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.     

Stimulus effects on concurrent performance in transition

Six experimentally naive pigeons were exposed to concurrent variable-interval variable-interval schedules in a three-key procedure in which food reinforcement followed pecks on the side keys and pecks on the center key served as changeover responses. In Phase 1, 3 birds were exposed to 20 combinations of five variable-interval values, with each variable-interval value consistently associated with a different color on the side keys. Another 3 pigeons were exposed to the same 20 conditions, but with a more standard procedure that used a nondifferential discriminative stimulus on the two side keys throughout all conditions. In Phase 2, the differential and nondifferential stimulus conditions were reversed for each pigeon. Each condition lasted for one 5-hr session and one subsequent 1-hr session. In the last 14 conditions of each phase, the presence of differential discriminative stimuli decreased the time necessary for differential responding to develop and increased the sensitivity of behavior to reinforcement distribution in the 1st hr of training; during the last hours of training in each condition, however, the effects of the differential discriminative stimuli could not be distinguished from the effects of reinforcement distribution per se. These results show the importance of studying transitions in behavior as well as final performance. They may also be relevant to discrepancies in the results of previous experiments that have used nonhuman and human subjects.     

Molecular contingencies in schedules of intermittent punishment

In two experiments, key pecking of pigeons was maintained by a variable-interval 180-s schedule of food presentation. Conjointly, a second schedule delivered response-dependent electric shock. In the first experiment, shocks were presented according to either a variable-interval or a nondifferential interval-percentile schedule. The variable-interval shock schedule differentially delivered shocks following long interresponse times. Although the nondifferential shock schedules delivered shocks less differentially with respect to interresponse times, the two shock schedules equally reduced the relative frequency of long interresponse times. The second experiment differentially shocked long or short interresponse times in different conditions, with resulting decreases in the relative frequency of the targeted interresponse times. These experiments highlight the importance of selecting the appropriate level of analysis for the interaction of behavior and environment. Orderly relations present at one level of analysis (e.g., interresponse times) may not be revealed at other levels of analysis (e.g., overall response rate).     

Inelastic supply: An economic approach to simple interval schedules

Economic theory predicts an inverse relationship between the quantity of a commodity supplied to the marketplace and the equilibrium market price of that commodity. This prediction was tested in three experiments. Pigeons responded on simple variable-interval schedules, and quantity of reinforcement supplied was varied in a different way in each experiment. In Experiment 1, quantity supplied was varied by manipulating reinforcement rate while keeping session length constant. In Experiment 2, quantity supplied was varied by manipulating reinforcement rate while keeping reinforcers per session constant. In Experiment 3, quantity supplied was varied by manipulating reinforcer magnitude while keeping number of reinforcers constant. As predicted by economic theory, the obtained behavioral cost (responses per reinforcer) increased as supply decreased. The results could not be explained by simple artifacts such as satiation and time available to respond. In addition, the function relating response rate to reinforcement rate was bitonic in 7 of 9 animals in Experiments 1 and 2, which supports economic and regulatory theories over more traditional reinforcement theories.     

Choice between repleting/depleting patches: A concurrent-schedule procedure

Six pigeons responded on two concurrently available keys that defined patches with the following characteristics. Reinforcer stores repleted on a patch as a linear function of time when the bird had last responded to the other patch, or else did not replete. Repletion schedules thus timed only when the bird was absent from the patch. Reinforcer stores on a patch could be depleted and reinforcers obtained, again as a linear function of time, when the bird responded on a key. Depletion schedules thus timed only when the birds were present at a patch. Experiment 1 investigated changing relative depletion rates when repletion rates were constant and equal (Part 1) and changing relative repletion rates when the depletion rates were constant and equal (Part 2). Response- and time-allocation ratios conformed to a generalized matching relation with obtained reinforcer ratios, and there appeared to be no control by the size of the reinforcer stores. In Experiment 2, absolute depletion rates were varied with a pair of unequal repletion rates (Part 3), and absolute repletion rates were varied with a pair of unequal depletion rates (Part 4). Dwell times in the patches were not affected by either variation. Melioration theory predicted the results of Experiment 1 quite closely but erroneously predicted changing dwell times in Experiment 2. Molar maximization theory did not accurately predict the results of either experiment.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Discriminability between alternatives in a switching-key concurrent schedule

Six pigeons were trained to discriminate between two intensities of white light in a symbolic matching-to-sample procedure. These stimuli were then used to signal which schedule was available on the main key in a switching-key concurrent schedule. The concurrent schedules led to a symbolic matching-to-sample phase in which the subject identified the concurrent schedule to which it last responded before a reinforcer could be obtained. The concurrent schedules were varied across conditions. Discriminability, measured during the symbolic matching-to-sample performance, was high throughout and did not differ across the two procedures. Performance in the concurrent schedules was like that typically obtained using these schedules. Delays were then arranged between completion of the concurrent schedules and presentations of the symbolic matching-to-sample phase. A series of conditions with an intervening delay of 10 s showed that both concurrent-schedule performance and symbolic matching-to-sample performance were affected by the delay in a similar way; that is, choice responding was closer to indifference.     

Children's choice: Sensitivity to changes in reinforcer density

Two experiments were carried out in which children's sensitivity to changes in reinforcer density (number of reinforcers per session) was measured in a choice paradigm. In Experiment 1, 24 girls (ages 6, 9, and 12 years) performed on concurrent-chain schedules of reinforcement. The initial links were variable-interval 10-s schedules. One terminal link always gave three tokens after 30 s, but the parameters associated with the other were varied. Independent manipulations of reinforcer size (two tokens or four tokens) and prereinforcement delay (25 s or 65 s) led to equal changes in the relative density of tokens that could be earned on the schedules. Subjects at all ages were sensitive to changes in reinforcer density brought about by changes in reinforcer size, whereas only 3 12-year-olds showed sensitivity to the changes brought about by manipulation of prereinforcer delay. In Experiment 2, titration procedures were used to test the extent of this insensitivity to delay in 32 6- and 12-year-old children. In these procedures, a repeated choice of the large reinforcer increased the delay to its delivery, and a repeated choice of the small reinforcer reduced the delay to the delivery of the large reinforcer. Whereas 6-year-old boys and girls tended to maintain a strong preference for the large reinforcer, so increasing the delay to its delivery, 12-year-olds tended to distribute their responses to both alternatives, thus producing a stable level of delay to the large reinforcer. The results from the two experiments support the idea of two stages in the development of adaptive intertemporal choice.     

A quantitative analysis of chain-schedule performance

Six pigeons were trained with a chain variable-interval variable-interval schedule on the left key and with reinforcers available on the right key on a single variable-interval schedule arranged concurrently with both links of the chain. All three schedules were separately and systematically varied over a wide range of mean intervals. During these manipulations, the obtained reinforcer rates on constant arranged schedules also frequently changed systematically. Increasing reinforcer rates in Link 2 of the chain increased response rates in both links and decreased response rates in the variable-interval schedule concurrently available with Link 2. Increasing Link-1 reinforcer rates increased Link-1 response rates and decreased Link-2 response rates. Increasing reinforcer rates on the right-key schedule decreased response rates in Link 1 of the chain but did not affect the rate in Link 2. The results extend and amplify previous analyses of chain-schedule performance and help define the effects that a quantitative model must describe. However, the complexity of the results, and the fact that constant arranged reinforcer schedules did not necessarily lead to constant obtained reinforcer rates, precluded a quantitative analysis.     

Algorithmic shaping and misbehavior in the acquisition of token deposit by rats

In two experiments, rats were trained to deposit ball bearings down a hole in the floor, using an algorithmic version of shaping. The experimenter coded responses expected to be precursors of the target response, ball bearing deposit; a computer program reinforced these responses, or not, according to an algorithm that mimicked the processes thought to occur in conventional shaping. In the first experiment, 8 of 10 rats were successfully shaped; in the second, 5 of 5 were successfully shaped, and the median number of sessions required was the same as for a control group trained using conventional shaping. In both experiments, “misbehavior,” that is, excessive handling and chewing of the ball bearings, was observed, and when the algorithmic shaping procedure was used, misbehavior could be shown to occur in spite of reduced reinforcement for the responses involved.