Pigeons' choices in situations of diminishing returns: fixed- versus progressive-ratio schedules.

In two different discrete-trial procedures, pigeons were faced with choices between fixed-ratio and progressive-ratio schedules. The latter schedules entail diminishing returns, a feature analogous to foraging situations in the wild. In the first condition (no reset), subjects chose between a progressive-ratio schedule that increased in increments of 20 throughout a session and a fixed-ratio schedule that was constant across blocks of sessions. The size of the fixed ratio was varied parametrically through an ascending and then a descending series. In the reset condition, the same fixed-ratio values were used, but each selection (and completion) of the fixed ratio reset the progressive-ratio schedule back to its minimal value. In the no-reset procedure, the pigeons tended to cease selecting the progressive ratio when it equaled or slightly exceeded the fixed-ratio value, whereas in reset, they chose the fixed ratio well in advance of that equality point. These results indicate sensitivity to molar as well as to molecular reinforcement rates, and those molar relationships are similar to predictions based on the marginal value theorem of optimal foraging theory (e.g., Charnov, 1976). However, although previous results with monkeys (Hineline & Sodetz, 1987) appeared to minimize responses per reinforcement, the present results corresponded more closely to predictions based on sums-of-reciprocals of distance from point of choice to each of the next four reinforcers. Results obtained by Hodos and Trumbule (1967) with chimpanzees in a similar procedure were intermediate between these two relationships. Variability of choices, as well as median choice points, differed between the reset and no-reset conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Strategies of schedule preference in chimpanzees

Two chimpanzees were required to choose between a fixed-ratio schedule and a progressive-ratio schedule which increased in response requirement by 20 responses each time it was chosen. Each choice of the fixed ratio reset the progressive ratio to its minimum value. The fixed-ratio requirement was varied from 40 to 1000 responses. The subjects' preferences for the progressive-ratio schedule varied as a function of the magnitude of the fixed-ratio requirement. An analysis of the preference data indicated that the animals tended to minimize reinforcement cost rather than match the progressive-ratio requirement to the fixed-ratio requirement. In a second experiment, selection of the fixed ratio did not reset the progressive-ratio requirement to its minimum value. In this case, the animals matched the progressive-ratio requirement to the fixed-ratio requirement. A model based on reinforcement cost is presented which permits accurate prediction of preferences between fixed and progressively increasing ratio schedules.     

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.     

Progressive-ratio schedules: effects of later schedule requirements on earlier performances

Four rats were studied with variants of a progressive-ratio schedule with a step size of 6 in which different terminal components followed completion of the 20th ratio: (a) a reversal of the progression, (b) a fixed-ratio 6 schedule, or (c) extinction. Responding in the progressive-ratio components of these schedules was compared to performances under conventional progressive-ratio baselines. Under baseline conditions, postreinforcement pauses increased exponentially as a function of increasing ratio size, whereas running rates showed modest declines. The procedure of linking the progressive-ratio schedule to the reversed progression or to the fixed-ratio component resulted in decreased pausing. Linking the progressive-ratio schedule to the extinction component had the opposite effect, that of producing weakened progressive-ratio performances as evidenced by increased pausing. Subjects whose responses were reinforced on half of the ratios also showed exponential increases; however, pauses were substantially shorter following ratios on which the reinforcer was omitted. The results suggested that progressive-ratio pausing reflects the influence of remote as well as local contingencies.     

Reversal of preference under progressive-ratio schedules by punishment

A progressive-ratio reinforcement schedule, in which successive reinforcements required an additional 50 responses, was programmed on one key. A response on a second key reset the progressive-ratio schedule to the first step. Before punishment, all pigeons consistently reset the schedule after reinforcement on the first step, thereby minimizing the number of responses required for reinforcement. Punishment was a brief electric shock contingent upon each response on the reset key. The first effect of punishment was to change the frequency of extra responses on the reset key. Under higher intensities of punishment, the pigeons completed the advanced steps of the progressive-ratio schedule before resetting to the first step. Completions of advanced steps were accompanied by decreases in the overall rate of responding and the rate of reinforcement. When the punishment contingency was removed, the major features of pre-punishment performance were recovered.     

Effects of reinforcement history on responding under progressive-ratio schedules of reinforcement.

The effects of experimental history on responding under a progressive-ratio schedule of reinforcement were examined. Sixteen pigeons were divided into four equal groups. Groups 1 to 3 were trained to peck a key for food under a fixed-ratio, variable-ratio, or differential-reinforcement-of-low-rate schedule of reinforcement. After training, these pigeons were shifted to a progressive-ratio schedule, later were shifted back to their original schedule (with decreased rates of reinforcement), and finally were returned to the progressive-ratio schedule. Pigeons in Group 4 (control) were maintained on the progressive-ratio schedule for the entire experiment. To test for potential "latent history" effects, pigeons responding under the progressive-ratio schedule were injected with d-amphetamine and given behavioral-momentum tests of prefeeding and extinction. Experimental histories affected responding in the immediate transition to the progressive-ratio schedule; response rates of pigeons with variable-ratio and fixed-ratio histories were higher than rates of pigeons with differential-reinforcement-of-low-rate and progressive-ratio-only histories. Pigeons with differential-reinforcement-of-low-rate histories, and to a lesser degree pigeons with variable-ratio and fixed-ratio histories, also had shorter postreinforcement pauses than pigeons with only a progressive-ratio history. No consistent long-term effects of prior contingencies on responding under the progressive-ratio schedule were evident. d-Amphetamine and resistance-to-change tests failed to reveal consistent latent history effects. The data suggest that history effects are sometimes transitory and not susceptible to latent influences.     

Cocaine and food as reinforcers: effects of reinforcer magnitude and response requirement under second-order fixed-ratio and progressive-ratio schedules.

Reinforcer magnitude and fixed-ratio requirement were varied under two second-order schedules. Under one, the first sequence of a fixed number of responses completed after the lapse of a 10-min fixed interval produced reinforcement. Under the second, a second-order progressive-ratio schedule, the fixed number of responses increased after each reinforcement. Either cocaine (0 to 300 micrograms/kg/inj) or food (0 to 5,700 mg/delivery) reinforcers were delivered. Under some conditions, a 2-s illumination of stimulus lights occurred on completion of each ratio sequence. Under the second-order schedule, as cocaine dose or amount of food increased, rates of responding increased; at the highest values, rates of responding decreased. Increases in the ratio requirement from 10 to 170 responses minimally decreased overall response rates. Under the second-order progressive-ratio schedule, increases in dose of cocaine or amount of food increased rates of responding; at the highest amounts of food, rates of responding decreased but response rates at the highest dose of cocaine remained relatively high. The highest ratio requirement that was completed (breaking point) depended on the dose of cocaine but was less dependent on the amount of food. Removing brief-stimulus presentations had a greater effect on completion of ratio requirements with cocaine compared to food.     

Changing the response unit from a single peck to a fixed number of pecks in fixed-interval schedules

Each of three pigeons was studied first under a standard fixed-interval schedule. With the fixed interval held constant, the schedule was changed to a second-order schedule in which the response unit was the behavior on a small fixed-ratio schedule (first a fixed-ratio 10 and then a fixed-ratio 20 schedule). That is, every completion of the fixed-ratio schedule produced a 0.7-sec darkening of the key and reset the response count to zero for the next ratio. The first fixed-ratio completed after the fixed-interval schedule elapsed produced the 0.7-sec blackout followed immediately by food. These manipulations were carried out under two different fixed-interval durations for each bird ranging from 3 min to 12 min. The standard fixed-interval schedules produced the typical pause after reinforcement followed by responding at a moderate rate until the next reinforcement. The second-order schedules also engendered a pause after reinforcement, but responding occurred in bursts separated by brief pauses after each blackout. For a particular fixed-interval duration, post-reinforcement pauses increased slightly as the number of pecks in the response unit increased despite large differences in the rate and pattern of key pecking. Post-reinforcement pause increased with the fixed-interval duration under all response units. These data confirm that the allocation of time between pausing and responding is relatively independent of the rate and topography of responding after the pause.     

Time limits for completing fixed ratios. II. Stimulus specificity

Pigeons were exposed to two stimuli that were each correlated with the same fixed-ratio schedule. During one stimulus, the ratio had to be completed in more than a specified time for food to be presented. During the other, the ratio had to be completed in less than a specified time. Failures to meet the time criterion produced a timeout and reset the ratio. Treating the entire behavioral sequence generated by a fixed-ratio schedule as a unitary response and scheduling differential reinforcement with respect to the duration of the sequence produced effects comparable to those observed previously with individual responses. The times taken to complete the ratios conformed to the time criteria under both stimulus conditions. Similar effects have been observed with differential reinforcement of the duration of individual responses and in experiments specifying running speed criteria under discrete trial conditions.     

The contribution of an added counter to a fixed-ratio schedule

Although previous research showed that a visual counter increased the rate of responding on a large fixed-ratio schedule, a theoretical analysis of the factors responsible for fixed-ratio performance suggests that the primary control by number of responses since reinforcement is to weaken the performance. The present experiment employed a multiple schedule in which the same fixed-ratio value alternated with and without an added counter. It tested the hypothesis that the differential reinforcement of high-rate responding masked the attenuation of the fixed-ratio performance from the unoptimal discriminative control produced by the fixed relation between number of responses and reinforcement. In the present experiment the postreinforcement pause was consistently longer in the components with the added counter, while running rates remained comparable between the components of the multiple schedule. Both components of the multiple schedule involved differential reinforcement of high-rate responding while only the components with the added counter amplified the discriminative control by number of pecks since reinforcement.     

Preference between variable-ratio and fixed-ratio schedules: local and extended relations.

Although it has repeatedly been demonstrated that pigeons, as well as other species, will often choose a variable schedule of reinforcement over an equivalent (or even richer) fixed schedule, the exact nature of that controlling relation has yet to be fully assessed. In this study pigeons were given repeated choices between concurrently available fixed-ratio and variable-ratio schedules. The fixed-ratio requirement (30 responses) was constant throughout the experiment, whereas the distribution of individual ratios making up the variable-ratio schedule changed across phases: The smallest and largest of these components were varied gradually, with the mean variable-ratio requirement constant at 60 responses. The birds' choices of the variable-ratio schedule tracked the size of the smallest variable-ratio component. A minimum variable-ratio component at or near 1 produced strong preference for the variable-ratio schedule, whereas increases in the minimum variable-ratio component resulted in reduced preference for the variable-ratio schedule. The birds' behavior was qualitatively consistent with Mazur's (1984) hyperbolic model of delayed reinforcement and could be described as approximate maximizing with respect to reinforcement value.     

Response-produced timeouts under a progressive-ratio schedule with a punished reset option

Three behavioral options were available to food-deprived pigeons: (1) pecking one key resulted in food reinforcement according to a 50-response progressive-ratio schedule, (2) pecking a second key reset the progressive-ratio schedule to the initial progressive-ratio step, and (3) pecking a third key produced a 3-min timeout period. Pecks on the reset key were shocked. Under low and intermediate shock intensities, timeouts were not produced; under high shock levels, timeouts were produced regularly. Timeouts occurred during the initial period of a progressive-ratio step and were more frequent during the longer steps of the progressive-ratio schedule. Response-produced timeouts under these experimental conditions could be interpreted either as an escape from aversive behavioral options or as a low-probability behavior emerging when the food reinforcement schedule exerted weaker control.     

SOME EFFECTS OF REINFORCEMENT SCHEDULES IN TEACHING PICTURE NAMES TO RETARDED CHILDREN1

The effects of several different schedules of primary reinforcement were compared in a picture-naming task with retarded children. In Experiment I, number of correct responses and learning rate were higher under fixed-ratio schedules than under continuous reinforcement. In Experiment II, number of correct responses and learning rate tended to be greater under intermediate than under low or high fixed-ratio schedules. In Experiment III, number of correct responses was higher under interlocking schedules, in which the response requirement increased with time following the previous reinforcement, than under comparable fixed-ratio schedules. Learning rates were generally low and, perhaps because of this, not very different under the two types of schedules in this experiment. Accuracy (i.e., proportion of trials on which correct responses occurred) was typically high and insensitive to variations in schedule and schedule parameter throughout each experiment.     

Choice for aperiodic versus periodic ratio schedules: A comparison of concurrent and concurrent-chain procedures

Choice between mixed-ratio schedules, consisting of equiprobable ratios of 1 and 99 responses per reinforcement, and fixed-ratio schedules of food reinforcement was assessed by two commonly used procedures: concurrent schedules and concurrent-chains schedules. Rats were trained under concurrent fixed-ratio mixed-ratio schedules, in which both ratio schedules were simultaneously available, and under a concurrent-chains schedule, in which access to one of the mutually exclusive ratio schedules comprising the terminal links was contingent on a single “choice” response. The distribution of responses between the two ratio schedules was taken as the choice proportion under the concurrent procedure, and the distribution of “choice” responses was taken as the choice proportion under the concurrent-chains procedure. Seven of eight rats displayed systematic choice; of those, each displayed nearly exclusive choice for fixed-ratio 35 to the mixed-ratio schedule under the concurrent procedure, but each displayed nearly exclusive choice for the mixed-ratio schedule to fixed-ratio 35 under the concurrent-chains procedure. Thus, preference for a fixed or a mixed schedule of reinforcement depended on the procedure used to assess preference.     

Choice in situations of time-based diminishing returns: immediate versus delayed consequences of action.

Pigeons chose between two schedules of food presentation, a fixed-interval schedule and a progressive-interval schedule that began at 0 s and increased by 20 s with each food delivery provided by that schedule. Choosing one schedule disabled the alternate schedule and stimuli until the requirements of the chosen schedule were satisfied, at which point both schedules were again made available. Fixed-interval duration remained constant within individual sessions but varied across conditions. Under reset conditions, completing the fixed-interval schedule not only produced food but also reset the progressive interval to its minimum. Blocks of sessions under the reset procedure were interspersed with sessions under a no-reset procedure, in which the progressive schedule value increased independent of fixed-interval choices. Median points of switching from the progressive to the fixed schedule varied systematically with fixed-interval value, and were consistently lower during reset than during no-reset conditions. Under the latter, each subject's choices of the progressive-interval schedule persisted beyond the point at which its requirements equaled those of the fixed-interval schedule at all but the highest fixed-interval value. Under the reset procedure, switching occurred at or prior to that equality point. These results qualitatively confirm molar analyses of schedule preference and some versions of optimality theory, but they are more adequately characterized by a model of schedule preference based on the cumulated values of multiple reinforcers, weighted in inverse proportion to the delay between the choice and each successive reinforcer.     

Changes in progressive-ratio performance under increased pressures of air

Rats performed on progressive-ratio schedules that required an increasing number of responses for each successive reinforcement. The number of responses required increased until the subjects failed to complete the next ratio in the sequence within 15 min. Response-ratio increments of two responses, five responses, and 20 responses were investigated. The size of the final completed ratio generally increased with increases in the progressive-ratio step size. Increased pressures of air in a hyperbaric chamber led to both increases and decreases in terminal ratio size, with the differential effects depending on both air pressure and on the size of the progressive-ratio increment. Changes in the number of responses in the final ratio were related to increased pressures of nitrogen, as similar pressures of helium produced few effects.     

Comparison of drug effects on fixed-ratio performance and chain performance maintained under a second-order fixed-ratio schedule.

In one component of a multiple schedule, pigeons were required to complete the same four-response chain each session by responding sequentially on three identically lighted keys in the presence of four successively presented colors (chain performance). Food presentation occurred after five completions of the chain (i.e., after 20 correct responses). Errors, such as responding on the center or right key when the left was designated correct, produced a brief timeout but did not reset the chain. In the other component, responding on a single key (lighted white) was maintained by food presentation under a fixed-ratio 20 schedule. In general, phencyclidine and d-amphetamine produced dose-dependent decreases in the overall response rates in both components. With pentobarbital, overall rate in each component generally increased at intermediate doses and decreased at higher doses. All three drugs produced dose-dependent disruptive effects on chain-performance accuracy. Phencyclidine and pentobarbital increased percent errors at doses that had little or no rate-decreasing effects, whereas d-amphetamine generally increased percent errors only at doses that substantially decreased overall rate. At high doses, all three drugs produced greater disruption of chain performance than of fixed-ratio performance, as indicated by a slower return to control responding, although the effects of d-amphetamine were less selective than those of phencyclidine or pentobarbital.     

Effects of anorectic drugs on food intake under progressive-ratio and free-access conditions in rats

The effects of two anorectic drugs, dexfenfluramine and phentermine, on food intake under different food-access conditions were examined. Experiment 1 compared the effects of these drugs on food intake under a progressive-ratio (PR) schedule and free-access conditions. Dexfenfluramine decreased food intake under both conditions, but the doses required to decrease intake under free-access conditions were higher than those required to reduce intake under the PR condition. Intermediate doses of phentermine sometimes increased breaking points, and higher doses decreased them. Phentermine decreased food intake at the same doses under both access conditions. Thus the potency of dexfenfluramine, but not phentermine, to decrease food-maintained behavior depended upon the food-access condition. Experiment 2 used a novel mixed progressive-ratio schedule of food delivery to study the duration of drug effects. Sessions consisted of five components separated by 3-hr timeouts. The ratio requirement reset at the beginning of each component and a new breaking point was obtained. Both dexfenfluramine and phentermine dose-dependently decreased breaking points early in the session. In some rats, compensatory increases in breaking point were observed. That is, breaking points later in the session increased over control levels, resulting in no change in the total number of food pellets earned for the session compared to control. The present findings suggest that the effects of some anorectic drugs depend upon the access conditions for food; increasing the effort to obtain food may enhance their ability to decrease food-maintained behavior.