Abstract
Previous studies showed that both human and non-human animals can discriminate between different quantities (i.e., time intervals, numerosities) with a limited level of precision due to their endogenous/representational uncertainty. In addition, other studies have shown that subjects can modulate their temporal categorization responses adaptively by incorporating information gathered regarding probabilistic contingencies into their time-based decisions. Despite the psychophysical similarities between the interval timing and nonverbal counting functions, the sensitivity of count-based decisions to probabilistic information remains an unanswered question. In the current study, we investigated whether exogenous probabilistic information can be integrated into numerosity-based judgments by mice. In the task employed in this study, reward was presented either after few (i.e., 10) or many (i.e., 20) lever presses, the last of which had to be emitted on the lever associated with the corresponding trial type. In order to investigate the effect of probabilistic information on performance in this task, we manipulated the relative frequency of different trial types across different experimental conditions. We evaluated the behavioral performance of the animals under models that differed in terms of their assumptions regarding the cost of responding (e.g., logarithmically increasing vs. no response cost). Our results showed for the first time that mice could adaptively modulate their count-based decisions based on the experienced probabilistic contingencies in directions predicted by optimality.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agrillo C, Dadda M, Serena G, Bisazza A (2009) Use of number by fish. PLoS ONE 4(3):e4786. doi:10.1371/journal.pone.0004786
Akdoğan B, Balcı F (2015) Stimulus probability effects on temporal bisection performance of mice (Mus musculus). Anim Cogn. doi:10.1007/s10071-015-0909-6
Allan LG, Gibbon J (1991) Human bisection at the geometric mean. Learn Motiv 22:39–58. doi:10.1016/0023-9690(91)90016-2
ASAB (2006) Guidelines for the treatment of animals in behavioural research and teaching. Anim Behav 71:245–253. doi:10.1016/j.anbehav.2005.10.001
Balcı F, Gallistel CR (2006) Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion? Psychon Bull Rev 13:636–642. doi:10.3758/BF03193974
Balcı F, Papachristos EB, Gallistel CR, Brunner D, Gibson J, Shumyatsky GP (2008) Interval timing in genetically modified mice: a simple paradigm. Genes Brain Behav 7(3):373–384. doi:10.1111/j.1601-183X.2007.00348.x
Balcı F, Freestone D, Gallistel CR (2009) Risk assessment in man and mouse. Proc Natl Acad Sci USA 106:2459–2463. doi:10.1073/pnas.0812709106
Balcı F, Freestone D, Simen P, deSouza L, Cohen JD, Holmes P (2011) Optimal temporal risk assessment. Front Integr Neurosci 5:1–15. doi:10.3389/fnint.2011.00056
Bar-Shai N, Keasar T, Shmida A (2011) The use of numerical information by bees in foraging tasks. Behav Ecol 22(2):317–325. doi:10.1093/beheco/arq206
Branch MN, Gollub LR (1974) A detailed analysis of the effects of d-amphetamine on behavior under fixed-interval schedules. J Exp Anal Behav 21(3):519–539. doi:10.1901/jeab.1974.21-519
Brannon EM, Roitman JD (2003) Nonverbal representations of time and number in animals and human infants. In: Meck WH (ed) Functional and neural mechanisms of interval timing. CRC Press, Boca Raton, pp 143–182
Carazo P, Fernández-Perea R, Font E (2012) Quantity estimation based on numerical cues in the mealworm beetle (Tenebrio molitor). Front Psychol 3:502. doi:10.3389/fpsyg.2012.00502
Çavdaroğlu B, Balcı F (2015) Mice can count and optimize count-based decisions. Psychon Bull Rev. doi:10.3758/s13423-015-0957-6
Çavdaroğlu B, Zeki M, Balcı F (2014) Time-based reward maximization. Phil Trans R Soc B Biol Sci 369:20120461. doi:10.1098/rstb.2012.0461
Chittka L, Geiger K (1995) Can honey bees count landmarks? Anim Behav 49(1):159–164. doi:10.1016/0003-3472(95)80163-4
Church RM, Deluty MZ (1977) Bisection of temporal intervals. J Exp Psychol Anim Behav Process 3(3):216–228. doi:10.1037/0097-7403.3.3.216
Cordes S, Gelman R, Gallistel CR, Whalen J (2001) Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychon Bull Rev 8(4):698–707. doi:10.3758/BF03196206
Cordes S, Gallistel CR, Gelman R, Latham P (2007a) Nonverbal arithmetic in humans: light from noise. Percept Psychophys 69(7):1185–1203. doi:10.3758/BF03193955
Cordes S, Williams CL, Meck WH (2007b) Common representations of abstract quantities. Curr Dir Psychol Sci 16(3):156–161. doi:10.1111/j.1467-8721.2007.00495.x
Çoşkun F, Sayalı ZC, Gürbüz E, Balcı F (2015) Optimal time discrimination. Q J Exp Psychol 68(2):381–401. doi:10.1080/17470218.2014.944921
Dacke M, Srinivasan MV (2008) Evidence for counting in insects. Anim Cogn 11(4):683–689. doi:10.1007/s10071-008-0159-y
Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, New York
Dews PB (1962) The effect of multiple SA periods on responding on a fixed-interval schedule. J Exp Anal Behav 5:369–374. doi:10.1901/jeab.1965.8-427
Emmerton J, Lohmann A, Niemann J (1997) Pigeons’ serial ordering of numerosity with visual arrays. Anim Learn Behav 25:234–244. doi:10.3758/BF03199062
Fernandes DM, Church RM (1982) Discrimination of the number of sequential events by rats. Anim Learn Behav 10(2):171–176. doi:10.3758/BF03212266
Ferster CB, Skinner BF (1957) Schedules of reinforcement. Appleton-Century-Crofts, New York
Fetterman JG, Killeen PR (1992) Time discrimination in Columbia livia and Homo sapiens. J Exp Psychol Anim Behav Process 11(3):388–404. doi:10.1037/0097-7403.11.3.388F
Fetterman JG, Killeen PR (2010) Categorical counting. Behav Process 85(1):28–35. doi:10.1016/j.beproc.2010.06.001
Fetterman JG, Dreyfus LR, Stubbs DA (1985) Scaling of response-based events. J Exp Psychol Anim Behav Process 18(1):80–94. doi:10.1037/0097-7403.18.1.80
Fetterman JG, Stubbs DA, Dreyfus LR (1986) Scaling of events spaced in time. Behav Process 13:53–68. doi:10.1016/0376-6357(86)90016-1
Freestone DM, Balcı F, Simen P, Church RM (2015) Optimal response rates in humans and rats. J Exp Psychol Anim Learn Cogn 41(1):39–51. doi:10.1037/xan0000049
Gallistel CR (1990) The organization of learning. Bradford Books/MIT Press, Cambridge
Gallistel CR, Gelman R (1992) Preverbal and verbal counting and computation. Cognition 44(1):43–74. doi:10.1016/0010-0277(92)90050-R
Gallistel CR, Gelman R (2000) Non-verbal numerical cognition: from reals to integers. Trends Cogn Sci 4(2):59–65
Gallistel CR, Gibbon J (2000) Time, rate, and conditioning. Psychol Rev 107(2):289–344. doi:10.1037//0033-295X.107.2.289
Gallistel C, King AP, Gottlieb D, Balcı F, Papachristos EB, Szalecki M, Carbone KS (2007) Is matching innate? J Exp Anal Behav 87:161–199. doi:10.1901/jeab.2007.92-05
Gelman R, Cordes S (2001) Counting in animals and humans. In: Dupoux E (ed) Language, brain and cognitive development: essays in honor of Jacques Mehler. MIT Press, Cambridge, pp 279–303
Gibbon J (1977) Scalar expectancy theory and Weber’s law in animal timing. Psychol Rev 84(3):279–325. doi:10.1037/0033-295X.84.3.279
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(3):296–303. doi:10.1037/0735-7036.119.3.296
Kaufmann EL, Lord MW, Reese TW, Volkmann J (1949) The discrimination of visual number. Am J Psychol 62(4):498–525. doi:10.2307/1418556
Kheifets A, Gallistel C (2012) Mice take calculated risks. Proc Natl Acad Sci USA 109:8776–8779. doi:10.1073/pnas.1205131109
Laties VG (1972) The modification of drug effects on behavior by external discriminative stimuli. J Pharmacol Exp Ther 183(1):1–13
Martin-Iverson MT, Fibiger HC, Wilkie DM (1988) Alteration in the perception of food quantity by rats induced by manipulations of hunger and food sweetness. Learn Motiv 19:44–65. doi:10.1016/0023-9690(88)90025-2
Mechner F (1958) Probability relations within response sequences under ratio reinforcement. J Exp Anal Behav 1:109–121. doi:10.1901/jeab.1958.1-109
Mechner F, Guevrekian L (1962) Effects of deprivation upon counting and timing in rats. J Exp Anal Behav 5(4):463–466
Meck WH, Church RM (1983) A mode control model of counting and timing processes. J Exp Psychol Anim Behav Process 9:320–334
Meck WH, Church RM, Gibbon J (1985) Temporal integration in duration and number discrimination. J Exp Psychol Anim Behav Process 11(4):591–597. doi:10.1037/0097-7403.11.4.591
Nelson XJ, Jackson RR (2012) The role of numerical competence in a specialized predatory strategy of an araneophagic spider. Anim Cogn 15(4):699–710. doi:10.1007/s10071-012-0498-6
Nieder A (2010) Neural bases of numerical cognition. In: Platt M, Ghazanfar A (eds) Primate neuroethology. Oxford University Press, Oxford. doi:10.1093/acprof:oso/9780195326598.003.0020
Nieder A, Miller EK (2004) Analog numerical representations in rhesus monkeys: evidence for parallel processing. J Cognitive Neurosci 16(5):889–901. doi:10.1162/089892904970807
Platt JR, Johnson DM (1971) Localization of position within a homogenous behavior chain: effects of error contingencies. Learn Motiv 2:386–414. doi:10.1016/0023-9690(71)90020-8
Rilling M (1967) Number of responses as a stimulus in fixed interval and fixed ratio schedules. J Comp Physiol Psych 63(1):60–65. doi:10.1037/h0024164
Roberts WA (1995) Simultaneous numerical and temporal processing in the pigeon. Curr Dir Psychol Sci 4(2):47–51. doi:10.1111/1467-8721.ep10771008
Roberts WA, Mitchell S (1994) Can a pigeon simultaneously process temporal and numerical information? J Exp Psychol Anim Behav Process 20:66–78. doi:10.1037/0097-7403.20.1.66
Rouder JN, Speckman PL, Sun D, Morey RD, Iverson G (2009) Bayesian t tests for accepting and rejecting the null hypothesis. Psychon B Rev 16(2):225–237. doi:10.3758/PBR.16.2.225
Stubbs DA (1976) Scaling of stimulus duration by pigeons. J Exp Anal Behav 26(1):15–25. doi:10.1901/jeab.1976.26-15
Trick LM, Pylyshyn ZW (1994) Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychol Rev 101(1):80–102. doi:10.1037/0033-295X.101.1.80
Walsh V (2003) A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn Sci 7(11):483–488. doi:10.1016/j.tics.2003.09.002
Whalen J, Gallistel CR, Gelman R (1999) Nonverbal counting in humans: the psychophysics of number representation. Psychol Sci 10(2):130–137. doi:10.1111/1467-9280.00120
Wickelgren WA (2014) Chunking, familiarity, and serial order in counting. In: Boysen ST, Capaldi EJ (eds) The development of numerical competence: animal and human models. Psychology Press, New York, pp 245–268
Wilkie DM, Webster JB, Leader LG (1979) Unconfounding time and number discrimination in a Mechner counting schedule. Bull Psychon Soc 13:390–392. doi:10.3758/BF03336904
Yaman S, Kilian A, von Fersen L, Güntürkün O (2012) Evidence for a numerosity category that is based on abstract qualities of “few” vs. “many” in the bottlenose dolphin (Tursiops truncatus). Front Psychol 3:473. doi:10.3389/fpsyg.2012.00473
Acknowledgments
This study was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK 1001 Grant No. 111K402) to FB.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Berkay, D., Çavdaroğlu, B. & Balcı, F. Probabilistic numerical discrimination in mice. Anim Cogn 19, 351–365 (2016). https://doi.org/10.1007/s10071-015-0938-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10071-015-0938-1