Can angelfish (Pterophyllum scalare) count? Discrimination between different shoal sizes follows Weber’s law

Trained quantity discrimination in invasive red-eared slider and a comparison with the native stripe-necked turtle

Little is known about the behavioral and cognitive traits that best predict invasion success. Evidence is mounting that cognitive performance correlates with survival and fecundity, two pivotal factors for the successful establishment of invasive populations. We assessed the quantity discrimination ability of the globally invasive red-eared slider (Trachemys scripta elegans). We further compared it to that of the native stripe-necked turtle (Mauremys sinensis), which has been previously evaluated for its superior quantity discrimination ability. Specifically, our experimental designs aimed to quantify the learning ability as numerosity pairs increased in difficulty (termed fixed numerosity tests), and the immediate response when turtles were presented with varied challenges concurrently in the same tests (termed mixed numerosity tests). Our findings reaffirm the remarkable ability of freshwater turtles to discern numerical differences as close as 9 vs 10 (ratio = 0.9), which was comparable to the stripe-necked turtle's performance. However, the red-eared slider exhibited a moderate decrease in performance in high ratio tests, indicating a potentially enhanced cognitive capacity to adapt to novel challenges. Our experimental design is repeatable and is adaptable to a range of freshwater turtles. These findings emphasize the potential importance of cognitive research to the underlying mechanisms of successful species invasions.

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.

A Shared Intuitive (Mis)understanding of Psychophysical Law Leads Both Novices and Educated Students to Believe in a Just Noticeable Difference (JND)

Humans are both the scientists who discover psychological laws and the thinkers who behave according to those laws. Oftentimes, when our natural behavior is in accord with those laws, this dual role serves us well: our intuitions about our own behavior can serve to inform our discovery of new laws. But, in cases where the laws that we discover through science do not agree with the intuitions and biases we carry into the lab, we may find it harder to believe in and adopt those laws. Here, we explore one such case. Since the founding of psychophysics, the notion of a Just Noticeable Difference (JND) in perceptual discrimination has been ubiquitous in experimental psychology-even in spite of theoretical advances since the 1950's that argue that there can be no such thing as a threshold in perceiving difference. We find that both novices and psychologically educated students alike misunderstand the JND to mean that, below a certain threshold, humans will be unable to tell which of two quantities is greater (e.g., that humans will be completely at chance when trying to judge which is heavier, a bag with 3000 grains of sand or 3001). This belief in chance performance below a threshold is inconsistent with psychophysical law. We argue that belief in a JND is part of our intuitive theory of psychology and is therefore very difficult to dispel.

Proportional processing of a visual mate choice signal in the green swordtail, Xiphophorus hellerii

During mate choice, receivers often assess the magnitude (duration, size, etc.) of signals that vary along a continuum and reflect variation in signaller quality. It is generally assumed that receivers assess this variation linearly, meaning each difference in signalling trait between signallers results in a commensurate change in receiver response. However, increasing evidence shows receivers can respond to signals non-linearly, for example through Weber's Law of proportional processing, where discrimination between stimuli is based on proportional, rather than absolute, differences in magnitude. We quantified mate preferences of female green swordtail fish, Xiphophorus hellerii, for pairs of males differing in body size. Preferences for larger males were better predicted by the proportional difference between males (proportional processing) than the absolute difference (linear processing). This demonstration of proportional processing of a visual signal implies that receiver perception may be an important mechanism selecting against the evolution of ever-larger signalling traits.

Congratulations to Animal Cognition on its 50th birthday! Some thoughts on the last 50 years of animal cognition research

In this article, the author reflects on some of the key issues that have arisen in comparative cognition and the role and impact of the journal Animal Cognition through its first 25 years by pretending to look back at this period from the year 2047. Successes within comparative cognition are described and the role that Animal Cognition has played in the growth of comparative cognition are discussed. Concerns are presented about issues that affect the opportunities that researchers have to work with nonhuman species and to produce good comparative cognitive science. Prescriptions for what the author hopes will happen next also are offered all in the lens of a prospectively imagined retrospective on this field.

A neural theory for counting memories

Keeping track of the number of times different stimuli have been experienced is a critical computation for behavior. Here, we propose a theoretical two-layer neural circuit that stores counts of stimulus occurrence frequencies. This circuit implements a data structure, called a count sketch, that is commonly used in computer science to maintain item frequencies in streaming data. Our first model implements a count sketch using Hebbian synapses and outputs stimulus-specific frequencies. Our second model uses anti-Hebbian plasticity and only tracks frequencies within four count categories ("1-2-3-many"), which trades-off the number of categories that need to be distinguished with the potential ethological value of those categories. We show how both models can robustly track stimulus occurrence frequencies, thus expanding the traditional novelty-familiarity memory axis from binary to discrete with more than two possible values. Finally, we show that an implementation of the "1-2-3-many" count sketch exists in the insect mushroom body.

Avoiding costly mistakes in groups: The evolution of error management in collective decision making

Individuals continuously have to balance the error costs of alternative decisions. A wealth of research has studied how single individuals navigate this, showing that individuals develop response biases to avoid the more costly error. We, however, know little about the dynamics in groups facing asymmetrical error costs and when social influence amplifies either safe or risky behavior. Here, we investigate this by modeling the decision process and information flow with a drift-diffusion model extended to the social domain. In the model individuals first gather independent personal information; they then enter a social phase in which they can either decide early based on personal information, or wait for additional social information. We combined the model with an evolutionary algorithm to derive adaptive behavior. We find that under asymmetric costs, individuals in large cooperative groups do not develop response biases because such biases amplify at the collective level, triggering false information cascades. Selfish individuals, however, undermine the group's performance for their own benefit by developing higher response biases and waiting for more information. Our results have implications for our understanding of the social dynamics in groups facing asymmetrical errors costs, such as animal groups evading predation or police officers holding a suspect at gunpoint.

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.

Comparison of anxiety-like and social behaviour in medaka and zebrafish

The medaka, Oryzias latipes, is rapidly growing in importance as a model in behavioural research. However, our knowledge of its behaviour is still incomplete. In this study, we analysed the performance of medaka in 3 tests for anxiety-like behaviour (open-field test, scototaxis test, and diving test) and in 3 sociability tests (shoaling test with live stimuli, octagonal mirror test, and a modified shoaling test with mirror stimulus). The behavioural response of medaka was qualitatively similar to that observed in other teleosts in the open-field test (thigmotaxis), and in 2 sociability tests, the shoaling test and in the octagonal mirror test (attraction towards the social stimulus). In the remaining tests, medaka did not show typical anxiety (i.e., avoidance of light environments and preference for swimming at the bottom of the aquarium) and social responses (attraction towards the social stimulus). As a reference, we compared the behaviour of the medaka to that of a teleost species with well-studied behaviour, the zebrafish, tested under the same conditions. This interspecies comparison indicates several quantitative and qualitative differences across all tests, providing further evidence that the medaka responds differently to the experimental settings compared to other fish models.

Numerosity Categorization by Parity in an Insect and Simple Neural Network

A frequent question as technology improves and becomes increasingly complex, is how we enable technological solutions and models inspired by biological systems. Creating technology based on humans is challenging and costly as human brains and cognition are complex. The honeybee has emerged as a valuable comparative model which exhibits some cognitive-like behaviors. The relative simplicity of the bee brain compared to large mammalian brains enables learning tasks, such as categorization, that can be mimicked by simple neural networks. Categorization of abstract concepts can be essential to how we understand complex information. Odd and even numerical processing is known as a parity task in human mathematical representations, but there appears to be a complete absence of research exploring parity processing in non-human animals. We show that free-flying honeybees can visually acquire the capacity to differentiate between odd and even quantities of 1–10 geometric elements and extrapolate this categorization to the novel numerosities of 11 and 12, revealing that such categorization is accessible to a comparatively simple system. We use this information to construct a neural network consisting of five neurons that can reliably categorize odd and even numerosities up to 40 elements. While the simple neural network is not directly based on the biology of the honeybee brain, it was created to determine if simple systems can replicate the parity categorization results we observed in honeybees. This study thus demonstrates that a task, previously only shown in humans, is accessible to a brain with a comparatively small numbers of neurons. We discuss the possible mechanisms or learning processes allowing bees to perform this categorization task, which range from numeric explanations, such as counting, to pairing elements and memorization of stimuli or patterns. The findings should encourage further testing of parity processing in a wider variety of animals to inform on its potential biological roots, evolutionary drivers, and potential technology innovations for concept processing.

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.

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.

Optimal Allocation Ratios: A Square Root Relationship between the Ratios of Symbiotic Costs and Benefits

AbstractAll organisms struggle to make sense of environmental stimuli in order to maximize their fitness. For animals, the responses of single cells and superorganisms to stimuli are generally proportional to stimulus ratios, a phenomenon described by Weber's law. However, Weber's law has not yet been used to predict how plants respond to stimuli generated from their symbiotic partners. Here we develop a model for quantitatively predicting the ratios of carbon (C) allocation to symbionts that provide nutrients to their plant host. Consistent with Weber's law, our model demonstrates that the optimal ratio of resources allocated to a less beneficial relative to a more beneficial symbiont scale to the ratio of the growth benefits of the two strains. As C allocation to symbionts increases, the ratio of C allocation to two strains approaches the square root of the ratio of symbiotic growth benefits (e.g., a worse symbiont providing one-fourth the benefits gets 1/4=1/2 the C of a better symbiont). We document a compelling correspondence between our square root model prediction and a meta-analysis of experimental literature on C allocation. This type of preferential allocation can promote coexistence between more beneficial and less beneficial symbionts, offering a potential mechanism behind the high diversity of microbial symbionts observed in nature.

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.

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.

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.

Why and how to apply Weber's Law to coevolution and mimicry

In mimicry systems, receivers discriminate between the stimuli of models and mimics. Weber's Law of proportional processing states that receiver discrimination is based on proportional, not absolute, differences between stimuli. Weber's Law operates in a variety of taxa and modalities, yet it has largely been ignored in the context of mimicry, despite its potential relevance to whether receivers can discriminate models from mimics. Specifically, Weber's Law implies that for a given difference in stimulus magnitude between a model and mimic, as stimulus magnitudes increase, the mimic will be less discriminable from their model. This implies that mimics should benefit when stimulus magnitudes are high, and that high stimulus magnitudes will reduce selection for mimetic fidelity. Whether models benefit from high stimulus magnitudes depends on whether mimicry is honest or deceptive. We present four testable predictions about evolutionary trajectories of models and mimics based on this logic. We then provide a framework for testing whether receiver discrimination adheres to Weber's Law and illustrate it using coevolutionary examples and case studies from avian brood parasitism. We conclude that, when studying mimicry systems, researchers should consider whether receiver perception conforms to Weber's Law, because it could drive stimulus evolution in counterintuitive directions.

Performance of Asian elephants (Elephas maximus) on a quantity discrimination task is similar to that of African savanna elephants (Loxodonta africana)

Using an object-choice task, we measured the relative quantity discrimination ability of Asian elephants. Two zoo-housed elephants were given auditory cues of food being dropped into two containers (Nonvisible condition), and in one condition they could also see the food on top of the containers (Visible condition). Elephants received sets of varying ratios and magnitudes. We found that the elephants chose the greater quantity of food significantly above chance in both the Visible and Nonvisible conditions. Additionally, we found the elephants' ability to discriminate between quantities decreased as the ratio, and not the absolute difference, between the quantities increased, which is predicted by the accumulator model. We also compare our findings to those from a study using the same methods with African savanna elephants and found that the two species performed at similar levels, but given our small sample size it is difficult to make strong species-level conclusions. In discussing our results, we consider differences between the two species' wild environments as well as the types of sensory cues provided in human care, and we provide recommendations for extensions of this work.

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.

A sense of number in invertebrates

Non-symbolic numerical abilities are widespread among vertebrates due to their important adaptive value. Moreover, these abilities were considered peculiar of vertebrate species as numerical competence is regarded as cognitively sophisticated. However, recent evidence convincingly showed that this is not the case: invertebrates, with their limited number of neurons, proved able to successfully discriminate different quantities (e.g., of prey), to use the ordinal property of numbers, to solve arithmetic operations as addition and subtraction and even to master the concept of zero numerosity. To date, though, the debate is still open on the presence and the nature of a «sense of number» in invertebrates. Whether this is peculiar for discrete countable quantities (numerosities) or whether this is part of a more general magnitude system dealing with both discrete and continuous quantities, as hypothesized for humans and other vertebrates. Here we reviewed the main studies on numerical abilities of invertebrates, discussing in particular the recent findings supporting the hypothesis of a general mechanism that allows for processing of both discrete (i.e., number) and continuous dimensions (e.g., space).

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.

Use of numerical and spatial information in ordinal counting by zebrafish

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

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.

Evidence for individual discrimination and numerical assessment in collective antipredator behaviour in wild jackdaws (Corvus monedula)

Collective responses to threats occur throughout the animal kingdom but little is known about the cognitive processes underpinning them. Antipredator mobbing is one such response. Approaching a predator may be highly risky, but the individual risk declines and the likelihood of repelling the predator increases in larger mobbing groups. The ability to appraise the number of conspecifics involved in a mobbing event could therefore facilitate strategic decisions about whether to join. Mobs are commonly initiated by recruitment calls, which may provide valuable information to guide decision-making. We tested whether the number of wild jackdaws responding to recruitment calls was influenced by the number of callers. As predicted, playbacks simulating three or five callers tended to recruit more individuals than playbacks of one caller. Recruitment also substantially increased if recruits themselves produced calls. These results suggest that jackdaws use individual vocal discrimination to assess the number of conspecifics involved in initiating mobbing events, and use this information to guide their responses. Our results show support for the use of numerical assessment in antipredator mobbing responses and highlight the need for a greater understanding of the cognitive processes involved in collective behaviour.

Impact of social rearing-environment on performance in a complex maze in females of a cichlid fish

Spatial orientation is an important skill as it improves, for example, foraging, localisation of recourses, predator avoidance or navigation. Habitat complexity positively affects spatial abilities in various fish species with a more complex environment promoting learning ability. However, to what extent a complex social environment affects cognitive abilities in fishes has received less attention. Here, we investigated differences in maze performance of adult females of the West African cichlid fish Pelvicachromis taeniatus, which had been reared and maintained either in a group or in isolation from an early age on. Fish had to master the route through a maze in order to gain a food reward. Our results indicate marked differences in performance contingent upon social rearing-environment: isolation fish ran successful trials (i.e. locating the food reward) significantly more often than group fish and were faster during trials, also in a reversed maze. However, the number of mistakes did not differ between isolation and group fish and the time needed to relocate the food reward did not diminish with elapsed training days. In a second experiment, the activity of group and isolation fish was analysed in an open field test. Here, isolation fish were less active than group fish. We discuss different possibilities for performance differences of group and isolation fish including enhanced cognitive abilities of isolation fish, motivational/emotional differences and hyperactivity.

An assessment of touchscreens for testing primate food preferences and valuations

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

Visuo-spatial (but not verbal) executive working memory capacity modulates susceptibility to non-numerical visual magnitudes during numerosity comparison

The present study tested whether visuo-spatial vs. verbal executive working memory capacity (hereafter EWM) modulates the degree to which non-numerical visual magnitudes influence numerosity comparison using pairs of dot arrays. We hypothesized that visuo-spatial (rather than verbal) EWM capacity would influence one’s ability to selectively focus on numerical as opposed to non-numerical visual properties (such as dot size, cumulative area, density) of the dot arrays during numerosity comparison. Participants’ performance was better on trials in which non-numerical visual magnitudes were negatively (vs. positively) correlated with numerosity (i.e., reverse congruency effect). The Low visuo-spatial EWM group manifested greater reverse congruency effect compared to the High visuo-spatial EWM group. A trial-based hierarchical regression on the accuracy of each trial using the ratio of (numerical and non-numerical) visual magnitudes as predictors revealed that the ratio of numerical vs. non-numerical visual magnitudes explained the greatest variance in the performance of the High vs. Low visuo-spatial EWM groups, respectively. In contrast, there was no difference between the High vs. Low verbal EWM groups from the same analysis. These results reveal differential susceptibility to numerical vs. non-numerical visual information depending on the capacity of visuo-spatial (but not verbal) EWM. Taken together, numerosity comparison performance measured with the dot comparison paradigm seems to reflect not only one’s acuity for numerosity discrimination but also visuo-spatial EWM capacity likely required during integration of visual magnitudes during numerosity comparison.

Cognitive access to numbers: the philosophical significance of empirical findings about basic number abilities

How can we acquire a grasp of cardinal numbers, even the first very small positive cardinal numbers, given that they are abstract mathematical entities? That problem of cognitive access is the main focus of this paper. All the major rival views about the nature and existence of cardinal numbers face difficulties; and the view most consonant with our normal thought and talk about numbers, the view that cardinal numbers are sizes of sets, runs into the cognitive access problem. The source of the problem is the plausible assumption that cognitive access to something requires causal contact with it. It is argued that this assumption is in fact wrong, and that in this and similar cases, we should accept that a certain recognize-and-distinguish capacity is sufficient for cognitive access. We can then go on to solve the cognitive access problem, and thereby support the set-size view of cardinal numbers, by paying attention to empirical findings about basic number abilities. To this end, some selected studies of infants, pre-school children and a trained chimpanzee are briefly discussed.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Evolution of cognitive and neural solutions enabling numerosity judgements: lessons from primates and corvids

Brains that are capable of representing numerosity, the number of items in a set, have arisen repeatedly and independently in different animal taxa. This review compares the cognitive and physiological mechanisms found in a nonhuman primate, the rhesus macaque, and a corvid songbird, the carrion crow, in order to elucidate the evolutionary adaptations underlying numerical competence. Monkeys and corvids are known for their advanced cognitive competence, despite them both having independently and distinctly evolved endbrains that resulted from a long history of parallel evolution. In both species, numerosity is represented as an analogue magnitude by an approximate number system that obeys the Weber-Fechner Law. In addition, the activity of numerosity-selective neurons in the fronto-parietal association cortex of monkeys and the telencephalic associative area nidopallium caudolaterale of crows mirrors the animals' performance. In both species' brains, neuronal activity is tuned to a preferred numerosity, encodes the numerical value in an approximate fashion, and is best represented on a logarithmic scale. Collectively, the data show an impressive correspondence of the cognitive and neuronal mechanisms for numerosity representations across monkeys and crows. This suggests that remotely related vertebrates with distinctly developed endbrains adopted similar physiological solutions to common computational problems in numerosity processing.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

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'.

Psychophysical Laws and the Superorganism

Through theoretical analysis, we show how a superorganism may react to stimulus variations according to psychophysical laws observed in humans and other animals. We investigate an empirically-motivated honeybee house-hunting model, which describes a value-sensitive decision process over potential nest-sites, at the level of the colony. In this study, we show how colony decision time increases with the number of available nests, in agreement with the Hick-Hyman law of psychophysics, and decreases with mean nest quality, in agreement with Piéron’s law. We also show that colony error rate depends on mean nest quality, and difference in quality, in agreement with Weber’s law. Psychophysical laws, particularly Weber’s law, have been found in diverse species, including unicellular organisms. Our theoretical results predict that superorganisms may also exhibit such behaviour, suggesting that these laws arise from fundamental mechanisms of information processing and decision-making. Finally, we propose a combined psychophysical law which unifies Hick-Hyman’s law and Piéron’s law, traditionally studied independently; this unified law makes predictions that can be empirically tested.

Relational concept learning in domestic dogs: Performance on a two-choice size discrimination task generalises to novel stimuli

One central issue in the study of animal cognition concerns conceptual behaviour, where an organism categorises objects, events, and relationships so as to transfer previously learned rules to novel contexts. In this study, we investigated whether or not dogs demonstrate conceptual behaviour in the form of simple relational class concept learning. A two-choice visual discrimination task was used to assess if dogs are capable of simple relational class concept learning by generalising the same rule (i.e. circle is larger or smaller than) to various novel shapes. Eight purebred Lagotto Romagnolos were included in the study. The results demonstrated that they were capable of generalising a previously learned size discrimination rule to novel stimuli; however, there were differences in dog's generalization capabilities across certain shapes. Considering their unique relationship with humans, and their immediacy in everyday life, a better understanding of conceptual behaviour and generalising abilities in domestic dogs may have implications for training and management methods, as well as contributing to comparative psychology and applied ethology.

Quantity discrimination in angelfish (Pterophyllum scalare) is maintained after a 30-s retention interval in the large but not in the small number range

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

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

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

Symbol-value association and discrimination in the archerfish

One of the most important aspects of mathematical cognition in humans is the ability to symbolically represent magnitudes and quantities. In the last 20 years it has been shown that not only humans but also other primates, birds and dolphins can use symbolic representation of quantities. However, it remains unclear to what extent this ability is spread across the animal kingdom. Here, by training archerfish to associate variable amounts of rewards with different geometric shapes, we show for the first time that lower vertebrates can also associate a value with a symbol and make a decision that maximizes their food intake based on this information. In addition, the archerfish is able to understand up to four different quantities and organize them mentally in an ordinal manner, similar to observations in higher vertebrates. These findings point in the direction of the existence of an approximate magnitude system in fish.

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

The ability to use quantitative information is thought to be adaptive in a wide range of ecological contexts. For nearly a century, the numerical abilities of mammals and birds have been extensively studied using a variety of approaches. However, in the last two decades, there has been increasing interest in investigating the numerical abilities of teleosts (i.e. a large group of ray-finned fish), mainly due to the practical advantages of using fish species as models in laboratory research. Here, we review the current state of the art in this field. In the first part, we highlight some potential ecological functions of numerical abilities in fish and summarize the existing literature that demonstrates numerical abilities in different fish species. In many cases, surprising similarities have been reported among the numerical performance of mammals, birds and fish, raising the question as to whether vertebrates' numerical systems have been inherited from a common ancestor. In the second part, we will focus on what we still need to investigate, specifically the research fields in which the use of fish would be particularly beneficial, such as the genetic bases of numerical abilities, the development of these abilities and the evolutionary foundation of vertebrate number sense.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Numerical abilities in fish: A methodological review

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

Animated images in the analysis of zebrafish behavior

This invited review is based upon a recent oral paper I presented at the Virtual Reality Symposium of the 34th International Ethological Conference (2015, Cairns, Australia), and as such it describes studies conducted mainly in my own laboratory. It reviews how we utilized visual stimuli for inducing behavioral responses in the zebrafish with a focus on shoaling, group forming behavior. The zebrafish is gaining increasing popularity in neuroscience. With this interest, its behavior is also more frequently studied. One of the many advantages of the zebrafish over traditional laboratory rodents is that this species is diurnal, and it relies heavily upon its visual system. Thus, similarly to our own species, zebrafish respond to visual stimuli in a robust and easily quantifiable manner. For the past decade, we have been exploring how to use such visual stimuli, and have developed numerous paradigms with which we can induce and quantify a variety of behavioral responses, including shoaling. This review summarizes some of these studies, and discusses questions including whether one should use live fish as stimulus, whether and how one could present animated (moving images) of fish, and how one could optimize a range of stimulus presentation parameters to elicit the most robust responses in zebrafish. Although the zebrafish is a relative newcomer in ethology and behavioral neuroscience, and although many of our findings only represent the first steps in this research, our results suggest that the behavioral analysis of the zebrafish will have an important place in biomedical research.

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

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