Skip to main content

Approximate Number System (ANS)

  • Living reference work entry
  • First Online:
Encyclopedia of Animal Cognition and Behavior

Synonyms

Core number system; Numerical cognition; Numerosity

Definition

The approximate number system (ANS) is a core cognitive system of numerical processing that governs animal and human nonsymbolic numerical representations. Weber’s law underlies the ANS, in which performance in discriminating set sizes increases as the ratio between sets also increases.

Introduction

The ability to perceive, discriminate, store, and represent numerical information supports a host of everyday human behaviors and makes possible engineering feats that drive many of our technological innovations. Of relevance to the current chapter, engineers, astronauts, banking institutions, store clerks, and elementary math students base their simplest and more complicated calculations and numerical processing on a core system of number that is shared among human individuals as well as across a wide range of nonhuman species. Nonhuman animals (hereafter animals) also are sensitive to the quantitative and numerical...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Addessi, E., Crescimbene, L., & Visalberghi, E. (2008). Food and token quantity discrimination in capuchin monkeys (Cebus apella). Animal Cognition, 11, 275–282.

    Article  PubMed  Google Scholar 

  • Agrillo, C., Miletto Petrazzini, E. M., & Bisazza, A. (2014). Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range. Animal Cognition, 17, 307–316.

    Article  PubMed  Google Scholar 

  • Agrillo, C., Parrish, A. E., & Beran, M. J. (2016). How illusory is the Solitaire illusion? Assessing the degree of misperception of numerosity in adult humans. Frontiers in Psychology, 7, 1663.

    Article  PubMed  PubMed Central  Google Scholar 

  • Barnard, A. M., Hughes, K. D., Gerhardt, R. R., DiVincenti, L. J., Bovee, J. M., & Cantlon, J. F. (2013). Inherently analog quantity representations in olive baboons (Papio anubis). Frontiers in Psychology, 4, 253.

    Article  PubMed  PubMed Central  Google Scholar 

  • Beran, M. J. (2001). Summation and numerousness judgments of sequentially presented sets of items by chimpanzees (Pan troglodytes). Journal of Comparative Psychology, 115, 181–191.

    Article  PubMed  Google Scholar 

  • Beran, M. J. (2004). Chimpanzees (Pan troglodytes) respond to nonvisible sets after one-by-one addition and removal of items. Journal of Comparative Psychology, 118, 25–36.

    Article  PubMed  Google Scholar 

  • Beran, M. J. (2007). Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations. Journal of Experimental Psychology: Animal Behavior Processes, 33, 55–63.

    PubMed  Google Scholar 

  • Beran, M. J., & Parrish, A. E. (2016). Capuchin monkeys (Cebus apella) treat small and large numbers of items similarly during a relative quantity judgment task. Psychonomic Bulletin & Review, 23, 1206–1213.

    Article  Google Scholar 

  • Bisazza, A., Agrillo, C., & Lucon-Xiccato, T. (2014). Extensive training extends numerical abilities of guppies. Animal Cognition, 17, 1413–1419.

    Article  PubMed  Google Scholar 

  • Brannon, E. M., & Roitman, J. D. (2003). Nonverbal representations of time and number in animals and human infants. In W. H. Meck (Ed.), Functional and neural mechanisms of interval timing (pp. 143–182). Boca Raton: CRC Press.

    Google Scholar 

  • Brannon, E. M., & Terrace, H. S. (2000). Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). Journal of Experimental Psychology: Animal Behavior Processes, 26, 31–49.

    PubMed  Google Scholar 

  • Call, J. (2000). Estimating and operating on discrete quantities in orangutans (Pongo pygmaeus). Journal of Comparative Psychology, 114, 136–147.

    Article  PubMed  Google Scholar 

  • Cantlon, J. F., & Brannon, E. M. (2007). How much does number matter to a monkey (Macaca mulatta)? Journal of Experimental Psychology: Animal Behavior Processes, 33, 32–41.

    PubMed  Google Scholar 

  • Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13, 83–91.

    Article  PubMed  PubMed Central  Google Scholar 

  • Cantlon, J. F., Safford, K. E., & Brannon, E. M. (2010). Spontaneous analog number representations in 3-year-old children. Developmental Science, 13, 289–297.

    Article  PubMed  PubMed Central  Google Scholar 

  • Choo, H., & Franconeri, S. L. (2014). Enumeration of small collections violates Weber’s law. Psychonomic Bulletin & Review, 21, 93–99.

    Article  Google Scholar 

  • Dooley, G. B., & Gill, T. (1977). Acquisition and use of mathematical skills by a linguistic chimpanzee. In D. M. Rumbaugh (Ed.), Language learning by a chimpanzee: The LANA project (pp. 247–260). New York: Academic Press.

    Chapter  Google Scholar 

  • Emmerton, J., Lohmann, A., & Niemann, J. (1997). Pigeons’ serial ordering of numerosity with visual arrays. Learning & Behavior, 25, 234–244.

    Article  Google Scholar 

  • Evans, T. A., Beran, M. J., Harris, E. H., & Rice, D. (2009). Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella). Animal Cognition, 12, 97–105.

    Article  PubMed  Google Scholar 

  • Feigenson, L., & Carey, S. (2005). On the limits of infants’ quantification of small object arrays. Cognition, 97, 295–313.

    Article  PubMed  Google Scholar 

  • Feigenson, L., Carey, S., & Hauser, M. D. (2002). The representations underlying infants’ choice of more: Object files versus analog magnitudes. Psychological Science, 13, 150–156.

    Article  PubMed  Google Scholar 

  • Franconeri, S. L., Alvarez, G. A., & Enns, J. T. (2007). How many locations can be selected at once? Journal of Experimental Psychology: Human Perception and Performance, 33, 1003–1012.

    PubMed  Google Scholar 

  • Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59–65.

    Article  PubMed  Google Scholar 

  • Garland, A., Low, J., & Burns, K. C. (2012). Large quantity discrimination by North Island robins (Petroica longipes). Animal Cognition, 15, 1129–1140.

    Article  PubMed  Google Scholar 

  • Hanus, D., & Call, J. (2007). Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus): The effect of presenting whole sets versus item-by-item. Journal of Comparative Psychology, 121, 241–249.

    Article  PubMed  Google Scholar 

  • Hauser, M. D., Carey, S., & Hauser, L. B. (2000). Spontaneous number representation in semi–free–ranging rhesus monkeys. Proceedings of the Royal Society of London. Series B: Biological Sciences, 267, 829–833.

    Article  PubMed  PubMed Central  Google Scholar 

  • Hyde, D. C. (2011). Two systems of non-symbolic numerical cognition. Frontiers in Human Neuroscience, 5, 150.

    Article  PubMed  PubMed Central  Google Scholar 

  • Judge, P. G., Evans, T. A., & Vyas, D. K. (2005). Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella). Journal of Experimental Psychology: Animal Behavior Processes, 31, 79–94.

    PubMed  Google Scholar 

  • Krusche, P., Uller, C., & Dicke, U. (2010). Quantity discrimination in salamanders. Journal of Experimental Biology, 213, 1822–1828.

    Article  PubMed  Google Scholar 

  • Merritt, D. J., MacLean, E. L., Crawford, J. C., & Brannon, E. M. (2011). Numerical rule-learning in ring-tailed Lemurs (Lemur catta). Frontiers in Comparative Psychology, 2, Article 23.

    Google Scholar 

  • Nieder, A., & Miller, E. K. (2004). Analog numerical representations in rhesus monkeys: Evidence for parallel processing. Journal of Cognitive Neuroscience, 16, 889–901.

    Article  PubMed  Google Scholar 

  • Smith, B. R., Piel, A. K., & Candland, D. K. (2003). Numerity of a socially housed hamadryas baboon (Papio hamadryas) and a socially housed squirrel monkey (Saimiri sciureus). Journal of Comparative Psychology, 117, 217–225.

    Article  PubMed  Google Scholar 

  • Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal counting in humans: The psychophysics of number representation. Psychological Science, 10, 130–137.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Audrey E. Parrish .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this entry

Cite this entry

Parrish, A.E., Beran, M.J. (2017). Approximate Number System (ANS). In: Vonk, J., Shackelford, T. (eds) Encyclopedia of Animal Cognition and Behavior. Springer, Cham. https://doi.org/10.1007/978-3-319-47829-6_1068-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47829-6_1068-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47829-6

  • Online ISBN: 978-3-319-47829-6

  • eBook Packages: Springer Reference Behavioral Science and PsychologyReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

Publish with us

Policies and ethics