Relative sensitivity to reinforcer amount and delay in a self-control choice situation.

Rats were exposed to concurrent-chains schedules in which a single variable-interval schedule arranged entry into one of two terminal-link delay periods (fixed-interval schedules). The shorter delay ended with the delivery of a single food pellet; the longer day ended with a larger number of food pellets (two under some conditions and six under others). In Experiment 1, the terminal-link delays were selected so that under all conditions the ratio of delays would exactly equal the ratio of the number of pellets. But the absolute duration of the delays differed across conditions. In one condition, for example, rats chose between one pellet delayed 5 s and six pellets delayed 30 s; in another condition rats chose between one pellet delayed 10 s and six pellets delayed 60 s. The generalized matching law predicts indifference between the two alternatives, assuming that the sensitivity parameters for amount and delay of reinforcement are equal. The rats' choices were, in fact, close to indifference except when the choice was between one pellet delayed 5 s and six pellets delayed 30 s. That deviation from indifference suggests that the sensitivities to amount and delay differ from each other depending on the durations of the delays. In Experiment 2, rats chose between one pellet following a 5-s delay and six pellets following a delay that was systematically increased over sessions to find a point of indifference. Indifference was achieved when the delay to the six pellets was approximately 55 s. These results are consistent with the possibility that the relative sensitivities to amount and delay differ as a function of the delays.     

Concurrent schedules: Interaction of reinforcer frequency and reinforcer duration

Six pigeons were trained on concurrent variable-interval schedules with unequal reinforcer durations for the two responses. The schedules arranged on the two keys were kept equal while they were varied in absolute size. As the overall reinforcer rate was increased, both response-allocation and time-allocation measures of choice showed a trend toward indifference, and measures of sensitivity to reinforcer-duration ratios significantly decreased. Recent reports have shown that the generalized matching law cannot describe the changes in behavior allocation under constant delay-, duration-, or rate-ratios when changes are made in the absolute levels of each of these variables. The present results complement these findings by demonstrating that the concatenated generalized matching law cannot describe the interactions of two reinforcer variables on behavior allocation.     

Effects of response type on pigeons' sensitivity to variation in reinforcer amount and reinforcer delay

Twelve pigeons, divided into two groups, responded on concurrent nonindependent variable-interval schedules to obtain access to grain by either pecking keys or pressing treadles. Either the amount of grain or the delay to the receipt of grain was varied in separate conditions to determine the sensitivity of relative responding to variation in reinforcer amount (s_A), the sensitivity to variation in reinforcer delay (s_D), and s_A/s_D, a measure related to self-control. There were no significant differences between the two groups in the values of s_A, s_D, and s_A/s_D. These results suggest that the values of s_A, s_D, and s_A/s_D for pigeons may be similar across these two types of responses.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

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.     

Concurrent schedules: reinforcer magnitude effects

Five pigeons were trained on pairs of concurrent variable-interval schedules in a switching-key procedure. The arranged overall rate of reinforcement was constant in all conditions, and the reinforcer-magnitude ratios obtained from the two alternatives were varied over five levels. Each condition remained in effect for 65 sessions and the last 50 sessions of data from each condition were analyzed. At a molar level of analysis, preference was described well by a version of the generalized matching law, consistent with previous reports. More local analyses showed that recently obtained reinforcers had small measurable effects on current preference, with the most recently obtained reinforcer having a substantially larger effect. Larger reinforcers resulted in larger and longer preference pulses, and a small preference was maintained for the larger-magnitude alternative even after long inter-reinforcer intervals. These results are consistent with the notion that the variables controlling choice have both short- and long-term effects. Moreover, they suggest that control by reinforcer magnitude is exerted in a manner similar to control by reinforcer frequency. Lower sensitivities when reinforcer magnitude is varied are likely to be due to equal frequencies of different sized preference pulses, whereas higher sensitivities when reinforcer rates are varied might result from changes in the frequencies of different sized preference pulses.     

Choice in a variable environment: effects of unequal reinforcer distributions

Six pigeons were trained in a procedure in which sessions included seven unsignaled components, each offering two pecking keys, and each providing a potentially different reinforcer ratio between the two keys. Across conditions, various combinations of reinforcer ratios and reinforcer-magnitude ratios were used to create unequal reinforcer distributions between the two alternatives when averaged across a session. The results extended previous research using the same basic procedure that had included only reinforcer distributions symmetrical around 1:1. Data analyses suggested that the variables controlling choice operated at a number of levels: First, individual reinforcers had local effects on choice; second, sequences of successive reinforcers obtained at the same alternative (continuations) had cumulative effects; and, third, when these sequences themselves occurred with greater frequency, their effects further cumulated. A reinforcer obtained at the other alternative following a sequence of continuations (a discontinuation) had a large effect and apparently reset choice to levels approximating the sessional reinforcer ratio.     

Effects of intertrial reinforcers on self-control choice.

In three experiments, pigeons chose between a small amount of food delivered after a short delay and a larger amount delivered after a longer delay. A discrete-trial adjusting-delay procedure was used to estimate indifference points--pairs of delay-amount combinations that were chosen about equally often. In Experiment 1, when additional reinforcers were available during intertrial intervals on a variable-interval schedule, preference for the smaller, more immediate reinforcer increased. Experiment 2 found that this shift in preference occurred partly because the variable-interval schedule started sooner after the smaller, more immediate reinforcer, but there was still a small shift in preference when the durations and temporal locations of the variable-interval schedules were identical for both alternatives. Experiment 3 found greater increases in preference for the smaller, more immediate reinforcer with a variable-interval 15-s schedule than with a variable-interval 90-s schedule. The results were generally consistent with a model that states that the impact of any event that follows a choice response declines according to a hyperbolic function with increasing time since the moment of choice.     

Relative reinforcer rates and magnitudes do not control concurrent choice independently

One assumption of the matching approach to choice is that different independent variables control choice independently of each other. We tested this assumption for reinforcer rate and magnitude in an extensive parametric experiment. Five pigeons responded for food reinforcement on switching-key concurrent variable-interval variable-interval schedules. Across conditions, the ratios of reinforcer rates and of reinforcer magnitudes on the two alternatives were both manipulated. Control by each independent variable, as measured by generalized-matching sensitivity, changed significantly with the ratio of the other independent variable. Analyses taking the model-comparison approach, which weighs improvement in goodness-of-fit against increasing number of free parameters, were inconclusive. These analyses compared a model assuming constant sensitivity to magnitude across all reinforcer-rate ratios with two alternative models. One of those alternatives allowed sensitivity to magnitude to vary freely across reinforcer-rate ratios, and was less efficient than the common-sensitivity model for all pigeons, according to the Schwarz-Bayes information criterion. The second alternative model constrained sensitivity to magnitude to be equal for pairs of reinforcer-rate ratios that deviated from unity by proportionately equal amounts but in opposite directions. This model was more efficient than the common-magnitude-sensitivity model for 2 of the pigeons, but not for the other 3. An analysis of variance, carried out independently of the generalized-matching analysis, also showed a significant interaction between the effects of reinforcer rate and reinforcer magnitude on choice. On balance, these results suggest that the assumption of independence inherent in the matching approach cannot be maintained. Relative reinforcer rates and magnitudes do not control choice independently.     

Choice, foraging, and reinforcer duration.

Pigeons were exposed to a foraging schedule characterized by three different states, beginning with a search state in which completion of a variable interval on a white key led to a choice state. In the choice state the subject could, by appropriate responding on a fixed ratio of three, either accept or reject the schedule offered. If the subject accepted the schedule, it entered a handling state in which the appropriate reinforcer amount was presented according to a variable-interval schedule. In Experiment 1 the shorter duration reinforcer was more likely to be accepted the longer the duration of the search state and the shorter the equal durations of the handling states. In Experiment 2 the shorter duration reinforcer was more likely to be accepted the longer the handling time preceding the longer duration reinforcer. All of the results were in qualitative--and some were in quantitative--agreement with those predicted by the delay-reduction hypothesis and the optimal-diet model.     

Choice, relative reinforcer duration, and the changeover ratio

Relative reinforcer duration was varied in concurrent schedules with a fixed-ratio four changeover requirement. The schedule in effect after each reinforcer was randomly chosen. For all three pigeons, relative response rates overmatched relative reinforcer durations. Time allocation was less extreme and, on the average, matched relative reinforcer duration. In a subsequent manipulation, the level of preference was shown to depend on the size of the changeover requirement. These results are similar to those from related unequal reinforcement-frequency procedures.     

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.     

The effect of variable delays on self-control

Five pigeons served as subjects in an experiment that examined the effects of variable as opposed to fixed delays on preference in a self-control paradigm (choice between larger, more delayed and smaller, less delayed reinforcers). Nonindependent concurrent variable-interval schedules were used to measure choice. When delays to the larger, more delayed reinforcers were variable as opposed to fixed, the subjects showed an increased preference for that alternative (the self-control alternative). A series of regressions revealed that the hyperbolic decay model and incentive theory provided poor fits to the data, but a modified version of the generalized matching law provided an adequate fit. Together, consistent with a general prediction made by discounting models, the data supported the conclusion that variable delays can increase self-control. However, specific discounting models were not able to explain the present data well.     

Choice in a self-control paradigm: Quantification of experience-based differences

Previous quantitative models of choice in a self-control paradigm (choice between a larger, more-delayed reinforcer and a smaller, less-delayed reinforcer) have not described individual differences. Two experiments are reported that provide additional quantitative data on experience-based differences in choice between reinforcers of varying sizes and delays. In Experiment 1, seven pigeons in a self-control paradigm were exposed to a fading procedure that increased choices of the larger, more-delayed reinforcer through gradually decreasing the delay to the smaller of two equally delayed reinforcers. Three control subjects, exposed to each of the small-reinforcer delays to which the experimental subjects were exposed, but for fewer sessions, demonstrated that lengthy exposure to each of the conditions in the fading procedure may be necessary in order for the increase to occur. In Experiment 2, pigeons with and without fading-procedure exposure chose between reinforcers of varying sizes and delays scheduled according to a concurrent variable-interval variable-interval schedule. In both experiments, pigeons with fading-procedure exposure were more sensitive to variations in reinforcer size than reinforcer delay when compared with pigeons without this exposure. The data were described by the generalized matching law when the relative size of its exponents, representing subjects' relative sensitivity to reinforcer size and delay, were grouped according to subjects' experience.     

Choice in a variable environment: every reinforcer counts

Six pigeons were trained in sessions composed of seven components, each arranged with a different concurrent-schedule reinforcer ratio. These components occurred in an irregular order with equal frequency, separated by 10-s blackouts. No signals differentiated the different reinforcer ratios. Conditions lasted 50 sessions, and data were collected from the last 35 sessions. In Part 1, the arranged overall reinforcer rate was 2.22 reinforcers per minute. Over conditions, number of reinforcers per component was varied from 4 to 12. In Part 2, the overall reinforcer rate was six per minute, with both 4 and 12 reinforcers per component. Within components, log response-allocation ratios adjusted rapidly as more reinforcers were delivered in the component, and the slope of the choice relation (sensitivity) leveled off at moderately high levels after only about eight reinforcers. When the carryover from previous components was taken into account, the number of reinforcers in the components appeared to have no systematic effect on the speed at which behavior changed after a component started. Consequently, sensitivity values at each reinforcer delivery were superimposable. However, adjustment to changing reinforcer ratios was faster, and reached greater sensitivity values, when overall reinforcer rate was higher. Within a component, each successive reinforcer from the same alternative ("confirming") had a smaller effect than the one before, but single reinforcers from the other alternative ("disconfirming") always had a large effect. Choice in the prior component carried over into the next component, and its effects could be discerned even after five or six reinforcement and nonreinforcement is suggested.     

Sensitivity of time allocation to concurrent-schedule reinforcement

Four pigeons were trained on concurrent variable-interval schedules programmed on a center response key, with access to those schedules controlled by responses on left or right side keys. Two procedures were used. In one, the pigeon was given limited access, in that each side-key response produced 3-s access to a center-key schedule, and in the other procedure, access was unlimited. Data were analyzed using the generalized matching law. Comparison of sensitivities to reinforcement of interchangeover time for both procedures showed them to be of similar magnitude. Response sensitivities were also similar in magnitude for both procedures. From the limited-access procedure a second time measure that was available, switched-in time, was relatively uncontaminated by time spent emitting behavior other than key pecking. Sensitivities to reinforcement for the switched-in time measure were always smaller than interchangeover-time sensitivities for either procedure, and were approximately equal to response sensitivities for the limited-access procedure. Two other access times (5 and 7.5 s) were studied to validate the choice of 3 s as the main access time. These results indicate that when time spent emitting other behavior is excluded from interchangeover time, time and response sensitivities will be approximately equal.     

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).     

Responding during reinforcement delay in a self-control paradigm.

Eight pigeons chose between a small, immediate reinforcer and a large, increasingly delayed reinforcer. Responding during the large-reinforcer delays was examined. During large-reinforcer delays, pecks on one key produced the small, immediate reinforcer; pecks on the other key had no effect. Thus, a pigeon could reverse its initial choice of the large, delayed reinforcer, or it could maintain its original choice. Pigeons that made a relatively high number of initial large-reinforcer choices tended to maintain these choices, and those pigeons that actually received a relatively high number of large reinforcers, tended to respond more frequently on the ineffective key during the delay periods. The findings suggest that some previous studies of self-control training in pigeons may have resulted in increased self-control partially due to a lack of opportunity for the pigeons to change their choices.     

Component probability and component reinforcer rate as biasers of free-operant detection

Six pigeons were trained on multiple schedules whose components were concurrent variable-interval extinction and concurrent extinction variable-interval schedules. In Experiments 1a and 1b the stimuli signaling the components were two different light intensities, and in Experiments 2a and 2b they were two identical intensities. The components of the multiple schedule changed probabilistically after each reinforcer. In Experiments 1a and 2a, the probability of presenting the components was varied over five conditions and a replication. In Experiments 1b and 2b, the component probability was .5 and the component reinforcer rates were varied systematically over five conditions and a replication. The data, analyzed according to the Davison-Tustin behavioral detection model, confirmed that the discriminability of the stimuli signaling the components was high when the stimuli were different, and low when the stimuli were the same. Discriminability, measured by log d, was unaffected by component probability variation and by component reinforcer-rate variation. When discriminability was high, bias, or the response allocation between the two keys, was more strongly affected by variation of reinforcer rate within components than by variation of component probability, but the reverse was found when discriminability was low. The results suggest that free-operant detection performance is controlled by the rates of reinforcers in periods of time in which stimuli signal differential contingencies. These periods comprise the components when the component stimuli are discriminable, and comprise the total session when the components are indiscriminable. An extension of the Davison-Tustin behavioral detection model that incorporates these results is presented.