Periodic reinforcement interval and number of periodic reinforcements as parameters of response strength.

In a temporally defined system of reinforcement schedules, the fixed interval case is defined when reinforcement probability, P, is equal to unity for the first response in any cycle length, T; when P is less than 1.0, random interval schedules emerge wherein T/P specifies the expected interval between reinforcements. Key-pecking rates were found to be: (a) inversely related to T/P; (b) higher at T = 1.0 second than at other T parameter values; (c) low and linear at several T and T/P values. The mean post-reinforcement pause, if initially small, increased, and if initially large, decreased, as T/P increased.In 1956, Schoenfeld, Cumming and Hearst proposed a method for defining reinforcement schedules that was based on the independent variable of time and that early demonstrated a certain subsumptive power by generating behavioral patterns hitherto associated with ratio schedules. Two basic variables used to define this temporal system of reinforcement schedules were, tD, a time period during which reinforcement is available, and t0, a time period during which it is not. Symbols used to express combinations of these two variables are: T (cycle length), which is equal to tD + tA, and T, which is equal to tD/tD + t0. Three of the parameters of the system were restricted to fixed values in the early papers (Brandauer, 1958;Clark, 1959;Hearst, 1958;Schoenfeld and Cumming, 1957) Another parameter of this system, which is the focus of the present study, is called P, and is the probability of reinforcement for the first response in any cycle length, T. With P at unity, and T at unity, and the three stated restrictions, schedules are produced which are equivalent to fixed-interval schedules (when the fixed interval is timed from the end of the preceding interval rather than from the reinforcement) if T is greater than reinforcement time. The fixed-time interval between reinforcement availabilities is stated by the value of T or cycle length. When P is reduced to values less than unity, however, T comes to specify a minimum, rather than a fixed, time interval separating reinforcement availabilities, since it is now possible that more than one cycle length will separate reinforcements. Given (a) equal probabilities of reinforcement in each cycle length, T, and (b) an organism responding at a rate equal to or greater than 1 /T, the actual number of these lengths which will separate reinforcements can be predicted by the equation P(N) = (1-P)N-1 P where P equals the probability of reinforcement for the first response in any cycle length T, N equals the number of cycle lengths between reinforcements, and P(N) is the probability of that number. According to this equation, the most probable number of cycle lengths between reinforcement availabilities as well as *the smallest number possible, is one; a larger number will occur with an exponentially smaller probability. The mean interval between reinforcement availabilities is expressed by the ratio T/P. Since reinforcement 607

Section: Apparatussupporting

confidence: 48%

PROPERTIES OF BEHAVIOR UNDER RANDOM INTERVAL REINFORCEMENT SCHEDULES¹

Farmer

1963

“…Herrnstein (1961) showed that the relative rate of responding on a key was linearly related to the relative rate of reinforcement obtained by responding on that key. Previous single-key experiments had demonstrated an increase in response rate as the frequency of reinforcement increased (Clark, 1958;Wilson, 1954). Catania showed that the relative rate of responding on a key increased as the reinforcement magnitude was increased for responses on that key.…”

Section: Discussionmentioning

confidence: 99%

Some Effects of Fixed‐interval Duration on Response Rate in a Two‐component Chain Schedule

Kendall

1967

In Exp. I three pigeons were trained on a two-component chain schedule. Responding on a 1-min variable-interval schedule in the initial component led to a sequence of two fixedinterval schedules in the terminal component. The rate of reinforcement in the terminal component was kept constant while the values of the two fixed intervals were varied. Three combinations of fixed-interval schedules were studied, Fl 0.25, FI 1.75 (minutes) or Fl 1.00, Fl 1.00, or Fl 1.75, Fl 0.25. The rate for each subject declined in the initial component as the value of the first fixed interval was increased. Experiment II was conducted to assess the role of the second fixed-interval schedule in the terminal component in determining the rate of responding in the initial component. For each chain schedule the rate of responding in the initial component was determined both with and without the second of the sequence of fixed intervals. In all three cases the rate of responding in the initial component decreased when the second fixed interval was removed. Increasing the first fixed interval in Exp. I had a greater effect on variable-interval performance than did the removal of the second fixed interval in Exp. II.

“…Both pigeons and rats have been studied in a variety of experimental contexts, usually over a narrower range of rates of reinforcement than was studied here. Monotonically increasing and negatively accelerated functions have been obtained from rats by Skinner (1936; data obtained early in the acquisition of Fl performance), Wilson (1954;Fl schedules), Clark (1958; VI schedules at several levels of deprivation), and Sherman (1959;Fl schedules). The same relationship may hold for schedules of negative reinforcement (Kaplan, 1952; Fl schedules of escape).…”

Section: Resultsmentioning

confidence: 99%

A QUANTITATIVE ANALYSIS OF THE RESPONDING MAINTAINED BY INTERVAL SCHEDULES OF REINFORCEMENT¹

Catania¹,

Reynolds²

1968

790

543

Interval schedules of reinforcement maintained pigeons' key-pecking in six experiments. Each schedule was specified in terms of mean interval, which determined the maximum rate of reinforcement possible, and distribution of intervals, which ranged from many-valued (variable-interval) to single-valued (fixed-interval). In Exp. 1, the relative durations of a sequence of intervals from an arithmetic progression were held constant while the mean interval was varied. Rate of responding was a monotonically increasing, negatively accelerated function of rate of reinforcement over a range from 8.4 to 300 reinforcements per hour. The rate of responding also increased as time passed within the individual intervals of a given schedule. In Exp. 2 and 3, several variable-interval schedules made up of different sequences of intervals were examined. In each schedule, the rate of responding at a particular time within an interval was shown to depend at least in part on the local rate of reinforcement at that time, derived from a measure of the probability of reinforcement at that time and the proximity of potential reinforcements at other times. The functional relationship between rate of responding and rate of reinforcement at different times within the intervals of a single schedule was similar to that obtained across different schedules in Exp. 1. Experiments 4, 5, and 6 examined fixed-interval and two-valued (mixed fixed-interval fixed-interval) schedules, and demonstrated that reinforcement at one time in an interval had substantial effects on responding maintained at other times. It was concluded that the rate of responding maintained by a given interval schedule depends not on the overall rate of reinforcement provided but rather on the summation of different local effects of reinforcement at different times within intervals.