Concurrent schedules of reinforcement: effects of gradual and abrupt increases in changeover delay

Pigeons' pecks were maintained on concurrent variable-interval 1-min variable-interval 3-min schedules of reinforcement, with a changeover delay of 2 sec. When changeover delay was increased successively to 5.0, 7.5, and 12.5 sec (Exp. I) the actual relative rate of reinforcement for the variable-interval 3-min key decreased progressively for two birds, abruptly for two other birds, and the subjects devoted proportionately less of their time and responding to that key. However, the relative performance measures (relative time and relative responding) approximated the actual relative rate of reinforcement, with a maximum discrepancy of 11%, over all changeover delay values investigated. Experiment II attempted to lengthen response-run durations on the variable-interval 3-min key so that they were long enough to meet the changeover delay requirement at each new changeover delay value, by progressively increasing the changeover delay by 0.5-sec increments. With this procedure the actual relative rate of reinforcement approximated more closely the scheduled relative rate as changeover delay increased. As in Exp. I, relative performance measures approximated the actual relative reinforcement rate (maximum discrepancy 17%).     

On the functions of the changeover delay

The function of changeover delays in producing matching was examined with pigeons responding on concurrent variable-interval variable-interval schedules. In Experiment 1, no changeover delay was compared to two different types of changeover delay. One type, designated generically as response-response but in the present example as peck-peck, was timed from the first response on the switched-to key; the other, designated generically as pause-response but in the present example as pause-peck, was timed from the last response on the switched-from key. High changeover rates occurred with no changeover delay. Peck-peck and pause-peck changeover delays produced low and intermediate changeover rates, respectively. In Experiment 2, pause-peck and peck-peck changeover delays were compared across a range of relative reinforcement rates. Similar matching relations developed despite differences in the changeover rates and local response patterns as a function of the type of changeover delay. In Experiment 3, both types of changeover delay yielded similar changeover rates when their obtained durations were equal via yoking. The results suggest that changeover delays function to separate responses on one key from reinforcers on the other or to delay reinforcement for changing over. In addition, the distribution of responding during and after the changeover delay may vary considerably without affecting matching.     

Local response-rate constancy on concurrent variable-interval schedules of reinforcement

Concurrent variable-interval schedules were arranged with a main key that alternated in color and schedule assignment, along with a changeover key on which a small fixed ratio was required to changeover. Acceptable matching was observed with pigeons in two replications, but there was a tendency toward overmatching. Local response rates were found to differ for unequal schedules of a concurrent pair: local response rate was greater for the variable-interval schedule with the smaller average interreinforcement interval, but qualifications based on an interresponse-time analysis were discussed. In a second experiment, two 3-minute variable-interval schedules were arranged concurrently, and the experimental variable was the changeover procedure: either a changeover delay was incurred by each changeover or a small fixed ratio on a changeover key was required to complete a changeover. Changeover delays of 2 and 5 seconds were compared with a fixed-ratio changeover of five responses. The response output on the main key (associated with the variable-interval schedules) was greater when a changeover delay was arranged than when a fixed ratio was required to changeover. A detailed analysis of stripchart records showed that a 2-second delay generated an increased response rate for 3 seconds after a changeover, while the fixed-ratio requirement generated an increased rate during the first second only, followed by a depressed response rate for 2 seconds.     

Concurrent responding with fixed relative rate of reinforcement

Responding by pigeons on one key of a two-key chamber alternated the color of the second key, on which responding produced food according to a variable-interval schedule of reinforcement. From time to time, reinforcement would be available for a response, but in the presence of a particular stimulus, either red or green light on the key. Red or green was chosen irregularly from reinforcement to reinforcement, so that a proportion of the total number of reinforcements could be specified for each color. Experimental manipulations involved variations of (1) the proportions for each color, (2) changeover delay, or, alternatively, (3) a fixed-ratio changeover requirement. The main findings were: (1) relative overall rates of responding and relative times in the presence of a key color approximated the proportions of reinforcements obtained in the presence of that color, while relative local rates of responding changed little; (2) changeover rate decreased as the proportions diverged from 0.50; (3) relative overall rate of responding and relative time remained constant as the changeover delay was increased from 2 to 32 sec, with reinforcement proportions for red and green of 0.75 and 0.25, but they increased above 0.90 when a fixed-ratio changeover of 20 responses replaced the changeover delay; (4) changeover rate decreased as the delay or fixed-ratio was increased.     

Changeover delay and concurrent schedules: some effects on relative performance measures

The pigeon and the rat partition total response output between both schedules of a concurrent variable-interval pair. The quantitative nature of a partition seems critically dependent on the relative rates with which the two schedules provide reinforcements for responding, in addition to the changeover delay. The manner in which the changeover delay controls the partition was studied by varying the duration of the changeover delay from 0 to 20 sec with each of two pairs of concurrent variable-interval schedules, viz., Conc VI 1.5-min VI 1.5-min and Conc VI 1-min VI 3-min. Rats served as the subjects and brain stimulation was employed as the reinforcer. When the schedules were Conc VI 1.5-min VI 1.5-min, relative response rate approximated 0.50 at all values of the changeover delay. When the schedules were Conc VI 1-min VI 3-min, relative response rate, computed with respect to the VI 1-min schedule, increased when the duration of the changeover delay increased. Changeover rate decreased when the duration of the changeover delay increased. The decrease was the same for both VI schedules of the Conc VI 1.5-min VI 1.5-min pair but was more rapid for the VI 3-min schedule of the Conc VI 1-min VI 3-min pair.     

Choice, rate of reinforcement, and the changeover delay

Pigeons distribute their responses on concurrently available variable-interval schedules in the same proportion as reinforcements are distributed on the two schedules only when a changeover delay is used. The present study shows that this equality between proportions of responses and proportions of reinforcements (“matching”) is obtained when the value of the changeover delay is varied. When responses are partitioned into the set of rapid response bursts occurring during the delay interval and the set of responses occurring subsequently, the proportion of neither set of responses matches the proportion of reinforcements. Instead, each set deviates from matching but in opposite directions. Matching on the gross level results from the interaction of two patterns evident in the local response rates: (I) the lengthening of the changeover delay response burst is accompanied by a commensurate decrease in the number of changeovers; (2) the changeover delay response burst is longer than the scheduled delay duration. When delay responses are eliminated by introducing a blackout during the delay interval, response matching is eliminated; the pigeon, however, continues to match the proportion of time spent responding on a key to the proportion of reinforcements obtained on that key.     

Unequal reinforcer magnitudes and relative preference for cooperation in the dyad

College-student subjects, who were paired with a confederate, chose to respond either independently or cooperatively for money reinforcers. The subject's relative preference for cooperation was assessed by a procedure (analogous to the psychophysical method of limits) in which response choice was monitored as reinforcer magnitude for one response mode was systematically varied while the other remained constant. Relative preference for cooperation was assessed when the confederate's payoff for cooperation was greater than the subject's (Experiment I) and when the confederate's payoff for independent responding was less than the subject's (Experiment II). For some subjects, changes in the confederate's reinforcer magnitudes resulted in shifts in relative preference for cooperation, which reduced the earnings differences, even though these preference shifts reduced the subject's absolute earnings. For those subjects for whom within-dyad differences in reinforcer magnitude produced no effect, a changeover button was introduced that allowed the subject to eliminate the payoff difference without reducing her own earnings; some subjects used this changeover button to eliminate earnings differences. Thus, the behavior of subjects varied, in part, as a function of reinforcer magnitudes provided for the confederate.     

Choice, changeover, and travel

Since foraging in nature can be viewed as instrumental behavior, choice between sources of food, known as “patches,” can be viewed as choice between instrumental response alternatives. Whereas the travel required to change alternatives deters changeover in nature, the changeover delay (COD) usually deters changeover in the laboratory. In this experiment, pigeons were exposed to laboratory choice situations, concurrent variable-interval schedules, that were standard except for the introduction of a travel requirement for changeover. As the travel requirement increased, rate of changeover decreased and preference for a favored alternative strengthened. When the travel requirement was small, the relations between choice and relative reinforcement revealed the usual tendencies toward matching and undermatching. When the travel requirement was large, strong overmatching occurred. These results, together with those from experiments in which changeover was deterred by punishment or a fixed-ratio requirement, deviate from the matching law, even when a correction is made for cost of changeover. If one accepted an argument that the COD is analogous to travel, the results suggest that the norm in choice relations would be overmatching. This overmatching, however, might only be the sign of an underlying strategy approximating optimization.     

Reinforcing staying and switching while using a changeover delay

Performance on concurrent schedules can be decomposed to run lengths (the number of responses before switching alternatives), or visit durations (time at an alternative before switching alternatives), that are a function of the ratio of the rates of reinforcement for staying and switching. From this analysis, a model of concurrent performance was developed and examined in two experiments. The first exposed rats to variable-interval schedules for staying and for switching, which included a changeover delay for reinforcers following a switch. With the changeover delay, run lengths and visit durations were functions of the ratios of the rates of reinforcement for staying and for switching, as found by previous research not using a changeover delay. The second directly assessed the effect of a changeover delay on run lengths and visit durations. Each component of a multiple schedule consisted of equivalent stay and switch schedules but only one component included a changeover delay. Run lengths and visit durations were longer when a changeover delay was used. Because visit duration is the reciprocal of changeover rate, these results are consistent with the established finding that a changeover delay reduces the frequency of switching. Together these results support the local model of concurrent performance as an alternative to the generalized matching law as a model of concurrent performance. The local model may be preferred when accounting for more molecular aspects of concurrent performance.     

Chained concurrent schedules: reinforcement as situation transition

Pigeons' pecks at two white response keys (initial-link situation) occasionally turned both keys red (terminal-link situation). When the two keys were red, pecks occasionally produced food, after which the keys were again white. In both situations, a changeover delay prevented the response-produced outcome from immediately following a change of responding from either key to the other. In the initial-link situation, the ratio of pecks at the keys closely paralleled the ratio of transitions into the terminal-link situation produced by the pecks, conforming to the well-known matching relation. In the terminal-link situation, the peck ratios deviated from the matching relation toward indifference. Overall response rate and rate of changeover were generally higher in the terminal-link situation than in the initial-link situation. The finding of matching in the initial-link situation supports a definition of reinforcement as situation transition. The differences in performance between the two situations, viewed in the light of other recent findings, suggest that the effects of a changeover delay depend on the overall reinforcing value of the choice alternatives.     

Changeover delay and concurrent-schedule performance in domestic hens

Six domestic hens were exposed to a series of five pairs of two-key concurrent variable-interval schedules with a range of changeover delays from no delay to 15 s. Times spent responding on each alternative and total, within_, and post-changeover-delay response ratios were analyzed in terms of the generalized matching law. The sensitivity parameters, a, for response and time data were generally low when no changeover delay was programmed but were not 0.0. They were higher for all other changeover-delay values, with some tendency to increase as the changeover delay lengthened at very short delays. Within-delay responding was insensitive to reinforcement-rate differences at all changeover delays (a values close to 0.0). As a result of this insensitivity, post-changeover-delay responding was more sensitive to reinforcement-rate changes than was total responding. Interchangeover intervals increased systematically with changeover-delay duration. Responding, particularly after the changeover delay, was well predicted by an equation based on a reinforcer-loss model.     

Choice behavior and the accessibility of the reinforcer

In Experiment 1, matching of relative response rates to relative rates of reinforcement was obtained in concurrent variable-interval schedules when the absolute values of the two concurrent variable-interval schedules varied from 6 sec and 12 sec to 600 sec and 1200 sec. Increases in the duration of the changeover delay, however, produced decreases in the relative response rates and, consequently, some deviation from matching. In Experiment 2, matching of relative response rates to the relative duration of the reinforcer failed to occur when the equal variable-interval schedules arranging access to the two different reinforcer durations (1.5 and 6 sec) were varied in size from concurrent variable-interval 10-sec schedules to concurrent variable-interval 600-sec schedules.     

A yoked-chamber comparison of concurrent and multiple schedules

Pigeons were exposed to alternative pairs of variable-interval schedules correlated with red and green lights on one key (the food key). In one experimental chamber, responses on a white key (the changeover key) changed the color of the food key and initiated a 2-sec changeover delay. Pigeons in a second chamber obtained food by pecking on a colored key whenever the pigeons in the first (concurrent) chamber had obtained food for a peck on that key color. There was no changeover key in the second (multiple) chamber: changeover responses in the first chamber alternated the schedules and colors in both chambers. The pigeons in both chambers emitted the same proportion of responses on each of the variable-interval schedules, and mastered discrimination reversals at the same rate. The pigeons differed only in their absolute response rates, which were greater under the concurrent schedules. In a second experiment, changes in key color occurred automatically, with different proportions of time allocated to the two variable-interval schedules. Matching of relative response frequency to relative reinforcement frequency was affected by the relative amounts of time in each component, by rate of changeovers, and by manipulations of the variable-interval scheduling.     

Response-rate invariance in concurrent schedules: effects of different changeover contingencies

In a two-key chamber, one key (the food key) was either red or green with different variable-interval schedules operating concurrently in each color and a second key (the changeover key) served to change the food-key color. Three pigeons were trained with either a 2-sec changeover delay or a 0-sec changeover delay and three birds with a fixed-ratio 2 on the changeover key instead of a changeover delay. The proportion of time spent in red approximated the proportion of reinforcers delivered in red for all birds. When the procedure was changed so that reinforcers were signalled in the green schedule, rates of reinforcement were unaltered, but the pigeons spent virtually the whole session in red. Changeovers to green were allowed only when a reinforcer was assigned by the schedule associated with green. For all pigeons with the fixed–ratio requirement on the changeover key or with a 0-sec changeover delay, the overall rate of red-key responses was higher during the signalling condition than during unsignalled, or baseline, condition. The present data question the generality of previous reports that the rate of one response is independent of the amount of time allocated to the alternative response.     

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.     

Concurrent fixed-interval variable-ratio schedules and the matching relation

Five rats responded under concurrent fixed-interval variable-ratio schedules of food reinforcement. Fixed-interval values ranged from 50-seconds to 300-seconds and variable-ratio values ranged from 30 to 360; a five-second changeover delay was in effect throughout the experiment. The relations between reinforcement ratios obtained from the two schedules and the ratios of responses and time spent on the schedules were described by Baum's (1974) generalized matching equation. All subjects undermatched both response and time ratios to reinforcement ratios, and all subjects displayed systematic bias in favor of the variable-ratio schedules. Response ratios undermatched reinforcement ratios less than did time ratios, but response ratios produced greater bias than did time ratios for every subject and for the group as a whole. Local rates of responding were generally higher on the variable-ratio than on the fixed-interval schedules. When responding was maintained by both schedules, a period of no responding on either schedule immediately after fixed-interval reinforcement typically was followed by high-rate responding on the variable-ratio schedule. At short fixed-interval values, when a changeover to the fixed-interval schedule was made, responding usually continued until fixed-interval reinforcement was obtained; at longer values, a changeover back to the variable-ratio schedule usually occurred when fixed-interval reinforcement was not forthcoming within a few seconds, and responding then alternated between the two schedules every few seconds until fixed-interval reinforcement finally was obtained.     

Choice dynamics in concurrent ratio schedules of reinforcement

The generalized matching law predicts performance on concurrent schedules when variable-interval schedules are programmed but is trivially applicable when independent ratio schedules are used. Responding usually is exclusive to the schedule with the lowest response requirement. Determining a method to program concurrent ratio schedules such that matching analyses can be usefully employed would extend the generality of matching research and lead to new avenues of research. In the present experiments, ratio schedules were programmed dependently such that responses to either of the two options progressed the requirement on both schedules. Responding is not exclusive because the probability of reinforcement increases on both schedules as responses are allocated to either schedule. In Experiment 1, performance on concurrent variable-ratio schedules was assessed, and reinforcer ratios were varied across conditions to investigate changes in sensitivity. Additionally, the length of a changeover delay was manipulated. In Experiment 2, performance was compared under concurrently available, dependently programmed variable-ratio and fixed-ratio schedules. Performance was well described by the generalized matching law. Increases in the changeover delay decreased sensitivity, whereas sensitivity was higher when variable-ratio schedules were employed, compared with fixed-ratio schedules. Concurrent ratio schedules can be a viable approach to studying functional differences between ratio and interval schedules.     

The general matching law describes choice on concurrent variable-interval schedules of wheel-running reinforcement.

Six male Wistar rats were exposed to concurrent variable-interval schedules of wheel-running reinforcement. The reinforcer associated with each alternative was the opportunity to run for 15 s, and the duration of the changeover delay was 1 s. Results suggested that time allocation was more sensitive to relative reinforcement rate than was response allocation. For time allocation, the mean slopes and intercepts were 0.82 and 0.008, respectively. In contrast, for response allocation, mean slopes and intercepts were 0.60 and 0.03, respectively. Correction for low response rates and high rates of changing over, however, increased slopes for response allocation to about equal those for time allocation. The results of the present study suggest that the two-operant form of the matching law can be extended to wheel-running reinforcement. 'I'he effects of a low overall response rate, a short Changeover delay, and long postreinforcement pausing on the assessment of matching in the present study are discussed.     

Momentary maximizing in concurrent schedules with a minimum interchangeover interval

Eight pigeons were trained on concurrent variable-interval variable-interval schedules with a minimum interchangeover time programmed as a consequence of changeovers. In Experiment 1 the reinforcement schedules remained constant while the minimum interchangeover time varied from 0 to 200 s. Relative response rates and relative time deviated from relative reinforcement rates toward indifference with long minimum interchangeover times. In Experiment 2 different reinforcement ratios were scheduled in successive experimental conditions with the minimum interchangeover time constant at 0, 2, 10, or 120 s. The exponent of the generalized matching equation was close to 1.0 when the minimum interchangeover time was 0 s (the typical procedure for concurrent schedules without a changeover delay) and decreased as that duration was increased. The data support the momentary maximizing theory and contradict molar maximizing theories and the melioration theory.     

Human choice on concurrent variable-interval variable-ratio schedules.

Each of 5 adult male humans sat in a 4 degrees C room where they could warm themselves by illuminating six heat lamps for 10-second periods according to a concurrent variable-interval variable-ratio schedule. Left-button presses on a response panel switched between the schedules and started a 2-second changeover delay. Right-button presses illuminated the heat lamps if assigned by the associated schedule and if the changeover delay had timed out. Panel lights identified the schedule in effect and each effective right-button press. A discrimination procedure--either a multiple variable-interval variable-ratio schedule or the presentation of each schedule individually on alternate days--preceded exposure to the choice procedure for some subjects. For subjects not exposed to a discrimination procedure prior to exposure to choice, or if such exposure failed to result in higher rates to the ratio than to the interval schedule, relative response rates matched relative reinforcement rates. However, if subjects responded at higher rates to the ratio schedule than to the interval schedule during a prior discrimination procedure, relative rates on a subsequent choice procedure deviated from matching in the direction of reinforcement-rate maximizing. In eight of 11 conditions, choice appeared to be governed by maximizing processes. In all cases, human concurrent ratio-interval performances differed from those of nonhumans in that matching was never obtained with local ratio-interval rate differences.