Conditioned reinforcement versus time to reinforcement in chain schedules.

Pigeons were trained on three-component chain schedules in which the initial component was either a fixed-interval or variable-interval schedule. The middle and terminal components were varied among fixed-interval fixed-interval, variable-interval variable-interval, and an interdependent variable-interval variable-interval schedule in which the sum of the durations of the two variable-interval components was always equal to the sum of the fixed-interval fixed-interval components. At issue was whether the response rate in the initial component was controlled by its time to primary reinforcement or by the temporal parameters of the stimulus correlated with the middle terminal link. The fixed-interval initial-link schedule maintained much lower response rates than the variable-interval initial-link schedule regardless of the schedules in the middle and terminal links. Nevertheless, the intervening schedules played some role: With fixed-interval schedules in the initial links, response rates were consistently highest with independent variable-interval schedules in the middle and terminal links and intermediate with the interdependent variable-interval schedules; these initial-link differences were predicted by the response rates in the middle link of the chain. With variable-interval schedules in the initial links, response rates were lowest with the fixed-interval fixed-interval schedules following the initial link and were not systematically different for the two types of variable-interval variable-interval schedules. The results suggest that time to reinforcement itself accounts for little if any variance in initial-link responding.     

Comparing preference and resistance to change in constant- and variable-duration schedule components

Two experiments explored preference and resistance to change in concurrent chains in which the terminal links were variable-interval schedules that ended either after a single reinforcer had been delivered (variable duration) or after a fixed period of access to the schedule (constant duration). In Experiment 1, pigeons' preference between the same pair of terminal links overmatched relative reinforcement rate when the terminal links were of constant duration, but not when they were of variable duration. Responding during the richer terminal link decreased less, relative to baseline, when response-independent food was presented during the initial links according to a variable-time schedule. In Experiment 2, all subjects consistently preferred a terminal link that consisted of 20-s access to a variable-interval 20-s schedule over a terminal link that ended after one reinforcer had been delivered by the same schedule. Results of resistance-to-change tests corresponded to preference, as responding during the constant-duration terminal link decreased less, relative to baseline, when disrupted by both response-independent food during the initial links and prefeeding. Overall, these data extend the general covariation of preference and resistance to change seen in previous studies. However, they suggest that reinforcement numerosity, including variability in the number of reinforcers per terminal-link entry, may sometimes affect preference and resistance to change in ways that are difficult to explain in terms of current models.     

Preference for less segmented fixed-time components in concurrent-chain schedules of reinforcement

A concurrent-chain procedure was used to examine choice between segmented and less segmented response-independent schedules of reinforcement. A pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link, along with a 1.5-s changeover delay. A chained fixed-interval fixed-time and its corresponding tandem schedule constituted the terminal links. The length of the fixed-interval schedule in the terminal link was varied between 5 s and 30 s while that of the fixed-time schedule was kept at 5 s over conditions. The first components of both terminal-link schedules were accompanied by the same stimulus. Except in the baseline condition, the onset of the second component of the terminal-link chained schedule was accompanied by either a localized (key color) or a nonlocalized (dark houselight) stimulus change. Stimulus conditions were constant during the terminal-link tandem schedule. With three exceptions, pigeons demonstrated a slight preference for the tandem over the chained schedule in the terminal link. Furthermore, this preference varied inversely with the length of the first component. In general, these results are consistent with previous studies that reported an adverse effect on choice by segmenting an interval schedule into two or more components, but they are inconsistent with studies that reported preference for signaled over unsignaled delay of reinforcement.     

Preference for fixed-interval terminal links in a three-key concurrent chain schedule

Pigeons were trained on three-key concurrent chain schedules in which the initial links were variable-interval schedules and the terminal links were fixed-interval schedules. In the first experiment, the initial links were all equal and the terminal-link schedule on one key only was varied. In the second part of the experiment, the terminal-link schedules were all fixed, but different, and the initial-link schedule on one key was varied. Relative response rates in the initial links did not match either the relative arranged, nor the relative obtained, terminal-link reinforcement rates. The relations between independent and dependent variables in three-key concurrent chains were similar to, but not identical with, those found in two-key chains comprising the same schedule types.     

Transfer tests of stimulus value in concurrent chains

We report two experiments that use transfer tests to investigate whether in concurrent chains the value of a terminal-link stimulus is affected by the alternate terminal link. In Experiment 1, two groups of pigeons were trained on multiple concurrent-chains schedules in which switching between the schedules was via pecking a changeover key. For one group, the terminal links were fixed-interval 8 s versus fixed-interval 16 s in one component and fixed-interval 16 s versus fixed-interval 32 s in the other component. For a second group, the terminal links were variable-interval 10 s versus variable-interval 20 s in one component and variable-interval 20 s versus variable-interval 40 s in the other. After sufficient baseline training had been given so that performances had stabilized, transfer tests were conducted in which the two chains with equal terminal-link schedules were presented together as a new concurrent pair. For 6 of the 7 subjects, initial-link responding changed fairly rapidly during the test in the manner predicted if the values of the terminal links were equal. In Experiment 2, pigeons were trained on multiple concurrent chains using a two-key procedure, and the terminal links were the same variable-interval schedules as in Experiment 1. After baseline training, transfer tests were conducted that assessed (a) the relative reinforcing strength of the terminal-link stimuli in a novel initial-link situation and (b) the relative ability of those stimuli to evoke responding. The data from the reinforcing strength test were consistent with those from Experiment 1, but those from the evocation strength test were not. Although this discrepancy shows that responding in transfer tests is not solely a function of stimulus value, the results from both experiments suggest, overall, that value is determined by the stimulus—reinforcer relation independently of the alternative terminal link.     

Concurrent-chains schedules as a method to study choice between alcohol-associated conditioned reinforcers

An extensive body of research using concurrent-chains schedules of reinforcement has shown that choice for one of two differentially valued food-associated stimuli is dependent upon the overall temporal context in which those stimuli are embedded. The present experiments examined whether the concurrent chains procedure was useful for the study of behavior maintained by alcohol and alcohol-associated stimuli. In Experiment 1, rats responded on concurrent-chains schedules with equal variable-interval (VI) 10-s schedules in the initial links. Across conditions, fixed-interval schedules in the terminal links were varied to yield 1∶1, 9∶1, and 1∶9 ratios of alcohol delivery. Initial-link response rates reflected changes in terminal-link schedules, with greater relative responding in the rich terminal link. In Experiment 2, terminal-link schedules remained constant with a 9∶1 ratio of alcohol delivery rates while the length of two equal duration initial-link schedules was varied. Preference for the rich terminal link was less extreme when initial links were longer (i.e., the initial-link effect), as has been previously reported with food reinforcers. This result suggests that the conditioned reinforcing value of an alcohol-associated stimulus depends on the temporal context in which it is embedded. The concurrent-chains procedure and quantitative models of concurrent chains performance may provide a useful framework within which to study how contextual variables modulate preference for drug-associated conditioned reinforcers.     

Conditioned reinforcement value and choice.

The delay-reduction hypothesis of conditioned reinforcement states that the reinforcing value of a food-associated stimulus is determined by the delay to primary reinforcement signaled by the onset of the stimulus relative to the average delay to primary reinforcement in the conditioning situation. In contrast, most contemporary models of conditioned reinforcement strength posit that the reinforcing strength of a stimulus is some simple function only of the delay to primary reinforcement in the presence of stimulus. The delay-reduction hypothesis diverges from other conditioned reinforcement models in that it predicts that a fixed-duration food-paired stimulus will have different reinforcing values depending on the frequency of its presentation. In Experiment 1, pigeons' key pecks were reinforced according to concurrent-chains schedules with variable-interval 10-second and variable-interval 20-second terminal-link schedules. The initial-link schedule preceding the shorter terminal link was always variable-interval 60 seconds, and the initial-link schedule requirement preceding the longer terminal link was varied between 1 second and 60 seconds across conditions. In Experiment 2, the initial-link schedule preceding the longer of two terminal links was varied for each of three groups of pigeons. The terminal links of the concurrent chains for the three groups were variable-interval 10 seconds and 20 seconds, variable-interval 10 seconds and 30 seconds, and variable-interval 30 seconds and 50 seconds. In both experiments, preference for the shorter terminal link was either a bitonic function or an inverse function of the initial-link schedule preceding the longer terminal-link schedule. Consistent with the predictions of the delay-reduction hypothesis, the relative values of the terminal-link stimuli changed as a function of the overall frequency of primary reinforcement. Vaughan's (1985) melioration model, which was shown to be formally similar to Squires and Fantino's (1971) delay-reduction model, can be modified so as to predict these results without changing its underlying assumptions.     

The effects of terminal-link fixed-interval and variable-interval schedules on responding under concurrent chained schedules

Previous work using variable-interval schedules in the terminal links of concurrent chained schedules suggested that relative choice proportion in the initial links equalled relative rate of reinforcement in the terminal links. With fixed-interval terminal-link schedules, however, matching was not obtained. The present study held pairs of fixed-interval terminal-link schedules in a constant ratio but varied absolute sizes. Relative choice for the smaller terminal-link fixed-interval schedule was a negatively accelerated, increasing function of absolute size of the fixed-interval pairs. Matching was found only with the fixed-interval pair of 5 and 10 sec. When pairs of variable-interval schedules were arranged so that the harmonic mean of the intervals equalled the fixed-interval parameter values, relative choice functions were like those for fixed-interval schedules.     

Preference and resistance to change with constant- and variable-duration terminal links: independence of reinforcement rate and magnitude

Pigeons responded in a three-component multiple concurrent-chains procedure in which the variable-interval reinforcement schedules were the same across components but magnitudes differed across components. The terminal links were arranged either as a variable delay followed by presentation of a reinforcer ("variable duration") or as a fixed period of access to the schedule during which a variable number of reinforcers could be earned ("constant duration"). Relative reinforcement rate was varied parametrically across both types of conditions. After baseline training in each condition, resistance to change of terminal-link responding was assessed by delivering food during the initial links according to a variable-time schedule. Both preference and resistance to change were more sensitive to reinforcement-rate differences in the constant-duration conditions. Sensitivities of preference and resistance to change to relative reinforcement rate did not change depending on relative reinforcement magnitude. Taken together, these results confirm and extend those of prior studies, and suggest that reinforcement rate and magnitude combine additively to determine preference and resistance to change. A single structural relation linking preference and resistance to change describes all the data from this and several related studies.     

Choice and delay of reinforcement: Effects of terminal-link stimulus and response conditions

In two experiments, pigeons were exposed to concurrent-chains schedules in which a single initial-link variable-interval schedule led to access to terminal links composed of fixed-interval or fixed-delay schedules. In Experiment 1, an 8-s (or 16-s) delay to reinforcement was associated with the standard key, while reinforcer delay values associated with the experimental key were varied from 4 to 32 s. The results of Experiment 1 showed undermatching of response ratios to delay ratios with terminal-link fixed-delay schedules, whereas in some pigeons matching or overmatching was evident with the fixed-interval schedules. In Experiment 2, one pair of reinforcer delay values, either 8 versus 16 s or 16 versus 32 s, was used. In the first condition of Experiment 2, different delays were associated with different keylight stimuli (cued condition). In the second condition, different terminal-link delays were associated with the same stimulus, either a blackout (uncued-blackout condition) or a white key (uncued-white condition). To examine the role of responses emitted during delays, the keys were retracted during a delay (key-absent condition) in the third condition and responses were required by a fixed-interval schedule in the fourth condition. Experiment 2 demonstrated that the choice proportions for the shorter delay were more extreme in the cued condition than in the uncued-blackout condition, and that the response requirement imposed by the fixed-interval schedules did not affect choice of the shorter delay, nor did the key-absent and key-present conditions. These results indicate that the keylight-stimulus conditions affected preference for the shorter of two delays and that the findings obtained in Experiment 1 depended mainly on the keylight-stimulus conditions of the terminal links (i.e., the conditioned reinforcing value of the terminal-link stimuli).     

Effects of reinforcement context on choice

Two experiments investigated the effects of successive reinforcement contexts on choice. In the first, concurrent variable-interval schedules of primary reinforcement operated during the initial links of concurrent chains. The rate of this reinforcement arranged by the concurrent schedules was decreased across conditions: When it was higher than the terminal-link rate, preference for the higher frequency initial-link schedule increased relative to baseline. (During baseline, a standard concurrent-schedule procedure was in effect). When the initial-link reinforcement rate was lower than the terminal-link rate, preference converged toward indifference. In the second experiment, a chain schedule was available on a third key while a concurrent schedule was in effect on the side keys. When the terminal link of the chain schedule was produced, the side keys became inoperative. Availability of the chain schedule did not affect choice between the concurrent schedules. These results show that only when successive reinforcement contexts are produced by choice responding do those successive contexts affect choice in concurrent schedules.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

Cued and uncued terminal links in concurrent-chains schedules

Pigeons were trained on a concurrent-chains schedule. The initial links were concurrent variable-interval schedules arranged on two side keys. Each terminal link was a fixed-interval schedule arranged on the center key. In cued conditions, different center-key colors signaled the two terminal-link schedules. In uncued conditions, the same center-key color appeared for both terminal links. Experiment 1 arranged unequal initial links and equal terminal links. Preference for the shorter initial-link schedule was greater when the terminal links were uncued. Experiment 2 arranged equal initial links and unequal terminal links. Preference for the shorter terminal-link schedule was greater when the terminal links were cued. Although the results of Experiment 2 successfully replicated previous research, the results of Experiment 1 are not easily reconciled with conditioned-reinforcement or discriminative-stimulus accounts of the role of terminal-link cues. Rather, terminal-link cues appear to decrease sensitivity to initial-link contingencies.     

Preference for mixed-interval versus fixed-interval schedules

Pigeons were trained on a two-link concurrent chain schedule in which responses on two keys were reinforced according to independent variable-interval schedules by the production of a change in key color. Further responses on the key on which the stimulus change had been produced gave a single food reinforcement and a return to concurrent variable-interval conditions. On one key the terminal link was a two-valued mixed-interval schedule, while on the other, the terminal link was a fixed-interval schedule. When the mixed-interval values were kept constant and the fixed-interval values varied, relative response rates in the initial concurrent links matched relative reinforcement rates in the terminal links when these were computed from cubic transformations of the reciprocals of the intervals comprising the terminal link schedules.     

Psychological distance to reward: A human replication

Choice behavior in college students was examined in two experiments using the concurrent-chains procedure. In both experiments, the concurrent chains were presented on a microcomputer in the form of an air-defense game in which subjects used two radar systems to detect and subsequently destroy enemy aircraft. Access to one of two radar systems was controlled by a pair of independent concurrent variable-interval 60-s schedules with a 4-s changeover delay always in effect. In the terminal link, the appearance of an enemy aircraft was determined by a pair of differentially segmented fixed-time schedules (Experiment 1) or fixed-interval schedules (Experiment 2) of equal overall duration. In Experiment 1, the terminal-link duration was either 20 s or 40 s, and subjects preferred the unsegmented to the segmented intervals. In Experiment 2, the duration was either 10 s or 60 s, and the reinforcement contingencies required responding during the terminal link. Prior to the reinstatement of the initial link, subjects estimated the duration of the terminal-link schedule. Segmentation affected choice in the 60-s conditions but not in the 10-s ones. Preference for the unsegmented schedule was correlated with an overestimation of the durations for the segmented schedules. These results replicated those found in animal experiments and support the notion of increasing the psychological distance to reward by segmenting a time-based schedule of reinforcement.     

Effects of reinforcer duration on responding in two-link chained interval schedules

Each of five pigeons was exposed to two or more durations of access to mixed grains on two-link, chained, interval schedules in which both links were identical fixed-interval or variable-interval schedules. Response rates were an increasing function of reinforcer duration for both initial and terminal links. For both types of interval schedules, initial-link response rates were more sensitive to reinforcer duration than were terminal-link response rates. The present results, together with prior ones, suggest that chaining and choice procedures are each sufficient for demonstrating substantial sensitivity of responding to changes in reinforcer duration.     

Effects of delayed conditioned reinforcement in chain schedules.

The contingency between responding and stimulus change on a chain variable-interval 33-s, variable-interval 33-s, variable-interval 33-s schedule was weakened by interposing 3-s delays between either the first and second or the second and third links. No stimulus change signaled the delay interval and responses could occur during it, so the obtained delays were often shorter than the scheduled delay. When the delay occurred after the initial link, initial-link response rates decreased by an average of 77% with no systematic change in response rates in the second or third links. Response rates in the second link decreased an average of 59% when the delay followed that link, again with little effect on response rates in the first or third links. Because the effect of delaying stimulus change was comparable to the effect of delaying primary reinforcement in a simple variable-interval schedule, and the effect of the unsignaled delay was specific to the link in which the delay occurred, the results provide strong evidence for the concept of conditioned reinforcement.     

Response strength in multiple periodic and aperiodic schedules

Responding in multiple periodic and aperiodic schedules of equal mean reinforcement rate was examined during extinction, satiation, and in the presence of various free-food schedules. In Experiments I and II, pigeons were trained on multiple variable-interval–fixed-interval schedules. Decreases in the rate of responding due to extinction, satiation, or food schedules were approximately equal regardless of the temporal pattern of reinforcer presentation. In Experiment III, pigeons responded on a two-component multiple schedule in which each component was a two-member homogeneous response chain terminating in a fixed-interval schedule during one component and in a variable-interval schedule during the other. The length of both terminal links was varied over a series of conditions. Initial-link responding in the fixed-interval component was reduced more by increasing terminal-link length than was initial-link responding in the variable-interval component. However, no differences in resistance to satiation and extinction were obtained across the fixed and variable components. If the relative decrease in responding produced by satiation and extinction is used as an index of the “value” of the conditions maintaining responding, then these data suggest that fixed and variable schedules of equal mean length are equally valued. This conclusion, however, is not consistent with findings of preference for variable over fixed schedules obtained in studies using concurrent-chain procedures.     

Choice in the time-left procedure and in concurrent chains with a time-left terminal link.

In two experiments, rats chose between a standard fixed-duration food-associated stimulus and a stimulus whose duration was the time remaining to reinforcement in an elapsing comparison interval. In Experiment 1, 4 rats responded in a time-left procedure wherein a single initial-link variable-interval schedule set up two potential terminal links simultaneously. As time elapsed in the initial-link schedule, the choice was between a standard fixed-interval 30-s terminal link and a time-left terminal link whose programmed interval requirement equaled 90 s minus the elapsed time in the initial link. Rats generally responded more on the lever with the shortest programmed terminal-link duration, but the temporal parameters of the procedure were found to vary with response distributions. Contrary to previous reports, therefore, time-left data were well predicted by choice models that make no assumptions about animal timing. In Experiment 2, 8 rats responded on a concurrent-chains schedule with independent variable-interval initial links and a time-left terminal link in one of the choice schedules. On the time-left lever, the programmed terminal-link delay equaled 90 s minus the elapsed time in the time-left initial link. On the standard lever, terminal-link responses were reinforced according to a variable-interval schedule whose average value varied over four conditions. Relative time-left initial-link responses increased in the elapsing time-left initial-link schedule as the time-left terminal link became shorter relative to the standard terminal link. Scalar expectancy theory failed to predict the resultant data, but a modified version of the delay-reduction model made good predictions. An analysis of the elaboration of scalar expectancy theory for variable delays demonstrated that the model is poorly formulated for arithmetically distributed delays.     

DOES SENSITIVITY TO MAGNITUDE DEPEND ON THE TEMPORAL DISTRIBUTION OF REINFORCEMENT?

Our research addressed the question of whether sensitivity to relative reinforcer magnitude in concurrent chains depends on the distribution of reinforcer delays when the terminal-link schedules are equal. In Experiment 1, 12 pigeons responded in a two-component procedure. In both components, the initial links were concurrent variable-interval 40-s variable-interval 40-s, and the terminal links were both 20-s interval schedules in which responses were reinforced by either 4-s of grain in one, or 2-s of grain in the other. The only difference between the components was whether the terminal-link schedules were fixed interval or variable intervals. For all subjects, the relative rate of responding in the initial links for the terminal link that produced the 4-s reinforcer was greater when the terminal links were fixed-interval schedules than when they were variable-interval schedules. This result is contrary to the prediction of Grace's (1994) contextual choice model, but is consistent with both Mazur's (2001) hyperbolic value-added model and Killeen's (1985) incentive theory. In Experiment 2, 4 pigeons responded in a concurrent-chains procedure in which 4-s or 2-s reinforcers were provided independently of responding according to equal fixed-time or mixed-time schedules. Preference for the 4-s reinforcer increased as the variability of the intervals comprising the mixed-time schedules was decreased. Generalized-matching sensitivity of initial-link response allocation to relative reinforcer magnitude was proportional to the geometric mean of the terminal-link delays.