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

Response to geometrical visual illusions in non-human animals: a meta-analysis

Visual illusions have been studied in many non-human species, spanning a wide range of biological and methodological variables. While early reviews have proved useful in providing an overview of the field, they have not been accompanied by quantitative analysis to systematically evaluate the contribution of biological and methodological moderators on the proportion of illusory choice. In the current meta-analytical study, we confirm that geometrical visual illusion perception is a general phenomenon among non-human animals. Additionally, we found that studies testing birds report stronger illusion perception compared to other classes, as do those on animals with lateral-positioned eyes compared to animals with forward-facing eyes. In terms of methodological choices, we found a positive correlation between the number of trials during training or testing and the effect sizes, while studies with larger samples report smaller effect sizes. Despite studies that trained animals with artificial stimuli showing larger effect sizes compared with those using spontaneous testing with naturalistic stimuli, like food, we found more recent studies prefer spontaneous choice over training. We discuss the challenges and bottlenecks in this area of study, which, if addressed, could lead to more successful advances in the future.

One-trial odour recognition learning and its underlying brain areas in the zebrafish

Distinguishing familiar from novel stimuli is critical in many animals' activities, and procedures based on this ability are among the most exploited in translational research in rodents. However, recognition learning and the underlying brain substrates remain unclear outside a few mammalian species. Here, we investigated one-trial recognition learning for olfactory stimuli in a teleost fish using a behavioural and molecular approach. With our behavioural analysis, we found that zebrafish can learn to recognise a novel odour after a single encounter and then, discriminate between this odour and a different one provided that the molecular structure of the cues is relatively differentiated. Subsequently, by expression analysis of immediate early genes in the main brain areas, we found that the telencephalon was activated when zebrafish encountered a familiar odour, whereas the hypothalamus and the optic tectum were activated in response to the novel odour. Overall, this study provided evidence of single-trial spontaneous learning of novel odours in a teleost fish and the presence of multiple neural substrates involved in the process. These findings are promising for the development of zebrafish models to investigate cognitive functions.

Inhibitory control in teleost fish: a methodological and conceptual review

Inhibitory control (IC) plays a central role in behaviour control allowing an individual to resist external lures and internal predispositions. While IC has been consistently investigated in humans, other mammals, and birds, research has only recently begun to explore IC in other vertebrates. This review examines current literature on teleost fish, focusing on both methodological and conceptual aspects. I describe the main paradigms adopted to study IC in fish, identifying well-established tasks that fit various research applications and highlighting their advantages and limitations. In the conceptual analysis, I identify two well-developed lines of research with fish examining IC. The first line focuses on a comparative approach aimed to describe IC at the level of species and to understand the evolution of interspecific differences in relation to ecological specialisation, brain size, and factors affecting cognitive performance. Findings suggest several similarities between fish and previously studied vertebrates. The second line of research focuses on intraspecific variability of IC. Available results indicate substantial variation in fish IC related to sex, personality, genetic, age, and phenotypic plasticity, aligning with what is observed with other vertebrates. Overall, this review suggests that although data on teleosts are still scarce compared to mammals, the contribution of this group to IC research is already substantial and can further increase in various disciplines including comparative psychology, cognitive ecology, and neurosciences, and even in applied fields such as psychiatry research.

Slowly walking down to the more food: relative quantity discrimination in African spurred tortoises (Centrochelys sulcata)

Quantity discrimination, is thought to be highly adaptive as it allows an organism to select greater amounts of food or larger social groups. In contrast to mammals, the processes underlying this ability are not as well understood in reptiles. This study examined the effects of ratio and number size on relative quantity discrimination in African spurred tortoises (Centrochelys sulcata). To assess these effects, tortoises were presented with trays containing favored food pieces in all possible number combinations between 1 and 7. The tortoises had to approach the tray they perceived as having the larger quantity. If correct, they received one piece of food as reinforcement. The results revealed that relative quantity discrimination was influenced by the ratio between the numbers of pieces, with performance improving as the ratio between the numbers increased. This finding suggests that the approximate number system or analogue magnitude estimation may control their behavior. However, as the number size increased, their performance declined, also suggesting that the approximate number system alone could not explain the present results.

Numerical discrimination in Drosophila melanogaster

Sensitivity to numbers is a crucial cognitive ability. The lack of experimental models amenable to systematic genetic and neural manipulation has precluded discovering neural circuits required for numerical cognition. Here, we demonstrate that Drosophila flies spontaneously prefer sets containing larger numbers of objects. This preference is determined by the ratio between the two numerical quantities tested, a characteristic signature of numerical cognition across species. Individual flies maintained their numerical choice over consecutive days. Using a numerical visual conditioning paradigm, we found that flies are capable of associating sucrose with numerical quantities and can be trained to reverse their spontaneous preference for large quantities. Finally, we show that silencing lobula columnar neurons (LC11) reduces the preference for more objects, thus identifying a neuronal substrate for numerical cognition in invertebrates. This discovery paves the way for the systematic analysis of the behavioral and neural mechanisms underlying the evolutionary conserved sensitivity to numerosity.

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.

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.

Muscimol-induced inactivation of the ventral prefrontal cortex impairs counting performance in rhesus monkeys

Numbers are one of the three basic concepts of human abstract thinking. When human beings count, they often point to things, one by one, and read numbers in a positive integer column. The prefrontal cortex plays a wide range of roles in executive functions, including active maintenance and achievement of goals, adaptive coding and exertion of general intelligence, and completion of time complexity events. Nonhuman animals do not use number names, such as "one, two, three," or numerals, such as "1, 2, 3" to "count" in the same way as humans do. Our previous study established an animal model of counting in monkeys. Here, we used this model to determine whether the prefrontal cortex participates in counting in monkeys. Two 5-year-old female rhesus monkeys (macaques), weighing 5.0 kg and 5.5 kg, were selected to train in a counting task, counting from 1 to 5. When their counting task performance stabilized, we performed surgery on the prefrontal cortex to implant drug delivery tubes. After allowing the monkeys' physical condition and counting performance to recover, we injected either muscimol or normal saline into their dorsal and ventral prefrontal cortex. Thereafter, we observed their counting task performance and analyzed the error types and reaction time during the counting task. The monkeys' performance in the counting task decreased significantly after muscimol injection into the ventral prefrontal cortex; however, it was not affected after saline injection into the ventral prefrontal cortex, or after muscimol or saline injection into the dorsal prefrontal cortex. The ventral prefrontal cortex of the monkey is necessary for counting performance.

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

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

Unimpaired groupitizing in children and adolescents with dyscalculia

When asked to estimate the number of items in the visual field, neurotypical adults are more precise and rapid if the items are clustered into subgroups compared to when they are randomly distributed. It has been suggested that this phenomenon, termed "groupitizing", relies on the recruitment of arithmetical calculation strategies and subitizing. Here the role of arithmetical skills in groupitizing was investigated by measuring the groupitizing effect (or advantage) in a sample of children and adolescents with and without math learning disability (dyscalculia). The results showed that when items were grouped, both groups of participants showed a similar advantage on sensory precision and response time in numerosity estimates. Correlational analyses confirmed a lack of covariation between groupitizing advantage and math scores. Bayesian statistics on sensory precision sustained the frequentist analyses providing decisive evidence in favor of no groups difference on groupitizing advantage magnitude (LBF = - 0.44) and no correlation with math scores (LBF = - 0.57). The results on response times, although less decisive, were again in favor of the null hypothesis. Overall, the results suggest that the link between groupitizing and mathematical abilities cannot be taken for granted, calling for further investigations on the factors underlying this perceptual phenomenon.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here, we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for covarying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs 6 elements; Exp. 2: 2 vs 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density, and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs 3, 5 vs 8, and 6 vs 9 in Exp. 1; 3 vs 4, 3 vs 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

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.

Magnitude integration in the Archerfish

We make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals' magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.

Quantitative abilities of invertebrates: a methodological review

Quantitative abilities are widely recognized to play important roles in several ecological contexts, such as foraging, mate choice, and social interaction. Indeed, such abilities are widespread among vertebrates, in particular mammals, birds, and fish. Recently, there has been an increasing number of studies on the quantitative abilities of invertebrates. In this review, we present the current knowledge in this field, especially focusing on the ecological relevance of the capacity to process quantitative information, the similarities with vertebrates, and the different methods adopted to investigate this cognitive skill. The literature argues, beyond methodological differences, a substantial similarity between the quantitative abilities of invertebrates and those of vertebrates, supporting the idea that similar ecological pressures may determine the emergence of similar cognitive systems even in distantly related species.

The Challenge of Illusory Perception of Animals: The Impact of Methodological Variability in Cross-Species Investigation

Simple Summary

Research in neurobiology and ethology has given us a glimpse into the different perceptual worlds of animals. More recently, visual illusions have been used in behavioural research to compare the perception between different animal species. The studies conducted so far have provided contradictory results, raising the possibility that different methodological approaches might influence illusory perception. Here, we review the literature on this topic, considering both field and laboratory studies. In addition, we compare the two approaches used in laboratories, namely spontaneous choice tests and training procedures, highlighting both their relevance and their potential weaknesses. Adopting both procedures has the potential to combine their advantages. Although this twofold approach has seldomly been adopted, we expect it will become more widely used in the near future in order to shed light on the heterogeneous pattern observed in the literature of visual illusions.

Abstract

Although we live on the same planet, there are countless different ways of seeing the surroundings that reflect the different individual experiences and selective pressures. In recent decades, visual illusions have been used in behavioural research to compare the perception between different vertebrate species. The studies conducted so far have provided contradictory results, suggesting that the underlying perceptual mechanisms may differ across species. Besides the differentiation of the perceptual mechanisms, another explanation could be taken into account. Indeed, the different studies often used different methodologies that could have potentially introduced confounding factors. In fact, the possibility exists that the illusory perception is influenced by the different methodologies and the test design. Almost every study of this research field has been conducted in laboratories adopting two different methodological approaches: a spontaneous choice test or a training procedure. In the spontaneous choice test, a subject is presented with biologically relevant stimuli in an illusory context, whereas, in the training procedure, a subject has to undergo an extensive training during which neutral stimuli are associated with a biologically relevant reward. Here, we review the literature on this topic, highlighting both the relevance and the potential weaknesses of the different methodological approaches.

Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus)

When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber's Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species.

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.

Rainbow trout discriminate 2-D photographs of conspecifics from distracting stimuli using an innovative operant conditioning device

Cognitive abilities were studied in rainbow trout, the first continental fish production in Europe. Increasing public concern for the welfare of farmed-fish species highlighted the need for better knowledge of the cognitive status of fish. We trained and tested 15 rainbow trout with an operant conditioning device composed of self-feeders positioned in front of visual stimuli displayed on a screen. The device was coupled with a two-alternative forced-choice (2-AFC) paradigm to test whether rainbow trout can discriminate 2-D photographs of conspecifics (S+) from different visual stimuli (S-). The S- were applied in four stages, the last three stages representing increasing discrimination difficulty: (1) blue shapes; (2) black shape (star); (3) photograph of an object (among a pool of 60); (4) photograph of another fish species (among a pool of 60). Nine fish (out of 15) correctly managed to activate the conditioning device after 30-150 trials. The rainbow trout were able to discriminate images of conspecifics from an abstract shape (five individuals out of five) or objects (four out of five) but not from other fish species. Their ability to learn the category "fish shape" rather than distinguishing between conspecifics and heterospecifics is discussed. The successful visual discrimination task using this complex operant conditioning device is particularly remarkable and novel for this farmed-fish species, and could be exploited to develop cognitive enrichments in future farming systems. This device can also be added to the existing repertoire of testing devices suitable for investigating cognitive abilities in fish.

Location- and object-based attention enhance number estimation

Humans and non-humans can extract an estimate of the number of items in a collection very rapidly, raising the question of whether attention is necessary for this process. Visual attention operates in various modes, showing selectivity both to spatial location and to objects. Here, we tested whether each form of attention can enhance number estimation, by measuring whether presenting a visual cue to increase attentional engagement will lead to a more accurate and precise representation of number, both when attention is directed to location and when it is directed to objects. Results revealed that enumeration of a collection of dots in the location previously cued led to faster, more precise, and more accurate judgments than enumeration in un-cued locations, and a similar benefit was seen when the cue and collection appeared on the same object. This work shows that like many other perceptual tasks, numerical estimation may be enhanced by the spread of active attention inside a pre-cued object.

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.

Wolves and Dogs May Rely on Non-numerical Cues in Quantity Discrimination Tasks When Given the Choice

A wide array of species throughout the animal kingdom has shown the ability to distinguish between quantities. Aside from being important for optimal foraging decisions, this ability seems to also be of great relevance in group-living animals as it allows them to inform their decisions regarding engagement in between-group conflicts based on the size of competing groups. However, it is often unclear whether these animals rely on numerical information alone to make these decisions or whether they employ other cues that may covary with the differences in quantity. In this study, we used a touch screen paradigm to investigate the quantity discrimination abilities of two closely related group-living species, wolves and dogs, using a simultaneous visual presentation paradigm. Both species were able to successfully distinguish between stimuli of different quantities up to 32 items and ratios up to 0.80, and their results were in accordance with Weber’s law (which predicts worse performances at higher ratios). However, our controls showed that both wolves and dogs may have used continuous, non-numerical cues, such as size and shape of the stimuli, in conjunction with the numerical information to solve this task. In line with this possibility, dogs’ performance greatly exceeded that which they had shown in other numerical competence paradigms. We discuss the implications these results may have on these species’ underlying biases and numerical capabilities, as well as how our paradigm may have affected the animals’ ability to solve the task.

Food Quantity Discrimination in Angelfish (Pterophyllum scalare): The Role of Number, Density, Size and Area Occupied by the Food Items

Quantity discrimination, the ability to identify, process, and respond to differences in number, has been shown in a variety of animal species and may have fitness value. In fish, the ability to distinguish between numerically different shoals has been well studied. However, little work has been devoted to the investigation of such ability in a foraging context. Nevertheless, angelfish (Pterophyllum scalare) have been previously shown to be able to discriminate numerically different sets of food items, with variables such as size and density of the food items playing important roles in making the choice. Here, we examine the possible role of other numerical and non-numerical variables. Using a spontaneous binary choice task, we contrasted sets of food items differing in specifically controlled ways: (1) different numerical size but equal inter-item distance; (2) different numerical size and different inter-item distance; and (3) identical total contour length and area occupied but different individual food size and inter-food distance between the contrasted food sets. In Experiment 1, angelfish were found to prefer the sets with a large number of food items. In Experiment 2, they preferred the numerically smaller sets with clustered items to the numerically larger sets with scattered items, but only when the sets were in the large number range (10 vs. 5 food items). Finally, in Experiment 3 fish preferred numerically smaller sets with large-sized and scattered food items in the large number range sets. We conclude that food item number, density, and size may not be considered individually by angelfish, but instead, the fish respond to all these factors attempting to maximize energy gained from eating the food while minimizing energy expenditure collecting and/or protecting the food.

Spontaneous quantity discrimination of artificial flowers by foraging honeybees

Many animals need to process numerical and quantity information in order to survive. Spontaneous quantity discrimination allows differentiation between two or more quantities without reinforcement or prior training on any numerical task. It is useful for assessing food resources, aggressive interactions, predator avoidance and prey choice. Honeybees have previously demonstrated landmark counting, quantity matching, use of numerical rules, quantity discrimination and arithmetic, but have not been tested for spontaneous quantity discrimination. In bees, spontaneous quantity discrimination could be useful when assessing the quantity of flowers available in a patch and thus maximizing foraging efficiency. In the current study, we assessed the spontaneous quantity discrimination behaviour of honeybees. Bees were trained to associate a single yellow artificial flower with sucrose. Bees were then tested for their ability to discriminate between 13 different quantity comparisons of artificial flowers (numeric ratio range: 0.08–0.8). Bees significantly preferred the higher quantity only in comparisons where ‘1’ was the lower quantity and where there was a sufficient magnitudinal distance between quantities (e.g. 1 versus 12, 1 versus 4, and 1 versus 3 but not 1 versus 2). Our results suggest a possible evolutionary benefit to choosing a foraging patch with a higher quantity of flowers when resources are scarce.

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.

Anisotropy of perceived space in non-primates? The horizontal-vertical illusion in bearded dragons (Pogona vitticeps) and red-footed tortoises (Chelonoidis carbonaria)

The horizontal-vertical illusion is a size illusion in which two same-sized objects appear to be different if presented on a horizontal or vertical plane, with the vertical one appearing longer. This illusion represents one of the main evidences of the anisotropy of the perceived space of humans, an asymmetrical perception of the object size presented in the vertical and horizontal space. Although this illusion has been widely investigated in humans, there is an almost complete lack of studies in non-human animals. Here we investigated whether reptiles perceive the horizontal-vertical illusion. We tested two reptile species: bearded dragons (Pogona vitticeps) and red-footed tortoises (Chelonoidis carbonaria). In control trials, two different-sized food strips were presented and animals were expected to choose the longer one. In test trials, animals received two same-sized strips, presented in a spatial arrangement eliciting the illusion. Only bearded dragons significantly preferred the longer strip in control trials; in test trials, bearded dragons selected the strip arranged vertically, suggesting a human-like perception of this pattern, while no clear choice for either array was observed in tortoises. Our results raise the interesting possibility that the anisotropy of perceived space can exists also in a reptile brain.

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.

Revisiting more or less: influence of numerosity and size on potential prey choice in the domestic cat

Quantity discrimination is of adaptive relevance in a wide range of contexts and across a wide range of species. Trained domestic cats can discriminate between different numbers of dots, and we have shown that they also spontaneously choose between different numbers and sizes of food balls. In the present study we performed two experiments with 24 adult cats to investigate spontaneous quantity discrimination in the more naturalistic context of potential predation. In Experiment 1 we presented each cat with the simultaneous choice between a different number of live prey (1 white mouse vs. 3 white mice), and in Experiment 2 with the simultaneous choice between live prey of different size (1 white mouse vs. 1 white rat). We repeated each experiment six times across 6 weeks, testing half the cats first in Experiment 1 and then in Experiment 2, and the other half in the reverse order. In Experiment 1 the cats more often chose the larger number of small prey (3 mice), and in Experiment 2, more often the small size prey (a mouse). They also showed repeatable individual differences in the choices which they made and in the performance of associated predation-like behaviours. We conclude that domestic cats spontaneously discriminate between the number and size of potential prey in a way that can be interpreted as adaptive for a lone-hunting, obligate carnivore, and show complex levels of risk-reward analysis.

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.

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.

Canine sense of quantity: evidence for numerical ratio-dependent activation in parietotemporal cortex

The approximate number system (ANS), which supports the rapid estimation of quantity, emerges early in human development and is widespread across species. Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms. Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals. To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging. Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing. We found evidence of ratio-dependent activation, which is a key feature of the ANS, in canine parietotemporal cortex in the majority of dogs tested. This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.

The role of item size on choosing contrasted food quantities in angelfish (Pterophyllum scalare)

Comparative studies on quantity discrimination in animals are important for understanding potential evolutionary roots of numerical competence. A previous study with angelfish has shown that they discriminate numerically different sets of same-sized food items and prefer the larger set. However, variables that covary with number were not controlled and choice could have been influenced by variables such as size or density of the food items rather than numerical attributes. Here using a recently developed approach, we examined whether contour length of the food items affects choice in a spontaneous binary choice task. In Experiment 1, a contrast of 1 vs. 1 food item was presented, but the ratio between the size (diameter) of the food items was varied. In Experiment 2, numerically different food sets were equated in overall size by increasing the size (diameter) of the items in the numerically small sets. In both Experiments, subjects showed a preference for the larger sized food items with a discrimination limit. These results show that item size plays a prominent role in foraging decisions in angelfish. Experiment 3 placed numerical and size attributes of the sets in conflict by presenting one larger-sized food item in the numerically smaller set that also had smaller overall size (diameter) of food items. Angelfish showed no preference in any of the contrasts, suggesting that they could not make optimal foraging decisions when these attributes were in conflict. Maximization of energy return is central to optimal foraging. Accordingly, here item size was also found to be a key feature of the sets, although the numerical attributes of the sets also influenced the choice.

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.

Honeybees use absolute rather than relative numerosity in number discrimination

Various vertebrate species use relative numerosity judgements in comparative assessments of quantities for which they use larger/smaller relationships rather than absolute number. The numerical ability of honeybees shares basic properties with that of vertebrates but their use of absolute or relative numerosity has not been explored. We trained free-flying bees to choose variable images containing three dots; one group ('larger') was trained to discriminate 3 from 2, while another group ('smaller') was trained to discriminate 3 from 4. In both cases, numbers were kept constant but stimulus characteristics and position were varied from trial to trial. Bees were then tested with novel stimuli displaying the previously trained numerosity (3) versus a novel numerosity (4 for 'larger' and 2 for 'smaller'). Both groups preferred the three-item stimulus, consistent with absolute numerosity. They also exhibited ratio-dependent discrimination of numbers, a property shared by vertebrates, as performance after 2 versus 3 was better than after 3 versus 4 training. Thus, bees differ from vertebrates in their use of absolute rather than of relative numerosity but they also have some numeric properties in common.

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

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

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

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

Insect-Inspired Sequential Inspection Strategy Enables an Artificial Network of Four Neurons to Estimate Numerosity

Varying levels of numerical cognition have been found in several animal species. Bees, in particular, have been argued to be able to count up to four items and solve complex numerical tasks. Here we present an exceedingly simple neural circuit that, when provided with the actual visual input that the bee is receiving while carrying out the task, can make reliable estimates on the number of items in the display. Thus we suggest that the elegance of numerical problem solving in bees might not lie in the formation of numerical concepts (such as “more,” “less,” or “zero”), but in the use of specific flight movements to scan targets, which streamlines the visual input and so renders the task of counting computationally inexpensive. Careful examination of the actual inspection strategies used by animals might reveal that animals often employ active scanning behaviors as shortcuts to simplify complex visual pattern discrimination tasks.

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Small-brained animals such as bees can solve counting tasks

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Exceedingly small neural circuits can mediate numerosity estimations

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The method requires a sequential inspection strategy to generate the visual input

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Active scanning behavior is suggested to play a role in complex cognitive tasks

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

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

Numerical assessment in the wild: insights from social carnivores

Playback experiments have proved to be a useful tool to investigate the extent to which wild animals understand numerical concepts and the factors that play into their decisions to respond to different numbers of vocalizing conspecifics. In particular, playback experiments have broadened our understanding of the cognitive abilities of historically understudied species that are challenging to test in the traditional laboratory, such as members of the Order Carnivora. Additionally, playback experiments allow us to assess the importance of numerical information versus other ecologically important variables when animals are making adaptive decisions in their natural habitats. Here, we begin by reviewing what we know about quantity discrimination in carnivores from studies conducted in captivity. We then review a series of playback experiments conducted with wild social carnivores, including African lions, spotted hyenas and wolves, which demonstrate that these animals can assess the number of conspecifics calling and respond based on numerical advantage. We discuss how the wild studies complement those conducted in captivity and allow us to gain insights into why wild animals may not always respond based solely on differences in quantity. We then consider the key roles that individual discrimination and cross-modal recognition play in the ability of animals to assess the number of conspecifics vocalizing nearby. Finally, we explore new directions for future research in this area, highlighting in particular the need for further work on the cognitive basis of numerical assessment skills and experimental paradigms that can be effective in both captive and wild settings.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Quantity Discrimination in Trained Lizards (Podarcis sicula)

Quantitative abilities have been reported in many animal species. Two main methods have been extensively used: spontaneous choice tests and training procedures. A recent study showed that ruin lizards are capable of spontaneously discriminating between the surface area of two food items of different size, but failed when food was presented in sets of discrete items differing in number. In the present study, we used a training procedure to further investigate quantitative abilities in ruin lizards. Subjects were presented with two sets of yellow disks differing either in number (Experiment 1) or in area (Experiment 2) and were trained on different discriminations of increasing difficulty (1 vs. 4, 2 vs. 4, and 2 vs. 3). Results showed that lizards were more accurate in discriminating sets of discrete items differing in number than the area of two individual items, in contrast to what had earlier been observed in spontaneous choice tests. Although we cannot exclude other factors that affected the performance of ruin lizards, the poor accuracy here observed in both experiments might reflect a true limit in lizards' quantitative abilities.