Delay and amount of reward in a concurrent chain

Effects of signaled and unsignaled delays of reinforcement on response maintenance in zebrafish (Danio rerio)

Effects of delays of reinforcement on zebrafish behavior were examined following training with immediate reinforcement. The delay was either signaled by an exteroceptive stimulus present for the entire delay period (fully signaled), signaled briefly only at delay onset (partial signal), or without a stimulus (unsignaled). Unsignaled delays consistently resulted in low response rates. Fully signaled delays resulted in higher response rates than unsignaled delays when the delay was 3 s, but this difference in response rates disappeared at 6-s delays. Partially signaled delays were less effective in maintaining responding than fully signaled delays, but more effective than unsignaled delays, although these results were only suggestive. These results indicate that stimulus changes that occur during delays to reinforcement have similar effects with zebrafish as with other species, but also that responding of zebrafish has a relatively low tolerance to the delay duration. A vast majority of experiments examining zebrafish behavior suggests that the fish have potential to serve as an interface between biological and behavioral science, but this may not be the case in some research areas involving delays, such as delay discounting.

Zebrafish choice behavior is sensitive to reinforcer rate, immediacy, and magnitude ratios

Behavioral flexibility has, in part, been defined by choice behavior changing as a function of changes in reinforcer payoffs. We examined whether the generalized matching law quantitatively described changes in choice behavior in zebrafish when relative reinforcer rates, delays/immediacy, and magnitudes changed between two alternatives across conditions. Choice was sensitive to each of the three reinforcer properties. Sensitivity estimates to changes in relative reinforcer rates were greater when 2 variable-interval schedules were arranged independently between alternatives (Experiment 1a) than when a single schedule pseudorandomly arranged reinforcers between alternatives (Experiment 1b). Sensitivity estimates for changes in relative reinforcer immediacy (Experiment 2) and magnitude (Experiment 3) were similar but lower than estimates for reinforcer rates. These differences in sensitivity estimates are consistent with studies examining other species, suggesting flexibility in zebrafish choice behavior in the face of changes in payoff as described by the generalized matching law.

Pigeons prefer to invest early for future reinforcers

Five pigeons were trained in a series of conditions in which food was delivered after 25 responses, but only when a different (Investing) response had been made before the 25 responses had been completed. If an Investing response was not made, the 25 responses ended in blackout. In various conditions, effective Investing responses either had to be made before the first of the 25 responses, or anywhere within the 25 responses; and effective Investing responses either resulted in a stimulus change or did not. Pigeons Invested even when the consequences were temporally and spatially distant, but Investing was most likely when it produced an immediate stimulus change. When given the choice, pigeons preferred to make Investing responses at the beginning of a trial. These findings again demonstrate that behavior may be maintained by events that are separated in time and space from the present.

Impulsivity and sensitivity to amount and delay of reinforcement in an animal model of ADHD

Previous research has been inconclusive about the degree of impulsivity displayed by spontaneously hypertensive rats (SHR), an animal model of Attention Deficit Hyperactivity Disorder (ADHD). In the present set of experiments, concurrent-chains schedules were employed in order to explore SHR's impulsivity, sensitivity to delay, and sensitivity to amount of reinforcement; Wistar rats (WIS) were used as comparison group. In the three experiments - performed with different subjects - non-independent variable interval 30s schedules were presented in the initial links; the difference between experiments was in the terminal links. For exploring impulsivity, one of the terminal links (SS) was associated to a short delay (2s) and a small reinforcer (1 pellet), whereas the other terminal link (LL) was associated to a longer delay (28s) and a larger reinforcer (4 pellets). The results indicated a remarkably higher impulsivity in SHR. Because this impulsivity may have as potential mechanisms an increased sensitivity to delay and/or a decreased sensitivity to the amount of reinforcement, in experiments 2 and 3 these possibilities were examined. For assessing sensitivity to delay, the following pairs of fixed interval (FI) schedules were used in the terminal links in five conditions: 2-28, 6-24, 15-15, 24-6, 28-2s; the magnitude of reinforcement was 1 pellet in all conditions for both alternatives. For assessing sensitivity to amount, in five conditions the alternatives were associated with different magnitudes of reinforcement: 1-5 pellets, 2-4, 3-3, 4-2 and 5-1 in left-right alternatives, respectively; the delay to reinforcement was controlled by a FI 15s in all conditions and for both alternatives. The sensitivity to delay and the sensitivity to amount were calculated according to the Generalized Matching Law. The results indicated a higher sensitivity to delay in SHR, and the same sensitivity to amount in SHR and WIS rats. These results suggest that the increased sensitivity to delay influences the high level of impulsivity observed in SHR.

Distributed and accumulated reinforcement arrangements: evaluations of efficacy and preference

We assessed the efficacy of, and preference for, accumulated access to reinforcers, which allows uninterrupted engagement with the reinforcers but imposes an inherent delay required to first complete the task. Experiment 1 compared rates of task completion in 4 individuals who had been diagnosed with intellectual disabilities when reinforcement was distributed (i.e., 30-s access to the reinforcer delivered immediately after each response) and accumulated (i.e., 5-min access to the reinforcer after completion of multiple consecutive responses). Accumulated reinforcement produced response rates that equaled or exceeded rates during distributed reinforcement for 3 participants. Experiment 2 used a concurrent-chains schedule to examine preferences for each arrangement. All participants preferred delayed, accumulated access when the reinforcer was an activity. Three participants also preferred accumulated access to edible reinforcers. The collective results suggest that, despite the inherent delay, accumulated reinforcement is just as effective and is often preferred by learners over distributed reinforcement.

Postreward delays and systematic biases in measures of animal temporal discounting

Intertemporal choice tasks, which pit smaller/sooner rewards against larger/later ones, are frequently used to study time preferences and, by extension, impulsivity and self-control. When used in animals, many trials are strung together in sequence and an adjusting buffer is added after the smaller/sooner option to hold the total duration of each trial constant. Choices of the smaller/sooner option are not reward maximizing and so are taken to indicate that the animal is discounting future rewards. However, if animals fail to correctly factor in the duration of the postreward buffers, putative discounting behavior may instead reflect constrained reward maximization. Here, we report three results consistent with this discounting-free hypothesis. We find that (i) monkeys are insensitive to the association between the duration of postreward delays and their choices; (ii) they are sensitive to the length of postreward delays, although they greatly underestimate them; and (iii) increasing the salience of the postreward delay biases monkeys toward the larger/later option, reducing measured discounting rates. These results are incompatible with standard discounting-based accounts but are compatible with an alternative heuristic model. Our data suggest that measured intertemporal preferences in animals may not reflect impulsivity, or even mental discounting of future options, and that standard human and animal intertemporal choice tasks measure unrelated mental processes.

Risky choice in pigeons: preference for amount variability using a token-reinforcement system

Pigeons were given repeated choices between variable and fixed numbers of token reinforcers (stimulus lamps arrayed above the response keys), with each earned token exchangeable for food. The number of tokens provided by the fixed-amount option remained constant within blocks of sessions, but varied parametrically across phases, assuming values of 2, 4, 6, or 8 tokens per choice. The number of tokens provided by the variable-amount option varied between 0 and 12 tokens per choice, arranged according to an exponential or rectangular distribution. In general, the pigeons strongly preferred the variable option when the fixed option provided equal or greater numbers of tokens than the variable amount. Preference for the variable amount decreased only when the alternatives provided widely disparate amounts favoring the fixed amount. When tokens were removed from the experimental context, preference for the variable option was reduced or eliminated, suggesting that the token presentation played a key role in maintaining risk-prone choice patterns. Choice latencies varied inversely with preferences, suggesting that local analyses may provide useful ancillary measures of reinforcer value. Overall, the results indicate that systematic risk sensitivity can be attained with respect to reinforcer amount, and that tokens may be critical in the development of such preferences.

Pigeons' choices with token stimuli in concurrent variable-interval schedules

Twelve pigeons responded on concurrent variable-interval schedules that delivered token stimuli (stimulus lights for some pigeons, and white circles on the response keys for others). During exchange periods, each token could be exchanged for food on a fixed-ratio 1 schedule. Across conditions, the exchange requirements (number of tokens that had to be earned before they could be exchanged for food) varied between one and four for the two response keys. The main findings were that the pigeons' response percentages varied as a function of the number of tokens earned at any given moment, and they were determined by both the delays to food and by the number of food deliveries in the exchange periods. In some conditions, tokens had to be earned but were not visible during the variable-interval schedules for one or both keys. When one key had visible tokens and the other did not, the pigeons showed a preference for the key without visible tokens. A model based on the matching law and a hyperbolic delay-discounting equation could account for the main patterns of choice responding, and for how response percentages changed as successive tokens were earned. The results are consistent with the view that the token stimuli served as discriminative stimuli that signaled the current delays to food.

Preference reversal between impulsive and self-control choice

In a concurrent-chains procedure, pigeons chose between reinforcers varying in delay and amount. Reinforcer amount was determined by duration of access to grain, and delay was determined by fixed-interval schedules in the terminal links. Preference was measured by the ratio of responses in initial links. Dependent scheduling of variable-interval schedules in initial links ensured that delay and amount were not confounded with frequency of outcomes, which remained equal for the two choices. In Experiment 1, in components signaled by red keys in the initial links, small and large reinforcers were delivered after delays of 1 s and 10 s respectively. In components signaled by green, additional time was added to both delays. Smaller-sooner reinforcers were preferred in red components. In green components, smaller-sooner reinforcers were preferred at short delays, and choices for the larger-later reinforcer generally increased with increasing duration of the added delay. At longer delays, up to 15 s, the larger-later reinforcer was preferred. That is, the pigeons showed within-session preference reversal, with impulsive choice at short delays in red components and self-control choice at long delays in green components. In Experiment 2, added delay to both reinforcement and reinforcer amount were varied. Sensitivity of initial-link response ratios to ratios of amount increased with increasing duration of the added delay. This interaction between delay and amount was predicted if the temporal discounting functions assumed the magnitude effect in which discounting rate was inversely proportional to amount. It was also predicted by the contextual choice model of performance in concurrent-chains procedures.

Incentive theory: IV. Magnitude of reward

Incentive theory is successfully applied to data from experiments in which the amount of food reward is varied. This is accomplished by assuming that incentive value is a negatively accelerated function of reward duration. The interaction of the magnitude of a reward with its delay is confirmed, and the causes and implications of this interaction are discussed.

Concurrent-chain performance: Effects of absolute and relative terminal-link entry frequency

Six pigeons were trained in a concurrent-chain procedure with constant variable-interval 6-s variable-interval 12-s terminal links. Five groups of conditions were arranged. Within a group of conditions, the duration of one initial-link schedule was held constant and the duration of the other initial link was varied. The duration of the varied initial link was always longer than, or equal to, the constant initial-link duration. The duration of the shorter initial link was varied across groups of conditions from 5 s to 70 s. The data from each group were well described by the generalized matching law. Sensitivity (a) to the terminal-link entry ratio increased as the shorter initial-link duration increased, but appeared to reach an asymptote at shorter initial-link durations greater than 32 s. Terminal-link bias did not change with changes in shorter initial-link duration for the response-allocation data, but showed a small increase with increasing shorter initial-link duration for the time-allocation data.

Sensitivity to reinforcer duration in a self-control procedure

In a concurrent-chains procedure, pigeons' responses on left and right keys were followed by reinforcers of different durations at different delays following the choice responses. Three pairs of reinforcer delays were arranged in each session, and reinforcer durations were varied over conditions. In Experiment 1 reinforcer delays were unequal, and in Experiment 2 reinforcer delays were equal. In Experiment 1 preference reversal was demonstrated in that an immediate short reinforcer was chosen more frequently than a longer reinforcer delayed 6 s from the choice, whereas the longer reinforcer was chosen more frequently when delays to both reinforcers were lengthened. In both experiments, choice responding was more sensitive to variations in reinforcer duration at overall longer reinforcer delays than at overall shorter reinforcer delays, independently of whether fixed-interval or variable-interval schedules were arranged in the choice phase. We concluded that preference reversal results from a change in sensitivity of choice responding to ratios of reinforcer duration as the delays to both reinforcers are lengthened.

Concurrent schedules: Interaction of reinforcer frequency and reinforcer duration

Six pigeons were trained on concurrent variable-interval schedules with unequal reinforcer durations for the two responses. The schedules arranged on the two keys were kept equal while they were varied in absolute size. As the overall reinforcer rate was increased, both response-allocation and time-allocation measures of choice showed a trend toward indifference, and measures of sensitivity to reinforcer-duration ratios significantly decreased. Recent reports have shown that the generalized matching law cannot describe the changes in behavior allocation under constant delay-, duration-, or rate-ratios when changes are made in the absolute levels of each of these variables. The present results complement these findings by demonstrating that the concatenated generalized matching law cannot describe the interactions of two reinforcer variables on behavior allocation.

The maximization of overall reinforcement rate on concurrent chains

We model behavioral allocation on concurrent chains in which the initial links are independent variable-interval schedules. We also quantify the relationship between behavior during the initial links and the probability of entering a terminal link. The behavior that maximizes overall reinforcement rate is then considered and compared with published experimental data. Although all the trends in the data are predicted by rate maximization, there are considerable deviations from the predictions of rate maximization when reward magnitudes are unequal. We argue from our results that optimal allocation on concurrent chains, and prey choice as used in the theory of optimal diets, are distinct concepts. We show that the maximization of overall rate can lead to apparent violations of stochastic transitivity.

Independence of reinforcement delay and magnitude in concurrent chains

A three-component concurrent-chains procedure was used to investigate preference between terminal-link schedules that differed in delay and magnitude of reinforcement. Response and time allocation data were well described by a generalized matching model. Sensitivity to delay appeared to be lower when reinforcement magnitudes were unequal than when they were equal, but when obtained rather than programmed time spent responding in the initial links was used in the model, the difference vanished. The results support independence of delay and magnitude as separate dimensions of reinforcement value, as required by the matching law, and the assumption of the contextual choice model (Grace, 1994) that sensitivities to delay and magnitude are affected similarly by temporal context. Although there was statistical evidence for interaction between successive components, the effects were small and transient. The multiple-component concurrent-chains procedure should prove useful in future research on multidimensional preference, although it may be necessary to control obtained initial-link time more precisely.

Research on self-control: An integrating framework

The tendency to choose a larger, more delayed reinforcer over a smaller, less delayed one has frequently been termed “selfcontrol.” Three very different research traditions – two models emphasizing the control of local contingencies of reinforcement (Mischel's social learning theory and Herrnstein's matching law) and molar maximization models (specifically optimal foraging theory) – have all investigated behavior within the self-control paradigm. A framework is proposed to integrate research from all three research areas. This framework consists of three parts: a procedural analysis, a causal analysis, and a theoretical analysis. The procedural analysis provides a common procedural terminology for all three areas. The causal analysis establishes that, in all three research traditions, self-control varies directly with the current physical values of the reinforcers; that is, choices increase with reinforcer amount and decrease with reinforcer delay. But self-control also varies according to past events to which a subject has been exposed, and according to current factors other than the reinforcers. Each of the three models has therefore incorporated these indirect effects on self-control by postulating unobservable mechanisms. In all three cases, these mechanisms represent a subject's behavior as a function of a perceived environment. The theoretical analysis demonstrates that evolutionary theory can encompass the research from all three areas by considering differences in the adaptiveness of self-control in different situations. This integration provides a better and more predictive description of self-control.

Choice between single and multiple reinforcers in concurrent-chains schedules

Pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links. One terminal link delivered a single reinforcer after a fixed delay, and the other terminal link delivered either three or five reinforcers, each preceded by a fixed delay. Some conditions included a postreinforcer delay after the single reinforcer to equate the total durations of the two terminal links, but other conditions did not include such a postreinforcer delay. With short initial links, preference for the single-reinforcer alternative decreased when a postreinforcer delay was present, but with long initial links, the postreinforcer delays had no significant effect on preference. In conditions with a postreinforcer delay, preference for the single-reinforcer alternative frequently switched from above 50% to below 50% as the initial links were lengthened. This pattern of results was consistent with delay-reduction theory (Squires & Fantino, 1971), but not with the contextual-choice model (Grace, 1994) or the hyperbolic value-added model (Mazur, 2001) as they have usually been applied. However, the hyperbolic value-added model could account for the results if its calculations were expanded to include reinforcers delivered in later terminal links. The implications of these findings for models of concurrent-chains performance are discussed.

Amount-dependent temporal discounting?

Amount-dependent temporal discounting has been demonstrated for human choice between outcomes differing in amount and delay. In the only study to date with non-humans, Grace reported no evidence for amount-dependent temporal discounting with pigeons in a concurrent-chains procedure. The present experiments repeated Grace's procedure but with modifications to enhance the discrimination between small and large magnitude outcomes. In Experiment 1, sensitivity of pigeons' initial-link choice to the terminal link delay ratio was greater with large reinforcer durations in the terminal links than with small reinforcer durations. This result is consistent with a greater rate of temporal discounting for larger reinforcers (the reverse of the result for humans), but can also be explained as enhanced discrimination of delay ratios with larger reinforcer durations. The results of a second experiment supported Grace's conclusion that amount-dependent temporal discounting does not characterize pigeons' choice in concurrent chains. Because reinforcer amount was held constant between choice alternatives in the present experiments and that of Grace, but varied in the human studies, our results question whether prior demonstrations of amount-dependent discounting reflect the effects of reinforcer delay or of reinforcer amount. Differences in the procedures used to study discounting in humans (titration procedures) and non-humans (concurrent chains) may contribute to the divergent results across species.

Does sensitivity to magnitude depend on the temporal distribution of reinforcement?

Our research addressed the question of whether sensitivity to relative reinforcer magnitude in concurrent chains depends on the distribution of reinforcer delays when the terminal-link schedules are equal. In Experiment 1, 12 pigeons responded in a two-component procedure. In both components, the initial links were concurrent variable-interval 40-s variable-interval 40-s, and the terminal links were both 20-s interval schedules in which responses were reinforced by either 4-s of grain in one, or 2-s of grain in the other. The only difference between the components was whether the terminal-link schedules were fixed interval or variable intervals. For all subjects, the relative rate of responding in the initial links for the terminal link that produced the 4-s reinforcer was greater when the terminal links were fixed-interval schedules than when they were variable-interval schedules. This result is contrary to the prediction of Grace's (1994) contextual choice model, but is consistent with both Mazur's (2001) hyperbolic value-added model and Killeen's (1985) incentive theory. In Experiment 2, 4 pigeons responded in a concurrent-chains procedure in which 4-s or 2-s reinforcers were provided independently of responding according to equal fixed-time or mixed-time schedules. Preference for the 4-s reinforcer increased as the variability of the intervals comprising the mixed-time schedules was decreased. Generalized-matching sensitivity of initial-link response allocation to relative reinforcer magnitude was proportional to the geometric mean of the terminal-link delays.

Variation, repetition, and choice

Experiment 1 investigated the controlling properties of variability contingencies on choice between repeated and variable responding. Pigeons were exposed to concurrent-chains schedules with two alternatives. In the REPEAT alternative, reinforcers in the terminal link depended on a single sequence of four responses. In the VARY alternative, a response sequence in the terminal link was reinforced only if it differed from the n previous sequences (lag criterion). The REPEAT contingency generated low, constant levels of sequence variation whereas the VARY contingency produced levels of sequence variation that increased with the lag criterion. Preference for the REPEAT alternative tended to increase directly with the degree of variation required for reinforcement. Experiment 2 examined the potential confounding effects in Experiment 1 of immediacy of reinforcement by yoking the interreinforcer intervals in the REPEAT alternative to those in the VARY alternative. Again, preference for REPEAT was a function of the lag criterion. Choice between varying and repeating behavior is discussed with respect to obtained behavioral variability, probability of reinforcement, delay of reinforcement, and switching within a sequence.

Determinants of pigeons' choices in token-based self-control procedures

Four pigeons were exposed to a token-based self-control procedure with stimulus lights serving as token reinforcers. Smaller-reinforcer choices produced one token immediately; larger-reinforcer choices produced three tokens following a delay. Each token could be exchanged for 2-s access to food during a signaled exchange period each trial. The main variables of interest were the exchange delays (delays from the choice to the exchange stimulus) and the food delays (also timed from the choice), which were varied separately and together across blocks of sessions. When exchange delays and food delays were shorter following smaller-reinforcer choices, strong preference for the smaller reinforcer was observed. When exchange delays and food delays were equal for both options, strong preference for the larger reinforcer was observed. When food delays were equal for both options but exchange delays were shorter for smaller-reinforcer choices, preference for the larger reinforcer generally was less extreme than under conditions in which both exchange and food delays were equal. When exchange delays were equal for both options but food delays were shorter for smaller-reinforcer choices, preference for the smaller reinforcer generally was less extreme than under conditions in which both exchange and food delays favored smaller-reinforcer choices. On the whole, the results were consistent with prior research on token-based self-control procedures in showing that choices are governed by reinforcer immediacy when exchange and food delays are unequal and by reinforcer amount when exchange and food delays are equal. Further, by decoupling the exchange delays from food delays, the results tentatively support a role for the exchange stimulus as a conditioned reinforcer.

Modelos de autocontrole na análise experimental do comportamento: utilidade e crítica

O presente trabalho discute o conceito de autocontrole na análise do comportamento nas contribuições de Skinner, Rachlin e Mischel a partir de diferentes usos do termo. Autocontrole envolve: (1) uma resposta controlada (Rc) que é parte de uma ou uma combinação de contingências que programam reforçamento e punição para a mesma resposta; (2) uma história individual que estabelece propriedades aversivas para Rc; (3) um comportamento controlador (Rc') que modifica algum aspecto das condições ambientais envolvidas no controle de Rc, e conseqüentemente produz (4) mudança na probabilidade de Rc. São apresentados dois modelos experimentais de autocontrole amplamente testados na literatura e discute-se que o que tem sido feito no laboratório é insuficiente para dar conta da amplitude do conceito como apresentado por Skinner.

Hyperbolic value addition and general models of animal choice

Three mathematical models of choice--the contextual-choice model (R. Grace, 1994), delay-reduction theory (N. Squires & E. Fantino, 1971), and a new model called the hyperbolic value-added model--were compared in their ability to predict the results from a wide variety of experiments with animal subjects. When supplied with 2 or 3 free parameters, all 3 models made fairly accurate predictions for a large set of experiments that used concurrent-chain procedures. One advantage of the hyperbolic value-added model is that it is derived from a simpler model that makes accurate predictions for many experiments using discrete-trial adjusting-delay procedures. Some results favor the hyperbolic value-added model and delay-reduction theory over the contextual-choice model, but more data are needed from choice situations for which the models make distinctly different predictions.

Three predictions of the economic concept of unit price in a choice context

Economic theory makes three predictions about consumption and response output in a choice situation: (a) When plotted on logarithmic coordinates, total consumption (i.e., summed across concurrent sources of reinforcement) should be a positively decelerating function, and total response output should be a bitonic function of unit price increases; (b) total consumption and response output should be determined by the value of the unit price ratio, independent of its cost and benefit components; and (c) when a reinforcer is available at the same unit price across all sources of reinforcement, consumption should be equal between these sources. These predictions were assessed in human cigarette smokers who earned cigarette puffs in a two-choice situation at a range of unit prices. In some sessions, smokers chose between different amounts of puffs, both available at identical unit prices. Individual subjects' data supported the first two predictions but failed to support the third. Instead, at low unit prices, the relatively larger reinforcer (and larger response requirement) was preferred, whereas at high unit prices, the smaller reinforcer (and smaller response requirement) was preferred. An expansion of unit price is proposed in which handling costs and the discounted value of reinforcers available according to ratio schedules are incorporated.

Relative sensitivity to reinforcer amount and delay in a self-control choice situation

Rats were exposed to concurrent-chains schedules in which a single variable-interval schedule arranged entry into one of two terminal-link delay periods (fixed-interval schedules). The shorter delay ended with the delivery of a single food pellet; the longer day ended with a larger number of food pellets (two under some conditions and six under others). In Experiment 1, the terminal-link delays were selected so that under all conditions the ratio of delays would exactly equal the ratio of the number of pellets. But the absolute duration of the delays differed across conditions. In one condition, for example, rats chose between one pellet delayed 5 s and six pellets delayed 30 s; in another condition rats chose between one pellet delayed 10 s and six pellets delayed 60 s. The generalized matching law predicts indifference between the two alternatives, assuming that the sensitivity parameters for amount and delay of reinforcement are equal. The rats' choices were, in fact, close to indifference except when the choice was between one pellet delayed 5 s and six pellets delayed 30 s. That deviation from indifference suggests that the sensitivities to amount and delay differ from each other depending on the durations of the delays. In Experiment 2, rats chose between one pellet following a 5-s delay and six pellets following a delay that was systematically increased over sessions to find a point of indifference. Indifference was achieved when the delay to the six pellets was approximately 55 s. These results are consistent with the possibility that the relative sensitivities to amount and delay differ as a function of the delays.

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.

Oral self-administration of pentobarbital by rhesus monkeys: maintenance of behavior by different concurrently available volumes of drug solution

For 4 rhesus monkeys, mouth-contact responses with either of two brass spouts were reinforced according to fixed-ratio schedules by 0.65-mL liquid deliveries during daily 3-hr sessions. Three experiments were conducted. In each experiment, independent fixed-ratio schedules were concurrently in effect at the two spouts. Following completion of each fixed ratio on a spout, a specified number of liquid deliveries were available from that spout under a continuous-reinforcement schedule. The number of such deliveries available at each spout was manipulated independently. In Experiment 1, a 1-mg/mL pentobarbital solution was simultaneously available with water (the drug vehicle) under concurrent fixed-ratio schedules of 32 responses for 3 subjects and 64 responses for the remaining subject. The number (N) of liquid deliveries that were available after completion of each fixed ratio was varied in the following order: 8, 4, 2, 1, and 8 (retest). For each subject at each condition, drug maintained more responding than water. The number of drug deliveries obtained per session was directly related to the amount of drug available per fixed ratio (i.e., to N), whereas the number of fixed ratios completed per session generally was inversely related to the value of N. In Experiment 2, fixed-ratio size was the same for each subject as in Experiment 1, but deliveries of a 1-mg/mL pentobarbital solution were available at both spouts. The number of drug deliveries available under one fixed-ratio schedule (Ns, the "standard" reinforcer amount) was held at eight, and the number of drug deliveries available under the second schedule (Nc, the "comparison" reinforcer amount) was changed across blocks of six sessions of stable responding in the following order: 1, 2, 4, 8, 4, 2, and 1. The identical series of comparison reinforcer amounts (Nc) was then tested twice more, but with the standard reinforcer (Ns) held first at four and then at two deliveries. Across the three choice series, reinforcing effects were directly related to reinforcer magnitude. In Experiment 3, deliveries of a 1-mg/mL pentobarbital solution again were available at both spouts. However, the two reinforcer amounts were held constant at N = 8 deliveries under one schedule and N = 4 deliveries under the second schedule, and fixed-ratio size was systematically varied. Across the range of fixed-ratio sizes from low to high, the degree to which behavior was better maintained by the larger of the two drug quantities was an inverted U-shaped function of fixed-ratio size.(ABSTRACT TRUNCATED AT 400 WORDS)