The Adaptive Value of Numerical Competence
Authors: Andreas Nieder
Journal: Trends in Ecology & Evolution (2020)

Numerical competence, the ability to estimate and process the number of objects and events, is of adaptive value.It enhances an animal's ability to survive by exploiting food sources, hunting prey, avoiding predation, navigating, and persisting in social interactions. It also plays a major role in successful reproduction, from monopolizing receptive mates to increasing the chances of fertilizing an egg and promoting the survival chances of offspring.In these ecologically relevant scenarios, animals exhibit a specific way of internally representing numbers that follows the Weber-Fechner law.A framework is provided for more dedicated and quantitative analyses of the adaptive value of numerical competence. Evolution selects for traits that are of adaptive value and increase the fitness of an individual or population. Numerical competence, the ability to estimate and process the number of objects and events, is a cognitive capacity that also influences an individual's survival and reproduction success. Numerical assessments are ubiquitous in a broad range of ecological contexts. Animals benefit from numerical competence during foraging, navigating, hunting, predation avoidance, social interactions, and reproductive activities. The internal number representations determine how animals perceive stimulus magnitude, which, in turn, constrains an animal's spontaneous decisions. These findings are placed in a framework to provide for a more quantitative analysis of the adaptive value and selection pressures of numerical competence. Evolution selects for traits that are of adaptive value and increase the fitness of an individual or population. Numerical competence, the ability to estimate and process the number of objects and events, is a cognitive capacity that also influences an individual's survival and reproduction success. Numerical assessments are ubiquitous in a broad range of ecological contexts. Animals benefit from numerical competence during foraging, navigating, hunting, predation avoidance, social interactions, and reproductive activities. The internal number representations determine how animals perceive stimulus magnitude, which, in turn, constrains an animal's spontaneous decisions. These findings are placed in a framework to provide for a more quantitative analysis of the adaptive value and selection pressures of numerical competence. Numerical competence (see Glossary) is a cognitive ability that is widespread across the animal kingdom [1.Nieder A. A Brain for Numbers: The Biology of the Number Instinct. MIT Press, 2019Crossref Google Scholar]. Species from diverse zoological groups, from primates to insects [2.Brannon E.M. Terrace H.S. Ordering of the numerosities 1 to 9 by monkeys.Science. 1998; 282: 746-749Crossref PubMed Scopus (374) Google Scholar, 3.Scarf D. et al.Pigeons on par with primates in numerical competence.Science. 2011; 334: 1664Crossref PubMed Scopus (77) Google Scholar, 4.Gazzola A. et al.Continuous and discrete quantity discrimination in tortoises.Biol. Lett. 2018; 1420180649Crossref PubMed Scopus (8) Google Scholar, 5.Uller C. et al.Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian.Anim. Cogn. 2003; 6: 105-112Crossref PubMed Google Scholar, 6.Potrich D. et al.Quantity discrimination by zebrafish (Danio rerio).J. Comp. Psychol. 2015; 29: 388-393Crossref Scopus (28) Google Scholar, 7.Howard S.R. et al.Numerical ordering of zero in honey bees.Science. 2018; 360: 1124-1126Crossref PubMed Scopus (26) Google Scholar], can discriminate the number of elements in a set: its numerosity. The contemporary study of the mechanisms of numerical competence, both at the behavioral and neural level, is a rich area of investigation in psychology and neuroscience and significant progress has been made over the past decades [1.Nieder A. A Brain for Numbers: The Biology of the Number Instinct. MIT Press, 2019Crossref Google Scholar]. However, while we are beginning to understand how numerical competence emerges in the lifetime of an individual, it is largely unknown why numerical abilities exist in evolutionary history. Despite the phylogenetic ubiquity and innate character of a fundamental 'sense of number' [8.Izard V. et al.Newborn infants perceive abstract numbers.Proc. Natl. Acad. Sci. U. S. 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Biol. 2018; 28: 1090-1094Abstract Full Text Full Text PDF PubMed Scopus (10) Google Scholar], the evolutionary basis and ecological pressures that give rise to it are rarely studied. This is surprising, because numerical talent, like any other trait, needs to have a significant advantage for survival and reproduction to emerge and to be maintained over generations. A close look at the literature suggests that numerical competence is indeed of adaptive value. In this review article, I outline the characteristics of numerical representations and how they affect the behaviors of different species in ecologically relevant situations. These findings can provide a framework for more dedicated and quantitative analyses of the adaptive value of numerical competence. Complementing mechanistic insights by evolutionary approaches is needed for an integrative study of the biology of numerical competence. Animals estimate numerosity not in a precise way, but approximately. Similar numerical values are difficult to discriminate, but discrimination performance is systematically enhanced the more different (or distant) two values are (an effect called 'numerical distance effect'). For example, when frogs (Bombina orientalis) chose between two patches of food items, their choice between three and four items is random, but they reliably chose six items over three [14.Stancher G. et al.Numerical discrimination by frogs (Bombina orientalis).Anim. Cogn. 2015; 18: 219-229Crossref PubMed Scopus (51) Google Scholar]. Moreover, discrimination becomes systematically less precise in proportion to increasing numbers (termed 'numerical size effect'). For example, even though frogs can discriminate between two and four food items, they fail to discriminate between four and six but yet can discriminate between four and eight [14.Stancher G. et al.Numerical discrimination by frogs (Bombina orientalis).Anim. Cogn. 2015; 18: 219-229Crossref PubMed Scopus (51) Google Scholar]. For the sets to be discriminable, the numerical distance between them has to increase in proportion with the absolute magnitudes; the ability to discriminate between quantities is 'ratio-dependent' [15.Cantlon J.F. Brannon E.M. Shared system for ordering small and large numbers in monkeys and humans.Psychol. Sci. 2006; 17: 401-406Crossref PubMed Scopus (294) Google Scholar] (Figure 1A ). Both distance and size effects are captured by Weber's law: the just-noticeable difference, ΔI, divided by the reference value, I, is a constant, c (i.e., ΔI/I = c) [17.Weber E.H. Der Tastsinn und das Gemeingefühl.in: Wagner R. Handwörterbuch der Physiologie. Vol. 3, Part 2. Nabu Press, 1850: 481-588Google Scholar]. Quantity discriminations that follow Weber's law are a clear signature of the internal approximate number system (ANS) that enables representations of all possible estimated numerical values (Figure 1B). The ANS has been found consistently for numerosity judgments in trained animals, from primates [15.Cantlon J.F. Brannon E.M. Shared system for ordering small and large numbers in monkeys and humans.Psychol. Sci. 2006; 17: 401-406Crossref PubMed Scopus (294) Google Scholar,18.Nieder A. Miller E.K. Analog numerical representations in rhesus monkeys: evidence for parallel processing.J. Cogn. Neurosci. 2004; 16: 889-901Crossref PubMed Scopus (86) Google Scholar] to bees [7.Howard S.R. et al.Numerical ordering of zero in honey bees.Science. 2018; 360: 1124-1126Crossref PubMed Scopus (26) Google Scholar,19.Bortot M. et al.Honey bees use absolute rather than relative numerosity in number discrimination.Biol. Lett. 2019; 1520190138Crossref PubMed Scopus (5) Google Scholar], but also for spontaneous numerosity discrimination in a multitude of vertebrate species [20.Beran M.J. Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes).J. Exp. Psychol. Anim. Behav. 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Second, animals also benefit from being able to detect absolute numerical differences in small magnitudes compared with large ones. This is because the relative gain of detecting a given absolute numerical difference decreases with increasing magnitudes due to the proportional relationship. For example, it is highly beneficial for an animal to discriminate between one and two food items because the amount doubles, whereas the increase from 10 to 11 items is only by a factor of 1.1. Because judgments are based on perception of stimuli, both relationships are crucial to the understanding of animal decision-making. Studies with trained animals provided a detailed measurement of how animals subjectively represent objective numbers [28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar, 29.Merten K. Nieder A. Compressed scaling of abstract numerosity representations in adult humans and monkeys.J. Cogn. Neurosci. 2009; 21: 333-346Crossref PubMed Scopus (43) Google Scholar, 30.Ditz H.M. Nieder A. Numerosity representations in crows obey the Weber-Fechner law.Proc. Biol. Sci. 2016; 28320160083Crossref PubMed Google Scholar] (Figure 1B). The resulting bell-shaped performance functions reflect the numerical distance effect. The progressive broadening of the functions, in proportion to increasing magnitude, mirrors the numerical size effect. In addition, a third aspect surfaces on top of Weber's law: relative to a given reference number, animals find it easier to discriminate between smaller numbers and more difficult to discriminate between larger ones. In the example in Figure 1B, an animal could just determine that 8 is a smaller number than 10, but cannot distinguish between 10 and 12, even though the difference is 2 in both cases. For larger numbers, only 13 or above would be discriminable from 10. This effect results in performance functions being mildly asymmetric when plotted on a linear number scale. However, when plotted on a nonlinearly compressed logarithmic scale, the functions become symmetric and of equal variance (Figure 1C). Thus, as objective numerical values increase, the numerical representations remain equidistant in perceptual (mental) number space. In other words, the subjective sensation of number, S, is proportional to the logarithm of the objective stimulus magnitude, I. This relationship is known as Fechner's law: S = k · log(I) [31.Fechner G.T. Elemente der Psychophysik.Vol. 2. Breitkopf & Härtel, 1860Google Scholar]. Because the way in which animals process quantity guides important decisions they make, the behavioral and neural representation of numbers (Box 1) has a strong impact on evolutionary processes [32.Akre K.L. Johnsen S. Psychophysics and the evolution of behavior.Trends Ecol. Evol. 2014; 29: 291-300Abstract Full Text Full Text PDF PubMed Scopus (42) Google Scholar].Box 1'Number Neurons' as Proximate Cause of Numerical CompetenceThe proximate causes of all behaviors are the workings of neurons in the brain. Numerosity-selective neurons, or 'number neurons', that can explain the behavioral approximate number representations [126.Nieder A. Neural constraints on human number concepts.Curr. Opin. Neurobiol. 2020; 60: 28-36Crossref PubMed Scopus (0) Google Scholar] have been found in the brains of crows (Corvus corone) [127.Ditz H.M. Nieder A. Sensory and working memory representations of small and large numerosities in the crow endbrain.J. Neurosci. 2016; 36: 12044-12052Crossref PubMed Scopus (20) Google Scholar,128.Ditz H.M. Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain.Proc. Natl. Acad Sci. USA. 2015; 112: 7827-7832Crossref PubMed Google Scholar], macaque monkeys (Macaca spp.) [28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar,129.Nieder A. et al.Representation of the quantity of visual items in the primate prefrontal cortex.Science. 2002; 297: 1708-1711Crossref PubMed Scopus (447) Google Scholar,130.Nieder A. The neuronal code for number.Nat. Rev. Neurosci. 2016; 17: 366-382Crossref PubMed Google Scholar], and humans [131.Kutter E.F. et al.Single neurons in the human brain encode numbers.Neuron. 2018; 100: 753-761Abstract Full Text Full Text PDF PubMed Scopus (9) Google Scholar]. As a neuronal reflection of the numerical distance effect, number neurons are tuned to numerosity by exhibiting maximum impulse rates to preferred numerical values with progressively decreasing rates to values more remote from the preferred one. Moreover, as a manifestation of a neuronal numerical size effect, the tuning precision of number neurons deteriorates with an increase in preferred numerical values. In addition to this Weber law signature, the neurons' tuning functions are also best described on a nonlinearly compressed, logarithmic number scale [28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar,127.Ditz H.M. Nieder A. Sensory and working memory representations of small and large numerosities in the crow endbrain.J. Neurosci. 2016; 36: 12044-12052Crossref PubMed Scopus (20) Google Scholar,128.Ditz H.M. Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain.Proc. Natl. Acad Sci. USA. 2015; 112: 7827-7832Crossref PubMed Google Scholar,132.Nieder A. Merten K. A labeled-line code for small and large numerosities in the monkey prefrontal cortex.J. Neurosci. 2007; 27: 5986-5993Crossref PubMed Scopus (120) Google Scholar] and thus follow the Fechner's law observed in behavior [29.Merten K. Nieder A. Compressed scaling of abstract numerosity representations in adult humans and monkeys.J. Cogn. Neurosci. 2009; 21: 333-346Crossref PubMed Scopus (43) Google Scholar,30.Ditz H.M. Nieder A. Numerosity representations in crows obey the Weber-Fechner law.Proc. Biol. Sci. 2016; 28320160083Crossref PubMed Google Scholar].Because such number neurons already exist in naïve animals that have never been trained in the laboratory [12.Viswanathan P. Nieder A. Neuronal correlates of a visual "sense of number" in primate parietal and prefrontal cortices.Proc. Natl. Acad. Sci. U. S. A. 2013; 110: 11187-11192Crossref PubMed Scopus (68) Google Scholar,13.Wagener L. et al.Neurons in the endbrain of numerically naive crows spontaneously encode visual numerosity.Curr. Biol. 2018; 28: 1090-1094Abstract Full Text Full Text PDF PubMed Scopus (10) Google Scholar], the brain seems to be automatically endowed with an approximate number system (ANS) and its capacity to extract numbers. In support of a putatively innate ANS, artificial number neurons obeying Weber's and Fechner's law spontaneously emerged also in a deep network that was merely trained on visual object recognition, never on numbers [133.Nasr K. et al.Number detectors spontaneously emerge in a deep neural network designed for visual object recognition.Sci. Adv. 2019; 5eaav7903Crossref PubMed Scopus (3) Google Scholar]. These findings together with the capability of wild animals to spontaneously exploit number suggest that a number sense is based on mechanisms inherent to the brain's sensory systems. Number neurons and numerical competence can emerge as a by-product of exposure to natural visual stimuli, without requiring any explicit training for numerosity estimation. This can explain why animals in the wild and across diverse taxa can readily assess numbers. The proximate causes of all behaviors are the workings of neurons in the brain. Numerosity-selective neurons, or 'number neurons', that can explain the behavioral approximate number representations [126.Nieder A. Neural constraints on human number concepts.Curr. Opin. Neurobiol. 2020; 60: 28-36Crossref PubMed Scopus (0) Google Scholar] have been found in the brains of crows (Corvus corone) [127.Ditz H.M. Nieder A. Sensory and working memory representations of small and large numerosities in the crow endbrain.J. Neurosci. 2016; 36: 12044-12052Crossref PubMed Scopus (20) Google Scholar,128.Ditz H.M. Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain.Proc. Natl. Acad Sci. USA. 2015; 112: 7827-7832Crossref PubMed Google Scholar], macaque monkeys (Macaca spp.) [28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar,129.Nieder A. et al.Representation of the quantity of visual items in the primate prefrontal cortex.Science. 2002; 297: 1708-1711Crossref PubMed Scopus (447) Google Scholar,130.Nieder A. The neuronal code for number.Nat. Rev. Neurosci. 2016; 17: 366-382Crossref PubMed Google Scholar], and humans [131.Kutter E.F. et al.Single neurons in the human brain encode numbers.Neuron. 2018; 100: 753-761Abstract Full Text Full Text PDF PubMed Scopus (9) Google Scholar]. As a neuronal reflection of the numerical distance effect, number neurons are tuned to numerosity by exhibiting maximum impulse rates to preferred numerical values with progressively decreasing rates to values more remote from the preferred one. Moreover, as a manifestation of a neuronal numerical size effect, the tuning precision of number neurons deteriorates with an increase in preferred numerical values. In addition to this Weber law signature, the neurons' tuning functions are also best described on a nonlinearly compressed, logarithmic number scale [28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar,127.Ditz H.M. Nieder A. Sensory and working memory representations of small and large numerosities in the crow endbrain.J. Neurosci. 2016; 36: 12044-12052Crossref PubMed Scopus (20) Google Scholar,128.Ditz H.M. Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain.Proc. Natl. Acad Sci. USA. 2015; 112: 7827-7832Crossref PubMed Google Scholar,132.Nieder A. Merten K. A labeled-line code for small and large numerosities in the monkey prefrontal cortex.J. Neurosci. 2007; 27: 5986-5993Crossref PubMed Scopus (120) Google Scholar] and thus follow the Fechner's law observed in behavior [29.Merten K. Nieder A. Compressed scaling of abstract numerosity representations in adult humans and monkeys.J. Cogn. Neurosci. 2009; 21: 333-346Crossref PubMed Scopus (43) Google Scholar,30.Ditz H.M. Nieder A. Numerosity representations in crows obey the Weber-Fechner law.Proc. Biol. Sci. 2016; 28320160083Crossref PubMed Google Scholar]. Because such number neurons already exist in naïve animals that have never been trained in the laboratory [12.Viswanathan P. Nieder A. Neuronal correlates of a visual "sense of number" in primate parietal and prefrontal cortices.Proc. Natl. Acad. Sci. U. S. A. 2013; 110: 11187-11192Crossref PubMed Scopus (68) Google Scholar,13.Wagener L. et al.Neurons in the endbrain of numerically naive crows spontaneously encode visual numerosity.Curr. Biol. 2018; 28: 1090-1094Abstract Full Text Full Text PDF PubMed Scopus (10) Google Scholar], the brain seems to be automatically endowed with an approximate number system (ANS) and its capacity to extract numbers. In support of a putatively innate ANS, artificial number neurons obeying Weber's and Fechner's law spontaneously emerged also in a deep network that was merely trained on visual object recognition, never on numbers [133.Nasr K. et al.Number detectors spontaneously emerge in a deep neural network designed for visual object recognition.Sci. Adv. 2019; 5eaav7903Crossref PubMed Scopus (3) Google Scholar]. These findings together with the capability of wild animals to spontaneously exploit number suggest that a number sense is based on mechanisms inherent to the brain's sensory systems. Number neurons and numerical competence can emerge as a by-product of exposure to natural visual stimuli, without requiring any explicit training for numerosity estimation. This can explain why animals in the wild and across diverse taxa can readily assess numbers. In addition to the ANS, a second representational system termed object tracking system (OTS) is discussed [33.Feigenson L. et al.Core systems of number.Trends Cogn. Sci. 2004; 8: 307-314Abstract Full Text Full Text PDF PubMed Scopus (1318) Google Scholar]. The OTS is thought to enable storage of one to four visual objects in an unconscious and automatic but relatively precise way [34.Trick L.M. Pylyshyn Z.W. Why are small and large numbers enumerated differently—a limited-capacity preattentive stage in vision.Psychol. Rev. 1994; 101: 80-102Crossref PubMed Google Scholar,35.Pylyshyn Z.W. Visual indexes, preconceptual objects, and situated vision.Cognition. 2001; 80: 127-158Crossref PubMed Scopus (353) Google Scholar]; larger numbers cannot be tracked, irrespective of the numerical distance. The rare support for the presence of an OTS in animals comes exclusively from spontaneous-choice tasks [36.Hauser M.D. et al.Spontaneous number representation in semi-free-ranging rhesus monkeys.Proc. Biol. Sci. 2000; 267: 829-833Crossref PubMed Google Scholar, 37.Hunt S. et al.Adaptive numerical competency in a food-hoarding songbird.Proc. Biol. Sci. 2008; 275: 2373-2379Crossref PubMed Scopus (84) Google Scholar, 38.Agrillo C. et al.Do fish count? Spontaneous discrimination of quantity in female mosquitofish.Anim. Cogn. 2008; 11: 495-503Crossref PubMed Scopus (0) Google Scholar], which are suboptimal in deciphering representational systems (Box 2). In addition, reported differences in ratio-dependence for small versus large numbers do not necessary imply the existence of two separate systems [39.Van Oeffelen M.P. Vos P.G. A probabilistic model for the discrimination of visual number.Percept. Psychophys. 1982; 32: 163-170Crossref PubMed Scopus (0) Google Scholar,40.Vetter P. et al.Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism.PLoS One. 2008; 3e3269Crossref PubMed Scopus (63) Google Scholar] because only the representation of larger numbers may exhibit sufficient variability that can cause an overlap for adjacent numbers, resulting in a ratio effect [41.Gallistel C.R. Gelman R. Preverbal and verbal counting and computation.Cognition. 1992; 44: 43-74Crossref PubMed Scopus (0) Google Scholar]. Finally, how implicit object file contents acquired by the OTS are turned into explicit number representations remains elusive. It is therefore unclear whether the OTS really constitutes a separate representational system. The majority of data gathered in spontaneously-behaving animals, and all the behavioral and neuronal results reported in trained animals discriminating controlled stimuli, argue for a single enumeration system, the ANS [15.Cantlon J.F. Brannon E.M. Shared system for ordering small and large numbers in monkeys and humans.Psychol. Sci. 2006; 17: 401-406Crossref PubMed Scopus (294) Google Scholar,18.Nieder A. Miller E.K. Analog numerical representations in rhesus monkeys: evidence for parallel processing.J. Cogn. Neurosci. 2004; 16: 889-901Crossref PubMed Scopus (86) Google Scholar,21.Barnard A.M. et al.Inherently analog quantity representations in olive baboons (Papio anubis).Front. Psychol. 2013; 4: 253Crossref PubMed Scopus (26) Google Scholar,28.Nieder A. Miller E.K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex.Neuron. 2003; 37: 149-157Abstract Full Text Full Text PDF PubMed Scopus (326) Google Scholar, 29.Merten K. Nieder A. Compressed scaling of abstract numerosity representations in adult humans and monkeys.J. Cogn. Neurosci. 2009; 21: 333-346Crossref PubMed Scopus (43) Google Scholar, 30.Ditz H.M. Nieder A. Numerosity representations in crows obey the Weber-Fechner law.Proc. Biol. Sci. 2016; 28320160083Crossref PubMed Google Scholar].Box 2Pros and Cons of Investigating Spontaneous and Trained BehaviorThe advantage of field studies and spontaneous choice tests is that they evaluate the ecological validity of numerical competence. However, these approaches also have severe limitations. The most notorious problem is the control for non-numerical quantity factors. Quantity can be continuous and uncountable (e.g., the amount of water) or discrete and countable (e.g., the number of individuals); only the latter type refers to 'numerical quantity' (also termed 'cardinal number', 'set size', or 'numerosity'). While continuous quantity is more concrete and directly related to spatial or temporal dimensions of sensory experience (such as size or duration), numerical quantity is an abstract representation because the sensory appearance of the elements comprising a set is meaningless. For instance, three apples and three alarm calls are both instances of numerical quantity 'three'.Without specific controls, numerical quantity is usually confounded by continuous quantity. For example, six red apples adopt twice as much red area than three and an animal may simply discriminate the amount of red area rather than the number of apples. A second problem is the unknown motivational status of wild animals, whether they are even willing to choose between quantities. Finally, current approaches are largely confined to test simple abilities, such as relative numerosity judgments that only require 'more than' versus 'less than' decisions. For these reasons, field studies and spontaneous choice tests alone provide only suggestive evidence that animals differentiate numerical quantity.These problems can be avoided when testing trained animals in a controlled laboratory setting. Using meticulous controls of sensory parameters in computer-controlled stimuli, laboratory studies in conditioned and highly motivated animals unequivocally demonstrate the animals' capability to discriminate and process numerical quantity irrespective of other parameters [2.Brannon E.M. Terrace H.S. Ordering of the numerosities 1 to 9 by monkeys.Science. 1998; 282: 746-749Crossref PubMed Scopus (374) Google Scholar,3.Scarf D. et al.Pigeons on par with primates in numerical competence.Science. 2011; 334: 1664Crossref PubMed Scopus (77) Google Scholar,18.Nieder A. Miller E.K. Analog numerical representations in rhesus monkeys: evidence for parallel processing.J. Cogn. Neurosci. 2004; 16: 889-901Crossref PubMed Scopus (86) Google Scholar,128.Ditz H.M. Nieder A. Neurons selective to the number of visual items in the corvid songbird endbrain.Proc. Natl. Acad Sci. USA. 2015; 112: 7827-7832Crossref