Abstract
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.
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References
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
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
Brainard DH (1997) The psychophysics toolbox. Spat Vis 10:433–436. doi:10.1163/156856897X00357
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
Cook RG, Wasserman EA (2007) Learning and transfer of relational matching-to-sample by pigeons. Psychon B Rev 14:1107–1114
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
Denison S, Xu F (2014) The origins of probabilistic inference in human infants. Cognition 130:335–347
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
Emmerton J (2001) Pigeons’ discrimination of color proportion in computer-generated visual displays. Anim Learn Behav 29:21–35
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
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
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
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
Flemming TM, Washburn DA (2012) Analogical reasoning in animals. In: Seel NM (ed) Encyclopedia of the sciences of learning. Springer, New York, pp 228–230
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
Gallistel CR (1990) Organization of learning. MIT Press, Cambridge, pp 351–383
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
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
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 32:120–131
Harper DGC (1982) Competitive foraging in mallards: ‘Ideal free’ ducks. Anim Behav 30:575–584
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
Hayden BY, Heilbronner SR, Platt ML (2010) Ambiguity aversion in rhesus macaques. Front Neurosci 4:1–7. doi:10.3389/fnins.2010.00166
Honig WK, Stewart KE (1989) Discrimination of relative numerosity by pigeons. Anim Learn Behav 17:134–146
Honig WK, Stewart KE (1993) Relative numerosity as a dimension of stimulus control: the peak shift. Anim Learn Behav 21:346–354
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
Kleiner M, Brainard D, Pelli D (2007) “What’s new in Psychtoolbox-3?” Perception 36 ECVP Abstract Supplement
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
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
Pica P, Lemer C, Izard V, Dehaene S (2004) Exact and approximate arithmetic in an Amazonian indigene group. Science 306:499–503
Premack D (1983) The codes of man and beasts. Behav Brain Sci 6:125–136. doi:10.1017/S0140525X00015077
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
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
Smirnova A, Zorina Z, Obozova T, Wasserman E (2015) Crows spontaneously exhibit analogical reasoning. Curr Biol 25:256–260
Spinillo AG, Bryant PE (1999) Proportional reasoning in young children: part–part comparisons about continuous and discontinuous quantity. Math Cogn 5:181–197
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
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
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
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
Vallentin D, Nieder A (2008) Behavioral and prefrontal representation of spatial proportions in the monkey. Curr Biol 18:1420–1425
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
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
Woodruff G, Premack D (1981) Primative mathematical concepts in the chimpanzee: proportionality and numerosity. Nature 293:568–570
Acknowledgments
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.
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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.
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Drucker, C.B., Rossa, M.A. & Brannon, E.M. Comparison of discrete ratios by rhesus macaques (Macaca mulatta). Anim Cogn 19, 75–89 (2016). https://doi.org/10.1007/s10071-015-0914-9
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DOI: https://doi.org/10.1007/s10071-015-0914-9