Interval timing as an emergent learning property

Interval timing in operant conditioning is the learned covariation of a temporal dependent measure such as wait time with a temporal independent variable such as fixed-interval duration. The dominant theories of interval timing all incorporate an explicit internal clock, or "pacemaker," despite its lack of independent evidence. The authors propose an alternative, pacemaker-free view that demonstrates that temporal discrimination can be explained by using only 2 assumptions: (a) variation and selection of responses through competition between reinforced behavior and all other, elicited, behaviors and (b) modulation of the strength of response competition by the memory for recent reinforcement. The model departs radically from existing timing models: It shows that temporal learning can emerge from a simple dynamic process that lacks a periodic time reference such as a pacemaker.     

Duration estimation and the phonological loop: Articulatory suppression and irrelevant sounds

Clock-based theories of time estimation propose that clock pulses are accumulated in working memory. Although these theories do not constrain the form of the memory trace, evidence reported in the literature suggests that active manipulation of a verbal trace may be involved. Four experiments are reported in which participants reproduced or verbally estimated short durations (up to a few seconds) either in a single-task condition or in a condition with a phonological load. Experiments 1, 2 and 4 showed that both interval reproduction and verbal estimation were impaired under concurrent articulatory suppression in comparison to a timing only control condition. Neither irrelevant speech (Experiments 1-3) nor irrelevant tones and music (Experiment 3) impaired timing performance. These findings are taken to show that time estimation is mediated by phonological working memory and the involvement of an active articulatory rehearsal process.     

The role of executive functions in human prospective interval timing

Human timing is thought to be based on the output of an internal clock. Whilst the functioning of this clock is well documented, it is unclear which other cognitive resources may moderate timing. Brown (2006) and Rattat (2010) suggest that the central executive of working memory may be recruited during timing. However it seems likely that the fractionated executive component processes identified by Miyake et al. (2000) and Fisk and Sharp (2004) may differentially contribute to timing performance; further exploration of this was the aim of the present study. An interference paradigm was employed in which participants completed an interval production task, and tasks which have been shown to tap the four key executive component processes (shifting, inhibition, updating and access) under single and dual-task conditions. Comparison of single and dual-task performance indicated that timing always became more variable when concurrently performing a second task. Bidirectional interference only occurred between the interval production task and the memory updating task, implying that both tasks are competing for the same executive resource of updating. There was no evidence in the current study to suggest that switching, inhibition or access was involved in timing, however they may be recruited under more difficult task conditions.     

The Timing Effects of Accent Production in Periodic Finger-Tapping Sequences

When subjects are required to produce short sequences of equally paced finger taps and to accentuate one of the taps, the interval preceding the forceful tap is shortened and the one that immediately follows the accent is lengthened. Assuming that the tapping movements are triggered by an internal clock, one explanation attributes the rnistiming of the taps to central factors: The momentary rate of the clock is accelerated or decelerated as a function of motor preparation to, respectively, increase or decrease the movement force. This hypothesis predicts that the interresponse intervals measured between either tap movement onsets or movement terminations (taps) will show the same timing pattern. A second explanation for the observed interval effects is that the tapping movements are triggered by a regular internal clock but the timing of the successive taps is altered because the forceful movement is completed in less time than the other tap movements are. This "peripheral" hypothesis predicts regular timing of movement onsets but distorted timing of movement terminations. In the present study, the trajectories of the movements performed by subjects were recorded and the interresponse intervals were measured at the beginning and the end of the tapping movements. The results of Experiment 1 showed that neither model can fully explain the interval effects: The fast forceful movements were initiated with an additional delay that took into account the small execution time of these movements. Experiment 2 reproduced this finding and showed that the timing of the onset and contact intervals did not evolve with the repetition of trial blocks. Therefore, the assumption of an internal clock that would trigger the successive movements must be rejected. The results are discussed in the framework of a modified two-stage model in which the internal clock, instead of triggering the tapping movements, provides target time points at which the movements have to produce their meaningful effects, that is, contacts with the response key. The timing distortions are likely to reflect both peripheral and central components.     

The Timing Effects of Accent Production in Periodic Finger-Tapping Sequences

When subjects are required to produce short sequences of equally paced finger taps and to accentuate one of the taps, the interval preceding the forceful tap is shortened and the one that immediately follows the accent is lengthened. Assuming that the tapping movements are triggered by an internal clock, one explanation attributes the mistiming of the taps to central factors: The momentary rate of the clock is accelerated or decelerated as a function of motor preparation to, respectively, increase or decrease the movement force. This hypothesis predicts that the interre-sponse intervals measured between either tap movement onsets or movement terminations (taps) will show the same timing pattern. A second explanation for the observed interval effects is that the tapping movements are triggered by a regular internal clock but the timing of the successive taps is altered because the forceful movement is completed in less time than the other tap movements are. This “peripheral” hypothesis predicts regular timing of movement onsets but distorted timing of movement terminations. In the present study, the trajectories of the movements performed by subjects were recorded and the interresponse intervals were measured at the beginning and the end of the tapping movements. The results of Experiment 1 showed that neither model can fully explain the interval effects: The fast forceful movements were initiated with an additional delay that took into account the small execution time of these movements. Experiment 2 reproduced this finding and showed that the timing of the onset and contact intervals did not evolve with the repetition of trial blocks. Therefore, the assumption of an internal clock that would trigger the successive movements must be rejected. The results are discussed in the framework of a modified two-stage model in which the internal clock, instead of triggering the tapping movements, provides target time points at which the movements have to produce their meaningful effects, that is, contacts with the response key. The timing distortions are likely to reflect both peripheral and central components.     

Les effets de la modalité sensorielle sur la perception du temps

The subjective duration of an event can be influenced by the modality of the signal demarcating that event. For example, auditory signals are often judged as of longer duration than equivalent duration visual signals. Within the framework of pacemaker-accumulator models of timing, such modality effects raise the question of whether the internal clock is modality specific or amodal. The answer to this question is quite important for the development of cognitively and neurologically realistic models of timing and time perception. Here, we argue that the internal clock has both modality specific and amodal components. Specifically, we claim there is a common amodal pacemaker, but the switch-accumulator systems are modality specific. Moreover, we also posit that long-term memory representations of duration are stored amodally.     

Neuropsychology of timing and time perception

Interval timing in the range of milliseconds to minutes is affected in a variety of neurological and psychiatric populations involving disruption of the frontal cortex, hippocampus, basal ganglia, and cerebellum. Our understanding of these distortions in timing and time perception are aided by the analysis of the sources of variance attributable to clock, memory, decision, and motor-control processes. The conclusion is that the representation of time depends on the integration of multiple neural systems that can be fruitfully studied in selected patient populations.     

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.     

Analysis of Memory as a Feedforward Control Mechanism

The properties of memory as a feedforward control mechanism of perception and motion have been investigated by requiring Ss to project in active space-time an observed stimulus wave pattern. Memory error was measured under conditions in which the visual feedback of the memory response was delayed and interrupted (sampled) at five time magnitudes (0.0, 0.2, 0.4, 0.6, and 0.8 sec). In addition, memory performance was measured under conditions of temporal pacing by an auditory clock and no such pacing. Results confirmed the hypotheses that memory error in projecting an observed stimulus target on a space-time basis would be improved by time pacing and systematically degraded by variable magnitudes of feedback delay and interruption of the projected movement patterns. The results indicate that memory, as well as learning, may be organized on a spacetime basis and that the critical time factors are related to feedback-and feedforward-control timing in temporally spanning past response and experience through learning and in projecting such space-time control of acquisition in-memory.     

Un modèle neurobiologique de la perception et de l'estimation du temps

Frontal-striatal circuits provide an important neurobiological substrate for timing and time perception as well as for working memory. In this review, we outline recent theoretical and empirical work to suggest that interval timing and working memory rely not only on the same anatomic structures, but also on the same neural representation of a specific stimulus. In the striatal beat-frequency model, cortical neurons fire in an oscillatory fashion to form representations of stimuli, and striatal medium spiny neurons detect those patterns of cortical firing that occur co-incident to important temporal events. Information about stimulus identity can be extracted from the specific cortical networks that are involved in the representation, and information about duration can be extracted from the relative phase of neural firing. The properties derived from these neurobiological models fit well with the psychophysics of timing and time perception as well as with information-processing models that emphasize the importance of temporal coding in a variety of working-memory phenomena.     

Interval timing with gaps: gap ambiguity as an alternative to temporal decay

C. V. Buhusi, D. Perera, and W. H. Meck (2005) proposed a hypothesis of timing in rats to account for the results of experiments that have used the peak procedure with gaps. According to this hypothesis, the introduction of a gap causes the animal's memory for the pregap interval to passively decay (subjectively shorten) in direct proportion to the duration and salience of the gap. Thus, animals should pause with short, nonsalient gaps but should reset their clock with longer, salient gaps. The present authors suggest that the ambiguity of the gap (i.e., the similarity between the gap and the intertrial interval in both appearance and relative duration) causes the animal to actively reset the clock and prevents adequate assessments of the fate of timed intervals prior to the gap. Furthermore, when the intertrial interval is discriminable from the gap, the evidence suggests that timed intervals prior to the gap are not lost but are retained in memory.     

Temporal order in memory and interval timing: an interference analysis

The effect of varying load in memory tasks performed during a time interval production was examined. In a first experiment, increasing load in memory search for temporal order affected concurrent time production more strongly than varying load in a spatial memory task of equivalent difficulty. This result suggests that timing uses some specific resources also required in processing temporal order in memory, resources that would not be used in the spatial memory task. A second experiment showed that the interference between time production and memory search involving temporal order was stronger when, during the timing task, a decision was made on the temporal position of a memory item, than when information on temporal order was retained throughout the interval to be produced. These results underscore the importance of considering the specific resources and processes involved when the interference between timing and concurrent non-temporal tasks is analyzed.     

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.     

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.     

Time, trace, memory

Objections to a trace hypothesis for interval timing do not apply to the multiple-time-scale (MTS) theory, which incorporates a dynamic trace tuned by the system history and can easily accommodate interval timing over a 1,000:1 range. The MTS model can also account for Weber's law as well as systematic deviations from it. Contrary to our critics, we contend that patterns of variance in interval timing experiments are not fully described by scalar expectancy theory, and that attempting to understand timing by assigning variance to different elements of a flexible model that lacks inductive support is a flawed strategy, because the attempt may be successful even if the model is wrong. We further argue that biological plausibility is an unreliable guide to the development of behavioral theory, that prediction is not the same as test, that induction should precede deduction, and that a rat is not a clock.     

Shared timing variability in eye and finger movements increases with interval duration: Support for a distributed timing system below and above one second

The origins of the ability to produce action at will at the hundreds of millisecond to second range remain poorly understood. A central issue is whether such timing is governed by one mechanism or by several different mechanisms, possibly invoked by different effectors used to perform the timing task. If two effectors invoke similar timing mechanisms, then they should both produce similar variability increase with interval duration (interonset interval) and thus adhere to Weber's law (increasing linearly with the duration of the interval to be timed). Additionally, if both effectors invoke the same timing mechanism, the variability of the effectors should be highly correlated across participants. To test these possibilities, we assessed the behavioural characteristics across fingers and eyes as effectors and compared the timing variability between and within them as a function of the interval to be produced (interresponse interval). Sixty participants produced isochronous intervals from 524 to 1431?ms with their fingers and their eyes. High correlations within each effector indicated consistent performance within participants. Consistent with a single mechanism, temporal variability in both fingers and eyes followed Weber's law, and significant correlations between eye and finger variability were found for several intervals. These results can support neither the single clock nor the multiple clock hypotheses but instead suggest a partially overlapping distributed timing system.     

标量计时模型的影响因素及发展

标量计时模型为人类时间知觉的研究提供了理论框架和研究范式, 它采用信息加工的观点, 包含时钟、记忆和决策三个阶段。时间二分任务是在标量计时模型的框架下研究时间知觉和加工的理想范式。它要求被试对时距进行与标量计时模型相对应的多阶段操作, 包含了时间知觉所涉及的各个过程, 能有效测量主观时距和时间敏感性的变化。通过这个范式, 研究者发现, 除了任务参数, 年龄和疾病都会影响人的主观时距和/或时间敏感性。这些时间二分任务的实验结果促进了标量计时模型的发展, 最近提出的两阶段决策模型和差别模型分别以不同的方式对标量计时模型进行了修正, 并解释了参数设置的影响和计时的个体差异。     

Timing of multiple overlapping intervals: how many clocks do we have?

Humans perceive and reproduce short intervals of time (e.g. 1-60 s) relatively accurately, and are capable of timing multiple overlapping intervals if these intervals are presented in different modalities [e.g., Rousseau, L., & Rousseau, R. (1996). Stop-reaction time and the internal clock. Perception and Psychophysics, 58(3), 434-448]. Tracking multiple intervals can be explained either by assuming multiple internal clocks or by strategic arithmetic using a single clock. The underlying timescale (linear or nonlinear) qualitatively influences the predictions derived from these accounts, as assuming a nonlinear timescale introduces systematic errors in added or subtracted intervals. Here, we present two experiments that provide support for a single clock combined with a nonlinear underlying timescale. When two equal but partly overlapping time intervals had to be estimated, the second estimate was positively correlated with the stimulus onset asynchrony. This effect was also found in a second experiment with unequal intervals that showed evidence of subtraction of intervals. The findings were supported by computational models implemented in a previously validated account of interval timing [Taatgen, N. A., Van Rijn, H., & Anderson, J. R. (2007). An integrated theory of prospective time interval estimation: The role of cognition, attention and learning. Psychological Review, 114(3), 577-598].     

On the Relation Between Time Perception and the Timing of Motor Action: Evidence for a Temporal Oscillator Controlling the Timing of Movement

Studies of time estimation have provided evidence that human time perception is determined by an internal clock containing a temporal oscillator and have also provided estimates of the frequency of this oscillator (Treisman, Faulkner, Naish, & Brogan, 1992; Treisman & Brogan, 1992). These estimates were based on the observation that when the intervals to be estimated are accompanied by auditory clicks that recur at certain critical rates, perturbations in time estimation occur. To test the hypothesis that the mechanisms that underlie the perception of time and those that control the timing of motor performance are similar, analogous experiments were performed on motor timing, with the object of seeing whether evidence for a clock would be obtained and if so whether its properties resemble those of the time perception clock. The prediction was made that perturbations in motor timing would be seen at the same or similar critical auditory click rates. The experiments examined choice reaction time and typing. The results support the hypothesis that a temporal oscillator paces motor performance and that this oscillator is similar to the oscillator underlying time perception. They also provide an estimate of the characteristic frequency of the oscillator.     

Single-trace fragility theory of memory dynamics

In single-trace fragility theory, forgetting is produced by two factors, time and interference. Memory traces are assumed to have two partially coupled dynamic properties, strength and fragility. Strength determines the probability of correct recall and recognition, while fragility determines the susceptibility of the trace to the time-decay process but not to the interference process. Consolidation is assumed to be a continual reduction in the fragility of the memory trace rather than any change in strength or availability. Decreasing fragility accounts for the continually decreasing forgetting rate, the temporal character of retrograde amnesia and recovery therefrom, and the type of internal clock necessary for nonassociative recency judgments. Data are presented to indicate that interference is independent of the interval between original and interpolated learning, that nonassociative recency discriminability approaches a limit at about 30 min, and that the decay rate of long-term retention in amnesic patients is the same as in normal Ss.