A molecular analysis of choice on concurrent-chains schedules.

Six pigeons responded on concurrent-chains schedules with either independent or interdependent equal variable-interval schedules in the initial links and unequal variable-interval schedules, always in a 2:1 ratio, in the terminal links. Relative response rates in the initial links increased across conditions as initial-link duration was shortened and decreased across conditions as terminal-link duration was shortened, replicating previous findings. Responses in the initial links were recorded in 5-s bins, and local or molecular relative response rates were calculated in order to ascertain how relative response rate varied as a function of time since the onset of the initial links. Two distinct molecular patterns were found. With interdependent initial links, relative response rates for the preferred key were elevated for the first 10 or 20 s of the initial links and then declined to an asymptotic value. With independent initial links, a negative recency effect was found similar to that reported by Killeen (1970). These two molecular patterns were related to the different momentary reinforcement probabilities resulting from independent and interdependent scheduling.     

Responding on concurrent-chains schedules in open and closed economies.

Pigeons' key pecks were reinforced according to concurrent-chains schedules of reinforcement. The programmed average time from the onset of the initial links to a terminal link entry was held constant across conditions while the value of variable-interval schedules in the terminal links was varied. Performance was assessed under two economic conditions: (a) an open economy in which session duration was limited to 1 hr and subjects were maintained at 80% of their free-feeding body weights with postsession food when necessary; and (b) a closed economy in which sessions were 23.5 hr long and no deprivation regimen was in effect. In all cases, the relative rate of responding in the initial links matched the reduction in overall delay to primary reinforcement correlated with entry into one terminal link relative to the reduction in delay correlated with entry into the other terminal link. Although the sum of responses made in the initial links and terminal links was found to increase, then decrease, as the rate of food presentation decreased in the closed economy, there was no consistent effect of overall rate of food presentation on total responding in the open economy. The choice data suggest that relative delay reduction predicts choice accurately, regardless of economic context.     

Matching, delay-reduction, and maximizing models for choice in concurrent-chains schedules.

Models of choice in concurrent-chains schedules are derived from melioration, generalized matching, and optimization. The resulting models are compared with those based on Fantino's (1969, 1981) delay-reduction hypothesis. It is found that all models involve the delay reduction factors (T - t2L) and (T - t2R), where T is the expected time to primary reinforcement and t2L, t2R are the durations of the terminal links. In particular, in the case of equal initial links, the model derived from melioration coincides with Fantino's original model for full (reliable) reinforcement and with the model proposed by Spetch and Dunn (1987) for percentage (unreliable) reinforcement. In the general case of unequal initial links, the model derived from melioration differs from the revised model advanced by Squires and Fantino (1971) only in the factors affecting the delay-reduction terms (T - t2L) and (T - t2R). The models of choice obtained by minimizing the expected time to reinforcement depend on the type of feedback functions used. In particular, if power feedback functions are used, the optimization model coincides with that obtained from melioration.     

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 signaled versus unsignaled reinforcement delay in concurrent-chain schedules

A concurrent-chain schedule was employed to examine pigeons' preferences for signaled versus unsignaled delay of reinforcement in which the delay durations ranged from zero to ten seconds. In general, pigeons preferred signaled delay over unsignaled delay especially when a variable-interval 30-second schedule operated in each initial link; when a variable-interval 90-second schedule operated in each initial link, these preferences tended toward indifference or were attenuated. In addition, prior training seemed to exert partial control over behavior. Responding in the terminal link was higher under signaled delay than unsignaled delay in a majority of the cases. Moreover, response rates under signaled delay remained fairly constant whereas responding under unsignaled delay was initially high, but decreased systematically with delay durations as short as 2.5 seconds. These results are consistent with a number of other studies demonstrating the significant role of a signal for impending positive stimuli.     

Token reinforcement, choice, and self-control in pigeons.

Pigeons were exposed to self-control procedures that involved illumination of light-emitting diodes (LEDs) as a form of token reinforcement. In a discrete-trials arrangement, subjects chose between one and three LEDs; each LED was exchangeable for 2-s access to food during distinct posttrial exchange periods. In Experiment 1, subjects generally preferred the immediate presentation of a single LED over the delayed presentation of three LEDs, but differences in the delay to the exchange period between the two options prevented a clear assessment of the relative influence of LED delay and exchange-period delay as determinants of choice. In Experiment 2, in which delays to the exchange period from either alternative were equal in most conditions, all subjects preferred the delayed three LEDs more often than in Experiment-1. In Experiment 3, subjects preferred the option that resulted in a greater amount of food more often if the choices also produced LEDs than if they did not. In Experiment 4, preference for the delayed three LEDs was obtained when delays to the exchange period were equal, but reversed in favor of an immediate single LED when the latter choice also resulted in quicker access to exchange periods. The overall pattern of results suggests that (a) delay to the exchange period is a more critical determinant of choice than is delay to token presentation; (b) tokens may function as conditioned reinforcers, although their discriminative properties may be responsible for the self-control that occurs under token reinforcer arrangements; and (c) previously reported differences in the self-control choices of humans and pigeons may have resulted at least in part from the procedural conventions of using token reinforcers with human subjects and food reinforcers with pigeon subjects.     

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.     

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.     

A quantitative analysis of sensitivity to the conditioned reinforcing value of terminal-link stimuli in a concurrent-chains schedule.

Pigeons were exposed to a concurrent-chains schedule in which a single variable-interval 30-s schedule was used in the initial links and fixed-time schedules were used in the terminal links. Three types of keylight conditions were used in the terminal links. In the first condition, different delays were associated with different keylight stimuli (cued condition). In the second condition, different delays were associated with the same stimulus, either a blackout (uncued blackout condition) or a white key (uncued white condition). Paired values of terminal-link fixed-time schedules differed by a constant ratio of 3:1, while the absolute value of delays was varied from 3 s to 54 s. The results showed that choice proportions for the shorter of two delays increased when the absolute size of the delays was increased for all keylight conditions. Further, the choice proportions for the shorter delay increased from the uncued blackout condition, to the uncued white condition, to the cued condition. A modified version of Fantino's (1969) delay-reduction model (expressed as a function relating the response ratio to the delay-reduction ratio) can be applied to these data by showing that sensitivity to delay reduction increased from the uncued blackout condition, to the uncued white condition, to the cued condition. Thus, the present study demonstrated that a modified version of the delay-reduction model can be used to assess quantitative differences in the terminal-link keylight condition in terms of sensitivity to delay reduction (i.e., the conditioned reinforcing value of the terminal-link keylight stimuli).     

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).     

Unsignalled delay of reinforcement in variable-interval schedules

Three pigeons responded on several tandem variable-interval fixed-time schedules in which the value of the fixed-time component was varied to assess the effects of different unsignalled delays of reinforcement. Actual (obtained) delays between the last key peck in an interval and reinforcement were consistently shorter than the nominal (programmed) delay. When nominal delays were relatively short, response rates were higher during the delay condition than during the corresponding nondelay condition. At longer nominal delay intervals, response rates decreased monotonically with increasing delays. The results were consistent with those obtained from delay-of-reinforcement procedures that impose either a stimulus change (signal) or a no-response requirement during the delay interval.     

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.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.     

Choice performance in several concurrent key-peck treadle-press reinforcement schedules

Five pigeons were exposed to several concurrent variable-interval food reinforcement schedules. For three subjects, one component of the schedule required a key-pecking response, the other a treadle-pressing response. For the other two subjects, both schedule components required treadle-pressing responses. The relative probability of reinforcement associated with the manipulanda was varied from 0 to 1.0 in 13 experimental conditions for the Key-Treadle subjects and nine conditions for the Treadle-Treadle subjects. The results indicated that the logarithms of relative time spent responding, and the logarithms of relative number of responses emitted on a manipulandum, approximated direct linear functions of logarithms of the relative frequencies of reinforcement associated with that manipulandum. No systematic bias in favor of time spent key pecking over time spent treadle pressing was apparent for the Key-Treadle subjects. All subjects exhibited undermatching, in that the ratios of time and response allocation at the alternatives systematically differed from the ratios of reinforcers obtained from the alternatives in the direction of indifference. Key pecking appeared to have no special link to food beyond treadle pressing or what would be expected on the basis of the reinforcement dependencies alone.     

Responding of pigeons under variable-interval schedules of signaled-delayed reinforcement: effects of delay-signal duration.

Two experiments with pigeons examined the relation of the duration of a signal for delay ("delay signal") to rates of key pecking. The first employed a multiple schedule comprised of two components with equal variable-interval 60-s schedules of 27-s delayed food reinforcement. In one component, a short (0.5-s) delay signal, presented immediately following the key peck that began the delay, was increased in duration across phases; in the second component the delay signal initially was equal to the length of the programmed delay (27 s) and was decreased across phases. Response rates prior to delays were an increasing function of delay-signal duration. As the delay signal was decreased in duration, response rates were generally higher than those obtained under identical delay-signal durations as the signal was increased in duration. In Experiment 2 a single variable-interval 60-s schedule of 27-s delayed reinforcement was used. Delay-signal durations were again increased gradually across phases. As in Experiment 1, response rates increased as the delay-signal duration was increased. Following the phase during which the signal lasted the entire delay, shorter delay-signal-duration conditions were introduced abruptly, rather than gradually as in Experiment 1, to determine whether the gradual shortening of the delay signal accounted for the differences observed in response rates under identical delay-signal conditions in Experiment 1. Response rates obtained during the second exposures to the conditions with shorter signals were higher than those observed under identical conditions as the signal duration was increased, as in Experiment 1. In both experiments, rates and patterns of responding during delays varied greatly across subjects and were not systematically related to delay-signal durations. The effects of the delay signal may be related to the signal's role as a discriminative stimulus for adventitiously reinforced intradelay behavior, or the delay signal may have served as a conditioned reinforcer by virtue of the temporal relation between it and presentation of food.     

Second-order schedules of token reinforcement with pigeons: implications for unit price

Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio). The token-production and exchange-production ratios were manipulated systematically across conditions. Response rates varied inversely with the token-production ratio at each exchange-production ratio. Response rates also varied inversely with the exchange-production ratio at each token-production ratio, particularly at the higher token-production ratios. At higher token-production and exchange-production ratios, response rates increased in token-production segments closer to exchange periods and food. Some conditions were conducted in a closed economy, in which the pigeons earned all their daily ration of food within the session. Relative to comparable open-economy conditions, response rates in the closed economy were less affected by changes in token-production ratio, resulting in higher levels of food intake and body weight. Some of the results are consistent with the economic concept of unit price, a cost-benefit ratio comprised of responses per unit of food delivery, but most are well accounted for by a consideration of the number of responses required to produce exchange periods, without regard to the amount of reinforcement available during those exchange periods.     

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.     

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.     

Evidence against a constant-difference effect in concurrent-chains schedules

Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect. Both experiments used equal variable-interval schedules as initial links. The terminal links were fixed delays to reinforcement in Experiment 1 and variable delays to reinforcement in Experiment 2. The durations of the terminal links were varied across conditions, but the difference between pairs of terminal links was always 10 s. In both experiments, preference for the shorter terminal link became less extreme as terminal-link durations increased, so a constant-difference effect was not found. It is argued, however, that this choice situation does not provide clear evidence for or against delay-reduction theory versus other theories of choice.     

Maximizing versus matching on concurrent variable-interval schedules

Maximization and matching predictions were examined for a time-based analogue of the concurrent variable-interval variable-ratio schedule. One alternative was a variable interval whose time base operated relatively independent of the schedule chosen, and the other was a discontinuous variable interval for which timing progressed only when selected. Pigeons switched between schedules by pecking a changeover key. The maximization hypothesis predicts that subjects will show a bias toward the discontinuous variable interval and undermatching; however the obtained results conformed closely to the predictions of the matching law. Finally, a quantitative comparison was made of the bias and sensitivity estimates obtained in published concurrent variable-interval variable-ratio analogue studies. Results indicated that only the ratio-based analogue of the concurrent variable interval variable ratio studied by Green, Rachlin, and Hanson (1983) produced significant bias toward the variable-ratio alternative and undermatching, as predicted by reinforcement maximization.