Increasing and Signaling Background Reinforcement: Effect on the Foreground Response—reinforcer Relation

Abstract

Herrnstein's (1970) hyperbolic matching equation describes the relationship between response rate and reinforcement rate. It has two estimated parameters, k and Re. According to one interpretation, k measures motor performance and Re measures the efficacy of the reinforcer maintaining responding relative to background sources of reinforcement. Experiment 1 tested this interpretation of the Re parameter by observing the effect of adding and removing an additional source of reinforcement to the context. Using a within-session procedure, estimates of Re were obtained from the responsereinforcer relation over a series of seven variable-interval schedules. A second, concurrently available variable-interval schedule of reinforcement was added and then removed from the context. Results showed that when the alternative was added to the context, the value of Re increased by 107 reinforcers per hour; this approximated the 91 reinforcers per hour obtained from this schedule. Experiment 2 investigated the effects of signaling background reinforcement on k and Re. The signal decreased Re, but did not have a systematic effect on k. In general, the results supported Herrnstein's interpretation that in settings with one experimenter-controlled reinforcement source, Re indexes the strength of the reinforcer maintaining responding relative to uncontrolled background sources of reinforcement.Key words: Herrnstein's hyperbola, matching law, background reinforcement, signaled reinforcement, lever press, rats Herrnstein (1970) formulated an elementary matching law equation for the case in which there is only a single measured source of reinforcement and a single measured response rate. The form of that equation is kRj BIRi+Re' (1) where B1 is response rate, R1 is reinforcement rate, and k and Re are fitted constants. The structural or curve-fitting definitions of the constants reveal the relationship between response rate and reinforcement rate implied by Equation 1. In the numerator, k is an estimate of the response-rate asymptote. For instance, as reinforcement rate increases, response rate approaches but does not exceed k. Thus, k is measured in the same units as the measured behavior (e.g., responses per minute). In the numerator, Re is equal to the rate of reinforcement that maintains a one-half asymp-The authors gratefully acknowledge the helpful comments of the reviewers and members of the Behavioral and Decision Analysis research seminar in the Department of Psychology at Harvard in the preparation of this manuscript. Correspondence regarding this article should be sent to Terry W. Belke, Department of Psychology, Biological Sciences Building, University of Alberta, Edmonton, Alberta T6G 2E9, Canada (E-mail: tbelke@cyber.psych.ualberta.ca).totic response rate. For example, when RI is equal to Re, response rate must be equal to k/2. Thus, Re is measured in the same units as the experimenter-controlled reinforcer (e.g., 0.10 mL sucrose servings per hour).On the basis of the matching law, Herrnstein (1970, 1974) provided em...

Concurrent Schedules: Reinforcer Magnitude Effects

“…The present experiment also makes contact with recent research that has shown that individual reinforcers have large effects on preference in a procedure introduced by Belke and Heyman (1994) in which the reinforcer ratio varies within sessions (Davison & Baum, 2000Landon & Davison, 2001). Landon and Davison showed that control over responding in this procedure was not purely local, but also included longer-term factors.…”

Qualitatively different reinforcers and parameters of Herrnstein’s (1970) response-strength equation

“…All dependent measures were also recorded for each reinforcement in order to examine within-session effects. Performance during each condition was judged stable when the following criteria were met (Belke & Heyman, 1994a, 1994bHeyman & Monaghan, 1987. First, the k and R, values over the last 5 consecutive days could be neither the highest nor the lowest for the condition.…”

Choice in a Variable Environment: Effects of Unequal Reinforcer Distributions

“…Both approaches have shown that previous reinforcer ratios affect current performance to some degree. Davison and Baum (2000) reported a study in which they used a procedure introduced by Belke and Heyman (1994) to study choice in conditions that changed even more frequently. Seven different reinforcer ratios (27: 1, 9:1, 3:1, 1:1, 1:3, 1:9, and 1:27) were presented to the subjects in a random order in each session.…”

“…One difference between these procedures, however, warrants investigation. Previous research using Belke and Heyman's (1994) procedure (Davison & Baum, 2000Landon & Davison, 2001) used reinforcer ratio distributions symmetrical around 1:1. Thus in every condition arranged in these studies approximately equal numbers of reinforcers were obtained for re-sponding to each of the two alternatives across each session.…”

“…To examine this further, the present experiment used Belke and Heyman's (1994) procedure and arranged various unequal reinforcer distributions to examine how these distributions affected choice within components. In Conditions 1 through 4, the range of reinforcer ratios used by Davison and Baum (2000;i.e., 27:1 to 1:27, spaced in equal logarithmic steps) was shifted so that it was centered at 3:1 (i.e., 81:1 to 1:9) or 1:3 (9:1 to 1:81).…”