstract relational magnitude rule to new domains. Here we show that angelfish initially trained to choose either the shorter of two lines in a spatial task (line-length discrimination task) or the array with “fewer” items (numerical discrimination task) spontaneously transferred the learnt rule to novel stimuli belonging to the previously unseen dimension demonstrating knowledge of the abstract concept of “smaller”. Our finding challenges the idea that the ability to master abstract magnitude concepts across domains is unique to humans and suggests that the circuits involved in rule learning and magnitude processing might be evolutionary conserved.

Poor numerical performance of guppies tested in a Skinner box

We tested the hypothesis that part of the gap in numerical competence between fish and warm-blooded vertebrates might be related to the more efficient procedures (e.g. automated conditioning chambers) used to investigate the former and could be filled by adopting an adapted version of the Skinner box in fish. We trained guppies in a visual numerosity discrimination task, featuring two difficulty levels (3 vs. 5 and 3 vs. 4) and three conditions of congruency between numerical and non-numerical cues. Unexpectedly, guppies trained with the automated device showed a much worse performance compared to previous investigations employing more “ecological” procedures. Statistical analysis indicated that the guppies overall chose the correct stimulus more often than chance; however, their average accuracy did not exceed 60% correct responses. Learning measured as performance improvement over training was significant only for the stimuli with larger numerical difference. Additionally, the target numerosity was selected more often than chance level only for the set of stimuli in which area and number were fully congruent. Re-analysis of prior studies indicate that the gap between training with the Skinner box and with a naturalistic setting was present only for numerical discriminations, but not for colour and shape discriminations. We suggest that applying automated conditioning chambers to fish might increase cognitive load and therefore interfere with achievement of numerosity discriminations.

Fisheries-induced selection against schooling behaviour in marine fishes

Group living is a common strategy used by fishes to improve their fitness. While sociality is associated with many benefits in natural environments, including predator avoidance, this behaviour may be maladaptive in the Anthropocene. Humans have become the dominant predator in many marine systems, with modern fishing gear developed to specifically target groups of schooling species. Therefore, ironically, behavioural strategies which evolved to avoid non-human predators may now actually make certain fish more vulnerable to predation by humans. Here, we use an individual-based model to explore the evolution of fish schooling behaviour in a range of environments, including natural and human-dominated predation conditions. In our model, individual fish may leave or join groups depending on their group-size preferences, but their experienced group size is also a function of the preferences of others in the population. Our model predicts that industrial fishing selects against individual-level behaviours that produce large groups. However, the relationship between fishing pressure and sociality is nonlinear, and we observe discontinuities and hysteresis as fishing pressure is increased or decreased. Our results suggest that industrial fishing practices could be altering fishes' tendency to school, and that social behaviour should be added to the list of traits subject to fishery-induced evolution.

Fast saccadic eye-movements in humans suggest that numerosity perception is automatic and direct

Fast saccades are rapid automatic oculomotor responses to salient and ecologically important visual stimuli such as animals and faces. Discriminating the number of friends, foe, or prey may also have an evolutionary advantage. In this study, participants were asked to saccade rapidly towards the more numerous of two arrays. Participants could discriminate numerosities with high accuracy and great speed, as fast as 190 ms. Intermediate numerosities were more likely to elicit fast saccades than very low or very high numerosities. Reaction-times for vocal responses (collected in a separate experiment) were slower, did not depend on numerical range, and correlated only with the slow not the fast saccades, pointing to different systems. The short saccadic reaction-times we observe are surprising given that discrimination using numerosity estimation is thought to require a relatively complex neural circuit, with several relays of information through the parietal and prefrontal cortex. Our results suggest that fast numerosity-driven saccades may be generated on a single feed-forward pass of information recruiting a primitive system that cuts through the cortical hierarchy and rapidly transforms the numerosity information into a saccade command.

The devil is in the detail: Zebrafish learn to discriminate visual stimuli only if salient

Due to their unique characteristics, the zebrafish plays a key role in the comprehension of neurobiology of cognition and its pathologies, such as neurodegenerative diseases. More and more molecular tools for this aim are being developed, but our knowledge about the cognitive abilities of zebrafish remains extremely scarce compared to other teleost fish. We aimed to investigate the complex cognitive abilities of zebrafish using a tracking-based automated conditioning chamber that allowed precise experimental control, avoided potential cueing provided by the observer (Clever Hans phenomenon), and was shown to considerably improve learning in other teleosts. A computer presented two visual stimuli in two sectors of the chamber, and zebrafish had to enter the correct sector to obtain a food reward. Zebrafish quickly learned to use the conditioning device and easily performed up to 80 trials per day. In Experiment 1, zebrafish efficiently discriminated between two differently coloured sides, reaching a 75 % accuracy in only 10 training sessions. Surprisingly, zebrafish failed to choose the correct chamber when the stimuli were two shapes, a small circle and a small triangle, even when, in Experiment 2, training on shape discrimination was prolonged for up to 30 sessions. In Experiment 3, we tested the hypothesis that simultaneously learning to use the conditioning chamber and learning discrimination imposes a too-high cognitive load. However, zebrafish that first successfully learned how the conditioning chamber functioned (in the colour discrimination) subsequently failed in the shape discrimination. Conversely, zebrafish that firstly failed the shape discrimination subsequently learned colour discrimination. In Experiment 4, zebrafish showed some evidence of learning when the stimuli were two large shapes, suggesting that zebrafish did not discriminate between the shapes of the previous experiments because they were not salient enough. Altogether, results suggest constraints in the discrimination learning abilities of zebrafish, which should be taken into account when developing cognitive tasks for this species.

The ontogeny of continuous quantity discrimination in zebrafish larvae (Danio rerio)

Several studies have investigated the ontogeny of the capacity to discriminate between discrete numerical information in human and non-human animals. Contrarily, less attention has been devoted to the development of the capacity to discriminate continuous quantities. Recently, we set up a fast procedure for screening continuous quantity abilities in adult individuals of an animal model in neurodevelopmental research, the zebrafish. Two different sized holes are presented in a wall that divides the home tank in two halves and the spontaneous preference of fish for passing through the larger hole is exploited to measure their discrimination ability. We tested zebrafish larvae in the first, second and third week of life varying the relative size of the smaller circle (0.60, 0.75, 0.86, 0.91 area ratio). We found that the number of passages increased across the age. The capacity to discriminate the larger hole decreased as the ratio between the areas increased. No difference in accuracy was found as a function of age. The accuracy of larval zebrafish almost overlaps that found in adults in a previous study, suggesting a limited role of maturation and experience on the ability to estimate areas in this species.

Food quantity discrimination in puppies (Canis lupus familiaris)

There is considerable evidence that animals are able to discriminate between quantities. Despite the fact that quantitative skills have been extensively studied in adult individuals, research on their development in early life is restricted to a limited number of species. We, therefore, investigated whether 2-month-old puppies could spontaneously discriminate between different quantities of food items. We used a simultaneous two-choice task in which puppies were presented with three numerical combinations of pieces of food (1 vs. 8, 1 vs. 6 and 1 vs. 4), and they were allowed to select only one option. The subjects chose the larger of the two quantities in the 1 vs. 8 and the 1 vs. 6 combinations but not in the 1 vs. 4 combination. Furthermore, the last quantity the puppies looked at before making their choice and the time spent looking at the larger/smaller amounts of food were predictive of the choices they made. Since adult dogs are capable of discriminating between more difficult numerical contrasts when tested with similar tasks, our findings suggest that the capacity to discriminate between quantities is already present at an early age, but that it is limited to very easy discriminations.

Anisotropy of perceived numerosity: Evidence for a horizontal-vertical numerosity illusion

Many studies have investigated whether numerical and spatial abilities share similar cognitive systems. A novel approach to this issue consists of investigating whether the same perceptual biases underlying size illusions can be identified in numerical estimation tasks. In this study, we required adult participants to estimate the number of white dots in arrays made of white and black dots displayed in such a way as to generate horizontal-vertical illusions with inverted T and L configurations. In agreement with previous literature, we found that participants tended to underestimate the target numbers. However, in the presence of the illusory patterns, participants were less inclined to underestimate the number of vertically aligned white dots. This reflects the perceptual biases underlying horizontal-vertical illusions. In addition, we identified an enhanced illusory effect when participants observed vertically aligned white dots in the T shape compared to the L shape, a result that resembles the length bisection bias reported in the spatial domain. Overall, we found the first evidence that numerical estimation differs as a function of the vertical or horizontal displacement of the stimuli. In addition, the involvement of the same perceptual biases observed in spatial tasks supports the idea that spatial and numerical abilities share similar cognitive processes.

Food density and preferred quantity: discrimination of small and large numbers in angelfish (Pterophyllum scalare)

Many animal species share the ability to discriminate between sets with different quantity of food items. In fish, this ability has rarely been investigated, although findings have been obtained do indicate a preference, as in other animals, for sets with large over small quantities. The role played by food item size has also been found to be important in the discrimination. However, another potentially important non-numerical variable, food density, has not been investigated. In this study, we examined the influence of density (inter-item distance) in the decision-making process of food discrimination in angelfish (Pterophyllum scalare). In a binary choice task, we kept the number and size of food items constant, but contrasted a set containing food items spaced further apart (sparse set) to another set with food items spaced more closely (dense set). We conducted this analysis with sets in the small (3 vs 3 food items) and in the large number range (5 vs 5 food items) and also varied the specific spatial arrangements of the food items in the sets. Contrary to expectations, angelfish showed a preference for the sparse sets over the dense sets in the five vs five contrasts irrespective of the specific spatial arrangement, but exhibited no preference in case of the three vs three contrasts. Subsequently, we slightly lengthened the inter-item distance in the dense sets, and found preference for the dense over the sparse sets. Last, we further examined the potential effect of spatial configuration of the items in the sets, but found no effect of this latter factor. Overall, these results indicate that higher density of the contrasted food item sets significantly influences choice in angelfish, which prefer denser sets if a clear discriminability of each individual item within the sets is provided.

Searching for the Critical p of Macphail's Null Hypothesis: The Contribution of Numerical Abilities of Fish

In 1985, Macphail argued that there are no differences among the intellects of non-human vertebrates and that humans display unique cognitive skills because of language. Mathematical abilities represent one of the most sophisticated cognitive skills. While it is unquestionable that humans exhibit impressive mathematical skills associated with language, a large body of experimental evidence suggests that Macphail hypothesis must be refined in this field. In particular, the evidence that also small-brained organisms, such as fish, are capable of processing numerical information challenges the idea that humans display unique cognitive skills. Like humans, fish may take advantage of using continuous quantities (such as the area occupied by the objects) as proxy of number to select the larger/smaller group. Fish and humans also showed interesting similarities in the strategy adopted to learn a numerical rule. Collective intelligence in numerical estimation has been also observed in humans and guppies. However, numerical acuity in humans is considerably higher than that reported in any fish species investigated, suggesting that quantitative but not qualitative differences do exist between humans and fish. Lastly, while it is clear that contextual factors play an important role in the performance of numerical tasks, inter-species variability can be found also when different fish species were tested in comparable conditions, a fact that does not align with the null hypothesis of vertebrate intelligence. Taken together, we believe that the recent evidence of numerical abilities in fish call for a deeper reflection of Macphail's hypothesis.

Size discrimination in adult zebrafish (Danio rerio): Normative data and individual variation

In humans, aging and neurodegenerative diseases have been found to be associated with impairment in both mathematical abilities and estimation of continuous quantities such as size, weight or distance. Zebrafish (Danio rerio) is rapidly becoming a model for human aging and brain disorders but we currently lack any instrument for rapid assessment of quantity estimation abilities in this species. Here we developed a simple method based on spontaneous preference of zebrafish for using the larger available hole to pass an obstacle. We collected a large amount of data from small groups of zebrafish moving between compartments of their tank and we used these normative data to compare the performance of individually tested fish. Zebrafish significantly discriminated size ratios from 0.60 to 0.91 with their performance decreasing while increasing the size ratio between the smaller and the larger hole presented. On average, individually tested fish showed the same performance, but a large inter-individual variability was observed. Test-retest analyses revealed a good reliability of this test, with 0.60 and 0.75 ratios being the most informative. Experience did not affect individual performance, suggesting the suitability of this test to measure the longitudinal changes and the effects of pharmacological treatments on cognitive abilities.

Everything is subjective under water surface, too: visual illusions in fish

The study of visual illusions has captured the attention of comparative psychologists since the last century, given the unquestionable advantage of investigating complex perceptual mechanisms with relatively simple visual patterns. To date, the observation of animal behavior in the presence of visual illusions has been largely confined to mammal and bird studies. Recently, there has been increasing interest in investigating fish, too. The attention has been particularly focused on guppies, redtail splitfin and bamboo sharks. Overall, the tested species were shown to experience a human-like perception of different illusory phenomena involving size, number, motion, brightness estimation and illusory contours. However, in some cases, no illusory effects, or evidence for a reverse illusion, were also reported. Here, we review the current state of the art in this field. We conclude that a wider investigation of visual illusions in fish is fundamental to form a broader comprehension of perceptual systems of vertebrates. Furthermore, we believe that this type of investigation could help us to address general important issues in perceptual studies, such as the role of ecology in shaping perceptual systems, the existence of interindividual variability in the visual perception of nonhuman species and the role of cortical activity in the emergence of visual illusions.

Numerical cognition: A meta-analysis of neuroimaging, transcranial magnetic stimulation and brain-damaged patients studies

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We review neuroimaging, TMS, and patients studies on numerical cognition.

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We focused on the predictions derived from the Triple Code Model (TCM).

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Our findings generally agree with TCM predictions.

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Our results open avenues for the study of the neural bases of numerical cognition.

This article offers the first comprehensive review examining the neurocognitive bases of numerical cognition from neuroimaging, Transcranial Magnetic Stimulation (TMS) and brain-damaged patients studies. We focused on the predictions derived from the Triple Code Model (TCM), particularly the assumption that the representation of numerical quantities rests on a single format-independent representation (i.e., the analogical code) involving both intraparietal sulci (IPS). To do so, we conducted a meta-analysis based on 28 neuroimaging, 12 TMS and 12 brain-damaged patients studies, including arithmetic and magnitude tasks in symbolic and non-symbolic formats. Our findings generally agree with the TCM predictions indicating that both IPS are engaged in all tasks. Nonetheless, the results of brain-damaged patients studies conflicted with neuroimaging and TMS studies, suggesting a right hemisphere lateralization for non-symbolic formats. Our findings also led us to discuss the involvement of brain regions other than IPS in the processing of the analogical code as well as the neural substrate of other codes underlying numerical cognition (i.e., the auditory-verbal code).