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.     

Resistance to change produced by access to fixed-delay versus variable-delay terminal links

Pigeons' responding was reinforced on a multiple schedule consisting of two two-link chain schedules presented in regular alternation. Responding in initial links (always variable-interval 60-s) produced a key-color change and access to a terminal link. The terminal link for one chain provided food after a fixed delay (fixed-interval or fixed-time); the terminal link for the other provided food after a variable delay (variable-interval or variable-time). The average duration of the terminal-link schedules was varied across conditions, but in every condition the arithmetic mean of the variable-delay terminal-link schedule was equal to the duration of the fixed delay. Response rates were higher in the initial links of the chains with the variable-delay terminal links. Response-decreasing operations (satiation, extinction) were used after performances reached asymptote. Response rates maintained by access to variable-delay terminal links tended to be more resistant to change than were rates maintained by access to fixed-delay terminal links. These results are consistent with the preference for variable- over fixed-interval terminal links observed with concurrent-chains schedules, suggesting (1) that immediacy of reinforcement influences the conditioned reinforcing potency of access to a terminal link and (2) that choice in concurrent chains and resistance of responding to change may be manifestations of the same effect of reinforcement.     

SOME EFFECTS OF PROCEDURAL VARIATIONS ON CHOICE RESPONDING IN CONCURRENT CHAINS

The present research used pigeons in a three‐key operant chamber and varied procedural features pertaining to both initial and terminal links of concurrent chains. The initial links randomly alternated on the side keys during a session, while the terminal links always appeared on the center key. Both equal and unequal initial‐link schedules were employed, with either differential or nondifferential terminal‐link stimuli across conditions. The research was designed to neutralize initial‐ and terminal‐link spatial cues in order to gain a clearer understanding of the roles of conditioned reinforcement and delayed primary reinforcement in choice. With both equal and unequal initial links and with differential terminal‐link stimuli, all pigeons reliably preferred the chain with the shorter terminal link. However, with equal initial links and nondifferential stimuli, all pigeons were indifferent. With unequal initial links and nondifferential stimuli, some pigeons were also indifferent, while others actually reversed and preferred the chain with the shorter initial link, even though it was followed by the longer terminal link. The decrease if not reversal of the previous preferences implies that preferences in concurrent chains are a function of the conditioned reinforcement afforded by terminal‐link stimuli, rather than delayed primary reinforcement.     

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.     

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.     

A contextual model of concurrent-chains choice

An extension of the generalized matching law incorporating context effects on terminal-link sensitivity is proposed as a quantitative model of behavior under concurrent chains. The contextual choice model makes many of the same qualitative predictions as the delay-reduction hypothesis, and assumes that the crucial contextual variable in concurrent chains is the ratio of average times spent, per reinforcement, in the terminal and initial links; this ratio controls differential effectiveness of terminal-link stimuli as conditioned reinforcers. Ninety-two concurrent-chains data sets from 19 published studies were fitted to the model. Averaged across all studies, the model accounted for 90% of the variance in pigeons' relative initial-link responding. The model therefore demonstrates that a matching law analysis of concurrent chains—the assumption that relative initial-link responding equals relative terminal-link value—remains quantitatively viable. Because the model reduces to the generalized matching law when terminal-link duration is zero, it provides a quantitative integration of concurrent schedules and concurrent chains.     

Choice: A local analysis

Analyses of free-operant choice usually employ one of two general procedures: the simple concurrent procedure (i.e., a concurrent variable-interval variable-interval schedule) or the concurrent-chains procedure (i.e., concurrently available initial links, each leading to an exclusively available terminal link). Theories about choice usually focus on only one of the two procedures. For example, maximization theories, which assert that behavior is distributed between two alternatives in such a way that overall rate of reinforcement is maximized, have been applied only to the simple concurrent procedure. In the present paper, a form of the pairing hypothesis (according to which pairings between one stimulus and another affect the value of the first, and pairings between responses and reinforcers affect the value of the former) is developed in a way that allows it to make qualitative predictions with regard to choice in a variety of simple concurrent and concurrent-chains procedures. The predictions include matching on concurrent variable-interval variable-interval schedules, preference reversal in the self-control paradigm, and preference for tandem over chained terminal links.     

Effects of primary reinforcement on pigeons' initial-link responding under a concurrent chains schedule with nondifferntial terminal links

The effect of primary reinforcement on initial-link responding under concurrent-chains schedules with nondifferential terminal links was assessed in 12 pigeons. The iniitial and terminal links were variable-interval schedules (always the same for both alternatives). The positions (left or right key) of the initial-link stimuli (red or green) were randomized while the correlation between color and food amount remained constant within each condition. The terminal-link stimuli were always presented on the center key. Except in two control groups and conditions, the terminal-link stimuli were the same color (nondifferential, blue or yellow). Over six conditions, the differences in food amont and the durations of the initial- and terminal-link schedules were manipulated. In 57 of 60 cases, birds generated choice proportions above .50 in favor of the initial-link stimlus that was correlated with the larger reinforcer. There was some indication that preference increased with shortened terminal-link durations. Because the terminal-link stimuli were nondifferential, differential responding in the initial links cannot be explained easily by conditioned reinforcement represented by the terminal-link stimuli. Thus, primiary reinforcement has a direct effect on initial-link responding in concurrent-chains schedules.     

Conditioned reinforcement dynamics in three-link chained schedules.

In two experiments rats were trained on three-link concurrent-chains schedules of reinforcement. In Experiment 1, additional entries to one terminal link were added during one of the middle links to a baseline schedule that was otherwise equal for the two chains, and, depending on the condition, these additional terminal-link presentations ended either in food or in no food. When food occurred, preference was always in favor of the chain with the additional terminal-link presentations (which also entailed a higher rate of reinforcement). When no food occurred at the end of the additional terminal links, the outcome depended on the nature of the stimuli associated with these additional terminal links. When stimuli different from the reinforced baseline terminal links were used for the no-food terminal links, preference was against the choice alternative that led to the extra periods of extinction. When the same stimulus was used for the two kinds of terminal links, preference was near indifference, that is, significantly greater than when different stimuli were used. In Experiment 2, rats learned repeated reversals of a simultaneous discrimination under a three-link concurrent-chains schedule, in which the food or no-food choice outcomes were delayed until the end of the chain. Different conditions were defined by the point in the chain at which differential stimuli occurred. When the middle and terminal links provided no differential stimuli, discrimination was acquired more slowly than when differential stimuli occurred in both links. When differential stimuli occurred in the middle but not the terminal links, acquisition rates were intermediate. Both experiments together show that the effects of stimuli in a chain schedule are due partly to the time to food correlated with the stimuli and partly to the time to the next conditioned reinforcer in the sequence.     

Exclusive preference develops less readily on concurrent ratio schedules with wheel-running than with sucrose reinforcement

Previous research suggested that allocation of responses on concurrent schedules of wheel‐running reinforcement was less sensitive to schedule differences than typically observed with more conventional reinforcers. To assess this possibility, 16 female Long Evans rats were exposed to concurrent FR FR schedules of reinforcement and the schedule value on one alternative was systematically increased. In one condition, the reinforcer on both alternatives was .1 ml of 7.5% sucrose solution; in the other, it was a 30‐s opportunity to run in a wheel. Results showed that the average ratio at which greater than 90% of responses were allocated to the unchanged alternative was higher with wheel‐running reinforcement. As the ratio requirement was initially increased, responding strongly shifted toward the unchanged alternative with sucrose, but not with wheel running. Instead, responding initially increased on both alternatives, then subsequently shifted toward the unchanged alternative. Furthermore, changeover responses as a percentage of total responses decreased with sucrose, but not wheel‐running reinforcement. Finally, for some animals, responding on the increasing ratio alternative decreased as the ratio requirement increased, but then stopped and did not decline with further increments. The implications of these results for theories of choice are discussed.     

Some effects of interreinforcement time upon choice

Pigeons' responses were reinforced on two identical and concurrently available chain variable-interval-schedules. Unlike the typical concurrent chains procedure, both links were operative throughout, thus producing three types of concurrency: (1) concurrent initial links; (2) concurrent initial and terminal links; (3) concurrent terminal links. Choice proportions in each of these three states suggested that the pigeons were sensitive to momentary likelihoods of reinforcement: choice proportions for a schedule were higher when the schedule had been operative for some time, resulting in a higher probability of reinforcement. The study also showed that the relative rates of responding did not match the relative rates of reinforcement in any of the three states of concurrency. Instead, the choice proportions in both the concurrent initial and in the concurrent terminal links were intermediate between the scheduled and the obtained relative rates of reinforcement, while the choice proportions for a terminal link concurrent with an initial link consistently overmatched the relative interreinforcement times (and were typically 1.00). These data indicate that an accurate characterization of choice may not be obtained by considering only the relative interreinforcement interval where one interreinforcement interval is segmented into a chain. Instead, the organism's choice for a schedule will be substantially lowered by the chaining operation.     

Dual effects on choice of conditioned reinforcement frequency and conditioned reinforcement value

Pigeons were presented with a concurrent‐chains schedule in which the total time to primary reinforcement was equated for the two alternatives (VI 30 s VI 60 s vs. VI 60 s VI 30 s). In one set of conditions, the terminal links were signaled by the same stimulus, and in another set of conditions they were signaled by different stimuli. Choice was in favor of the shorter terminal link when the terminal links were differentially signaled but in favor of the shorter initial link (and longer terminal link) when the terminal links shared the same stimulus. Preference reversed regularly with reversals of the stimulus condition and was unrelated to the discrimination between the two terminal links during the nondifferential stimulus condition. The present results suggest that the relative value of the terminal‐link stimuli and the relative rate of conditioned reinforcer presentation are important influences on choice behavior, and that models of conditioned reinforcement need to include both factors.     

Choice for conditioned reinforcers in the signaled absence of primary reinforcement

Pigeons responded in a multiple schedule in which concurrent schedules of brief-stimulus presentation alternated with a component in which food was available (concurrent-chains component). In the initial links of the concurrent-chains component subjects chose either of two stimuli each correlated with the terminal link of one chain. The terminal links involved either variable-interval 30-second or variable-interval 60-second schedules. In the brief-stimulus component subjects chose between 0.5-second presentations of the terminal-link stimuli from the concurrent-chains component. Responding was generally maintained in the brief-stimulus component in two subjects for more than 300 sessions, suggesting that brief stimuli were conditioned reinforcers. During the brief-stimulus component, in 17 of 21 cases for which a minimal number of responses occurred, choice proportions above 0.55 were obtained for the brief-stimulus presentations correlated with the higher rate of primary reinforcement in the concurrent-chains component. These results support the suggestion that choice in conventional concurrent-chains procedures is partially controlled by production of the terminal-link stimuli.     

Reinforcement uncertainty enhances preference for choice in humans

Under concurrent‐chains schedules of reinforcement, participants often prefer situations that allow selection among alternatives (free choice) to situations that do not (forced choice). The present experiment examined the effects of reinforcement probability on choice preferences. Preferences for free versus forced choice were measured under a condition in which participants' choices were always reinforced (reinforcement probability of 1.0) and a condition in which outcomes were uncertain (reinforcement probability of 0.5). Forty‐four college students participated and preferences were examined under a concurrent‐chains schedule of reinforcement. Participants preferred free choice under uncertain reinforcement, but a bias toward free choice was not observed when reinforcement was certain. These results align with previous findings of preference for free choice under conditions of uncertainty, but suggest that preference may be dependent upon probabilistic reinforcement contingencies in the terminal links of the concurrent‐chains arrangement. Thus, reinforcement probability is an important variable to consider when conducting similar studies on the value of choice.     

Delay and number of food reinforcers: Effects on choice and latencies

Pigeons were given a choice between two identical-duration situations (terminal links of chain schedules). One terminal link of the choice pair provided two food deliveries, and the other provided five. The exact times of these food deliveries differed between the terminal links and were varied over conditions. A single response during the initial link gave immediate access to the corresponding terminal link. Forced trials, during which only one of the initial-link keys was lighted, were interspersed with choice trials during which both initial-link keys were lighted. Choice tended to favor whichever terminal link was correlated with the higher sum of the immediacies (i.e., the sum of the reciprocals of the delays to each of the reinforcers following the choice, with all delays measured from the choice). Latencies on forced trials and on choice trials also were related (negatively) to the sum of the immediacies. This correlation among response measures (choice and latencies) suggests that both measures are manifestations of the effect of conditioned reinforcement on response tendencies.     

Effects of experience on preference between forced and free choice

Preference between forced choice and free choice in concurrent-chain schedules of reinforcement was investigated in pigeons after exposure to particular combinations of terminal links. In Experiment 1, in which terminal links always ended with reinforcers, one of three pairs of terminal links was arranged as preexposure: (a) both terminal links had only one key (forced choice), (b) both terminal links had two keys (free choice), or (c) a combination of forced and free choice was arranged across sessions. In test sessions following the preexposure, pigeons' preferences rapidly shifted to the terminal links with which they had no recent experience. In Experiment 2, the same procedure was repeated except that each terminal link ended intermittently with reinforcers with a probability of .5 and there was no terminal-link arrangement with a combination of free and forced choice. Pigeons showed the same preference changes as in Experiment 1, but the preference changes did not appear immediately at the beginning of test sessions. These data suggest that recent previous experience was a more important determinant of preference than the difference between forced-choice and free-choice terminal links.     

Choice and conditioned reinforcement.

A potential weakness of one formulation of delay-reduction theory is its failure to include a term for rate of conditioned reinforcement, that is, the rate at which the terminal-link stimuli occur in concurrent-chains schedules. The present studies assessed whether or not rate of conditioned reinforcement has an independent effect upon choice. Pigeons responded on either modified concurrent-chains schedules or on comparable concurrent-tandem schedules. The initial link was shortened on only one of two concurrent-chains schedules and on only one of two corresponding concurrent-tandem schedules. This manipulation increased rate of conditioned reinforcement sharply in the chain but not in the tandem schedule. According to a formulation of delay-reduction theory, when the outcomes chosen (the terminal links) are equal, as in Experiment 1, choice should depend only on rate of primary reinforcement; thus, choice should be equivalent for the tandem and chain schedules despite a large difference in rate of conditioned reinforcement. When the outcomes chosen are unequal, however, as in Experiment 2, choice should depend upon both rate of primary reinforcement and relative signaled delay reduction; thus, larger preferences should occur in the chain than in the tandem schedules. These predictions were confirmed, suggesting that increasing the rate of conditioned reinforcement on concurrent-chains schedules may have no independent effect on choice.     

Freedom and knowledge: an experimental analysis of preference in pigeons

Relative responding in initial links of concurrent-chain schedules showed that pigeons preferred free to forced choices and informative to uninformative stimuli. Variable-interval initial links on two lower keys (white) of a six-key chamber produced terminal links on either two upper-left keys (blue and/or amber) or two upper-right keys (green and/or red). Terminal.links in which pecks on either of two lit keys produced fixed-interval reinforcement (free choice) were preferred to links with only one lit fixed-interval key available (forced choice). Terminal links with different key colors correlated with concurrent fixed-interval reinforcement and extinction (informative stimuli) were preferred to links with these schedules operating on same-color keys (uninformative stimuli). Scheduling extinction for one of the two free-choice keys assessed preference for two lit keys over one lit key, but confounded number with whether stimuli were informative. Fixed-interval reinforcement for both keys in each terminal link, but with different-color keys in one link and same-color keys in the other, showed that preference for informative stimuli did not depend on stimulus variety. Preferences were independent of relative responses per reinforcement and other properties of terminal-link performance.     

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.     

Choice: Some quantitative relations

Six pigeons responded in fifty-six conditions on a concurrent-chains procedure. Conditions included several with equal initial links and unequal terminal links, several with unequal initial links and equal terminal links, and several with both unequal initial and terminal links. Although the delay-reduction hypothesis accounted well for choice when the initial links were equal (mean deviation of .04), it fit the data poorly when the initial links were unequal (mean deviation of .18). A modification of the delay-reduction hypothesis, replacing the rates of reinforcement with the square roots of these rates, fit the data better than either the unmodified delay-reduction equation or Killeen's (1982) model. The modified delay-reduction equation was also consistent with data from prior studies using concurrent chains. The absolute rates of responding in each terminal link were well described by the same hyperbola (Herrnstein, 1970) that describes response rates on simple interval schedules.