Molar optimization versus delayed reinforcement as explanations of choice between fixed-ratio and progressive-ratio schedules.

In a discrete-trials procedure, pigeons chose between a fixed-ratio 81 schedule and a progressive-ratio schedule by making a single peck at the key correlated with one or the other of these schedules. The response requirement on the progressive-ratio schedule began at 1 and increased by 10 each time the progressive-ratio schedule was chosen. Each time the fixed-ratio schedule was chosen, the requirement on the progressive-ratio schedule was reset to 1 response. In conditions where there was no intertrial interval, subjects chose the progressive-ratio schedule for an average of about five consecutive trials (during which the response requirement increased to 41), and then chose the fixed-ratio schedule. This ratio was larger than that predicted by an optimality analysis that assumes that subjects respond in a pattern that minimizes the response-reinforcer ratio or one that assumes that subjects respond in a pattern that maximizes the overall rate of reinforcement. In conditions with a 25-s or 50-s intertrial interval, subjects chose the progressive-ratio schedule for an average of about eight consecutive trials before choosing the fixed-ratio schedule. This change in performance with the addition of an intertrial interval was also not predicted by an optimality analysis. On the other hand, the results were consistent with the theory that choice is determined by the delays to the reinforcers delivered on the present trial and on subsequent trials.     

Signal detection and matching: analyzing choice on concurrent variable-interval schedules.

Pigeons' pecks on a red key and a green key were followed by access to grain according to pairs of concurrent independent variable-interval schedules in a combined signal detection/matching law paradigm. Pecks on the red key were reinforced by the richer variable-interval schedule if a short-duration tone had been presented; pecks on the green key were reinforced by the richer variable-interval schedule if a long-duration tone had been presented. Pecks on the green key given a short-duration tone, or on the red key given a long-duration tone, were reinforced by the leaner variable-interval schedule. The data were analyzed according to both signal detection's and the matching law's separate measures of, first, the discrimination of the choices and, second, the bias to make one response or another. Increasing the difficulty of the tone-duration discrimination decreased both methods' measures of the discrimination of the choices and did not change both methods' measures of the bias to make one response or another. Changing the leaner variable-interval schedule so that it approached the richer variable-interval schedule decreased signal detection's measure of discrimination but left its measure of response bias and the matching law measures unchanged. Data collected only until a subject's first changeover response following presentation of a long or a short tone showed higher values for both methods' measures of discrimination, no change in signal detection's measure of response bias, and lower values for the matching law's measure of response bias. Relationships between the matching law's and signal detection's methods of analyzing choice are discussed. It is concluded that a signal detection analysis is more efficient for examining changes in the difficulty of a discrimination, whereas a matching law analysis is more effective for examining the effects of changes in relative reinforcer frequency.     

Delayed choice responding by pigeons when the correct response is not predictable from the sample stimulus.

Food-deprived pigeons were presented with a row of four response keys situated above a grain hopper aperture. At the start of a trial, three of four keys were randomly selected and illuminated white for six seconds. After a variable blackout period, one of the three previously white keys and the previously dark key were illuminated green, and the remaining white keys were reilluminated as before. A response to the green key that was previously white was reinforced with three-second access to gain, a response to any other key resulted in a three-second blackout and the start of a new trial. Five of six subjects responded to the correct green key more often than chance at an interstimulus interval of 1.5 seconds, and they displayed maximal performance at different intertrial interval values ranging from 15 to 60 seconds. Choice accuracy decreased for all but one subject as the interstimulus interval was increased. For the range of interstimulus interval durations employed, decrements in choice accuracy were qualitatively similar to, but lower than those typically obtained from, delayed-matching-to-sample or delayed-pair comparison procedures.     

Choice with a fixed requirement for food, and the generality of the matching relation

Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.     

Effects of reinforcer probability, delay, and response requirements on the choices of rats and pigeons: possible species differences

In Experiment 1 with rats, a left lever press led to a 5-s delay and then a possible reinforcer. A right lever press led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials to estimate an indifference point, or a delay at which the two alternatives were chosen about equally often. Indifference points increased as the probability of reinforcement for the left lever decreased. In some conditions with a 20% chance of food, a light above the left lever was lit during the 5-s delay on all trials, but in other conditions, the light was only lit on those trials that ended with food. Unlike previous results with pigeons, the presence or absence of the delay light on no-food trials had no effect on the rats' indifference points. In other conditions, the rats showed less preference for the 20% alternative when the time between trials was longer. In Experiment 2 with rats, fixed-interval schedules were used instead of simple delays, and the presence or absence of the fixed-interval requirement on no-food trials had no effect on the indifference points. In Experiment 3 with rats and Experiment 4 with pigeons, the animals chose between a fixed-ratio 8 schedule that led to food on 33% of the trials and an adjusting-ratio schedule with food on 100% of the trials. Surprisingly, the rats showed less preference for the 33% alternative in conditions in which the ratio requirement was omitted on no-food trials. For the pigeons, the presence or absence of the ratio requirement on no-food trials had little effect. The results suggest that there may be differences between rats and pigeons in how they respond in choice situations involving delayed and probabilistic reinforcers.     

Cocaine tolerance: acute versus chronic effects as dependent upon fixed-ratio size.

The effects of cocaine on operant behavior were studied by examining fixed-ratio value as a factor in the development of tolerance. Pigeons pecked a response key under a three-component multiple schedule, with each bird being exposed to fixed-ratio values that were categorized as small, medium, or large. Administered acutely, cocaine (1.0 to 10.0 mg/kg) produced dose-related decreases in overall rate of responding. Responding maintained by the largest ratio was decreased by lower doses than those required to reduce rates of responding maintained by the other two ratio schedules. Following repeated daily administration of 5.6 mg/kg of cocaine, dose-effect functions (obtained from sessions during the chronic regimen by making substitutions for the daily dose) indicated tolerance under the smaller ratios, but no tolerance or less tolerance under the largest ratio. Thus, whether tolerance developed, and the degree to which it developed, depended on the ratio value. The results are partially consistent with the notion that tolerance to drug effects on schedule-controlled behavior will develop if drug administration initially reduces reinforcement frequency, but they indicate that reinforcement loss alone is not a sufficient condition for the generation of tolerance under such conditions. The findings suggest that amount of responding required for reinforcement, or "effort," may contribute to the development of tolerance to effects of cocaine.     

Delayed matching-to-sample performance of hens: Effects of sample duration and response requirements during the sample

Six domestic hens were trained under a delayed matching-to-sample procedure with red and green keylights as sample and comparison stimuli and a 1.5-s delay interval. The hens were trained to stop pecking the sample stimuli when a tone sounded. Duration of the sample stimuli (2 to 10 s) and the number of pecks required on the key on which these stimuli were presented (0 to 10) were altered across conditions. Both the response requirement on the sample key and the duration of sample presentations affected accuracy. These findings are in agreement with those of earlier studies using other species and somewhat different procedures.     

Transfer of pigeons' matching to sample to novel sample locations

This study examined the conditions under which conditional stimulus control by the sample stimuli in three-key matching-to-sample paradigms would generalize across the different possible sample locations. In Experiments 1 and 2, the samples appeared on the left and right side keys during initial training and then on the center key during testing. Transfer of pigeons' matching performances to the center-key samples was evident after both identity and symbolic matching training. In Experiment 3, pigeons trained on symbolic matching with two side-key samples or with a side-key and a center-key sample generally transferred their learned matching performances to those samples when they subsequently appeared in the remaining (novel) location. These results indicate that, when two-choice conditional discriminations are learned with more than one sample location, the visual characteristics of the sample per se predominantly come to control the pigeons' comparison choices. This finding encourages the use of the multiple-location training procedure as a way of reducing control by location, thus providing a more discriminating test of symmetry in animals.     

Effects of methadone on alternative fixed-ratio fixed-interval performance: latent influences on schedule-controlled responding.

Effects of methadone on pigeons' key pecking were examined under four conditions selected to analyze the control of behavior under alternative fixed-ratio fixed-interval schedules. In Condition 1, pigeons pecked under one of three different alternative schedules (alternative fixed-ratio 50 fixed-interval 90 s, alternative fixed-ratio 75 fixed-interval 90 s and alternative fixed-ratio 200 fixed-interval 90 s) each week. In Condition 2, fixed-ratio 50 or fixed-ratio 75 schedules were in effect during baseline sessions, and alternative fixed-ratio 50 fixed-interval 90-s or alternative fixed-ratio 75 fixed-interval 90-s schedules were in effect during sessions in which methadone was administered. In Condition 3, effects of methadone on key pecking maintained under fixed-ratio 50 and fixed-ratio 75 schedules were examined, whereas in Condition 4 the effects of methadone on key pecking under a fixed-interval 90-s schedule as well as fixed-ratio 50 and fixed-ratio 75 schedules were investigated. Control by the fixed-interval contingency was assessed by computing the proportion of total session reinforcers delivered under the fixed-interval schedule. Methadone administration (0.5-4.0 mg/kg) shifted the predominant source of schedule control under the alternative schedule from the fixed-ratio schedule to the fixed-interval contingency. This shift was dependent on methadone dose and fixed-ratio size. Control by the fixed-interval contingency was greatest following extensive exposure to the interval component embedded within the alternative schedule (Condition 1), but was apparent to a lesser degree with even very limited exposure to the alternative fixed-ratio fixed-interval schedule (Condition 2). Interreinforcement intervals comparable to those under fixed-interval schedule were not observed under the fixed-ratio schedules presented alone (Condition 3). Repeated exposure to the fixed-interval contingency outside the context of the alternative fixed-ratio fixed-interval schedule did not engender performance changes under a fixed-ratio schedule which would mimic those of increased fixed-interval contingency control (Condition 4). These data suggest that drug administration can be used to unmask the influence of contingencies that are latent under baseline conditions and reveal influences of both past and present environmental variables.     

Choice between delayed reinforcers and fixed-ratio schedules requiring forceful responding.

This experiment measured pigeons' choices between delayed reinforcers and fixed-ratio schedules in which a force of approximately 0.48 N was needed to operate the response key. In ratio-delay conditions, subjects chose between a fixed-ratio schedule and an adjusting delay. The delay was increased or decreased several times a session in order to estimate an indifference point--a delay duration at which the two alternatives were chosen about equally often. Each ratio-delay condition was followed by a delay-delay condition in which subjects chose between the adjusting delay and a variable-time schedule, with the components of this schedule selected to match the ratio completion times of the preceding ratio-delay condition. The adjusting delays at the indifference point were longer when the alternative was a fixed-ratio schedule than when it was a matched variable-time schedule, which indicated a preference for the matched variable-time schedules over the fixed-ratio schedules. This preference increased in a nonlinear manner with increasing ratio size. This nonlinearity was inconsistent with a theory that states that indifference points for both time and ratio schedules can be predicted by multiplying the choice response-reinforcer intervals of the two types of schedules by different multiplicative constants. Two other theories, which predict nonlinear increases in preference for the matched variable-time schedules, are discussed.     

Molecular maximizing characterizes choice on Vaughan's (1981) procedure

Pigeons keypecked on a two-key procedure in which their choice ratios during one time period determined the reinforcement rates assigned to each key during the next period (Vaughan, 1981). During each of four phases, which differed in the reinforcement rates they provided for different choice ratios, the duration of these periods was four minutes, duplicating one condition from Vaughan's study. During the other four phases, these periods lasted six seconds. When these periods were long, the results were similar to Vaughan's and appeared compatible with melioration theory. But when these periods were short, the data were consistent with molecular maximizing (see Silberberg & Ziriax, 1982) and were incompatible with melioration, molar maximizing, and matching. In a simulation, stat birds following a molecular-maximizing algorithm responded on the short- and long-period conditions of this experiment. When the time periods lasted four minutes, the results were similar to Vaughan's and to the results of the four-minute conditions of this study; when the time periods lasted six seconds, the choice data were similar to the data from real subjects for the six-second conditions. Thus, a molecular-maximizing response rule generated choice data comparable to those from the short- and long-period conditions of this experiment. These data show that, among extant accounts, choice on the Vaughan procedure is most compatible with molecular maximizing.     

A comparison of delays and ratio requirements in self-control choice.

In a discrete-trial procedure, pigeons could choose between 2-s and 6-s access to grain by making a single key peck. In Phase 1, the pigeons obtained both reinforcers by responding on fixed-ratio schedules. In Phase 2, they received both reinforcers after simple delays, arranged by fixed-time schedules, during which no responses were required. In Phase 3, the 2-s reinforcer was available through a fixed-time schedule and the 6-s reinforcer was available through a fixed-ratio schedule. In all conditions, the size of the delay or ratio leading to the 6-s reinforcer was systematically increased or decreased several times each session, permitting estimation of an "indifference point," the schedule size at which a subject chose each alternative equally often. By varying the size of the schedule for the 2-s reinforcer across conditions, several such indifference points were obtained from both fixed-time conditions and fixed-ratio conditions. The resulting "indifference curves" from fixed-time conditions and from fixed-ratio conditions were similar in shape, and they suggested that a hyperbolic equation describes the relation between ratio size and reinforcement value as well as the relation between reinforcer delay and its reinforcement value. The results from Phase 3 showed that subjects chose fixed-time schedules over fixed-ratio schedules that generated the same average times between a choice response and reinforcement.     

Formation of transitivity in conditional matching to sample by pigeons

Four homing pigeons were trained over 5 months in a zero-delay, “arbitrary” matching-to-sample procedure with sample and comparison stimuli presented on any of three response keys. Birds were also required to complete a fixed-ratio 10 requirement on both sample and comparison stimuli to terminate their presentation. The procedure resulted in the establishment of relations that were not specifically trained and that can be characterized by the property of transitivity in a stimulus equivalence context. This result was in contrast with the findings obtained from most previous research with nonhuman subjects.     

A comparison of response patterns on fixed-, variable-, and random-ratio schedules

The behavior of individual pigeons on fixed-ratio, variable-ratio, and random-ratio schedules was examined. Within each type of ratio schedule the size of the ratio was varied in an irregular sequence. At various ratio sizes (5, 10, 40, 80) no differences were found among overall response rates (postreinforcement pause plus running response rate) as a function of ratio type. This similarity in overall response rates held despite noticeable differences in the microstructure of performance both within and across subjects; the primary performance difference on the three types of ratio schedules was the relatively longer postreinforcement pause duration on the fixed-ratio schedule. We concluded that the gross temporal characteristics of performance determined by the relative weightings of the postreinforcement pause and running response rate were primarily controlled by the type of ratio schedule (fixed, variable, or random), whereas the overall rate of responding was controlled by the size of the ratio.     

Delayed reinforcement and delayed choice in symbolic matching to sample: Effects on stimulus discriminability

Six pigeons were trained to peck a red side key when the brighter of two white lights (S₁) had been presented on the center key, and to peck a green side key when the dimmer of two white lights (S₂) had been presented on the center key. Equal frequencies of reinforcers were provided for the two types of correct choice. Incorrect choices, red side-key pecks following S₂ presentations and green side-key pecks following S₁ presentations, resulted in blackout. With 0-s delay between choice and reinforcement, the delay between sample presentation and choice was varied from 0 to 20 s. Then, with 0-s delay between sample presentation and choice, the delay between choice and reinforcement was varied from 0 to 20 s. Both types of delay resulted in decreased discriminability (defined in terms of a signal-detection analysis) of the center-key stimuli, but delayed choice had more effect on discriminability than did delayed reinforcement. These data are consistent with the view that the two kinds of delay operate differently. The effect of a sample-choice delay may result from a degradation of the conditional discriminative stimuli during the delay; the effect of a choice-reinforcer delay may result from a decrement in control by differential reinforcement.     

Procrastination by pigeons with fixed-interval response requirements.

Two experiments studied the phenomenon of procrastination, in which pigeons chose a larger, more delayed response requirement over a smaller, more immediate response requirement. The response requirements were fixed-interval schedules that did not lead to an immediate food reinforcer, but that interrupted a 55-s period in which food was delivered at random times. The experiments used an adjusting-delay procedure in which the delay to the start of one fixed-interval requirement was varied over trials to estimate an indifference point--a delay at which the two alternatives were chosen about equally often. Experiment 1 found that as the delay to a shorter fixed-interval requirement was increased, the adjusting delay to a longer fixed-interval requirement also increased, and the rate of increase depended on the duration of the longer fixed-interval requirement. Experiment 2 found a strong preference for a fixed delay of 10 s to the start of a fixed-interval requirement compared to a mixed delay of either 0 or 20 s. The results help to distinguish among different equations that might describe the decreasing effectiveness of a response requirement with increasing delay, and they suggest that delayed reinforcers and delayed response requirements have symmetrical but opposite effects on choice.     

Choice, experience, and the generalized matching law

Five pigeons were exposed to different pairs of concurrent variable-interval, variable-interval schedules on nine experimental conditions of 30 sessions each. For every session, the parameters of the generalized matching equation were computed for the first five, six, seven, eight, and nine experimental conditions. The exponent a, both for response and time distribution, tended to decrease with increases in number of experimental conditions and to increase with number of sessions per condition, but values of k (bias) varied unsystematically. When the subjects were exposed to five new pairs of schedules, with 55 sessions per condition, the findings were confirmed. Data from the literature on the generalized matching law suggest that the variability of exponent values may be explained in part by the use of naive or experienced subjects in different investigations and by the variability in number of experimental conditions and in number of sessions per condition.     

Development and maintenance of choice in a dynamic environment

Four pigeons were exposed to a concurrent procedure similar to that used by Davison, Baum, and colleagues (e.g., Davison & Baum, 2000, 2006) in which seven components were arranged in a mixed schedule, and each programmed a different left∶right reinforcer ratio (1∶27, 1∶9, 1∶3, 1∶1, 3∶1, 9∶1, 27∶1). Components within each session were presented randomly, lasted for 10 reinforcers each, and were separated by 10-s blackouts. These conditions were in effect for 100 sessions. When data were aggregated over Sessions 16-50, the present results were similar to those reported by Davison, Baum, and colleagues: (a) preference adjusted rapidly (i.e., sensitivity to reinforcement increased) within components; (b) preference for a given alternative increased with successive reinforcers delivered via that alternative (continuations), but was substantially attenuated following a reinforcer on the other alternative (a discontinuation); and (c) food deliveries produced preference pulses (immediate, local, increases in preference for the just-reinforced alternative). The same analyses were conducted across 10-session blocks for Sessions 1-100. In general, the basic structure of choice revealed by analyses of data from Sessions 16-50 was preserved at a smaller level of aggregation (10 sessions), and it developed rapidly (within the first 10 sessions). Some characteristics of choice, however, changed systematically across sessions. For example, effects of successive reinforcers within a component tended to increase across sessions, as did the magnitude and length of the preference pulses. Thus, models of choice under these conditions may need to take into account variations in behavior allocation that are not captured completely when data are aggregated over large numbers of sessions.     

Procrastination by pigeons: preference for larger, more delayed work requirements.

In three experiments, pigeons chose between alternatives that required the completion of a small ratio schedule early in the trial or a larger ratio schedule later in the trial. Completion of the ratio requirement did not lead to an immediate reinforcer, but simply allowed the events of the trial to continue. In Experiment 1, the ratio requirements interrupted periods in which food was delivered on a variable-time schedule. In Experiments 2 and 3, each ratio requirement was preceded and followed by a delay, and only one reinforcer was delivered, at the end of each trial. Two of the experiments used an adjusting-ratio procedure in which the ratio requirement was increased and decreased over trials so as to estimate an indifference point--a ratio size at which the two alternatives were chosen about equally often. These experiments found clear evidence for "procrastination"--the choice of a larger but more delayed response requirement. In some cases, subjects chose the more delayed ratio schedule even when it was larger than the more immediate alternative by a factor of four or more. The results suggest that as the delay to the start of a ratio requirement is increased, it has progressively less effect on choice behavior, in much the same way that delaying a positive reinforcer reduces it effect on choice.