Effects of time between trials on rats' and pigeons' choices with probabilistic delayed reinforcers

Parallel experiments with rats and pigeons examined reasons for previous findings that in choices with probabilistic delayed reinforcers, rats' choices were affected by the time between trials whereas pigeons' choices were not. In both experiments, the animals chose between a standard alternative and an adjusting alternative. A choice of the standard alternative led to a short delay (1 s or 3 s), and then food might or might not be delivered. If food was not delivered, there was an "interlink interval," and then the animal was forced to continue to select the standard alternative until food was delivered. A choice of the adjusting alternative always led to food after a delay that was systematically increased and decreased over trials to estimate an indifference point--a delay at which the two alternatives were chosen about equally often. Under these conditions, the indifference points for both rats and pigeons increased as the interlink interval increased from 0 s to 20 s, indicating decreased preference for the probabilistic reinforcer with longer time between trials. The indifference points from both rats and pigeons were well described by the hyperbolic-decay model. In the last phase of each experiment, the animals were not forced to continue selecting the standard alternative if food was not delivered. Under these conditions, rats' choices were affected by the time between trials whereas pigeons' choices were not, replicating results of previous studies. The differences between the behavior of rats and pigeons appears to be the result of procedural details, not a fundamental difference in how these two species make choices with probabilistic delayed reinforcers.     

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.     

DELAY‐AMOUNT TRADEOFFS IN CHOICES BY PIGEONS AND RATS: HYPERBOLIC VERSUS EXPONENTIAL DISCOUNTING

An adjusting‐delay procedure was used to study the choices of pigeons and rats when both delay and amount of reinforcement were varied. In different conditions, the choice alternatives included one versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the adjusting alternative) was increased or decreased many times a session so as to estimate an indifference point—a delay at which the two alternatives were chosen about equally often. Indifference functions were constructed by plotting the adjusting delay as a function of the standard delay for each pair of reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer amounts. Combined with other data, these findings provide further evidence that delay discounting is well described by a hyperbolic equation for both species, but not by an exponential equation. Quantitative differences in the y‐intercepts of the indifference functions from the two species suggested that the rate at which reinforcer strength decreases with increasing delay may be four or five times slower for rats than for pigeons.     

Token reinforcement, choice, and self-control in pigeons.

Pigeons were exposed to self-control procedures that involved illumination of light-emitting diodes (LEDs) as a form of token reinforcement. In a discrete-trials arrangement, subjects chose between one and three LEDs; each LED was exchangeable for 2-s access to food during distinct posttrial exchange periods. In Experiment 1, subjects generally preferred the immediate presentation of a single LED over the delayed presentation of three LEDs, but differences in the delay to the exchange period between the two options prevented a clear assessment of the relative influence of LED delay and exchange-period delay as determinants of choice. In Experiment 2, in which delays to the exchange period from either alternative were equal in most conditions, all subjects preferred the delayed three LEDs more often than in Experiment-1. In Experiment 3, subjects preferred the option that resulted in a greater amount of food more often if the choices also produced LEDs than if they did not. In Experiment 4, preference for the delayed three LEDs was obtained when delays to the exchange period were equal, but reversed in favor of an immediate single LED when the latter choice also resulted in quicker access to exchange periods. The overall pattern of results suggests that (a) delay to the exchange period is a more critical determinant of choice than is delay to token presentation; (b) tokens may function as conditioned reinforcers, although their discriminative properties may be responsible for the self-control that occurs under token reinforcer arrangements; and (c) previously reported differences in the self-control choices of humans and pigeons may have resulted at least in part from the procedural conventions of using token reinforcers with human subjects and food reinforcers with pigeon subjects.     

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.     

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.     

Effects of intertrial reinforcers on self-control choice.

In three experiments, pigeons chose between a small amount of food delivered after a short delay and a larger amount delivered after a longer delay. A discrete-trial adjusting-delay procedure was used to estimate indifference points--pairs of delay-amount combinations that were chosen about equally often. In Experiment 1, when additional reinforcers were available during intertrial intervals on a variable-interval schedule, preference for the smaller, more immediate reinforcer increased. Experiment 2 found that this shift in preference occurred partly because the variable-interval schedule started sooner after the smaller, more immediate reinforcer, but there was still a small shift in preference when the durations and temporal locations of the variable-interval schedules were identical for both alternatives. Experiment 3 found greater increases in preference for the smaller, more immediate reinforcer with a variable-interval 15-s schedule than with a variable-interval 90-s schedule. The results were generally consistent with a model that states that the impact of any event that follows a choice response declines according to a hyperbolic function with increasing time since the moment of choice.     

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.     

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.     

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 ratio schedules: Fixed vs. variable response requirements

Rats were trained on concurrent fixed-ratio variable-ratio or concurrent fixed-ratio mixed-ratio schedules of food reinforcement. The variable-ratio schedule was composed of an arithmetic sequence of 11 ratios that averaged 50; the mixed-ratio schedule consisted of equiprobable ratios of 1 and 99. Fixed-ratio values, varied over experimental conditions, included 25, 35, 50, 60, and 99. The proportion of responses and time allocated to the variable- or mixed-ratio schedule increased as the size of the fixed ratio increased. For most subjects, higher proportions of responses and time were maintained on the fixed-ratio schedule at fixed-ratio values of 25 and 35; higher proportions of responses and time were maintained on the variable- or mixed-ratio schedule at fixed-ratio values of 50 or higher. On concurrent variable-ratio fixed-ratio schedules, the tendency for responding to be maintained exclusively by one schedule was related to the difference in local reinforcement rates obtained from those schedules. Exclusive responding was approximated when the difference in local reinforcement rates obtained from those schedules was large; responding was more evenly distributed between the schedules as the difference in the rates at which reinforcement was obtained from each decreased.     

Effects of methylphenidate and morphine on delay-discount functions obtained within sessions

Four rats responded under a "self-control" procedure designed to obtain delay-discount functions within sessions. Each session consisted of seven blocks, with seven trials within each block. Each block consisted of two initial forced-choice trials followed by five free-choice trials. On choice trials, the rats could press either of two retractable levers. A press on one lever was followed by presentation of a smaller reinforcer (a single dipper presentation of a sucrose solution); a press on the other lever was followed by presentation of a larger reinforcer (four consecutive dipper presentations). The delay associated with the smaller reinforcer always was 0 s, whereas the signaled delay associated with the larger reinforcer increased across blocks (from 0 to 50 s). Under these conditions, the percentage of choices of the larger reinforcer decreased across blocks, and relatively reliable delay-discount functions were obtained within sessions. Doses of methylphenidate (1.0 to 17.0 mg/kg) and morphine (0.3 to 17.0 mg/kg) were then administered prior to selected sessions. Typically, intermediate doses of methylphenidate shifted the discount functions to the right (increased choices of the larger reinforcer). For 2 of the rats, this effect was pronounced; for the other 2 rats, this effect occurred after the range of delays for the larger reinforcer was decreased (0 to 20 s). On the other hand, in most cases morphine produced a slight leftward shift in the discount function (decreased choices of the larger reinforcer). The present procedure appears to be a useful and efficient method to characterize drug effects on an entire delay-discount function. As with many procedures used to study self-control choices, however, sources of control other than reinforcement delay and amount may have been operating in the present study, and these sources must be considered when interpreting drug effects.     

Tests of behavior momentum in simple and multiple schedules with rats and pigeons.

Four experiments examined the relationship between rate of reinforcement and resistance to change in rats' and pigeons' responses under simple and multiple schedules of reinforcement. In Experiment 1, 28 rats responded under either simple fixed-ratio, variable-ratio, fixed-interval, or variable-interval schedules; in Experiment 2, 3 pigeons responded under simple fixed-ratio schedules. Under each schedule, rate of reinforcement varied across four successive conditions. In Experiment 3, 14 rats responded under either a multiple fixed-ratio schedule or a multiple fixed-interval schedule, each with two components that differed in rate of reinforcement. In Experiment 4, 7 pigeons responded under either a multiple fixed-ratio or a multiple fixed-interval schedule, each with three components that also differed in rate of reinforcement. Under each condition of each experiment, resistance to change was studied by measuring schedule-controlled performance under conditions with prefeeding, response-independent food during the schedule or during timeouts that separated components of the multiple schedules, and by measuring behavior under extinction. There were no consistent differences between rats and pigeons. There was no direct relationship between rates of reinforcement and resistance to change when rates of reinforcement varied across successive conditions in the simple schedules. By comparison, in the multiple schedules there was a direct relationship between rates of reinforcement and resistance to change during most tests of resistance to change. The major exception was delivering response-independent food during the schedule; this disrupted responding, but there was no direct relationship between rates of reinforcement and resistance to change in simple- or multiple-schedule contexts. The data suggest that rate of reinforcement determines resistance to change in multiple schedules, but that this relationship does not hold under simple schedules.     

Effects of reinforcer delays on choice as a function of income level

Three rats earned their daily food ration by responding during individual trials either on a lever that delivered one food pellet immediately or on a second lever that delivered three pellets after a delay that was continuously adjusted to ensure substantial responding to both alternatives. Choice of the delayed reinforcer increased when the number of trials per session was reduced. This result suggests that models seeking closure on choice effects must include a parameter reflecting how preference changes with sessionwide income. Moreover, models positing that reinforcer probability and immediacy (1/delay) function equivalently in choice are called into question by the finding that probability and immediacy produce opposing effects when income level is changed.     

Interlocking schedules: the relationship between response and time requirements.

Rats were exposed to an interlocking fixed-ratio 150 fixed-interval 5-minute schedule of food reinforcement and then to yoked variable-ratio schedules in which individual ratios corresponded exactly to the ratios of responses to reinforcement obtained on the interlocking schedule. After additional training with the interlocking schedule, the rats were exposed to yoked variable-interval schedules in which intervals corresponded to the intervals between successive reinforcements obtained on the second interlocking schedule. Response rates were highest in the yoked VR condition and lowest in the yoked VI, while intermediate rates characterized the interlocking schedule. Break-run patterns of responding were generated by the interlocking schedule for all subjects, while both the yoked VR and VI schedules produced comparatively stable local rates of responding. These results indicate that responding is sensitive to the interlocking schedule's inverse relationship between reinforcement frequency and responses per reinforcement.     

The effects of differing response-force requirements on fixed-ratio responding of rats.

Rats were exposed to two-component multiple schedules of food delivery. In the first experiment, 15 responses were required to produce food in both components. A downward force of 0.25 N (25 g) was always required to operate the response lever in one component. In the other, the required force was 0.25, 0.50, 1.00, or 2.00 N (25, 50, 100, or 200 g). In the second experiment, 0.25 N of force operated the lever in one component, but in the other, the force requirement for five consecutive responses at the beginning, middle, or end of each ratio was increased from 0.25 to 2.00 N. In the third experiment, the number of responses required to produce food was reduced from 15 to 5, and then to 1. Again, the effects of altering response force from 0.25 to 2.00 N were examined. In general, as response force increased in all experiments, mean response rates decreased and mean interresponse times increased.     

The effects of reinforcement frequency and response requirements on the maintenance of behavior.

Six rats responded under fixed-interval and tandem fixed-interval fixed-ratio schedules of food reinforcement. Basic fixed-interval schedules alternated over experimental conditions with tandem fixed-interval fixed-ratio schedules with the same fixed-interval value. Fixed-interval length was varied within subjects over pairs of experimental conditions; the ratio requirement of the tandem schedules was varied across subjects. For both subjects with a ratio requirement of 10, overall response rates and running response rates typically were higher under the tandem schedules than under the corresponding basic fixed-interval schedules. For all subjects with ratio requirements of 30 or 60, overall response rates and running response rates were higher under the tandem schedules than under the corresponding basic fixed-interval schedules only with relatively short fixed intervals. At longer fixed intervals, higher overall response rates and running rates were maintained by the basic fixed-interval schedules than by the tandem schedules. These findings support Zeiler and Buchman's (1979) reinforcement-theory account of response strength as an increasing monotonic function of both the response requirement and reinforcement frequency. Small response requirements added in tandem to fixed-interval schedules have little effect on reinforcement frequency and so their net effect is to enhance responding. Larger response requirements reduce reinforcement frequency more substantially; therefore their net effect depends on the length of the fixed interval, which limits overall reinforcement frequency. At the longest fixed intervals studied in the present experiment, reinforcement frequency under the tandem schedules was sufficiently low that responding weakened or ceased altogether.     

Choice behavior of rats in a concurrent-chains schedule: Amount and delay of reinforcement

Rats were exposed to concurrent-chains schedules in which the terminal links were equal fixed-interval schedules terminating in one or three food pellets. Choice proportions for large reward increased with increases in delay intervals programmed on fixed-interval schedules and supported the predictions derived from a general choice model originally formulated by Fantino and later developed by Navarick and Fantino. In addition, a functional equivalence of two alternatives was established by increasing delay intervals with large reward, whereas delay intervals for small reward were held constant. Functionally equivalent delay intervals with large reward, for each delay interval with small reward, can be described by a power function with exponent smaller than 1.0. A better prediction of choice proportions resulted when this function was used to derive predicted choice proportions.     

Effects of reinforcement rate and delay on the acquisition of lever pressing by rats.

The acquisition of lever pressing by naive rats, in the absence of shaping, was studied as a function of different rates and unsignaled delays of reinforcement. Groups of 3 rats were each exposed to tandem schedules that differed in either the first or the second component. First-component schedules were either continuous reinforcement or random-interval 15, 30, 60 or 120 s; second-component schedules were fixed-time 0, 1, 3, 6, 12, or 24 s. Rate of responding was low under continuous immediate reinforcement and higher under random-interval 15 s. Random interval 30-s and 60-s schedules produced lower rates that were similar to each other. Random-interval 120 s controlled the lowest rate in the immediate-reinforcement condition. Adding a constant 12-s delay to each of the first-component schedule parameters controlled lower response rates that did not vary systematically with reinforcement rate. The continuous and random-interval 60-s schedules of immediate reinforcement controlled higher global and first-component response rates than did the same schedules combined with longer delays, and first-component rates showed some graded effects of delay duration. In addition, the same schedules controlled higher second-component response rates in combination with a 1-s delay than in combination with longer delays. These results were related to those from previous studies on acquisition with delayed reinforcement as well as to those from similar reinforcement procedures used during steady-state responding.     

Delay discounting of qualitatively different reinforcers in rats

Humans discount larger delayed rewards less steeply than smaller rewards, whereas no such magnitude effect has been observed in rats (and pigeons). It remains possible that rats' discounting is sensitive to differences in the quality of the delayed reinforcer even though it is not sensitive to amount. To evaluate this possibility, Experiment 1 examined discounting of qualitatively different food reinforcers: highly preferred versus nonpreferred food pellets. Similarly, Experiment 2 examined discounting of highly preferred versus nonpreferred liquid reinforcers. In both experiments, an adjusting-amount procedure was used to determine the amount of immediate reinforcer that was judged to be of equal subjective value to the delayed reinforcer. The amount and quality of the delayed reinforcer were varied across conditions. Discounting was well described by a hyperbolic function, but no systematic effects of the quantity or the quality of the delayed reinforcer were observed.