An Insect's Sense of Number

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.

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.

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.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

Numerosity as a visual property: Evidence from two highly evolutionary distant species

Most animals, from humans to invertebrates, possess an ability to estimate numbers. This evolutionary advantage facilitates animals' choice of environments with more food sources, more conspecifics to increase mating success, and/or reduced predation risk among others. However, how the brain processes numerical information remains largely unknown. There are currently two lines of research interested in how numerosity of visual objects is perceived and analyzed in the brain. The first argues that numerosity is an advanced cognitive ability processed in high-order brain areas, while the second proposes that "numbers" are attributes of the visual scene and thus numerosity is processed in the visual sensory system. Recent evidence points to a sensory involvement in estimating magnitudes. In this Perspective, we highlight this evidence in two highly evolutionary distant species: humans and flies. We also discuss the advantages of studying numerical processing in fruit flies in order to dissect the neural circuits involved in and required for numerical processing. Based on experimental manipulation and the fly connectome, we propose a plausible neural network for number sense in invertebrates.

Individual consistency in the learning abilities of honey bees: cognitive specialization within sensory and reinforcement modalities

The question of whether individuals perform consistently across a variety of cognitive tasks is relevant for studies of comparative cognition. The honey bee (Apis mellifera) is an appropriate model to study cognitive consistency as its learning can be studied in multiple elemental and non-elemental learning tasks. We took advantage of this possibility and studied if the ability of honey bees to learn a simple discrimination correlates with their ability to solve two tasks of higher complexity, reversal learning and negative patterning. We performed four experiments in which we varied the sensory modality of the stimuli (visual or olfactory) and the type (Pavlovian or operant) and complexity (elemental or non-elemental) of conditioning to examine if stable correlated performances could be observed across experiments. Across all experiments, an individual's proficiency to learn the simple discrimination task was positively and significantly correlated with performance in both reversal learning and negative patterning, while the performances in reversal learning and negative patterning were positively, yet not significantly correlated. These results suggest that correlated performances across learning paradigms represent a distinct cognitive characteristic of bees. Further research is necessary to examine if individual cognitive consistency can be found in other insect species as a common characteristic of insect brains.

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.

Magnitudes for Nervous Systems: Theoretical Issues and Experimental Evidence

Animals’ negotiations with the environment frequently involve quantitative assessments. However, it is largely unknown how different nervous systems can deal with information about magnitude and perform operations on it. Here we review some of the literature on this topic and discuss a few issues worthy of debate that can guide future research directions. First, we present experimental evidence suggesting that, in addition to the cortical (pallial) brain regions that are widely acknowledged to play a role in magnitude estimation, subcortical (more generally, subpallial) brain regions also play an important role. Second, we discuss interactions between different domains of magnitude and put forward a hypothesis to account for the directionality of associations between discrete and continuous magnitude. Finally, we suggest how the distinction between the concepts of number and discrete quantity should foster more attention to the role of sensory areas and circuits in assessing discrete quantities.

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.

Visual learning in a virtual reality environment upregulates immediate early gene expression in the mushroom bodies of honey bees

Free-flying bees learn efficiently to solve numerous visual tasks. Yet, the neural underpinnings of this capacity remain unexplored. We used a 3D virtual reality (VR) environment to study visual learning and determine if it leads to changes in immediate early gene (IEG) expression in specific areas of the bee brain. We focused on kakusei, Hr38 and Egr1, three IEGs that have been related to bee foraging and orientation, and compared their relative expression in the calyces of the mushroom bodies, the optic lobes and the rest of the brain after color discrimination learning. Bees learned to discriminate virtual stimuli displaying different colors and retained the information learned. Successful learners exhibited Egr1 upregulation only in the calyces of the mushroom bodies, thus uncovering a privileged involvement of these brain regions in associative color learning and the usefulness of Egr1 as a marker of neural activity induced by this phenomenon.

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.

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

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

Evidence of cognitive specialization in an insect: proficiency is maintained across elemental and higher-order visual learning but not between sensory modalities in honey bees

Individuals differing in their cognitive abilities and foraging strategies may confer a valuable benefit to their social groups as variability may help responding flexibly in scenarios with different resource availability. Individual learning proficiency may either be absolute or vary with the complexity or the nature of the problem considered. Determining if learning abilities correlate between tasks of different complexity or between sensory modalities has a high interest for research on brain modularity and task-dependent specialisation of neural circuits. The honeybee Apis mellifera constitutes an attractive model to address this question due to its capacity to successfully learn a large range of tasks in various sensory domains. Here we studied whether the performance of individual bees in a simple visual discrimination task (a discrimination between two visual shapes) is stable over time and correlates with their capacity to solve either a higher-order visual task (a conceptual discrimination based on spatial relations between objects) or an elemental olfactory task (a discrimination between two odorants). We found that individual learning proficiency within a given task was maintained over time and that some individuals performed consistently better than others within the visual modality, thus showing consistent aptitude across visual tasks of different complexity. By contrast, performance in the elemental visual-learning task did not predict performance in the equivalent elemental olfactory task. Overall, our results suggest the existence of cognitive specialisation within the hive, which may contribute to ecological social success.

Dissections of Larval, Pupal and Adult Butterfly Brains for Immunostaining and Molecular Analysis

Butterflies possess impressive cognitive abilities, and investigations into the neural mechanisms underlying these abilities are increasingly being conducted. Exploring butterfly neurobiology may require the isolation of larval, pupal, and/or adult brains for further molecular and histological experiments. This procedure has been largely described in the fruit fly, but a detailed description of butterfly brain dissections is still lacking. Here, we provide a detailed written and video protocol for the removal of Bicyclus anynana adult, pupal, and larval brains. This species is gradually becoming a popular model because it uses a large set of sensory modalities, displays plastic and hormonally controlled courtship behaviour, and learns visual mate preference and olfactory preferences that can be passed on to its offspring. The extracted brain can be used for downstream analyses, such as immunostaining, DNA or RNA extraction, and the procedure can be easily adapted to other lepidopteran species and life stages.

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.

Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli

Several studies have suggested that vertebrate and invertebrate species may possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal way the numerousness of a set of items. However, this hypothesis has been challenged by the presence of other non-numerical continuous physical variables, which vary along with numerosity (i.e., any change in the number of visual physical elements in a set naturally involves a related change in visual features such as area, density, contour length and convex hull of the stimulus). It is therefore necessary to control and manipulate the continuous physical information when investigating the ability of humans and other animals to perceive numerousness. During decades of research, different methods have been implemented in order to address this issue, which has implications for experiment replicability and inter-species comparisons, since no general standardized procedure is currently being used. Here we present the ‘Generation of Numerical Elements Images Software’ (GeNEsIS) for the creation of non-symbolic numerical arrays in a standardized and user-friendly environment. The main aim of this tool is to provide researchers in the field of numerical cognition a manageable and precise instrument to produce visual numerical arrays controlled for all the continuous variables. Additionally, we implemented the ability to actively guide stimuli presentation during habituation/dishabituation and dual-choice comparison tasks used in human and comparative research.

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.

Charles Henry Turner and the cognitive behavior of bees

Social movements in several countries are stimulating a reconsideration of academic structures and historic figures and promoting reparation and recognition of marginalized and forgotten black scientists. A paradigmatic case in that sense is Charles Henry Turner (1867-1923) who was the first African American to receive a graduate degree at the University of Cincinnati and one of the first in earning a PhD degree of the University of Chicago. He performed numerous experiments on sensory perception, orientation, and mating of solitary and social bees, most of which have been unjustly forgotten despite the fact that they anticipated fundamental concepts of animal cognition. We review these studies and highlight the importance of his ideas for modern views of animal cognition and the study of bee behavior. We conclude that besides his scientific contributions, Turner is an inspiration for scientists fighting against social adversity and prejudices.

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.

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).

Different mechanisms underlie implicit visual statistical learning in honey bees and humans

The ability of developing complex internal representations of the environment is considered a crucial antecedent to the emergence of humans' higher cognitive functions. Yet it is an open question whether there is any fundamental difference in how humans and other good visual learner species naturally encode aspects of novel visual scenes. Using the same modified visual statistical learning paradigm and multielement stimuli, we investigated how human adults and honey bees (Apis mellifera) encode spontaneously, without dedicated training, various statistical properties of novel visual scenes. We found that, similarly to humans, honey bees automatically develop a complex internal representation of their visual environment that evolves with accumulation of new evidence even without a targeted reinforcement. In particular, with more experience, they shift from being sensitive to statistics of only elemental features of the scenes to relying on co-occurrence frequencies of elements while losing their sensitivity to elemental frequencies, but they never encode automatically the predictivity of elements. In contrast, humans involuntarily develop an internal representation that includes single-element and co-occurrence statistics, as well as information about the predictivity between elements. Importantly, capturing human visual learning results requires a probabilistic chunk-learning model, whereas a simple fragment-based memory-trace model that counts occurrence summary statistics is sufficient to replicate honey bees' learning behavior. Thus, humans' sophisticated encoding of sensory stimuli that provides intrinsic sensitivity to predictive information might be one of the fundamental prerequisites of developing higher cognitive abilities.

Poor numerical performance of guppies tested in a Skinner box

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

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

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

Spontaneous quantity discrimination of artificial flowers by foraging honeybees

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