A temporal intermediate stimulus problem.

Pigeons discriminated the serial position of a target duration among a sequence of 3 stimulus durations; the specific duration sequences changed across trials. In different conditions, the target duration was the shortest, intermediate, or longest duration in the sequence. Conditions involved a series of transitions in which new duration sequences were added to the stimulus set, providing an assessment of transfer. Pigeons learned and transferred the discrimination when the target was the shortest or longest duration. When, however, the target was the intermediate duration, the birds had great difficulty learning the task and exhibited little transfer to novel sequences. These findings are similar to those observed with nontemporal stimuli in a classic discrimination task, the intermediate stimulus problem. They provide an extension of work on relational timing to a more complex situation.

Judging relative duration: the role of rule and instructional variables.

Humans compared 2 durations according to different rules. Some judged which duration lasted longer, some judged whether the duration ratio was less or greater than 3:1, and others judged according to a same-different rule. Under each condition, 1/2 of the participants had advance knowledge of the rule, whereas the others acquired the discrimination solely on the basis of informative feedback. Discrimination was affected by both factors. Same-different and ratio comparisons were less accurate than ordinal comparisons. Rule knowledge affected the ratio and same-different comparisons but did not affect judgment about which duration lasted longer. Debriefing of uninformed participants revealed that most guessed that the rule involved judging which duration lasted longer. These results highlight the role of linguistic variables in humans' relational comparisons of duration.

Dimensions of stimulus complexity.

Animal learning research has increasingly used complex stimuli that approximate natural objects, events, and locations, a trend that has accompanied a resurgence of interest in the role of cognitive factors in learning. Accounts of complex stimulus control have focused mainly on cognitive mechanisms and largely ignored the contribution of stimulus information to perception and memory for complex events. It is argued here that research on animal learning stands to benefit from a more detailed consideration of the stimulus and that James Gibson's stimulus-centered theory of perception serves as a useful framework for analyses of complex stimuli. Several issues in the field of animal learning and cognition are considered from the Gibsonian perspective on stimuli, including the fundamental problem of defining the effective stimulus.

Categorical scaling of time: implications for clock-counter models.

Pigeons partitioned time into three intervals. Responses to one key could be reinforced after a short time, to a second key after an intermediate time, and to a third key after a long time. The values of the short, intermediate, and long times and the proportion of trials ending with reinforcement were varied. Absolute and relative response rates on each key were an orderly function of time and showed approximately proportional changes with changes in the interval values, consistent with Weber's law, Gibbon's (1977) scalar expectancy theory, and Killeen and Fetterman's (1988) behavioral theory of timing (BeT). Standard deviations of the times at which subjects switched between successive keys increased more slowly within a condition than across conditions, as predicted by BeT. Increases and decreases in reinforcement probability produced both transient and longer lasting changes in timing behavior, once again, in accord with predictions of BeT.

Duration comparison: relative stimulus differences stimulus age, and stimulus predictiveness.

Under a psychophysical trials procedure, pigeons were presented with a red light of one duration followed by a green light of a second duration. Eight geometrically spaced base durations were paired with one of four shorter and four longer durations as the alternate member of a duration pair, with different pairs randomly intermixed. One choice was reinforced if red had lasted longer than green, and a second choice was reinforced if green had lasted longer. Performance was compared when all the base durations and their pair members were included (entire-range condition) or when only the four longest base durations and their comparison durations (restricted-range condition) were used. Discrimination sensitivity decreased for longer duration pairs under both conditions, supporting a memory-based account. Sensitivity was lower under the restricted-range condition. Under both conditions, a bias to report "green as longer" increased as the second green duration increased. Bias changed as a matching function of the green-duration predictiveness of the correct choice. The results are related to a quantitative model of timing and remembering proposed by Staddon.

Numerosity discrimination: both time and number matter.

Pigeons were trained on a psychophysical choice task to discriminate between 2 fixed ratios and tested with probe ratios intermediate to the training requirements. Absolute and relative ratio size were varied over conditions. In a final condition, subjects were transferred from the number-based discrimination to a time-based discrimination. The times taken to emit the ratios were recorded, and ratio value and ratio time were used to predict choice in a multiple regression analysis. Psychophysical analyses of the response number dimension suggested a scalar counting principle of numerosity discrimination, similar to that found with temporal dimensions. The multiple regression analysis indicated that both number and time contributed to the discrimination of ratio value. The results of the transfer test indicated individual differences in the degree to which responding was controlled by temporal versus numerical factors.

Discrimination of duration ratios by pigeons (Columba livia) and humans (Homo sapiens).

Humans (Homo sapiens) were trained on 2 versions of a 2-alternative, forced-choice procedure. First, subjects judged which of 2 successive stimulus durations was longer. Second, subjects judged whether the ratio of the 2 durations was less or greater than a criterion ratio (e.g., 2:1). Accuracy was significantly lower for the task in which the judgment was made according to the ratio of the 2 durations. This result is different than that obtained by Fetterman, Dreyfus, and Stubbs (1989), who trained pigeons (Columbia livia) on a similar pair of tasks and found that pigeons' performance was comparable for the 2 discriminations. Comparisons of the pigeon and human data suggest that humans were more accurate than pigeons when the judgment involved which duration was longer, but that accuracy was comparable for the ratio-based task.

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.

Changing rates of reinforcement perturbs the flow of time.

This experiment tested the hypothesis that changes in rate of reinforcement affect the rate of an internal pacemaker as suggested by the Behavioral Theory of Timing (BeT: Killeen and Fetterman, 1988). Pigeons were trained to discriminate durations of 10 s and 20 s, and then exposed to higher or lower rates of freely delivered reinforcers. When returned to the discrimination task, judgments were reliably biased in the predicted directions: those returning from a richer context judged standard durations to be longer than did those returning from a poorer context. These results validate a key assumption of BeT, and provide an explanation of how changing tempos of life bias the perception of time.

Time discrimination in Columba livia and Homo sapiens.

Pigeons' ability to discriminate stimulus duration, focusing on stimuli less than 1 s in duration, was evaluated in 4 experiments. In Experiment 1, the performances of pigeons and humans were compared with a staircase technique, and in Experiment 2, the method of constant stimuli was used. Both experiments produced similar results: The pigeon and human data were well described by the generalized form of Weber's law (Getty, 1975). Experiment 3 demonstrated that the birds did not use perceived brightness to mediate the discrimination of brief visual durations. Experiment 4 used a modified staircase procedure that yielded a continuous measure of discrimination from absolute threshold (0 s) to about 1 s. The difference thresholds were constant over a considerable range, similar to findings reported by Kristofferson (1980) for human timing.

A componential analysis of pacemaker-counter timing systems.

Why does counting improve the accuracy of temporal judgments? Killeen and Weiss (1987) provided a formal answer to this question, and this article provides tests of their analysis. In Experiments 1 and 2, subjects responded on a telegraph key as they reproduced different intervals. Individual response rates remained constant for different target times, as predicted. The variance of reproductions was recovered from the weighted sum of the first and second moments of the component timing and counting processes. Variance in timing long intervals was mainly due to counting error, as predicted. In Experiments 3-5, unconstrained response rate was measured and subjects responded at (a) their unconstrained rate, (b) faster, or (c) slower. When subjects responded at the preferred rate, the accuracy of time judgment improved. Deviations in rates tended to increase the variability of temporal estimates. Implications for pacemaker-counter models of timing are discussed.

Short-term memory for responses: the "choose-small" effect.

Pigeons' short-term memory for fixed-ratio requirements was assessed using a delayed symbolic matching-to-sample procedure. Different choices were reinforced after fixed-ratio 10 and fixed-ratio 40 requirements, and delays of 0, 5, or 20 s were sometimes placed between sample ratios and choice. All birds made disproportionate numbers of responses to the small-ratio choice alternative when delays were interposed between ratios and choice, and this bias increased as a function of delay. Preference for the small fixed-ratio alternative was also observed on "no-sample" trials, during which the choice alternatives were presented without a prior sample ratio. This "choose-small" bias is analogous to results obtained by Spetch and Wilkie (1983) with event duration as the discriminative stimulus. The choose-small bias was attenuated when the houselight was turned on during delays, but overall accuracy was not influenced systematically by the houselight manipulation.

Discrimination of duration ratios.

Trained pigeons to make discriminations on the basis of the ratio of two stimulus durations. A red light of one duration was followed by a green light of a different duration, with 900 red-green pairs intermixed over trials. A choice followed the red-green pair; a response to a green side key was reinforced if the red-green ratio was less than a criterion ratio, and a response to a red side key was reinforced if the ratio exceeded the criterion. Reinforcement depended on whether red or green was longer under the basic condition; in other conditions, however, reinforcement depended on whether one duration was two or four times longer than the other. Sensitivity was similar across conditions, for the basic shorter-longer rule, and for the more complex rule of one duration as two or four times the other. Most choices were made on the basis of the ratio relation between the two durations and according to Weber's law. These results extend the findings of Dreyfus, Fetterman, Smith, and Stubbs (1988), and provide a new methodology for psychophysical scaling with animals.

Discrimination of temporal relations by pigeons.

In four experiments, pigeons were tested on a duration comparison task involving the successive presentation of two visual stimuli that varied in duration from trial to trial. Following presentation of the durations, two choice keys were lit, and reinforcement for choices was based on the temporal relation between duration of the pair. In Experiment 1, the range of durations was varied over conditions. Responding changed as an orderly function of the ratio of the two durations. There was a decrease in discrimination accuracy as average duration increased over condition but no difference in accuracy between shorter and longer problems within a duration range. There was no systematic response bias over conditions for all problems within a range, but there was a bias to report the second duration longer than the first for "long" problems within a range. In Experiment 2, the pigeons were transferred from a task involving spatially differentiated choices to one involving hue-differentiated choices. Performance was similar to that of the spatial procedure of Experiment 1. Additional analyses revealed that although information provided by a single duration of the pair was sometimes predictive of the temporal relation between pair members, responding was also based on the relation and comparison of both durations. In Experiment 3, the pigeons were exposed to a single duration range that included many durations from the four ranges of Experiment 1. Discrimination accuracy was comparable in the fourth and longest category. Manipulation of absolute reinforcement rate in Experiment 4 resulted in no chang in discrimination accuracy, suggesting that the decline in accuracy over conditions of Experiment 1 could not be attributed to decreases in reinforcement rate that accompanied lengthier durations. The results are discussed in terms of theories of animal timing, with Staddon's (1983, 1984) temporal perspective model providing the most systematic account of all aspects of performance.

Choice with a fixed requirement for food, and the generality of the matching relation.

Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.

Pair comparison of durations.

Pigeons were trained on a pair comparison task where a red light of one duration was followed by a green light of a second duration. Following a duration pair two choice keys were lit and one choice was reinforced if the duration of red was longer than green, and the alternate choice was reinforced if green was longer than red. Duration pairs consisted of all possible combinations of the durations .5, 1, 2, and 4 sec in one condition, and 2, 4, 8, and 16 sec in a second condition. Generalization tests with novel duration pairs were given under both conditions. Under a final set of conditions, interstimulus intervals of 2, 5, 10, and 30 sec were interposed between the first (red) and second (green) durations. Pigeons responded appropriately in most cases, with accuracy a function of the relative temporal difference between the members of a duration pair. Accuracy on transfer problems was above 70% in most instances, but in some cases suggests factors apart from relative temporal differences influenced performance. Accuracy declined with increases in the interstimulus interval, but remained above chance levels even when the longest interstimulus interval was used.

Scaling of events spaced in time.

Pigeons were trained to peck on a key, which could be lit by red or green light, and produce feeder-light stimuli intermittently. On some trials, food followed the fourth feeder flash providing the key color was red, while on other trials food followed the sixteenth flash providing the color was green. The change in color from red to green was produced by a peck to a second, changeover key. Pigeons typically responded in the presence of red until four or more flashes occured and then, if food had not been delivered, changed the main-key color and responded on the green key. Following training, the variable-interval schedule arranging-feeder light events was changed to longer and shorter values to alter the amount of time (and number of responses) between events. Data from these test days indicate that the change from red to green was influenced by the number of events, but also by the time elapsed and/or responses emitted since the onset of a trial. The results suggest multiple sources of related information and stimulus control when events and behavior occur over time.

An invariant relation between changing over and reinforcement.

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.