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.     

Changeover ratio effects on concurrent variable-interval performance

Rats' bar-pressing was maintained by concurrent variable-interval schedules of reinforcement. A fixed-ratio of pulls on a chain (the changeover ratio) was required for switching between schedules. The first experiment employed equal variable-interval schedules and symmetrical changeover ratios. Increasing these ratios resulted in a decrease in the rate of switching between schedules and an increase in local response rate. In the second experiment, a range of asymmetrical changeover ratios was used with equal variable-interval schedules, and a preference was found for the schedule associated with the larger switching-into ratio. Both the distributions of responses and time between the two schedules deviated from those expected on the basis of obtained reinforcers. In the third experiment, the switching-out-of ratio was dependent on the amount of time spent in a variable-interval 2-minute schedule; a constant ratio permitted switching out of the alternative variable-interval 1-minute schedule. A strong preference was shown for the variable-interval 2-minute schedule. The fourth experiment used equal variable-interval schedules; one changeover ratio was varied while the second remained constant. The results failed to show systematic differences in local response rates immediately after a changeover.     

Undermatching: a reappraisal of performance on concurrent variable-interval schedules of reinforcement

The extant data for pigeons' performance on concurrent variable-interval schedules were examined in detail. Least-squares lines relating relative pecks and time to the corresponding relative reinforcements were obtained for four studies. The between-study group slopes for time and pecks and five of seven within-study group slopes from individual studies were less than 1.00. This suggested the generality that pigeons respond less to the richer reinforcement schedule than predicted by matching. For pecks, a nonparametric test for distribution of points also supported this concept of undermatching (to the richer reinforcement schedule). In addition, using mean squared error as the criterion, a cubic curve fit the peck proportion data better than any line or other polynomial. This indicates that the relation between peck and reinforcement proportions may be nonlinear.     

Multiple and concurrent schedule performance: independence from concurrent and successive schedule contexts

Six pigeons were trained on multiple variable-interval schedules and performance was measured in the presence or absence of another variable-interval schedule (the common schedule) arranged concurrently with both components. Manipulations included varying the rate of reinforcement on the common schedule, leaving the common schedule unchanged while the components of the multiple schedule were varied, varying the multiple schedule components in the absence of the common schedule, and varying one component of the multiple schedule while the other component and the common schedule were unchanged. The normal rate-increasing and rate-decreasing effects of reinforcement rate increase were found, except that changing one multiple schedule component did not affect the response rate in the successively available common schedule component. Both concurrent and multiple schedule performance undermatched obtained reinforcement-rate ratios, but the degree of undermatching in multiple schedules was reliably greater. Allocation of responses between multiple schedule components was unaffected by the concurrent availability of reinforcement, and allocation of responses between concurrent schedules was unaffected by the successive availability of different reinforcement rates.     

The effects of different component response requirements in multiple and concurrent schedules

Six pigeons were trained on multiple and concurrent schedules. The reinforcement rates were varied systematically (a) when lever pressing was required in one component and key pecking in the successive component; (b) when lever pressing was required in both multiple components; (c) when key pecking was required in both multiple components; and (d) when key pecking was required on one schedule and lever pressing was required on the concurrently-available schedule. Only the absolute level of responding was changed by different response requirements. Analyzed by the generalized matching law, performance under different response requirements resulted in a bias toward key pecking, and the measured response bias was the same in multiple and concurrent schedule arrangements. The bias in time measures obtained from concurrent schedule performance was reliably smaller than the obtained response biases. The sensitivity to reinforcement-rate changes was ordered: concurrent key-lever; multiple key-key; multiple lever-key; and, the least sensitive, multiple lever-lever. The results confirm that requirements of different topographical responses can be handled by the generalized matching law mainly in the bias parameter, but problems for this type of analysis may be caused by the changing sensitivity to reinforcement in multiple schedule performance as response requirements are changed.     

Sensitivity to reinforcement in concurrent arithmetic and exponential schedules

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

Determinants of human performance on concurrent schedules.

Six experiments, each with 5 human adults, were conducted to investigate the determinants of human performance on multiple concurrent variable-interval schedules. A two-key procedure was employed in which subjects' key presses produced points exchangeable for money. Variables manipulated across experiments were (a) changeover delay (Experiments 2, 4, and 6), (b) ordinal cues related to scheduled reinforcement frequencies (Experiments 3 and 4), and (c) instructions describing the ordinal relations between schedule-correlated stimuli and scheduled reinforcement frequency (Experiments 5 and 6). The performances of only 13 of the 30 subjects could be described by the generalized matching equation and were within a range of values typical of those reported in the animal literature. Eight subjects showed indifference, 9 undermatched, 7 approximated matching, 3 overmatched, and a further 3 responded exclusively to the richer component of the concurrent schedules. These differing modes of responding were closely related to the different types of performance rules reported by subjects in postexperimental questionnaires. The results are in good agreement with those from studies of human performance on single schedules, suggesting that rule-governed behavior, in interaction with contingencies, may be an important determinant of human choice.     

The effect of signaled reinforcement availability on concurrent performances in humans

During Phase I, three female human subjects pressed a button for monetary reinforcement in two-component concurrent variable-interval schedules. Five different reinforcement frequencies were used in component A, whereas the reinforcement frequency in component B was held constant. Absolute rates of responding conformed to equations proposed by Herrnstein to describe concurent performances, and the ratios of the response rates and the times spent in the two components conformed to the matching law. During Phase II, the availability of reinforcement in component A was signaled by the illumination of a lamp. This resulted in suppression of response rates in component A and elevation of response rates in component B, these changes being reflected in a distortion of the matching relationship which took the form of a bias in favor of component B.     

Choice and the rate of punishment in concurrent schedules

Rats' responses on two levers were reinforced according to independent random-interval 1.5-min food schedules. In addition, both lever presses were intermittently punished according to several concurrent random-interval random-interval shock schedules. For the left, the scheduled rate of punishment was kept constant according to a random-interval 6-min schedule. For the right, the rate of punishment varied. As the frequency of punishment for the right lever press increased, its rate decreased. The rate of the left punished lever press increased, however, even though its scheduled reinforcement rate and punishment rate remained unchanged.     

Matching and maximizing with concurrent ratio-interval schedules.

Animals exposed to standard concurrent variable-ratio variable-interval schedules could maximize overall reinforcement rate if, in responding, they showed a strong response bias toward the variable-ratio schedule. Tests with the standard schedules have failed to find such a bias and have been widely cited as evidence against maximization as an explanation of animal choice behavior. However, those experiments were confounded in that the value of leisure (behavior other than the instrumental response) partially offsets the value of reinforcement. The present experiment provides another such test using a concurrent procedure in which the confounding effects of leisure were mostly eliminated while the critical aspects of the concurrent variable-ratio variable-interval contingency were maintained: Responding in one component advanced only its ratio schedule while responding in the other component advanced both ratio schedules. The bias toward the latter component predicted by maximization theory was found.     

Human choice in concurrent ratio-interval schedules of reinforcement.

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

A parametric evaluation of the hedonic and motoric effects of drugs: pimozide and amphetamine

This study uses a curve-fitting approach to evaluate the effects of drugs on reinforced responding in rats. The subjects obtained reinforcement according to a series of five different variable-interval schedules (a five-component multiple schedule). For each rat, pimozide, a neuroleptic, decreased response rate, and the decrease was associated with (1) a decrease in the estimated asymptotic response rate and (2) an increase in the rate of reinforcement necessary for half-asymptotic responding. That is, pimozide decreased the proportion of responding maintained by a given rate of reinforcement. In contrast, intermediate doses of amphetamine increased response rate and increased the proportion of responding maintained by a given rate of reinforcement. It was proposed that the response rate asymptote indexes motor capacity, and the rate of reinforcement necessary for half-asymptotic responding indexes reinforcement efficacy; accordingly, pimozide decreased motor capacity and reinforcement strength and amphetamine increased reinforcement strength.     

Undermatching on concurrent variable-interval schedules and the power law.

The phenomenon of undermatching on concurrent variable-interval schedules is shown to be derivable by transforming the individual interreinforcement intervals of each variable-interval schedule and averaging the transformed values to produce an "estimate" of the rate of reinforcement the schedules deliver. If the transformation is based on a power function with a fractional exponent, such as is found in many studies of temporal control in animals, matching response rations to the ratios of these estimated rates of reinforcement yields undermatching. If the concurrent variable-interval schedules are arranged such that the individual intervals in each schedule have a constant proportionality (a procedure found in many commonly used variable-interval schedules) the slope of the line relating logarithms of response ratios and of programmed reinforcement ratios is identical to the exponent of the power transformation applied to the individual time intervals in the variable-interval schedules. In other cases this simple relation does not hold but the degree of undermatching is greater the lower the value of the exponent of the power function. This account of undermatching predicts values similar to those typically observed.     

The economics of daily consumption controlling food- and water-reinforced responding

In the first experiment, two rhesus monkeys earned their entire ration of food and water during daily sessions with no provisions to ensure constant daily intakes. Two variable-interval schedules of food presentations were concurrent with one variable-interval schedule of water presentations; the maximum rate of food presentations arranged by one food schedule was varied. As the rate of food presentations was increased, the absolute level of responding on the two food schedules combined decreased, while responding on the water schedule increased. The preference for the variable food schedule compared to the other food schedule approximately matched the proportion of reinforcers obtained from it. The preference for the variable food schedule compared to the water schedule did not match, but greatly decreased, as the proportion of reinforcers from the food schedule increased. When Experiment I was replicated, with provisions to ensure constant daily intakes of food and water (Experiment II), the absolute response rates under the two food schedules combined and under the water schedule no longer changed with increases in the rate of food during the sessions. On the other hand, choice between the two food schedules remained proportional to the distribution of obtained food pellets. These results were interpreted as indicating that behavior to obtain nonsubstitutable commodities, such as food and water, is strongly controlled by the economic conditions of daily consumption, while choice between substitutable commodities is independent of these factors.     

Performance of humans in concurrent avoidance/positive-reinforcement schedules

Performance maintained under concurrent schedules consisting of a variable-interval avoidance component and a variable-interval positive-reinforcement component was studied in three human subjects using points exchangeable for money as the reinforcer. The rate of responding in the avoidance component increased, and the rate of responding in the positive-reinforcement component declined, as a function of the frequency of point-losses avoided in the avoidance component. The performance of all three subjects conformed to equations proposed by Herrnstein to describe behavior in concurrent schedules. The logarithms of the ratios of the response rates in the two components, and the logarithms of the ratios of the times spent in the two components, were linearly related to the logarithms of the ratios of the frequency of loss avoidance in the avoidance component to the frequency of reinforcement in the positive-reinforcement component. When a changeover delay of 5.0 sec was imposed, the slopes of the linear functions were close to 1.0 in the case of two subjects, whereas the third subject exhibited significant undermatching. For two subjects the changeover delay was then reduced to 2.0 sec; in both cases the slopes of the linear functions were lower than under the 5.0-sec condition. One subject participated in a third phase, in which no changeover delay was imposed; there was a further reduction in the slopes of the linear functions.     

Behavior-dependent reinforcer-rate changes in concurrent schedules: A further analysis

Six pigeons were trained on concurrent variable-interval schedules in three different procedures. The first procedure was a standard concurrent schedule, and the relative reinforcer frequency for responding was varied. The second was a schedule in which a relative left-key response rate (over a fixed period of time) exceeding .75 produced, in the next identical time period a higher reinforcer rate on the right key. If this criterion was not exceeded, equal reinforcer rates were arranged on the two keys in this period. This was the dependent procedure. In the third (independent) procedure, the periods of higher right-key reinforcer rates occurred with the same probability as in the second procedure, but occurred independently of behavior. In the second and third procedures, the fixed-time period (window) was varied from 5 s to 60 s, and to 240 s in the second procedure only. Performance on the two keys was similar in the concurrent and independent procedures. The procedure used in the dependent conditions generally affected performance when the windows were shorter than about 30 s. Models of performance that assume that subjects do not discriminate changes in local relative reinforcer rates cannot account for the data. Moreover, existing models are inherently unable to account for the effects of contingencies of reinforcement between responding on one alternative and gaining reinforcers on another that are arranged or that emerge as a result of time allocated to alternative schedules. Undermatching on concurrent variable-interval schedules may result from such emergent contingencies.     

The effects of concurrent responding and reinforcement on behavioral output

Four birds key pecked on concurrent variable-interval one-minute variable-interval four-minute schedules with a two-second changeover delay. Response rates to the variable-interval one-minute key were then reduced by signaling its reinforcer availability and later by providing its reinforcers independently of responding. Each manipulation increased response rates to the variable-interval four-minute key even though relative reinforcement rates were unchanged. In a final phase, eliminating the variable-interval one-minute key and its schedule produced the highest rates of all to the variable-interval four-minute key. These results show that both reinforcement and response rates to one schedule influence response rates to another schedule. These results join those of Guilkey, Shull, & Brownstein (1975) in failing to replicate Catania (1963). Moreover, they violate the predictions of the equation for simple action (de Villiers & Herrnstein, 1976). In terms of a median-rate measure (reciprocal of the median interresponse time), rates to the variable-interval four-minute key were high when responding was not reduced to the variable-interval one-minute key and were low when it was reduced. This rate difference suggests a process difference between concurrent-schedule procedures that maintain high concurrent response rates versus those that do not. This process difference jeopardizes attempts to integrate single- and concurrent-operant performances within a single formulation.     

Combinations of response-dependent and response-independent schedule-correlated stimulus presentation in an observing procedure

Pigeons pecked a response key on a variable-interval (VI) schedule, in which responses produced food every 40 s, on average. These VI periods, or components, alternated in irregular fashion with extinction components in which food was unavailable. Pecks on a second (observing) key briefly produced exteroceptive stimuli (houselight flashes) correlated with the component schedule currently in effect. Across conditions within a phase, the dependency between observing and presentation of the stimuli was decreased systematically while the density of stimulus presentation was held constant. Across phases, the proportion of session time spent in the VI component was adjusted from 0.5 to 0.25, and then to 0.75. Results indicate that rate of observing decreased as the dependency between responses and stimulus presentations was decreased. Further, discriminative control by the schedule-correlated stimuli was systematically weakened as dependency was decreased. Increasing the proportion of session time spent in VI decreased the rate of observing. This effect was additive with the manipulation of the dependency between observing and presentation of the stimuli. Overall, these results show that conditioned reinforcers function similarly to unconditioned reinforcers with respect to response-consequence dependencies, and that stimulus control is enhanced under conditions in which the relevant stimuli are produced by an organism's behavior.