The Adaptive Value of Numerical Competence

Crows recognize geometric regularity

The perception of geometric regularity in shapes, a form of elementary Euclidean geometry, is a fundamental mathematical intuition in humans. We demonstrate this geometric understanding in an animal, the carrion crow. Crows were trained to detect a visually distinct intruder shape among six concurrent arbitrary shapes. The crows were able to immediately apply this intruder concept to quadrilaterals, identifying the one that exhibited differing geometric properties compared to the others in the set. The crows exhibited a geometric regularity effect, showing better performance with shapes featuring right angles, parallel lines, or symmetry over more irregular shapes. This performance advantage did not require learning. Our findings suggest that geometric intuitions are not specific to humans but are deeply rooted in biological evolution.

The origins of number sense: a commentary on "Is there an innate sense of number in the brain?"

The question of whether a "sense of number" is innate has been posed in a new article by Lorenzi et al. (2025). The article explores the behavioral and neurobiological evidence from newborn animals to delve into the evolutionary origins of a sense of number. Lorenzi et al.(2025) raises new questions, interpretations, and ideas for future work to understand how number sense has evolved in humans and nonhuman animals. In this commentary, I discuss the arguments for an innate number sense, evaluate the implications for numerical cognition, and suggest how future work could fill the current gaps in our knowledge.

Hierarchical representations of relative numerical magnitudes in the human frontoparietal cortex

The ability to estimate numerical magnitude is essential for decision-making and is thought to underlie arithmetic skills. In humans, neural populations in the frontoparietal regions are tuned to represent numerosity. However, it remains unclear whether their response properties are fixed to a specific numerosity (i.e., absolute code) or dynamically scaled according to the range of numerosities relevant to the context (i.e., relative code). Here, using functional magnetic resonance imaging combined with multivariate pattern analysis, we uncover evidence that representations of relative numerosity coding emerge gradually as visual information processing advances in the frontoparietal regions. In contrast, the early sensory areas predominantly exhibit absolute coding. These findings indicate a hierarchical organization of relative numerosity representations that adapt their response properties according to the context. Our results highlight the existence of a context-dependent optimization mechanism in numerosity representation, enabling the efficient processing of infinite magnitude information with finite neural resources.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Proto-arithmetic abilities in zebrafish (Danio rerio)

The increasing use of zebrafish (Danio rerio) as a model for studying the neural bases of numerical/quantity abilities pushes toward the development of fast and reliable behavioral tasks for this species. Here, we investigated the spontaneous use of proto-arithmetic in quantity discrimination in zebrafish taking advantage of their shoaling behavior. Male fish underwent preference choice tests in which sets of live female conspecifics sequentially disappeared one by one behind one of two opaque identical panels. Fish spontaneously approached the panel occluding the larger set in a "1 vs. 2" comparison, but failed at "2 vs. 3" and "2 vs. 4". Limited to an overall amount of three elements in the two groups, zebrafish appeared to be able to deal with additions and subtractions, also suggesting the implicit understanding of an "empty set" (zero) concept. The velocity and the sequential/simultaneous presentation of the stimuli affected the spontaneous preference towards the group with the largest quantity.

Automatic Experimental Numerosity Generation and Numerical Training for Rodents

Non-symbolic stimuli representing numerosities are invariably associated with continuous magnitudes, complicating the interpretation of experimental studies on numerosity perception. Although various algorithms for experimental numerosity generation have been proposed, they do not consider the quantifiable distribution of values of continuous magnitudes and the degree of numerosity-magnitudes association. Consequently, they cannot thoroughly exclude the possibility of magnitudes integration or strategy switch between different magnitudes in numerical stimulus perception. Here, we introduce a protocol for numerosity generation, animal training, and behavior outcomes analysis that takes the aforementioned issues into consideration. This protocol has been applied to rodents and is applicable to other animals in numerosity studies. © 2024 Wiley Periodicals LLC. Basic Protocol 1: Algorithm for generating non-symbolic numerical stimuli Alternate Protocol: General algorithm for generating non-symbolic numerical stimuli Basic Protocol 2: Numerical training and testing for rodents.

Visual imagination can influence visual perception - towards an experimental paradigm to measure imagination

During visual imagination, a perceptual representation is activated in the absence of sensory input. This is sometimes described as seeing with the mind's eye. A number of physiological studies indicate that the brain uses more or less the same neural resources for visual perception of sensory information and visual imagination. The intensity of visual imagination is typically assessed with questionnaires, while more objective measures are missing. Aim of the present study was, to test a new experimental paradigm that may allow to objectively quantify imagination. For this, we used priming and adaptation effects during observation of ambiguous figures. Our perception of an ambiguous stimulus is unstable and alternates spontaneously between two possible interpretations. If we first observe an unambiguous stimulus variant (the conditioning stimulus), the subsequently presented ambiguous stimulus can either be perceived in the same way as the test stimulus (priming effect) or in the opposite way (adaptation effect) as a function of the conditioning time. We tested for these conditioning effects (priming and adaptation) using an ambiguous Necker Cube and an ambiguous Letter /Number stimulus as test stimuli and unambiguous variants thereof as conditioning stimuli. In a second experimental condition, we tested whether the previous imagination of an unambiguous conditioning stimulus variant - instead of its observation - can have similar conditioning effects on the subsequent test stimulus. We found no systematic conditioning effect on the group level, neither for the two stimulus types (Necker Cube stimuli and Letter /Number stimuli) nor for the two conditions (Real and Imaginary). However, significant correlations between effects of Real and Imaginary Condition were observed for both stimulus types. The absence of conditioning effects at the group level may be explained by using only one conditioning time, which may fit with individual priming and adaptation constants of some of our participants but not of others. Our strong correlation results indicate that observers with clear conditioning effects have about the same type (priming or adaptation) and intensity of imaginary conditioning effects. As a consequence, not only past perceptual experiences but also past imaginations can influence our current percepts. This is further confirmation that the mechanisms underlying perception and imagination are similar. Our post-hoc qualitative observations from three self-defined aphantasic observers indicate that our paradigm may be a promising objective measure to identify aphantasia.

Bistable perception of symbolic numbers

Numerals, that is, semantic expressions of numbers, enable us to have an exact representation of the amount of things. Visual processing of numerals plays an indispensable role in the recognition and interpretation of numbers. Here, we investigate how visual information from numerals is processed to achieve semantic understanding. We first found that partial occlusion of some digital numerals introduces bistable interpretations. Next, by using the visual adaptation method, we investigated the origin of this bistability in human participants. We showed that adaptation to digital and normal Arabic numerals, as well as homologous shapes, but not Chinese numerals, biases the interpretation of a partially occluded digital numeral. We suggest that this bistable interpretation is driven by intermediate shape processing stages of vision, that is, by features more complex than local visual orientations, but more basic than the abstract concepts of numerals.

Crows "count" the number of self-generated vocalizations

Producing a specific number of vocalizations with purpose requires a sophisticated combination of numerical abilities and vocal control. Whether this capacity exists in animals other than humans is yet unknown. We show that crows can flexibly produce variable numbers of one to four vocalizations in response to arbitrary cues associated with numerical values. The acoustic features of the first vocalization of a sequence were predictive of the total number of vocalizations, indicating a planning process. Moreover, the acoustic features of vocal units predicted their order in the sequence and could be used to read out counting errors during vocal production.

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.

Convergent Circuit Computation for Categorization in the Brains of Primates and Songbirds

Categorization is crucial for behavioral flexibility because it enables animals to group stimuli into meaningful classes that can easily be generalized to new circumstances. A most abstract quantitative category is set size, the number of elements in a set. This review explores how categorical number representations are realized by the operations of excitatory and inhibitory neurons in associative telencephalic microcircuits in primates and songbirds. Despite the independent evolution of the primate prefrontal cortex and the avian nidopallium caudolaterale, the neuronal computations of these associative pallial circuits show surprising correspondence. Comparing cellular functions in distantly related taxa can inform about the evolutionary principles of circuit computations for cognition in distinctly but convergently realized brain structures.

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.

Effects of prefrontal and parietal neuromodulation on magnitude processing and integration

Numerical cognition is an essential skill for survival, which includes the processing of discrete and continuous quantities, involving a mainly right fronto-parietal network. However, the neurocognitive systems underlying the processing and integration of discrete and continuous quantities are currently under debate. Noninvasive brain stimulation techniques have been used in the study of the neural basis of numerical cognition with a spatial, temporal and functional resolution superior to other neuroimaging techniques. The present randomized sham-controlled single-blinded trial addresses the involvement of the right dorsolateral prefrontal cortex and the right intraparietal sulcus in magnitude processing and integration. Multifocal anodal transcranial direct current stimulation was applied online during the execution of magnitude comparison tasks in three conditions: right prefrontal, right parietal and sham stimulation. The results show that prefrontal stimulation produced a moderated decrease in response times in all magnitude processing and integration tasks compared to sham condition. While parietal stimulation had no significant effect on any of the tasks. The effect found is interpreted as a generalized improvement in processing speed and magnitude integration due to right prefrontal neuromodulation, which may be attributable to domain-general or domain-specific factors.

Association neurons in the crow telencephalon link visual signs to numerical values

Many animals can associate signs with numerical values and use these signs in a goal-directed way during task performance. However, the neuronal basis of this semantic association has only rarely been investigated, and so far only in primates. How mechanisms of number associations are implemented in the distinctly evolved brains of other animal taxa such as birds is currently unknown. Here, we explored this semantic number-sign mapping by recording single-neuron activity in the crows' nidopallium caudolaterale (NCL), a brain structure critically involved in avian numerical cognition. Crows were trained to associate visual shapes with varying numbers of items in a number production task. The responses of many NCL neurons during stimulus presentation reflected the numerical values associated with visual shapes in a behaviorally relevant way. Consistent with the crow's better behavioral performance with signs, neuronal representations of numerical values extracted from shapes were more selective compared to those from dot arrays. The existence of number association neurons in crows points to a phylogenetic preadaptation of the brains of cognitively advanced vertebrates to link visual shapes with numerical meaning.

Grouping rule in tadpole: is quantity more or size assortment more important?

The ability to perceive group size and discriminate the ontogeny of conspecifics would play a crucial role in the grouping behavior of animals. However, the relative importance of numerical quantity and size-assortative preferences in shaping grouping rules remains poorly understood. In this study, I examined the responses of Miyako toad (Bufo gargarizans miyakonis) tadpoles to number quantity and size discrimination by choice tests at different ontogenetic stages (small, medium, and large). The results revealed that small-sized tadpoles in early developmental stages significantly preferred larger numbers (4) compared to smaller ones (1). However, this preference was not observed in later developmental stages (medium and large). And interestingly, when there was no quantity bias, size discrimination was not observed in tadpoles, irrespective of their ontogeny. These findings suggest that Miyako toad tadpoles discern quantity, i.e., the number of conspecifics, but exhibit ontogeny-dependent utilization of this ability. Understanding the interplay between numerical quantity and size-assortative preferences in grouping behavior will provide esteemed insights into the adaptive value of number sense in vertebrates and shed light on evolutionary processes.

Syntactic theory of mathematical expressions

Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.

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.

Weber's Law

Bullough et al. introduce Weber's Law and proportional processing during perception.

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.

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

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

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.

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.

The neural correlates of individual differences in numerosity perception: A voxel-based morphometry study

Numerosity perception is a fundamental cognitive function in humans and animals. Using an individual difference approach with a comprehensive dataset (N = 249), we performed a voxel-based morphometry analysis to unravel the neuroanatomical substrates associated with individual differences in numerosity perception sensitivity, measured by a classical non-symbolic numerical judgment task. Results showed that greater gray matter volume (GMV) in the left cerebellum, right temporal pole, and right parahippocampal was positively correlated to higher perceptual sensitivity to numerosity. In contrast, the GMV in the left intraparietal sulcus, and bilateral precentral/postcentral gyrus was negatively correlated to the sensitivity of numerosity perception. These findings indicate that a wide range of brain structures, rather than a specific anatomical structure or circuit, forms the neuroanatomical basis of numerosity perception, lending support to the emerging network view of the neural representation of numerosity. This work contributes to a more comprehensive understanding of how the brain processes numerical information.

•Unveils neuroanatomical basis of numerosity perception •Discovers positive and negative greater GMV correlations •Links GMV in a wide range of brain regions to numerical sensitivity •Supports the network view of the neural representation of numerosity perception

Keep numbers in view: red-eared sliders (Trachemys scripta elegans) learn to discriminate relative quantities

The ability to discriminate relative quantities, one of the numerical competences, is considered an adaptive trait in uncertain environments. Besides humans, previous studies have reported this capacity in several non-human primates and birds. Here, we test whether red-eared sliders (Trachemys scripta elegans) can discriminate different relative quantities. Subjects were first trained to distinguish different stimuli with food reward. Then, they were tested with novel stimulus pairs to demonstrate how they distinguished the stimuli. The results show that most subjects can complete the initial training and use relative quantity rather than absolute quantity to make choices during the testing phase. This study provides behavioural evidence of relative quantity discrimination in a reptile species and suggests that such capacity may be widespread among vertebrates.

Quantity discrimination in newly hatched zebrafish suggests hardwired numerical abilities

An intriguing hypothesis to explain the ubiquity of numerical abilities is that all vertebrates are born with hardwired neuronal networks for processing numbers. To date, only studies on human foetuses have clearly supported this hypothesis. Zebrafish hatch 48-72 h after fertilisation with an embryonic nervous system, providing a unique opportunity for investigating this hypothesis. Here, we demonstrated that zebrafish larvae exposed to vertical bars at birth acquired an attraction for bar stimuli and we developed a numerical discrimination task based on this preference. When tested with a series of discriminations of increasing difficulty (1vs.4, 1vs.3, 1vs.2, and 2vs.4 bars), zebrafish larvae reliably selected the greater numerosity. The preference was significant when stimuli were matched for surface area, luminance, density, and convex hull, thereby suggesting a true capacity to process numerical information. Converging results from two phylogenetically distant species suggests that numerical abilities might be a hallmark feature of vertebrates' brains.

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.

The current state of carnivore cognition

The field of animal cognition has advanced rapidly in the last 25 years. Through careful and creative studies of animals in captivity and in the wild, we have gained critical insights into the evolution of intelligence, the cognitive capacities of a diverse array of taxa, and the importance of ecological and social environments, as well as individual variation, in the expression of cognitive abilities. The field of animal cognition, however, is still being influenced by some historical tendencies. For example, primates and birds are still the majority of study species in the field of animal cognition. Studies of diverse taxa improve the generalizability of our results, are critical for testing evolutionary hypotheses, and open new paths for understanding cognition in species with vastly different morphologies. In this paper, we review the current state of knowledge of cognition in mammalian carnivores. We discuss the advantages of studying cognition in Carnivorans and the immense progress that has been made across many cognitive domains in both lab and field studies of carnivores. We also discuss the current constraints that are associated with studying carnivores. Finally, we explore new directions for future research in studies of carnivore cognition.

Assessing cognitive flexibility in humans and rhesus macaques with visual motion and neutral distractors

Introduction

Cognitive flexibility is the ability of an individual to make behavioral adjustments in response to internal and/or external changes. While it has been reported in a wide variety of species, established paradigms to assess cognitive flexibility vary between humans and non-human animals, making systematic comparisons difficult to interpret.

Methods

We developed a computer-based paradigm to assess cognitive flexibility in humans and non-human primates. Our paradigm (1) uses a classical reversal learning structure in combination with a set-shifting approach (4 stimuli and 3 rules) to assess flexibility at various levels; (2) it employs the use of motion as one of three possible contextual rules; (3) it comprises elements that allow a foraging-like and random interaction, i.e., instances where the animals operate the task without following a strategy, to potentially minimize frustration in favor of a more positive engagement.

Results and Discussion

We show that motion can be used as a feature dimension (in addition to commonly used shape and color) to assess cognitive flexibility. Due to the way motion is processed in the primate brain, we argue that this dimension is an ideal candidate in situations where a non-binary rule set is needed and where participants might not be able to fully grasp other visual information of the stimulus (e.g., quantity in Wisconsin Card Sorting Test). All participants in our experiment flexibly shifted to and from motion-based rules as well as color- and shape-based rules, but did so with different proficiencies. Overall, we believe that with such approach it is possible to better characterize the evolution of cognitive flexibility in primates, as well as to develop more efficient tools to diagnose and treat various executive function deficits.

Number selective sensorimotor neurons in the crow translate perceived numerosity into number of actions

Translating a perceived number into a matching number of self-generated actions is a hallmark of numerical reasoning in humans and animals alike. To explore this sensorimotor transformation, we trained crows to judge numerical values in displays and to flexibly plan and perform a matching number of pecks. We report number selective sensorimotor neurons in the crow telencephalon that signaled the impending number of self-generated actions. Neuronal population activity during the sensorimotor transformation period predicted whether the crows mistakenly planned fewer or more pecks than instructed. During sensorimotor transformation, both a static neuronal code characterized by persistently number-selective neurons and a dynamic code originating from neurons carrying rapidly changing numerical information emerged. The findings indicate there are distinct functions of abstract neuronal codes supporting the sensorimotor number system.

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.

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

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

Number sense: the mediating effect between nonverbal intelligence and children's mathematical performance

The study explored the mediating effect of number sense between nonverbal intelligence and children's mathematical performance. The sample consisted of 131 pupils in Shaoxing City of China from grades 1, 3, and 5. The students completed measures of nonverbal intelligence, number sense, basic arithmetic ability, mathematical performance, rapid automatized naming, and working memory. Results show that although all variables significantly relate with each other (all p < .01), only nonverbal intelligence, number sense, and basic arithmetic ability significantly affect children's mathematical performance (all p < .01). According to multiple-mediation model, nonverbal intelligence significantly predicts children's mathematical performance through number sense and basic arithmetic ability. These findings suggest that domain-specific mathematical skills play a prominent role in children's mathematical performance in primary school, rather than domain-general cognitive functions. Educators should pay attention to develop children's number sense in order to improve children's mathematical ability.

Characteristics of the Mating Behavior of Domesticated Geese from Anser cygnoides and Anser anser

Mating behavior is a critically important component of poultry reproduction. Here, a total of 135 geese were selected, specifically, Sichuan white geese (Anser cygnoides), Zhedong white geese (Anser cygnoides), and Hungarian geese (Anser anser) (300-day-old), and the mating behavior was monitored daily from 6:00 a.m. to 6:00 p.m. during the 20-day observation period. The results showed that the mating process included mounting, female cooperation, and successful copulation. Overall, the three breeds preferred mating on land. More than thirty percent of the mating time was primarily concentrated from 4:00 p.m. to 6:00 p.m. in domesticated geese from Anser cygnoides, the corresponding values for Sichuan white geese and Zhedong white geese were 32.0% and 33.3%, respectively. The mating of the Hungarian geese usually took place in the morning. In addition, the frequency of successful copulation of Sichuan white geese and Zhedong white geese were 2.31 and 1.94 times per day, significantly greater than that of Hungarian geese (0.89 times). Furthermore, a significant positive correlation between successful copulation and laying rates (r = 0.985) or fertilization rates (r = 0.992) was observed in Hungarian geese. Taken together, the mating behaviors among the different breeds were mainly reflected in time preference and successful copulation frequency.

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.

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.

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’.

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.

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.

Spontaneous representation of numerosity zero in a deep neural network for visual object recognition

Conceiving "nothing" as a numerical value zero is considered a sophisticated numerical capability that humans share with cognitively advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to real neurons from animals, numerosity zero network units show maximum activity to empty sets and a gradual decrease in activity with increasing countable numerosities. This indicates that the network spontaneously ordered numerosity zero as the smallest numerical value along the number line. Removal of empty-set network units caused specific deficits in the network's judgment of numerosity zero, thus reflecting these units' functional relevance. These findings suggest that processing visual information is sufficient for a visual number sense that includes zero to emerge and explains why cognitively advanced animals with whom we share a nonverbal number system exhibit rudiments of numerosity zero.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Consciousness and cognition in plants

Unlike animal behavior, behavior in plants is traditionally assumed to be completely determined either genetically or environmentally. Under this assumption, plants are usually considered to be noncognitive organisms. This view nonetheless clashes with a growing body of empirical research that shows that many sophisticated cognitive capabilities traditionally assumed to be exclusive to animals are exhibited by plants too. Yet, if plants can be considered cognitive, even in a minimal sense, can they also be considered conscious? Some authors defend that the quest for plant consciousness is worth pursuing, under the premise that sentience can play a role in facilitating plant's sophisticated behavior. The goal of this article is not to provide a positive argument for plant cognition and consciousness, but to invite a constructive, empirically informed debate about it. After reviewing the empirical literature concerning plant cognition, we introduce the reader to the emerging field of plant neurobiology. Research on plant electrical and chemical signaling can help shed light into the biological bases for plant sentience. To conclude, we shall present a series of approaches to scientifically investigate plant consciousness. In sum, we invite the reader to consider the idea that if consciousness boils down to some form of biological adaptation, we should not exclude a priori the possibility that plants have evolved their own phenomenal experience of the world. This article is categorized under: Cognitive Biology > Evolutionary Roots of Cognition Philosophy > Consciousness Neuroscience > Cognition.

Rhesus Monkeys Have a Counting Ability and Can Count from One to Six

Counting ability is one of the many aspects of animal cognition and has enjoyed great interest over the last couple of decades. The impetus for studying counting ability in nonhuman animals has likely come from more than a general interest in animal cognition, as the analysis of animal abilities amplifies our understanding of human cognition. In addition, a model animal with the ability to count could be used to replace human subjects in related studies. Here we designed a behavioral paradigm to train rhesus monkeys to count 1-to-6 visual patterns presented sequentially with long and irregular interpattern intervals on a touch screen. The monkeys were required to make a response to the sixth pattern exclusively, inhibiting response to any patterns appearing at other ordinal positions. All stimulus patterns were of the same size, color, location, and shape to prevent monkeys making the right choice due to non-number physical cues. In the long delay period, the monkey had to enumerate how many patterns had been presented sequentially and had to remember in which ordinal position the current pattern was located. Otherwise, it was impossible for them to know which pattern was the target one. The results show that all three monkeys learned to correctly choose the sixth pattern within 3 months. This study provides convincing behavioral evidence that rhesus monkeys may have the capacity to count.

Topographic numerosity maps cover subitizing and estimation ranges

Numerosity, the set size of a group of items, helps guide behaviour and decisions. Non-symbolic numerosities are represented by the approximate number system. However, distinct behavioural performance suggests that small numerosities, i.e. subitizing range, are implemented differently in the brain than larger numerosities. Prior work has shown that neural populations selectively responding (i.e. hemodynamic responses) to small numerosities are organized into a network of topographical maps. Here, we investigate how neural populations respond to large numerosities, well into the ANS. Using 7 T fMRI and biologically-inspired analyses, we found a network of neural populations tuned to both small and large numerosities organized within the same topographic maps. These results demonstrate a continuum of numerosity preferences that progressively cover both the subitizing range and beyond within the same numerosity map, suggesting a single neural mechanism. We hypothesize that differences in map properties, such as cortical magnification and tuning width, underlie known differences in behaviour.

Biological scaling analyses are more than statistical line fitting

The magnitude of many biological traits relates strongly and regularly to body size. Consequently, a major goal of comparative biology is to understand and apply these 'size-scaling' relationships, traditionally quantified by using linear regression analyses based on log-transformed data. However, recently some investigators have questioned this traditional method, arguing that linear or non-linear regression based on untransformed arithmetic data may provide better statistical fits than log-linear analyses. Furthermore, they advocate the replacement of the traditional method by alternative specific methods on a case-by-case basis, based simply on best-fit criteria. Here, I argue that the use of logarithms in scaling analyses presents multiple valuable advantages, both statistical and conceptual. Most importantly, log-transformation allows biologically meaningful, properly scaled (scale-independent) comparisons of organisms of different size, whereas non-scaled (scale-dependent) analyses based on untransformed arithmetic data do not. Additionally, log-based analyses can readily reveal biologically and theoretically relevant discontinuities in scale invariance during developmental or evolutionary increases in body size that are not shown by linear or non-linear arithmetic analyses. In this way, log-transformation advances our understanding of biological scaling conceptually, not just statistically. I hope that my Commentary helps students, non-specialists and other interested readers to understand the general benefits of using log-transformed data in size-scaling analyses, and stimulates advocates of arithmetic analyses to show how they may improve our understanding of scaling conceptually, not just statistically.

Behavioral and Neuronal Representation of Numerosity Zero in the Crow

Different species of animals can discriminate numerosity, the countable number of objects in a set. The representations of countable numerosities have been deciphered down to the level of single neurons. However, despite its importance for human number theory, a special numerical quantity, the empty set (numerosity zero), has remained largely unexplored. We explored the behavioral and neuronal representation of the empty set in carrion crows. Crows were trained to discriminate small numerosities including the empty set. Performance data showed a numerical distance effect for the empty set in one crow, suggesting that the empty set and countable numerosities are represented along the crows' "mental number line." Single-cell recordings in the endbrain region nidopallium caudolaterale (NCL) showed a considerable proportion of NCL neurons tuned to the preferred numerosity zero. As evidenced by neuronal distance and size effects, NCL neurons integrated the empty set in the neural number line. A subsequent neuronal population analysis using a statistical classifier approach showed that the neuronal numerical representations were predictive of the crows' success in the task. These behavioral and neuronal data suggests that the conception of the empty set as a cognitive precursor of a zero-like number concept is not an exclusive property of the cerebral cortex of primates. Zero as a quantitative category cannot only be implemented in the layered neocortex of primates, but also in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.SIGNIFICANCE STATEMENT The conception of "nothing" as number "zero" is celebrated as one of the greatest achievements in mathematics. To explore whether precursors of zero-like concepts can be found in vertebrates with a cerebrum that anatomically differs starkly from our primate brain, we investigated this in carrion crows. We show that crows can grasp the empty set as a null numerical quantity that is mentally represented next to number one. Moreover, we show that single neurons in an associative avian cerebral region specifically respond to the empty set and show the same physiological characteristics as for countable quantities. This suggests that zero as a quantitative category can also be implemented in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution.

Tuned neural responses to haptic numerosity in the putamen

The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.