Animal Cognition

, Volume 19, Issue 1, pp 75–89 | Cite as

Comparison of discrete ratios by rhesus macaques (Macaca mulatta)

  • Caroline B. DruckerEmail author
  • Marley A. Rossa
  • Elizabeth M. Brannon
Original Paper


Perceiving and comparing ratios are crucial skills for humans. Little is known about whether other animals can compare ratios. We trained two rhesus macaques (Macaca mulatta) to choose arrays that contained the greater ratio of positive to negative stimuli, regardless of the absolute number of stimuli in each of the two choice arrays. Subjects learned this task, and their performance generalized to novel ratios. Moreover, performance was modulated by the ratio between ratios; subjects responded more quickly and accurately when the ratio between ratios was higher. Control conditions ruled out the possibility that subjects were relying on surface area, although the ratio between ratios of surface area did seem to influence their choices. Our results demonstrate that rhesus monkeys can compare discrete ratios, demonstrating not only proportional reasoning ability but also the ability to reason about relations between relations.


Ratios Proportion Numerical cognition Rhesus macaques Monkeys Relations between relations 



We thank Monica Carlson, Nick DeWind, Erin Koballa, Rosa Li, James Powers, Ariel Starr, Emily Szkudlarek, and all members of Dr. Elizabeth Brannon’s and Dr. Michael Platt’s labs for assistance with data collection and helpful discussions of this study. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1106401 and the Holland-Trice Graduate Fellowship in Brain Science and Disease to CBD, and a McDonnell Scholars Award to EMB.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All applicable international, national, and/or institutional guidelines for the care and use of animals were followed. All procedures performed in studies involving animals were in accordance with the ethical standards of the institution or practice at which the studies were conducted. All procedures were approved by Duke University’s Institutional Animal Care and Use Committee.


  1. Agrillo C, Piffer L, Bisazza A (2011) Number versus continuous quantity in numerosity judgments by fish. Cognition 119:281–287. doi: 10.1016/j.cognition.2010.10.022 PubMedCrossRefGoogle Scholar
  2. Boyer TW, Levine SC, Huttenlocher J (2008) Development of proportional reasoning: where young children go wrong. Dev Psychol 44:1478–1490. doi: 10.1037/a0013110 PubMedPubMedCentralCrossRefGoogle Scholar
  3. Brainard DH (1997) The psychophysics toolbox. Spat Vis 10:433–436. doi: 10.1163/156856897X00357 PubMedCrossRefGoogle Scholar
  4. Cantlon JF, Brannon EM (2007) How much does number matter a monkey (Macaca mulatta)? J Exp Psychol: Anim B 33:32–41. doi: 10.1037/0097-7403.33.1.32 Google Scholar
  5. Cook RG, Wasserman EA (2007) Learning and transfer of relational matching-to-sample by pigeons. Psychon B Rev 14:1107–1114CrossRefGoogle Scholar
  6. Denison S, Xu F (2010) Twelve- to 14-month-old infants can predict single-event probability with large set sizes. Dev Sci 13:798–803. doi: 10.1111/j.1467-7687.2009.00943.x PubMedCrossRefGoogle Scholar
  7. Denison S, Xu F (2014) The origins of probabilistic inference in human infants. Cognition 130:335–347PubMedCrossRefGoogle Scholar
  8. DeWind NK, Adams GK, Platt ML, Brannon EM (2015) Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition 142:247–265. doi: 10.1016/j.cognition.2015.05.016 PubMedCrossRefGoogle Scholar
  9. Emmerton J (2001) Pigeons’ discrimination of color proportion in computer-generated visual displays. Anim Learn Behav 29:21–35CrossRefGoogle Scholar
  10. Fagot J, Maugard A (2013) Analogical reasoning in baboons (Papio papio): flexible reencoding of the source relation depending on the target relation. Learn Behav 41:229–237. doi: 10.3758/s13420-012-0101-7 PubMedCrossRefGoogle Scholar
  11. Fazio LK, Bailey DH, Thompson CA, Siegler RS (2014) Relations of different types of numerical magnitude representations to each other and to mathematics achievement. J Exp Child Psych 123:53–72. doi: 10.1016/j.jecp.2014.01.013 CrossRefGoogle Scholar
  12. Flemming TM, Beran MJ, Thompson RKR et al (2008) What meaning means for same and different: analogical reasoning in humans (Homo sapiens), chimpanzees (Pan troglodytes), and rhesus monkeys (Macaca mulatta). J Comp Psychol 122:176–185. doi: 10.1037/0735-7036.122.2.176 PubMedPubMedCentralCrossRefGoogle Scholar
  13. Flemming TM, Thompson RKR, Beran MJ, Washburn DA (2011) Analogical reasoning and the differential outcome effect: transitory bridging of the conceptual gap for rhesus monkeys (Macaca mulatta). J Exp Psychol Anim B 37:353–360. doi: 10.1037/a0022142 CrossRefGoogle Scholar
  14. Flemming TM, Washburn DA (2012) Analogical reasoning in animals. In: Seel NM (ed) Encyclopedia of the sciences of learning. Springer, New York, pp 228–230Google Scholar
  15. Fontanari L, Gonzalez M, Vallortigara G, Girotto V (2014) Probabilistic cognition in two indigenous Mayan groups. P Natl Acad Sci USA 111:17075–17080. doi: 10.1073/pnas.1410583111 CrossRefGoogle Scholar
  16. Gallistel CR (1990) Organization of learning. MIT Press, Cambridge, pp 351–383Google Scholar
  17. Gebuis T, Reynvoet B (2012a) The interplay between nonsymbolic number and its continuous visual properties. J Exp Psychol Gen 141(4):642–648. doi: 10.1037/a0026218 PubMedCrossRefGoogle Scholar
  18. Gebuis T, Reynvoet B (2012b) The role of visual information in numerosity estimation. PLoS One 7(5):e37426. doi: 10.1371/journal.pone.0037426.g003 PubMedPubMedCentralCrossRefGoogle Scholar
  19. Godin JGJ, Keenleyside MHA (1984) Foraging on patchily distributed prey by a cichlid fish (Teleostei, Cichlidae): a test of the ideal free distribution theory. Anim Behav 32:120–131CrossRefGoogle Scholar
  20. Harper DGC (1982) Competitive foraging in mallards: ‘Ideal free’ ducks. Anim Behav 30:575–584CrossRefGoogle Scholar
  21. Hartnett P, Gelman R (1998) Early understandings of numbers: paths or barriers to the construction of new understandings? Learn Instr 8:341–374. doi: 10.1016/S0959-4752(97)00026-1 CrossRefGoogle Scholar
  22. Hayden BY, Heilbronner SR, Platt ML (2010) Ambiguity aversion in rhesus macaques. Front Neurosci 4:1–7. doi: 10.3389/fnins.2010.00166 CrossRefGoogle Scholar
  23. Honig WK, Stewart KE (1989) Discrimination of relative numerosity by pigeons. Anim Learn Behav 17:134–146CrossRefGoogle Scholar
  24. Honig WK, Stewart KE (1993) Relative numerosity as a dimension of stimulus control: the peak shift. Anim Learn Behav 21:346–354CrossRefGoogle Scholar
  25. Jeong Y, Levine SC, Huttenlocher J (2007) The development of proportional reasoning: effect of continuous versus discrete quantities. J Cogn Dev 8:237–256. doi: 10.1080/15248370701202471 CrossRefGoogle Scholar
  26. Kleiner M, Brainard D, Pelli D (2007) “What’s new in Psychtoolbox-3?” Perception 36 ECVP Abstract SupplementGoogle Scholar
  27. McCrink K, Wynn K (2007) Ratio abstraction by 6-month-old infants. Psychol Sci 18:740–745. doi: 10.1111/j.1467-9280.2007.01969.x PubMedCrossRefGoogle Scholar
  28. Penn DC, Holyoak KJ, Povinelli DJ (2008) Darwin’s mistake: explaining the discontinuity between human and nonhuman minds. Behav Brain Sci 31:109–178. doi: 10.1017/S0140525X08003543 PubMedGoogle Scholar
  29. Pica P, Lemer C, Izard V, Dehaene S (2004) Exact and approximate arithmetic in an Amazonian indigene group. Science 306:499–503PubMedCrossRefGoogle Scholar
  30. Premack D (1983) The codes of man and beasts. Behav Brain Sci 6:125–136. doi: 10.1017/S0140525X00015077 CrossRefGoogle Scholar
  31. Rakoczy H, Clüver A, Saucke L, Stoffregen N, Gräbener A, Migura J, Call J (2014) Apes are intuitive statisticians. Cognition 131:60–68. doi: 10.1016/j.cognition.2013.12.011 PubMedCrossRefGoogle Scholar
  32. Siegler RS, Fazio LK, Bailey DH, Zhou X (2013) Fractions: the new frontier for theories of numerical development. Trends Cogn Sci 17:13–19. doi: 10.1016/j.tics.2012.11.004 PubMedCrossRefGoogle Scholar
  33. Smirnova A, Zorina Z, Obozova T, Wasserman E (2015) Crows spontaneously exhibit analogical reasoning. Curr Biol 25:256–260PubMedCrossRefGoogle Scholar
  34. Spinillo AG, Bryant PE (1999) Proportional reasoning in young children: part–part comparisons about continuous and discontinuous quantity. Math Cogn 5:181–197CrossRefGoogle Scholar
  35. Suanda SH, Tompson W, Brannon EM (2008) Changes in the ability to detect ordinal numerical relationships between 9 and 11 months of age. Infancy 13:308–337. doi: 10.1080/15250000802188800 PubMedPubMedCentralCrossRefGoogle Scholar
  36. Thompson CA, Opfer JE (2008) Costs and benefits of representational change: effects of context on age and sex differences in symbolic magnitude estimation. J Exp Child Psychol 101:20–51. doi: 10.1016/j.jecp.2008.02.003 PubMedCrossRefGoogle Scholar
  37. Thompson RKR, Oden DL (2000) Categorical perception and conceptual judgments by nonhuman primates: the paleological monkey and the analogical ape. Cogn Sci 24:363–396. doi: 10.1016/S0364-0213(00)00029-X CrossRefGoogle Scholar
  38. Truppa V, Piano Mortari E, Garofoli D, Privitera S, Visalberghi E (2011) Same/different concept learning by capuchin monkeys in matching-to-sample tasks. PLoS One 6:e23809. doi: 10.1371/journal.pone.0023809.s003 PubMedPubMedCentralCrossRefGoogle Scholar
  39. Vallentin D, Nieder A (2008) Behavioral and prefrontal representation of spatial proportions in the monkey. Curr Biol 18:1420–1425PubMedCrossRefGoogle Scholar
  40. Vamvakoussi X (2015) The development of rational number knowledge: old topic, new insights. Learn Instr 37:50–55. doi: 10.1016/j.learninstruc.2015.01.002 CrossRefGoogle Scholar
  41. Vonk J (2003) Gorilla (Gorilla gorilla gorilla) and orangutan (Pongo abelii) understanding of first- and second-order relations. Anim Cogn 6:77–86. doi: 10.1007/s10071-003-0159-x PubMedCrossRefGoogle Scholar
  42. Woodruff G, Premack D (1981) Primative mathematical concepts in the chimpanzee: proportionality and numerosity. Nature 293:568–570PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Neurobiology and Center for Cognitive NeuroscienceDuke UniversityDurhamUSA
  2. 2.Department of Psychology and Neuroscience and Center for Cognitive NeuroscienceDuke UniversityDurhamUSA

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