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Time and memory: towards a pacemaker-free theory of interval timing

Profile image of John StaddonJohn Staddon

1999, Journal of The Experimental Analysis of Behavior

https://doi.org/10.1901/JEAB.1999.71-215
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Abstract

A popular view of interval timing in animals is that it is driven by a discrete pacemaker-accumulator mechanism that yields a linear scale for encoded time. But these mechanisms are fundamentally at odds with the Weber law property of interval timing, and experiments that support linear encoded time can be interpreted in other ways. We argue that the dominant pacemaker-accumulator theory, scalar expectancy theory (SET), fails to explain some basic properties of operant behavior on interval-timing procedures and can only accommodate a number of discrepancies by modifications and elaborations that raise questions about the entire theory. We propose an alternative that is based on principles of memory dynamics derived from the multiple-time-scale (MTS) model of habituation. The MTS timing model can account for data from a wide variety of time-related experiments: proportional and Weber law temporal discrimination, transient as well as persistent effects of reinforcement omission and reinforcement magnitude, bisection, the discrimination of relative as well as absolute duration, and the choose-short effect and its analogue in number-discrimination experiments. Resemblances between timing and counting are an automatic consequence of the model. We also argue that the transient and persistent effects of drugs on time estimates can be interpreted as well within MTS theory as in SET. Recent real-time physiological data conform in surprising detail to the assumptions of the MTS habituation model. Comparisons between the two views suggest a number of novel experiments.

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Bizo, L. A., & White, K. G. (1994). Pacemaker rate in the behavioral theory of timing. Journal of Experimental Psychology: Animal Behavior Processes, 20, 308-321.
Lewis A Bizo

Journal of Experimental Psychology: Animal Behavior Processes, 1994

The assumption by the behavioral theory of timing that pacemaker rate is proportional to reinforcer density was tested in 2 experiments. Pigeons discriminated between the 1st and 2nd halves of a 50-s trial. Responses on a left key were reinforced at variable intervals for the first 25 s of the trial, and right-key responses were reinforced at variable intervals during the second 25 s. In Experiment 1, overall reinforcement rate was varied by manipulating the intertrial interval (ITI) duration. Pacemaker rate, estimated by fitting predictions to psychometric functions, was an inverse function of ITI. In Experiment 2, reinforcer duration was manipulated as a means of altering reinforcer density. Pacemaker rate was found to be directly related to reinforcer duration. The present results support the assumption that pacemaker rate is determined by reinforcer density.

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Bizo, L. A., & White, K. G. (1995). Reinforcement context and pacemaker rate in the behavioral theory of timing. Animal Learning & Behavior, 23, 376-382.
Lewis A Bizo

Animal Learning & Behavior, 1995

In the present experiment, an attempt was made to extend the base of evidence for the assumption of the behavioral theory of timing that pacemaker rate is determined by reinforcement rate. Pigeons discriminated the first half from the second half of a 50-sec trial in a free-operant psy-chophysical procedure. Left-key responding was reinforced at variable intervals during the first 25 sec, and right-key responding was reinforced at variable intervals during the second 25 sec. The rate of "extraneous" reinforcers delivered at variable intervals following responses to a center key was manipulated independently of performance in the temporal discrimination. Quantitative estimates of pacemaker rate were not directly proportional to extraneous rate of reinforcement, whether extraneous reinforcers were available during the intertrial interval, the entire session, or the trial only. Instead, estimates of pacemaker rate were inversely related to the rate of extraneous reinforcement , which suggests that pacemaker rate is determined by the ratio of the rate of reinforcement for the timing response relative to other sources of reinforcement.

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The behavioral theory of timing: Reinforcer rate determines pacemaker rate
Lewis A Bizo

Journal of the Experimental Analysis of Behavior, 1994

In the behavioral theory of timing, pulses from a hypothetical Poisson pacemaker produce transitions between states that are correlated with adjunctive behavior. The adjunctive behavior serves as a discriminative stimulus for temporal discriminations. The present experiments tested the assumption that the average interpulse time of the pacemaker is proportional to interreinforcer interval. Responses on a left key were reinforced at variable intervals for the first 25 s since the beginning of a 50-s trial, and right-key responses were reinforced at variable intervals during the second 25 s. Psychometric functions relating proportion of right-key responses to time since trial onset, in 5-s intervals across the 50-s trial, were sigmoidal in form. Average interpulse times derived by fitting quantitative predictions from the behavioral theory of timing to obtained psychometric functions decreased when the interreinforcer interval was decreased and increased when the interreinforcer interval was increased, as predicted by the theory. In a second experiment, average interpulse times estimated from trials without reinforcement followed global changes in interreinforcer interval, as predicted by the theory. Changes in temporal discrimination as a function of interreinforcer interval were therefore not influenced by the discrimination of reinforcer occurrence. The present data support the assumption of the behavioral theory of timing that interpulse time is determined by interreinforcer interval. Key words: timing, temporal discrimination, behavioral theory of timing, psychometric function, interreinforcer interval, variable-interval schedules, key peck, pigeon This research was supported by grants from the New Zealand University Grants Committee and Otago University to K. G. White and by an Otago Postgraduate Award to L. A. Bizo. A table of absolute response and reinforcer frequencies can be obtained from the authors. The authors thank John Wixted for writing the nonlinear least squares regression procedure and Peter Killeen for suggesting the analysis in Equation 4 and Figure 4 and many helpful comments. The authors also thank Neroli Harris and Barry Dingwall and his team for technical assistance and the lab group for their help during the experiments. Reprints may be obtained from either author,

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Interval Timing Behavior: Comparative and Integrative Approaches
Fuat Balci

International Journal of Comparative Psychology, 2015

The ability of animals to keep track of, remember, and act upon short time intervals has received growing scientific attention attested by the increasing number of papers published and scientific activities organized in this area of research. Arguably, one of the driving forces behind this dynamic is the fact that interval timing captures a fundamental currency, constituent of many derived quantities of critical biological significance. Thus, temporal information processing presumably interacts with many other processes that support the adaptiveness of organisms in their environment by operating on variables that are derived from time intervals.

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Bizo, L. A., & White, K. G. (1994). Behavioral theory of timing: Reinforcement rate determines pacemaker rate. Journal of the Experimental Analysis of Behavior, 61, 19-33.
Lewis A Bizo

Journal of the Experimental Analysis of Behavior, 1994

In the behavioral theory of timing, pulses from a hypothetical Poisson pacemaker produce transitions between states that are correlated with adjunctive behavior. The adjunctive behavior serves as a discriminative stimulus for temporal discriminations. The present experiments tested the assumption that the average interpulse time of the pacemaker is proportional to interreinforcer interval. Responses on a left key were reinforced at variable intervals for the first 25 s since the beginning of a 50‐s trial, and right‐key responses were reinforced at variable intervals during the second 25 s. Psychometric functions relating proportion of right‐key responses to time since trial onset, in 5‐s intervals across the 50‐s trial, were sigmoidal in form. Average interpulse times derived by fitting quantitative predictions from the behavioral theory of timing to obtained psychometric functions decreased when the interreinforcer interval was decreased and increased when the interreinforcer interval was increased, as predicted by the theory. In a second experiment, average interpulse times estimated from trials without reinforcement followed global changes in interreinforcer interval, as predicted by the theory. Changes in temporal discrimination as a function of interreinforcer interval were therefore not influenced by the discrimination of reinforcer occurrence. The present data support the assumption of the behavioral theory of timing that interpulse time is determined by interreinforcer interval.

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    Attention Perception & Psychophysics, 2001

    This article presents the results of three experiments on the discrimination of time intervals presented in sequences marked by brief visual signals. In Experiment 1A (continuous condition), the participants had to indicate whether, in a series of 2–4 intervals marked by 3–5 visual signals, the last interval was shorter or longer than the previous one(s). In Experiment 1B (discontinuous condition),

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    Scalar properties in human timing: Conformity and violations
    John Wearden

    The Quarterly Journal of Experimental Psychology, 2008

    Data from studies of timing in human participants were reviewed with respect to their conformity to the two scalar properties of timing: mean accuracy and the scalar property of variance. Results reviewed were taken from studies of temporal generalization, temporal bisection, discrimination methods, and "classical" timing tasks such as the reproduction, production, and verbal estimation of duration. Evidence for one or both scalar properties was found in many studies, including those using children and elderly participants, but systematic violations were sometimes noted. These violations occurred (a) when very short durations (,100 ms) were timed, (b) in situations in which timing tasks varying in difficulty were compared, (c) when classical timing tasks were employed, and (d) in situations where highly practised observers exhibited unusual patterns of variance. A later section attempted to reconcile some of these violations with an underlying scalar-consistent timing mechanism.

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    Interactions of numerical and temporal stimulus characteristics on the control of response location by brief flashes of light
    Peter Killeen

    Learning & Behavior, 2011

    Pigeons pecked on three keys, responses to one of which could be reinforced after 3 flashes of the houselight, to a second key after 6, and to a third key after 12. The flashes were arranged according to variable-interval schedules. Response allocation among the keys was a function of the number of flashes. When flashes were omitted, transitions occurred very late. Increasing flash duration produced a leftward shift in the transitions along a number axis. Increasing reinforcement probability produced a leftward shift, and decreasing reinforcement probability produced a rightward shift. Intermixing different flash rates within sessions separated allocations: Faster flash rates shifted the functions sooner in real time, but later in terms of flash count, and conversely for slower flash rates. A model of control by fading memories of number and time was proposed.

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    Interval timing
    John Staddon

    Nature Reviews Neuroscience, 2006

    The review of timing behaviour by Buhusi and Meck 1 misrepresents current understanding both of pacemaker-accumulator (PA) timing models and of behavioural research on interval timing in general. The article is not as balanced as it should have been, and the authors should have pointed out that the strongest evidence against PA models has always been theoretical/conceptual, behavioural and, to some extent, pharmacological, rather than physiological. The brain is sufficiently rich in processes to be at least compatible with a wide range of behavioural models. Therefore, existing physiological data do not clearly favour either PA models, or the coincidencedetection model Buhusi and Meck offer as an alternative, over other possibilities. We briefly review the theoretical, behavioural and pharmacological evidence that supports non-PA approaches to the interval timing problem.

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    Causing Students to Choose More Language Arts Work: Enhancing the Validity of the Additive Interspersal Procedure
    Christopher Skinner

    Journal of Behavioral Education, 2005

    Research on the additive interspersal procedure was extended by exposing seventh-grade students to curricula-based (e.g., educationally valid) language arts assignments. In Experiment I, each student was given a control language arts assignment containing 20 discrete target items and an experimental assignment containing 24 equivalent target items, plus eight interspersed briefer items. After working on both assignments for 10 minutes, significantly more students chose a new experimental assignment for homework. Individual analysis showed that 85% of the students preferred or chose the assignment associated with higher discrete task completion rates. In Experiment II, students completed both assignments. Results extended previous research by showing that even after expending more effort to complete the 20% more target items plus the additional interspersed items on the experimental assignments, significantly more students chose an experimental assignment for homework. Applied and theoretical implications are discussed along with limitations of the current study and directions for future research.

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