Concurrent schedules of interresponse time reinforcement: probability of reinforcement and the lower bounds of the reinforced interresponse time intervals

Data were obtained with rats on the effects of interresponse time contingent reinforcement of the lever press response using schedules in which interresponse times falling within either of two temporal intervals could be reinforced. Some of the findings were (a) the mode of the interresponse time distribution generally occurred near the first lower bound when the maximum reinforcement rate for the two lower bounds was equal; this also frequently occurred even when the reinforcement rate was less for the first lower bound; (b) as is the case with schedules using a single interval of reinforced interresponse times the values of the lower bounds partially determined the location and spread of the distributions; but the particular pair of values used did not seem to influence the effects of the probabilities of reinforcement; (c) although the modal interresponse time was usually at the lower bound of one of the two intervals of reinforced interresponse times, no simple relation existed between either the probability or rate of reinforcement of interresponse times in these two intervals and the location of this mode.     

Studies on responding under fixed-interval schedules of reinforcement: the effects on the pattern of responding of changes in requirements at reinforcement

In pigeons responding under a 180-sec fixed-interval schedule of reinforcement, the frequency distribution of the duration of the final interresponse time before the reinforcer was compared with the distribution of the preceding two interresponse times. The results confirmed qualitatively and quantitatively the expected preferential reinforcement of longer interreinforcement times under fixed-interval reinforcement. Requirements at reinforcement were then changed to eliminate the preferential reinforcement of longer interresponse times. Local patterns and mean rate of responding could change, without the characteristic fixed-interval pattern of increasing responding through the interval (scalloping) being much affected. It is concluded that this characteristic pattern of fixed-interval responding does not depend crucially on effects of the reinforcer at the moment of reinforcement, but rather to effects extending over much longer periods of time than just the last interresponse time.     

Magnitude and frequency of reinforcement and frequencies of interresponse times

The relative magnitude and relative frequency of reinforcement for two concurrent interresponse times (1.5 to 2.5 sec and 3.5 to 4.5 sec) were simultaneously varied in an experiment in which pigeons obtained grain by pecking on a single key. Visual discriminative stimuli accompanied the two time intervals in which reinforcements were arranged by a one-minute variable-interval schedule. The resulting interresponse times of each of three pigeons fell into two groups; "short" (1.0 to 2.5 sec) and "long" (3.0 to 4.5 sec). Steady-state relative frequencies of these interresponse times were orderly functions of both reinforcement variables. The combined effects of both independent variables were well summarized by a linear function of one variable, relative access to food. Unlike corresponding two-key concurrent variable-interval schedules, the present schedule did not produce an equality between the relative frequency of an operant and either the relative magnitude or the relative frequency of reinforcement of that operant. A tentative account is provided for this difference between one-key and two-key functions.     

Effects of timeout on spaced responding in pigeons

Three pigeons were trained under a differential-reinforcement-of-low-rate schedule of 20 sec, and then exposed to a schedule under which responses terminating interresponse times less than 20 sec produced timeout and responses terminating interresponse times greater than 20 sec produced reinforcement. Response-produced timeouts selectively decreased the probability of short interresponse times and thereby produced a higher frequency of reinforcement. The suppressive effect of timeout was independent of timeout duration, with timeouts of 5, 10, or 20 sec. Similar effects were found when the minimum interresponse time that could be terminated by response-produced reinforcement was increased to 30 sec. The suppressive effects of timeout on responding maintained by these schedules were similar to previous reports in which responding was punished with electric shock.     

Molar And Molecular Control In Variable-interval And Variable-ratio Schedules

Response rates are typically higher under variable-ratio than under variable-interval schedules of reinforcement, perhaps because of differences in the dependence of reinforcement rate on response rate or because of differences in the reinforcement of long interresponse times. A variable-interval-with-added-linear-feedback schedule is a variable-interval schedule that provides a response rate/reinforcement rate correlation by permitting the minimum interfood interval to decrease with rapid responding. Four rats were exposed to variable-ratio 15, 30, and 60 food reinforcement schedules, variable-interval 15-, 30-, and 60-s food reinforcement schedules, and two versions of variable-interval-with-added-linear-feedback 15-, 30-, and 60-s food reinforcement schedules. Response rates on the variable-interval-with-added-linear-feedback schedule were similar to those on the variable-interval schedule; all three schedules led to lower response rates than those on the variable-ratio schedules, especially when the schedule values were 30. Also, reinforced interresponse times on the variable-interval-with-added-linear-feedback schedule were similar to those on variable interval and much longer than those produced by variable ratio. The results were interpreted as supporting the hypothesis that response rates on variable-interval schedules in rats are lower than those on comparable variable-ratio schedules, primarily because the former schedules reinforce long interresponse times.     

Parametric manipulation of interresponse-time contingency independent of reinforcement rate

Pecking of pigeons was reinforced under a modified interval-percentile procedure that allowed independent manipulation of overall reinforcement rate and the degree to which reinforcement depended on interresponse-time duration. Increasing the contingency, as measured by the phi coefficient, between reinforcement and long interresponse times while controlling the overall rate of reinforcement systematically increased the frequency of those interresponse times and decreased response rate under both of the reinforcement rates studied. Increasing reinforcement rate also generally increased response rate, particularly under weaker interresponse-time contingencies. Random-interval schedules with comparable reinforcement rates generated response rates and interresponse-time distributions similar to those obtained with moderate-to-high interresponse-time reinforcement contingencies. These results suggest that interresponse-time reinforcement contingencies inherent in random-interval and constant-probability variable-interval schedules exercise substantial control over responding independent of overall reinforcement rate effects. The interresponse-time reinforcement contingencies inherent in these schedules may actually mask the effects of overall reinforcement rate; thus differences in response rate as a function of reinforcement rate when interresponse-time reinforcement is eliminated may be underestimated.     

Interresponse time duration in fixed-interval schedules of reinforcement: control by ordinal position and time since reinforcement

The times between each of the first thirteen responses after reinforcement (the first twelve interresponse times) were determined for two pigeons whose pecking was reinforced on fixed-interval schedules of food reinforcement ranging from 0.5 min to 5 min. These interresponse times were classified with respect to their ordinal position in the sequence of responses and with respect to the time since the preceding reinforcement at which the initiating response occurred. The median interresponse time durations were essentially constant after the sixth response after reinforcement regardless of the time at which the interresponse time was initiated. The durations of the first few interresponse times after reinforcement decreased as the number of preceding responses increased and as the time since the preceding reinforcement increased.     

Preference as a function of active interresponse times: a test of the active time model

In this article, we describe a test of the active time model for concurrent variable interval (VI) choice. The active time model (ATM) suggests that the time since the most recent response is one of the variables controlling choice in concurrent VI VI schedules of reinforcement. In our experiment, pigeons were trained in a multiple concurrent similar to that employed by Belke (1992), with VI 20-s and VI 40-s schedules in one component, and VI 40-s and VI 80-s schedules in the other component. However, rather than use a free-operant design, we used a discrete-trial procedure that restricted interresponse times to a range of 0.5-9.0 s. After 45 sessions of training, unreinforced probe periods were mixed with reinforced training periods. These probes paired the two stimuli associated with the VI 40-s schedules. Further, the probes were defined such that during their occurrence, interresponse times were either "short" (0.5-3.0 s) or "long" (7.5-9.0 s). All pigeons showed a preference for the stimulus associated with the relatively rich VI 40-s schedule--a result mirroring that of Belke. We also observed, though, that this preference was more extreme during long probes than during short probes--a result predicted by ATM.     

Changes in functional response units with briefly delayed reinforcement

In two experiments, key-peck responding of pigeons was compared under variable-interval schedules that arranged immediate reinforcement and ones that arranged unsignaled delays of reinforcement. Responses during the nominal unsignaled delay periods had no effect on the reinforcer presentations. In Experiment 1, the unsignaled delays were studied using variable-interval schedules as baselines. Relative to the immediate reinforcement condition, 0.5-s unsignaled delays decreased the duration of the reinforced interresponse times and increased the overall frequency of short (<0.5-s) interresponse times. Longer, 5.0-s unsignaled delays increased the duration of the reinforced interresponse times and decreased the overall frequency of the short interresponse times. In Experiment 2, similar effects to those of Experiment 1 were obtained when the 0.5-s unsignaled delays were imposed upon a baseline schedule that explicitly arranged reinforcement of short interresponse times and therefore already generated a large number of short interresponse times. The results support earlier suggestions that the unsignaled 0.5-s delays change the functional response unit from a single key peck to a multiple key-peck unit. These findings are discussed in terms of the mechanisms by which contingencies control response structure in the absence of specific structural requirements.     

Signalled reinforcement in differential-reinforcement-of-low rate schedules

At several fixed and variable minimum reinforced interresponse times, a stimulus was added to differential-reinforcement-of-low-rate schedules to signal the availability or nonavailability of reinforcement. As the minimum reinforced interresponse time increased, the rate of unreinforced responding decreased. Changing from fixed to variable minimum interresponse time in the basic differential-reinforcement-of-low-rate schedule further decreased the rate of unreinforced responding. Both effects were to some degree reversible. For fixed minimum reinforced interresponse times of 30 sec or shorter, most unreinforced responses terminated interresponse times just short of that required for reinforcement. The minimum reinforced interresponse time and the number of short response latencies (≤0.5 sec) to the onset of the signal were negatively correlated. Both of these analyses suggested that at values of 30 sec or shorter, the subjects discriminated the availability of the reinforcer more on the basis of time than on the basis of presence or absence of the signal.     

SUPPRESSIVE AND FACILITATIVE EFFECTS OF SHOCK INTENSITY AND INTERRESPONSE TIMES FOLLOWED BY SHOCK

Although response‐dependent shock often suppresses responding, response facilitation can occur. In two experiments, we examined the suppressive and facilitative effects of shock by manipulating shock intensity and the interresponse times that produced shock. Rats' lever presses were reinforced on a variable‐interval 40‐s schedule of food presentation. Shock followed either long or short interresponse times. Shock intensity was raised from 0.05 mA to 0.4 mA or 0.8 mA. Overall, shock contingent on long interresponse times punished long interresponse times and increased response rates. Shock contingent on short interresponse times punished short interresponse times and decreased response rates. In Experiment 1, raising the range of interresponse times that produced shock enhanced these effects. In Experiment 2, the effects of shock intensity depended on the interresponse times that produced shock. When long interresponse times produced shock, low intensities increased response rates. High intensities decreased response rates. When short interresponse times produced shock, high shock intensities punished short interresponse times and decreased response rates more than low intensities. The results may explain why punishment procedures occasionally facilitate responding and establish parameters for future studies of punishment.     

Synthetic variable-interval schedules of reinforcement

Three pigeons pecked for food on a synthetic variable-interval schedule of reinforcement that had two independent parts: a variable-interval schedule that arranged a distribution of interreinforcement intervals, and a device that randomly assigned each reinforcement to one of 10 classes of interresponse times. The frequencies of reinforcement for the 10 classes of interresponse times were systematically varied, while the overall frequency of reinforcement was held within a comparatively narrow range. The 10 classes extended either from 0.1 to 0.6 sec in 0.05-sec intervals, or from 1.0 to 6.0 sec in 0.5-sec intervals. In the former case, some control by reinforcement was obtained, but it was weak and no simple relationships were discernible. In the latter case, the relative frequency of an interresponse time was a generally increasing function of its relative frequency of reinforcement, and two simple controlling relationships were found. First, the function relating interresponse times per opportunity to reinforcements per opportunity was, over a restricted range, approximately linear with a slope of unity. Second, when all 10 classes of interresponse times were reinforced equally often, the relative frequency of an interresponse time approximately equalled the relative reciprocal of its length.     

Maximizing present value: A model to explain why moderate response rates obtain on variable-interval schedules

In Phases 1 and 3, two Japanese monkeys responded on a multiple variable-ratio 80 variable-interval X schedule, where the value of X was adjusted to ensure equal between-schedule reinforcement rates. Components strictly alternated following the delivery of a food pellet, and each session ended following 50 components. Phase 2 differed from the others only in that the 50 pellets previously earned during the session were delivered together at session's end. Variable-ratio response rates did not decrease across phases, but variable-interval response rates decreased substantially during the Phase 2 procedure. This rate decrease was attributed to the food-at-session's-end manipulation removing the greater immediacy of reinforcement provided by short interresponse times relative to long interresponse times. Without this time preference for short interresponse times, the variable-interval interresponse-time reinforcement feedback function largely controlled response emission, dictating a response-rate reduction. This result was explained in terms of the economic notion of “maximizing present value.”     

The concurrent reinforcement of two interresponse times: the relative frequency of an interresponse time equals its relative harmonic length

The relative lengths of two concurrently reinforced interresponse times were varied in an experiment in which three pigeons obtained food by pecking on a single key. Visual discriminative stimuli accompanied the two time intervals in which reinforcements were scheduled according to a one-minute variable-interval. The steady-state relative frequency of an interresponse time approximately equalled the complement of its relative length, that is, its relative harmonic length. Thus, lengths of interresponse times and delays of reinforcement have the same effect on the relative frequencies of interresponse times and choices in one-key and two-key concurrent variable-interval schedules, respectively. A second experiment generalized further the functional equivalence between the effects of these one-key and two-key concurrent schedules by revealing that the usual matching-to-relative-immediacy in two-key concurrent schedules is undisturbed if reinforcement depends upon the occurrence of a response at the end of the delay interval, as it does in the one-key schedules. The results of both experiments are consistent with a quantitative theory of concurrent operant behavior.     

A quantitative interresponse-time analysis of DRL performance differentiates similar effects of the antidepressant desipramine and the novel anxiolytic gepirone.

We describe an interresponse-time analysis of performance on a differential-reinforcement-of-low-rate 72-s schedule. This analysis compares the obtained interresponse-time distribution of individual rats to a corresponding random interresponse-time distribution. The random interresponse-time distribution is a negative exponential probability function; it predicts the relative distribution of interresponse times if the rat emitted the same number of responses randomly (i.e., with a constant probability) with respect to time. The analysis provides quantitative measures of peak location and dispersion of the interresponse times toward random performance. In Experiment 1, an unexpected outcome of this analysis was that the rats would have obtained more reinforcers had they responded at the same rate but randomly. Based on the interresponse-time analysis in Experiment 1, it was shown that rats trained on the differential-reinforcement-of-low-rate 72-s schedule could increase the number of reinforcers obtained in two ways: first, by a coherent shift of the interresponse-time distribution toward longer durations and, second, by dispersal of the interresponse times toward a random interresponse-time distribution. Experiment 2 applied the analysis described in Experiment 1 to the effects of desipramine and gepirone. Both drugs decreased response rate and increased reinforcement rate, but their effects on the distribution of interresponse times were different. The increase in reinforcement rate observed with desipramine was accompanied by a coherent shift of the reinforcement rate observed with gepirone was accompanied by dispersal of the interresponse-time distribution toward the random negative exponential prediction.     

Reinforcement frequency and contingency as factors in fixed-ratio behavior

Two variables often confounded in fixed-ratio schedules are reinforcement frequency and response requirement. These variables were isolated by a technique that yoked the distributions of reinforcements in time for one group of pigeons to those of pigeons responding on various fixed-ratio schedules. The contingencies for the yoked birds were then manipulated by adding various tandem fixed-ratio requirements to their schedules. Post-reinforcement pause was approximately equal for the yoked and ratio pigeons, and was relatively insensitive to changes in the tandem requirement. Terminal response rate increased with increases in the tandem requirement, even though reinforcement rate was invariant. This increase was attributed to the progressive interference of the tandem requirement with the differential reinforcement of long interresponse times.     

A molecular analysis of multiple schedule interactions: negative contrast

The present experiments investigated the relationship between changes in the relative reinforced interresponse-time distributions and the occurrence of positive and negative contrast in multiple variable-interval—variable-interval and multiple variable-interval—extinction schedules of reinforcement. Experiment I demonstrated that changes in the interresponse-time distributions were consistently correlated with response-rate changes referred to as positive and negative contrast. Corresponding changes in the reinforced interresponse-time distributions suggested that negative contrast resulted as an inductive effect of selectively reinforcing long interresponse times in the altered component at the moment the baseline schedule was reintroduced. Experiment II demonstrated that the magnitude of the negative-contrast effect could be significantly decreased if the altered component schedule was modified in order to prevent the reinforcement of these interresponse times during the first few sessions of baseline recovery. The results supported a proposal that interresponse time—reinforcer relations may act as amplifiers or attenuators of negative contrast.     

The development of fixed-ratio performance under the influence of ribonucleic acid

The transition from fixed-ratio 1 performance (every response reinforced) to fixed-ratio 30 performance (every thirtieth response reinforced) was studied in nine pigeons. These were divided into three treatment groups given daily oral doses of saline, or 250 mg/kg/day or 500 mg/kg/day of yeast ribonucleic acid. Detailed computer-assisted analyses of how fixed-ratio behavior develops revealed the following typical sequence. After the transition, the first few ratios typically were emitted without long interresponse times within the ratio. Steady responding then ceased, and numerous long interresponse times occurred, with no systematic relationship to ordinal position within the ratio. Gradually, a new pattern evolved, characterized by a consistently long post-reinforcement time, a border region of the next few interresponse times within which the mean interresponse time monotonically decreased, and short interresponse times within the last 80% of the ratio. Long interresponse times were eliminated from this last section of the ratio without regard to proximity to reinforcement. Various analytical procedures suggested that the final pattern can be conceived, in part, as the shaping of a reliable response topography. The group of three pigeons given 250 mg/kg/day of yeast ribonucleic acid responded at higher rates than the saline and 500 mg/kg/day groups. The latter group, in contrast to the saline and lower dose groups, which continued to increase their rates, reached a rate asymptote very early.     

Two-key concurrent paced variable-interval paced variable-interval schedules of reinforcement

Nine pigeons were used in two experiments in which a response was reinforced if a variable-interval schedule had assigned a reinforcement and if the response terminated an interresponse time within a certain interval, or class, of interresponse times. One such class was scheduled on one key, and a second class was scheduled on a second key. The procedure was, therefore, a two-key concurrent paced variable-interval paced variable-interval schedule. In Exp. I, the lengths of the two reinforced interresponse times were varied. The relative frequency of responding on a key approximately equalled the relative reciprocal of the length of the interresponse time reinforced on that key. In Exp. II, the relative frequency and relative magnitude of reinforcement were varied. The relative frequency of responding on the key for which the shorter interresponse time was reinforced was a monotonically increasing, negatively accelerated function of the relative frequency of reinforcement on that key. The relative frequency of responding depended on the relative magnitude of reinforcement in approximately the same way as it depended on the relative frequency of reinforcement. The relative frequency of responding on the key for which the shorter interresponse time was reinforced depended on the lengths of the two reinforced interresponse times and on the relative frequency and relative magnitude of reinforcement in the same way as the relative frequency of the shorter interresponse time depended on these variables in previous one-key concurrent schedules of reinforcement for two interresponse times.     

Intermittent reinforcement of an interresponse time

Rats were exposed to schedules in which reinforcement was contingent upon the emission of a 1.0- to 2.0-sec interresponse time. The rate of emission and the temporal distribution of this interresponse time was recorded. Several different contingencies between the emission of the interresponse time and reinforcement were examined. Both the rate of emission and the temporal distribution of the 1.0- to 2.0-sec interresponse time varied as a function of the schedule on which it was reinforced. This finding, which suggests that an interresponse time behaves as other operants, has implications for the analysis of conventional reinforcement schedules in terms of the differential reinforcement of interresponse times.