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.     

Sensitivity to reinforcement in concurrent arithmetic and exponential schedules

The generalized matching law states that the logarithm of the ratio of responses emitted or time spent responding in concurrent variable-interval schedules is a linear function of the logarithm of the ratio of reinforcements obtained. The slope of this relation, sensitivity to reinforcement, varies about 1.0 but has been shown to be different when obtained in different laboratories. The present paper analyzed the results from 18 experiments on concurrent variable-interval schedule performance and showed that response-allocation sensitivity to reinforcement was significantly smaller when arithmetic, rather than exponential, progressions were used to produce variable-interval schedules. There were no differences in time-allocation sensitivity between the two methods of constructing variable-interval schedules. Since the two laboratories have consistently used different methods for constructing variable-interval schedules, the differences in obtained sensitivities to reinforcement are explained. The reanalysis suggests that animals may be sensitive to differences in the distribution of reinforcements in time.     

Response Form, Force, And Number: Effects On Concurrent-schedule Performance

Six hens responded on concurrent variable-interval (key-peck) variable-interval (door-push) schedules of reinforcement in which the second-order (fixed-ratio) requirements on the alternatives (Experiment 1) or the required door forces (Experiment 2) were varied. The key-peck and door-push response (measured as fixed-ratio completion) and time data were well described by the generalized matching law. However, the manipulations of fixed-ratio requirement and required response force differed in their effects. The manipulations of fixed-ratio size affected the response and time measures differently, producing fairly constant, multiplicative biases only in terms of response allocation. It was argued that variations in fixed-ratio size necessarily change the time allocated to that response unit, and thus changes in time bias were not necessarily a fundamental effect of changing the ratio. In contrast, the changes in response bias were a fundamental result of changes in ratio size. The response-force manipulations produced similar bias shifts in terms of response and time allocation, but they appeared to combine with relative reinforcement rate to affect choice interactively. Specifically, behavior appeared to be biased towards the least effortful (i.e., key-peck) response, but the increases in door force had a larger effect on bias when the hens were making this response infrequently (on a lean schedule). The different effects of the fixed-ratio and response-force manipulations on concurrent performance were partially accounted for by the differing times required to complete each response unit under those manipulations, but this would not account for the interaction. The interaction would be consonant with increased response effort decreasing the effective value of the associated reinforcement schedule.     

Bias and sensitivity to reinforcement in a concurrent-chain schedule

Six pigeons were trained on concurrent-chain schedules in which the initial links were either dependent (Experiment 1) or independent (Experiment 2) concurrent variable-interval schedules and the terminal links were fixed-duration delays to reinforcement in blackout. A changeover delay of three seconds operated in the initial links. Both the initial- and terminal-link schedule values were varied over 61 experimental conditions. An analysis of the data using the generalized matching law showed that the sensitivity of initial-link response allocation to the frequency of terminal-link production was independent of both the duration of the terminal-link delays and, though less clearly, of the duration of the initial-link schedules. Sensitivity of initial-link response allocation to terminal-link reinforcer-rate ratios was a joint function of the terminal-link durations and the smaller average initial-link duration. The results showed that the generalized matching law is useful in analyzing concurrent-chain schedule performance and that a changeover delay in the initial links eliminates some terminal- to initial-link interactions that have made quantitative predictions for concurrent-chain performances difficult.     

Stimulus control of behavioral history.

Pigeons were exposed to two different reinforcement schedules under different stimulus conditions in each of two daily sessions separated by 6 hr (Experiments 1 and 2) or in a single session (Experiment 3). Following this, either a fixed-interval (Experiment 1) or a variable-interval schedule (Experiments 2 and 3) was effected in both stimulus conditions. In the first two experiments, exposure to fixed-ratio or differential-reinforcement-of-low-rate schedules led to response-rate, but not pattern, differences in subsequent performance on fixed- or variable-interval schedules that persisted for up to 60 sessions. The effects of reinforcement-schedule history on fixed-interval schedule performance generally were more persistent. In Experiment 3, a history of high and low response rates in different components of a multiple schedule resulted in subsequent response-rate differences under identical variable-interval schedules. Higher response rates initially occurred in the component previously correlated with high response rates. For 3 of 4 subjects, the differences persisted for 20 or more sessions. Previous demonstrations of behavioral history effects have been confined largely to between-subject comparisons. By contrast, the present results demonstrate strong behavioral effects of schedule histories under stimulus control within individual subjects.     

Schedule-induced defecation by rats during ratio and interval schedules of food reinforcement.

Lever pressing in rats was maintained by continuous and intermittent schedules of food while defecation was monitored. In Experiment 1, reinforcement densities were matched across variable-ratio and variable-interval schedules for three pairs of rats. Defecation occurred in all 3 rats on the variable-ratio schedule and in all 3 rats on the yoked variable-interval schedule. In Experiment 2, fixed-ratio and fixed-interval schedules with similar reinforcement densities maintained lever pressing. Defecation occurred in 3 of 4 rats on the fixed-ratio schedule and in 4 of 4 rats on the fixed-interval schedule. Almost no defecation occurred during continuous reinforcement in either experiment. These results demonstrate that defecation may occur during both ratio and interval schedules and that the inter-reinforcement interval is more important than the behavioral requirements of the schedule in generating schedule-induced defecation.     

Matching under nonindependent variable-ratio schedules of drug reinforcement.

Response-contingent deliveries of oral pentobarbital maintained responding of 3 rhesus monkeys during daily 3-hr sessions. Deliveries of pentobarbital were arranged under nonindependent concurrent variable-ratio variable-ratio schedules. Responses to either schedule counted toward completion of both variable-ratio schedule requirements. This schedule is similar in some respects to conventional concurrent variable-interval variable-interval schedules, in which passage of time counts toward completion of the interval value on both schedules. Restricted nonindependent concurrent variable-ratio variable-ratio schedules were also studied. On that schedule, when a drug delivery was assigned to one spout, it had to be collected before responses on the opposite spout again counted toward completion of the schedule requirements. Relative reinforcer magnitude was varied by changing the drug concentration on one schedule while keeping the drug concentration constant on the other variable-ratio schedule. Under both types of concurrent variable-ratio schedules, the relative rate of responding corresponded to the relative drug intake. Unlike earlier studies of concurrent variable-interval variable-interval intravenous cocaine reinforcement, preference was proportionate to concentration, and exclusive preferences did not develop. The relationship between relative rate of responding and relative drug intake was well described by the generalized matching law.     

Tests of behavior momentum in simple and multiple schedules with rats and pigeons.

Four experiments examined the relationship between rate of reinforcement and resistance to change in rats' and pigeons' responses under simple and multiple schedules of reinforcement. In Experiment 1, 28 rats responded under either simple fixed-ratio, variable-ratio, fixed-interval, or variable-interval schedules; in Experiment 2, 3 pigeons responded under simple fixed-ratio schedules. Under each schedule, rate of reinforcement varied across four successive conditions. In Experiment 3, 14 rats responded under either a multiple fixed-ratio schedule or a multiple fixed-interval schedule, each with two components that differed in rate of reinforcement. In Experiment 4, 7 pigeons responded under either a multiple fixed-ratio or a multiple fixed-interval schedule, each with three components that also differed in rate of reinforcement. Under each condition of each experiment, resistance to change was studied by measuring schedule-controlled performance under conditions with prefeeding, response-independent food during the schedule or during timeouts that separated components of the multiple schedules, and by measuring behavior under extinction. There were no consistent differences between rats and pigeons. There was no direct relationship between rates of reinforcement and resistance to change when rates of reinforcement varied across successive conditions in the simple schedules. By comparison, in the multiple schedules there was a direct relationship between rates of reinforcement and resistance to change during most tests of resistance to change. The major exception was delivering response-independent food during the schedule; this disrupted responding, but there was no direct relationship between rates of reinforcement and resistance to change in simple- or multiple-schedule contexts. The data suggest that rate of reinforcement determines resistance to change in multiple schedules, but that this relationship does not hold under simple schedules.     

Choice between response units: The rate constancy model

In a conjoint schedule, reinforcement is available simultaneously on two or more schedules for the same response. The present experiments provided food for key pecking on both a random-interval and a differential-reinforcement-of-low-rate (DRL) schedule. Experiment 1 involved ordinary DRL schedules; Experiment 2 added an external stimulus to indicate when the required interresponse time had elapsed. In both experiments, the potential reinforcer frequency from each component was varied by means of a second-order fixed-ratio schedule, and the DRL time parameter was changed as well. Response rates were described by a model stating that time allocation to each component matches the relative frequency of reinforcement for that component. When spending time in a given component, the subject is assumed to respond at the rate characteristic of baseline performance. This model appeared preferable to the absolute-rate version of the matching law. The model was shown to be applicable to multiple-response concurrent schedules as well as to conjoint schedules, and it described some of the necessary conditions for response matching, undermatching, and bias. In addition, the pigeons did not optimize reinforcer frequency.     

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.     

Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules

Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.     

Multiple determinants of the effects of reinforcement magnitude on free-operant response rates

Four experiments examined the effects of increasing the number of food pellets given to hungry rats for a lever-press response. On a simple variable-interval 60-s schedule, increased number of pellets depressed response rates (Experiment 1). In Experiment 2, the decrease in response rate as a function of increased reinforcement magnitude was demonstrated on a variable-interval 30-s schedule, but enhanced rates of response were obtained with the same increase in reinforcement magnitude on a variable-ratio 30 schedule. In Experiment 3, higher rates of responding were maintained by the component of a concurrent variable-interval 60-s variable-interval 60-s schedule associated with a higher reinforcement magnitude. In Experiment 4, higher rates of response were produced in the component of a multiple variable-interval 60-s variable-interval 60-s schedule associated with the higher reinforcement magnitude. It is suggested that on simple schedules greater reinforcer magnitudes shape the reinforced pattern of responding more effectively than do smaller reinforcement magnitudes. This effect is, however, overridden by another process, such a contrast, when two magnitudes are presented within a single session on two-component schedules.     

Asymmetry of reinforcement and punishment in human choice

The hypothesis that a penny lost is valued more highly than a penny earned was tested in human choice. Five participants clicked a computer mouse under concurrent variable-interval schedules of monetary reinforcement. In the no-punishment condition, the schedules arranged monetary gain. In the punishment conditions, a schedule of monetary loss was superimposed on one response alternative. Deviations from generalized matching using the free parameters c (sensitivity to reinforcement) and log k (bias) were compared in the no-punishment and punishment conditions. The no-punishment conditions yielded values of log k that approximated zero for all participants, indicating no bias. In the punishment condition, values of log k deviated substantially from zero, revealing a 3-fold bias toward the unpunished alternative. Moreover, the c parameters were substantially smaller in punished conditions. The values for bias and sensitivity under punishment did not change significantly when the measure of net reinforcers (gains minus losses) was applied to the analysis. These results mean that punishment reduced the sensitivity of behavior to reinforcement and biased performance toward the unpunished alternative. We concluded that a single punisher subtracted more value than a single reinforcer added, indicating an asymmetry in the law of effect.     

Concurrent second-order schedules: some effects of variations in response number and duration

To examine the effects on concurrent performance of independent manipulations of response-unit duration and number, 6 hens were exposed to concurrent second-order schedules of reinforcement. Each first-order operant unit required completion of a fixed-ratio schedule within the time specified by a fixed-interval schedule, with one further response completing the fixed-interval schedule. The fixed-ratio and fixed-interval requirements comprising the first-order operant units were systematically and independently varied under three pairs of concurrent variable-interval schedules to produce differences in the first-order response and duration requirements (response and duration differentials). These manipulations produced consistent changes in response, time, and operant-unit biases. A 1:4 response differential biased the time and operant-unit measures towards the smaller fixed ratio, but to a degree less than the imposed response differential. The response-based biases favored the larger fixed ratio. Duration differentials of 4:1 and 8:1 biased the response and operant-unit measures towards the shorter fixed interval, again less than the imposed duration differential, but the time biases remained close to zero. Both sorts of differentials acted to bias operant-unit completions more systematically than the other measures, but undermatching to the differentials occurred. The undermatching appears to have arisen from a pattern of fix and sample (in which visits to the less preferred alternative involved only a single completed operant unit) under combinations of unequal operant-unit requirements and reinforcer rates. The response and time bias measures appeared to arise as by-products of the changes in operant-unit completions.     

Melloration and maximization of reinforcement minus costs of behavior

Eight pigeons were exposed to independent concurrent schedules. Concurrent variable-interval 60-second variable-interval 60-second schedules were presented to one group of four subjects. Following baseline training, a limited hold was added to one of the schedules and the duration of the hold was decreased in successive conditions. Concurrent variable-interval 120-second variable-interval 40-second schedules were presented to another group of four subjects. These subjects were first exposed to decreasing durations of a limited hold in the variable-interval 40-second component. After replication of the baseline, a limited hold in the variable-interval 120-second component was decreased in duration. The initial durations of the holds were determined from the subjects' responding in the baseline conditions. A duration was chosen such that approximately 25% of the scheduled reinforcers would be canceled if responding remained unchanged.

Approximate matching of time proportions and reinforcement proportions was observed when the limited hold was added to the variable-interval 60-second schedule and when the limited hold was added to the variable-interval 40-second schedule. Time proportions were less extreme than reinforcement proportions when the limited hold operated in a variable-interval 120-second schedule. Overall reinforcement rates tended to decrease with continued training in concurrent schedules with a limited hold. Absolute deviations from time matching also decreased. The results provide evidence against the principle of reinforcement maximization, and support Herrnstein and Vaughan's (1980) melioration hypothesis.

     

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.     

Human choice in concurrent ratio-interval schedules of reinforcement.

Seven undergraduates participated in a concurrent-choice experiment with monetary reinforcers. Response-independent analogues of variable-interval and variable-ratio schedules were used to assess whether subjects would maximize reinforcement rate. The optimal pattern of behavior, in terms of maximizing reinforcement rate, involved a large bias toward the ratio alternative, with only occasional sampling of the interval schedule. Most experiments with pigeons, however, demonstrate matching of response rates to reinforcement rates, with only slight biases for the ratio schedule. Although subjects in the present experiment allocated more time to the ratio alternative than required by matching, the magnitude of the bias did not approximate that predicted by a maximizing account. After exposure to clock stimuli correlated with the operation of each schedule, 1 subject's behavior did show a substantial level of bias, increasing the total number of reinforcers obtained, and lay at a point between the predictions of matching and maximizing. The other subjects, however, continued to respond less optimally. The present results can be accounted for by a view of matching that incorporates the effects of delayed reinforcement.     

Behavioral contrast as differential time allocation

In Experiment I, hooded rats were exposed to multiple variable-interval schedules of reinforcement in which manipulanda and reinforcement magazines at opposite ends of the experimental chamber were associated with the different components. Time allocated to each component was measured by recording the time spent by the subject in the appropriate half of the chamber. Positive behavioral contrast was observed for the comparison between multiple variable-interval 30-second variable-interval 30-second and multiple variable-interval 30-second variable-interval 90-second conditions for both response frequency and time allocation measures, but not for mean local response rate (response frequency per time allocated to a component). In Experiment II, rats were exposed to multiple variable-time schedules in which reinforcement was response independent. Time allocated to each component was measured for two conditions, multiple variable-time 30-second variable-time 30-second and multiple variable-time 30-second variable-time 90-second. Positive behavioral contrast of time allocation was exhibited. The results indicated that time allocation was differentially sensitive to changes in reinforcement probability, and that behavioral contrast may result from the differential allocation of time to the different components of the multiple schedule.     

Variable-interval schedules of timeout from avoidance

Rats were trained on concurrent schedules in which pressing one lever postponed shock and pressing the other occasionally produced a 2-min timeout during which the shock-postponement schedule was suspended and its correlated stimuli were removed. Throughout, the shock-postponement schedule maintained proficient levels of avoidance. Nevertheless, in Experiment 1 responding on the timeout lever was established rapidly, was maintained at stable levels on variable-interval schedules, was extinguished by withholding timeout, was reestablished when timeout was reintroduced, and was brought under discriminative control with a multiple variable-interval extinction schedule of timeout. These results are in contrast with Verhave's (1962) conclusion that timeout is an ineffective reinforcer when presented to rats on intermittent schedules. In Experiment 2 the consequence of responding on the timeout lever was altered so that the shock-postponement schedule remained in effect even though the stimulus conditions associated with timeout were produced for 2 min. Responding extinguished, indicating that suspension of the shock-postponement schedule, not stimulus change, was the source of reinforcement. By establishing the reinforcing efficacy of timeout with standard variable-interval schedules, these experiments illustrate a procedure for studying negative reinforcement in the same way as positive reinforcement.     

Concurrent schedules: Quantifying the aversiveness of noise

Four hens worked under independent multiple concurrent variable-interval schedules with an overlaid aversive stimulus (sound of hens in a poultry shed at 100dBA) activated by the first peck on a key. The sound remained on until a response was made on the other key. The key that activated the sound in each component was varied over a series of conditions. When the sound was activated by the left (or right) key in one component, it was activated by the right (or left) key in the other component. Bias was examined under a range of different variable-interval schedules, and the applicability of the generalized matching law was examined. It was found that the hens' behavior was biased away from the sound independently of the schedule in effect and that this bias could be quantified using a modified version of the generalized matching law. Behavior during the changeover delays was not affected by the presence of the noise or by changes in reinforcement rate, even though the total response measures were. Insensitivity shown during the delay suggests that behavior after the changeover delay may be more appropriate as a measure of preference (or aversiveness) of stimuli than are overall behavior measures.