Extensive training extends numerical abilities of guppies


Recent studies on animal mathematical abilities suggest that all vertebrates show comparable abilities when they are given spontaneous preference tests, such as selecting the larger number of food items, but that mammals and birds generally achieve much better performance than fish when tested with training procedures. At least part of these differences might be due to the fact that fish are usually trained with only one or two dozen trials while extensive training, sometimes with thousands of trials, is normally performed in studies of mammals and birds. To test this hypothesis, female guppies were trained on four consecutive numerical discriminations of increasing difficulty (from 2 vs. 3 to 5 vs. 6 items), with up to 120 trials with each discrimination. Five out of eight subjects discriminated all contrasts up to 4 versus 5 objects at levels significantly better than chance, a much higher limit than the 2 versus 3 limit previously reported in studies that provided fish with only short training sequences. Our findings indicate that the difference in numerical cognition between teleosts and warm-blooded vertebrates might be smaller than previously supposed.

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  1. Agrillo C, Bisazza A (2014) Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals. J Neurosci Meth, online first. doi:10.1016/j.jneumeth.2014.04.027

  2. Agrillo C, Dadda M, Serena G, Bisazza A (2008) Do fish count? Spontaneous discrimination of quantity in female mosquitofish. Anim Cogn 11:495–503

  3. Agrillo C, Piffer L, Bisazza A (2010) Large number discrimination by fish. PLoS ONE 5(12):e15232

  4. Agrillo C, Piffer L, Bisazza A (2011) Number versus continuous quantity in numerosity judgments by fish. Cognition 119:281–287

  5. Agrillo C, Miletto Petrazzini ME, Tagliapietra C, Bisazza A (2012a) Inter-specific differences in numerical abilities among teleost fish. Front Psych 3:483. doi:10.3389/fpsyg.2012.00483

  6. 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 230:343–348

  7. Agrillo C, Piffer L, Bisazza A, Butterworth B (2012c) Evidence for two numerical systems that are similar in humans and guppies. PLoS ONE 7(2):e31923

  8. Agrillo C, Miletto Petrazzini ME, Bisazza A (2014) Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range. Anim Cogn 17(2):307–316

  9. Al Aïn S, Giret N, Grand M, Kreutzer M, Bovet D (2009) The discrimination of discrete and continuous amounts in African grey parrots (Psittacus erithacus). Anim Cogn 12:145–154

  10. Arsalidou M, Taylor MJ (2011) Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage 54:2382–2393

  11. Barnard AM, Hughes KD, Gerhardt RR, DiVincenti L Jr, Bovee JM, Cantlon JF (2013) Inherently analog quantity representations in olive baboons (Papio anubis). Front Psychol 4:253. doi:10.3389/fpsyg.2013.00253

  12. Beran MJ (2001) Summation and numerousness judgments of sequentially presented sets of items by chimpanzees (Pan troglodytes). J Comp Psychol 155:181–191

  13. Beran MJ (2004) Chimpanzees (Pan troglodytes) respond to nonvisible sets after one-by-one addition and removal of items. J Comp Psychol 118:25–36

  14. Beran MJ (2008a) Monkeys (Macaca mulatta and Cebus apella) track, enumerate, and compare multiple sets of moving items. J Exp Psych Anim Behav Proc 34:63–74

  15. Beran MJ (2008b) The evolutionary and developmental foundations of mathematics. PLoS Biol 6:e19

  16. Bisazza A (2010) Cognition. In: Evans F, Pilastro A, Schlupp I (eds) Ecology and evolution of poeciliid fishes. Chicago University Press, Chicago, pp 165–173

  17. Bisazza A, Piffer L, Serena G, Agrillo C (2010) Ontogeny of numerical abilities in fish. PLoS ONE 5:e15516

  18. Brown C, Laland KN (2003) Social learning in fishes: a review. Fish Fish 4:280–288

  19. Bshary R, Wickler W, Fricke H (2002) Fish cognition: a primate’s eye view. Anim Cogn 5:1–13

  20. Cantlon JF, Brannon EM (2007) How much does number matter to a monkey (Macaca mulatta)? J Exp Psych Anim Behav Proc 33(1):32–41

  21. Cantrell L, Smith LB (2013) Open questions and a proposal: a critical review of the evidence on infant numerical abilities. Cognition 128(3):331–352

  22. Cheek JM, Smith LR (1999) Music training and mathematics achievement. Adolescence 34:759–761

  23. Dadda M, Piffer L, Agrillo C, Bisazza A (2009) Spontaneous number representation in mosquitofish. Cognition 112:343–348

  24. Emmerton J, Delius JD (1993) Beyond sensation: visual cognition in pigeons. In: Zeigler HP, Bischof H-J (eds) Vision, brain, and behavior in birds. MIT Press, Cambridge, MA, pp 377–390

  25. Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trends Cogn Sci 8:307–314

  26. Gauthier I, Skudlarski P, Gore JC, Anderson AW (2000) Expertise for cars and birds recruits brain areas involved in face recognition. Nat Neurosci 3:191–197

  27. Goldman M, Shapiro S (1979) Matching-to-sample and oddity-from sample in goldfish. J Exp Anal Behav 31:259–266

  28. Gómez-Laplaza LM, Gerlai R (2011) Spontaneous discrimination of small quantities: shoaling preferences in angelfish (Pterophyllum scalare). Anim Cogn 14:565–574

  29. Halberda J, Feigenson L (2008) Developmental change in the acuity of the “Number Sense”: the approximate number system in 3-, 4-, 5-, 6-year-olds and adults. Dev Psych 44(5):1457–1465

  30. 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 121:241–249

  31. Hauser MD, Carey S, Hauser LB (2000) Spontaneous number representation in semi-free-ranging rhesus monkeys. Proc R Soc Lond B 267:829–833

  32. Hunt S, Low J, Burns CK (2008) Adaptive numerical competency in a food-hoarding songbird. Proc R Soc Lond B 10:1098–1103

  33. 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 119:286–303

  34. Libertus ME, Feigenson L, Halberda J (2013) Is approximate number precision a stable predictor of math ability? Learn Indiv Differ 1(25):126–133

  35. Pahl M, Si A, Zhang S (2013) Numerical cognition in bees and other insects. Front Psychol 4(162). doi:10.3389/fpsyg.2013.00162

  36. Pepperberg IM (2006) Grey parrot numerical competence: a review. Anim Cogn 9:377–391

  37. Piffer L, Agrillo C, Hyde DC (2012) Small and large number discrimination in guppies. Anim Cogn 15:215–221

  38. Roberts WA, Mitchell S (1994) Can a pigeon simultaneously process temporal and numerical information? J Exp Psych Anim Behav Proc 20:66–78

  39. Rodd F, Hughes K, Grether G, Baril C (2002) A possible non-sexual origin of mate preference: are male guppies mimicking fruit? Proc R Soc Lond B 269(1490):475–481

  40. Schartl M, Walter RB, Shen Y, Garcia T, Catchen J, Amores A, Braasch I, Chalopin D, Volff JN, Lesch KP, Bisazza A, Minx P, Hillier L, Wilson RK, Fuerstenberg S, Boore J, Searle S, Postlethwait JH, Warren WC (2013) The genome of the platyfish, Xiphophorus maculatus, provides insights into evolutionary adaptation and several complex traits. Nat Genet 45:567–572

  41. Sokal RR, Rohlf FJ (1995) Biometry: the principals and practice of statistics in biological research. WH Freeman and Company, New York

  42. Tomonaga M (2008) Relative numerosity discrimination by chimpanzees (Pan troglodytes): evidence for approximate numerical representations. Anim Cogn 11:43–57

  43. Uller C, Jaeger R, Guidry G, Martin C (2003) Salamanders (Plethodon cinereus) go for more: rudiments of number in a species of basal vertebrate. Anim Cogn 6:105–112

  44. Volff JN (2005) Genome evolution and biodiversity in teleost fish. Heredity 94:280–294

  45. Wittbrodt J, Meyer A, Schartl M (1998) More genes in fish? BioEssays 20:511–515

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The authors would like to thank Michael J Beran for his useful comments and Michela Giovagnoni for her help in testing the animals. This work was funded by the FIRB grant (RBFR13KHFS) from Ministero dell’Istruzione, Università e Ricerca (MIUR, Italy) to Christian Agrillo. Experiments comply with all laws of the country (Italy) in which they were performed.

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Correspondence to Tyrone Lucon-Xiccato.

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

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  • Numerical cognition
  • Poecilia reticulata
  • Training procedure
  • Numerical acuity