Experiments on single, multiple, and concurrent schedules of reinforcement find various correlations between the rate of responding and the rate or magnitude of reinforcement. For concurrent schedules (i.e., simultaneous choice procedures), there is matching between the relative frequencies of responding and reinforcement; for multiple schedules (i.e., successive discrimination procedures), there are contrast effects between responding in each component and reinforcement in the others; and for single schedules, there are a host of increasing monotonic relations between the rate of responding and the rate of reinforcement. All these results, plus several others, can be accounted for by a coherent system of equations, the most general of which states that the absolute rate of any response is proportional to its associated relative reinforcement.

On the law of effect

A previous paper (Herrnstein, 1958) reported how pigeons behave on a concurrent schedule under which they peck at either of two response-keys The significant finding of this investigation was that the relative frequency of responding to each of the keys may be controlled within narrow limits by adjustments in an independent variable In brief, the requirement for reinforcement in this procedure is the emission of a minimum number of pecks to each of the keys The pigeon receives food when it completes the requirement on both keys The frequency of responding to each key was a close approximation to the minimum requirement The present experiment explores the relative frequency of responding further In the earlier study it was shown that the output of behavior to each of two keys may be controlled by specific requirements of outputs Now we are investigating output as a function of frequency of reinforcement The earlier experiment may be considered a study of differential reinforcement; the present one, a study of strength of response Both experiments are attempts to elucidate the properties of rdlative frequency of responding as a dependent variable

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Relative and absolute strength of response as a function of frequency of reinforcement

Data on choice generally conform closely to an equation of the form: log(B1/B2)=a log(r1/r2+log k, where B1 and B2 are the frequencies of responding at Alternatives 1 and 2, r1 and r2 are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B1/B2=r1/r2. Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.

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On two types of deviation from the matching law: bias and undermatching

Progressive ratio schedules in drug self-administration studies in rats: a method to evaluate reinforcing efficacy

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.

A quantitative analysis of the responding maintained by interval schedules of reinforcement

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Preference and Switching under Concurrent Scheduling.

Cocaine, methylphenidate and secobarbital were compared on a drug maintained progressive-ratio procedure in baboon subjects. Trials, scheduled throughout the day, occurred at a minimum interval of 3 hrs after completion of the preceding trial. A ratio response requirement on the “initiate” lever was required during each trial which terminated in a single intravenous infusion of drug. A drug was introduced on the progressive-ratio procedure with a low ratio requirement in order to obtain a baseline performance of a high stable frequency of trial completion. The ratio requirement was systematically increased every 7 days until the “breaking point” when the rate of completing trials fell below a criterion level. Within-subject comparison revealed that cocaine produced higher breaking points than methylphenidate at the same absolute dose, 0.4 mg/kg. At the range of doses studied, manipulation of doses of methylphenidate (0.1–0.8 mg/kg) and cocaine (0.4–1.6 mg/kg) had little effect on breaking point. In contrast, increasing doses of secobarbital (6.0 and 12.0 mg/kg) produce higher breaking points within the same subjects.

Comparison of progressive-ratio performance maintained by cocaine, methylphenidate and secobarbital.

Blood pressure and heart rate were monitored continuously in four baboons during extended exposure to a daily 12-hour conditioning procedure providing food and shock-avoidance as contingent consequences of prespecified increases in diastolic blood pressure. Sustained and significant increases (30 to 40 mm-Hg) in both systolic and diastolic blood pressure were maintained throughout the daily 12-hour conditioning sessions, accompanied by elevated heart rates.

https://science.sciencemag.org/content/sci/182/4108/175.full.pdf

Instrumental conditioning of large-magnitude, daily, 12-hour blood pressure elevations in the baboon.

Monkeys were exposed to a 24 h continuous experimental procedure which provided a periodic forced choice between the self-infusion of secobarbital versus saline. Preference for secobarbital over saline was readily obtained using choice trials programmed approximately every 2 h at a dose of 9 mg/kg of secobarbital per infusion. Preference for self-infusion of chlordiazepoxide over saline was obtained using choice trials every 3 h, and a dose on the order of 1 mg/kg per infusion. In a subsequent experiment, two of the animals addicted to chlordiazepoxide were given a choice every 3 h between an infusion of chlordiazepoxide or secobarbital. Following a period of intake of both drugs, a gradual shift in preference from chlordiazepoxide to secobarbital was observed over a period of some 60 days. In general, this preference procedure provides a flexible technique with several dependent measures for single or multiple drug addiction studies.

Jack D. Findley

Papers

Preference and Switching under Concurrent Scheduling.

Comparison of progressive-ratio performance maintained by cocaine, methylphenidate and secobarbital.

Instrumental conditioning of large-magnitude, daily, 12-hour blood pressure elevations in the baboon.

Addiction to secobarbital and chlordiazepoxide in the rhesus monkey by means of a self-infusion preference procedure.

A restraint system for chronic study of the baboon.