Animal Cognition

, Volume 18, Issue 5, pp 1125–1131 | Cite as

Quantification acuity in spontaneous shoaling decisions of three-spined sticklebacks

  • Marion Mehlis
  • Timo ThünkenEmail author
  • Theo C. M. Bakker
  • Joachim G. FrommenEmail author
Original Paper


The ability to discriminate between different quantities is widespread throughout the animal kingdom, and the underlying mechanisms of quantity discrimination are currently intensely discussed. In contrast, questions elucidating the limits of quantity estimation received rather little attention so far. Here, we examined fine-tuned quantity estimation in the three-spined stickleback (Gasterosteus aculeatus) in a natural context, i.e. during shoaling decisions. Wild-caught focal fish were given the spontaneous choice between two shoals which differed in group size by 1 fish (0 vs. 1, 1 vs. 2, 2 vs. 3, 3 vs. 4, 4 vs. 5, 5 vs. 6 and 6 vs. 7), based on visual assessment. The results show that sticklebacks generally prefer to shoal with the larger group. They discriminated numerical contrasts up to 6 versus 7, equalling a numerical ratio of 0.86. Preference patterns followed Weber’s law, i.e. decreased with increasing numerical ratio. This pattern was found across all numerical conditions as well as within the small number range (ranging from 1 vs. 2 to 3 vs. 4). The results suggest that wild-caught three-spined sticklebacks are spontaneously able (i.e. without prior learning) to detect subtle differences in shoal sizes. Further, they confirm findings of previous studies highlighting the contribution of the analogue magnitude system to quantity estimation in fishes.


Counting Fishes Gasterosteus aculeatus Numerical abilities Shoaling Weber’s law 



We are grateful to Rebecca Deutsch, Nicole Ehrenfried, Kathrin Kunz and Juliana Monteiro for their help in conducting the experiments. We thank Ken Cheng and anonymous referees for useful comments on the manuscript. TT was funded by SNF Grant No. 31003A_144191 provided to JGF.

Ethical standard

The experiments comply with the current laws of the country in which they were performed.

Conflict of interest

The authors declare that they have no competing interests.


  1. Agrillo C, Dadda M, Bisazza A (2007) Quantity discrimination in female mosquitofish. Anim Cogn 10:63–70CrossRefPubMedGoogle Scholar
  2. Agrillo C, Dadda M, Serena G, Bisazza A (2009) Use of number by fish. PLoS One 4:e62466CrossRefGoogle Scholar
  3. Agrillo C, Piffer L, Bisazza A (2010) Large number discrimination by mosquitofish. PLoS One 5:e15232CrossRefPubMedPubMedCentralGoogle Scholar
  4. Agrillo C, Miletto Petrazzini ME, Tagliapietra C, Bisazza A (2012a) Inter-specific differences in numerical abilities among teleost fish. Front Psychol 3:483PubMedPubMedCentralGoogle Scholar
  5. Agrillo C, Piffer L, Bisazza A, Butterworth B (2012b) Evidence for two numerical systems that are similar in humans and guppies. PLoS One 7:e31923CrossRefPubMedPubMedCentralGoogle Scholar
  6. Agrillo C, Petrazzini MEM, Bisazza A (2014) Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range. Anim Cogn 17:307–316CrossRefPubMedGoogle Scholar
  7. Baker JM, Shivik J, Jordan KE (2011) Tracking of food quantity by coyotes (Canis latrans). Behav Process 88:72–75CrossRefGoogle Scholar
  8. Beran MJ (2001) Summation and numerousness judgments of sequentially presented sets of items by chimpanzees (Pan troglodytes). J Comp Psychol 115:181–191CrossRefPubMedGoogle 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 Process 33:42–54Google Scholar
  10. Bolger T, Connolly PL (1989) The selection of suitable indices for the measurement and analysis of fish condition. J Fish Biol 34:171–182CrossRefGoogle Scholar
  11. Bradner J, McRobert SP (2001) The effect of shoal size on patterns of body colour segregation in mollies. J Fish Biol 59:960–967CrossRefGoogle Scholar
  12. Call J (2000) Estimating and operating on discrete quantities in orangutans (Pongo pygmaeus). J Comp Psychol 114:136–147CrossRefPubMedGoogle Scholar
  13. Cantlon JF, Brannon EM (2007) Basic math in monkeys and college students. PLoS Biol 5:e328CrossRefPubMedPubMedCentralGoogle Scholar
  14. Cote J, Fogarty S, Sih A (2012) Individual sociability and choosiness between shoal types. Anim Behav 83:1469–1476CrossRefGoogle Scholar
  15. Cresswell W, Quinn JL (2011) Predicting the optimal prey group size from predator hunting behaviour. J Anim Ecol 80:310–319CrossRefPubMedGoogle Scholar
  16. Doucette LI, Skulason S, Snorrason SS (2004) Risk of predation as a promoting factor of species divergence in threespine sticklebacks (Gasterosteus aculeatus L.). Biol J Linn Soc 82:189–203CrossRefGoogle Scholar
  17. Evans SR, Finnie M, Manica A (2007) Shoaling preferences in decapod crustacea. Anim Behav 74:1691–1696CrossRefGoogle Scholar
  18. Feigenson L, Dehaene S, Spelke E (2004) Core systems of number. Trends Cogn Sci 8:307–314CrossRefPubMedGoogle Scholar
  19. Fischer S, Frommen JG (2013) Eutrophication alters social preferences in three-spined sticklebacks (Gasterosteus aculeatus). Behav Ecol Sociobiol 67:293–299CrossRefGoogle Scholar
  20. Foster WA, Treherne JE (1981) Evidence for the dilution effect in the selfish herd from fish predation on a marine insect. Nature 293:466–467CrossRefGoogle Scholar
  21. Frommen JG, Luz C, Bakker TCM (2007) Nutritional state influences shoaling preference for familiars. Zoology 110:369–376CrossRefPubMedGoogle Scholar
  22. 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
  23. Frommen JG, Bakker TCM, Proscurcin LC, Mehlis M (2012) Gravidity-associated shoaling decisions in three-spined sticklebacks (Gasterosteus aculeatus). Ethology 118:1149–1156CrossRefGoogle Scholar
  24. Gallistel CR, Gelman R (1992) Preverbal and verbal counting and computation. Cognition 44:43–74CrossRefPubMedGoogle Scholar
  25. Garland A, Low J, Burns KC (2012) Large quantity discrimination by North Island robins (Petroica longipes). Anim Cogn 15:1129–1140CrossRefPubMedGoogle Scholar
  26. Godin JGJ, Crossman SL (1994) Hunger-dependent predator inspection and foraging behaviours in the threespine stickleback (Gasterosteus aculeatus) under predation risk. Behav Ecol Sociobiol 34:359–366CrossRefGoogle Scholar
  27. Gómez-Laplaza LM (2012) Shoal size and shoaling in fish. Indian J Soc Nat Sci 1:7–18Google Scholar
  28. Gómez-Laplaza LM, Gerlai R (2011) Can angelfish (Pterophyllum scalare) count? Discrimination between different shoal sizes follows Weber’s law. Anim Cogn 14:1–9CrossRefPubMedGoogle Scholar
  29. Gómez-Laplaza LM, Gerlai R (2013) Quantification abilities in angelfish (Pterophyllum scalare): the influence of continuous variables. Anim Cogn 16:373–383CrossRefPubMedGoogle Scholar
  30. Hager MC, Helfman GS (1991) Safety in numbers: shoal choice by minnows under predatory threat. Behav Ecol Sociobiol 29:271–276CrossRefGoogle Scholar
  31. Hain TJA, Neff BD (2007) Multiple paternity and kin recognition mechanisms in a guppy population. Mol Ecol 16:3938–3946CrossRefPubMedGoogle Scholar
  32. Halberda J, Feigenson L (2008) Developmental change in the acuity of the “Number sense”: the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Dev Psychol 44:1457–1465CrossRefPubMedGoogle Scholar
  33. 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 121:241–249CrossRefPubMedGoogle Scholar
  34. 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 B 270:1441–1446CrossRefPubMedPubMedCentralGoogle Scholar
  35. Hoare DJ, Couzin ID, Godin JGJ, Krause J (2004) Context-dependent group size choice in fish. Anim Behav 67:155–164CrossRefGoogle Scholar
  36. Irie-Sugimoto N, Kobayashi T, Sato T (2009) Relative quantity judgment by asian elephants (Elephas maximus). Anim Cogn 12:193–199CrossRefPubMedGoogle Scholar
  37. Jaakkola K, Fellner W, Erb L, Rodriguez M, Guarino E (2005) Understanding of the concept of numerically “less” by bottlenose dolphins (Tursiops truncatus). J Comp Psychol 119:296–303CrossRefPubMedGoogle Scholar
  38. Kaufman EL, Lord MW, Reese TW, Volkmann J (1949) The discrimination of visual number. Am J Psychol 62:498–525CrossRefPubMedGoogle Scholar
  39. Kilian A, Yaman S, von Fersen L, Güntürkün O (2003) A bottlenose dolphin discriminates visual stimuli differing in numerosity. Learn Behav 31:133–142CrossRefPubMedGoogle Scholar
  40. Krause J (1993) The influence of hunger on shoal size choice by three-spined sticklebacks, Gasterosteus aculeatus. J Fish Biol 43:775–780CrossRefGoogle Scholar
  41. Krause J, Godin JGJ (1994) Shoal choice in the banded killifish (Fundulus diaphanus, Teleostei, Cyprinodontidae): effects of predation risk, fish size, species composition and size of shoals. Ethology 98:128–136CrossRefGoogle Scholar
  42. Krause J, Godin JGJ, 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. Lipton JS, Spelke ES (2003) Origins of number sense: large-number discrimination in human infants. Psychol Sci 14:396–401CrossRefPubMedGoogle Scholar
  44. Magurran AE (1990) The adaptive significance of schooling as an anti-predator defence in fish. Ann Zool Fenn 27:51–66Google Scholar
  45. Miletto Petrazzini ME, Agrillo C, Piffer L, Bisazza A (2014) Ontogeny of the capacity to compare discrete quantities in fish. Dev Psychobiol 56:529–536CrossRefPubMedGoogle Scholar
  46. Pepperberg IM (2006) Grey parrot numerical competence: a review. Anim Cogn 9:377–391CrossRefPubMedGoogle Scholar
  47. Peuhkuri N (1998) Shoal composition, body size and foraging in sticklebacks. Behav Ecol Sociobiol 43:333–337CrossRefGoogle Scholar
  48. Piffer L, Agrillo C, Hyde DC (2012) Small and large number discrimination in guppies. Anim Cogn 15:215–221CrossRefPubMedGoogle Scholar
  49. Piffer L, Miletto Petrazzini ME, Agrillo C (2013) Large number discrimination in newborn fish. PLoS One 8:e62466CrossRefPubMedPubMedCentralGoogle Scholar
  50. 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
  51. Poulin R (1999) Parasitism and shoal size in juvenile sticklebacks: conflicting selection pressures from different ectoparasites? Ethology 105:959–968CrossRefGoogle Scholar
  52. Pulliam HR (1973) Advantages of flocking. J Theor Biol 38:419–422CrossRefPubMedGoogle Scholar
  53. R-Development-Core-Team (2009) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  54. Reebs SG, Saulnier N (1997) The effect of hunger on shoal choice in golden shiners (Pisces: Cyprinidae, Notemigonus crysoleucas). Ethology 103:642–652CrossRefGoogle Scholar
  55. Reznikova Z, Ryabko B (2011) Numerical competence in animals, with an insight from ants. Behaviour 148:405–434CrossRefGoogle Scholar
  56. Roberts G (1996) Why individual vigilance declines as group size increases. Anim Behav 51:1077–1086CrossRefGoogle Scholar
  57. Rugani R, Regolin L, Vallortigara G (2010) Imprinted numbers: newborn chicks’ sensitivity to number vs. continuous extent of objects they have been reared with. Dev Sci 13:790–797CrossRefPubMedGoogle Scholar
  58. Rugani R, Cavazzana A, Vallortigara G, Regolin L (2013) One, two, three, four, or is there something more? Numerical discrimination in day-old domestic chicks. Anim Cogn 16:557–564CrossRefPubMedGoogle Scholar
  59. Ruhl N, McRobert SP (2005) The effect of sex and shoal size on shoaling behaviour in Danio rerio. J Fish Biol 67:1318–1326CrossRefGoogle Scholar
  60. Shettleworth SJ (2009) Cognition, evolution, and behavior. Oxford University Press, OxfordGoogle Scholar
  61. Shumaker RW, Palkovich AM, Beck BB, Guagnano GA, Morowitz H (2001) Spontaneous use of magnitude discrimination and ordination by the orangutan (Pongo pygmaeus). J Comp Psychol 115:385–391CrossRefPubMedGoogle Scholar
  62. Stancher G, Sovrano VA, Potrich D, Vallortigara G (2013) Discrimination of small quantities by fish (redtail splitfin, Xenotoca eiseni). Anim Cogn 16:307–312CrossRefPubMedGoogle Scholar
  63. Stancher G, Rugani R, Regolin L, Vallortigara G (2015) Numerical discrimination by frogs (Bombina orientalis). Anim Cogn 18:210–229CrossRefGoogle Scholar
  64. Thünken T, Eigster M, Frommen JG (2014) Context-dependent group size preferences in large shoals of three-spined stickleback. Anim Behav 90:205–210CrossRefGoogle Scholar
  65. Uller C, Jaeger R, Guidry G, Martin C (2003) Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim Cogn 6:105–112CrossRefPubMedGoogle Scholar
  66. Vonk J (2003) Gorilla (Gorilla gorilla gorilla) and orangutan (Pongo abelii) understanding of first- and second-order relations. Anim Cogn 6:77–86CrossRefPubMedGoogle Scholar
  67. Vonk J, Beran MJ (2012) Bears ‘count’ too: quantity estimation and comparison in black bears, Ursus americanus. Anim Behav 84:231–238CrossRefPubMedPubMedCentralGoogle Scholar
  68. Ward AJW, Currie S (2013) Shoaling fish can size-assort by chemical cues alone. Behav Ecol Sociobiol 67:667–673CrossRefGoogle Scholar
  69. Ward C, Smuts BB (2007) Quantity-based judgments in the domestic dog (Canis lupus familiaris). Anim Cogn 10:71–80CrossRefPubMedGoogle Scholar
  70. Weber EH (1905) Tastsinn und Gemeingefühl. Verlag von Wilhelm Engelmann, LeibzigGoogle Scholar
  71. West RE, Young RJ (2002) Do domestic dogs show any evidence of being able to count? Anim Cogn 5:183–186CrossRefPubMedGoogle Scholar
  72. Wootton RJ (1984) A functional biology of the sticklebacks. Croom Helm, LondonCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Evolutionary Biology and EcologyUniversity of BonnBonnGermany
  2. 2.Department of Behavioural Ecology, Institute of Ecology and EvolutionUniversity of BerneHinterkappelenSwitzerland

Personalised recommendations