Modeling choice across time: Effects of response–reinforcer discriminability

Abstract

This experiment asks whether timing is affected by animals' discrimination of response-reinforcer contingencies, and if so, how this effect can be understood. Six pigeons were trained on a procedure in which concurrent-schedule reinforcer ratios between left and right keys changed at 30 s after the last reinforcer. One stimulus signaled a reinforcer-ratio reversal from 9:1 to 1:9 on that key, and the other stimulus signaled the inverse reversal, with the key on which these stimuli occurred randomized. Across conditions, the physical difference between the stimuli signaling the two responses was varied and the directional changes in the reinforcer ratio signaled by each stimulus were reversed. Choice changed appropriately across time when the two stimuli were discriminable, and points of subjective equality fell with decreasing stimulus difference. A model which assumed that reinforcers obtained in time bins were redistributed across other time bins according to ogivally changing standard deviations, and between response locations according to an ogivally changing redistribution measure, accounted well for the data. This model was shown to be preferable to one in which across-time redistributions were scalar, and across-location redistribution was constant. These results show the critical importance of stimulus-response-reinforcer discriminability to measures of timing.

The generalization‐across‐dimensions model applied to conditional temporal discrimination

“…The first concerns the parameters of the model. We found here that the standard deviation of temporal discrimination, σ s , increased linearly with blackout duration, which is inconsistent with Davison and Cowie's (2022) finding that it increased ogivally. A linear increase is consistent with scalar timing (Gibbon, 1977); an ogival increase is not.…”

“…Equation 3 describes the reallocation of reinforcers between response keys in a different way from the redistribution of reinforcers across time. However, the data from Davison et al (2020) suggested that reinforcers were redistributed between responses (in their case, saccadic latencies) rather than reallocated. Reallocation implies that all reinforcers lost from one response are allocated to the other response, whereas redistribution implies that reinforcers may be allocated to nonmeasured locations.…”

“…In the general case, if m t is some function of time since the marker event, the model used by Cowie and Davison (2020) and Davison and Cowie (2022) to predict log response ratio (log[B 1t /B 2t ]) at each time bin t of n total time bins was…”

“…Over this period, the specific quantitative models used to understand behavior have evolved in the face of new empirical evidence (for the major theoretical developments, see Cowie & Davison, 2020; Davison & Cowie, 2022; Davison & Jenkins, 1985; Davison & Nevin, 1999; Davison & Tustin, 1978). Rather than detailing this history, here we focus on the latest iteration of the model as offered by Cowie and Davison (2020) and by Davison and Cowie (2022).…”

Divided stimulus control depends on differential and nondifferential reinforcement: Testing a quantitative model

“…Control by arranged contingencies is stronger when the stimuli signaling or the response alternatives associated with those contingencies are more discriminable (see Davison & Nevin, 1999, for reviews). For example, choice is more sensitive to changes in reinforcer ratios when the stimuli associated with each alternative are more disparate (e.g., Alsop & Davison, 1991, 1992Davison & Jenkins, 1985;Godfrey & Davison, 1998;Miller et al, 1980), and likewise conditional-discrimination performance is better when correct and incorrect responses are more disparate (e.g., Davison & Cowie, 2022;Eckerman, 1970;Godfrey & Davison, 1998;Jones, 2003). Based on this research, discrimination of-and thus control by-reinforcer contingencies should be stronger when the dimension to report was signaled in Phase 2 than when it was unsignaled in Phase 1.…”