Russell M. Church

Scalar Timing in Memory

A recent report of ours’ proposed an information-processing account of temporal generalization. The account posited a clock process, which was the basic time measurement device, and working and reference memory for storing the output of the clock either temporarily or relatively permanently. Records of time intervals in working and reference memory were then compared using a binary decision process, which dictated responding or not responding. The analysis concentrated on a relativistic Weber’s law property of the data from temporal generalization, and the constraints this property imposed on sources of variance in the information-processing stages. Our purpose here is to summarize that work and generalize the model in two ways: First we consider several sources of variance operating simultaneously. The original analysis demonstrated that if only one source of variance is present, it must be a scalar source, that is, it must result in a variable memory for which variance increases with the square of the mean.’ In the generalized account proposed here, we will develop the conclusion that scalar sources dominate in some time ranges, while other sources may dominate in others. These ideas are then applied to two additional timing tasks with different characteristics.

Properties of the internal clock.

Evidence has been cited for the following properties of the parts of the psychological process used for timing intervals: The pacemaker has a mean rate that can be varied by drugs, diet, and stress. The switch has a latency to operate and it can be operated in various modes, such as run, stop, and reset. The accumulator times up, in absolute, arithmetic units. Working memory can be reset on command or, after lesions have been created in the fimbria fornix, when there is a gap in a signal. The transformation from the accumulator to reference memory is done with a multiplicative constant that is affected by drugs, lesions, and individual differences. The comparator uses a ratio between the value in the accumulator (or working memory) and reference memory. Finally, there must be multiple switch-accumulator modules to handle simultaneous temporal processing; and the psychological timing process may be used on some occasions and not on others.

Bisection of temporal intervals.

Eight rats were trained to make one response if a signal was shorter than a criterion duration and a different response if the signal was longer than the criterion. When exposed to intermediate durations, the rats bisected the interval at the geometric mean and the difference limen divided by the geometric mean was a constant. The rats learned new temporal discriminations more easily when the response maintained its relative, rather than its absolute, meaning. These data were interpreted in terms of a model of an internal clock that included a clock, a criterion, and a response rule.

Hippocampus, time, and memory.

Five experiments were conducted to determine the effects of hippocampal damage on timing and the memory for temporal events. In Experiments 1-3, rats were trained to discriminate between auditory signals that differed in both duration (2 or 8 s) and rate (2 or 16 cycles/s). Half of the rats were trained to discriminate duration, and half were trained to discriminate rate. After rats acquired the relevant discrimination, signals with intermediate durations and rates were presented to obtain psychophysical functions that related signal duration and/or rate to response choice. Rats then received either lesions of the fimbria-fornix or control operations. Postoperatively, the accuracy of duration and rate discriminations as measured by the difference limen (DL) was unaffected by the lesion, but the point of subjective equality (PSE) was shifted to a shorter duration and a slower rate by the lesion in Experiment 1. Both rats with lesions and rats with control operations showed cross-modal transfer of duration and rate from the auditory signals used in training to visual signals used in testing in Experiment 2. A 5-s delay was imposed between the end of a signal and the opportunity to respond in Experiment 3. The delay served as a retention interval for the rats trained in the rate discrimination, and the rats with fimbria-fornix lesions were selectively impaired by the addition of the delay as measured by an increase in the DL. The delay did not serve as a retention interval for rats trained in the duration discrimination because they were able to continue timing through the delay. A peak procedure was employed in Experiment 4. The maximum response rate of control rats was approximately at the time of scheduled reinforcement (20 s), but the maximum response rate of rats with fimbria-fornix lesions was reliably earlier than the time of scheduled reinforcement. When a 5-s gap was imposed in the signal, control rats summed the signal durations before and after the gap, whereas rats with fimbria-fornix lesions showed no retention of the signal duration prior to the gap. Experiment 5 continued the testing of the rats used in Experiments 1-4 and showed that rats with lesions had an impairment in a test of spatial working memory in an eight-arm radial maze. Taken together, these results demonstrate that a fimbria-fornix lesion interferes with temporal and spatial working memory, reduces the remembered time of reinforcement stored in reference memory, and has no effect on the animals sensitivity to stimulus duration.

Application of scalar timing theory to individual trials.

Our purpose was to infer the characteristics of the internal clock, temporal memory, and decision processes involved in temporal generalization behavior on the basis of the analysis of individual trials. Three groups of 10 rats each were trained on a peak procedure with reinforcement at 15, 30, or 60 s, with several nonfood trial durations. On nonfood trials, the mean response rate gradually increased to a maximum near the time that reinforcement sometimes occurred and then gradually decreased. Individual trials were characterized by a period of high response rate, preceded and followed by a low response rate. The covariance pattern among measures of the temporal characteristics of the high response rate (start, stop, middle, and spread) supported a parallel, scalar timing model in which animals used on each trial a single sample from memory of the time of reinforcement and separate response thresholds to decide when to start and stop responding. An alternative model, the quasi-serial model (J. Gibbon & R. M. Church, 1992), was not consistent with the obtained relationships between covariances or with the scalar property seen across different nonfood signal durations.

Alternative representations of time, number, and rate.

Three facts of time perception are described based upon a temporal generalization task for rats (the peak procedure) in which food reinforcement is delivered on half the trials following the first lever-press response after some fixed interval after signal onset. (1) The mean response rate as a function of time is a smooth, slightly asymmetric, function with a maximum near the time of reinforcement; (2) the response rate on individual trials is characterized by an abrupt change from a state of low responding to a state of high responding and finally another state of low responding (break-run-break pattern); and (3) the mean response rate in 12-s and 20-s peak procedures is similar when plotted against time relative to the time of reinforcement (superposition). An information-processing version of scalar timing theory is described and compared to an alternative connectionist version of scalar timing theory that involves multiple oscillators and an autoassociation network. Psychological, mathematical and biological descriptions of the two versions are described and some possible extensions of the connectionist version are proposed to deal with perception of number, rate, and spatial orientation.

Representation of time

Memory representation for time was studied in two settings. First, an analysis of timing in a laboratory analog of a foraging situation revealed that departure times from a patchy resource followed a Weber Law-like property implied by scalar timing. A trial-by-trial analysis was then pursued in a similar but more structured experimental paradigm, the Peak procedure. Study of covariance structures in the data implicated scalar variance in the memory for time as well as in the decision process, but the correlation pattern ruled out multiple access to memory within a trial.

ATTENTION AND THE FRONTAL CORTEX AS EXAMINED BY SIMULTANEOUS TEMPORAL PROCESSING

The brain mechanisms involved in attention and memory were examined by testing rats in temporal discriminations designed to emphasize these cognitive processes. Normal rats were able to time each of two stimuli whether they were presented alone or together. Rats with lesions of the frontal cortex (FC) or nucleus basalis magnocellularis (NBM) were able to time each stimulus when it was presented alone, but not when it was presented together with another stimulus. Rather, these rats timed only the intruding stimulus and ignored the other, demonstrating a failure of divided attention. Rats with lesions of the fimbria-fornix (FF) or medial septal area (MSA) performed the divided attention task normally, but failed to remember the duration of a stimulus that had been terminated temporarily earlier in the trial, demonstrating a failure of working memory. These results provide another informative dissociation between the functions of the frontal and hippocampal systems, emphasizing frontal involvement in attention, and hippocampal involvement in working memory.

The differential effects of haloperidol and methamphetamine on time estimation in the rat

Forty rats were trained to make a left lever response if a signal (white noise) was 2.5s and to make a right lever response if the signal was 6.3s. When seven intermediate signal durations, to which responses were not reinforced, were randomly interspersed the probability of a right-lever (‘long’) response increased as a function of signal duration. Methamphetamine shifted this psychometric function leftward and decreased its slope: haloperidol also decreased the slope but shifted the function rightward. A combination of haloperidol and methamphetamine led to a function similar to the saline control function. The leftward shift probably reflects an increase in the speed of an internal clock, and the rightward shift probably reflects a decrease in its speed. Since methamphetamine releases several catecholamines, including dopamine, and haloperidol blocks dopamine receptors, it is plausible that the horizontal location of the psychometric function (the speed of the clock) is related to the effective level of dopamine.

Time left: linear versus logarithmic subjective time.

In two experiments, subjects were given a choice between a standard fixed interval to reinforcement and the time left to reinforcement in an elapsing comparison interval. In Experiment 1, rats were trained to respond on a comparison 60-sec fixed-interval schedule on one lever and a standard 30-sec fixed-interval schedule on a second lever. Then combined trials were given that began with the entry of the comparison 60-sec lever, followed by the standard 30-sec lever after 15, 30, or 45 sec. Rats preferred to respond on the standard lever when it entered early (at 15 sec), they preferred to respond on the comparison lever when the standard entered late (at 45 sec), and they were approximately indifferent between the two levers when the standard entered halfway through the comparison interval so that the remaining time to food was equal on both levers. In Experiment 2, pigeons were trained to choose between the time left to food in an elapsing comparison interval (C sec long) and a standard fixed interval one half as long (S = C/2) in a concurrent-chains paradigm. Birds came to choose the standard early and the comparison late in the trial interval. The indifference point was linearly related to the midpoint of the elapsing C interval at a variety of S,C pairs. The results of both experiments are consistent with a Scalar Timing theory in which subjective time is linear in real time and memory variance is scalar, and they are inconsistent with a logarithmic time scale.