Scalar properties in animal timing: Conformity and violations

The article reviews data from animal subjects on a range of timing tasks (including fixed-interval and temporal differentiation schedules, stimulus timing, aversive conditioning, and Pavlovian methods) with respect to conformity to the two scalar properties of timing behaviour: mean accuracy and scalar (Weberian) variance. Systematic deviations were found in data from temporal differentiation schedules, timing of very short (<100 ms) or very long (>100 s) durations, effects of “task difficulty”, and some special cases where circadian and interval timing seemed to interact, or where some specific durations seemed to be timed more precisely than others. Theoretical reconciliation of some of these deviations with underlying scalar timing can be achieved, but a number of problematical cases remain unexplained.     

Scalar properties in human timing: Conformity and violations

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.     

Scalar properties in human timing: conformity and violations

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.     

Scalar timing without reference memory? Episodic temporal generalization and bisection in humans

Three experiments tested whether the scalar property of timing could occur when humans timed short durations under conditions in which it was unlikely that they developed reference memories of temporal "standards". Experiment 1 used an episodic version of a temporal generalization task where judgements were made of the potential equality of two durations presented on each trial. Unknown to the subject, one of these was always 200, 400, 600, or 800 ms, and the other was of variable duration. Temporal generalization gradients showed the scalar property of superimposition at standard values greater than 200 ms. Experiment 2 used a variant of the "roving bisection" method invented by Rodriguez-Girones and Kacelnik (1998) modified so that the scalar property of timing could be observed empirically. Data from bisection with short/long standard pairs of 100/400, 200/800, and 300/1,200 ms showed nearly perfect scalar-type superimposition. Experiment 3 again used episodic temporal generalization, but durations were never repeated and came from three distinct time ranges. Superimposition was found across these ranges except for the shortest visual stimuli timed. The data suggested that scalar timing could occur in humans in conditions where the formation of reference memories of temporal standards was highly improbable.     

Pure timing in temporal differentiation

Temporal control appears to depend on whether the critical durations are those of stimuli or those of responses. Stimulus timing (temporal discrimination) supports Weber's law, whereas response timing (temporal differentiation) indicates decreasing relative sensitivity with longer time intervals. The two types of procedure also yield different conclusions in scaling experiments designed to study the functional midpoint of two or more durations (temporal bisection procedures). In addition, the fractional-exponent power relation between emitted and required duration usually found with animals in differentiation experiments conflicts with deductions from formal analyses. The experiment reported here derived from considering differentiation arrangements as schedules of reinforcement. When analyzed from this perspective, the procedures are tandem schedules involving a required pause followed by a response, and it is the pause alone that involves temporal control. A choice procedure separated timing from responding, and enabled observations of pause timing in isolation. Pure temporal control in differentiation consisted of linear overestimation of the standard duration, and Weber's law described sensitivity. These results indicate that the two problems, the fractional-exponent power relations and the apparently different nature of sensitivity in differentiation and discrimination, disappear when temporal control is observed alone in differentiation.     

Distressed Mothers and Their Infants Use a Less Efficient Timing Mechanism in Creating Expectancies of Each Other’s Looking Patterns

The prediction of events and the creation of expectancies about their time course is a crucial aspect of an infant's mental life, but temporal mechanisms underlying these predictions are obscure. Scalar timing, in which the ratio of mean durations to their standard deviations is held constant, enables a person to use an estimate of the mean for its standard deviation. It is one efficient mechanism that may facilitate predictability and the creation of expectancies in mother-infant interaction. We illustrate this mechanism with the dyadic gaze rhythm of mother and infant looking at and looking away from each other's faces. Two groups of Hi- and Lo-Distress mothers were created using self-reported depression, anxiety, self-criticism and childhood experiences. Lo-Distress infants (controls) used scalar timing 100% of the time, about double that of Hi-Distress infants. Lo-Distress mothers used scalar timing about nine times as much as Hi-Distress mothers. The diminished use of scalar timing patterns in Hi-Distress mothers and infants may make the anticipation of each other's gaze patterns more difficult for both partners.     

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.     

短时距估计中的标量特性

使用单任务研究程序,采用预期式研究范式和再现时距的研究方法,从心理物理学的视角,通过三个实验系统地考查了人类短时距估计的标量特性、变异源、时距估计中的转换点和韦伯函数的形态等问题。结果表明,刺激物的运动、变化、速度和物理时距是被试进行短时距估计的重要变异源;被试在实验中表现出高估较短时距和低估较长时距的倾向,时距估计的转换点为11.1s;计时过程中得到的韦伯函数是个分段连续函数, 韦伯函数的拐点有两个12s和21s,这两点与本研究得到的时距估计转换点具有部分一致性     

“One-thousand<Emphasis Type="Italic">one</Emphasis> … one-thousand<Emphasis Type="Italic">two</Emphasis> …”: Chronometric counting violates the scalar property in interval timing

Medical College of Wisconsin, Milwaukee, Wisconsin Weber’s law applied to interval timing is called thescalar property. A hallmark of timing in the secondsto-minutes range, the scalar property is characterized by proportionality between the standard deviation of a response distribution and the duration being timed. In this temporal reproduction study, we assessed whether the scalar property was upheld when participants chronometrically counted three visually presented durations (8, 16, and 24 sec) as compared with explicitly timing durations without counting. Accuracy for timing and accuracy for counting were similar. However, whereas timing variability showed the scalar property, counting variability did not. Counting variability across intervals was accurately modeled by summing a random variable representing an individual count. A second experiment replicated the first and demonstrated that task differences were not due to presentation order or practice effects. The distinct psychophysical properties of counting and timing behaviors argue for greater attention to participant strategies in timing studies.     

Interval production as an analogue of the peak procedure: Evidence for similarity of human and animal timing processes

Humans subjects repeatedly produced durations ranging from 0.5 to 1.3 sec, with each trial being followed by accurate feedback as to the time produced. An analogy was drawn between this production task and the peak procedure, a technique used to examine temporal control in rats which typically produces data conforming to scalar timing theory. Human production data were analysed in a way similar to that employed in peak procedure experiments. Using non-linear regression, it was found that the peak of relative frequency distributions of times produced varied accurately with the target time, and that the coefficient of variation of fitted curves was approximately constant as peak location and target time varied. In both these respects human production data were very similar to those collected from rats in peak procedure experiments, and thus compatible with scalar timing and Weber's law. Weber fractions obtained in this experiment were about half the value of those produced by rats in peak procedure studies, but only slightly lower than those obtained from animals in some other experimental situations.     

Temporal Bisection in Humans with Longer Stimulus Durations

Normal adults were tested in eight temporal bisection conditions, using 500-Hz tones as stimuli. Stimulus lengths matched, or overlapped with, durations normally used in bisection experiments with animals, and chronometric counting was prevented by using a concurrent digit-shadowing task. Four experimental groups were used to investigate any effects of stimulus spacing, and stimuli were logarithmically or linearly spaced between standard 'short' and 'long' durations of 1 and 4, or 2 and 8 sec. A slight leftward shift of the psychophysical function was found in the logarithmic spacing condition, relative to linear spacing. Four other groups tested the conjecture that the ratio of the short and long standards might play some role in determining the location of the bisection point, and conditions with long/short ratios of 2: 1 and 5: 1 were used. In all cases the bisection point was close to the arithmetic mean of the short and long standards, rather than the geometric mean, as in animal studies. Overall, however, smaller long/short ratios (which may indicate more difficult temporal discriminations) produced more sensitive timing. When the long/short ratio was held constant, however, data showed nearly perfect superimposition, indicating conformity to scalar timing. In general, results were similar to those from experiments with humans that used much shorter durations, indicating the animal/human differences in bisection do not depend on the absolute lengths of the stimuli used.     

More consistent,yet less sensitive: Interval timing in autism spectrum disorders

Even though phenomenological observations and anecdotal reports suggest atypical time processing in individuals with an autism spectrum disorder (ASD), very few psychophysical studies have investigated interval timing, and the obtained results are contradictory. The present study aimed to clarify which timing processes function atypically in ASD and whether they are related to the ASD diagnostic profile. Visual, auditory, and cross-modal interval timing was assessed in 18 individuals with ASD using a repeated standards version of the temporal generalization task. The use of two different standard durations (600 and 1,000 ms) allowed for an assessment of the scalar property of interval timing in ASD, a fundamental characteristic of interval timing. The ASD group showed clearer adherence to the scalar property of interval timing than the control group. In addition, both groups showed the normal effect that auditory stimuli had longer subjective durations than visual ones. Yet, signal detection analysis showed that the sensitivity of temporal discrimination was reduced in the ASD group across modalities, in particular for auditory standards. Moreover, response criteria in the ASD group were related to symptom strength in the communication domain. The findings suggest that temporal intervals are fundamentally processed in the same way in ASD and TD, but with reduced sensitivity for temporal interval differences in ASD. Individuals with ASD may show a more conservative response strategy due to generally decreased sensitivity for the perception of time intervals.     

Temporal reproduction

A signal appeared for a certain time period. After the period elapsed, pigeons had to begin and complete a sequence of 15 responses in a time window ranging from the signal duration to 50% longer. Sessions involved as many as 10 different signal durations occurring in a random sequence. The times produced by pigeons often were in the same ranges as those that have been found with adult human subjects. The average times were described equally well as linear or power functions of signal duration. However, instead of the overestimation of durations usually found when animals have timed the duration of antecedent stimuli, the linear functions suggested that the pigeons underestimated the durations of their own behavior. The birds showing the strongest control when the conditions involved eight or 10 different duration requirements revealed the constant coefficients of variation that support Weber's law and scalar timing theory. Scalar timing in temporal differentiation appears to depend on non-ambiguous information about the duration required for reinforcement and on a high degree of sensitivity to the duration requirement.     

Scalar timing in temporal generalization in children with short and long stimulus durations.

This experiment investigated temporal generalization performance in children aged 3, 5, and 8 years by using auditory stimulus durations where the standard was 0.4 s or 4.0 s, and non-standard stimuli were spaced linearly around the standard. At all ages, generalization gradients superimposed well when plotted on the same relative scale, indicating conformity to scalar timing. Whatever the standard duration used, the principal developmental changes were the increasing steepness of the generalization gradient with increasing age and a shift from symmetrical gradients, in the 3- and 5-year-olds, to adult-like asymmetrical gradients in the 8-year-olds.     

Timing and classifying brief acoustic stimuli by songbirds and humans.

The durations of animals' brief vocalizations provide conspecifics with important recognition cues. In the present experiments, zebra finches and humans (trained musicians) were rewarded for responding after S+ (standard) auditory signals from 56 to 663 ms and not for responding after shorter or longer S- (comparison) durations from 10 to 3684 ms. With either a single standard (Experiment 1) or multiple standards (Experiment 2), both zebra finches and humans timed brief signals to about the same level of accuracy. The results were in qualitative agreement with predictions from scalar timing theory and its connectionist implementation in both experiments. The connectionist model provides a good quantitative account of temporal gradients with a single standard (Experiment 1) but not with multiple standards (Experiment 2).     

Temporal control of behavior and the power law

The performance of rats and pigeons under fixed-interval schedules was studied in two experiments. The duration of postreinforcement pause was a declining proportion of fixed-interval duration. For pigeons this was true both when the duration of the reinforcer was fixed and when it was increased in direct proportion to increases in fixed-interval duration; the longer reinforcer durations did, however, lengthen the postreinforcement pause at higher schedule values. A quantitative analysis of data from Experiments 1 and 2 and from other studies showed that fractional exponent power functions described the relationship between postreinforcement pause and fixed-interval value; similar functions have previously been observed in studies of temporal differentiation. It was concluded that power functions reflect a direct causal, rather than artifactual, relationship between performance and the temporal requirements of reinforcement schedules.     

Interference between auditory and visual duration judgements suggests a common code for time

Auditory stimuli usually have longer subjective durations than visual ones for the same real duration, although performance on many timing tasks is similar in form with different modalities. One suggestion is that auditory and visual stimuli are initially timed by different mechanisms, but later converted into some common duration code which is amodal. The present study investigated this using a temporal generalization interference paradigm. In test blocks, people decided whether comparison durations were or were not a 400-ms standard on average. Test blocks alternated with interference blocks where durations were systematically shorter or longer than in test blocks, and interference was found, in the direction of the durations in the interference blocks, even when the interfering blocks used stimuli in a different modality from the test block. This provides what may be the first direct experimental evidence for a “common code” for durations initially presented in different modalities at some level of the human timing system.     

Good vibrations: Human interval timing in the vibrotactile modality

This article reports a detailed examination of timing in the vibrotactile modality and comparison with that of visual and auditory modalities. Three experiments investigated human timing in the vibrotactile modality. In Experiment 1, a staircase threshold procedure with a standard duration of 1,000 ms revealed a difference threshold of 160.35 ms for vibrotactile stimuli, which was significantly higher than that for auditory stimuli (103.25 ms) but not significantly lower than that obtained for visual stimuli (196.76 ms). In Experiment 2, verbal estimation revealed a significant slope difference between vibrotactile and auditory timing, but not between vibrotactile and visual timing. That is, both vibrations and lights were judged as shorter than sounds, and this comparative difference was greater at longer durations than at shorter ones. In Experiment 3, performance on a temporal generalization task showed characteristics consistent with the predications of scalar expectancy theory (SET: Gibbon, 1977) with both mean accuracy and scalar variance exhibited. The results were modelled using the modified Church and Gibbon model (MCG; derived by Wearden, 1992, from Church & Gibbon 1982). The model was found to give an excellent fit to the data, and the parameter values obtained were compared with those for visual and auditory temporal generalization. The pattern of results suggest that timing in the vibrotactile modality conforms to SET and that the internal clock speed for vibrotactile stimuli is significantly slower than that for auditory stimuli, which is logically consistent with the significant differences in difference threshold that were obtained.     

Human performance on an analogue of an interval bisection task

Two experiments used normal adult human subjects in an analogue of a time interval bisection task frequently used with animals. All presented durations were defined by the time between two very brief clicks, and all durations were less than 1 sec, to avoid complications arising from chronometric counting. In Experiment 1 different groups of subjects received standard durations of either 0.2 and 0.8 or 0.1 and 0.9 sec and then classified a range of durations including these values in terms of their similarity to the standard short (0.2- or 0.1-sec) and long (0.8- or 0.9-sec) durations. The bisection point (defined as the duration classified as "long" on 50% of trials) was located at 0.43 sec in the 0.2-0.8 group, and at 0.46 sec in the 0.1-0.9 group. Experiment 2 replicated Experiment 1 using a within-subject procedure. The bisection point of both 0.2- and 0.8 sec and 0.1- and 0.9-sec durations was found to be 0.44 sec. Both experiments thus found the bisection point to be located at a duration just lower than the arithmetic mean of the standard short and long durations, rather than at the geometric mean, as in animal experiments. Some other performance measures, such as difference limen, and Weber ratio, were, however, of similar values to those found in bisection tasks with animals. A theoretical model assuming that humans bisect by taking the difference between a presented duration and the short and long standards, as well as having a bias to respond "long", fitted the data well. The model incorporated scalar representations of standard durations and thus illustrated a way in which the obtained results, although different from those found with animal subjects, could be reconciled with scalar timing theory.     

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.