Titration of schedule parameters by pigeons

Pigeons were tested in a computer-controlled two-key chamber. A standard (nonchanging) schedule of reinforcement was in force on one key, and an adjusting schedule on the other. The schedules were available concurrently after each reinforcement, but after the first peck on either key (the choice peck), the schedule on the other key was made inoperative. The parameter of the adjusting schedule was decreased when the standard schedule was chosen and increased when the adjusting schedule was chosen. The standard schedule was changed only between sessions. Fixed intervals and fixed ratios were used as standard schedules, and intervals and ratios were used as adjusting schedules. When standard and adjusting schedules were of the same type, median parameters on the adjusting key equalled those of the standard schedules, at four values of each standard schedule. For four of five birds, and for the group median, similar curves could be plotted through the indifference points obtained from a standard ratio with an adjusting interval, and from a standard interval with an adjusting ratio. These points showed consistent individual differences, but they could be predicted by assuming that the median time from the choice peck to reinforcement should be the same on both keys. This is equivalent to treating the schedule as a concurrent chain and assuming that Herrnstein's quantitative law of effect applies.     

The reinforcement of four interresponse times in a two-alternative situation

Pigeons pecked for food in a two-key procedure. A concurrent variable-interval variable-interval schedule of reinforcement for two classes of interresponse times was arranged on each key. A visual stimulus set the occasion for potential reinforcement of the four operant classes: shorter and longer interresponse times on left and right keys. In Exp. I, the relative frequency of respones on a key equalled the relative frequency of reinforcement on that key. In Exp. II, the relative frequency of an interresponse time equalled the relative reciprocal of its length. In Exp. III, the relative frequency of an interresponse time was a monotonically increasing function of its relative frequency of reinforcement. These functions relating the relative frequency of an interresponse time to its relative length and to its relative frequency of reinforcement were the same as if there had been no second key. Also, the distribution of responses between keys was independent of the relative frequency of an interresponse time on either key. Experiment IV replicated Exp. I except that choices between keys were controlled by a stimulus that signalled the availability of reinforcement on the right key. A comparison of Exp. I and IV suggested that the relative frequency of an interresponse time on one key generally was independent of behavior on the other key, but that the number of responses per minute on a key did depend on behavior on the other key.     

Effects on concurrent performances of a stimulus correlated with reinforcer availability

A multiple schedule was arranged in which each component consisted of two, concurrent variable-interval schedules of reinforcement. A changeover-key procedure was used, and the components of the multiple schedule were distinguished (initially) by the color of the changeover key. During one component of the multiple schedule, the availability of a reinforcer arranged by one of the variable-interval schedules was marked by an exteroceptive stimulus, provided that that variable-interval schedule was not at the time assigned to the main key. During the other component of the multiple schedule, no reinforcer-correlated stimuli were ever presented. During the latter component of the multiple schedule, the distribution of responses and time for the concurrent variable-interval schedules suggested control by the distribution of reinforcements. During the former component, most main-key responses were emitted on the key in the presence of which reinforcer-correlated stimuli were presented. Changeover rate in the presence of that key color was depressed. The discriminative control over the changeover was easily established and was reversible.     

Some effects of relative reinforcement rate and changeover delay in response-independent concurrent schedules of reinforcement

Reinforcements were arranged independently of the pigeon's behavior by concurrent variable-interval schedules. The reinforcements arranged by one of the schedules occurred when the chamber was illuminated with amber light, and the reinforcements arranged by the other schedule occurred when the chamber was illuminated with blue light. Both schedules functioned concurrently, but reinforcers were delivered by each only in the presence of the appropriate stimulus condition. A response on a white key, the only key in the chamber, alternated the stimulus condition and the effective schedule. The results of this procedure were similar to those obtained with concurrent response-dependent variable-interval schedules of reinforcement. The proportion of the total session time spent in the presence of a schedule component approximated the proportion of the total number of reinforcements in the component. Changeover rate was a decreasing function of the changeover delay and of the difference between the relative rates of reinforcement for each pair of concurrent schedules.     

The concurrent reinforcement of two interresponse times: the relative frequency of an interresponse time equals its relative harmonic length

The relative lengths of two concurrently reinforced interresponse times were varied in an experiment in which three pigeons obtained food by pecking on a single key. Visual discriminative stimuli accompanied the two time intervals in which reinforcements were scheduled according to a one-minute variable-interval. The steady-state relative frequency of an interresponse time approximately equalled the complement of its relative length, that is, its relative harmonic length. Thus, lengths of interresponse times and delays of reinforcement have the same effect on the relative frequencies of interresponse times and choices in one-key and two-key concurrent variable-interval schedules, respectively. A second experiment generalized further the functional equivalence between the effects of these one-key and two-key concurrent schedules by revealing that the usual matching-to-relative-immediacy in two-key concurrent schedules is undisturbed if reinforcement depends upon the occurrence of a response at the end of the delay interval, as it does in the one-key schedules. The results of both experiments are consistent with a quantitative theory of concurrent operant behavior.     

Performance in concurrent interval schedules

Four pigeons were trained under concurrent variable-interval variable-interval and fixed-interval variable-interval schedules in a two-key situation. Both response allocation and time allocation to the two schedules were measured when various reinforcement rates were arranged on each key. All animals showed an approximately constant proportional preference for the variable-interval schedule over the fixed-interval schedule. These results support Schneider's (1969) analysis of fixed-interval schedule performance.     

Magnitude and frequency of reinforcement and frequencies of interresponse times

The relative magnitude and relative frequency of reinforcement for two concurrent interresponse times (1.5 to 2.5 sec and 3.5 to 4.5 sec) were simultaneously varied in an experiment in which pigeons obtained grain by pecking on a single key. Visual discriminative stimuli accompanied the two time intervals in which reinforcements were arranged by a one-minute variable-interval schedule. The resulting interresponse times of each of three pigeons fell into two groups; "short" (1.0 to 2.5 sec) and "long" (3.0 to 4.5 sec). Steady-state relative frequencies of these interresponse times were orderly functions of both reinforcement variables. The combined effects of both independent variables were well summarized by a linear function of one variable, relative access to food. Unlike corresponding two-key concurrent variable-interval schedules, the present schedule did not produce an equality between the relative frequency of an operant and either the relative magnitude or the relative frequency of reinforcement of that operant. A tentative account is provided for this difference between one-key and two-key functions.     

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.     

Response rate as a function of amount of reinforcement for a signalled concurrent response

Pigeons were exposed to two equal, concurrent variable-interval schedules of reinforcement on two response keys. One key was continuously illuminated. Pecking on that key produced reinforcements of constant duration. The other key was normally dark, except that availability of reinforcement was signalled by illuminating the key. The duration of access to a grain reinforcer was varied on the key that signalled reinforcement. Rate of response on the first key, the one that did not signal reinforcement, was found to vary inversely with duration of signalled reinforcement on the other key. The latency between the signal and the peck that produced signalled reinforcement remained about constant. These results show that responding on one key in concurrent variable-interval schedules depends on the reinforcement delivered by both schedules and is independent of responding on the other key.     

Response and time allocation in concurrent second-order schedules

Six pigeons were trained on two-key concurrent variable-interval schedules in which the required response was the completion of a fixed number of key pecks. When the required number of pecks was equal on the two keys, response- and time-allocation ratios under-matched obtained reinforcement rate ratios. A similar result was found when the required number of pecks was unequal, except that performance, measured in response terms, was biased to the shorter required number of pecks and was less sensitive to reinforcement-rate changes. No such differences were found in the data on time spent responding. When the variable-interval schedules were kept constant and the required numbers of pecks were systematically varied, response ratios changed inversely with the ratio of the required number of pecks, but time-allocation ratios varied directly with the same independent variable. Thus, on response measures, pigeons “prefer” the schedule with the smaller peck requirement, but on time measures they “prefer” the schedule with the larger peck requirement. This finding is inconsistent with a commonsense notion of choice, which sees response and time-allocation measures as equivalent.     

Choice and segmented interreinforcement intervals

Pigeons were trained on a two-key concurrent schedule, where food reinforcers on one key were arranged by a simple variable-interval schedule and on the other key by a chain variable-interval variable-interval schedule. When the initial link of the chain was in effect, the pigeons tended to respond more on the simple variable-interval schedule, and hence less on the chain, than would be expected from a comparison of both the local and overall rates of reinforcement of the two schedules. When the terminal link of the chain was in effect, the pigeons responded more on the chain than would be expected from a comparison of the rates of reinforcement of the schedules then in effect. Overall responding on the chain was not proportional to overall reinforcement on the chain but rather was a by-product of responding during initial- and terminal-link phases.     

Rates and patterns of responding with concurrent fixed-interval and variable-interval reinforcement

Pigeons were exposed to concurrent fixed-interval and variable-interval schedules of food reinforcement on two keys. The times between reinforcement were varied systematically on both keys. The overall relative frequency of responding on the fixed-interval key depended on the relative frequency of reinforcement, but did not match it. Instead, the ratio of responses on the fixed-interval key to responses on the variable-interval key was a power function of the ratio of reinforcements, with an exponent of 0.5. Patterns of responding between reinforcements on the fixed-interval key depended on both relative and absolute values of the reinforcement schedules. Similar overall relative responding was obtained at different absolute schedule values with equal relative reinforcement, despite some differences in patterns of responding.     

Interval reinforcement of choice behavior in discrete trials

Pigeons were trained to peck at red or green keys presented simultaneously in discrete trials. In one experiment, reinforcements were arranged by concurrent variable-interval schedules. The proportion of responses to green approximately matched the proportion of reinforcements produced by pecking green. Detailed analysis of responding revealed a systematic decrease in the probability of switching from green to red within sequences of trials after reinforcement. This trend corresponded to sequential changes in the relative frequency of reinforcement, and not to sequential changes in probability of reinforcement. In a second experiment, reinforcements were scheduled probabilistically every seventh trial. Even though there were no contingencies on pecking during the first six post-reinforcement trials, choices of green on the first response after reinforcement matched the proportion of reinforcements for pecking green. These results extend the generality of overall matching under concurrent reinforcement.     

Choice between two-component chained and tandem schedules

Pigeons were trained on a two-key choice procedure in which a pair of equal and concurrently available variable-interval schedules (initial links) arranged entry into one or the other of two mutually exclusive schedules (terminal links) that ended in primary reinforcement. The terminal links were two-component chained or tandem schedules. Responses during the initial links were distributed equally on the two keys whenever the terminal links were associated with the same sets of interreinforcement intervals. Whether or not the terminal-link interreinforcement intervals were the same on the two keys, initial-link responding was affected by neither the presence nor relative durations of differentially signalled components within a terminal-link schedule. The simplest interpretation of these results is that initial-link responding is maintained directly by delayed primary reinforcement, rather than conditioned reinforcement afforded by the stimuli correlated with the terminal-link schedule components. This finding suggests that aspects of chained schedule performance usually attributed to conditioned reinforcement might best be reinterpreted in terms of delayed primary reinforcement and various discriminative functions served by the component-correlated stimuli.     

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.     

Punishment of observing by the negative discriminative stimulus

To determine the effect of a negative discriminative stimulus on the response producing it, two pigeons were each studied in a three-key conditioning chamber. During alternating periods of unpredictable duration, pecking the center (food) key either was reinforced with grain on a variable-interval schedule or was never reinforced. On equal but independent variable-interval schedules, pecking either of the side (observing) keys changed the color of all keys for 30 sec from yellow to either green or red. When the schedule on the center key was variable-interval reinforcement, the color was green (positive discriminative stimulus); when no reinforcements were scheduled, the color was red (negative discriminative stimulus). Since pecking the side keys did not affect grain deliveries, changes in the rate of pecking could not be ascribed to changes in the frequency of primary reinforcement. In subsequent sessions, red was withheld as one of the possible consequences of pecking a given side key. When red was omitted, the rate on that key increased, and when red was restored, the rate decreased. It was concluded that red illumination of the keys, the negative discriminative stimulus, had a suppressive effect on the response that produced it.     

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.     

Concurrent performances: rate constancies without changeover delays

Pigeons' pecks on two keys were maintained, without changeover delays, by independent variable-interval schedules of food reinforcement. Four regularly cycling 2-min components scheduled reinforcement respectively for both keys, left key only, both keys, and right key only. Initially, reinforcement scheduled for one key alone produced more responding on that key than reinforcement scheduled concurrently for both keys. Continued sessions reduced this difference; response rate on a given key approached constancy, or invariance with respect to the performance on and schedule for the other key. When extinction replaced the reinforcement schedule on either key, responding on that key decreased more during components that scheduled reinforcement for the other key than during those that did not. This demonstration that responses on one key were not supported by reinforcers on the other key suggested that the alternation of concurrent responding and either-key-alone responding prevented concurrent superstitions from developing.     

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.