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.

Through an animal's eye: the implications of diverse sensory systems in scientific experimentation

'Accounting for the sensory abilities of animals is critical in experimental design.' No researcher would disagree with this statement, yet it is often the case that we inadvertently fall for anthropocentric biases and use ourselves as the reference point. This paper discusses the risks of adopting an anthropocentric view when working with non-human animals, and the unintended consequences this has on our experimental designs and results. To this aim, we provide general examples of anthropocentric bias from different fields of animal research, with a particular focus on animal cognition and behaviour, and lay out the potential consequences of adopting a human-based perspective. Knowledge of the sensory abilities, both in terms of similarities to humans and peculiarities of the investigated species, is crucial to ensure solid conclusions. A more careful consideration of the diverse sensory systems of animals would improve many scientific fields and enhance animal welfare in the laboratory.

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.

Using pupae as appetitive reinforcement to study visual and tactile associative learning in the Ponerine ant Diacamma indicum

Associative learning is of great importance to animals, as it enhances their ability to navigate, forage, evade predation and improve fitness. Even though associative learning abilities of Hymenopterans have been explored, many of these studies offered food as appetitive reinforcement. In the current study, we focus on tactile and visual cue learning in an ant Diacamma indicum using a Y-maze setup with pupa as a positive reinforcement. Using pupa as a reward resulted in a significantly higher proportion of ants completing the training in a shorter time as compared to using food as reinforcement. Ants spent significantly more time in the conditioned arm for both visual cues (white dots or black dots) and tactile cues (rough or smooth surfaces) presented on the floor when associated with pupa, thus showing that they were capable of associative learning. On encountering a conflict between visual and tactile cues during the test, ants chose to spend significantly more time on the arm with the tactile cues indicating that they had made a stronger association between pupa and the tactile cue as compared to the visual cue during training. Using pupa as an ecologically relevant reward, we show that these solitary foraging ants living in small colonies are capable of visual and tactile associative learning and are likely to learn tactile cues over visual cues in association with pupa.

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.

Numerosity Categorization by Parity in an Insect and Simple Neural Network

A frequent question as technology improves and becomes increasingly complex, is how we enable technological solutions and models inspired by biological systems. Creating technology based on humans is challenging and costly as human brains and cognition are complex. The honeybee has emerged as a valuable comparative model which exhibits some cognitive-like behaviors. The relative simplicity of the bee brain compared to large mammalian brains enables learning tasks, such as categorization, that can be mimicked by simple neural networks. Categorization of abstract concepts can be essential to how we understand complex information. Odd and even numerical processing is known as a parity task in human mathematical representations, but there appears to be a complete absence of research exploring parity processing in non-human animals. We show that free-flying honeybees can visually acquire the capacity to differentiate between odd and even quantities of 1–10 geometric elements and extrapolate this categorization to the novel numerosities of 11 and 12, revealing that such categorization is accessible to a comparatively simple system. We use this information to construct a neural network consisting of five neurons that can reliably categorize odd and even numerosities up to 40 elements. While the simple neural network is not directly based on the biology of the honeybee brain, it was created to determine if simple systems can replicate the parity categorization results we observed in honeybees. This study thus demonstrates that a task, previously only shown in humans, is accessible to a brain with a comparatively small numbers of neurons. We discuss the possible mechanisms or learning processes allowing bees to perform this categorization task, which range from numeric explanations, such as counting, to pairing elements and memorization of stimuli or patterns. The findings should encourage further testing of parity processing in a wider variety of animals to inform on its potential biological roots, evolutionary drivers, and potential technology innovations for concept processing.

Zebrafish excel in number discrimination under an operant conditioning paradigm

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

The evolution of quantitative sensitivity

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

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

Naïve and Experienced Honeybee Foragers Learn Normally Configured Flowers More Easily Than Non-configured or Highly Contrasted Flowers

Angiosperms have evolved to attract and/or deter specific pollinators. Flowers provide signals and cues such as scent, colour, size, pattern, and shape, which allow certain pollinators to more easily find and visit the same type of flower. Over evolutionary time, bees and angiosperms have co-evolved resulting in flowers being more attractive to bee vision and preferences, and allowing bees to recognise specific flower traits to make decisions on where to forage. Here we tested whether bees are instinctively tuned to process flower shape by training both flower-experienced and flower-naïve honeybee foragers to discriminate between pictures of two different flower species when images were either normally configured flowers or flowers which were scrambled in terms of spatial configuration. We also tested whether increasing picture contrast, to make flower features more salient, would improve or impair performance. We used four flower conditions: (i) normally configured greyscale flower pictures, (ii) scrambled flower configurations, (iii) high contrast normally configured flowers, and (iv) asymmetrically scrambled flowers. While all flower pictures contained very similar spatial information, both experienced and naïve bees were better able to learn to discriminate between normally configured flowers than between any of the modified versions. Our results suggest that a specialisation in flower recognition in bees is due to a combination of hard-wired neural circuitry and experience-dependent factors.

Spontaneous choices for insect-pollinated flower shapes by wild non-eusocial halictid bees

The majority of angiosperms require animal pollination for reproduction, and insects are the dominant group of animal pollinators. Bees are considered one of the most important and abundant insect pollinators. Research into bee behaviour and foraging decisions has typically centred on managed eusocial bee species, including Apis mellifera and Bombus terrestris. Non-eusocial bees are understudied with respect to foraging strategies and decision making, such as flower preferences. Understanding whether there are fundamental foraging strategies and preferences that are features of insect groups can provide key insights into the evolution of flower-pollinator co-evolution. In the current study, Lasioglossum (Chilalictus) lanarium and Lasioglossum (Parasphecodes) sp., two native Australian generalist halictid bees, were tested for flower shape preferences between native insect-pollinated and bird-pollinated flowers. Each bee was presented with achromatic images of either insect-pollinated or bird-pollinated flowers in a circular arena. Both native bee species demonstrated a significant preference for images of insect-pollinated flowers. These preferences are similar to those found in A. mellifera, suggesting that flower shape preference may be a deep-rooted evolutionary occurrence within bees. With growing interest in the sensory capabilities of non-eusocial bees as alternative pollinators, the current study also provides a valuable framework for further behavioural testing of such species.

Comparative psychophysics of colour preferences in two species of non-eusocial Australian native halictid bees

Colour signalling by flowers appears to be the main plant-pollinator communication system observed across many diverse species and locations worldwide. Bees are considered one of the most important insect pollinators; however, native non-eusocial bees are often understudied compared to managed eusocial species, such as honeybees and bumblebees. Here, we tested two species of native Australian non-eusocial halictid bees on their colour preferences for seven different broadband colours with bee-colour-space dominant wavelengths ranging from 385 to 560 nm and a neutral grey control. Lasioglossum (Chilalictus) lanarium demonstrated preferences for a UV-absorbing white (455 nm) and a yellow (560 nm) stimulus. Lasioglossum (Parasphecodes) sp. showed no colour preferences. Subsequent analyses showed that green contrast and spectral purity had a significant positive relationship with the number of visits by L. lanarium to stimuli. Colour preferences were consistent with other bee species and may be phylogenetically conserved and linked to how trichromatic bees processes visual information, although the relative dearth of empirical evidence on different bee species currently makes it difficult to dissect mechanisms. Past studies and our current results suggest that both innate and environmental factors might both be at play in mediating bee colour preferences.

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

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

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.

Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus)

When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber's Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species.

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

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

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.

Use of temporal and colour cueing in a symbolic delayed matching task by honey bees

Honey bees (Apis mellifera) are known for their capacity to learn arbitrary relationships between colours, odours and even numbers. However, it is not known whether bees can use temporal signals as cueing stimuli in a similar way during symbolic delayed matching-to-sample tasks. Honey bees potentially process temporal signals during foraging activities, but the extent to which they can use such information is unclear. Here, we investigated whether free-flying honey bees could use either illumination colour or illumination duration as potential context-setting cues to enable their subsequent decisions for a symbolic delayed matching-to-sample task. We found that bees could use the changing colour context of the illumination to complete the subsequent spatial vision task at a level significantly different from chance expectation, but could not use the duration of either a 1 or 3 s light as a cueing stimulus. These findings suggest that bees cannot use temporal information as a cueing stimulus as efficiently as other signals such as colour, and are consistent with previous field observations suggesting a limited interval timing capacity in honey bees.

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.