Honeybees use absolute rather than relative numerosity in number discrimination

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.

What, if anything, can be considered an amodal sensory dimension?

The term 'amodal' is a key topic in several different research fields across experimental psychology and cognitive neuroscience, including in the areas of developmental and perception science. However, despite being regularly used in the literature, the term means something different to the researchers working in the different contexts. Many developmental scientists conceive of the term as referring to those perceptual qualities, such as, for example, the size and shape of an object, that can be picked up by multiple senses (e.g., vision and touch potentially providing information relevant to the same physical stimulus/property). However, the amodal label is also widely used in the case of those qualities that are not directly sensory, such as, for example, numerosity, rhythm, synchrony, etc. Cognitive neuroscientists, by contrast, tend to use the term amodal to refer to those central cognitive processes and brain areas that do not appear to be preferentially responsive to a particular sensory modality or to those symbolic or formal representations that essentially lack any modality and that are assumed to play a role in the higher processing of sensory information. Finally, perception scientists sometimes refer to the phenomenon of 'amodal completion', referring to the spontaneous completion of perceptual information that is missing when occluded objects are presented to observers. In this paper, we review the various different ways in which the term 'amodal' has been used in the literature and the evidence supporting the various uses of the term. Morever, we highlight some of the various properties that have been suggested to be 'amodal' over the years. Then, we try to address some of the questions that arise from the reviewed evidence, such as: Do different uses of the 'term' refer to different domains, for example, sensory information, perceptual processes, or perceptual representations? Are there any commonalities among the different uses of the term? To what extent is research on cross-modal associations (or correspondences) related to, or can shed light on, amodality? And how is the notion of amodal related to multisensory integration? Based on the reviewed evidence, it is argued that there is, as yet, no convincing empirical evidence to support the claim that amodal sensory qualities exist. We thus suggest that use of the term amodal would be more meaningful with respect to abstract cognition rather than necessarily sensory perception, the latter being more adequately explained/understood in terms of highly redundant cross-modal correspondences.

Quantity misperception by hymenopteran insects observing the solitaire illusion

Visual illusions are errors in signal perception and inform us about the visual and cognitive processes of different animals. Invertebrates are relatively less studied for their illusionary perception, despite the insight that comparative data provides on the evolution of common perceptual mechanisms. The Solitaire Illusion is a numerosity illusion where a viewer typically misperceives the relative quantities of two items of different colors consisting of identical quantity, with more centrally clustered items appearing more numerous. We trained European honeybees (Apis mellifera) and European wasps (Vespula vulgaris) to select stimuli containing a higher quantity of yellow dots in arrays of blue and yellow dots and then presented them with the Solitaire Illusion. Insects learnt to discriminate between dot quantities and showed evidence of perceiving the Solitaire Illusion. Further work should determine whether the illusion is caused by numerical cues only or by both quantity and non-numerical spatial cues.

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.

Transfer from continuous to discrete quantities in honeybees

Honeybees can estimate quantities having different dimensions: continuous and uncountable such as the relative size of visual objects in an array, or discrete and countable such as the number of objects of the array. Honeybees can transfer quantity discrimination (i.e., choosing the larger/smaller stimulus) from number to size. Here, we investigated whether honeybees could also generalize from the size (continuous) to the number (discrete) dimension. We trained free-flying foragers to discriminate between large- and small-size elements. At test, bees were presented with a comparison between larger and smaller numerosities controlled for different continuous variables covarying with numerosity such as total area, total perimeter, convex hull, and element size. Results showed that bees generalized from the size to the numerical dimension of the stimuli. This cross-dimensional transfer supports the idea of a universal mechanism for the encoding of abstract magnitudes in invertebrate species comparable to that of vertebrate species.

Neural coding of numerousness

Perception of numerousness, i.e. number of items in a set, is an important cognitive ability, which is present in several animal taxa. In spite of obvious differences in neuroanatomy, insects, fishes, reptiles, birds, and mammals all possess a "number sense". Furthermore, information regarding numbers can belong to different sensory modalities: animals can estimate a number of visual items, a number of tones, or a number of their own movements. Given both the heterogeneity of stimuli and of the brains processing these stimuli, it is hard to imagine that number cognition can be traced back to the same evolutionary conserved neural pathway. However, neurons that selectively respond to the number of stimuli have been described in higher-order integration brain centres both in primates and in birds, two evolutionary distant groups. Although most probably not of the same evolutionary origin, these number neurons share remarkable similarities in their response properties. Instead of homology, this similarity might result from computational advantages of the underlying coding mechanism. This means that one might expect numerousness information to undergo similar steps of neural processing even in evolutionary distant neural pathways. Following this logic, in this review we summarize our current knowledge of how numerousness is processed in the brain from sensory input to coding of abstract information in the higher-order integration centres. We also propose a list of key open questions that might promote future research on number cognition.

Numerical discrimination in Drosophila melanogaster

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

Information Theory Opens New Dimensions in Experimental Studies of Animal Behaviour and Communication

Over the last 40–50 years, ethology has become increasingly quantitative and computational. However, when analysing animal behavioural sequences, researchers often need help finding an adequate model to assess certain characteristics of these sequences while using a relatively small number of parameters. In this review, I demonstrate that the information theory approaches based on Shannon entropy and Kolmogorov complexity can furnish effective tools to analyse and compare animal natural behaviours. In addition to a comparative analysis of stereotypic behavioural sequences, information theory can provide ideas for particular experiments on sophisticated animal communications. In particular, it has made it possible to discover the existence of a developed symbolic “language” in leader-scouting ant species based on the ability of these ants to transfer abstract information about remote events.

An insect brain organizes numbers on a left-to-right mental number line

The ability to judge numbers exists in various vertebrate species but also in honey bees, thus raising the question of the phylogenetic origins of numerosity systems. Here, we studied if bees, like humans, organize numbers spatially from left to right according to their magnitude. As the cultural vs. biological origins of this mental number line (MNL) are a subject of debate, our study provides an important perspective for this discussion. We show that bees order numbers from left to right according to their magnitude and that the location of a number on that line varies with the reference number previously trained. Thus, the MNL is a biological numeric representation that is common to the nervous system with distant evolutionary origins.

The “mental number line” (MNL) is a form of spatial numeric representation that associates small and large numbers with the left and right spaces, respectively. This spatio-numeric organization can be found in adult humans and has been related to cultural factors such as writing and reading habits. Yet, both human newborns and birds order numbers consistently with an MNL, thus raising the question of whether culture is a main explanation for MNL. Here, we explored the numeric sense of honey bees and show that after being trained to associate numbers with a sucrose reward, they order numbers not previously experienced from left to right according to their magnitude. Importantly, the location of a number on that scale varies with the reference number previously trained and does not depend on low-level cues present on numeric stimuli. We provide a series of neural explanations for this effect based on the extensive knowledge accumulated on the neural underpinnings of visual processing in honey bees and conclude that the MNL is a form of numeric representation that is evolutionarily conserved across nervous systems endowed with a sense of number, irrespective of their neural complexity.

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.

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

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

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.

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.

Zebrafish excel in number discrimination under an operant conditioning paradigm

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

The evolution of quantitative sensitivity

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

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

Exploring Higher-Order Conceptual Learning in an Arthropod with a Large Multisensory Processing Center

Simple Summary

It is difficult to measure animal intelligence because the definition of ‘intelligence’ varies, and many animals are good at specific tasks used to measure intelligence or cognition. To address this, scientists often look for evidence of common cognitive abilities. One such ability, the ability to learn concepts, is thought to be rare in animals, especially invertebrates. Concepts include the ideas of ‘same’ and ‘different’. These concepts can be applied to anything in the environment while also being independent of those objects and can help animals understand and survive their environment. Amblypygids, a relative of spiders, live in tropical and subtropical areas, are very good learners, and have a large, complex brain region known to process information from multiple senses. We tested whether amblypygids could learn the concept of ‘same’ by training them to move toward a stimulus that matched with an initial stimulus. We also trained some individuals to learn the concept ‘different’ by training them to move toward a non-matching stimulus. When we used new stimuli, the amblypygids did not move toward the correct stimulus significantly more often than the incorrect stimulus, suggesting either they are unable to learn these higher-order concepts or our experimental design failed to elicit that ability.

Abstract

Comparative cognition aims to understand the evolutionary history and current function of cognitive abilities in a variety of species with diverse natural histories. One characteristic often attributed to higher cognitive abilities is higher-order conceptual learning, such as the ability to learn concepts independent of stimuli—e.g., ‘same’ or ‘different’. Conceptual learning has been documented in honeybees and a number of vertebrates. Amblypygids, nocturnal enigmatic arachnids, are good candidates for higher-order learning because they are excellent associational learners, exceptional navigators, and they have large, highly folded mushroom bodies, which are brain regions known to be involved in learning and memory in insects. In Experiment 1, we investigate if the amblypygid Phrynus marginimaculatus can learn the concept of same with a delayed odor matching task. In Experiment 2, we test if Paraphrynus laevifrons can learn same/different with delayed tactile matching and nonmatching tasks before testing if they can transfer this learning to a novel cross-modal odor stimulus. Our data provide no evidence of conceptual learning in amblypygids, but more solid conclusions will require the use of alternative experimental designs to ensure our negative results are not simply a consequence of the designs we employed.

Archerfish number discrimination

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

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.

Quantitative abilities of invertebrates: a methodological review

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

Wild non-eusocial bees learn a colour discrimination task in response to simulated predation events

Despite representing the majority of bee species, non-eusocial bees (e.g. solitary, subsocial, semisocial, and quasisocial species) are comparatively understudied in learning, memory, and cognitive-like behaviour compared to eusocial bees, such as honeybees and bumblebees. Ecologically relevant colour discrimination tasks are well-studied in eusocial bees, and research has shown that a few non-eusocial bee species are also capable of colour learning and long-term memory retention. Australia hosts over 2000 native bee species, most of which are non-eusocial, yet evidence of cognitive-like behaviour and learning abilities under controlled testing conditions is lacking. In the current study, I examine the learning ability of a non-eusocial Australian bee, Lasioglossum (Chilalictus) lanarium, using aversive differential conditioning during a colour discrimination task. L. lanarium learnt to discriminate between salient blue- and yellow-coloured stimuli following training with simulated predation events. This study acts as a bridge between cognitive studies on eusocial and non-social bees and introduces a framework for testing non-eusocial wild bees on elemental visual learning tasks using aversive conditioning. Non-eusocial bee species are far more numerous than eusocial species and contribute to agriculture, economics, and ecosystem services in Australia and across the globe. Thus, it is important to study their capacity to learn flower traits allowing for successful foraging and pollination events, thereby permitting us a better understanding of their role in plant-pollinator interactions.

Hard limits to cognitive flexibility: ants can learn to ignore but not avoid pheromone trails

Learning allows animals to respond to changes in their environment within their lifespan. However, many responses to the environment are innate, and need not be learned. Depending on the level of cognitive flexibility an animal shows, such responses can either be modified by learning or not. Many ants deposit pheromone trails to resources, and innately follow such trails. Here, we investigated cognitive flexibility in the ant Lasius niger by asking whether ants can overcome their innate tendency and learn to avoid conspecific pheromone trails when these predict a negative stimulus. Ants were allowed to repeatedly visit a Y-maze, one arm of which was marked with a strong but realistic pheromone trail and led to a punishment (electric shock and/or quinine solution), and the other arm of which was unmarked and led to a 1 mol l-1 sucrose reward. After ca. 10 trials, ants stopped relying on the pheromone trail, but even after 25 exposures they failed to improve beyond chance levels. However, the ants did not choose randomly: rather, most ants began to favour just one side of the Y-maze, a strategy which resulted in more efficient food retrieval over time, when compared with the first visits. Even when trained in a go/no-go paradigm which precludes side bias development, ants failed to learn to avoid a pheromone trail. These results show rapid learning flexibility towards an innate social signal, but also demonstrate a rarely seen hard limit to this flexibility.

The Evolutionary History of Brains for Numbers

Humans and other animals share a number sense', an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of the telencephalon has been implicated in number processing. This suggests that properties of the telencephalon make it ideally suited to host number representations that evolved by convergent evolution as a result of common selection pressures. In addition, promising candidate regions in the brains of invertebrates, such as insects, spiders, and cephalopods, can be identified, opening the possibility of even deeper commonalities for number sense.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

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.

Non-numerical strategies used by bees to solve numerical cognition tasks

We examined how bees solve a visual discrimination task with stimuli commonly used in numerical cognition studies. Bees performed well on the task, but additional tests showed that they had learned continuous (non-numerical) cues. A network model using biologically plausible visual feature filtering and a simple associative rule was capable of learning the task using only continuous cues inherent in the training stimuli, with no numerical processing. This model was also able to reproduce behaviours that have been considered in other studies indicative of numerical cognition. Our results support the idea that a sense of magnitude may be more primitive and basic than a sense of number. Our findings highlight how problematic inadvertent continuous cues can be for studies of numerical cognition. This remains a deep issue within the field that requires increased vigilance and cleverness from the experimenter. We suggest ways of better assessing numerical cognition in non-speaking animals, including assessing the use of all alternative cues in one test, using cross-modal cues, analysing behavioural responses to detect underlying strategies, and finding the neural substrate.

Learning of sameness/difference relationships by honey bees: performance, strategies and ecological context

Humans and non-human primates learn conceptual relationships such as ‘same’ and ‘different, which have to be encoded independently of the physical nature of objects linked by the relation. Consequently, concepts are associated with high-level cognition and are not expected in an insect brain. Yet, various works have shown that the miniature brain of honey bees also learns the conceptual relationships of sameness and difference and transfers these relationships to novel stimuli. We review evidence about sameness/difference learning in bees and analyze its adaptive value within an ecological context. The experiments reviewed cannot be accounted for by low-level strategies and challenge, therefore, the traditional view attributing supremacy to larger brains when it comes to the elaboration of concepts.

Ants Can Anticipate the Following Quantity in an Arithmetic Sequence

Workers of the ant Myrmica sabuleti have been previously shown to be able to add and subtract numbers of elements and to expect the time and location of the next food delivery. We wanted to know if they could anticipate the following quantity of elements present near their food when the number of these elements increases or decreases over time according to an arithmetic sequence. Two experiments were therefore carried out, one with an increasing sequence, the other with a decreasing sequence. Each experiment consisted of two steps, one for the ants to learn the numbers of elements successively present near their food, the other to test their choice when they were simultaneously in the presence of the numbers from a previously learned sequence and the following quantity. The ants anticipated the following quantity in each presented numerical sequence. This forethinking of the next quantity applies to numerosity, thus, to concrete items. This anticipatory behavior may be explained by associative learning and by the ants’ ability to memorize events and to estimate the elapsing time.

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).

Response of male and female domestic chicks to change in the number (quantity) of imprinting objects

When facing two sets of imprinting objects of different numerousness, domestic chicks prefer to approach the larger one. Given that choice for familiar and novel stimuli in imprinting situations is known to be affected by the sex of the animals, we investigated how male and female domestic chicks divide the time spent in the proximity of a familiar versus an unfamiliar number of objects, and how animals interact (by pecking) with these objects. We confirmed that chicks discriminate among the different numerousnesses, but we also showed that females and males behave differently, depending on the degree of familiarity of the objects. When objects in the testing sets were all familiar, females equally explored both sets and pecked at all objects individually. Males instead selectively approached the familiar numerousness and pecked more at it. When both testing sets comprised familiar as well as novel objects, both males and females approached the larger numerousness of familiar objects. However, chicks directed all their pecks toward the novel object within the set. Differences in the behavior of males and females can be accounted for in terms of sex difference in the motivation to reinstate social contact with the familiar objects and to explore novel ones, likely associated with the ecology and the social structure of the species before domestication.

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.

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.

Bumblebees Use Sequential Scanning of Countable Items in Visual Patterns to Solve Numerosity Tasks

Most research in comparative cognition focuses on measuring if animals manage certain tasks; fewer studies explore how animals might solve them. We investigated bumblebees’ scanning strategies in a numerosity task, distinguishing patterns with two items from four and one from three, and subsequently transferring numerical information to novel numbers, shapes, and colors. Video analyses of flight paths indicate that bees do not determine the number of items by using a rapid assessment of number (as mammals do in “subitizing”); instead, they rely on sequential enumeration even when items are presented simultaneously and in small quantities. This process, equivalent to the motor tagging (“pointing”) found for large number tasks in some primates, results in longer scanning times for patterns containing larger numbers of items. Bees used a highly accurate working memory, remembering which items have already been scanned, resulting in fewer than 1% of re-inspections of items before making a decision. Our results indicate that the small brain of bees, with less parallel processing capacity than mammals, might constrain them to use sequential pattern evaluation even for low quantities.

Transfer from Number to Size Reveals Abstract Coding of Magnitude in Honeybees

Number discrimination has been documented in honeybees. It is not known, however, whether it reflects, as in vertebrates, the operating of an underlying general magnitude system that estimates quantities irrespective of dimensions (e.g., number, space, time) and format (discrete, continuous). We trained bees to discriminate between different numerical comparisons having either a 0.5 (2 versus 4; 4 versus 8) or 0.67 ratio (2 versus 3; 4 versus 6). Bees were then tested for spontaneous choice using comparisons with identical numbers but different sizes. Irrespective of the ratio of stimuli, bees trained to select the smaller numerical quantity chose the congruent smaller size; bees trained to select the larger numerical quantity chose the congruent larger size. This finding provides the evidence for a cross-dimensional transfer between discrete (numerical) and continuous (spatial) dimensions in an invertebrate species and supports the hypothesis of a cognitive universality of a coding for general magnitude.

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Honeybees exhibit a cross-dimensional transfer from discrete to continuous dimensions

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Honeybees trained to choose the smaller numerosity, choose the congruent smaller size

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Honeybees trained to choose the larger numerosity, choose the congruent larger size

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This supports the hypothesis of a cognitive universality of a coding for magnitudes

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.

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

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

Achieving arithmetic learning in honeybees and examining how individuals learn

In recent years honeybees have demonstrated intriguing numerical capacities, leading to the recent discovery of their ability to perform simple arithmetic by learning to add or subtract ‘one’ using symbolic representations of operators. When training an insect with a miniature brain containing less than one million neurons to understand a conceptual rule, the procedure is of vital importance. We explain in detail the controls and process of designing an experiment to test for complex behaviors in a relatively simple brained animal. Furthermore, we will discuss the finding that individual honeybees do not demonstrate a consistent learning scenario when trained to perform the same tasks, rather they appear to acquire arithmetic rules through individual processes.

An Insect's Sense of Number

Recent studies revealed numerosity judgments in bees, which include the concept of zero, subtraction and addition, and matching symbols to numbers. Despite their distant origins, bees and vertebrates share similarities in their numeric competences, thus suggesting that numerosity is evolutionary conserved and can be implemented in miniature brains without neocortex.

Honeybees use absolute rather than relative numerosity in number discrimination

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