Response rate and changeover performance on concurrent variable-interval schedules

Six pigeons were exposed to variable-interval schedules arranged on one, two, three, and four response keys. The reinforcement rate was also varied across conditions. Numbers of responses, the time spent responding, the number of reinforcements, and the number of changeovers between keys were recorded. Response rates on each key were an increasing function of reinforcement rate on that key and a decreasing function of the reinforcement rate on other keys. Response and time-allocation ratios under-matched ratios of obtained reinforcements. Three sets of equations were developed to express changeover rate as a function of response rate, time allocation, and reinforcement rate respectively. These functions were then applied to a broad range of experiments in the literature in order to test their generality. Further expressions were developed to account for changeover rates reported in experiments where changeover delays were varied.     

On the measurement of time allocation on multiple variable-interval schedules

Six pigeons were trained on a modified multiple-schedule procedure. In a three-key chamber, the center key was lighted red or green, depending upon which component schedule was in effect. A response on this key transferred this color to each of two side keys, and responses on one of those keys produced reinforcers according to the component schedule. After 2 s, the side-key lights were extinguished, the center key was reilluminated, and a further center-key response was required to give access, as before, to the component schedules. Components alternated every 3 min. This limited-access procedure allowed both times spent switched into the side keys and time spent not switched in to be measured in the two components. Component reinforcer rates were varied over eight experimental conditions. Both component response rate and component time allocation were increasing functions of relative component reinforcer rate, and these functions were not significantly different. This finding implies that local response rates (responses divided by time switched in) were unaffected by changing component reinforcer rates on multiple schedules. Because a similar result was recently obtained for concurrent schedules, models of multiple and concurrent-schedule performance may need to consider only the time allocation of behavior emitted at equal tempo in the component schedules.     

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.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Choice, time allocation, and response rate during stimulus generalization

Six pigeons were trained to discriminate between two noise intensities using a procedure that assessed choice, time allocation, and response rate simultaneously and independently. Responses on the left or right key (R1 or R2) were respectively correct in the presence of two different intensities, S1 and S2. After a correct response, reinforcement became available for pecks on the center key. Reinforcement density for R1¦S1 relative to R2¦S2 was varied across experimental conditions. Generalization tests followed extensive training at each condition. As a function of stimulus intensity, proportions of initial choices of R2, of time spent in R2-initiated components, and of center-key responses emitted in R2-initiated components all yielded sigmoidal gradients of similar slope, which shifted slightly in location when relative reinforcement density changed. Changeovers were maximal where initial choice proportions approximated 0.5. Gradients relating the absolute number of center-key responses to stimulus intensity were also roughly sigmoidal, but were more sensitive to changes in reinforcement density. Gradients of momentary response rate also depended on reinforcement density. During training, large but transitory shifts in choice responding occurred when reinforcement density changed, while differences in momentary response rate developed slowly, suggesting separate control of choice and response rate by the contingencies of reinforcement.     

Inhibitory stimulus control in concurrent schedules

Six pigeons were exposed to two keys, a main key and a changeover key. Pecking the main key was reinforced on a variable-interval 5-min schedule when the key was blue and never reinforced when the key displayed a vertical line on a blue background. Each peck on the changeover key changed the stimulus displayed on the main key. Each subject was given two generalization tests, consisting of presentations on the main key of six orientations of the line on the blue background, with no reinforcements being given. In one test changeover-key pecks changed the stimulus; in the other test the changeover key was covered and the experimenter controlled stimulus changes. Both responses to the six stimuli and time spent in the presence of the stimuli gave U-shaped gradients when the changeover key was operative. With most subjects, absolute rates of responding to each stimulus produced unsystematic gradients, whether or not the changeover key was operative.     

Time allocation in human vigilance

Three human subjects detected unpredictable signals by pressing either of two telegraph keys. The relative frequencies with which detections occurred for the two alternatives were varied. The procedure included a changeover delay and response cost for letting go of a key. All subjects matched the relative time spent holding each key to the relative number of detections for that key, in conformity with the matching law. One subject's performance, which at first deviated from the relation, came into conformity with it when response cost was increased. Another subject's performance approximated matching more closely when the changeover delay was increased. The results confirm and extend the notions that choice consists in time allocation and that all behavior can be measured on the common scale of time.     

Time allocation in concurrent schedules: the effect of signalled reinforcement

The responses of five pigeons were reinforced on concurrent variable-interval variable-interval reinforcement schedules in which changeover key responses changed the stimulus and reinforcement schedules associated with the food key. While the reinforcement availability in one component remained unchanged throughout the experiment, the reinforcement availability in the other component was, during several conditions, signalled by the onset of an additional discriminative stimulus. During unsignalled conditions, both the relative frequency of responding and the relative time spent in each component approximated the obtained relative reinforcement frequency in each component. The effect of signalling reinforcer availability in one component was to (1) reduce responding in the signalled component to near-zero levels, and (2) increase the relative time in the unsignalled component, without a corresponding increase in the obtained relative reinforcement frequency. The magnitude of the increase in relative time in the unsignalled component decreased as the overall frequency of reinforcement increased. This deviation in the matching relation between relative time and the obtained relative reinforcement frequency was eliminated if the overall reinforcement frequency was increased before the signal was introduced and then, without removing the signal, gradually reduced.     

Resurgence of time allocation

The resurgence of time allocation with pigeons was studied in three experiments. In Phase 1 of each experiment, response‐independent food occurred with different probabilities in the presence of two different keylights. Each peck on the key changed its color and the food probability in effect. In Phase 2, the food probabilities associated with each keylight were reversed and, in Phase 3, food was discontinued in the presence of either keylight. The food probabilities were .25 and .75, in Experiment 1, and 0.0 and 1.0 in Experiment 2. More time was allocated to the keylight correlated with more probable food in Phases 1 and 2, and in Phase 3 resurgence of time allocation occurred for two of three pigeons in Experiment 1, and for each of four pigeons in Experiment 2. Because time had to be allocated to either of the two alternatives in Experiments 1 and 2, however, it was difficult to characterize the time allocation patterns in Phase 3 as resurgence when changeover responding approached zero. In Experiment 3 this issue was addressed by providing a third alternative uncorrelated with food such that in each phase, after 30 s in the presence of either keylight correlated with food, the third alternative always was reinstated, requiring a response to access either of the two keylights correlated with food. In this experiment, the food probabilities were similar to those in Experiment 1. Resurgence of time allocation occurred for each of three pigeons under this procedure. The results of these experiments suggest that patterns of time allocation resurge similarly to discrete responses and to spatial and temporal patterns of responding.     

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.     

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, 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.     

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.     

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.     

Choice between concurrent schedules

Six pigeons pecked for food in a three-key experiment. A subject at any time could choose the left or right key and receive reinforcement according to one two-key concurrent variable-interval variable-interval schedule of reinforcement, or it could peck the center key. A peck on the center key arranged the complementary two-key concurrent variable-interval variable-interval schedule on the left and right keys. The two different two-key concurrent schedules arranged reinforcements concurrently and were signalled by two different colors of key lights. Choice behavior in the presence of a given color conformed to the usual relationship in two-key concurrent schedules: the relative frequency of responding on a key approximately equalled the relative frequency of reinforcement on that key. Preference for a two-key concurrent schedule, which was equivalent to preference for a color, was measured by the percentage of all responses on the left and right keys in the presence of that color: this percentage approximately equalled the percentage of all reinforcements that were delivered in the presence of that color. Thus, choice between concurrent schedules conforms approximately to the same relationship as does choice between alternatives in a single concurrent schedule.     

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.     

Peak shift in concurrent schedules

Pigeons were exposed to two keys, a main key and a changeover key. Initially non-differential training was given in which pecking the main key was reinforced on a variable-interval 2-min schedule when the key displayed the first stimulus, a black line on a blue background, and was reinforced on an identical but independent variable-interval 2-min schedule when the key displayed a plain blue stimulus. Later, differential training was given in which pecking the main key was reinforced on a variable-interval 2-min schedule when the first stimulus was displayed; and was reinforced on a variable-interval 10-min schedule when a second stimulus, a black line of another orientation on a blue background, was displayed. During non-differential and differential training, each peck on the changeover key changed the stimulus on the main key. Generalization tests were given before and after the differential training. These consisted of presentations on the main key of seven orientations of the black line on the blue background, including the first and second stimuli, with no reinforcements being given. Changeover-key pecks changed the stimuli on the main key. Generalization gradients were obtained using three measures: time spent, responses, and response rate in the presence of each test stimulus. Typically, maximum values on these measures occurred to stimuli away from the first in a direction opposite the second stimulus, and minimum values occurred to stimuli away from the second in a direction opposite the first.     

Performance on variable-interval schedules arranged singly and concurrently

Extensive parametric data were obtained from pigeons responding on variable-interval schedules arranged on three, two, and one response keys. Number of responses on the keys, the time spent responding on the keys, and the number of reinforcements obtained on the keys were measured. Response rates on each key were an increasing function of the reinforcement rate on that key, and an inverse function of the reinforcement rate on the other keys. In terms of preference, both response and time-allocation ratios undermatched ratios of obtained reinforcements, and the degree of undermatching was consistent both within, and between, two- and three-schedule data. When absolute response-rate data were analyzed according to Herrnstein's (1970) quantitative account, obtained values of assumed constants were not consistent either within or between conditions. However, a power-function modification of Herrnstein's account fitted the data well and provided similar exponent values to those obtained for the undermatching of preference ratios.     

Effects of response-allocation constraints on multiple-schedule performance

Four pigeons were trained on multiple variable-interval schedules in which components alternated after a fixed number of responses had been emitted. In Part 1, each component change occurred after 20 responses; in Part 2, the number was 40; and in Part 3, the number of responses before change was 10. Component reinforcer rates were varied over five experimental conditions in each of Parts 1 to 3. Component response rates decreased as the specified number of responses per component was increased. However, the relation between component response-rate ratios and component reinforcer-rate ratios was independent of the specified number of responses per component, and was similar to that found when components alternate after fixed time periods. In the fourth part of the experiment, the results from Parts 1 to 3 were systematically replicated by keeping the component reinforcer rates constant, but different, while the number of responses that produced component alternation was varied from 5 to 60 responses. The results showed that multiple-schedule performance under component-response-number constraint is similar to that under conventional component-duration constraint. They further suggest that multiple-schedule response rates are controlled by component reinforcer rates and not by principles of maximizing overall reinforcer rates or meliorating component reinforcer rates.