Numerical abilities in fish: A methodological review

Lessons in cognition: A review of maze designs and procedures used to measure spatial learning in fish

The use of different mazes to assess spatial learning has become more common in fish behavior studies in recent decades. This increase in fish cognition research has opened the door to numerous possibilities for exciting and diverse questions, such as identifying ecological drivers of spatial cognition and understanding the role individual variation plays in navigational abilities. There are many different types of mazes, each with its own specific considerations, making it challenging to determine exactly which spatial test is the most relevant and appropriate for a particular experiment. Many spatial mazes, such as the T-maze and Y-maze, have been successfully adapted from rodent studies, particularly with respect to zebrafish, a widely accepted non-mammalian model in biomedical studies. Standardization across studies is increasing with these easily accessible maze designs, validating them for use in fish; however, variations in design (e.g., length of arms and scale) and procedure still exist, and the impact of these variations on results is largely unknown. The efforts to standardize mazes outside zebrafish work are also more limited. Other mazes have been developed specifically for use on fish, with design modifications varying widely, making it difficult to draw comparisons. In this review, we have highlighted the many design and procedural elements that should be considered for the acquisition of reliable behavioral data, with the goal of drawing readers' attention to aspects of experimentation that are often not given the careful consideration that they deserve. We then argue that additional focused research and reporting is needed to produce more reliable methods in spatial learning research across a broader range of subjects.

Neurobiology of numerical learning

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

Numerical Representation for Action in Crows Obeys the Weber-Fechner Law

The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows (Corvus corone) to judge numerical values of instruction stimuli from one to five and to flexibly perform a matching number of pecks. Our quantitative analysis of the crows' number production performance shows the same behavioral regularities that have previously been demonstrated for the judgment of sensory numerosity, such as the numerical distance effect, the numerical magnitude effect, and the logarithmical compression of the number line. The presence of these psychophysical phenomena in crows producing number of pecks suggests a unified sensorimotor number representation system underlying the judgment of the number of external stimuli and internally generated actions.

Teleosts as behaviour test models for social stress

Stress is an important aspect of our everyday life and exposure to it is an unavoidable occurrence. In humans, this can come in the form of social stress or physical stress from an injury. Studies in animal models have helped researchers to understand the body's adaptive response to stress in human. Notably, the use of behavioural tests in animal models plays a pivotal role in understanding the neural, endocrine and behavioural changes induced by social stress. Under socially stressed conditions, behavioural parameters are often measured physiological and molecular parameters as changes in behaviour are direct responses to stress and are easily assessed by behavioural tests. Throughout the past few decades, the rodent model has been used as a well-established animal model for stress and behavioural changes. Recently, more attention has been drawn towards using fish as an animal model. Common fish models such as zebrafish, medaka, and African cichlids have the advantage of a higher rate of reproduction, easier handling techniques, sociability and most importantly, share evolutionary conserved genetic make-up, neural circuitry, neuropeptide molecular structure and function with mammalian species. In fact, some fish species exhibit a clear diurnal or seasonal rhythmicity in their stress response, similar to humans, as opposed to rodents. Various social stress models have been established in fish including but not limited to chronic social defeat stress, social stress avoidance, and social stress-related decision-making. The huge variety of behavioural patterns in teleost also aids in the study of more behavioural phenotypes than the mammalian species. In this review, we focus on the use of fish models as alternative models to study the effects of stress on different types of behaviours. Finally, fish behavioural tests against the typical mammalian model-based behavioural test are compared and discussed for their viability.

Crows flexibly apply statistical inferences based on previous experience

Statistical inference, the ability to use limited information to draw conclusions about the likelihood of an event, is critical for decision-making during uncertainty. The ability to make statistical inferences was thought to be a uniquely human skill requiring verbal instruction and mathematical reasoning.1 However, basic inferences have been demonstrated in both preliterate and pre-numerate individuals,2,3,4,5,6,7 as well as non-human primates.8 More recently, the ability to make statistical inferences has been extended to members outside of the primate lineage in birds.9,10 True statistical inference requires subjects use relative rather than absolute frequency of previously experienced events. Here, we show that crows can relate memorized reward probabilities to infer reward-maximizing decisions. Two crows were trained to associate multiple reward probabilities ranging from 10% to 90% to arbitrary stimuli. When later faced with the choice between various stimulus combinations, crows retrieved the reward probabilities associated with individual stimuli from memory and used them to gain maximum reward. The crows showed behavioral distance and size effects when judging reward values, indicating that the crows represented probabilities as abstract magnitudes. When controlling for absolute reward frequency, crows still made reward-maximizing choices, which is the signature of true statistical inference. Our study provides compelling evidence of decision-making by relative reward frequency in a statistical inference task.

The role of non-numerical information in the perception of temporal numerosity

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

Environmental enrichment improves cognitive flexibility in rainbow trout in a visual discrimination task: first insights

Research on fish cognition provides strong evidence that fish are endowed with high level cognitive skills. However, most studies on cognitive flexibility and generalization abilities, two key adaptive traits for captive animals, focused on model species, and farmed fish received too little attention. Environmental enrichment was shown to improve learning abilities in various fish species, but its influence on cognitive flexibility and generalization abilities is still unknown. We studied farmed rainbow trout (Oncorhynchus mykiss) as an aquaculture model to study how environmental enrichment impacts their cognitive abilities. Using an operant conditioning device, allowing the expression of a motivated choice, we measured fish cognitive flexibility with serial reversal learning tests, after a successful acquisition phase based on two colors discrimination (2-alternative forced choice, 2-AFC), and their ability to generalize a rewarded color to any shape. Eight fish were divided into two groups: Condition E (fish reared from fry stages under enriched conditions with plants, rocks and pipes for ~9 months); Condition B (standard barren conditions). Only one fish (condition E) failed in the habituation phase of the device and one fish (condition B) failed in the 2-AFC task. We showed that after a successful acquisition phase in which the fish correctly discriminated two colors, they all succeeded in four reversal learnings, supporting evidence for cognitive flexibility in rainbow trout. They were all successful in the generalization task. Interestingly, fish reared in an enriched environment performed better in the acquisition phase and in the reversal learning (as evidenced by fewer trials needed to reach the learning criterion), but not in the generalization task. We assume that color-based generalization may be a simpler cognitive process than discriminative learning and cognitive flexibility, and does not seem to be influenced by environmental conditions. Given the small number of individuals tested, our results may be considered as first insights into cognitive flexibility in farmed fish using an operant conditioning device, but they pave the way for future studies. We conclude that farming conditions should take into account the cognitive abilities of fish, in particular their cognitive flexibility, by allowing them to live in an enriched environment.

Brain areas activated during visual learning in the cichlid fish Pseudotropheus zebra

The neural correlates of most cognitive functions in fish are unknown. This project aimed to identify brain regions involved in visual learning in the cichlid fish Pseudotropheus zebra. The expression of the protein pS6 was measured in 19 brain areas and compared between groups of individuals subjected to four different behavioral contexts (control, avoidance, trained, and novelty groups). Control group individuals were sacrificed with minimal interactions. Fish in the avoidance group were chased with a net for an hour, after which they were sacrificed. Individuals in the trained group received daily training sessions to associate a visual object with a food reward. They were sacrificed the day they reached learning criterion. Fish in the novelty group were habituated to one set of visual stimuli, then faced a change in stimulus type (novelty stimulus) before they were sacrificed. Fish in the three treatment groups showed the largest activation of pS6 in the inferior lobes and the tectum opticum compared to the control group. The avoidance group showed additional activation in the preoptic area, several telencephalic regions, the torus semicircularis, and the reticular formation. The trained group that received a food reward, showed additional activation of the torus lateralis, a tertiary gustatory center. The only area that showed strong activation in all three treatment groups was the nucleus diffusus situated within the inferior lobe. The inferior lobe receives prominent visual input from the tectum via the nucleus glomerulosus but so far, nothing is known about the functional details of this pathway. Our study showed for the first time that the inferior lobes play an important role in visual learning and object recognition.

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.

Assessing the performance of brushtail possums (Trichosurus vulpecula) on the Mechner counting procedure

This study assessed brushtail possums' performance on the Mechner counting procedure. Six brushtail possums were required to produce different Fixed-Ratio (FR) response targets by lever pressing. Their responses provided access to food reinforcement delivered either upon completing the target FR response requirement on a single lever or, in different conditions, on completing the target FR before producing an additional response on a second lever. The mean number of responses on the first lever before switching to the second lever typically occurred just above the target FR response requirement (FR: 4, 8, 16, 32 and 64). The variability in the number of switches between the levers around the target FR decreased from the first 10 days to the last 10 days, indicating an improvement in counting accuracy over sessions. The time to switch between the first and second lever was consistently variable across response requirements suggesting that it is unlikely the possums were using time to predict when to switch levers. This research further supports the use of the Mechner procedure as a method for measuring counting ability in animals and confirms the possibility of numerical competence in a marsupial species.

Zebrafish excel in number discrimination under an operant conditioning paradigm

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

Neurons in the Dorso-Central Division of Zebrafish Pallium Respond to Change in Visual Numerosity

We found a region of the zebrafish pallium that shows selective activation upon change in the numerosity of visual stimuli. Zebrafish were habituated to sets of small dots that changed in individual size, position, and density, while maintaining their numerousness and overall surface. During dishabituation tests, zebrafish faced a change in number (with the same overall surface), in shape (with the same overall surface and number), or in size (with the same shape and number) of the dots, whereas, in a control group, zebrafish faced the same stimuli as during the habituation. Modulation of the expression of the immediate early genes c-fos and egr-1 and in situ hybridization revealed a selective activation of the caudal part of the dorso-central division of the zebrafish pallium upon change in numerosity. These findings support the existence of an evolutionarily conserved mechanism for approximate magnitude and provide an avenue for understanding its underlying molecular correlates.

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.

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

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

Understanding behaviour to improve the welfare of an ornamental fish

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

Neuroethology of number sense across the animal kingdom

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

Understanding fish cognition: a review and appraisal of current practices

With over 30,000 recognized species, fishes exhibit an extraordinary variety of morphological, behavioural, and life-history traits. The field of fish cognition has grown markedly with numerous studies on fish spatial navigation, numeracy, learning, decision-making, and even theory of mind. However, most cognitive research on fishes takes place in a highly controlled laboratory environment and it can therefore be difficult to determine whether findings generalize to the ecology of wild fishes. Here, we summarize four prominent research areas in fish cognition, highlighting some of the recent advances and key findings. Next, we survey the literature, targeting these four areas, and quantify the nearly ubiquitous use of captive-bred individuals and a heavy reliance on lab-based research. We then discuss common practices that occur prior to experimentation and within experiments that could hinder our ability to make more general conclusions about fish cognition, and suggest possible solutions. By complementing ecologically relevant laboratory-based studies with in situ cognitive tests, we will gain further inroads toward unraveling how fishes learn and make decisions about food, mates, and territories.

Nonhuman rationality: a predictive coding perspective

How can we rethink 'rationality' in the wake of animal and artificial intelligence studies? Can nonhuman systems be rational in any nontrivial sense? In this paper, we propose that all organisms, under certain circumstances, exhibit rationality to a diverse degree and aspect in the sense of the standard picture (SP): Their inferential processes conform to logic and probability rules. We first show that according to Calvo and Friston (J R Soc Interface 14(131):20170096, 2017) and Orlandi (2018), all biological systems must embody a top-down process (active inference) to minimize free energy. Next, based on Maddy's (Second philosophy, Oxford University Press, Oxford, 2007; The logical must: Wittgenstein on logic, Oxford University Press, Oxford, 2014) analysis, we argue that this inferential process conforms to logic and probability rules; thus, it satisfies the SP, which explains the rudimentary logic and arithmetic (e.g., categorizing and numbering) found among pigeons and mice. We also hold that the mammalian brain is only one among many ways of implementing rationality. Finally, we discuss data from microorganisms to support this view.

Does Brain Lateralization Affect the Performance in Binary Choice Tasks? A Study in the Animal Model Danio rerio

Researchers in behavioral neuroscience commonly observe the behavior of animal subjects in the presence of two alternative stimuli. However, this type of binary choice introduces a potential confound related to side biases. Understanding whether subjects exhibit this bias, and the origin of it (pre-existent or acquired throughout the experimental sessions), is particularly important to interpreting the results. Here, we tested the hypothesis according to which brain lateralization may influence the emergence of side biases in a well-known model of neuroscience, the zebrafish. As a measure of lateralization, individuals were observed in their spontaneous tendencies to monitor a potential predator with either the left or the right eye. Subjects also underwent an operant conditioning task requiring discrimination between two colors placed on the left–right axis. Although the low performance exhibited in the operant conditioning task prevents firm conclusions from being drawn, a positive correlation was found between the direction of lateralization and the tendency to select the stimulus presented on one specific side (e.g., right). The choice for this preferred side did not change throughout the experimental sessions, meaning that this side bias was not the result of the prolonged training. Overall, our study calls for a wider investigation of pre-existing lateralization biases in animal models to set up methodological counterstrategies to test individuals that do not properly work in a binary choice task with stimuli arranged on the left–right axis.

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.

Response to change in the number of visual stimuli in zebrafish:A behavioural and molecular study

Evidence has shown that a variety of vertebrates, including fish, can discriminate collections of visual items on the basis of their numerousness using an evolutionarily conserved system for approximating numerical magnitude (the so-called Approximate Number System, ANS). Here we combine a habituation/dishabituation behavioural task with molecular biology assays to start investigating the neural bases of the ANS in zebrafish. Separate groups of zebrafish underwent a habituation phase with a set of 3 or 9 small red dots, associated with a food reward. The dots changed in size, position and density from trial to trial but maintained their numerousness, and the overall areas of the stimuli was kept constant. During the subsequent dishabituation test, zebrafish faced a change (i) in number (from 3 to 9 or vice versa with the same overall surface), or (ii) in shape (with the same overall surface and number), or (iii) in size (with the same shape and number). A control group of zebrafish was shown the same stimuli as during the habituation. RT-qPCR revealed that the telencephalon and thalamus were characterized by the most consistent modulation of the expression of the immediate early genes c-fos and egr-1 upon change in numerousness; in contrast, the retina and optic tectum responded mainly to changes in stimulus size.

Sex differences in cognitive performance and style across domains in mosquitofish (Gambusia affinis)

Given that the sexes often differ in their ecological and sexual selection pressures, sex differences in cognitive properties are likely. While research on sexually dimorphic cognition often focuses on performance, it commonly overlooks how sexes diverge across cognitive domains and in behaviors exhibited during a cognitive task (cognitive style). We tested male and female western mosquitofish (Gambusia affinis) in three cognitive tasks: associative learning (numerical discrimination), cognitive flexibility (detour task), and spatio-temporal learning (shuttlebox). We characterized statistical relationships between cognitive performances and cognitive style during the associative learning task with measures of anxiety, boldness, exploration, reaction time, and activity. We found sex differences in performance, cognitive style, and the relationships between cognitive domains. Females outperformed males in the spatio-temporal learning task, while the sexes performed equally in associate learning and cognitive flexibility assays. Females (but not males) exhibited a 'fast-exploratory' cognitive style during associative learning trials. Meanwhile, only males showed a significant positive relationship between domains (associative learning and cognitive flexibility). We propose that these sexually dimorphic cognitive traits result from strong sexual conflict in this taxon; and emphasize the need to explore suites of sex-specific cognitive traits and broader comparative work examining sexual selection and cognition.

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

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

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

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

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

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

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

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

Neural constraints on human number concepts

True counting and arithmetic abilities are unique to humans and are inextricably linked to symbolic competence. However, our unprecedented numerical skills are deeply rooted in our neuronal heritage as primates and vertebrates. In this article, I argue that numerical competence in humans is the result of three neural constraints. First, I propose that the neuronal mechanisms of quantity estimation are part of our evolutionary heritage and can be witnessed across primate and vertebrate phylogeny. Second, I suggest that a basic understanding of number, what numerical quantity means, is innately wired into the brain and gives rise to an intuitive number sense, or number instinct. Third and finally, I argue that symbolic counting and arithmetic in humans is rooted in an evolutionarily and ontogenetically primeval neural system for non-symbolic number representations. These three neural constraints jointly determine the basic processing of number concepts in the human mind.

The Impact of Brain Lateralization and Anxiety-Like Behaviour in an Extensive Operant Conditioning Task in Zebrafish (Danio rerio)

Several studies in mammals, birds, and fish have documented better cognitive abilities associated with an asymmetrical distribution of cognitive functions in the two halves of the brain, also known as ‘functional brain lateralization’. However, the role of brain lateralization in learning abilities is still unclear. In addition, although recent studies suggest a link between some personality traits and accuracy in cognitive tasks, the relation between anxiety and learning skills in Skinner boxes needs to be clarified. In the present study, we tested the impact of brain lateralization and anxiety-like behaviour in the performance of an extensive operant conditioning task. Zebrafish tested in a Skinner box underwent 500 trials in a colour discrimination task (red vs. yellow and green vs. blue). To assess the degree of lateralization, fish were observed in a detour test in the presence of a dummy predator, and anxiety-like behaviour was studied by observing scototaxis response in an experimental tank divided into light and dark compartments. Although the low performance in the colour discrimination task did not permit the drawing of firm conclusions, no correlation was found between the accuracy in the colour discrimination task and the behaviour in the detour and scototaxis tests. This suggests that neither different degrees of asymmetries in brain lateralization nor anxiety may significantly impact the learning skills of zebrafish.

Psychophysical evidence for the number sense

It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.

This article is part of the discussion meeting issue ‘The origins of numerical abilities’.

Cleaner fish Labroides dimidiatus discriminate numbers but fail a mental number line test

Several species of primates, including humans, possess a spontaneous spatial mental arrangement (i.e. mental number line MNL) of increasing numbers or continuous quantities from left to right. This cognitive process has recently been documented in domestic chicken in a spatial-numerical task, opening the possibility that MNL is a cognitive capacity that has been conserved across vertebrate taxa. In this scenario, fish might possess the MNL as well. Here we investigated whether cleaner fish Labroides dimidiatus show evidence for MNL in two experiments. In Experiment I, we tested fish's abilities in number discrimination, presenting simultaneously either small (2 vs 5) or large (5 vs 8) continuous quantities where one quantity was systematically rewarded. Experiment II used a protocol of an MNL task similar to the study on chickens. We trained cleaners with a target number (i.e. 5 elements), then we presented them with an identical pair of panels depicting either 2 elements or 8 elements, and we recorded their spontaneous choice for the left or right panel on each presentation. Cleaner fish showed high abilities in discriminating small and large numbers in Experiment I. Importantly, cleaners achieved this discrimination using numerical cues instead of non-numerical cues such as the cumulative surface area, density, and overall space. In contrast, cleaners did not allocate continuous quantities to space in Experiment II. Our findings suggest that cleaner fish possess numbering skills but they do not have an MNL. While similar studies on animals from various clades are needed to trace the evolution of MNL within vertebrates, our results suggest that this cognitive process might not be a capacity conserved across all vertebrate taxa.

Sex-specific cognitive-behavioural profiles emerging from individual variation in numerosity discrimination in Gambusia affinis

The relationship between an individual's cognitive abilities and other behavioural attributes is complex, yet critical to understanding how individual differences in cognition arise. Here we use western mosquitofish, Gambusia affinis, to investigate the relationship between individual associative learning performance in numerical discrimination tests and independent measures of activity, exploration, anxiety and sociability. We found extensive and highly repeatable inter-individual variation in learning performance (r = 0.89; ICC = 0.89). Males and females exhibited similar learning performance, yet differed in sociability, activity and their relationship between learning and anxiety/exploration tendencies. Sex-specific multivariate behaviour scores successfully predicted variation in individual learning performance, whereas combined sex analyses did not. Female multivariate behaviour scores significantly predict learning performance across females (ρ = 0.80, p = 0.005) with high-performing female learners differentiated from female non-learners and low-performing learners by significant contributions of activity and sociability measures. Meanwhile, males of different learning performance levels (high-, low- and non-learners) were distinguished from each other by unique behavioural loadings of sociability, activity and anxiety/exploration scores, respectively. Our data suggest that despite convergence on learning performance, the sexes diverge in cognitive-behavioural relationships that are likely products of different sexual selection pressures.

Sex differences in discrimination reversal learning in the guppy

In several mammalian and avian species, females show a higher performance than males in tasks requiring cognitive flexibility such as the discrimination reversal learning. A recent study showed that female guppies are twice as efficient as males in a reversal learning task involving yellow-red discrimination, suggesting a higher cognitive flexibility in female guppies. However, the possibility exists that the superior performance exhibited by females does not reflect a general sex difference in cognitive abilities, but instead, is confined to colour discrimination tasks. To address this issue, we compared male and female guppies in two different discrimination reversal learning tasks and we performed a meta-analysis of these experiments and the previous one involving colour discrimination. In the first experiment of this study, guppies were tested in a task requiring them to learn to select the correct arm of a T-maze in order to rejoin a group of conspecifics. In experiment 2, guppies were observed in a numerical task requiring them to discriminate between 5 and 10 dots in order to obtain a food reward. Although females outperformed males in one condition of the T-maze, we did not find any clear evidence of females' greater reversal learning performance in either experiment. However, the meta-analysis of the three experiments supported the hypothesis of females' greater reversal learning ability. Our data do not completely exclude the idea that female guppies have a generally higher cognitive flexibility than males; however, they suggest that the size of this sex difference might depend on the task.

Personality and Cognition: Sociability Negatively Predicts Shoal Size Discrimination Performance in Guppies

Evidence from a growing number of organisms suggests that individuals show consistent performance differences in cognitive tasks. According to empirical and theoretical studies, these cognitive differences might be at least partially related to personality. We tested this hypothesis in the guppy, Poecilia reticulata, by comparing individuals with different degree of sociability in the discrimination of shoals formed by a different number of conspecifics. We found that individual guppies show repeatability of sociability as expected for personality traits. Furthermore, individuals with higher sociability showed poorer shoal size discrimination performance and were less efficient in choosing the larger shoal compared to individuals with low sociability. As choosing the larger shoal is an important strategy of defense against predators for guppies, we discuss this relationship between personality and cognition in the light of its fitness consequences.

An emergentist perspective on the origin of number sense

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

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'.