Endowed with an elaborate cerebral cortex, humans and other primates can assess the number of items in a set, or numerosity, from birth on [] and without being trained []. Whether spontaneous numerosity extraction is a unique feat of the mammalian cerebral cortex [] or rather an adaptive property that can be found in differently designed and independently evolved neural substrates, such as the avian enbrain [], is unknown. To address this question, we recorded single-cell activity from the nidopallium caudolaterale (NCL), a high-level avian association brain area [], of numerically naive crows. We found that a proportion of NCL neurons were spontaneously responsive to numerosity and tuned to the number of items, even though the crows were never trained to assess numerical quantity. Our data show that numerosity-selective neuronal responses are spontaneously present in the distinct endbrains of diverge vertebrate taxa. This seemingly hard-wired property of the avian endbrain to extract numerical quantity explains how birds in the wild, or right after hatching, can exploit numerical cues when making foraging or social decisions. It suggests that endbrain circuitries that evolved based on convergent evolution, such as the avian endbrain, give rise to the same numerosity code.

To create average neural filter functions, activity rates were normalized by setting the maximum activity to the most preferred numerosity as 100% and the activity to the least preferred numerosity as 0%. Tuning functions to each of the sample numerosities were constructed by averaging the normalized spike rates of all neurons that had the same preferred numerosity. This resulted in overlapping numerosity tuning curves ( Figure 4 B). Across the population, NCL neurons covered the entire tested range of numerosities 1–5. Finally, we plotted the average normalized activity across the population of numerosity-selective neurons as a function of the numerical distance from the preferred numerosity ( Figure 4 C). On average, neuronal activity dropped as a function of the numerical distance from the preferred numerosity, a neuronal correlate of the “numerical distance effect” that has been reported for numerosity-selective NCL neurons in trained crows [].

These neurons were tuned to the number of dots; they showed the highest discharge rates to a specific numerosity, its preferred numerosity, and a progressive decay of activity for neighboring numerosities (see tuning curve insets in Figures 3 B–3D). Most of the selective neurons preferred numerosity 1 and 5; fewer neurons were tuned to the other intermediate numerosities ( Figure 4 A). Note that an increased frequency count for preferred numerosity 5 is even expected as the tested numerosity range was truncated to numerosity 5, and few neurons assigned to this class may, in fact, have been tuned to numerosities larger than 5.

(C) Average normalized activity of all numerosity-selective neurons as a function of numerical distance from the preferred numerosity. Error bars indicate SEM.

A three-factor ANOVA (numerosity × color × protocol) was used to statistically test the neurons’ selectivity to the different stimulus parameters. Neurons that showed a significant main effect for numerosity (p < 0.01), but no significant main effect for protocol or any interaction, were identified as numerosity-selective neurons and considered for further analyses. The behaviorally irrelevant parameter “numerosity” significantly modulated the activity of 12% (48/403) of the NCL neurons. Of those 48 numerosity-selective cells, 19 neurons (39.6%) showed an additional main effect for color. All neurons depicted in Figure 3 were numerosity selective according to this criterion. Table S1 shows the proportions of neurons that were significant to each of the main factors and interactions. These proportions of significant neurons are well beyond the chance level of about 1% of selective cells that we got when the spike rates of individual neurons were shuffled and analyzed in the same way ( Table S2 ).

We recorded the activity of 403 single neurons (crow T: 289; crow V: 114) in the NCL ( Figure 3 A) while the crows performed the color-discrimination task with colored-dot stimuli. We found cells that responded differently to specific numbers of dots (i.e., numerosities) during the sample presentation. Figure 3 shows the activity of three exemplary neurons. The example neuron in Figure 3 B showed the highest activity to numerosity 1, whereas the other neurons responded strongest to numerosity 2 ( Figure 3 C) and 5 ( Figure 3 D).

(B–D) Neuronal responses of exemplary neurons to the number of presented dots in the sample stimulus. The neurons were selective to numerosity 1 (A), 2 (B), and 5 (C). Top: Dot-raster histograms with each line indicating one trial and each dot representing an action potential. Activity is separated for standard and control conditions. Bottom: Corresponding spike-density functions, representing the time course of the average response to each numerosity (smoothed by a 150 ms Gauss kernel). Colors of dot-raster histograms and spike-density functions correspond to the numerosity of the sample stimulus. Vertical line at 0 ms indicates onset of the sample that was shown for 800 ms. Tuning function insets indicate the average firing rate to numerosity in the standard (std) and control (cntr) condition. Error bars represent SEM. See also Tables S1 and S2

Both crows performed the color-discrimination task proficiently well above the 50% chance level (crow T: 99% ± 0.2% SEM, n = 50 sessions; crow V: 95% ± 0.3% SEM, n = 43 sessions; Figure 2 A) for all sample colors (all binomial tests, p < 0.001). To ensure that the crows had indeed discriminated color and not numerosity, we inserted a small fraction of generalization trials during the ongoing color-discrimination task. In generalization trials, the dots of both sample and test stimuli were all black. If the crows were ignorant of numerosity and relied on color, they would perform at chance level for the all black dot arrays. Indeed, both crows performed at chance level in black-dot trials (crow T: 52%, n = 283 trials; crow V: 52%, n = 270 trials; both binomial tests, p ≥ 0.5; Figure 2 B).

(A) Performance in the color discrimination task during recording sessions (crow T: n = 50; crow V: n = 43). Chance level is 50%. Error bars indicate SEM across the sessions.

Two crows (Corvus corone) were trained to discriminate color in variable dot displays in a delayed match-to-sample (DMS) task. This ensured that the crows paid attention to the stimulus displays during recording ( Figure 1 A). The crows saw two colored-dot displays (first sample, then test) separated by a 1 s delay. They were trained to respond by moving their head whenever the (1–5) dots in the sample and test displays were of the same color. Five colors (red, blue, green, yellow, purple) were used ( Figure 1 B). Importantly, the crows were only trained to discriminate color, not numerosity. All five colors and numerosities were displayed as “standard stimuli,” with variable dot sizes and positions, and “control stimuli” equating the total area and the average density of all dots across numerosities. All parameters (color, numerosity, stimulus protocol, match versus non-match trials, etc.) were balanced and pseudo-randomly presented in each session.

(B) Example stimulus displays. Each of the five colors was presented in five different numerosities and two different stimulus sets (standard and control).

(A) The crows performed a delayed match-to-sample task in which they discriminated the color of dot arrays. A trial was initiated by moving the head into a light barrier in front of the screen and keeping it in this position. After a short pre-sample phase, a sample stimulus (colored-dot array) was presented for 800 ms, followed by a delay of 1,000 ms. In the subsequent test phase, a match stimulus (same color as the sample) was shown as test 1 in 50% of the trials, in the other half a non-match stimulus (different color as the sample) was presented first and followed by a match stimulus. The crow was rewarded for responding by moving its head out of the light barrier whenever the color of a test stimulus matched the color of the sample.

We therefore investigated the question of spontaneous numerosity selectivity in a bird species: the carrion crow. Instead of a cerebral cortex, birds possess nuclear telencephalic areas [] as highest integration centers that evolved independently since the last common reptilian-like ancestor of birds and mammals lived 320 million years ago []. We recently showed that neurons in the endbrain region nidopallium caudolaterale (NCL), a brain area considered to be the avian analog of the primate prefrontal cortex [], respond selectively to the number of visual items in numerically trained crows []. In the current study, we explored spontaneous neuronal selectivity to numerosity in crows that had never been trained to discriminate the number of items in a set.

However, all of these data have been collected in primate species that possess an elaborate six-layered cerebral cortex as highest integration center in the brain. Whether spontaneous numerosity extraction is a special feature of the cerebral cortex or rather an adaptive property that can be found in differently designed and independently evolved endbrains is unknown.

Whether humans and animals are endowed with an innate faculty to perceive the number of items in a set (that is, numerosity) is intensely discussed. The idea of a “number sense” [] argues that numerosity is assessed intuitively as a spontaneous category by hard-wired brain processes, without the need to be learned. Support for the direct and spontaneous assessment of numerosity resulted from psychophysical experiments in humans showing that approximate visual number assessments are subject to adaptation []. In addition, recent imaging evidence suggests that the direct and automatic extraction of numerosity also occurs in the human brain []. The most direct support for the notion of a “number sense” comes from recordings in monkeys that had not been trained to judge number; these recordings showed that single neurons in both the parietal and prefrontal cortices spontaneously responded to numerosity and were tuned to preferred numerosities [].

Discussion

17 Veit L.

Nieder A. Abstract rule neurons in the endbrain support intelligent behaviour in corvid songbirds. 18 Moll F.W.

Nieder A. Cross-modal associative mnemonic signals in crow endbrain neurons. 19 Veit L.

Pidpruzhnykova G.

Nieder A. Associative learning rapidly establishes neuronal representations of upcoming behavioral choices in crows. In the current study, we tested the core idea of the “number sense” and explored, for the first time in a non-primate species, whether numerosity-selective neurons spontaneously exist in the brain of crows. To that aim, we recorded single-cell activity from the NCL, a high-level avian association brain area [], of numerically naive crows. We show that a proportion of NCL neurons is selectively tuned to the number of items in a set. This demonstrates that numerosity-selective neurons are not the result of behavioral training but spontaneously exist in crows that have never been trained to discriminate numerosity.

15 Ditz H.M.

Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain. 20 Ditz H.M.

Nieder A. Numerosity representations in crows obey the Weber-Fechner law. Without numerosity training, we found that 12% of NCL neurons responded selectively to the number of presented dots. This proportion was significantly smaller compared to the 20% of numerosity-selective neurons from the same NCL region in crows trained to perform a numerosity-discrimination task [] (chi-square tests, p < 0.01). However, the selectivity of the numerosity-selective responses was comparable for data from naive and trained crows. We compared the widths of the numerosity-tuning curves as measured by sigma of Gauss-fits to the (logarithmically scaled) tuning functions [] and found no difference between numerically naive and trained crows (Mann-Whitney-U test, p = 0.86). Based on these comparisons, we conclude that numerosity training may increase the proportion of numerosity-selective cells in NCL but not their coding properties.

21 Nieder A. The neuronal code for number. 22 Viswanathan P.

Nieder A. Differential impact of behavioral relevance on quantity coding in primate frontal and parietal neurons. 7 Viswanathan P.

Nieder A. Neuronal correlates of a visual “sense of number” in primate parietal and prefrontal cortices. The only other animal species for which single-unit data about numerosity coding is available are macaque monkeys. In these primates, the ventral intraparietal area (VIP) and prefrontal cortex (PFC) have been identified as key areas for number representations []. Interestingly, the proportion of selective neurons (12%) in the NCL of numerically naive crows is almost identical to the 13% and 14% of numerosity-selective neurons in the VIP and PFC, respectively, of numerically naive monkeys []. This suggests the NCL as a neuronal substrate for representing numerical information, much in the way as the VIP and PFC constitute the core number system in primates.

23 Roitman J.D.

Brannon E.M.

Platt M.L. Monotonic coding of numerosity in macaque lateral intraparietal area. 21 Nieder A. The neuronal code for number. 24 Dehaene S.

Changeux J.P. Development of elementary numerical abilities: a neuronal model. 25 Verguts T.

Fias W. Representation of number in animals and humans: a neural model. 15 Ditz H.M.

Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain. 16 Ditz H.M.

Nieder A. Sensory and working memory representations of small and large numerosities in the crow endbrain. 26 Nieder A.

Freedman D.J.

Miller E.K. Representation of the quantity of visual items in the primate prefrontal cortex. 27 Nieder A.

Miller E.K. A parieto-frontal network for visual numerical information in the monkey. 28 Nieder A.

Diester I.

Tudusciuc O. Temporal and spatial enumeration processes in the primate parietal cortex. 29 Sawamura H.

Shima K.

Tanji J. Numerical representation for action in the parietal cortex of the monkey. 30 Nieder A. Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices. 31 Ramirez-Cardenas A.

Moskaleva M.

Nieder A. Neuronal representation of numerosity zero in the primate parieto-frontal number network. 7 Viswanathan P.

Nieder A. Neuronal correlates of a visual “sense of number” in primate parietal and prefrontal cortices. 32 Nieder A. Evolution of cognitive and neural solutions enabling numerosity judgements: lessons from primates and corvids. Our study also speaks to the question of the neuronal code for numerical quantity in the animal kingdom. Two competing hypotheses have been proposed. Numbers could either be encoded by a “summation code” as witnessed by monotonic discharges as a function of quantity [], or by a “labeled-line code” as evidenced by neurons tuned to preferred numerosities []. In agreement with influential computational models of number processing [], the numerosity-selective neurons we found in the NCL of numerically naive crows were tuned to their individual preferred numerical value. The same code has been found in numerically trained crows [] and multiple times in single-cell recordings in monkeys, both trained [] and numerially naive []. It therefore seems that the neuronal code for number information is a labeled-line code. This code seems to have evolved independently in phylogeny in birds and mammals, two distantly related vertebrate taxa []. The labeled-line code may be computationally superior when compared to alternative neuronal representations such as summation coding.

33 Bogale B.A.

Kamata N.

Mioko K.

Sugita S. Quantity discrimination in jungle crows, Corvus macrorhynchos. 34 Ujfalussy D.J.

Miklósi Á.

Bugnyar T.

Kotrschal K. Role of mental representations in quantity judgments by jackdaws (Corvus monedula). 35 Hunt S.

Low J.

Burns K.C. Adaptive numerical competency in a food-hoarding songbird. 36 Stancher G.

Rugani R.

Regolin L.

Vallortigara G. Numerical discrimination by frogs (Bombina orientalis). 37 Potrich D.

Sovrano V.A.

Stancher G.

Vallortigara G. Quantity discrimination by zebrafish (Danio rerio). 2 Wilson M.L.

Hauser M.D.

Wrangham R.W. Does participation in intergroup conflict depend on numerical assessment, range location, or rank for wild chimpanzees?. 38 McComb K.

Packer C.

Pusey A. Roaring and numerical assessment in contests between groups of female lions, Panthera leo. 39 Benson-Amram S.

Heinen K.

Dryer S.L.

et al. Numerical assessment and individual call discrimination by wild spotted hyaenas, Crocuta crocuta. The ability to spontaneously assess the number of items in an approximate way is widespread across the animal kingdom, indicating that it is of adaptive value. Tests in which animals can choose between sets of food objects show that different species spontaneously “go for more” and pick the sets containing more food items []. Similarly, animals in the wild spontaneously exploit quantitative information in social interactions []. For these animals to successfully discriminate set size, numerosity-selective neurons must spontaneously be implemented in their brains. Without such neurons, they could not solve such numerical tasks in the first place.

7 Viswanathan P.

Nieder A. Neuronal correlates of a visual “sense of number” in primate parietal and prefrontal cortices. The current data in crows together with a report about numerosity-selective neurons in the parietal and prefrontal cortex of monkeys [] argue that the neuronal mechanisms for approximate number discrimination are readily available without number training in differently designed endbrains. This begs the question whether animals might be born with hard-wired neuronal networks that can represent numerical information. Alternatively, numerosity selectivity could emerge implicitly as a function of increased visual experience with different numbers of objects throughout development. To address this question directly, recordings in juvenile crows at the moment of eye opening would be necessary. However, even without such data, behavioral investigations suggest that numerical competence is present from early on in birds.

40 Rugani R.

Regolin L.

Vallortigara G. Discrimination of small numerosities in young chicks. 41 Rugani R.

Fontanari L.

Simoni E.

Regolin L.

Vallortigara G. Arithmetic in newborn chicks. 1 Izard V.

Sann C.

Spelke E.S.

Streri A. Newborn infants perceive abstract numbers. The young domestic chick is an extremely precocial species and has been tested for numerical competence right after hatching from the egg and thus with a minimum of visual experience. Exploiting filial imprinting few hours after hatching, chicks have been shown to discriminate numerosity and even perform rudimentary arithmetic []. Moreover, newborn human infants at the age of 50 hr also discriminate abstract numerosity, even across sensory modality and sequential and simultaneous presentation formats [].

All of these data together argue that numerosity selectivity may indeed be inborn, not only in primates but also in other vertebrates. This suggests that hard-wired (but, of course, modifiable) neuronal connections extracting numerical information are not a special property of the cerebral cortex but are also implemented in the anatomically distinct endbrain circuitries of birds that evolved based on convergent evolution. How these distinct endbrain designs give rise to the same type of numerosity code needs to be addressed in the future.