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

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.     

A tuned-trace theory of interval-timing dynamics

Animals on interval schedules of reinforcement can rapidly adjust a temporal dependent variable, such as wait time, to changes in the prevailing interreinforcement interval. We describe data on the effects of impulse, step, sine-cyclic, and variable-interval schedules and show that they can be explained by a tuned-trace timing model with a one-back threshold-setting rule. The model can also explain steady-state timing properties such as proportional and Weber law timing and the effects of reinforcement magnitude. The model assumes that food reinforcers and other time markers have a decaying effect (trace) with properties that can be derived from the rate-sensitive property of habituation (the multiple-time-scale model). In timing experiments, response threshold is determined by the trace value at the time of the most recent reinforcement. The model provides a partial account for the learning of multiple intervals, but does not account for scalloping and other postpause features of responding on interval schedules and has some problems with square-wave schedules.     

The behavioral theory of timing: Reinforcer rate determines pacemaker rate

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.     

Timing for the absence of a stimulus: the gap paradigm reversed

Contrary to data showing sensitivity to nontemporal properties of timed signals, current theories of interval timing assume that animals can use the presence or absence of a signal as equally valid cues as long as duration is the most predictive feature. Consequently, the authors examined rats' behavior when timing the absence of a visual or auditory stimulus in trace conditioning and in a "reversed" gap procedure. Memory for timing was tested by presenting the stimulus as a reversed gap into its timed absence. Results suggest that in trace conditioning (Experiment 1), rats time for the absence of a stimulus by using its offset as a time marker. As in the standard gap procedure, the insertion of a reversed gap was expected to "stop" rats' internal clock. In contrast, a reversed gap of 1-, 5-, or 15-s duration "reset" the timing process in both trace conditioning (Experiment 2) and the reversed gap procedure (Experiment 3). A direct comparison of the standard and reversed gap procedures (Experiment 4) supported these findings. Results suggest that attentional mechanisms involving the salience or content of the gap might contribute to the response rule adopted in a gap procedure.     

Weber (slope) analyses of timing variability in tapping and drawing tasks

Timing variability in continuous drawing tasks has not been found to be correlated with timing variability in repetitive finger tapping in recent studies (S. D. Robertson et al., 1999; H. N. Zelaznik, R. M. C. Spencer, & R. B. Ivry, 2002). Furthermore, the central component of timing variability, as measured by the slope of the timing variance versus the square of the timed interval, differed for tapping and drawing tasks. On the basis of those results, the authors posited that timing in tapping is explicit and as such uses a central representation of the interval to be timed, whereas timing in drawing tasks is implicit, that is, the temporal component is an emergent property of the trajectory produced. The authors examined that hypothesis in the present study by determining the linear relationship between timing variance and squared duration for tapping, circle-drawing, and line-drawing tasks. Participants (N = 50) performed 1 of 5 tasks: finger tapping, line drawing in the x dimension, line drawing in the y dimension, continuous circle drawing timed in the x dimension, or continuous circle drawing timed in the y dimension. The slopes differed significantly between finger tapping, line drawing, and circle drawing, suggesting separable sources of timing variability. The slopes of the 2 circle-drawing tasks did not differ from one another, nor did the slopes of the 2 line-drawing tasks differ significantly, suggesting a shared timing process within those tasks. Those results are evidence of a high degree of specificity in timing processes.     

The choose-short effect and trace models of timing

The tuned-trace multiple-time-scale (MTS) theory of timing can account both for the puzzling choose-short effect in time-discrimination experiments and for the complementary choose-long effect. But it cannot easily explain why the choose-short effect seems to disappear when the intertrial and recall intervals are signaled by different stimuli. Do differential stimuli actually abolish the effect, or merely improve memory? If the latter, there are ways in which an expanded MTS theory might explain differential-context effects in terms of reduced interference. If the former, there are observational and experimental ways to determine whether differential context favors prospective encoding or some other nontemporal discrimination.     

The influence of dominant versus non-dominant hand on event and emergent motor timing

It has been hypothesized that timing in tapping utilizes event timing; a clock-like process, whereas timing in circle drawing is emergent. Three experiments examined timing in tapping and circle drawing by the dominant and non-dominant hand. Participants were right-hand dominant college aged males and females. The relationship between variance and the square of the timed interval (the Weber fraction), thought to capture clock-like timekeeping processes, was compared. Furthermore, timing variance was decomposed into a clock and a motor component. The slopes for timing were different for dominant hand tapping and circle drawing, but equal for non-dominant and dominant hand tapping. Negative lag one covariance, consistent with motor implementation variability, was found for non-dominant but not for dominant hand circle drawing (Experiment 1). Practice did not influence this relation (Experiment 2). A significant correlation for clock variability was found between non-dominant hand circle drawing and tapping (Experiment 3). Collectively, these findings indicate that event timing is shareable across hands while emergent timing is specific to an effector. Emergent timing does not appear to be obligatory for the non-dominant hand in circle drawing. We suggest that the use of emergent timing might depend upon the extensive practice experienced by a person's dominant hand.     

Mechanisms of perceptual timing: Beat-based or interval-based judgements?

Summary What is the nature of the human timing mechanism for perceptual judgements about short temporal intervals? One possibility is that initial periodic events, such as tones, establish internal beats which continue after the external events and serve as reference points for the perception of subsequent events. A second possibility is that the timer records the intervals produced by events. Later, the stored intervals can be reproduced or compared to other intervals. A study by Schulze (1978) provided evidence favoring beat-based timing. In contrast, our two experiments support an interval theory. The judgements of intervals between tones is not improved when the events are synchronized with internal beats established by the initial intervals. The conflict between the two sets of results may be resolved by the fact that an interval timer can recycle from one interval to the next, thus operating in a beat-like mode. However, a timer of this sort is just as accurate when comparing intervals that are off the beat.     

Timing of the CS-US Interval by Pigeons in Trace and Delay Autoshaping

Evidence for timing during Pavlovian trace and delay conditioning trials was sought by exposing pigeons to differentially cued trial durations of 18, 24, and 60 sec. For a delay group, one of three visual patterns (CSs) was presented on a key for the entire trial; for a trace group, each CS was 12 sec in duration, creating trace gaps of 6, 12, or 48 sec. Intertrial interval duration was 48 sec. The most informative data were provided by measures of time spent proximal to the CS (proximity). Stimulus control was evident in that proximity was inversely related to trial duration for both groups. Evidence for timing was obtained from the relation of relative proximity during each CS to relative elapsed trial time for individual birds. The obtained superposition of the three functions for each bird is consistent with a scalar timing process and implies that subjects learned the temporal relation between each CS and the unconditioned stimulus. Associative status of the CSs differed between groups and among CS-US intervals, as reflected in proximity data during a higher-order test in which the CSs served as reinforcers. The results are consistent with a two-dimensional model of Pavlovian conditioning according to which the associative strength accruing to a CS is orthogonal to the temporal information encoded for that stimulus.     

Weber (Slope) Analyses of Timing Variability in Tapping and Drawing Tasks

Timing variability in continuous drawing tasks has not been found to be correlated with timing variability in repetitive finger tapping in recent studies (S. D. Robertson et al., 1999; H. N. Zelaznik, R. M. C. Spencer, & R. B. Ivry, 2002). Furthermore, the central component of timing variability, as measured by the slope of the timing variance versus the square of the timed interval, differed for tapping and drawing tasks. On the basis of those results, the authors posited that timing in tapping is explicit and as such uses a central representation of the interval to be timed, whereas timing in drawing tasks is implicit, that is, the temporal component is an emergent property of the trajectory produced. The authors examined that hypothesis in the present study by determining the linear relationship between timing variance and squared duration for tapping, circle-drawing, and line-drawing tasks. Participants (N = 501 performed 1 of 5 tasks: finger tapping, line drawing in the x dimension, line drawing in the y dimension, continuous circle drawing timed in the x dimension, or continuous circle drawing timed in the y dimension. The slopes differed significantly between finger tapping, line drawing, and circle drawing, suggesting separable sources of timing variability. The slopes of the 2 circle-drawing tasks did not differ from one another, nor did the slopes of the 2 line-drawing tasks differ significantly, suggesting a shared timing process within those tasks. Those results are evidence of a high degree of specificity in timing processes.     

施动感研究的意向捆绑范式述评

施动感是自我意识的一个重要部分。意向捆绑即人的动作及动作的感觉结果两者的时间点主观上被感知为相互靠近的现象,为研究人类的施动感提供了一个重要的测量手段。本文综述意向捆绑的实验范式和认知机制,发现目前线索整合理论能最好的解释意向捆绑现象。意向捆绑的范式可以用于临床疾病和跨文化的研究。今后还应深入研究意向捆绑机制及意向捆绑与施动感的关系。     

Support for a theory of memory for event duration must distinguish between test-trial ambiguity and actual memory loss

Staddon and Higa's (1999) trace-strength theory of timing and memory for event duration can account for pigeons' bias to "choose short" when retention intervals are introduced and to "choose long" when, following training with a fixed retention interval, retention intervals are shortened. However, it does not account for the failure of pigeons to choose short when the intertrial interval is distinct from the retention interval. That finding suggests that stimulus generalization (or ambiguity) between the intertrial interval and the retention interval may result in an effect that has been attributed to memory loss. Such artifacts must be eliminated before a theory of memory for event duration can be adequately tested.     

Interval timing: memory, not a clock

Anticipation of periodic events signalled by a time marker, or interval timing, has been explained by a separate pacemaker-counter clock. However, recent research has added support to an older idea: that memory strength can act as a clock. The way that memory strength decreases with time can be inferred from the properties of habituation, and the underlying process also provides a unified explanation for proportional timing, the Weber-law property and several other properties of interval timing.     

THE BEHAVIORAL THEORY OF TIMING: TRANSITION ANALYSES

Gibbon and Church (1990, 1992) have recently confirmed an important, parameter-free prediction of the behavioral theory of timing (Killeen & Fetterman, 1988): The times of exiting from a bout of activity are positively correlated with the times of entrance to it. The correlations were slightly less than predicted, however, and the correlations between the start of an activity and the time spent engaged in that activity were negative, rather than zero. We adapted their serial model as an augmented (one-parameter) version of the behavioral theory, positing a lag between the receipt of a pulse from the pacemaker and transition into the next class of responses. The augmented version of the behavioral theory further improved the correspondence between the theory and the correlational data reported by Gibbon and Church. It also accounts for previously unpublished data from our laboratory derived from a new timing technique, the “peak choice” procedure. We show that the measured variance of movement times from one key to another closely approximates the estimated variance of transition times recovered from fits of the augmented model to the data. Such correspondence both attests to the correct identification of this source of variance and suggests ways to remove it, both from behavior and from our models of behavior.     

Counting processes in human timing

A subject reproducing a long duration, t, may time out either a single interval of duration t or a succession of n intervals, each of duration t/n. It is shown that a class of timing models obeying Weber’s law predicts the variance of reproductions of t to be a decreasing function of the number of subdivisions, n. In contrast, a second class of proportional variance models, which includes Creelman’s pulse counter model (1962), predicts no change in the variance as a function of n. Data are presented from a duration reproduction experiment in which subjects counted silently at a specified rate up to a given number and then responded. Several statistics involving the variance of the reproduced durations are shown to be predicted significantly better by the Weber’s law class of models than by the proportional variance class of models.     

Short-term memory in the pigeon with presentation time precisely controlled

Delayed matching-to-sample was studied in the pigeon using a procedure which precisely controlled the presentation time of the sample stimulus. Experiments 1 and 2 revealed that (a) accuracy of matching increased as a negatively accelerated function of presentation time, (b) accuracy declined when an interstimulus interval was introduced between successive presentations of the sample stimulus, and (c) the rate at which accurate matching was restored after an interstimulus interval was greatest when the initial presentation of the sample was short and the interval was long. It was concluded that a theory of STM based on the growth and decay of trace strength could account adequately for all of these findings. Experiment 3 studied trace interaction by presenting two sample stimuli first in succession and then simultaneously for choice. Predictions from trace competition theory about the specific lengths of presentation of these stimuli at which choice of the second stimulus should be 50% or deviate systematically below 50% were not supported. It appears that a recency mechanism in addition to competition is necessary to explain trace interaction effects.     

The power law and Weber's law in fixed-interval postreinforcement pausing: A scalar timing model

Some quantitative properties of the postreinforcement pause under fixed-interval schedules were simulated by a computer model embodying two processes, either of which could initiate responding in an interval. The first was a scalar timing system similar to that hypothesized to underlie behaviour on other tasks. The second was a process that initiated responding without regard to elapsed time in the interval. The model produced simulated pauses with a mean that varied as a power function of the interval value, and a standard deviation that appeared to grow as a linear function of the mean. Both these features were found in real data. The model also predicted several other features of pausing and responding under fixed-interval schedules and was also consistent with the results produced under some temporal differentiation contingencies. The model thus illustrated that behaviour that conformed to the power law could nevertheless be reconciled with scalar timing theory, if an additional non-timing process could also initiate responding.     

Suitability of the IBM XT,AT, and PS/2 keyboard,mouse, and game port as response devices in reaction time paradigms

The IBM PC keyboard is a convenient response panel for subjects in a reaction time task when the stimuli are presented on the same machine. However, there is a mean delay of about 10 msec and a random error of ±7.5 msec (±5 msec on the AT or PS/2). Our analyses show that for typical single response experimental situations, this added variance is acceptable. With mouse buttons, timing resulted in a delay of 31 ±2 msec if the mouse ball was steady but 45 ±15 msec if it was moving, and a 25-msec refractory period before a second response could be detected. With keys connected to the game port, timing was accurate to 1 msec. For timing the interval between two nearly simultaneous responses, only the game port method is recommended. Any research application should provide an external check on reaction timing accuracy and should correct any mean error.     

Detecting changes in simulated events II: Using variations of momentary time‐sampling to measure changes in duration events

The extent to which a greater proportion of small behavior changes could be detected with momentary time‐sampling (MTS) was evaluated by (a) combining various interval sizes of partial‐interval recording (PIR) with 20 s, 30 s, 1 min MTS and (b) using variable interval sizes of MTS that were based on means of 20 s and 1 min. For each targeted percentage, low, moderate, and high inter‐response times (IRTs) to event‐run ratios were compared with reversal designs to determine whether sensitivity increased with either variation of MTS. The results showed that (a) combinations of 30 s and 1 min MTS/PIR yielded increased sensitivity over MTS alone; however, the increased sensitivity was offset by an increased probability of generating false positives and (b) variable‐interval MTS produced comparable sensitivity to fixed‐interval MTS. Thus, none of the methods increased detection of small behavior changes (decreased false negatives) without also increasing false positives. Copyright © 2009 John Wiley & Sons, Ltd.     

The foreperiod effect revisited: conditioning as a basis for nonspecific preparation

The foreperiod (FP) is the interval between a warning stimulus and the imperative stimulus. It is a classical finding that both the duration and the intertrial variability of FP considerably affects response time. These effects are invariably attributed to the participant's state of nonspecific preparation at the moment the imperative stimulus is presented. In this article, we examined a proposal by Los, S. A. (1996) [On the origin of mixing costs: exploring information processing in pure and mixed blocks of trials. Acta Psychologica, 94, 145-188] that the real-time development of nonspecific preparation during FP relies on the same principle as trace conditioning. To this end, we adjusted the formal conditioning model developed by Machado, A. (1997) [Learning the temporal dynamics of behavior. Psychological Review, 104 (2), 241-265], and fitted this model to a representative data set we obtained from nine participants. Although the model accounted for only a moderate proportion of the variance, it accurately reproduced several key features of the data. We therefore concluded that the model is a promising first step toward a theory of nonspecific preparation.