Animal Cognition

, Volume 17, Issue 2, pp 307–316 | Cite as

Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range

  • Christian Agrillo
  • Maria Elena Miletto Petrazzini
  • Angelo Bisazza
Original Paper


There is controversy in comparative psychology about whether on the one hand non-symbolic number estimation of small (≤4) and large numbers involves a single mechanism (an approximate number system), or whether on the other hand enumeration of the numbers 1–4 is accomplished by a separate mechanism, an object tracking system. To date, support for the latter hypothesis has come only from the different ratio-dependency of performance seen in the two numerical ranges, a reading that has been criticized on several grounds. In humans, the two-system hypothesis is supported by evidence showing that manipulation of the physical properties of the stimuli (e.g., the motion of the items) has dissimilar effects on small- and large-number discrimination. In this research, we studied this effect on guppies. Initially, fish were trained to simultaneously discriminate two numerical contrasts having the same easy ratio (0.50): one in the small-number (2 vs. 4) range and one in the large-number (6 vs. 12) range. Half of the fish were presented with moving items; the other half were shown the same stimuli without motion. Fish were then subjected to non-reinforced probe trials in the presence of a more difficult ratio (0.75: 3 vs. 4 and 9 vs. 12). Under both static and moving conditions, the fish significantly discriminated 6 versus 12, but not 9 versus 12 items. As regards small numbers, both groups learned to discriminate a 0.50 ratio, but only fish tested with moving stimuli also discriminated 3 and 4 items. This differential effect suggests that fish may possess two separate systems for small- and large-number discrimination.


OTS ANS Subitizing Numerical cognition Continuous variables Guppies 



This study was supported by the “Progetto Giovani Studiosi 2010” (prot.: GRIC101125) research grant, given by the University of Padua to Christian Agrillo; and by PRIN 2009 (Prin (2009WZXK7T), given by MIUR to Angelo Bisazza. The reported experiments comply with all of the laws of the country (Italy) in which they were performed.


  1. Agrillo C, Dadda M, Serena G (2008a) Choice of female groups by male mosquitofish (Gambusia holbrooki). Ethology 114(5):479–488CrossRefGoogle Scholar
  2. Agrillo C, Dadda M, Serena G, Bisazza A (2008b) Do fish count? Spontaneous discrimination of quantity in female mosquitofish. Anim Cogn 11:495–503PubMedCrossRefGoogle Scholar
  3. Agrillo C, Dadda M, Serena G, Bisazza A (2009) Use of number by fish. PLoS ONE 4(3):e4786PubMedCentralPubMedCrossRefGoogle Scholar
  4. Agrillo C, Piffer L, Bisazza A (2010) Large number discrimination by fish. PLoS ONE 5(12):e15232PubMedCentralPubMedCrossRefGoogle Scholar
  5. Agrillo C, Piffer L, Bisazza A (2011) Number versus continuous quantity in numerosity judgments by fish. Cognition 119:281–287PubMedCrossRefGoogle Scholar
  6. Agrillo C, Piffer L, Bisazza A, Butterworth B (2012a) Evidence for two numerical systems that are similar in humans and guppies. PLoS ONE 7(2):e31923PubMedCentralPubMedCrossRefGoogle Scholar
  7. Agrillo C, Miletto Petrazzini ME, Piffer L, Dadda M, Bisazza A (2012b) A new training procedure for studying discrimination learning in fishes. Behav Brain Res 230:343–348PubMedCrossRefGoogle Scholar
  8. Agrillo C, Miletto Petrazzini ME, Tagliapietra C, Bisazza A (2012c) Inter-specific differences in numerical abilities among teleost fish. Front Psychol 3:483. doi: 10.3389/fpsyg.2012.00483 PubMedCentralPubMedGoogle Scholar
  9. Alston L, Humphreys GW (2004) Subitization and attentional engagement by transient stimuli. Spat Vis 17:17–50PubMedCrossRefGoogle Scholar
  10. Assad JA, Maunsell JHR (1995) Neuronal correlates of inferred motion in primate posterior parietal cortex. Nature 373:518–521PubMedCrossRefGoogle Scholar
  11. Beran MJ (2004) Chimpanzees (Pan troglodytes) respond to nonvisible sets after one-by-one addition and removal of items. J Comp Psychol 118:25–36PubMedCrossRefGoogle Scholar
  12. Beran MJ (2008a) The evolutionary and developmental foundations of mathematics. PLoS Biol 6:221–223CrossRefGoogle Scholar
  13. Beran MJ (2008b) Monkeys (Macaca mulatta and Cebus apella) track, enumerate, and compare multiple sets of moving items. J Exp Psych Anim Behav Proc 34:63–74CrossRefGoogle Scholar
  14. Beran MJ, Evans TA, Leighty KA, Harris EH, Rice D (2008) Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella). Am J Primatol 70:191–194PubMedCrossRefGoogle Scholar
  15. Beran MJ, Perdue BM, Parrish AE, Evans TA (2012) Do social conditions affect capuchin monkeys’ (Cebus apella) choices in a quantity judgment task? Front Psychol 3:492. doi: 10.3389/fpsyg.2012.00492 PubMedCentralPubMedGoogle Scholar
  16. Beran MJ, McIntyre JM, Garland A, Evans TA (2013) What counts for “counting”? Chimpanzees (Pan troglodytes) respond appropriately to relevant and irrelevant information in a quantity judgment task. Anim Behav 85:987–993PubMedCrossRefGoogle Scholar
  17. Bisazza A, Serena G, Piffer L, Agrillo C (2010) Ontogeny of numerical abilities in guppies. PLoS ONE 5(11):e15516PubMedCentralPubMedCrossRefGoogle Scholar
  18. Bonanni R, Natoli E, Cafazzo S, Valsecchi P (2011) Free ranging dogs assess the quantity of opponents in intergroup conflicts. Anim Cogn 14:103–115PubMedCrossRefGoogle Scholar
  19. Buckingham JN, Wong BBM, Rosenthal GG (2007) Shoaling decision in female swordtails: how do fish gauge group size? Behaviour 144:1333–1346CrossRefGoogle Scholar
  20. Cantlon JF, Brannon EM (2007) Basic math in monkeys and college students. PLoS Biol 5(12):e328PubMedCentralPubMedCrossRefGoogle Scholar
  21. Chesney DL, Haladjian H (2011) Evidence for a shared mechanism used in multiple-object tracking and subitizing. Atten Percept Psychophys 73:2457–2480PubMedCrossRefGoogle Scholar
  22. Cordes S, Brannon EM (2009) Crossing the divide: infants discriminate small from large numerosities. Dev Psychol 45:1583–1594PubMedCentralPubMedCrossRefGoogle Scholar
  23. Cutini S, Bonato M (2012) Subitizing and visual short term memory in human and non-human species: a common shared system? Front Psychol 3:469. doi: 10.3389/fpsyg.2012.00469 PubMedCentralPubMedCrossRefGoogle Scholar
  24. Dacke M, Srinivasan MV (2008) Evidence for counting in insects. Anim Cogn 11:683–689PubMedCrossRefGoogle Scholar
  25. Durgin FH (1995) Texture density adaptation and the perceived numerosity and distribution of texture. J Exp Psychol Hum Percept Perform 21:149–169CrossRefGoogle Scholar
  26. Evans TA, Beran MJ, Harris EH, Rice D (2009) Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella). Anim Cogn 12:97–105PubMedCrossRefGoogle Scholar
  27. Evans TA, Beran MJ, Addessi E (2010) Can nonhuman primates use tokens to represent and sum quantities? J Comp Psychol 124:369–380PubMedCrossRefGoogle Scholar
  28. Feigenson L, Carey S (2005) On the limits of infants’ quantification of small object arrays. Cognition 97:295–313PubMedCrossRefGoogle Scholar
  29. Feigenson L, Carey S, Hauser MD (2002a) The representations underlying infants’ choice of more: object files versus analog magnitudes. Psychol Sci 13:150–156PubMedCrossRefGoogle Scholar
  30. Feigenson L, Carey S, Spelke ES (2002b) Infants’ discrimination of number vs. continuous extent. Cogn Psychol 44:33–66PubMedCrossRefGoogle Scholar
  31. Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trends Cogn Sci 8(7):307–314PubMedCrossRefGoogle Scholar
  32. Flombaum JI, Junge JA, Hauser MD (2005) Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition 97:315–325PubMedCrossRefGoogle Scholar
  33. Gallistel CR, Gelman R (1992) Preverbal and verbal counting and computation. Cognition 44:43–74PubMedCrossRefGoogle Scholar
  34. Garland A, Low J, Burns KC (2012) Large quantity discrimination by North Island robins (Petroica longipes). Anim Cogn 15:1129–1140PubMedCrossRefGoogle Scholar
  35. Gebuis T, Reynvoet B (2012) The role of visual information in numerosity estimation. PLoS ONE 7(5):e37426PubMedCentralPubMedCrossRefGoogle Scholar
  36. Gelman R, Gallistel C (1978) The child’s understanding of number. Harvard University Press, CambridgeGoogle Scholar
  37. Gómez-Laplaza LM, Gerlai R (2011) Spontaneous discrimination of small quantities: shoaling preferences in angelfish (Pterophyllum scalare). Anim Cogn 14(4):565–574PubMedCrossRefGoogle Scholar
  38. Gómez-Laplaza LM, Gerlai R (2012) Activity counts: the effect of swimming activity on quantity discrimination in fish. Front Psychol 3:484. doi: 10.3389/fpsyg.2012.00484 PubMedCentralPubMedCrossRefGoogle Scholar
  39. Gross HJ, Pahl M, Si A, Zhu H, Tautz J, Zhang S (2009) Number-based visual generalisation in the honeybee. PLoSONE 4:e4263CrossRefGoogle Scholar
  40. Halberda J, Mazzocco M, Feigenson L (2008) Individual differences in nonverbal number acuity predict maths achievement. Nature 455:665–668PubMedCrossRefGoogle Scholar
  41. Hauser MD, Spelke ES (2004) Evolutionary and developmental foundations of human knowledge: a case study of mathematics. In: Gazzaniga M (ed) The cognitive neurosciences, vol 3. MIT Press, CambridgeGoogle Scholar
  42. Hauser MD, Carey S, Hauser LB (2000) Spontaneous number representation in semi-free-ranging rhesus monkeys. Proc R Soc Lond B 267:829–833CrossRefGoogle Scholar
  43. Hunt S, Low J, Burns KC (2008) Adaptive numerical competency in a food-hoarding songbird. Proc R Soc Lond B 275:2373–2379CrossRefGoogle Scholar
  44. Jevons WS (1871) The power of numerical discrimination. Nature 3(67):281–282CrossRefGoogle Scholar
  45. Kaufman EL, Lord MW, Reese TW, Volkmann J (1949) The discrimination of visual number. Am J Psychol 62(4):498–525PubMedCrossRefGoogle Scholar
  46. Kilian A, Yaman S, Fersen L, Güntürkün O (2003) A bottlenose dolphin (Tursiops truncatus) discriminates visual stimuli differing in numerosity. Learn Behav 31:133–142PubMedCrossRefGoogle Scholar
  47. Krusche P, Uller C, Ursula D (2010) Quantity discrimination in salamanders. J Exp Biol 213:1822–1828PubMedCrossRefGoogle Scholar
  48. Lipton J, Spelke ES (2003) Origins of number sense: large number discrimination in human infants. Psychol Sci 14:396–401PubMedCrossRefGoogle Scholar
  49. Mandler G, Shebo BJ (1982) Subitizing: an analysis of its component processes. J Exp Psychol Gen 111:1–22PubMedCrossRefGoogle Scholar
  50. Matsuno T, Tomonaga M (2006) Visual search for moving and stationary items in chimpanzees (Pan troglodytes) and humans (Homo sapiens). Behav Brain Res 172:219–232PubMedCrossRefGoogle Scholar
  51. Miletto Petrazzini ME, Agrillo C, Piffer L, Dadda M, Bisazza A (2012) Development and application of a new method to investigate cognition in newborn guppies. Behav Brain Res 233:443–449PubMedCrossRefGoogle Scholar
  52. Miletto Petrazzini ME, Agrillo C, Piffer L, Bisazza A (2013) Ontogeny of the capacity to compare discrete quantities in fish. Dev Psychobiol, online first, doi: 10.1002/dev.21122
  53. Neisser U (1967) Cognitive psychology. Prentice-Hall, Englewood CliffsGoogle Scholar
  54. Nieder A, Dehaene S (2009) Representation of number in the brain. Annu Rev Neurosci 32:185–208PubMedCrossRefGoogle Scholar
  55. Pahl M, Si A, Zhang S (2013) Numerical cognition in bees and other insects. Front Psychol 4:162. doi: 10.3389/fpsyg.2013.00162 PubMedCentralPubMedCrossRefGoogle Scholar
  56. Perdue BM, Talbot CF, Stone A, Beran MJ (2012) Putting the elephant back in the herd: elephant relative quantity judgments match those of other species. Anim Cogn 15:955–961PubMedCrossRefGoogle Scholar
  57. Piffer L, Agrillo C, Hyde CD (2012) Small and large number discrimination in guppies. Anim Cogn 15:215–221PubMedCrossRefGoogle Scholar
  58. Piffer L, Miletto Petrazzini ME, Agrillo C (2013) Large number discrimination in newborn fish. PLoS ONE 8(4):e62466PubMedCentralPubMedCrossRefGoogle Scholar
  59. Pisa PE, Agrillo C (2009) Quantity discrimination in felines: a preliminary investigation of the domestic cat (Felis silvestris catus). J Ethol 27:289–293CrossRefGoogle Scholar
  60. Revkin SK, Piazza M, Izard V, Cohen L, Dehaene S (2008) Does subitizing reflect numerical estimation? Psychol Sci 19:607–614PubMedCrossRefGoogle Scholar
  61. Ross J (2003) Visual discrimination of number without counting. Percept 32:867–870CrossRefGoogle Scholar
  62. Scholl BJ, Pylyshyn ZW (1999) Tracking multiple items through occlusion: clues to visual objecthood. Cogn Psychol 38:259–290PubMedCrossRefGoogle Scholar
  63. Sokal RR, Rohlf FJ (1995) Biometry. Freeman and Company, New YorkGoogle Scholar
  64. Trick LM (2008) More than superstition: differential effects of featural heterogeneity and change on subitizing and counting. Percept Psychophys 70:743–760PubMedCrossRefGoogle Scholar
  65. Trick LM, Pylyshyn ZW (1994) Why are small and large number enumerated differently: a limited-capacity preattentive stage in vision. Psychol Rev 101(1):80–102PubMedCrossRefGoogle Scholar
  66. Trick LM, Audet D, Dales L (2003) Age differences in enumerating things that move: implications for the development of multiple-object tracking. Mem Cogn 31(8):1229–1237CrossRefGoogle Scholar
  67. Van Marle K (2013) Infants use different mechanisms to make small and large number ordinal judgments. J Exp Child Psych 114(1):102–110CrossRefGoogle Scholar
  68. Van Oeffelen MP, Vos PG (1982) A probabilistic model for the discrimination of visual number. Percept Psychophys 32:163–170PubMedCrossRefGoogle Scholar
  69. Vetter P, Butterworth B, Bahrami B (2008) Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism. PLoS ONE 3(9):e3269PubMedCentralPubMedCrossRefGoogle Scholar
  70. Vonk J, Beran MJ (2012) Bears “count” too: quantity estimation and comparison in black bears (Ursus americanus). Anim Behav 84:231–238PubMedCentralPubMedCrossRefGoogle Scholar
  71. Vos PG, Van Oeffelen MP, Tibosch HJ, Allik J (1988) Area-numerosity interactions. Psychol Res 50:148–150PubMedCrossRefGoogle Scholar
  72. Ward C, Smuts BB (2007) Quantity-based judgments in the domestic dog (Canis lupus familiaris). Anim Cogn 10:71–80PubMedCrossRefGoogle Scholar
  73. Wood JN, Spelke ES (2005) Infants’ enumeration of actions: numerical discrimination and its signature limits. Dev Sci 8(2):173–181PubMedCrossRefGoogle Scholar
  74. Woodworth RS, Schlosberg H (1954) Experimental psychology. Holt, New YorkGoogle Scholar
  75. Xu F (2003) Numerosity discrimination in infants: evidence for two systems of representations. Cognition 89(1):B15–B25PubMedCrossRefGoogle Scholar
  76. Xu F, Spelke ES (2000) Large number discrimination in 6-month-old infants. Cognition 74:B1–B11CrossRefGoogle Scholar
  77. Xu F, Spelke ES, Goddard S (2005) Number sense in human infants. Dev Sci 8(1):88–101PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christian Agrillo
    • 1
  • Maria Elena Miletto Petrazzini
    • 1
  • Angelo Bisazza
    • 1
  1. 1.Department of General PsychologyUniversity of PadovaPaduaItaly

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