Detection of invariants in probabilistic relations between events through exploratory behaviors

Pablo Covarrubias, Felipe Cabrera, Ángel Andrés Jiménez


Research has demonstrated that individuals are sensitive to contingent probabilistic relations between events in the environment. However, the factors that underlie this adaptation are not fully understood. Thus, the aim of this study was to assess whether repetitions and variations in participants’ responses contributed to the detection of invariance in probabilistic environments. In Experiment 1, participants were exposed to relations between the initial and final trajectories of an arrow under probabilities of 1.0, 0.9 and 0.8. In the first half of the session, the arrows followed predominantly straight trajectories, but in the second half they changed to broken ones, or vice versa. In Experiment 2, sessions began with no relation between the arrows’ initial and final trajectories (p= 0.5), but in the second half probabilities of 1.0, 0.9 and 0.8 were presented for straight or broken trajectories. In both experiments, as the relation between the arrow’s initial and final trajectories became more changeable variations of behavior increased, while under more constant relations repetitions increased. Results support the notion that adaptation to probabilistic relations between events entails exploratory behaviors performed to detect invariant information of the environment.

Palabras clave

invariants, contingency, probability of continuity, information, exploratory behaviors


Antonitis, J. J. (1951). Response variability in the white rat during conditioning, extinction, and reconditioning. Journal of Experimental Psychology, 42, 273-281.

Baum, W. M. (2012). Rethinking reinforcement: Allocation, induction, and contingency. Journal of the Experimental Analysis of Behavior, 97, 101–124.

Cabrera, F., Sanabria, F., Shelley, D., & Killeen, P.R. (2009). The "lunching" effect: Pigeons track motion towards food more than motion away from it. Behavioural Processes, 82, 229-235.

Costall, A.P. (1984). Are theories of perception necessary? A review of Gibson's 'The ecological approach to visual perception'. Journal of the Experimental Analysis of Behavior, 41, 109-115.

Costall, A.P., Sinico, M., & Parovel, G. (2003). The concept of ‘invariants’ and the problem of perceptual constancy. Rivista di Estetica, 24, 45-49.

Covarrubias, P., Cabrera, F., & Jiménez, Á.A. (2017). Invariants and information pickup in The senses considered as perceptual systems: Implications for the Experimental Analysis of Behavior. Ecological Psychology, 29, 231-242.

Cowie, S. (2019). Some weakness of a response-strenght account of reinforcer effects. European Journal of Behavior Analysis

de Paz. C., Travieso, D., Ibáñez-Gijón, J., Bravo, M., Lobo L., & Jacobs, D.M. (2019). Sensory substitution: The affordance of passability, body- scaled perception, and exploratory movements. PLoS ONE 14(3): e0213342. 10.1371/journal.pone.0213342

Gharib, A., Derby, S., & Roberts, S. (2001). Timing and the control of variation. Journal of Experimental Psychology: Animal Behavior Processes, 27, 165-178.

Gibson, J.J. (1966). The senses considered as perceptual systems. Boston, MA: Houghton Mifflin.

Gibson, J.J. (1967). New reasons for realism. Synthese, 17, 162-172.

Guerin, B. (1990). Gibson, Skinner and perceptual responses. Behavior and Philosophy, 18, 43-54.

Katagiri, M., Kao, S.-F., Simon, A.M., Castro, L. & Wasserman, E.A. (2007). Judgments of causal efficacy under constant and changing interevent contingencies. Behavioural Processes, 74, 251-264.

Killeen, P.R. (1981). Learning as causal inference. In M.L. Commons & J.A. Nevin (Eds.), Quantitative analysis of behavior (Vol. I): Discriminative properties of reinforcement schedules. Cambridge, MA: Ballinger.

Mantel, B., Stoffregen, T.A., Campbell, A., & Bardy, B.G. (2015). Exploratory movement generates higher- order information that is sufficient for accurate perception of scaled egocentric distance. PLoS ONE 10(4): e0120025.

McGuckian, T.B., Cole, M.H., Chalkley, D., Jordet, G., & Pepping, G-J. (2019). Visual exploration when surrounded by affordances: Frequency of head movements is predictive of response speed. Ecological Psychology, 31, 30-48.

Michotte, A. (1963). The perception of causality. New York: Basic Books Publishers.

Morris, E.K. (2009). Behavior analysis and ecological psychology: Past, present, and future. A review of Harry Heft's 'Ecological psychology in context'. Journal of the Experimental Analysis of Behavior, 92, 275-304.

Stahlman, W. D. & Blaisdell, A. P. (2011a). Reward probability and the variability of foraging behavior in rats. International Journal of Comparative Psychology, 24, 168-176.

Stahlman, W. D. & Blaisdell, A. P. (2011b). The modulation of operant variation by the probability, magnitude, and delay of reinforcement. Learning and Motivation, 42, 221-236.

Stahlman, W. D., Roberts, S., & Blaisdell, A. P. (2010). Effect of reward probability on spatial and temporal variation. Journal of Experimental Psychology: Animal Behavior Processes, 36, 77-91.

Tolman, E.C. & Brunswik, E. (1935). The organism and the causal texture of the environment. Psychological Review, 42, 43-77.

Tonneau, F. (2011). Holt's realism: New reasons for behavior analysis. In E. Charles (Ed.), A new look at new realism. The psychology and philosophy of E.B. Holt (pp. 33-55). New

Brunswick: Transaction Publishers.

Wasserman, E.A. (1990). Detecting response-outcome relations: Toward an understanding of the causal texture of the environment. In G.H. Bower (Ed.). The psychology of learning and motivation: Advances of research and theory (Vol. 26). Academic Press.

Wasserman, E.A., Elek, S.M., Chatlosh, D.L., & Baker, A.G. (1993). Rating causal relations: Role of probability in judgments of response-outcome contingency. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19, 174-188.

Wasserman, E.A. & Neunaber, D.J. (1986). College students’ responding to and ratings of contingency relations: The role of temporal contiguity. Journal of the Experimental Analysis of Behavior, 46, 15-35.

Wasserman, E.A. & Shaklee, H. (1984). Judging response-outcome relations: The role of response-outcome contingency, outcome probability, and method of information presentation. Memory & Cognition, 12, 270-286.

Yu, Y. & Stoffregen, T.A. (2012). Postural and locomotor contributions to affordance perception. Journal of Motor Behavior, 44, 3015-311.