Animal Cognition

, Volume 16, Issue 3, pp 373–383 | Cite as

Quantification abilities in angelfish (Pterophyllum scalare): the influence of continuous variables

Original Paper


Previous studies investigating quantity discrimination have shown that angelfish are able to select the larger of two groups of conspecifics (shoals). The discrimination limits shown by angelfish were similar to those found for other vertebrates when large (≥4) and small quantities (<4) were presented. However, in these studies, no attempt was made to control for non-numerical features of the stimulus shoals and thus the question whether numerical or some quantitative attributes of the shoals were utilized for making the choices could not be answered. Here, we investigate whether angelfish can discriminate between shoals differing in numerical size using non-numerical attributes. We systematically manipulate density, inter-fish distance, and overall space occupied by the shoals, one factor at a time, and analyse the choices angelfish made between the contrasting stimulus shoals. The stimulus shoals consisted of contrasts between large (10 vs. 5) and small (3 vs. 2) number of conspecifics. We found density to be a sufficient condition for discrimination between large shoals as the test subjects preferred the more dense shoal. Manipulation of inter-fish distance indicated that this variable is not a necessary factor in discrimination at either shoal size contrast. Likewise, we found that the size of space occupied by the contrasted shoals also did not significantly influence discrimination. Sensitivity to the density of large shoals indicates that angelfish can discriminate shoal size using this non-numerical cue. Nevertheless, the factors we examined may represent only a subset of all possible non-numerical features upon which angelfish may base their discrimination. Thus, we suggest that further research is required to clarify whether and under what circumstances angelfish may use numerical or non-numerical features when discriminating between shoals of differing size.


Quantity discrimination Continuous variables Angelfish Shoal choice Numerical cognition 



We would like to thank anonymous reviewers for their valuable comments and insightful suggestions for improving the manuscript. We thank Miguel Sánchez Santillán for his help during experiments. This research was supported by grant MICINN-10-PSI2010-16487 from the Ministerio de Ciencia e Innovación (Spain) to L.M.G.-L., and an NSERC (Canada) Discovery grant to R.G. The experiments described here comply with the current laws of the country (Spain) in which they were performed.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Agrillo C, Dadda M (2007) Discrimination of the larger shoal in the poeciliid fish Girardinus falcatus. Ethol Ecol Evol 19:145–157CrossRefGoogle Scholar
  2. Agrillo C, Dadda M, Bisazza A (2007) Quantity discrimination in female mosquitofish. Anim Cogn 10:63–70PubMedCrossRefGoogle Scholar
  3. Agrillo C, Dadda M, Serena G, Bisazza A (2008) Do fish count? Spontaneous discrimination of quantity in female mosquitofish. Anim Cogn 11:495–503PubMedCrossRefGoogle Scholar
  4. Agrillo C, Dadda M, Serena G, Bisazza A (2009) Use of number by fish. PLoS ONE 4:e4786. doi: 10.1371/journal.pone.0004786 PubMedCrossRefGoogle Scholar
  5. Agrillo C, Piffer L, Bisazza A (2010) Large number discrimination by mosquitofish. PLoS ONE 5:e15232. doi: 10.1371/journal.pone.0015232 PubMedCrossRefGoogle Scholar
  6. Al Aïn S, Giret N, Grand M, Kreuitzer M, Bovet D (2009) The discrimination of discrete and continuous amounts in African grey parrots (Psittacus erithacus). Anim Cogn 12:145–154CrossRefGoogle Scholar
  7. Barber I, Wright HA (2001) How strong are familiarity preferences in shoaling fish? Anim Behav 61:973–979CrossRefGoogle Scholar
  8. Bar-Shai N, Keasar T, Shmida A (2011) The use of numerical information by bees in foraging tasks. Behav Ecol 22:317–325CrossRefGoogle Scholar
  9. Beran MJ (2007) Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations. J Exp Psychol Anim Behav Proc 33:42–54CrossRefGoogle Scholar
  10. Beran MJ, Evans TA, Harris EH (2008) Perception of food amounts by chimpanzees based on the number, size, contour length and visibility of items. Anim Behav 75:1793–1802PubMedCrossRefGoogle Scholar
  11. Binoy VV, Thomas KJ (2004) The climbing perch (Anabas testudineus Bloch), a freshwater fish, prefers larger unfamiliar shoals to smaller familiar shoals. Curr Sci 86:207–211Google Scholar
  12. Bisazza A, Piffer L, Serena G, Agrillo C (2010) Ontogeny of numerical abilities in fish. PLoS ONE 5:e15516. doi: 10.1371/journal.pone.0015516 PubMedCrossRefGoogle Scholar
  13. 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
  14. Brannon EM, Terrace HS (2000) Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). J Exp Psychol Anim Behav Proc 26:31–49CrossRefGoogle Scholar
  15. Buckingham JN, Wong BBM, Rosenthal GG (2007) Shoaling decisions in female swordtails: how do fish gauge group size? Behaviour 144:1333–1346CrossRefGoogle Scholar
  16. Clearfield MW, Mix KS (1999) Number versus contour length in infants’ discrimination of small visual sets. Psychol Sci 10:408–411CrossRefGoogle Scholar
  17. Cordes S, Brannon EM (2008) The difficulties of representing continuous extent in infancy: using number is just easier. Child Dev 79:476–489PubMedCrossRefGoogle Scholar
  18. Cordes S, Brannon EM (2009) The relative salience of discrete and continuous quantity in young infants. Dev Sci 12:453–463PubMedCrossRefGoogle Scholar
  19. Dadda M, Piffer L, Agrillo C, Bisazza A (2009) Spontaneous number representation in mosquitofish. Cognition 122:343–348CrossRefGoogle Scholar
  20. Emmerton J (1998) Numerosity differences and effects of stimulus density on pigeons’ discrimination performance. Anim Learn Behav 26:243–256CrossRefGoogle Scholar
  21. Emmerton J, Renner JC (2006) Scalar effects in the visual discrimination of numerosity by pigeons. Learn Behav 34:176–192PubMedCrossRefGoogle Scholar
  22. Emmerton J, Renner JC (2009) Local rather than global processing of visual arrays in numerosity discrimination by pigeons (Columba livia). Anim Cogn 12:511–526PubMedCrossRefGoogle Scholar
  23. Evans TA, Beran MJ, Harris EH, Rice DF (2009) Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella). Anim Cogn 12:97–105PubMedCrossRefGoogle Scholar
  24. Feigenson L, Carey S (2003) Tracking individuals via object files: evidence from infants’ manual search task. Dev Sci 6:568–584CrossRefGoogle Scholar
  25. Feigenson L, Carey S, Hauser MD (2002a) The representations underlying infants’ choice of more: object files vs. analog magnitudes. Psychol Sci 13:150–156PubMedCrossRefGoogle Scholar
  26. Feigenson L, Carey S, Spelke ES (2002b) Infants’ discrimination of number vs. continuous extent. Cogn Psychol 44:33–66PubMedCrossRefGoogle Scholar
  27. Feigenson L, Dehaene S, Spelke E (2004) Core systems of number. Trends Cogn Sci 8:307–314PubMedCrossRefGoogle Scholar
  28. Flombaum JI, Junge JA, Hauser MD (2005) Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition 97:315–325PubMedCrossRefGoogle Scholar
  29. Fontanari L, Rugani R, Regolin L, Vallortigara G (2011) Object individuation in 3-day-old chicks: use of property and spatiotemporal information. Dev Sci 14:1235–1244PubMedCrossRefGoogle Scholar
  30. Frommen JG, Hiermes M, Bakker TCM (2009) Disentangling the effects of group size and density on shoaling decisions of three-spined sticklebacks (Gasterosteus aculeatus). Behav Ecol Sociobiol 63:1141–1148CrossRefGoogle Scholar
  31. Gómez-Laplaza LM, Gerlai R (2011a) Can angelfish (Pterophyllum scalare) count? Discrimination between different shoal sizes follows Weber’s law. Anim Cogn 14:1–9PubMedCrossRefGoogle Scholar
  32. Gómez-Laplaza LM, Gerlai R (2011b) Spontaneous discrimination of small quantities: shoaling preferences in angelfish (Pterophyllum scalare). Anim Cogn 14:565–574PubMedCrossRefGoogle Scholar
  33. Gross HJ, Pahl M, Si A, Zhu H, Tautz J, Zhang S (2009) Number-based visual generalisation in the honeybee. PLoS ONE 4:e4263. doi: 10.1371/journal.pone.0004263 PubMedCrossRefGoogle Scholar
  34. Hager MC, Helfman GS (1991) Safety in numbers: shoal size choice by minnows under predatory threat. Behav Ecol Sociobiol 29:271–276CrossRefGoogle Scholar
  35. 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. J Comp Psychol 121:241–249PubMedCrossRefGoogle Scholar
  36. Hauser MD, Carey S, Hauser L (2000) Spontaneous number representation in semi-free-ranging rhesus monkeys. Proc R Soc Lond B Biol Sci 267:829–833CrossRefGoogle Scholar
  37. Hauser MD, Tsao F, Garcia P, Spelke ES (2003) Evolutionary foundations of number: spontaneous representation of numerical magnitudes by cotton-top tamarins. Proc R Soc Lond B Biol Sci 270:1441–1446CrossRefGoogle Scholar
  38. Kilian A, Yaman S, von Fersen L, Güntürkün O (2003) A bottlenose dolphin discriminates visual stimuli differing in numerosity. Learn Behav 31:133–142PubMedCrossRefGoogle Scholar
  39. Kitchen DM (2004) Alpha male black howler monkey responses to loud calls: effect of numeric odds, male companion behaviour and reproductive investment. Anim Behav 67:125–139CrossRefGoogle Scholar
  40. Krakauer DC (1995) Groups confuse predators by exploiting perceptual bottlenecks: a connectionist model of the confusion effect. Behav Ecol Sociobiol 36:421–429CrossRefGoogle Scholar
  41. Krause J (1993) The effect of ‘Schreckstoff’’ on the shoaling behaviour of the minnow: a test of Hamilton’s selfish herd theory. Anim Behav 45:1019–1024CrossRefGoogle Scholar
  42. Krause J, Godin J-GJ, Rubenstein D (1998) Group choice as a function of group size differences and assessment time in fish: the influence of species vulnerability to predation. Ethology 104:68–74CrossRefGoogle Scholar
  43. Krusche P, Uller C, Dicke U (2010) Quantity discrimination in salamanders. J Exp Biol 213:1822–1828PubMedCrossRefGoogle Scholar
  44. Lipton JS, Spelke E (2003) Origins of number sense: large-number discrimination in human infants. Psychol Sci 14:396–401PubMedCrossRefGoogle Scholar
  45. Mathis A, Smith RJF (1993) Chemical alarm signals increase the survival time of fathead minnows (Pimephales promelas) during encounters with northern pike (Esox lucius). Behav Ecol 4:260–265CrossRefGoogle Scholar
  46. Miller N, Gerlai R (2008) Oscillations in shoal cohesion in zebrafish (Danio rerio). Behav Brain Res 193:148–151PubMedCrossRefGoogle Scholar
  47. Mix KS, Huttenlocher J, Levine SC (2002) Multiple cues for quantification in infancy: is number one of them? Psychol Bull 128:278–294PubMedCrossRefGoogle Scholar
  48. Newcombe N (2002) The nativist-empiricist controversy in the context of recent research on spatial and quantitative development. Psychol Sci 13:395–401PubMedCrossRefGoogle Scholar
  49. 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
  50. Pitcher TJ, Parrish JK (1993) Functions of shoaling behaviour in teleosts. In: Pitcher TJ (ed) Behaviour of teleost fishes, 2nd edn. Chapman and Hall, London, pp 363–439CrossRefGoogle Scholar
  51. Reznikova Z, Ryabko B (2011) Numerical competence in animals, with an insight from ants. Behaviour 148:405–434CrossRefGoogle Scholar
  52. Rugani R, Regolin L, Vallortigara G (2008) Discrimination of small numerosities in young chicks. J Exp Psychol Anim Behav Proc 34:388–399CrossRefGoogle Scholar
  53. Rugani R, Fontanari L, Simoni E, Regolin L, Vallortigara G (2009) Arithmetic in newborn chicks. Proc R Soc Lond B Biol Sci 276:2451–2460CrossRefGoogle Scholar
  54. Rugani R, Kelly DM, Szelest I, Regolin L, Vallortigara G (2010a) Is it only humans that count from left to right? Biol Lett 6:290–292PubMedCrossRefGoogle Scholar
  55. Rugani R, Regolin L, Vallortigara G (2010b) Imprinted numbers: newborn chicks’ sensitivity to number vs. continuous extent of objects they have been reared with. Dev Sci 13:790–797PubMedCrossRefGoogle Scholar
  56. Rugani R, Regolin L, Vallortigara G (2011) Summation of large numerousness by newborn chicks. Front Psychology 2:179. doi: 10.3389/fpsyg.2011.00179 CrossRefGoogle Scholar
  57. Stevens JR, Wood J, Hauser MD (2007) When quantity trumps number: discrimination experiments in cotton-top tamarins (Saguinus oedipus) and common marmosets (Callithrix jacchus). Anim Cogn 10:429–437PubMedCrossRefGoogle Scholar
  58. Tegeder RW, Krause J (1995) Density dependence and numerosity in fright stimulated aggregation behaviour of shoaling fish. Phil Trans R Soc Lond B 350:381–390CrossRefGoogle Scholar
  59. Tomonaga M (2008) Relative numerosity discrimination by chimpanzees (Pan troglodytes): evidence for approximate numerical representations. Anim Cogn 11:43–57PubMedCrossRefGoogle Scholar
  60. Uller C, Lewis J (2009) Horses (Equus caballus) select the greater of two quantities in small numerical contrasts. Anim Cogn 12:733–738PubMedCrossRefGoogle Scholar
  61. Uller C, Jaeger R, Guidry G, Martin C (2003) Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim Cogn 6:105–112PubMedGoogle Scholar
  62. vanMarle K, Wynn K (2009) Infants’ auditory enumeration: evidence for analog magnitudes in the small number range. Cognition 111:302–316PubMedCrossRefGoogle Scholar
  63. Ward C, Smuts B (2007) Quantity based judgments in the domestic dog (Canis lupus familiaris). Anim Cogn 10:71–80PubMedCrossRefGoogle Scholar
  64. West R, Young R (2002) Do domestic dogs show any evidence of being able to count? Anim Cogn 5:183–186PubMedGoogle Scholar
  65. Wood JN, Spelke ES (2005) Infants’ enumeration of actions: numerical discrimination and its signature limits. Dev Sci 8:173–181PubMedCrossRefGoogle Scholar
  66. Wood JN, Hauser MD, Glynn DD, Barner D (2008) Free-ranging rhesus monkeys spontaneously individuate and enumerate small numbers of non-solid portions. Cognition 106:207–221PubMedCrossRefGoogle Scholar
  67. Xu F (2003) Numerosity discrimination in infants: evidence for two systems of representations. Cognition 89:B15–B25PubMedCrossRefGoogle Scholar
  68. Xu F, Spelke ES, Goddard S (2005) Number sense in human infants. Dev Sci 8:88–101PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PsychologyUniversity of OviedoOviedoSpain
  2. 2.Department of PsychologyUniversity of Toronto MissisaugaMississaugaCanada

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