Preference as a function of absolute response durations

The durations of 2 responses, 2 categories of reinforced nondiscriminated interresponse times, were varied while their relative durations were held approximately constant, with the longer about 2 1/2 times longer than the shorter. Three pigeons pecked for food. Reinforcers for the shorter and longer responses were arranged by a concurrent variable-interval, variable-interval schedule. Preference for the shorter response increased when both were lengthened. These results, taken together with previous results for discriminated interresponse times, show that preference for the shorter of 2 responses depends on their absolute durations, whether they are discriminated or not and regardless of autoshaped key pecks that may occur in the discriminated case. Time-allocation-matching was not generally obtained. The results qualitatively agree with an associative learner, a computational processing model derived from a molecular analysis of behavior.     

Preference for starting and finishing behavior patterns

Pigeon's key pecking was reinforced with food in two experiments in which the correspondence between preference for starting one of two reinforced behavior patterns and the likelihood of finishing it subsequently was examined. Reinforcers were scheduled according to concurrent schedules for two classes of interresponse times, modified such that reinforcers followed a center-key peck terminating either a shorter interresponse time started by a left-key peck or a longer interresponse time started by a right-key peck. In Experiment 1, the times when reinforcers potentially were available were not discriminated, whereas in Experiment 2 they were. Absolute reinforced pattern durations were varied. The relative frequency of starting a particular pattern was highly correlated with relative frequency of that completed pattern in both experiments. Other relations between starting and finishing a pattern depended on whether reinforced interresponse times were discriminated. For instance, preference for starting a pattern sometimes correlated negatively with the likelihood of subsequently completing it. The present experiments are described as capturing part of the ordinary language meaning of "intention," according to which an organism's behavior at one moment sets the occasion for an observer to say that the organism "intends" in the future to engage in one behavior rather than another.     

Effects of variations in local reinforcement rate on local response rate in variable interval schedules

Rats trained to lever press for sucrose were exposed to variable-interval schedules in which (i) the probability of reinforcement in each unit of time was a constant, (ii) the probability was high in the first ten seconds after reinforcement and low thereafter, (iii) the probability was low for ten seconds and high thereafter, (iv) the probability increased with time since reinforcement, or (v) the probability was initially zero and then increased with time since reinforcement. All schedules generated similar overall reinforcement rates. A peak in local response rate occurred several seconds after reinforcement under those schedules where reinforcement rate at this time was moderate or high ([i], [ii], and [iv]). Later in the inter-reinforcement interval, local response rate was roughly constant under those schedules with a constant local reinforcement rate ([i], [ii], and [iii]), but increased steadily when local reinforcement rate increased with time since reinforcement ([iv] and [v]). Postreinforcement pauses occurred on all schedules, but were much longer when local reinforcement rate was very low in the ten seconds after reinforcement ([iii]). The interresponse time distribution was highly correlated with the distribution of reinforced interresponse times, and the distribution of postreinforcement pauses was highly correlated with the distribution of reinforced postreinforcement pauses on some schedules. However, there was no direct evidence that these correlations resulted from selective reinforcement of classes of interresponse times and pauses.     

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.     

The copyist model of response emission

The variety of different performances maintained by schedules of reinforcement complicates comprehensive model creation. The present account assumes the simpler goal of modeling the performances of only variable reinforcement schedules because they tend to maintain steady response rates over time. The model presented assumes that rate is determined by the mean of interresponse times (time between two responses) between successive reinforcers, averaged so that their contribution to that mean diminishes exponentially with distance from reinforcement. To respond, the model randomly selects an interresponse time from the last 300 of these mean interresponse times, the selection likelihood arranged so that the proportion of session time spent emitting each of these 300 interresponse times is the same. This interresponse time defines the mean of an exponential distribution from which one is randomly chosen for emission. The response rates obtained approximated those found on several variable schedules. Furthermore, the model reproduced three effects: (1) the variable ratio maintaining higher response rates than does the variable interval; (2) the finding for variable schedules that when the reinforcement rate varies from low to high, the response rate function has an ascending and then descending limb; and (3) matching on concurrent schedules. Because these results are due to an algorithm that reproduces reinforced interresponse times, responding to single and concurrent schedules is viewed as merely copying what was reinforced before.     

Response-rate differences in variable-interval and variable-ratio schedules: An old problem revisited

In Experiment 1, a variable-ratio 10 schedule became, successively, a variable-interval schedule with only the minimum interreinforcement intervals yoked to the variable ratio, or a variable-interval schedule with both interreinforcement intervals and reinforced interresponse times yoked to the variable ratio. Response rates in the variable-interval schedule with both interreinforcement interval and reinforced interresponse time yoking fell between the higher rates maintained by the variable-ratio schedule and the lower rates maintained by the variable-interval schedule with only interreinforcement interval yoking. In Experiment 2, a tandem variable-interval 15-s variable-ratio 5 schedule became a yoked tandem variable-ratio 5 variable-interval x-s schedule, and a tandem variable-interval 30-s variable-ratio 10 schedule became a yoked tandem variable-ratio 10 variable-interval x-s schedule. In the yoked tandem schedules, the minimum interreinforcement intervals in the variable-interval components were those that equated overall interreinforcement times in the two phases. Response rates did not decline in the yoked schedules even when the reinforced interresponse times became longer. Experiment 1 suggests that both reinforced interresponse times and response rate–reinforcement rate correlations determine response-rate differences in variable-ratio 10 and yoked variable-interval schedules in rats. Experiment 2 suggests a minimal role for the reinforced interresponse time in determining response rates on tandem variable-interval 30-s variable-ratio 10 and yoked tandem variable-ratio 10 variable-interval x-s schedules in rats.     

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.     

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.     

Dissociation of value and response strength

Four pigeons were exposed to multiple schedules and later to concurrent-chains schedules, with terminal links that had previously been multiple-schedule components. For 2 birds, the terminal-link schedules arranged an inverse relationship between response rate and reinforcement rate; for the other 2 birds a direct corresponding relationship was arranged. Those response rates were further modified by differentially reinforcing either longer or shorter interresponse times, relative to the current means. Although the birds' initial-link responses indicated preferences for terminal links with higher rates of reinforcement, in half the cases the birds responded during the terminal links in such a way as to produce lower rates of reinforcement, rates their initial-link behavior indicated they did not prefer. That outcome is inconsistent with maximization theory, but consistent with a strengthening analysis of behavior on single-key schedules.     

A test of the effectiveness of the differential-reinforcement-of-low-rate schedule

Pigeons and rats were used in a yoked-control design that equated the reinforcement distributions of differential-reinforcement-of-low-rate and variable-interval schedules. Both a between-subjects design and a within-subjects design found response rate higher for the variable-interval schedule than for the differential-reinforcement-of-low-rate schedule, thus demonstrating the effectiveness of the differential-reinforcement-of-low-rate contingency. The interresponse-time distributions were unimodal for all subjects under the variable-interval schedule and bimodal for pigeons under the differential-reinforcement-of-low-rate schedule. The interresponse-time distributions for rats under the differential-reinforcement-of-low-rate schedule were also bimodal in three of four cases but the height of the modes at the shorter interresponse times were small in both absolute value and in relation to the height of the modes at the shorter interresponse times of the pigeons' distributions.     

The reinforcement of least-frequent interresponse times

A new schedule of reinforcement was used to maintain key-pecking by pigeons. The schedule reinforced only pecks terminating interresponse times which occurred least often relative to the exponential distribution of interresponse times to be expected from an ideal random generator. Two schedule parameters were varied: (1) the rate constant of the controlling exponential distribution and (2) the probability that a response would be reinforced, given that it met the interresponse-time contingency. Response rate changed quickly and markedly with changes in the rate constant; it changed only slightly with a fourfold change in the reinforcement probability. The schedule produced stable rates and high intra- and inter-subject reliability, yet interresponse time distributions were approximately exponential. Such local interresponse time variability in the context of good overall control suggests that the schedule may be used to generate stable, predictable, yet sensitive baseline rates. Implications for the measurement of rate are discussed.     

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.     

Time allocation and response rate

Food reinforcement for key pecking by three pigeons was arranged by a variable-interval schedule and a device that assigned each reinforcement to one of 10 component response rates corresponding to 10 classes of equally reinforced interresponse times ranging from 1.0 to 6.0 sec in 0.5-sec classes. The overall number of reinforcements per hour was varied from one to more than 60. Overall response rate was a monotonically increasing, negatively accelerated function of the overall number of reinforcements per hour. This function was decomposed into two time-allocation functions: (1) the time allocated to all of the reinforced component response rates as a function of the total reinforcement rate, and, (2) the time allocated to a particular reinforced component response rate as a function of the reinforcement rate for that component. Asymptotic response rate was predicted by combining the asymptotes of the two separate time-allocation functions: virtually all of the time was spent responding, and the percentage of the time spent responding that was allocated to a particular reinforced component response rate roughly equalled the relative reinforcements per hour for that component.     

Choice and behavioral patterning

Ten pigeons pecked left and right keys in a discrete-trials experiment in which access to food was contingent upon changeovers to the right key after particular runs of left-key pecks. In each of three sets of conditions, two run lengths were reinforced according to a concurrent variable-interval schedule: reinforcement followed runs of either 1 or 2, 1 or 4, or 2 or 4 left-key pecks preceding changeovers. The intertrial interval separating successive pecks was varied from .5 to 10.0 sec, and the relative frequency of reinforcement for the shorter of the two reinforced runs was varied from 0 to .75. The contingencies established local behavioral patterning that roughly approximated that required for reinforcement. For a fixed pair of reinforced run lengths, preference for the shorter of the two frequently increased as the intertrial interval increased and therefore as the minimum temporal durations of both reinforced runs increased. Preference for the shorter of the two also increased as its corresponding relative frequency of reinforcement increased. Both of these effects on preference were qualitatively similar to corresponding effects in previous research with two different kinds of reinforced behavioral patterns, interresponse times and interchangeover times. In all these experiments, analytical units were found in the temporal patterns of behavior, not in the behavior immediately contiguous with a reinforcer. It is suggested that a particular local temporal pattern of behavior is established to the extent to which it is repeatedly remembered when reinforcers are delivered, regardless of whether the delivery of a reinforcer is explicitly contingent upon that pattern.     

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.     

The concurrent reinforcement of two interresponse times: absolute rate of reinforcement

Three pigeons obtained food on a one-key schedule of reinforcement for two concurrent, discriminated interresponse times. The overall rate of reinforcement was determined by a family of variable-interval schedules and by a continuous reinforcement schedule. The average frequency of reinforcement varied from 1.1 to 300 reinforcements per hour; the relative frequency of reinforcement for each of the two interresponse times was 0.5 throughout the experiment. The number of responses per minute increased sharply as the number of reinforcements per hour increased from 1 to 20. Beyond 30 reinforcements per hour, the curve was approximately flat, although it sometimes decreased slightly at the highest reinforcement rates. The relative frequency of the shorter interresponse time also increased sharply as the number of reinforcements per hour increased from 1 to 20. The asymptote of the relative frequency function approximately equalled the relative reciprocal of the length of the shorter interresponse time for reinforcement rates greater than 30 or 40 reinforcements per hour. This approximation was obscured by the response-rate function.     

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.     

Time-allocation, matching, and contrast

A variable-interval schedule arranged food reinforcement for key pecking by pigeons on a single operandum at two rates, corresponding to two classes of reinforced interresponse times ranging from 1.5 to 2.5 sec and from 3.5 to 4.5 sec. The scheduled reinforcement rate for the higher component response rate was constant and equivalent to that of a variable-interval 4-min schedule. The scheduled reinforcement rate for the lower component response rate varied from zero to over 100 per hour. The number of occurrences of the constant component response rate varied inversely with the reinforcement rate for the variable component. This result, by definition a concurrent reinforcement interaction, or contrast, was the combined effect of two time-allocation functions, which together determine mean response rate: the time allocated to both component rates as a function of the total reinforcement rate, and the time allocated to a particular component rate as a function of the percentage of reinforcements for that component. The present experiment reveals a further parallel between the controlling relations for free responding on a single operandum and those for choice between two operanda; in each case, a concurrent reinforcement interaction can be found that corresponds to matching.     

On the primacy of molecular processes in determining response rates under variable-ratio and variable-interval schedules

This study focused on variables that may account for response-rate differences under variable-ratio (VR) and variable-interval (VI) schedules of reinforcement. Four rats were exposed to VR, VI, tandem VI differential-reinforcement-of-high-rate, regulated-probability-interval, and negative-feedback schedules of reinforcement that provided the same rate of reinforcement. Response rates were higher under the VR schedule than the VI schedule, and the rates on all other schedules approximated those under the VR schedule. The median reinforced interresponse time (IRT) under the VI schedule was longer than for the other schedules. Thus, differences in reinforced IRTs correlated with differences in response rate, an outcome suggestive of the molecular control of response rate. This conclusion was complemented by the additional finding that the differences in molar reinforcement-feedback functions had little discernible impact on responding.     

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.