Increasing and signaling background reinforcement: effect on the foreground response-reinforcer relation.

Herrnstein's (1970) hyperbolic matching equation describes the relationship between response rate and reinforcement rate. It has two estimated parameters, k and Re. According to one interpretation, k measures motor performance and Re measures the efficacy of the reinforcer maintaining responding relative to background sources of reinforcement. Experiment 1 tested this interpretation of the Re parameter by observing the effect of adding and removing an additional source of reinforcement to the context. Using a within-session procedure, estimates of Re were obtained from the response-reinforcer relation over a series of seven variable-interval schedules. A second, concurrently available variable-interval schedule of reinforcement was added and then removed from the context. Results showed that when the alternative was added to the context, the value of Re increased by 107 reinforcers per hour; this approximated the 91 reinforcers per hour obtained from this schedule. Experiment 2 investigated the effects of signaling background reinforcement on k and Re. The signal decreased Re, but did not have a systematic effect on k. In general, the results supported Herrnstein's interpretation that in settings with one experimenter-controlled reinforcement source, Re indexes the strength of the reinforcer maintaining responding relative to uncontrolled background sources of reinforcement.     

Reinforcer magnitude (sucrose concentration) and the matching law theory of response strength

This experiment investigated the relationship between reinforcer magnitude (sucrose concentration) and response rate. The purpose was to evaluate the behavior of two parameters of an equation that predicts absolute response rate as a function of reinforcement rate and two free parameters. According to Herrnstein's (1970) theory of reinforced behavior, one parameter of this "response-strength equation" measures the efficacy of the reinforcer maintaining responding and the other parameter measures motoric components of response rate, such as response duration. Seven rats served as subjects. Experimental sessions consisted of a series of five different variable-interval schedules of reinforcement, each in effect for 5 minutes. Within each session, obtained reinforcement rates varied over more than a 30-fold range, from about 20 per hour to 700 per hour. The reinforcer was sucrose solution, and, between sessions, its concentration was varied from 0.0 to 0.64 molar (0 to 21.9%). For sucrose concentrations of 0.16 to 0.64 m, response rate was a negatively accelerated function of reinforcement rate. Increases in sucrose concentration increased response rates maintained by low but not high reinforcement rates. This pattern of changes corresponds to a change in the reinforcement-efficacy parameter of the response-strength equation. In contrast, the motor-performance parameter did not change as a function of sucrose concentration. These findings are inconsistent with the results of a similar study (Bradshaw, Szabadi, & Bevan, 1978) but support Herrnstein's theory of reinforced behavior.     

Topography of signal-centered behavior in the rat: Effects of deprivation state and reinforcer type

In a series of three experiments, groups of food-deprived and water-deprived rats were given pairings of a retractable lever (CS⁺) with response-independent deliveries of either solid or liquid reinforcers. In Experiment 1 food-deprived rats given a solid-pellet reinforcer differentially tended to sniff, paw, mouth, and bite the CS⁺ lever more often than a lever that was not paired with food (CS⁻), whereas food-deprived rats given a liquid reinforcer tended to differentially sniff, paw, and lick the CS⁺ lever. 23½-hour water-deprived rats given liquid reinforcers showed very little CS⁺ contact. In Experiment 2 increasing the severity of water deprivation from 23½ to 47½ hours significantly increased CS⁺ contact. In Experiment 3, subjects that were simultaneously food and water deprived and given a water reinforcer failed to exhibit differential CS⁺ contact, but subjects that were simultaneously food and water deprived and given a food reinforcer did acquire differential CS⁺-contact behavior. These results suggest that (a) even under a single motivational state the nature of signal-centered behavior can be determined by type of reinforcer, (b) although water reinforcement produces less signal contact than food reinforcement, this can be facilitated with more severe water-deprivation levels, and (c) high CS-contact rates using food reinforcement are not simply a product of reductions in body weight with food deprivation.     

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.     

Within-session changes in key and lever pressing for water during several multiple variable-interval schedules

Rats pressed keys or levers for water reinforcers delivered by several multiple variable-interval schedules. The programmed rate of reinforcement varied from 15 to 240 reinforcers per hour in different conditions. Responding usually increased and then decreased within experimental sessions. As for food reinforcers, the within-session changes in both lever and key pressing were smaller, peaked later, and were more symmetrical around the middle of the session for lower than for higher rates of reinforcement. When schedules provided high rates of reinforcement, some quantitative differences appeared in the within-session changes for lever and key pressing and for food and water. These results imply that basically similar factors produce within-session changes in responding for lever and key pressing and for food and water. The nature of the reinforcer and the choice of response can also influence the quantitative properties of within-session changes at high rates of reinforcement. Finally, the results show that the application of Herrnstein's (1970) equation to rates of responding averaged over the session requires careful consideration.     

Tests of behavioral-economic assessments of relative reinforcer efficacy II: economic complements

This experiment was conducted to test the predictions of two behavioral-economic approaches to quantifying relative reinforcer efficacy. The normalized demand analysis suggests that characteristics of averaged normalized demand curves may be used to predict progressive-ratio breakpoints and peak responding. By contrast, the demand analysis holds that traditional measures of relative reinforcer efficacy (breakpoint, peak response rate, and choice) correspond to specific characteristics of non-normalized demand curves. The accuracy of these predictions was evaluated in rats' responding for food or water: two reinforcers known to function as complements. Consistent with the first approach, predicted peak normalized response output values obtained under single-schedule conditions ordinally predicted progressive-ratio breakpoints and peak response rates obtained in a separate condition. Combining the minimum-needs hypothesis with the normalized demand analysis helped to interpret prior findings, but was less useful in predicting choice between food and water--two strongly complementary reinforcers. Predictions of the demand analysis had mixed success. Peak response outputs predicted from the non-normalized water demand curves were significantly correlated with obtained peak responding for water in a separate condition, but none of the remaining three predicted correlations was statistically significant. The demand analysis fared better in predicting choice--relative consumption of food and water under single schedules of reinforcement predicted preference under concurrent schedules significantly better than chance.     

The sensitivity of response rate to the rate of variable-interval reinforcement for pigeons and rats: a review

The relation between the rate of a response (B) and the rate of its reinforcement (R) is well known to be approximately hyperbolic: B = kR/(R + Ro), where k represents the maximum response rate, and Ro indicates the rate of reinforcers that will engender a response rate equal to half its maximum value. A review of data reported in 17 published papers revealed that, under variable-interval schedules of reinforcement, Ro was usually lower when pigeons were the subjects than when rats were the subjects. The value of k, in contrast, did not differ consistently between pigeons and rats. Some accounts interpret Ro as the rate of alternative, unscheduled reinforcers in the situation, expressed in units of the scheduled reinforcer. So interpreted, the difference in Ro implies that less alternative reinforcement (relative to the scheduled reinforcement) typically is available to pigeons in their operant conditioning chambers than it is to rats in theirs. Whether or not that interpretation of Ro is valid, the pigeon-rat difference in Ro ensures that for reinforcer rates above about 10 per hour, response rate will be noticeably less sensitive to changes in reinforcer rate (and presumably to changes in other incentive and motivational operations) with pigeons than with rats as subjects, at least with the experimental conditions typically employed.     

Effects of reinforcer consumption and magnitude on response rates during noncontingent reinforcement

Results of previous research on the effects of noncontingent reinforcement (NCR) have been inconsistent when magnitude of reinforcement was manipulated. We attempted to clarify the influence of NCR magnitude by including additional controls. In Study 1, we examined the effects of reinforcer consumption time by comparing the same magnitude of NCR when session time was and was not corrected to account for reinforcer consumption. Lower response rates were observed when session time was not corrected, indicating that reinforcer consumption can suppress response rates. In Study 2, we first selected varying reinforcer magnitudes (small, medium, and large) on the basis of corrected response rates observed during a contingent reinforcement condition and then compared the effects of these magnitudes during NCR. One participant exhibited lower response rates when large-magnitude reinforcers were delivered; the other ceased responding altogether even when small-magnitude reinforcers were delivered. We also compared the effects of the same NCR magnitude (medium) during 10-min and 30-min sessions. Lower response rates were observed during 30-min sessions, indicating that the number of reinforcers consumed across a session can have the same effect as the number consumed per reinforcer delivery. These findings indicate that, even when response rate is corrected to account for reinforcer consumption, larger magnitudes of NCR (defined on either a per-delivery or per-session basis) result in lower response rates than do smaller magnitudes.     

Effects of reinforcer rate and reinforcer quality on time allocation: Extensions of matching theory to educational settings

We examined how 3 special education students allocated their responding across two concurrently available tasks associated with unequal rates and equal versus unequal qualities of reinforcement. The students completed math problems from two alternative sets on concurrent variable-interval (VI) 30-s VI 120-s schedules of reinforcement. During the equal-quality reinforcer condition, high-quality (nickels) and low-quality items ("program money" in the school's token economy) were alternated across sessions as the reinforcer for both sets of problems. During the unequal-quality reinforcer condition, the low-quality reinforcer was used for the set of problems on the VI 30-s schedule, and the high-quality reinforcer was used for the set of problems on the VI 120-s schedule. Equal- and unequal-quality reinforcer conditions were alternated using a reversal design. Results showed that sensitivity to the features of the VI reinforcement schedules developed only after the reinforcement intervals were signaled through countdown timers. Thereafter, when reinforcer quality was equal, the time allocated to concurrent response alternatives was approximately proportional to obtained reinforcement, as predicted by the matching law. However the matching relation was disrupted when, as occurs in most natural choice situations, the quality of the reinforcers differed across the response options.     

IMPULSIVITY IN STUDENTS WITH SERIOUS EMOTIONAL DISTURBANCE: THE INTERACTIVE EFFECTS OF REINFORCER RATE,DELAY, AND QUALITY

We conducted two studies extending basic matching research on self-control and impulsivity to the investigation of choices of students diagnosed as seriously emotionally disturbed. In Study 1 we examined the interaction between unequal rates of reinforcement and equal versus unequal delays to reinforcer access on performance of concurrently available sets of math problems. The results of a reversal design showed that when delays to reinforcer access were the same for both response alternatives, the time allocated to each was approximately proportional to obtained reinforcement. When the delays to reinforcer access differed between the response alternatives, there was a bias toward the response alternative and schedule with the lower delays, suggesting impulsivity (i.e., immediate reinforcer access overrode the effects of rate of reinforcement). In Study 2 we examined the interactive effects of reinforcer rate, quality, and delay. Conditions involving delayed access to the high-quality reinforcers on the rich schedule (with immediate access to low-quality reinforcers earned on the lean schedule) were alternated with immediate access to low-quality reinforcers on the rich schedule (with delayed access to high-quality reinforcers on the lean schedule) using a reversal design. With 1 student, reinforcer quality overrode the effects of both reinforcer rate and delay to reinforcer access. The other student tended to respond exclusively to the alternative associated with immediate access to reinforcers. The studies demonstrate a methodology based on matching theory for determining influential dimensions of reinforcers governing individuals' choices.     

Closed-economy multiple-schedule performance: Effects of deprivation and session duration

Three pigeons responded for food reinforcement on multiple variable-interval schedules in which the total consumption of food was entirely determined by the subjects' interaction with the schedules (a closed economy). The finding of overmatching, where response allocation between components is more extreme than the distribution of reinforcers, was reconfirmed. Generalized-matching sensitivity decreased from overmatching to undermatching values typical of conventional multiple schedules when food deprivation was increased by decreasing session duration, but not when deprivation was increased by decreasing overall reinforcer rate. Sensitivity also increased from undermatching to overmatching as session duration increased from 100 min to 24 hr, while deprivation was held constant by decreasing overall reinforcer rate. These results can be understood in terms of increases in the value of extraneous reinforcers relative to food reinforcers as deprivation decreases or as the economy for extraneous reinforcers becomes more closed. However, no published quantitative expression of the effects of extraneous reinforcers is entirely consistent with the results.     

Autoshaping the pigeon's gape response: acquisition and topography as a function of reinforcer type and magnitude.

The pigeon's key-pecking response is experimentally dissociable into transport (head movement) and gape (jaw movement) components. During conditioning of the key-pecking response, both components come under the control of the conditioned stimulus. To study the acquisition of gape conditioned responses and to clarify the contribution of unconditioned stimulus (reinforcer) variables to the form of the response, gape and key-contact responses were recorded during an autoshaping procedure and reinforcer properties were systematically varied. One group of 8 pigeons was food deprived and subgroups of 2 birds each were exposed to four different pellet sizes as reinforcers, each reinforcer signaled by a keylight conditioned stimulus. A second group was water deprived and received water reinforcers paired with the conditioned stimulus. Water- or food-deprived control groups received appropriate water or food reinforcers that were randomly delivered with respect to the keylight stimulus. Acquisition of the conditioned gape response frequently preceded key-contact responses, and gape conditioned responses were generally elicited at higher rates than were key contacts. The form of the conditioned gape was similar to, but not identical with, the form of the unconditioned gape. The gape component is a critical topographical feature of the conditioned key peck, a sensitive measure of conditioning during autoshaping, and an important source of the observed similarities in the form of conditioned and consummatory responses.     

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.     

Temporal constraint on choice: Sensitivity and bias in multiple schedules

In multiple schedules of reinforcement, ratios of responses in successive components are relatively insensitive to ratios of obtained reinforcers. An analysis is proposed that attributes changes in absolute response rates to concurrent interactions between programmed reinforcement and extraneous reinforcement in other components. The analysis predicts that ratios of responses in successive components vary with reinforcer ratios, qualified by a term describing the reinforcement context, that is, programmed and extraneous reinforcers. Two main predictions from the analysis were confirmed in an experiment in which pigeons' responses were reinforced in the components of a multiple schedule and analog extraneous reinforcement was scheduled for an alternative response in each component. Sensitivity of response and time ratios to reinforcer ratios in the multiple schedules varied as a function of the rate of extraneous reinforcers. Bias towards responding in one component of the multiple schedule varied as an inverse function of the ratios of extraneous reinforcer rate in the two components. The data from this and previous studies of multiple-concurrent performance were accurately predicted by our analysis and supported our contention that the allocation of behavior in multiple-schedule components depends on the relative values of concurrently-available reinforcers within each component.     

Relationship between response rate and reinforcement frequency in variable-interval schedules: the effect of the concentration of sucrose reinforcement

Four rats were exposed to variable-interval schedules specifying a range of different reinforcement frequencies, using sucrose of two different concentrations and distilled water as the reinforcer. With sucrose, the rates of responding of all four rats were increasing negatively accelerated functions of reinforcement frequency, the data conforming closely to Herrnstein's equation; this was also true of the data from three of the four rats when distilled water was used as the reinforcer. The values of both constants in Herrnstein's equation were related to the sucrose concentration: the asymptotic response rate decreased, and the reinforcement frequency corresponding to the half-maximal response rate increased, with decreasing sucrose concentration.     

Motivational influences on performance maintained by food reinforcement

In Study 1, we examined the independent effects of reinforcer consumption during sessions and meal consumption prior to sessions on performance maintained by food reinforcement. Nine individuals with developmental disabilities participated. On alternate days, a preferred edible item was delivered during (a) seven sessions conducted before lunch (repeated-reinforcement condition) versus (b) one session each conducted before and after lunch (pre- and postmeal conditions). Results for 7 of 9 participants showed decreased response rates across sessions in the repeated-reinforcement condition; results for 3 of 9 participants showed decreased rates during postmeal relative to premeal conditions. Two participants who did not show a decrement in responding during either comparison participated in Study 2, in which reinforcer consumption during sessions, combined with meal consumption prior to sessions, also had no effect on their performance. In Study 3, we determined whether (a) choice of reinforcers, (b) increased break time between sessions, (c) varied reinforcers, or (d) intermittent reinforcement schedules mitigated the satiation effects observed for the 7 participants in Study 1. Presession choice of reinforcers resulted in maintained performance for 2 of 6 participants exposed to this condition. Varied reinforcement resulted in maintained performance for only 1 of 5 participants exposed to this condition. Neither the increased break between sessions nor the intermittent reinforcement schedule was effective in maintaining performance for the participants who were exposed to these conditions.     

EFFECTS OF POINT‐LOSS PUNISHERS ON HUMAN SIGNAL‐DETECTION PERFORMANCE

Three experiments using human participants varied the distribution of point‐gain reinforcers or point‐loss punishers in two‐alternative signal‐detection procedures. Experiment 1 varied the distribution of point‐gain reinforcers for correct responses (Group A) and point‐loss punishers for errors (Group B) across conditions. Response bias varied systematically as a function of the relative reinforcer or punisher frequencies. Experiment 2 arranged two conditions — one where an unequal ratio of reinforcement (5:1 or 1:5) was presented without punishment (R‐only), and another where the same reinforcer ratio was presented with an equal distribution of point‐loss punishers (R+P). Response bias was significantly greater in the R‐only condition than the R+P condition, supporting a subtractive model of punishment. Experiment 3 varied the distribution of point‐gain reinforcers for correct responses across four unequal reinforcer ratios (5:1, 2:1, 1:2, 1:5) both without (R‐only) and with (R+P) an equal distribution of point‐loss punishers for errors. Response bias varied systematically with changes in relative reinforcer frequency for both R‐only and R+P conditions, with 5 out of 8 participants showing increases in sensitivity estimates from R‐only to R+P conditions. Overall, the results indicated that punishers have similar but opposite effects to reinforcers in detection procedures and that combined reinforcer and punisher effects might be better modeled by a subtractive punishment model than an additive punishment model, consistent with research using concurrent‐schedule choice procedures.     

Secondary reinforcement and number of primary reinforcements

Pigeons' pecks on either of two concurrently available response keys produced secondary reinforcers according to independent one-minute variable-interval schedules. Different secondary reinforcers, in the presence of which the rates of primary reinforcement were equal, were associated with each key. The rate of pecking maintained by each secondary reinforcer varied directly, but nonproportionally, with the number of primary reinforcements given in the presence of the secondary reinforcer.     

Earning and obtaining reinforcers under concurrent interval scheduling

Contingencies of reinforcement specify how reinforcers are earned and how they are obtained. Ratio contingencies specify the number of responses that earn a reinforcer, and the response satisfying the ratio requirement obtains the earned reinforcer. Simple interval schedules specify that a certain time earns a reinforcer, which is obtained by the first response after the interval. The earning of reinforcers has been overlooked, perhaps because simple schedules confound the rates of earning reinforcers with the rates of obtaining reinforcers. In concurrent variable-interval schedules, however, spending time at one alternative earns reinforcers not only at that alternative, but at the other alternative as well. Reinforcers earned for delivery at the other alternative are obtained after changing over. Thus the rates of earning reinforcers are not confounded with the rate of obtaining reinforcers, but the rates of earning reinforcers are the same at both alternatives, which masks their possibly differing effects on preference. Two experiments examined the separate effects of earning reinforcers and of obtaining reinforcers on preference by using concurrent interval schedules composed of two pairs of stay and switch schedules (MacDonall, 2000). In both experiments, the generalized matching law, which is based on rates of obtaining reinforcers, described responding only when rates of earning reinforcers were the same at each alternative. An equation that included both the ratio of the rates of obtaining reinforcers and the ratio of the rates of earning reinforcers described the results from all conditions from each experiment.     

Discrete-trial choice in pigeons: Effects of reinforcer magnitude

The preference of pigeons for large reinforcers which occasionally followed a response versus small reinforcers which invariably followed a response was studied in a discrete-trial situation. Two differently colored keys were associated with the two reinforcement alternatives, and preference was measured as the proportion of choice trials on which the key associated with uncertain reinforcement was pecked. A combination of choice and guidance trials insured that received distributions of reinforcement equalled the scheduled distributions. For five of six subjects, preference for the uncertain reinforcer appeared to be a linear function of the magnitude of the certain reinforcer. In addition, there was greater preference for the response alternative associated with uncertain reinforcement than would be expected on the basis of net reinforcer value.