Evidence for Two Numerical Systems That Are Similar in Humans and Guppies Christian Agrillo1*, Laura Piffer1, Angelo Bisazza1, Brian Butterworth2 1 Department of General Psychology, University of Padova, Padova, Italy, 2 Institute of Cognitive Neuroscience, University College of London, London, United Kingdom Abstract Background: Humans and non-human animals share an approximate non-verbal system for representing and comparing numerosities that has no upper limit and for which accuracy is dependent on the numerical ratio. Current evidence indicates that the mechanism for keeping track of individual objects can also be used for numerical purposes; if so, its accuracy will be independent of numerical ratio, but its capacity is limited to the number of items that can be tracked, about four. There is, however, growing controversy as to whether two separate number systems are present in other vertebrate species. Methodology/Principal Findings: In this study, we compared the ability of undergraduate students and guppies to discriminate the same numerical ratios, both within and beyond the small number range. In both students and fish the performance was ratio-independent for the numbers 1–4, while it steadily increased with numerical distance when larger numbers were presented. Conclusions/Significance: Our results suggest that two distinct systems underlie quantity discrimination in both humans and fish, implying that the building blocks of uniquely human mathematical abilities may be evolutionarily ancient, dating back to before the divergence of bony fish and tetrapod lineages. Citation: Agrillo C, Piffer L, Bisazza A, Butterworth B (2012) Evidence for Two Numerical Systems That Are Similar in ?Humans and Guppies. PLoS ONE 7(2): e31923. doi:10.1371/journal.pone.0031923 Editor: Sarah Frances Brosnan, Georgia State University, United States of America Received October 19, 2011; Accepted January 20, 2012; Published February 15, 2012 Copyright: 2012 Agrillo et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was funded by research grant ‘‘Progetto di Eccellenza CARIPARO 2007’’, and ‘‘Progetto Giovani Studiosi 2010’’ from University of Padova to Christian Agrillo. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: christian.agrillo@unipd.it Introduction Numerousness, like shape, size and color, is a basic property of our perceptual world. It has long been recognized that adults, infants and non-human animals can instantly extract the numerical information from a visual scene without counting the elements [1,2,3,4]. In humans, this ability is thought to be based on two distinct non-verbal systems that operate over different parts of the number range [5,6,7]. One is a system for representing approximate numerosities as analog magnitudes, and is usually referred to as the ‘analog magnitude system’ (ANS) [8,9,10] that has virtually no upper limit but is subject to a ratio limit in accordance with Weber’s Law, which states that the capacity to discriminate between two quantities becomes increasingly accurate as the ratio between them increases. The second system is referred to as the ‘object-file system’ and is held to depend on a mechanism for representing and tracking small numbers of individual objects [3,7,11]. If this object-tracking system operates by keeping track of individual elements, it is precise but allows for the parallel representation of a small number of objects (usually three-four elements in adults). It is often assumed that this is the system that supports ‘subitizing’ – the accurate reporting of the numerosity of small sets without serial counting [6,7]. The two mechanisms appear to differ in many respects, including speed, accuracy and cognitive load [11,12]. The lack of a ratio effect is the main signature that allows experimental differentiation of the object-file system from the analog magnitude system [3]: the performance of an adult is very similar when discriminating 3 vs. 4 or 1 vs. 4 objects, whereas we are much more accurate in discriminating 5 from 20 objects than 15 from 20 objects. Not all the studies, however, reported a different ratio-effect between small and large numbers [13,14,15]. For instance, in a task requiring to apply an ordinal numerical rule, Cantlon and Brannon [16] also found evidence of a ratio- effect in the small number range. Recent neuropsychological, electrophysiological and brain imaging data suggest that these two non-verbal numerical systems probably have distinct neural substrates [17,18,19,20,21]. The analog magnitude system appears to be shared among many vertebrates. When required to determine the larger of two sets of elements, infants, macaques, dogs, swordtails and mosquitofish give approximate responses and their capacity to discriminate is strongly influenced by the numerical ratio [4,16,22,23,24]. Some have proposed that human infants and non-human vertebrates may also share with adults a distinct mechanism for precisely representing quantities up to four. However, evidence of separate systems in human infants and animals is less clear. In some studies, infants were found to discriminate different ratios in the small and large number range. For instance they were found to discriminate 2 vs. 3 but not 4 vs. 6 items in a habituation task despite the identical ratio difference [25]. Moreover, a study showed that children with Williams syndrome report a specific impairment in large number discrim- ination while the discrimination capacity in the small number PLoS ONE | www.plosone.org 1 February 2012 | Volume 7 | Issue 2 | e31923