Performance of humans in variable-interval avoidance schedules programmed singly, and concurrently with variable-interval schedules of positive reinforcement

Performance maintained under single variable-interval avoidance schedules, single variable-interval schedules of positive reinforcement, and concurrent schedules consisting of a variable-interval avoidance component and a variable-interval positive reinforcement component, was studied in three human subjects, using points exchangeable for money as the reinforcer. Response rate in the single variable-interval avoidance schedules was an increasing function of the frequency of monetary loss avoidance. Response rate in the single variable-interval positive reinforcement schedules was an increasing function of the frequency of obtained monetary reinforcement. In the concurrent avoidance/reinforcement schedules, the rate of responding in the avoidance component increased, and the rate of responding in the positive reinforcement schedule decreased (with one exception) as a function of the frequency of loss avoidance in the avoidance component. The logarithms of the ratios of the response rates in the two components, and the logarithms of the ratios of the times spent in the two components, were linearly related to the logarithms of the ratios of the frequency of loss avoidance in the avoidance component to the frequency of reinforcement in the positive reinforcement component. All three subjects exhibited marked undermatching of response rate ratios to reinforcement frequency ratios. The results are discussed in the context of Herrnstein's quantitative model of operant performance.     

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%).     

Matching under concurrent fixed-ratio variable-interval schedules of food presentation

Four pigeons were exposed to concurrent fixed-ratio, variable-interval schedules of food presentation. The fixed-ratio requirement was either 25, 50, 75, or 100 responses, with the variable-interval schedule parameter held constant at 4 minutes. A delay time was imposed between a changeover from one schedule to the other and subsequent food availability. The delay time was varied at each ratio requirement over four values; no delay, 0-second delay, 1.5-second delay, and 5.0-second delay. As the fixed-ratio requirement or the delay time increased, a greater proportion of the total responses and time spent responding occurred under the variable-interval schedule relative to the proportion of food deliveries under that schedule. Neither relative overall response rate nor relative time spent responding equalled the relative frequency of food presentation, as would be predicted by a linear “matching” model. Rather, these data were described by power functions with slopes of approximately 1.0 and intercepts greater than 1.0. In the terms of Baum's (1974) analysis, these deviations from linear matching represent bias in favor of responding under the interval schedule. Bias, as reflected in the intercept of the power function, was greater for the ratio of time than the ratio of responses.     

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.     

Local patterns of responding maintained by concurrent and multiple schedules

Local patterns of responding were studied when pigeons pecked for food in concurrent variable-interval schedules (Experiment I) and in multiple variable-interval schedules (Experiment II). In Experiment I, similarities in the distribution of interresponse times on the two keys provided further evidence that responding on concurrent schedules is determined more by allocation of time than by changes in local pattern of responding. Relative responding in local intervals since a preceding reinforcement showed consistent deviations from matching between relative responding and relative reinforcement in various postreinforcement intervals. Response rates in local intervals since a preceding changeover showed that rate of responding is not the same on both keys in all postchangeover intervals. The relative amount of time consumed by interchangeover times of a given duration approximately matched relative frequency of reinforced interchangeover times of that duration. However, computer simulation showed that this matching was probably a necessary artifact of concurrent schedules. In Experiment II, when component durations were 180 sec, the relationship between distribution of interresponse times and rate of reinforcement in the component showed that responding was determined by local pattern of responding in the components. Since responding on concurrent schedules appears to be determined by time allocation, this result would establish a behavioral difference between multiple and concurrent schedules. However, when component durations were 5 sec, local pattern of responding in a component (defined by interresponse times) was less important in determining responding than was amount of time spent responding in a component (defined by latencies). In fact, with 5-sec component durations, the relative amount of time spent responding in a component approximately matched relative frequency of reinforcement in the component. Thus, as component durations in multiple schedules decrease, multiple schedules become more like concurrent schedules, in the sense that responding is affected by allocation of time rather than by local pattern of responding.     

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.     

Concurrent schedules: a quantitative relation between changeover behavior and its consequences

Data from several published experiments on concurrent variable-interval schedules were analyzed with respect to the effects of changeover delay on the time spent responding on a schedule before changing to an alternate schedule: i.e., the interchangeover time. Interchangeover time increases as the duration of the changeover delay increases, and the present analysis shows that a power function describes the relation. The power relation applied in spite of numerous differences in the experiments: different variable-interval schedules for the concurrent pairs; equal or unequal reinforcement rates for the schedules of the concurrent pairs; different durations of the changeover delay; response-dependent or response-independent reinforcers; pigeons or rats as subjects; different reinforcers. A power function also described the data in experiments where the changeover incurred a timeout, where a fixed ratio was required to changeover, and also when asymmetrical changeover delays were used.     

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.     

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.     

Matching to relative reinforcement frequency in multiple schedules with a short component duration

Three pigeons performed on two-component multiple variable-interval variable-interval schedules of reinforcement. There were two independent variables: component duration and the relative frequency of reinforcement in a component. The component duration, which was always the same in both components, was varied over experimental conditions from 2 to 180 sec. Over these conditions, the relative frequency of reinforcement in a component was either 0.2 or 0.8 (±0.03). As the component duration was shortened, the relative frequency of responding in a component approached a value equal to the relative frequency of reinforcement in that component. When the relative frequency of reinforcement was varied over conditions in which the component duration was fixed at 5 sec, the relative frequency of responding in a component closely approximated the relative frequency of reinforcement in that component. That is, the familiar matching relationship, obtained previously only with concurrent schedules, was obtained in multiple schedules with a short component duration.     

Matching with a trio of concurrent variable-interval schedules of reinforcement

A trio of concurrent variable-interval schedules of reinforcement was arranged according to a changeover-key procedure, including a changeover delay of 1.5 sec. The three schedules provided a combined maximum reinforcement rate of 45 reinforcements per hour. With that restriction, the nine experimental conditions included several combinations of variable-interval schedules, sometimes including extinction. The pigeons matched relative response rate and relative time to relative reinforcement rate. Relative time appeared to match some-what better than relative response rate. Performance adjusted rapidly from one experimental condition to the next, whether the change involved two or all three schedules of the concurrent trio.     

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 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.     

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.     

A yoked-chamber comparison of concurrent and multiple schedules: the relationship between component duration and responding

Two experimental chambers were electrically connected so that the component selected by a pigeon confronting concurrent variable-interval schedules in one chamber could be successively presented as a multiple schedule to a second pigeon in the other chamber. Component duration was regulated by the use of a changeover delay, the value of which was systematically varied between 0 and 30 sec. It was found that the relative local response rates on the preferred key (absolute response rate to that component divided by the sum of the absolute response rates during both components) tended to increase with increasing component durations for the birds in the concurrent chamber, but decreased for the birds in the multiple chamber. These data support the interpretation that there are fundamental differences in the mode of responding to multiple and concurrent schedules. Based on these findings, it was concluded that previous demonstrations of matching on multiple schedules do not establish that response allocation is controlled by a process equivalent to that found on choice paradigms. It now appears that matching on multiple (but not concurrent) schedules is a consequence of selecting short component durations. The implications of these data for Herrnstein's (1970) and Rachlin's (1973) formulations of the relationship between multiple and concurrent schedules are examined.     

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.     

The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.     

Changeover ratio effects on concurrent variable-interval performance

Rats' bar-pressing was maintained by concurrent variable-interval schedules of reinforcement. A fixed-ratio of pulls on a chain (the changeover ratio) was required for switching between schedules. The first experiment employed equal variable-interval schedules and symmetrical changeover ratios. Increasing these ratios resulted in a decrease in the rate of switching between schedules and an increase in local response rate. In the second experiment, a range of asymmetrical changeover ratios was used with equal variable-interval schedules, and a preference was found for the schedule associated with the larger switching-into ratio. Both the distributions of responses and time between the two schedules deviated from those expected on the basis of obtained reinforcers. In the third experiment, the switching-out-of ratio was dependent on the amount of time spent in a variable-interval 2-minute schedule; a constant ratio permitted switching out of the alternative variable-interval 1-minute schedule. A strong preference was shown for the variable-interval 2-minute schedule. The fourth experiment used equal variable-interval schedules; one changeover ratio was varied while the second remained constant. The results failed to show systematic differences in local response rates immediately after a changeover.     

Performance of rats under concurrent variable-interval schedules of negative reinforcement

The behavior of rats under concurrent variable-interval schedules of negative reinforcement was examined. A single one-minute variable-interval programmer determined the availability of 30-second timeouts from electric shock. These were assigned to one or the other of the two component schedules with a probability of 0 to 1.0. The response requirement for the component schedules was standing to the right or left of the center of the experimental chamber. With a six-second changeover delay, the relative time spent under one component schedule varied directly and linearly with the relative number of timeouts earned under that component schedule. The absolute number of changeovers was highest when a similar number of timeouts was earned under each component schedule, and lowest when all or nearly all timeouts were earned under one component schedule. In general, these relations are similar to those reported with concurrent variable-interval schedules of positive reinforcement.     

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.