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.     

Temporal patterns of responding in small fixed-ratio schedules

Pigeons were exposed to an ascending series of small fixed-ratio schedules from fixed-ratio 1 to 7. Two of those pigeons were later placed on a fixed-ratio 30 schedule. The two primary dependent variables were the postreinforcement pause and the interresponse time. Changes in these variables under small fixed ratios were sometimes opposite to changes reported with large fixed ratios. For example, postreinforcement pauses decreased in length as the fixed-ratio requirement increased from fixed-ratio 1 to fixed-ratio 3. Also, the interresponse times early in the small fixed-ratio schedule were shorter than those immediately preceding reinforcement. These findings question the role of interresponse-time reinforcement in determining temporal patterns of responding under small fixed-ratio schedules. They also suggest that there may be a limited region in which the independent variable, fixed-ratio size, does not operate as previously described.     

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.     

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.     

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.     

Fixed-ratio performance with and without a postreinforcement timeout

Pigeons pecked a key, producing food reinforcement on fixed-ratio (FR) schedules requiring 50, 100, or 150 responses. In each session, 30-second timeouts were inserted before a random half of the FR trials, whereas the other trials began immediately after reinforcement. In general, preratio pauses were shorter on trials preceded by timeouts. On these trials, the probability of a first response tended to be highest in the first 20 seconds of the trials, suggesting that the shorter pauses were the result of transient behavioral contrast. Direct observations and analyses of interresponse times (IRTs) after the preratio pause indicated that IRTs could be grouped into three categories: (1) IRTs of about .1 second, which were produced by small head movements in the vicinity of the key; (2) IRTs of about .3 second, which were produced by distinct pecking motions; and (3) IRTs greater than .5 second, which were accompanied by pausing or movements away from the key. At all ratio sizes, as a subject progressed through a trial, the probability of a long IRT decreased, whereas the probability of an intermediate IRT usually increased at first and then decreased. The probability of a short IRT increased monotonically across a trial. The results show that responding changes systematically as a subject progresses through a ratio on an FR schedule. Some characteristics of performance varied as functions of the absolute size of the response requirement, whereas others appeared to depend on the relative location within a ratio (i.e., the proportion of the ratio completed at a given moment).     

A comparison of responding maintained under second-order schedules of intramuscular cocaine injection or food presentation in squirrel monkeys.

Key pressing by squirrel monkeys was maintained under second-order schedules of either intramuscular cocaine injection or food presentation. Under one schedule, each completion of a 10-response fixed-ratio unit produced a brief visual stimulus; the first fixed-ratio unit completed after 30 minutes elapsed produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Rates of responding increased within the fixed-interval units, and to a greater extent over the entire 10 fixed-interval units. Patterns of responding depended more on the schedule of reinforcement than on whether cocaine or food maintained responding. Omitting the brief stimuli following all but the last fixed-ratio or fixed-interval units decreased average rates and altered the patterns of responding. Substituting a visual stimulus that was never paired with cocaine or food following all but the last fixed-ratio or fixed-interval units decreased response rates to a lesser extent and did not substantially alter patterns of responding. When the duration of the paired stimulus was varied from .3 to 30.0 seconds, the highest response rates occurred at intermediate durations (1.0 to 10.0 seconds). The manner in which the stimulus changes affected performances depended more on the schedule of reinforcement than on whether cocaine injection or food presentation maintained responding.     

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.     

Separating response dependency and response-reinforcer contiguity within a recycling conjunctive schedule

A procedure is described which disrupts response-reinforcer contiguity and response dependency and which demonstrates how the location of the response dependency in interval schedules can be regarded as a controlling variable in its own right. Rats' lever pressing produced sucrose on a recycling conjunctive fixed-time 30-second fixed-ratio 1 schedule of reinforcement. Reinforcement occurred only at the end of the fixed-time component on this schedule and only if a response had occurred during that component. This produced a pause-respond-pause pattern during the interreinforcer interval for all animals. When the location of the response dependency was then restricted to a 10-second period in the middle of the fixed-time component, the pattern was accentuated and response rates increased for all animals, while postreinforcement pauses decreased sharply for two animals. When responding was required in the first 10 seconds of the fixed-time component, responding peaked earlier in the interval for all animals. Response rates were slightly below those in the previous conditions, while postreinforcement pauses were between 2 and 6 seconds across animals.     

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

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

Preference for mixed- versus fixed-ratio schedules

Pigeons' pecks on one key produced a stimulus correlated with a mixed-ratio schedule of food reinforcement. Pecks on a second key produced a stimulus correlated with a fixed-ratio schedule. When the arithmetic mean of the mixed ratios equaled the fixed ratio, the former stimulus maintained a higher rate of pecking. When the fixed ratio was sufficiently smaller, preference shifted to it. The pigeons' relative preference for the schedules could be described by comparing the geometric mean of the reinforcement rates in the several mixed-ratio components with the reinforcement rates in the fixed-ratio components.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

Fixed-ratio punishment by timeout of concurrent variable-interval behavior

Pigeons' responding was maintained by two concurrently available variable-interval reinforcement schedules. A fixed-ratio punishment schedule of timeout periods from the concurrent reinforcement schedules was arranged for responding during one of the variable-interval schedules. The greater the probability of a timeout after a response on the punished variable-interval schedule (the smaller the fixed ratio that produced timeout), the greater the decline in the relative punished response rates. Relative reinforcement rates remained invariant when relative response rates declined. Both behavioral contrast and induction effects were observed on the unpunished variable-interval schedule as a function of timeout punishment of the other schedule.     

The effect of punishment shock intensity upon responding under multiple schedules

In the first of two experiments, responses of two pigeons were maintained by multiple variable-interval, variable-ratio schedules of food reinforcement. Concurrent punishment was introduced, which consisted of a brief electric shock after each tenth response. The initial punishment intensities had no lasting effect upon responding. Then, as shock intensity increased, variable-ratio response rates were suppressed more quickly than variable-interval response rates. When shock intensity decreased, variable-interval responding recovered more quickly, but the rates under both schedules eventually returned to their pre-punishment levels. In the second experiment, the following conditions were studied in three additional pigeons: (1) With each shock intensity in effect for a number of sessions, punishment shock intensity was gradually increased and decreased and responding was maintained by multiple variable-ratio, fixed-ratio schedules of food reinforcement; (2) Changes in punishment shock intensity as described above with responding maintained by either a variable-ratio or a fixed-ratio schedule, which were presented on alternate days; (3) Session-to-session changes in shock intensity with responding maintained by multiple variable-ratio, fixed-ratio schedules. Responding under the two schedules was suppressed to approximately the same extent by a particular shock intensity. Also, post-reinforcement pauses under the fixed-ratio schedule increased as response suppression increased.     

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.     

Changeover behavior under pairs of fixed-ratio and variable-ratio schedules of reinforcement

Three pigeons were studied under a pair of equal fixed-ratio schedules and a pair of equal variable-ratio schedules. Each pair was arranged as independent, concurrent schedules and also in a non-independent relation where each peck in a schedule counted toward the response requirement of both schedules. The non-independent pair of variable-ratio schedules maintained much higher changeover rates than any of the other three arrangements. Thus, two factors seemed necessary for generating high changeover rates. Responding on a schedule had to count toward the response requirement of both schedules, and the component schedules had to be variable. These data are consistent with the hypothesis that changeovers are at least partly controlled by the probability of reinforcement following a changeover.     

The effects of schedule history and the opportunity for adjunctive responding on behavior during a fixed-interval schedule of reinforcement.

The effects of schedule history and the availability of an adjunctive response (polydipsia) on fixed-interval schedule performance were investigated. Two rats first pressed levers under a schedule of food reinforcement with an interresponse time greater than 11 s, and 2 others responded under a fixed-ratio 40 schedule. All 4 were then exposed to a fixed-interval 15-s schedule. Water was continuously available under these conditions, but after responding became stable on the fixed-interval schedule, access was experimentally manipulated. With water freely available, subjects did not display characteristic fixed-interval response rates and patterns (i.e., scalloping or break-and-run). Instead, they exhibited predictable, stable patterns of behavior as a function of their schedule histories: Subjects with the interresponse-time history exhibited low response rates, and those with the fixed-ratio history exhibited high rates. Manipulating the amount of water available resulted in marked changes in response rates for rats with the interresponse-time history but not for those with the fixed-ratio history. The results illustrate the multiple causation of behavior by its previous and current schedules of reinforcement and other concurrent factors.     

Fixed-ratio reinforcement of spaced responding

Responses by rats were reinforced with food under a second-order schedule involving fixed-ratio reinforcement of temporally spaced responses. Requirements of 20, 8, and 3 responses were examined. The typical characteristic of spaced responding was maintained under the ratio schedules: interresponse time distributions were similar to those typically seen, and were not noticeably affected by the ratio value. Comparison of total response rate, correct response rate, and accuracy showed correct response rate to be the most consistently affected by changes in the ratio value. Substantial evidence of schedule control was seen only for correct responses. Incorrect response records were erratic, but rates generally declined as reinforcement was approached. Correct response records were characterized by increasing rate as reinforcement was approached. It was suggested that the pattern of fixed-ratio performance revealed may be affected by the behavioral unit examined.     

Effects of reinforcement magnitude and ratio values on behaviour maintained by a cyclic ratio schedule of reinforcement

In Experiments 1 and 2, lever pressing by rats was reinforced on a cyclic ratio schedule of food reinforcement, comprising a repeated sequence of fixed-ratio component schedules. Reinforcement magnitude was varied, on occasional sessions in Experiment 1 and across blocks of sessions in Experiment 2, from one to two or three 45-mg food pellets. In the one-pellet condition, post-reinforcement pauses increased with component schedule value. At higher magnitudes, post-reinforcement pauses increased, and overall response rates declined. Response rate on component schedules was a decreasing linear function of the obtained rate of reinforcement in all conditions. Plotted against component schedule value, response rate increased exponentially to an asymptote that decreased when reinforcement magnitude increased. These findings are consistent with regulatory accounts of food reinforced behaviour. In Experiment 3, rats were trained under a cyclic ratio schedule comprising fixed-ratio components including higher values, and some inverted U-shaped response functions were obtained. Those rats that did not showthis relationship were trained on cyclic ratios with even higher values, and all showed inverted U-shaped response functions. This suggests that behaviour on cyclic ratio schedules can reflect activating of reinforcement as well as the satiating effects seen in Experiments 1 and 2.     

An inverse relationship between baseline fixed-interval response rate and the effects of a tandem response requirement.

Previous experiments examining the effects of adding a tandem fixed-ratio response requirement on fixed-interval schedule performance have reported inconsistent results. One variable that may account for such inconsistencies is the baseline response rate in the fixed-interval condition. This possibility was investigated in the present study. Rats were given histories with either interresponse times greater than 11 s or fixed-ratio 40 schedules of reinforcement, which engendered either relatively low or high rates of responding, respectively, in the subsequent fixed-interval condition. A tandem ratio response requirement (fixed-ratio 9) was then introduced. The effects of adding this tandem response requirement were inversely related to the baseline fixed-interval response rates; low rates of responding in the fixed-interval condition were markedly increased, whereas high rates of responding were relatively unaffected. This inverse relationship appears to be similar to the rate-dependent relations observed in behavioral pharmacology. These results may provide an explanation for the inconsistent findings reported in previous studies on tandem fixed-interval fixed-ratio schedules and suggest that principles of behavioral pharmacology research may be applicable to the study of the effects of nonpharmacological variables on schedule-controlled behavior.