Some effects of discriminative training with equated frequency of reinforcement

Pigeons were exposed to a multiple schedule which provided equally frequent reinforcement in the presence of two stimuli but which produced markedly different rates of key-pecking. Generalization gradients were displaced away from the stimulus associated with the lower rate of key-pecking. Another group of pigeons had similar training, except that a low rate of key-pecking was established in a stimulus with a much higher frequency of food reinforcement. In this case, the generalization gradients were not affected by the training on the schedule producing a low response rate.     

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.     

An invariant relation between changing over and reinforcement

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.     

Fixed and variable schedules of response-independent reinforcement

After response-dependent reinforcement established key-pecking as the predominant response, pigeons received schedules in which reinforcements occurred without reference to responding. These response-independent schedules involved either a reinforcement every 5 min, or reinforcements at irregular intervals that averaged 5 min. The response-independent schedules generated characteristic patterns of responding. The fixed schedule produced positively accelerated responding between reinforcements, and the variable schedule produced either steady rates, erratic, or negatively accelerated patterns. The patterns developed independent of the distribution of responses existing when the schedule was first imposed. The rate of responding varied for the three birds, but, for all, response-independent schedules decreased the rates below the level maintained by response-dependent reinforcement. Although the rate of responding was affected primarily by the events contiguous with reinforcement, the pattern of responding appeared to be determined mainly by the presentation of reinforcements in relation to time.     

Matching, contrast, and equalizing in the concurrent lever-press responding of rats

Five rats pressed levers for food reinforces delivered by several concurrent variable-interval variable-interval schedules. The rate of reinforcement available for responding on one component schedule was held constant at 60 reinforcers per hour. The rate of reinforcement available for responding on the other schedule varied from 30 to 240 reinforcers per hour. The behavior of the rats resembled the behavior of pigeons pecking keys for food reinforcers. The ratio of the overall rates of responding emitted under, and the ratio of the time spent responding under, the two components of each concurrent schedule were approximately equal to the ratio of the overall rates of reinforcement obtained from the components. The overall rate of responding emitted under, and the time spent responding under, the variable component schedule varied directly with the overall rate of reinforcement from that schedule. The overall rate of responding emitted under, and the time spent responding under, the constant component schedule varied inversely with the overall rate of reinforcement obtained from the variable component. The local rates of responding emitted under, and the local rates of reinforcement obtained from, the two components did not differ consistently across subjects. But they were not exactly equal either.     

The reinforcement of least-frequent interresponse times

A new schedule of reinforcement was used to maintain key-pecking by pigeons. The schedule reinforced only pecks terminating interresponse times which occurred least often relative to the exponential distribution of interresponse times to be expected from an ideal random generator. Two schedule parameters were varied: (1) the rate constant of the controlling exponential distribution and (2) the probability that a response would be reinforced, given that it met the interresponse-time contingency. Response rate changed quickly and markedly with changes in the rate constant; it changed only slightly with a fourfold change in the reinforcement probability. The schedule produced stable rates and high intra- and inter-subject reliability, yet interresponse time distributions were approximately exponential. Such local interresponse time variability in the context of good overall control suggests that the schedule may be used to generate stable, predictable, yet sensitive baseline rates. Implications for the measurement of rate are discussed.     

Conditioning of the aggressive behavior of pigeons by a fixed-interval schedule of reinforcement

Operant reinforcement of aggression was studied in food-deprived pigeons by delivering food for attacks against a target pigeon. The food was delivered according to a fixed-interval schedule and attack behavior was recorded automatically. Attack could be conditioned and extinguished, and the proportion of time spent in attack was a direct function of the frequency of reinforcement of the attack. The fixed-interval schedule produced an increasing rate of attack during the interval between food reinforcements. This positive curvature was an inverse function of the duration of the interval. The findings revealed that the duration and temporal patterning of the complex social behavior of attack can be influenced in a substantial and predictable manner by the schedule and frequency of operant reinforcement.     

Alternative reinforcement effects on fixed-interval performance

Pigeons' key pecks were reinforced with food on a fixed-interval schedule. Food also was available at variable time periods either independently of responding or for not key pecking (a differential-reinforcement-of-other-behavior schedule). The latter condition arranged reinforcement following the first pause of t seconds after it became available according to a variable-time schedule. This schedule allowed separation of the effects of pause requirements ≤ five-seconds and reinforcement frequency. The time spent pausing increased as the duration of the pause required for reinforcement increased from 0 to 30 seconds and as the frequency of reinforcement for pausing increased from 0 to 2 reinforcers per minute. Key pecking was more evenly distributed within each fixed interval with shorter required pauses and with more frequent reinforcement for pausing. The results complement those obtained with other concurrent schedules in which the same operant response was reinforced in both components.     

The roles of stimulus control and reinforcement frequency in modulating the behavioral effects of d-amphetamine in the rat.

The behavioral effects of d-amphetamine have been shown to be modulated by stimulus control, with less impairment of performance occurring when control is great. When the fixed-consecutive-number schedule is used (on which at least a specified consecutive number of responses must be made on one operandum before a single response on another will produce a reinforcer), response rate tends to be invariant but reinforcement frequency is not. This study asks whether the differences in reinforcement frequency that usually accompany changes in stimulus control could themselves be responsible for the performance differences. Two versions of the fixed-consecutive-number schedule of reinforcement were combined into a multiple schedule within which stimulus control was varied but differences in reinforcement frequency were minimized by omitting some reinforcer deliveries during the component that usually had the higher reinforcement frequency. In one component, a compound discriminative stimulus was added with the eighth consecutive response on the first lever; a single response on the second lever was then reinforced. In the other component, no such stimulus was presented. With no added stimulus, large decreases occurred in the number of runs satisfying the minimum requirement for reinforcement at doses of drug that produced only minimal changes when an added stimulus controlled behavior. Thus, increased stimulus control diminishes the behavioral changes produced by d-amphetamine even when the possible contribution by baseline reinforcement rate is minimized.     

The reinforcement value of schedule-induced drinking

The effect of food reinforcement schedules on the reinforcement value of drinking water was evaluated. Food-deprived rats were exposed to concurrent, identical variable-time schedules of food presentation, the food thus being delivered independently of the rats' behavior. When the relative amount of time spent in a schedule component stabilized, an opportunity to drink water was introduced into one schedule component. The value of the variable-time schedules was varied from 60 to 90 to 270 sec. The relative amount of time spent in the schedule component associated with drinking water was a decreasing function of food frequency for two animals and remained constant for the third. Drinking rates were direct functions of food frequency, and the amount of water drunk per pellet was an inverse function of food frequency. The reinforcement value of drinking water, according to the Matching Law, was a direct function of the frequency of food presentation. It was concluded that food reinforcement schedules indirectly influence rates of drinking by altering the reinforcement value of drinking water and that certain properties of schedule-induced drinking can be accounted for in terms of the reinforcement value of drinking water, the rate of drinking, and the frequency of food presentation.     

Some factors controlling preference between fixed-ratio and variable-ratio schedules of reinforcement

A multiple schedule of food reinforcement for key-pecking was arranged which consisted of nine fixed-ratios, each of which operated in the presence of a different stimulus. Pigeons could complete a given fixed-ratio within the multiple schedule or, by pecking a second key, could switch from the fixed-ratio schedule to a variable-ratio schedule consisting of the same nine ratios. Stable switching behavior was established which did not maximize simple probability or rate of reinforcement. Instead, the subjects showed a stable preference for the variable-ratio schedule of food reinforcement. Increasing the number of responses required to switch, and removing the occasions on which reinforcement was delivered after a single response in the variable schedule, decreased the number of switches to the variable schedule. Periods of delay interposed between a completed switch and the availability of reinforcement after one response in the variable schedule also decreased switching to the variable schedule, particularly at long delay intervals.     

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

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

Aftereffects of reinforcement on variable-ratio schedules

On each of variable-ratio 10, 40, and 80 schedules of reinforcement, when rats' lever-pressing rates were stable, the concentration of a liquid reinforcer was varied within sessions. The duration of the postreinforcement pause was an increasing function of the reinforcer concentration, this effect being more marked the higher the schedule parameter. The running rate, calculated by excluding the postreinforcement pause, was unaffected by concentration. The duration of the postreinforcement pause increased with the schedule parameter, but the proportion of the interreinforcement interval taken up by the pause decreased. Consequently, the overall response rate was an increasing function of the schedule parameter; i.e., it was inversely related to reinforcement frequency, contrary to the law of effect. The running rate, however, decreased with the reinforcement frequency, in accord with the law of effect. When 50% of reinforcements were randomly omitted, the postomission pause was shorter than the postreinforcement pause, but the running rate of responses was not affected.     

Relative frequency of reinforcement and rate of punished behavior

After training on a multiple variable-interval variable-interval schedule of reinforcement, each response in one component of the schedule was followed by a brief electric shock. When the rate of punished responses stabilized, the frequency of reinforcement in the other component was first decreased and then increased from the baseline frequency. The effects of these manipulations were consistent with reports of interactions in multiple schedules involving only unpunished behavior, i.e., the rate of punished responses increased with a higher relative frequency of reinforcement in the punishment component and decreased with a lower relative frequency of reinforcement in that component. The relevance of such findings to a further generality of behavioral contrast effects is discussed.     

A quantitative analysis of the responding maintained by interval schedules of reinforcement

Interval schedules of reinforcement maintained pigeons' key-pecking in six experiments. Each schedule was specified in terms of mean interval, which determined the maximum rate of reinforcement possible, and distribution of intervals, which ranged from many-valued (variable-interval) to single-valued (fixed-interval). In Exp. 1, the relative durations of a sequence of intervals from an arithmetic progression were held constant while the mean interval was varied. Rate of responding was a monotonically increasing, negatively accelerated function of rate of reinforcement over a range from 8.4 to 300 reinforcements per hour. The rate of responding also increased as time passed within the individual intervals of a given schedule. In Exp. 2 and 3, several variable-interval schedules made up of different sequences of intervals were examined. In each schedule, the rate of responding at a particular time within an interval was shown to depend at least in part on the local rate of reinforcement at that time, derived from a measure of the probability of reinforcement at that time and the proximity of potential reinforcements at other times. The functional relationship between rate of responding and rate of reinforcement at different times within the intervals of a single schedule was similar to that obtained across different schedules in Exp. 1. Experiments 4, 5, and 6 examined fixed-interval and two-valued (mixed fixed-interval fixed-interval) schedules, and demonstrated that reinforcement at one time in an interval had substantial effects on responding maintained at other times. It was concluded that the rate of responding maintained by a given interval schedule depends not on the overall rate of reinforcement provided but rather on the summation of different local effects of reinforcement at different times within intervals.     

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.     

Economic and biological influences on key pecking and treadle pressing in pigeons

Pigeons were studied on a two-component multiple schedule in which the required operant was, in different conditions, biologically relevant (i.e., key pecking) or nonbiologically relevant (i.e., treadle pressing). Responding was reinforced on a variable-interval (VI) 2-min schedule in both components. In separate phases, additional food was delivered on a variable-time (VT) 15-s schedule (response independent) or a VI 15-s schedule (response dependent) in one of the components. The addition of response-independent food had different effects on responding depending on the operant response and on the frequency with which the components alternated. When components alternated frequently (every 10 s), all pigeons keypecked at a much higher rate during the component with the additional food deliveries, whether response dependent or independent. In comparison, treadle pressing was elevated only when the additional food was response dependent; rate of treadling was lower when the additional food was response independent. When components alternated infrequently (every 20 min), pigeons key pecked at high rates at points of transition into the component with the additional food deliveries. Rate of key pecking decreased with time spent in the 20-min component when the additional food was response independent, whereas rate of pecking remained elevated in that component when the additional food was response dependent. Under otherwise identical test conditions, rate of treadle pressing varied only as a function of its relative rate of response-dependent reinforcement. Delivery of response-independent food thus had different, but predictable, effects on responding depending on which operant was being studied, suggesting that animal-learning procedures can be integrated with biological considerations without the need to propose constraints that limit general laws of learning.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Hill-climbing by pigeons

Pigeons were exposed to two types of concurrent operant-reinforcement schedules in order to determine what choice rules determine behavior on these schedules. In the first set of experiments, concurrent variable-interval, variable-interval schedules, key-peck responses to either of two alternative schedules produced food reinforcement after a random time interval. The frequency of food-reinforcement availability for the two schedules was varied over different ranges for different birds. In the second series of experiments, concurrent variable-ratio, variable-interval schedules, key-peck responses to one schedule produced food reinforcement after a random time interval, whereas food reinforcement occurred for an alternative schedule only after a random number of responses. Results from both experiments showed that pigeons consistently follow a behavioral strategy in which the alternative schedule chosen at any time is the one which offers the highest momentary reinforcement probability (momentary maximizing). The quality of momentary maximizing was somewhat higher and more consistent when both alternative reinforcement schedules were time-based than when one schedule was time-based and the alternative response-count based. Previous attempts to provide evidence for the existence of momentary maximizing were shown to be based upon faulty assumptions about the behavior implied by momentary maximizing and resultant inappropriate measures of behavior.