Time limits for completing fixed ratios. IV. Components of the ratio

Pigeons received food after completing a fixed ratio if the temporal properties of responding exceeded minimum duration requirements. In one set of conditions, a minimum time had to elapse before the first response of the ratio (the initial pause). In another set, the minimum duration was the time between the first and last response of the ratio. Obtained times increased as a power function of required times in both conditions. The power function resembled that occurring in experiments involving temporal differentiation of individual responses, interresponse times, latencies, and entire fixed-ratio sequences. Moreover, in all of these experiments individual performances could be described as a function of the base duration (the duration occurring in the absence of temporal requirements) and the specific time requirement. Control conditions indicated that the effects resulted from temporal requirements and not from reinforcer intermittency.     

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.     

The role of verbal behavior in human learning: II. Developmental differences

When children in four different age ranges operated a response device, reinforcers were presented according to fixed-interval schedules ranging in value from 10 to 70 seconds. Only the behavior of the subjects in the youngest of the four groups, the preverbal infants, resembled that of other animal species. The children in age ranges 5 to 6½ and 7½ to 9 years exhibited either the low-rate or high-rate response patterns typical of human adults. Those who showed the low-rate pattern reported a time-based formulation of the contingencies and some of them were observed to occasionally count out the interval before responding. The performance of children aged 2½ to 4 years differed from that of both infants and older children, though containing some patterning elements similar to those produced by the older and younger subjects. The predominant response pattern of the infants consisted of a pause after reinforcement followed by an accelerated rate of responding that terminated when the next reinforcer was delivered. Analysis of postreinforcement-pause duration and response rate showed that infant performance, but not that of the older children, consistently exhibited the same kinds of schedule sensitivity observed in animal behavior. The evidence supports the suggestion that the development of verbal behavior greatly alters human operant performance and may account for many of the differences found between human and animal learning.     

Reinforcement magnitude and pausing on progressive-ratio schedules

Rats responded under progressive-ratio schedules for sweetened milk reinforcers; each session ended when responding ceased for 10 min. Experiment 1 varied the concentration of milk and the duration of postreinforcement timeouts. Postreinforcement pausing increased as a positively accelerated function of the size of the ratio, and the rate of increase was reduced as a function of concentration and by timeouts of 10 s or longer. Experiment 2 varied reinforcement magnitude within sessions (number of dipper operations per reinforcer) in conjunction with stimuli correlated with the upcoming magnitude. In the absence of discriminative stimuli, pausing was longer following a large reinforcer than following a small one. Pauses were reduced by a stimulus signaling a large upcoming reinforcer, particularly at the highest ratios, and the animals tended to quit responding when the past reinforcer was large and the stimulus signaled that the next one would be small. Results of both experiments revealed parallels between responding under progressive-ratio schedules and other schedules containing ratio contingencies. Relationships between pausing and magnitude suggest that ratio pausing is under the joint control of inhibitory properties of the past reinforcer and excitatory properties of stimuli correlated with the upcoming reinforcer, rather than under the exclusive control of either factor alone.     

Analysis of fixed-ratio behavior maintained by drug reinforcers.

Behavior maintained by intravenously delivered alfentanil, cocaine, or ketamine was assessed using a fixed-ratio schedule of reinforcement. As the dose of each drug was increased, rate of responding also increased up to a maximum. Further increases in dose resulted in decreased response rates (inverted U-shaped curve). An analysis of postreinforcement-pause-time and run-time measures for the ascending limb of the inverted U-shaped functions revealed that behavior was characterized by systematic decreases in both pause time and run time as dose and rate increased. An examination of the descending limb of the dose-response functions revealed that lowered response rates for cocaine and ketamine were correlated with increases in run time and small and inconsistent effects on postreinforcement pause time. Behavior maintained by rate-reducing doses of alfentanil was characterized by lengthened postreinforcement pauses with small increases in run time. These data suggest that at larger doses, drug reinforcers may have unconditioned or direct effects on the behavior that the drug is maintaining, and more important, that the nature of these unconditioned effects depends on the drug that is maintaining behavior.     

Interreinforcement time, work time, and the postreinforcement pause

Six rats were trained with food deliveries contingent upon their pressing a lever and holding it down for fixed, cumulative durations. Hold requirements were varied from 7.5 seconds to 120 seconds. Lever holding was maintained reliably at hold requirements as long as 30 seconds to 105 seconds for different rats. At longer hold requirements, lever holding was erratic and tended to occur only early in sessions. At shorter and intermediate requirements, the patterns of lever holding resembled those of responding under fixed-ratio schedules for discrete responses, with breaks in responding immediately after reinforcement alternating with relatively continuous lever holding until the next reinforcement. At longer hold requirements, postpause lever holding frequently was interrupted with additional pauses. The duration of postreinforcement pauses increased linearly with the scheduled hold requirement. However, for five of six rats, the hold requirement, which represents the actual time spent lever holding per reinforcer, accounted for somewhat less variance in pause duration than did interreinforcement time.     

Inhibiting function of reinforcement: magnitude effects on variable-interval schedules

In two experiments, the performance of rats under constant-probability and arithmetic variable-interval schedules respectively was compared when the concentration of a liquid reinforcer was varied within sessions; in other sessions, half of the reinforcers were randomly omitted. When the discriminative function of the reinforcer as a signal for a decrease in the probability of reinforcement was attenuated (the constant-probability schedule) the postreinforcement pause duration was nevertheless an increasing function of reinforcer magnitude. This relationship was also present, but more marked, when the temporal discriminative function of the reinforcer was enhanced (the arithmetic schedule). These results suggested that reinforcement has an unconditioned suppressive effect on the reinforced response distinct from any discriminative function it may acquire. The reinforcement-omission effect, where response rate accelerates following omission, was observed when the reinforcer functioned as an effective temporal discriminative stimulus, but not when such temporal control was absent.     

Species differences in temporal control of behavior II: human performance

Human subjects responded on two panels. A differential-reinforcement-of-low-rate schedule with a limited-hold contingency operated on Panel A. In Condition 1, responses on Panel B produced a stimulus on the panel that signalled whether reinforcement was available on Panel A. In Condition 2, responses on Panel B briefly illuminated a digital clock. In both conditions, performance on Panel A was very efficient; with few exceptions, Panel A was pressed only when reinforcement was available. Thus, in effect, a fixed-interval schedule operated on Panel B. In Condition 1, a “break-and-run” response pattern occurred on Panel B; with increasing temporal parameters, the duration of the postreinforcement pause on Panel B increased linearly while overall response rate and running rate (calculated by excluding the postreinforcement pauses) remained approximately constant. In Condition 2, the response pattern on Panel B was scalloped; the postreinforcement pause was a negatively accelerated increasing function of schedule value, while overall response rate and running rate were negatively accelerated decreasing functions of schedule value. The performance of subjects in Condition 2, but not in Condition 1, was highly sensitive to the contingencies in operation, and resembled that of other species on the fixed-interval schedule.     

Random versus rational strategies for initial configurations in nonmetric multidimensional scaling

An examination is made concerning the utility and design of studies comparing nonmetric scaling algorithms and their initial configurations, as well as the agreement between the results of such studies. Various practical details of nonmetric scaling are also considered.This research was supported by NSF Grants SOC 76-24512 and SOC 76-24394.     

Monte Carlo studies in nonmetric scaling

In response to Arabie several random ranking studies are compared and discussed. Differences are typically very small, however it is noted that those studies which used arbitrary configurations tend to produce slightly higher stress values. The choice of starting configuration is discussed and we suggest that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.This research was supported by the National Research Council of Canada (Grant No. A8351) and by the National Institute of Mental Health (Grant Nos. MH10006 and MH26504). The authorship order has been determined by Monte Carlo methods.