Choice for periodic schedules of reinforcement

Pigeons' responses in the presence of two concurrently available (initial-link) stimuli produced one of two different (terminal-link) stimuli according to identical but independent variable-interval schedules. Responding in the mutually exclusive terminal links was reinforced with food according to fixed-ratio schedules for six pigeons and according to fixed-interval schedules for two pigeons. None of the pigeons matched the proportion of (choice) responses in the initial links to the proportion of the rates of reinforcement obtained during the terminal links. Instead, as the values of each of the terminal-link schedules were increased by a constant amount, the choice proportions for the stimulus associated with the smaller of the two values increased, even though the relative rates of reinforcement during the terminal links decreased. These results are incompatible with those from previous studies with aperiodic (variable-interval or variable-ratio) schedules. The present results do suggest, however, that in transforming aperiodic schedules into their periodic equivalents, it may be necessary to consider the size of the smallest interreinforcement interval comprising the terminal-link schedules.     

Notes on fixed-ratio and fixed-interval escape responding in the pigeon

After learning to peck a key when each peck removed a slowly increasing series of electric shocks, pigeons were placed on fixed-ratio and fixed-interval escape schedules. The resulting behavior was comparable to that of other species on ratio and interval escape schedules. Thus, while the pigeon apparently requires special techniques for the initial shaping of a key-peck response with negative reinforcement, this response, once obtained, can be subjected to intermittent schedules of negative reinforcement with no great difficulty.     

Motivational aspects of escape from punishment

Punishment and escape were studied simultaneously by allowing a subject to escape from a stimulus situation in which responses were punished, into a stimulus situation in which responses were not punished. The frequency of the punished responses was found to be an inverse function of the intensity of punishment, whereas the frequency of the escape response was a direct function of the intensity of punishment. Both of these functions were obtained under three different schedules of food reinforcement. The strength of the escape behavior was evidenced by (1) the emergence of the escape response even when the frequency of food reinforcement decreased as a consequence of the escape response, (2) the maintenance of the escape response by fixed-interval and fixed-ratio schedules of escape reinforcement, and (3) the occurrence of escape responses at intensities of punishment that otherwise produced only mild suppression of the punished response when no escape was possible. This last finding indicates that a subject may be driven out of a situation involving punishment even though the punishment is relatively ineffective in suppressing the punished responses when no escape is possible.     

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.     

An analysis of reinforcement history effects

Four pigeons were exposed to two tandem variable-interval differential-reinforcement-of-low-rate schedules under different stimulus conditions. The values of the tandem schedules were adjusted so that reinforcement rates in one stimulus condition were higher than those in the other, even though response rates in the two conditions were nearly identical. Following this, a fixed-interval schedule of either shorter or longer values than, or equal to the baseline schedule, was introduced in the two stimulus conditions respectively. Response rates during those fixed-interval schedules typically were higher in the presence of the stimuli previously correlated with the lower reinforcement rates than were those in the presence of the stimuli previously correlated with the higher reinforcement rates. Such effects of the reinforcement history were most prominent when the value of the fixed-interval schedule was shorter. The results are consistent with both incentive contrast and response strength conceptualizations of related effects. They also suggest methods for disentangling the effects of reinforcement rate on subsequent responding, from the response rate with which it is confounded in many conventional schedules of reinforcement.     

Concurrent ratio schedules: Fixed vs. variable response requirements

Rats were trained on concurrent fixed-ratio variable-ratio or concurrent fixed-ratio mixed-ratio schedules of food reinforcement. The variable-ratio schedule was composed of an arithmetic sequence of 11 ratios that averaged 50; the mixed-ratio schedule consisted of equiprobable ratios of 1 and 99. Fixed-ratio values, varied over experimental conditions, included 25, 35, 50, 60, and 99. The proportion of responses and time allocated to the variable- or mixed-ratio schedule increased as the size of the fixed ratio increased. For most subjects, higher proportions of responses and time were maintained on the fixed-ratio schedule at fixed-ratio values of 25 and 35; higher proportions of responses and time were maintained on the variable- or mixed-ratio schedule at fixed-ratio values of 50 or higher. On concurrent variable-ratio fixed-ratio schedules, the tendency for responding to be maintained exclusively by one schedule was related to the difference in local reinforcement rates obtained from those schedules. Exclusive responding was approximated when the difference in local reinforcement rates obtained from those schedules was large; responding was more evenly distributed between the schedules as the difference in the rates at which reinforcement was obtained from each decreased.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

Effects of delayed reinforcement in a concurrent situation

Pigeons were trained to peck either of two response keys for food reinforcement on equated aperiodic schedules. Delays of reinforcement for pecks at one key reduced the relative frequency of pecking exponentially as a function of the delay interval. Similar functions were obtained when other dependent variables were plotted against the delay interval.     

Rates and patterns of responding with concurrent fixed-interval and variable-interval reinforcement

Pigeons were exposed to concurrent fixed-interval and variable-interval schedules of food reinforcement on two keys. The times between reinforcement were varied systematically on both keys. The overall relative frequency of responding on the fixed-interval key depended on the relative frequency of reinforcement, but did not match it. Instead, the ratio of responses on the fixed-interval key to responses on the variable-interval key was a power function of the ratio of reinforcements, with an exponent of 0.5. Patterns of responding between reinforcements on the fixed-interval key depended on both relative and absolute values of the reinforcement schedules. Similar overall relative responding was obtained at different absolute schedule values with equal relative reinforcement, despite some differences in patterns of responding.     

Temporal patterns of responding in small fixed-ratio schedules

Pigeons were exposed to an ascending series of small fixed-ratio schedules from fixed-ratio 1 to 7. Two of those pigeons were later placed on a fixed-ratio 30 schedule. The two primary dependent variables were the postreinforcement pause and the interresponse time. Changes in these variables under small fixed ratios were sometimes opposite to changes reported with large fixed ratios. For example, postreinforcement pauses decreased in length as the fixed-ratio requirement increased from fixed-ratio 1 to fixed-ratio 3. Also, the interresponse times early in the small fixed-ratio schedule were shorter than those immediately preceding reinforcement. These findings question the role of interresponse-time reinforcement in determining temporal patterns of responding under small fixed-ratio schedules. They also suggest that there may be a limited region in which the independent variable, fixed-ratio size, does not operate as previously described.     

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.     

Relative rate of response and relative magnitude of reinforcement in multiple schedules

Pigeons were trained on a multiple schedule in which the duration of access to grain reinforcement was varied independently in the two components. The relative response rate in one component was an increasing function of the relative duration of reinforcement in that component. The similarity of this interaction to that found in multiple schedules of different reinforcement frequency is discussed. Extinction data were also similar to those obtained after training on multiple schedules of different reinforcement frequency.     

Reinforcement frequency and contingency as factors in fixed-ratio behavior

Two variables often confounded in fixed-ratio schedules are reinforcement frequency and response requirement. These variables were isolated by a technique that yoked the distributions of reinforcements in time for one group of pigeons to those of pigeons responding on various fixed-ratio schedules. The contingencies for the yoked birds were then manipulated by adding various tandem fixed-ratio requirements to their schedules. Post-reinforcement pause was approximately equal for the yoked and ratio pigeons, and was relatively insensitive to changes in the tandem requirement. Terminal response rate increased with increases in the tandem requirement, even though reinforcement rate was invariant. This increase was attributed to the progressive interference of the tandem requirement with the differential reinforcement of long interresponse times.     

The relation between response rates and reinforcement rates in a multiple schedule

In a multiple schedule, exteroceptive stimuli change when the reinforcement schedule is changed. Each performance in a multiple schedule may be considered concurrent with other behavior. Accordingly, two variable-interval schedules of reinforcement were arranged in a multiple schedule, and a third, common variable-interval schedule was programmed concurrently with each of the first two. A quantitative statement was derived that relates as a ratio the response rates for the first two (multiple) variable-interval schedules. The value of the ratio depends on the rates of reinforcement provided by those schedules and the reinforcement rate provided by the common variable-interval schedule. The following implications of the expression were evaluated in an experiment with pigeons: (a) if the reinforcement rates for the multiple variable-interval schedules are equal, then the ratio of response rates is unity at all reinforcement rates of the common schedule; (b) if the reinforcement rates for the multiple schedules are unequal, then the ratio of response rates increases as the reinforcement rate provided by the common schedule increases; (c) the limit of the ratio is equal to the ratio of the reinforcement rates. Satisfactory confirmation was obtained for the first two implications, but the third was left in doubt.     

Contingency and stimulus change in chained schedules of reinforcement

Higher rates of pecking were maintained by pigeons in the middle component of three-component chained fixed-interval schedules than in that component of corresponding multiple schedules (two extinction components followed by a fixed-interval component). This rate difference did not occur in equivalent tandem and mixed schedules, in which a single stimulus was correlated with the three components. The higher rates in components of chained schedules demonstrate a reinforcing effect of the stimulus correlated with the next component; the acquired functions of this stimulus make the vocabulary of conditioned reinforcement appropriate. Problems in defining conditioned reinforcement arise not from difficulties in demonstrating reinforcing effects but from disagreements about which experimental operations allow such reinforcing effects to be called conditioned.     

A sequential analysis of the partial reinforcement extinction effect in children*

In a series of studies employing children between the ages of 7.6 and 10.6 years of age guessing on a modified Humphreys’s board, extinction training was administered following either continuous reinforcement or various schedules of partial reinforcement training. Besides the observation of a partial reinforcement extinction effect, it was found that resistance to extinction appeared to be regulated by those sequential variables specified by extensions of Capaldi’s theory of instrumental learning.     

ASSESSMENT OF STEREOTYPIC AND SELF-INJURIOUS BEHAVIOR AS ADJUNCTIVE RESPONSES

Certain responses of both humans and nonhumans appear to be maintained indirectly by intermittent reinforcement schedules and have been referred to collectively as adjunctive behavior. Although basic research has examined adjunctive behavior extensively, relatively few studies have been conducted with humans, particularly those with developmental disabilities who often engage in frequent and varied stereotypic behavior. This study assessed possible adjunctive characteristics of self-injurious and stereotypic behaviors using a multielement design containing two types of control conditions. Four subjects who engaged in both self-injurious behavior and stereotypy participated after variables maintaining their self-injury were identified via functional analyses. Each day, subjects were exposed to three 15-min sessions in random order: (a) noncontingent presentation of food on a fixed-time schedule (e.g., FT 30 s), (b) a massed-reinforcement (food) control, and (c) a no-reinforcement control. A variety of fixed-time schedules were examined during different experimental phases. Results of this preliminary study suggested that self-injury was not induced by intermittent reinforcement schedules, whereas the stereotypic behavior of some individuals showed characteristics of adjunctive behavior. The importance of research on adjunctive behavior and suggestions for future studies are discussed.     

Obtained versus programmed reinforcement practical considerations in the treatment of escape-reinforced aggression

This investigation provides a preliminary examination of the difference between programmed and obtained reinforcement rates and its potential influence during treatment of aggression in a natural setting. Following a functional analysis that suggested that the aggression of a boy with autism was negatively reinforced, intervention was implemented by the boy's mother. Concurrent fixed-ratio (FR) 1 FR 1 schedules of escape were arranged for manding and aggression. When mands failed to compete effectively with aggression, obtained reinforcement ratios were calculated; these indicated that obtained reinforcement varied from the programmed schedule for aggression but not for mands. Increasing the rate of prompts for mands resulted in an increase in mands and a decrease in aggression to near-zero levels.     

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.     

Concurrent schedules of interresponse time reinforcement: probability of reinforcement and the lower bounds of the reinforced interresponse time intervals

Data were obtained with rats on the effects of interresponse time contingent reinforcement of the lever press response using schedules in which interresponse times falling within either of two temporal intervals could be reinforced. Some of the findings were (a) the mode of the interresponse time distribution generally occurred near the first lower bound when the maximum reinforcement rate for the two lower bounds was equal; this also frequently occurred even when the reinforcement rate was less for the first lower bound; (b) as is the case with schedules using a single interval of reinforced interresponse times the values of the lower bounds partially determined the location and spread of the distributions; but the particular pair of values used did not seem to influence the effects of the probabilities of reinforcement; (c) although the modal interresponse time was usually at the lower bound of one of the two intervals of reinforced interresponse times, no simple relation existed between either the probability or rate of reinforcement of interresponse times in these two intervals and the location of this mode.