Choice performance in several concurrent key-peck treadle-press reinforcement schedules

Five pigeons were exposed to several concurrent variable-interval food reinforcement schedules. For three subjects, one component of the schedule required a key-pecking response, the other a treadle-pressing response. For the other two subjects, both schedule components required treadle-pressing responses. The relative probability of reinforcement associated with the manipulanda was varied from 0 to 1.0 in 13 experimental conditions for the Key-Treadle subjects and nine conditions for the Treadle-Treadle subjects. The results indicated that the logarithms of relative time spent responding, and the logarithms of relative number of responses emitted on a manipulandum, approximated direct linear functions of logarithms of the relative frequencies of reinforcement associated with that manipulandum. No systematic bias in favor of time spent key pecking over time spent treadle pressing was apparent for the Key-Treadle subjects. All subjects exhibited undermatching, in that the ratios of time and response allocation at the alternatives systematically differed from the ratios of reinforcers obtained from the alternatives in the direction of indifference. Key pecking appeared to have no special link to food beyond treadle pressing or what would be expected on the basis of the reinforcement dependencies alone.     

Negative behavioral contrast on multiple treadle-press schedules

Eight pigeons pressed treadles for food reinforcers delivered by several multiple variable-interval schedules. The rate of reinforcement for responding during one component schedule was held constant at 30 reinforcers per hour. The rate of reinforcement for responding during the other component varied from 0 to 120 or 240 reinforcers per hour. The schedules were presented in different orders for different subjects. The rate of responding emitted during the variable component schedule varied directly with the rate of reinforcement it provided. The rate of responding during the constant component did not increase consistently when the rate of reinforcement obtained from the variable component decreased from 30 to 0 reinforcers per hr. The rate of responding emitted during the constant component decreased when the rate of reinforcement obtained from the variable component increased from 30 reinforcers per hour to a higher rate. That is, negative but not positive behavioral contrast occurred. The failure to find positive contrast is consistent with one of the predictions of the additive theories of behavioral contrast. Finding negative contrast has ambiguous implications for the additive theories.     

Matching in concurrent variable-interval avoidance schedules

After pretraining with multiple variable-interval avoidance schedules, two rats were exposed to a series of concurrent variable-interval avoidance schedules. Responses on two levers cancelled delivery of electric shocks arranged according to two independent variable-interval schedules. The ratio of responses and time spent on the two levers approximately matched the ratio of shocks avoided on each. Matching to the number of shocks received was not obtained. Concurrent variable-interval avoidance can therefore be added to the group of positive and negative reinforcement schedules that can be expressed in the quantitative framework of the matching law.     

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.     

Matching under concurrent fixed-ratio variable-interval schedules of food presentation

Four pigeons were exposed to concurrent fixed-ratio, variable-interval schedules of food presentation. The fixed-ratio requirement was either 25, 50, 75, or 100 responses, with the variable-interval schedule parameter held constant at 4 minutes. A delay time was imposed between a changeover from one schedule to the other and subsequent food availability. The delay time was varied at each ratio requirement over four values; no delay, 0-second delay, 1.5-second delay, and 5.0-second delay. As the fixed-ratio requirement or the delay time increased, a greater proportion of the total responses and time spent responding occurred under the variable-interval schedule relative to the proportion of food deliveries under that schedule. Neither relative overall response rate nor relative time spent responding equalled the relative frequency of food presentation, as would be predicted by a linear “matching” model. Rather, these data were described by power functions with slopes of approximately 1.0 and intercepts greater than 1.0. In the terms of Baum's (1974) analysis, these deviations from linear matching represent bias in favor of responding under the interval schedule. Bias, as reflected in the intercept of the power function, was greater for the ratio of time than the ratio of responses.     

Matching with a trio of concurrent variable-interval schedules of reinforcement

A trio of concurrent variable-interval schedules of reinforcement was arranged according to a changeover-key procedure, including a changeover delay of 1.5 sec. The three schedules provided a combined maximum reinforcement rate of 45 reinforcements per hour. With that restriction, the nine experimental conditions included several combinations of variable-interval schedules, sometimes including extinction. The pigeons matched relative response rate and relative time to relative reinforcement rate. Relative time appeared to match some-what better than relative response rate. Performance adjusted rapidly from one experimental condition to the next, whether the change involved two or all three schedules of the concurrent trio.     

Dynamical concurrent schedules

Previous work on the matching law has predominantly focused on the molar effects of the contingency by examining only one reinforcer ratio for extended periods. Responses are distributed as a function of reinforcer ratios under these static conditions. But the outcome under a dynamic condition in which reinforcer ratios change continuously has not been determined. The present study implemented concurrent variable-interval schedules that changed continuously across a fixed 5-min trial. The schedules were reciprocally interlocked. The variable interval for one key changed continuously from a variable-interval 15-s to a variable-interval 480-s, while the schedule for the other key changed from a variable-interval 480-s to a variable-interval 15-s. This dynamical concurrent schedule shifted behavior in the direction of matching response ratios to reinforcer ratios. Sensitivities derived from the generalized matching law were approximately 0.62, the mean absolute bias was approximately 0.11, and r2s were approximately 0.86. It was concluded that choice behavior can come to adapt to reinforcer ratios that change continuously over a relatively short time and that this change does not require extensive experience with a fixed reinforcer ratio. The results were seen as supportive of the view that all behavior constitutes choice.     

Maximizing and matching on concurrent ratio schedules

Pigeons on concurrent variable-ratio variable-ratio schedules usually, though not always, maximize reinforcements per response. When the ratios are equal, maximization implies no particular distribution of responses to the two alternatives. When the ratios are unequal, maximization calls for exclusive preference for the smaller ratio. Responding conformed to these requirements for maximizing, which are further shown to be consistent with the conception of reinforcement implicit in the matching law governing relative responding in concurrent interval schedules.     

Choice between concurrent schedules

Six pigeons pecked for food in a three-key experiment. A subject at any time could choose the left or right key and receive reinforcement according to one two-key concurrent variable-interval variable-interval schedule of reinforcement, or it could peck the center key. A peck on the center key arranged the complementary two-key concurrent variable-interval variable-interval schedule on the left and right keys. The two different two-key concurrent schedules arranged reinforcements concurrently and were signalled by two different colors of key lights. Choice behavior in the presence of a given color conformed to the usual relationship in two-key concurrent schedules: the relative frequency of responding on a key approximately equalled the relative frequency of reinforcement on that key. Preference for a two-key concurrent schedule, which was equivalent to preference for a color, was measured by the percentage of all responses on the left and right keys in the presence of that color: this percentage approximately equalled the percentage of all reinforcements that were delivered in the presence of that color. Thus, choice between concurrent schedules conforms approximately to the same relationship as does choice between alternatives in a single concurrent schedule.     

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

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

Performance in concurrent interval schedules

Four pigeons were trained under concurrent variable-interval variable-interval and fixed-interval variable-interval schedules in a two-key situation. Both response allocation and time allocation to the two schedules were measured when various reinforcement rates were arranged on each key. All animals showed an approximately constant proportional preference for the variable-interval schedule over the fixed-interval schedule. These results support Schneider's (1969) analysis of fixed-interval schedule performance.     

Maximizing versus matching on concurrent variable-interval schedules

Maximization and matching predictions were examined for a time-based analogue of the concurrent variable-interval variable-ratio schedule. One alternative was a variable interval whose time base operated relatively independent of the schedule chosen, and the other was a discontinuous variable interval for which timing progressed only when selected. Pigeons switched between schedules by pecking a changeover key. The maximization hypothesis predicts that subjects will show a bias toward the discontinuous variable interval and undermatching; however the obtained results conformed closely to the predictions of the matching law. Finally, a quantitative comparison was made of the bias and sensitivity estimates obtained in published concurrent variable-interval variable-ratio analogue studies. Results indicated that only the ratio-based analogue of the concurrent variable interval variable ratio studied by Green, Rachlin, and Hanson (1983) produced significant bias toward the variable-ratio alternative and undermatching, as predicted by reinforcement maximization.     

Performance in concurrent fixed-interval schedules

Six pigeons were trained on a variety of concurrent fixed-interval fixed-interval schedules. Matching between response or time ratios and ratios of obtained numbers of reinforcements was found for eight of 12 schedules studied. Cumulative records showed both typical burst-and-break patterns and also atypical response patterns in which response rate was constant between reinforcements on a schedule. Matching occurred only when the same pattern was present on both concurrent schedules. When different response patterns were generated by the two schedules, the pigeons consistently emitted fewer responses to the shorter fixed-interval than required by matching.     

Timeout from concurrent schedules.

Response-contingent timeouts of equal duration and frequency were added to both alternatives of unequal concurrent schedules of reinforcement. For each of 4 pigeons in Experiment 1, relative response rates generally became less extreme as the frequency of timeout increased. In Experiment 2, relative response rates consistently approached indifference as the duration of timeout was increased. Variation in time allocation was less consistent in both experiments. Absolute response rates did not vary with the timeout contingency in either experiment. In a third experiment, neither measure of choice varied systematically when the duration of a postreinforcement blackout was varied. In contrast to the present results, preference has been shown to vary directly with the parameters of shock delivery in related procedures. The pattern of results in the first two experiments follows that obtained with other manipulations of the overall rate of reinforcement in concurrent schedules. The results of the third experiment suggest that an intertrial interval following reinforcement is not a critical feature of the overall rate of reinforcement.     

Peak shift in concurrent schedules

Pigeons were exposed to two keys, a main key and a changeover key. Initially non-differential training was given in which pecking the main key was reinforced on a variable-interval 2-min schedule when the key displayed the first stimulus, a black line on a blue background, and was reinforced on an identical but independent variable-interval 2-min schedule when the key displayed a plain blue stimulus. Later, differential training was given in which pecking the main key was reinforced on a variable-interval 2-min schedule when the first stimulus was displayed; and was reinforced on a variable-interval 10-min schedule when a second stimulus, a black line of another orientation on a blue background, was displayed. During non-differential and differential training, each peck on the changeover key changed the stimulus on the main key. Generalization tests were given before and after the differential training. These consisted of presentations on the main key of seven orientations of the black line on the blue background, including the first and second stimuli, with no reinforcements being given. Changeover-key pecks changed the stimuli on the main key. Generalization gradients were obtained using three measures: time spent, responses, and response rate in the presence of each test stimulus. Typically, maximum values on these measures occurred to stimuli away from the first in a direction opposite the second stimulus, and minimum values occurred to stimuli away from the second in a direction opposite the first.     

Response rate and changeover performance on concurrent variable-interval schedules

Six pigeons were exposed to variable-interval schedules arranged on one, two, three, and four response keys. The reinforcement rate was also varied across conditions. Numbers of responses, the time spent responding, the number of reinforcements, and the number of changeovers between keys were recorded. Response rates on each key were an increasing function of reinforcement rate on that key and a decreasing function of the reinforcement rate on other keys. Response and time-allocation ratios under-matched ratios of obtained reinforcements. Three sets of equations were developed to express changeover rate as a function of response rate, time allocation, and reinforcement rate respectively. These functions were then applied to a broad range of experiments in the literature in order to test their generality. Further expressions were developed to account for changeover rates reported in experiments where changeover delays were varied.     

Variable-time reinforcement in multiple and concurrent schedules

Experiment I examined the role of a reduced rate of responding in the occurrence of behavioral contrast. Four rats and a pigeon were exposed to a two-component multiple schedule in which one component was always a variable-interval schedule. The second component was, at different times, either a variable-time schedule in which food was delivered independently of responding, or extinction. Both extinction and the variable-time schedule reduced the rate of responding in the second component. Behavioral contrast was observed, however, only when extinction was scheduled in the second component. Experiment II examined preference, as measured by time allocation in concurrent schedules for a variable-interval schedule relative to a variable-time schedule. Two rats displayed a lack of preference between the two schedules. The results of these experiments support a preference interpretation of behavioral contrast, which holds that behavioral contrast is the result of the introduction of a less-preferred condition in one component of a multiple schedule.     

The effects of terminal-link fixed-interval and variable-interval schedules on responding under concurrent chained schedules

Previous work using variable-interval schedules in the terminal links of concurrent chained schedules suggested that relative choice proportion in the initial links equalled relative rate of reinforcement in the terminal links. With fixed-interval terminal-link schedules, however, matching was not obtained. The present study held pairs of fixed-interval terminal-link schedules in a constant ratio but varied absolute sizes. Relative choice for the smaller terminal-link fixed-interval schedule was a negatively accelerated, increasing function of absolute size of the fixed-interval pairs. Matching was found only with the fixed-interval pair of 5 and 10 sec. When pairs of variable-interval schedules were arranged so that the harmonic mean of the intervals equalled the fixed-interval parameter values, relative choice functions were like those for fixed-interval schedules.