Skip to main content
Log in

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

  • Original Paper
  • Published:
Animal Cognition Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Agrillo C, Dadda M, Serena G (2008a) Choice of female groups by male mosquitofish (Gambusia holbrooki). Ethology 114(5):479–488

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Agrillo C, Dadda M, Serena G, Bisazza A (2009) Use of number by fish. PLoS ONE 4(3):e4786

    Article  PubMed Central  PubMed  Google Scholar 

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

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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):e31923

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • 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

    PubMed Central  PubMed  Google Scholar 

  • Alston L, Humphreys GW (2004) Subitization and attentional engagement by transient stimuli. Spat Vis 17:17–50

    Article  PubMed  Google Scholar 

  • Assad JA, Maunsell JHR (1995) Neuronal correlates of inferred motion in primate posterior parietal cortex. Nature 373:518–521

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Beran MJ (2008a) The evolutionary and developmental foundations of mathematics. PLoS Biol 6:221–223

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  • 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 70:191–194

    Article  PubMed  Google Scholar 

  • 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

    PubMed Central  PubMed  Google Scholar 

  • 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 85:987–993

    Article  PubMed  Google Scholar 

  • Bisazza A, Serena G, Piffer L, Agrillo C (2010) Ontogeny of numerical abilities in guppies. PLoS ONE 5(11):e15516

    Article  PubMed Central  PubMed  Google Scholar 

  • Bonanni R, Natoli E, Cafazzo S, Valsecchi P (2011) Free ranging dogs assess the quantity of opponents in intergroup conflicts. Anim Cogn 14:103–115

    Article  PubMed  Google Scholar 

  • Buckingham JN, Wong BBM, Rosenthal GG (2007) Shoaling decision in female swordtails: how do fish gauge group size? Behaviour 144:1333–1346

    Article  Google Scholar 

  • Cantlon JF, Brannon EM (2007) Basic math in monkeys and college students. PLoS Biol 5(12):e328

    Article  PubMed Central  PubMed  Google Scholar 

  • Chesney DL, Haladjian H (2011) Evidence for a shared mechanism used in multiple-object tracking and subitizing. Atten Percept Psychophys 73:2457–2480

    Article  PubMed  Google Scholar 

  • Cordes S, Brannon EM (2009) Crossing the divide: infants discriminate small from large numerosities. Dev Psychol 45:1583–1594

    Article  PubMed Central  PubMed  Google Scholar 

  • 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

    Article  PubMed Central  PubMed  Google Scholar 

  • Dacke M, Srinivasan MV (2008) Evidence for counting in insects. Anim Cogn 11:683–689

    Article  PubMed  Google Scholar 

  • Durgin FH (1995) Texture density adaptation and the perceived numerosity and distribution of texture. J Exp Psychol Hum Percept Perform 21:149–169

    Article  Google Scholar 

  • Evans TA, Beran MJ, Harris EH, Rice D (2009) Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella). Anim Cogn 12:97–105

    Article  PubMed  Google Scholar 

  • Evans TA, Beran MJ, Addessi E (2010) Can nonhuman primates use tokens to represent and sum quantities? J Comp Psychol 124:369–380

    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 MD (2002a) The representations underlying infants’ choice of more: object files versus analog magnitudes. Psychol Sci 13:150–156

    Article  PubMed  Google Scholar 

  • Feigenson L, Carey S, Spelke ES (2002b) Infants’ discrimination of number vs. continuous extent. Cogn Psychol 44:33–66

    Article  PubMed  Google Scholar 

  • Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trends Cogn Sci 8(7):307–314

    Article  PubMed  Google Scholar 

  • Flombaum JI, Junge JA, Hauser MD (2005) Rhesus monkeys (Macaca mulatta) spontaneously compute addition operations over large numbers. Cognition 97:315–325

    Article  PubMed  Google Scholar 

  • Gallistel CR, Gelman R (1992) Preverbal and verbal counting and computation. Cognition 44:43–74

    Article  CAS  PubMed  Google Scholar 

  • Garland A, Low J, Burns KC (2012) Large quantity discrimination by North Island robins (Petroica longipes). Anim Cogn 15:1129–1140

    Article  PubMed  Google Scholar 

  • Gebuis T, Reynvoet B (2012) The role of visual information in numerosity estimation. PLoS ONE 7(5):e37426

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Gelman R, Gallistel C (1978) The child’s understanding of number. Harvard University Press, Cambridge

    Google Scholar 

  • Gómez-Laplaza LM, Gerlai R (2011) Spontaneous discrimination of small quantities: shoaling preferences in angelfish (Pterophyllum scalare). Anim Cogn 14(4):565–574

    Article  PubMed  Google Scholar 

  • 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

    Article  PubMed Central  PubMed  Google Scholar 

  • Gross HJ, Pahl M, Si A, Zhu H, Tautz J, Zhang S (2009) Number-based visual generalisation in the honeybee. PLoSONE 4:e4263

    Article  Google Scholar 

  • Halberda J, Mazzocco M, Feigenson L (2008) Individual differences in nonverbal number acuity predict maths achievement. Nature 455:665–668

    Article  CAS  PubMed  Google Scholar 

  • 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, Cambridge

    Google Scholar 

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

    Article  CAS  Google Scholar 

  • Hunt S, Low J, Burns KC (2008) Adaptive numerical competency in a food-hoarding songbird. Proc R Soc Lond B 275:2373–2379

    Article  Google Scholar 

  • Jevons WS (1871) The power of numerical discrimination. Nature 3(67):281–282

    Article  Google Scholar 

  • Kaufman EL, Lord MW, Reese TW, Volkmann J (1949) The discrimination of visual number. Am J Psychol 62(4):498–525

    Article  CAS  PubMed  Google Scholar 

  • Kilian A, Yaman S, Fersen L, Güntürkün O (2003) A bottlenose dolphin (Tursiops truncatus) discriminates visual stimuli differing in numerosity. Learn Behav 31:133–142

    Article  PubMed  Google Scholar 

  • Krusche P, Uller C, Ursula D (2010) Quantity discrimination in salamanders. J Exp Biol 213:1822–1828

    Article  PubMed  Google Scholar 

  • Lipton J, Spelke ES (2003) Origins of number sense: large number discrimination in human infants. Psychol Sci 14:396–401

    Article  PubMed  Google Scholar 

  • Mandler G, Shebo BJ (1982) Subitizing: an analysis of its component processes. J Exp Psychol Gen 111:1–22

    Article  CAS  PubMed  Google Scholar 

  • Matsuno T, Tomonaga M (2006) Visual search for moving and stationary items in chimpanzees (Pan troglodytes) and humans (Homo sapiens). Behav Brain Res 172:219–232

    Article  PubMed  Google Scholar 

  • 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 233:443–449

    Article  PubMed  Google Scholar 

  • 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

  • Neisser U (1967) Cognitive psychology. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Nieder A, Dehaene S (2009) Representation of number in the brain. Annu Rev Neurosci 32:185–208

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed Central  PubMed  Google Scholar 

  • 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 15:955–961

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Piffer L, Miletto Petrazzini ME, Agrillo C (2013) Large number discrimination in newborn fish. PLoS ONE 8(4):e62466

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Pisa PE, Agrillo C (2009) Quantity discrimination in felines: a preliminary investigation of the domestic cat (Felis silvestris catus). J Ethol 27:289–293

    Article  Google Scholar 

  • Revkin SK, Piazza M, Izard V, Cohen L, Dehaene S (2008) Does subitizing reflect numerical estimation? Psychol Sci 19:607–614

    Article  PubMed  Google Scholar 

  • Ross J (2003) Visual discrimination of number without counting. Percept 32:867–870

    Article  Google Scholar 

  • Scholl BJ, Pylyshyn ZW (1999) Tracking multiple items through occlusion: clues to visual objecthood. Cogn Psychol 38:259–290

    Article  CAS  PubMed  Google Scholar 

  • Sokal RR, Rohlf FJ (1995) Biometry. Freeman and Company, New York

    Google Scholar 

  • Trick LM (2008) More than superstition: differential effects of featural heterogeneity and change on subitizing and counting. Percept Psychophys 70:743–760

    Article  PubMed  Google Scholar 

  • Trick LM, Pylyshyn ZW (1994) Why are small and large number enumerated differently: a limited-capacity preattentive stage in vision. Psychol Rev 101(1):80–102

    Article  CAS  PubMed  Google Scholar 

  • 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):1229–1237

    Article  Google Scholar 

  • Van Marle K (2013) Infants use different mechanisms to make small and large number ordinal judgments. J Exp Child Psych 114(1):102–110

    Article  Google Scholar 

  • Van Oeffelen MP, Vos PG (1982) A probabilistic model for the discrimination of visual number. Percept Psychophys 32:163–170

    Article  PubMed  Google Scholar 

  • Vetter P, Butterworth B, Bahrami B (2008) Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism. PLoS ONE 3(9):e3269

    Article  PubMed Central  PubMed  Google Scholar 

  • Vonk J, Beran MJ (2012) Bears “count” too: quantity estimation and comparison in black bears (Ursus americanus). Anim Behav 84:231–238

    Article  PubMed Central  PubMed  Google Scholar 

  • Vos PG, Van Oeffelen MP, Tibosch HJ, Allik J (1988) Area-numerosity interactions. Psychol Res 50:148–150

    Article  CAS  PubMed  Google Scholar 

  • Ward C, Smuts BB (2007) Quantity-based judgments in the domestic dog (Canis lupus familiaris). Anim Cogn 10:71–80

    Article  PubMed  Google Scholar 

  • Wood JN, Spelke ES (2005) Infants’ enumeration of actions: numerical discrimination and its signature limits. Dev Sci 8(2):173–181

    Article  PubMed  Google Scholar 

  • Woodworth RS, Schlosberg H (1954) Experimental psychology. Holt, New York

    Google Scholar 

  • Xu F (2003) Numerosity discrimination in infants: evidence for two systems of representations. Cognition 89(1):B15–B25

    Article  PubMed  Google Scholar 

  • Xu F, Spelke ES (2000) Large number discrimination in 6-month-old infants. Cognition 74:B1–B11

    Article  Google Scholar 

  • Xu F, Spelke ES, Goddard S (2005) Number sense in human infants. Dev Sci 8(1):88–101

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian Agrillo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agrillo, C., Miletto Petrazzini, M.E. & Bisazza, A. Numerical acuity of fish is improved in the presence of moving targets, but only in the subitizing range. Anim Cogn 17, 307–316 (2014). https://doi.org/10.1007/s10071-013-0663-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10071-013-0663-6

Keywords

Navigation