Response rate and sensitivity to the molar feedback function relating response and reinforcement rate on VI+ schedules of reinforcement

In 5 experiments, the author examined rats' sensitivity to the molar feedback function relating response rate to reinforcement rate on schedules of reinforcement. These studies demonstrated that, at lower rates of responding, rats' performance on variable ratio (VR), variable interval (VI), and variable interval with linear feedback loop (VI+) schedules was determined largely by reinforcement of interresponse times; response rates were faster on VR than on both VI and VI+ schedules. In contrast, when procedures were adopted to maintain high rates of response, rats showed sensitivity to the molar characteristics of the schedules; they responded as fast on a VI+ schedule as on a VR schedule and faster on both of these schedules than on a yoked VI schedule. When the variance of response rate was manipulated, this factor was noted as an important element in determining sensitivity to the molar characteristics of the schedule.     

Free-operant performance on variable interval schedules with a linear feedback loop: no evidence for molar sensitivities in rats

Four experiments examined rats' sensitivity to molar and molecular factors on instrumental schedules of reinforcement. Rats were exposed to a variable interval schedule with a positive feedback loop (VI+), such that faster responding led to a shorter interreinforcement interval. In Experiments 1 and 2, rats responded faster on a variable response (VR) schedule than on either a VI schedule matched for reinforcement rate or a VI+ schedule matched for the feedback function. In Experiment 3, rats responded no differently on a VI schedule than they did on a VI+ schedule with equated rates of reinforcement. In Experiment 4, rats responded faster on a VI+ schedule with an interresponse time requirement yoked to that experienced on a VR schedule, than on a VI+ schedule with the same feedback function as the VR schedule. Taken together these results suggest that rats are more sensitive to the molecular than the molar properties of the schedules.     

On the primacy of molecular processes in determining response rates under variable-ratio and variable-interval schedules

This study focused on variables that may account for response-rate differences under variable-ratio (VR) and variable-interval (VI) schedules of reinforcement. Four rats were exposed to VR, VI, tandem VI differential-reinforcement-of-high-rate, regulated-probability-interval, and negative-feedback schedules of reinforcement that provided the same rate of reinforcement. Response rates were higher under the VR schedule than the VI schedule, and the rates on all other schedules approximated those under the VR schedule. The median reinforced interresponse time (IRT) under the VI schedule was longer than for the other schedules. Thus, differences in reinforced IRTs correlated with differences in response rate, an outcome suggestive of the molecular control of response rate. This conclusion was complemented by the additional finding that the differences in molar reinforcement-feedback functions had little discernible impact on responding.     

Interlocking schedules: the relationship between response and time requirements.

Rats were exposed to an interlocking fixed-ratio 150 fixed-interval 5-minute schedule of food reinforcement and then to yoked variable-ratio schedules in which individual ratios corresponded exactly to the ratios of responses to reinforcement obtained on the interlocking schedule. After additional training with the interlocking schedule, the rats were exposed to yoked variable-interval schedules in which intervals corresponded to the intervals between successive reinforcements obtained on the second interlocking schedule. Response rates were highest in the yoked VR condition and lowest in the yoked VI, while intermediate rates characterized the interlocking schedule. Break-run patterns of responding were generated by the interlocking schedule for all subjects, while both the yoked VR and VI schedules produced comparatively stable local rates of responding. These results indicate that responding is sensitive to the interlocking schedule's inverse relationship between reinforcement frequency and responses per reinforcement.     

Rats' performance on variable-interval schedules with a linear feedback loop between response rate and reinforcement rate

Three experiments investigated whether rats are sensitive to the molar properties of a variable-interval (VI) schedule with a positive relation between response rate and reinforcement rate (i.e., a VI+ schedule). In Experiment 1, rats responded faster on a variable ratio (VR) schedule than on a VI+ schedule with an equivalent feedback function. Reinforced interresponse times (IRTs) were shorter on the VR as compared to the VI+ schedule. In Experiments 2 and 3, there was no systematic difference in response rates maintained by a VI+ schedule and a VI schedule yoked in terms of reinforcement rate. This was found both when the yoking procedure was between-subject (Experiment 2) and within-subject (Experiment 3). Mean reinforced IRTs were similar on both the VI+ and yoked VI schedules, but these values were more variable on the VI+ schedule. These results provided no evidence that rats are sensitive to the feedback function relating response rate to reinforcement rate on a VI+ schedule.     

Instrumental performance on negative schedules

Three experiments examined the performance of rats pressing a lever for food reinforcement on a schedule in which high rates of response resulted in lowered rates of reinforcement (i.e. a schedule with a negative component). In Experiment 1, rats responded on a variable interval (VI) schedule with a conjoint component such that every 30 responses a reinforcement programmed by the VI schedule was cancelled. These subjects generally emitted a lower response rate than rats responding on a VI schedule yoked to the former subjects with respect to the delivery of reinforcement, although response rate differences were sometimes not large. Similar response-rate effects were obtained in Experiment 2 using a within-subject yoking procedure. In Experiment 3, reinforced interresponse times were matched on negative and VI schedules yoked in terms of reinforcement rate, and the response rate emitted in these conditions were similar. These results give support to theories of instrumental conditioning that stress the strengthening and shaping properties of reinforcement.     

Drug discrimination under concurrent variable-ratio variable-ratio schedules

Pigeons were trained to discriminate 5 mg/kg pentobarbital from saline under concurrent variable-ratio (VR) VR schedules, in which responses on the pentobarbital-biased lever were reinforced under the VR schedule with the smaller response requirements when pentobarbital was given before the session, and responses on the saline-biased key were reinforced under the VR schedule with the larger response requirements. When saline was administered before the session, the reinforcement contingencies associated with the two response keys were reversed. When responding stabilized under concurrent VR 20 VR 30, concurrent VR 10 VR 40, or concurrent VR 5 VR 50 schedules, pigeons responded almost exclusively on the key on which fewer responses were required to produce the reinforcer. When other doses of pentobarbital and other drugs were substituted for the training dose, low doses of all drugs produced responding on the saline-biased key. Higher doses of pentobarbital and chlordiazepoxide produced responding only on the pentobarbital-biased key, whereas higher doses of ethanol and phencyclidine produced responding only on this key less often. d-Amphetamine produced responding primarily on the saline-biased key. When drugs generalized to pentobarbital, the shape of the generalization curve under concurrent VR VR schedules was more often graded than quantal in shape. Thus, drug discrimination can be established under concurrent VR VR schedules, but the shapes of drug-discrimination dose-response curves under concurrent VR VR schedules more closely resemble those seen under interval schedules than those seen under fixed-ratio schedules. Graded dose-response curves under concurrent VR VR schedules may relate to probability matching and difficulty in discriminating differences in reinforcement frequency.     

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.     

Cooperative responding in rats maintained by fixed‐ and variable‐ratio schedules

The present study investigated the effects of fixed‐ratio (FR) and variable‐ratio (VR) reinforcement schedules on patterns of cooperative responding in pairs of rats. Experiment 1 arranged FR 1, FR 10, and VR 10 schedules to establish cooperative responding (water delivery depended on the joint responding of two rats). Cooperative response rates and proportions were higher under intermittent schedules than under continuous reinforcement. The FR 10 schedule generated a break‐and‐run pattern, whereas the VR 10 schedule generated a relatively high and constant rate pattern. Experiment 2 evaluated the effects of parametric manipulations of FR and VR schedules on cooperative responding. Rates and proportions of cooperative responding generally increased between ratio sizes of 1 and 5 but showed no consistent trend as the ratio increased from 5 to 10. Experiment 3 contrasted cooperative responding between an FR6 schedule and a yoked control schedule. Coordinated behavior occurred at a higher rate under the former schedule. The present study showed that external consequences and the schedules under which the delivery of these consequences are based, select patterns of coordinated behavior.     

Influence of the cost of responding

In three experiments, the effect of costs associated with responding on judgments of the causal effectiveness of the response was examined. In Experiment 1, the temporal interval between outcomes was matched on a variable interval (VI) and a variable ratio (VR) schedule. When each response was made at some “cost,” and outcomes represented some “gain” for the subject, the rating of causal effectiveness for responses was higher on the VR than on the VI schedule. This relationship was absent when the outcome was a triangle Hash. In Experiment 2, the number of responses required per outcome on a VI and a VR schedule were matched, and responses on the VR schedule were rated as more causally effective. In Experiment 3, a VI-to-VR yoking procedure was used. With minimal response costs, judgments were similar on the VI and VR schedules, but with greater response costs, responses performed on the VR schedule were rated as more causally effective than those emitted on the VI schedule.     

The linear system theory's account of behavior maintained by variable-ratio schedules.

The mathematical theory of linear systems, which has been used successfully to describe behavior maintained by variable-interval schedules, is extended to describe behavior maintained by variable-ratio schedules. The result of the analysis is a pair of equations, one of which expresses response rate on a variable-ratio schedule as a function of the mean ratio requirement (n) that the schedule arranges. The other equation expresses response rate on a variable-ratio schedule as a function of reinforcement rate. Both equations accurately describe existing data from variable-ratio schedules. The theory accounts for two additional characteristics of behavior maintained by variable-ratio schedules; namely, the appearance of strained, two-valued (i.e., zero or very rapid) responding at large ns, and the abrupt cessation of responding at a boundary n. The theory also accounts for differences between behavior on variable-interval and variable-ratio schedules, including (a) the occurrence of strained responding on variable-ratio but not on variable-interval schedules, (b) the abrupt cessation of responding on occurrence of higher response rates on variable-ratio than on variable-interval schedules. Furthermore, given data from a series of variable-interval schedules and from a series of concurrent variable-ratio variable-interval schedules, the theory permits quantitative prediction of many properties of behavior on single-alternative variable-ratio schedules. The linear system theory's combined account of behavior on variable-interval and variable-ratio schedules is superior to existing versions of six other mathematical theories of variable-interval and variable-ratio responding.     

The schedule dependency of the signaled reinforcement effect

In Experiment 1, rats leverpressed for food reinforcement on either a variable ratio (VR) 30 schedule or a variable interval (VI) 15-s schedule. One group in each condition received a signal filling a 500-ms delay of reinforcement. This treatment enhanced rates on the VR schedule, and attenuated rates on the VI schedule, relative to the rate seen in an unsignaled control condition. In Experiment 2 there was no delay of reinforcement and the signal and food were presented simultaneously. Attenuated rates of responding were observed on VI schedules with a range of mean interval values (15 to 300 s). Experiment 3 used a range of VR schedules (10 to 150) with simultaneous presentations of signal and food. A signal-induced enhancement of response rate was found at all VR values. In Experiment 4, a signal elevated response rates on a tandem VI VR schedule, but depressed rates on a tandem VR VI schedule, compared to control conditions receiving unsignaled delayed reinforcement. These results are taken to show that the effect of a signal accompanying reinforcement depends upon the nature of the behavior that is reinforced during exposure to a given schedule.     

Independence of concurrent responding maintained by interval schedules of reinforcement

A pigeon's responses were reinforced on a variable-interval schedule on one key; and, concurrently, either a multiple or a fixed-interval schedule of reinforcement was in effect on a second key. These concurrent schedules, conc VI 3 (mult VI 3 EXT) or conc VI 3 FI 6, were programmed with or without a changeover delay (COD). Because the COD provided that responses on one key could not be followed by reinforced responses on the other key, responding on one key was not likely to accidentally come under the control of the reinforcement schedule on the other. When the COD was used, the performances on each key were comparable to the performances maintained when these interval schedules are programmed separately. The VI schedule maintained a relatively constant rate of responding, even though the rate of responding on the second key varied in a manner appropriate to the schedule on the second key. The mult VI 3 EXT schedule maintained two separate rates of responding: a relatively high rate during the VI 3 component, and almost no responding during the EXT component. The FI schedule maintained the gradually increasing rate of responding within each interval that is characteristic of the performance maintained by this schedule. The concurrent performances, however, did include certain interactions involving the local characteristics of responding and the over-all rates of responding maintained by the various schedules. The relevance of the present findings to an inter-response time analysis of VI responding, a chaining account of FI responding, and the concept of the reflex reserve was discussed.     

Changeover delay and concurrent schedules: some effects on relative performance measures

The pigeon and the rat partition total response output between both schedules of a concurrent variable-interval pair. The quantitative nature of a partition seems critically dependent on the relative rates with which the two schedules provide reinforcements for responding, in addition to the changeover delay. The manner in which the changeover delay controls the partition was studied by varying the duration of the changeover delay from 0 to 20 sec with each of two pairs of concurrent variable-interval schedules, viz., Conc VI 1.5-min VI 1.5-min and Conc VI 1-min VI 3-min. Rats served as the subjects and brain stimulation was employed as the reinforcer. When the schedules were Conc VI 1.5-min VI 1.5-min, relative response rate approximated 0.50 at all values of the changeover delay. When the schedules were Conc VI 1-min VI 3-min, relative response rate, computed with respect to the VI 1-min schedule, increased when the duration of the changeover delay increased. Changeover rate decreased when the duration of the changeover delay increased. The decrease was the same for both VI schedules of the Conc VI 1.5-min VI 1.5-min pair but was more rapid for the VI 3-min schedule of the Conc VI 1-min VI 3-min pair.     

Arousal, changeover responses, and preference in concurrent schedules

Pigeons were trained on multiple schedules that provided concurrent reinforcement in each of two components. In Experiment 1, one component consisted of a variable-interval (VI) 40-s schedule presented with a VI 20-s schedule, and the other a VI 40-s schedule presented with a VI 80-s schedule. After extended training, probe tests measured preference between the stimuli associated with the two 40-s schedules. Probe tests replicated the results of Belke (1992) that showed preference for the 40-s schedule that had been paired with the 80-s schedule. In a second condition, the overall reinforcer rate provided by the two components was equated by adding a signaled VI schedule to the component with the lower reinforcer rate. Probe results were unchanged. In Experiment 2, pigeons were trained on alternating concurrent VI 30-s VI 60-s schedules. One schedule provided 2-s access to food and the other provided 6-s access. The larger reinforcer magnitude produced higher response rates and was preferred on probe trials. Rate of changeover responding, however, did not differ as a function of reinforcer magnitude. The present results demonstrate that preference on probe trials is not a simple reflection of the pattern of changeover behavior established during training.     

Exchange schedules in token economies: A preliminary investigation of second‐order schedule effects

Basic research shows that token‐production and exchange‐production schedules in token economies affect each other as second‐order schedules (i.e., the exchange‐production schedule's requirements affect responding toward the token‐production schedule). This relationship has not been investigated with children in academic settings despite the widespread use of token economies in this context. This study compared the effects of fixed‐ratio (FR) and variable‐ratio (VR) exchange‐production schedules of equal ratios (2, 5, and 10) on responding toward an FR 1 token‐production schedule with a child diagnosed with autism. A concurrent chains assessment was also conducted to assess the participant's relative preference for FR and VR exchange‐production schedule arrangements within her typical discrete trial training. Results showed no difference in response rate between the two schedule types. However, the concurrent chains assessment revealed an exclusive preference for the VR arrangement.     

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.     

Human sensitivity to reinforcement feedback functions

Two experiments investigated human sensitivity to the temporally extended aspects of reinforcement schedules. Experiment 1 investigated human sensitivity to the extended and local aspects of three reinforcement schedules: variable ratio (VR), variable interval (VI), and variable-interval-plus-linear-feedback (VI+) schedules. Experiment 2 investigated this sensitivity on two reinforcement schedules: VI and VI+ schedules. In both experiments, there was evidence of sensitivity to the temporally extended aspects of the schedule: There were differences between the response rate on the VI+ and yoked-VI schedules, but no statistical difference in rates of response between the VR and VI+ schedules. The VI+ versus VI difference was much more pronounced when a lower response force needed to depress a lever was used. These results suggest that human subjects do show some sensitivity to temporally extended aspects of schedules of reinforcement.     

Marking effects in instrumental performance on DRH schedules

Three experiments investigated the effect of presenting a brief stimulus after a response sequence on the rate of lever-pressing by rats on differential reinforcement of high rate (DRH) schedules. In Experiment 1 enhanced responding was produced by a visual stimulus presented during a 500-msec delay of reinforcement compared to a condition in which no stimulus was presented. In Experiment 2 rats responded on a multiple DRH DRH schedule in which the DRH contingency was reinforced on a 50% schedule in each component. Equivalent levels of responding occurred in the components when reinforcement was signalled in one component and when the signal was presented following the non-reinforced schedules in the other components. A further group of rats received the stimulus presented after non-reinforced schedules in one component but not at all in the other component; responding was enhanced in the former component relative to the latter component. In Experiment 3 brief stimuli presented after the completion of DRH components on a second-order VR (DRH) schedule elevated response rates irrespective of whether the signal was presented paired or unpaired with reinforcement. The present data support the view that a brief signal may serve to mark a response sequence in memory and facilitate instrumental performance.     

Second-order schedules with paired auditory brief stimuli

Pigeons were exposed to multiple second-order schedules of paired and unpaired brief stimuli in which responding on the main key was reinforced according to a fixed-interval thirty-second schedule by a brief stimulus (a tone in the paired schedule) and advancement to the next segment of the second-order schedule. In Experiment 1, a response on the second key was required during the tone in its fourth and final presentation to produce food. Responses during earlier brief stimuli indicated the extent to which the final brief stimulus was discriminated from preceding ones. Responding was comparable during all tones, extending prior findings with visual paired brief stimuli and weakening explanations of subjects' failure to discriminate between brief-stimulus presentations in terms of elicited responding. In Experiment 2 the number of fixed-interval segments comprising the second-order schedules varied from one through eight. Although main-key response rates increased across segments in both experiments, they increased much less sharply with a variable number of segments. These results suggest that the increase in main-key response rates across segments is due primarily to a degree of temporal discrimination not reflected on the second key. Main-key response rates were higher on paired auditory brief-stimulus schedules than on unpaired visual brief-stimulus schedules, especially in Experiment 2, thus further extending findings with visual brief stimuli to second-order schedules with auditory brief stimuli.