On the measurement of time allocation on multiple variable-interval schedules

Six pigeons were trained on a modified multiple-schedule procedure. In a three-key chamber, the center key was lighted red or green, depending upon which component schedule was in effect. A response on this key transferred this color to each of two side keys, and responses on one of those keys produced reinforcers according to the component schedule. After 2 s, the side-key lights were extinguished, the center key was reilluminated, and a further center-key response was required to give access, as before, to the component schedules. Components alternated every 3 min. This limited-access procedure allowed both times spent switched into the side keys and time spent not switched in to be measured in the two components. Component reinforcer rates were varied over eight experimental conditions. Both component response rate and component time allocation were increasing functions of relative component reinforcer rate, and these functions were not significantly different. This finding implies that local response rates (responses divided by time switched in) were unaffected by changing component reinforcer rates on multiple schedules. Because a similar result was recently obtained for concurrent schedules, models of multiple and concurrent-schedule performance may need to consider only the time allocation of behavior emitted at equal tempo in the component schedules.     

Choice in situations of time-based diminishing returns: immediate versus delayed consequences of action.

Pigeons chose between two schedules of food presentation, a fixed-interval schedule and a progressive-interval schedule that began at 0 s and increased by 20 s with each food delivery provided by that schedule. Choosing one schedule disabled the alternate schedule and stimuli until the requirements of the chosen schedule were satisfied, at which point both schedules were again made available. Fixed-interval duration remained constant within individual sessions but varied across conditions. Under reset conditions, completing the fixed-interval schedule not only produced food but also reset the progressive interval to its minimum. Blocks of sessions under the reset procedure were interspersed with sessions under a no-reset procedure, in which the progressive schedule value increased independent of fixed-interval choices. Median points of switching from the progressive to the fixed schedule varied systematically with fixed-interval value, and were consistently lower during reset than during no-reset conditions. Under the latter, each subject's choices of the progressive-interval schedule persisted beyond the point at which its requirements equaled those of the fixed-interval schedule at all but the highest fixed-interval value. Under the reset procedure, switching occurred at or prior to that equality point. These results qualitatively confirm molar analyses of schedule preference and some versions of optimality theory, but they are more adequately characterized by a model of schedule preference based on the cumulated values of multiple reinforcers, weighted in inverse proportion to the delay between the choice and each successive reinforcer.     

Stimulus control of behavioral history.

Pigeons were exposed to two different reinforcement schedules under different stimulus conditions in each of two daily sessions separated by 6 hr (Experiments 1 and 2) or in a single session (Experiment 3). Following this, either a fixed-interval (Experiment 1) or a variable-interval schedule (Experiments 2 and 3) was effected in both stimulus conditions. In the first two experiments, exposure to fixed-ratio or differential-reinforcement-of-low-rate schedules led to response-rate, but not pattern, differences in subsequent performance on fixed- or variable-interval schedules that persisted for up to 60 sessions. The effects of reinforcement-schedule history on fixed-interval schedule performance generally were more persistent. In Experiment 3, a history of high and low response rates in different components of a multiple schedule resulted in subsequent response-rate differences under identical variable-interval schedules. Higher response rates initially occurred in the component previously correlated with high response rates. For 3 of 4 subjects, the differences persisted for 20 or more sessions. Previous demonstrations of behavioral history effects have been confined largely to between-subject comparisons. By contrast, the present results demonstrate strong behavioral effects of schedule histories under stimulus control within individual subjects.     

Behavioral contrast: Pavlovian effects and anticipatory contrast.

Two sources of behavioral contrast have been identified previously: Pavlovian stimulus-reinforcer relations and component sequence effects (anticipatory contrast). This study sought to isolate these sources of control procedurally in a four-ply multiple schedule composed of two fixed two-component sequences. Different cues were associated with the first component of each sequence, and contrast effects were studied in these target components. In Experiment 1, differential cuing of Component 2 between sequences and availability of reinforcement during target components were varied across three groups of pigeons; the stimulus-reinforcer relation between target-component cues and schedule of reinforcement in Component 2 was varied within subjects. Control by the Pavlovian relation was demonstrated under all conditions, and anticipatory contrast was not observed. In Experiment 2, target-component duration was systematically varied in the three groups of Experiment 1. Control by the Pavlovian relation was reliably obtained only when target-component behavior was unreinforced, and diminished with increases in component duration. Anticipatory contrast emerged in the two groups for which target-component reinforcement was available. These and other data indicate that Pavlovian effects in multiple schedules may be obscured when the requisite conditions for anticipatory contrast are present.     

Key pecking of pigeons under variable-interval schedules of briefly signaled delayed reinforcement: effects of variable-interval value.

Key pecking of 4 pigeons was maintained under a multiple variable-interval 20-s variable-interval 120-s schedule of food reinforcement. When rates of key pecking were stable, a 5-s unsignaled, nonresetting delay to reinforcement separated the first peck after an interval elapsed from reinforcement in both components. Rates of pecking decreased substantially in both components. When rates were stable, the situation was changed such that the peck that began the 5-s delay also changed the color of the keylight for 0.5 s (i.e., the delay was briefly signaled). Rates increased to near-immediate reinforcement levels. In subsequent conditions, delays of 10 and 20 s, still briefly signaled, were tested. Although rates of key pecking during the component with the variable-interval 120-s schedule did not change appreciably across conditions, rates during the variable-interval 20-s component decreased greatly in 1 pigeon at the 10-s delay and decreased in all pigeons at the 20-s delay. In a control condition, the variable-interval 20-s schedule with 20-s delays was changed to a variable-interval 35-s schedule with 5-s delays, thus equating nominal rates of reinforcement. Rates of pecking increased to baseline levels. Rates of pecking, then, depended on the value of the briefly signaled delay relative to the programmed interfood times, rather than on the absolute delay value. These results are discussed in terms of similar findings in the literature on conditioned reinforcement, delayed matching to sample, and classical conditioning.     

Waiting in pigeons: the effects of daily intercalation on temporal discrimination.

Pigeons trained on cyclic-interval schedules adjust their postfood pause from interval to interval within each experimental session. But on regular fixed-interval schedules, many sessions at a given parameter value are usually necessary before the typical fixed-interval "scallop" appears. In the first case, temporal control appears to act from one interfood interval to the next; in the second, it appears to act over hundreds of interfood intervals. The present experiments look at the intermediate case: daily variation in schedule parameters. In Experiments 1 and 2 we show that pauses proportional to interfood interval develop on short-valued response-initiated-delay schedules when parameters are changed daily, that additional experience under this regimen leads to little further improvement, and that pauses usually change as soon as the schedule parameter is changed. Experiment 3 demonstrates identical waiting behavior on fixed-interval and response-initiated-delay schedules when the food delays are short (less than 20 s) and conditions are changed daily. In Experiment 4 we show that daily intercalation prevents temporal control when interfood intervals are longer (25 to 60 s). The results of Experiment 5 suggest that downshifts in interfood interval produce more rapid waiting-time adjustments than upshifts. These and other results suggest that the effects of short interfood intervals seem to be more persistent than those of long intervals.     

Inverse relations between preference and contrast

Pigeons were trained on a multiple schedule in which two target components with identical reinforcement schedules were followed by either the same-valued schedule or by extinction. Response rate increased in both target components but was higher in the target component followed by extinction, replicating previous findings of positive anticipatory contrast. A similar design was used to study negative contrast, in that the two target components were followed either by the same-valued schedule or by a higher valued schedule. Negative contrast occurred equally, on average, in both target components, thus failing to demonstrate negative contrast that is specifically anticipatory in nature. When the stimuli correlated with the two target components were paired in choice tests, the pattern of preference was in the opposite direction. For the positive contrast procedure, no significant preference between the two target stimuli was evident. But for the negative contrast procedure, preference favored the stimulus followed by the higher valued schedule. The results demonstrate a functional dissociation between positive and negative contrast in relation to stimulus value. More generally, the results demonstrate an inverse relation between response rate and preference and challenge existing accounts of contrast in terms of the concept of relative value.     

Schedule-induced defecation: No-food and massed-food baselines

Defecation rate was monitored during daily 30-min periods as 16 rats were exposed to different sequences of the following three experimental conditions: (a) a fixed-time 60-s food delivery schedule, (b) a massed-food presentation baseline, and/or (c) a no-food baseline. All food delivery was response independent. Rate of defecation increased during fixed-time 60-s food delivery when compared to baseline rates of defecation established during no-food and massed-food baselines. This effect was present for 12 of 16 rats during four alternative sequences of experimental conditions. Within-subject reversals established reliability of this effect. Schedule induction of defecation is clearly demonstrated under these conditions.     

Improving assignment preference through interspersing additional problems: Brief versus easy problems

College students were exposed to a control mathematics assignment containing 16 three-digit by two-digit multiplication (3×2) problems and two experimental assignments that contained 16 equivalent 3×2 problems and six additional interspersed problems. On one experimental assignment, 4-digit plus 4-digit problems (4+4) were interspersed. On the other experimental assignment, 2-digit divided by 1-digit with whole number answers problems (2/1) were interspersed. When given a choice, significantly more students choose the 2/1 assignment over the control and 1+4 assignment. Students also ranked the 2/1 sheet as requiring less time to complete than the control or 4+4 assignment but no differences were found on assignment difficulty rankings between the 4+4 and 2/1 assignments. No differences were found on accuracy levels or rates of responding on the target 3×2 problems across assignments. Results showed that interspersing additional problems that take relatively less time to complete may be more important for altering student preference for assignments than interspersing easier problems. Discussion focuses on schedules of reinforcement and resource efficient procedures for increasing student preference for assignment without compromising curricula integrity.     

EFFECTS OF PROBLEM DIFFICULTY AND REINFORCER QUALITY ON TIME ALLOCATED TO CONCURRENT ARITHMETIC PROBLEMS

Students with learning difficulties participated in two studies that analyzed the effects of problem difficulty and reinforcer quality upon time allocated to two sets of arithmetic problems reinforced according to a concurrent variable-interval 30-s variable-interval 120-s schedule. In Study 1, high- and low-difficulty arithmetic problems were systematically combined with rich and lean concurrent schedules (nickels used as reinforcers) across conditions using a single-subject design. The pairing of the high-difficulty problems with the richer schedule failed to offset time allocated to that alternative. Study 2 investigated the interactive effects of problem difficulty and reinforcer quality (nickels vs. program money) upon time allocation to arithmetic problems maintained by the concurrent schedules of reinforcement. Unlike problem difficulty, the pairing of the lesser quality reinforcer (program money) with the richer schedule reduced the time allocated to that alternative. The magnitude of this effect was greatest when combined with the low-difficulty problems. These studies have important implications for a matching law analysis of asymmetrical reinforcement variables that influence time allocation.