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

Heuristic strategy of intuitive statistical inferences in 7- to 10-year-old children

Intuitive statistical inferences refer to making inferences about uncertain events based on limited probabilistic information, which is crucial for both human and non-human species' survival and reproduction. Previous research found that 7- and 8-year-old children failed in intuitive statistical inference tasks after heuristic strategies had been controlled. However, few studies systematically explored children's heuristic strategies of intuitive statistical inferences and their potential numerical underpinnings. In the current research, Experiment 1 (N = 81) examined 7- to 10-year-olds' use of different types of heuristic strategies; results revealed that children relied more on focusing on the absolute number strategy. Experiment 2 (N = 99) and Experiment 3 (N = 94) added continuous-format stimuli to examine whether 7- and 8-year-olds could make genuine intuitive statistical inferences instead of heuristics. Results revealed that both 7- and 8-year-olds and 9- and 10-year-olds performed better in intuitive statistical inference tasks with continuous-format stimuli, even after focusing on the absolute number strategy had been controlled. The results across the three experiments preliminarily hinted that the ratio processing system might rely on the approximate number system. Future research could clarify what specific numerical processing mechanism may be used and how it might support children's statistical intuitions.

Transfer from continuous to discrete quantities in honeybees

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

Neural coding of numerousness

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

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.

Number neurons in the nidopallium of young domestic chicks

Numerosity, that is, the number of items in a set, is a significant aspect in the perception of the environment. Behavioral and in silico experiments suggest that number sense belongs to a core knowledge system and can be present already at birth. However, neurons sensitive to the number of visual items have been so far described only in the brain of adult animals. Therefore, it remained unknown to what extent their selectivity would depend on visual learning and experience. We found number neurons in the caudal nidopallium (a higher associative area functionally similar to the mammalian prefrontal cortex) of very young, numerically naïve domestic chicks. This result suggests that numerosity perception is possibly an inborn feature of the vertebrate brain.

Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe number neurons in the caudal nidopallium (functionally equivalent to the mammalian prefrontal cortex) of young domestic chicks. Number neurons that we found in young chicks showed remarkable similarities to those in the prefrontal cortex and caudal nidopallium of adult animals. Thus, our results suggest that numerosity perception based on number neurons might be an inborn feature of the vertebrate brain.

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.

Steps towards a computational ethology: an automatized, interactive setup to investigate filial imprinting and biological predispositions

Soon after hatching, the young of precocial species, such as domestic chicks or ducklings, learn to recognize their social partner by simply being exposed to it (imprinting process). Even artificial objects or stimuli displayed on monitor screens can effectively trigger filial imprinting, though learning is canalized by spontaneous preferences for animacy signals, such as certain kinds of motion or a face-like appearance. Imprinting is used as a behavioural paradigm for studies on memory formation, early learning and predispositions, as well as number and space cognition, and brain asymmetries. Here, we present an automatized setup to expose and/or test animals for a variety of imprinting experiments. The setup consists of a cage with two high-frequency screens at the opposite ends where stimuli are shown. Provided with a camera covering the whole space of the cage, the behaviour of the animal is recorded continuously. A graphic user interface implemented in Matlab allows a custom configuration of the experimental protocol, that together with Psychtoolbox drives the presentation of images on the screens, with accurate time scheduling and a highly precise framerate. The setup can be implemented into a complete workflow to analyse behaviour in a fully automatized way by combining Matlab (and Psychtoolbox) to control the monitor screens and stimuli, DeepLabCut to track animals' behaviour, Python (and R) to extract data and perform statistical analyses. The automated setup allows neuro-behavioural scientists to perform standardized protocols during their experiments, with faster data collection and analyses, and reproducible results.