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

Abstract

Previous research that compared the estimated parameters (i.e., k and R e ) from Herrnstein's (1970) hyperbolic matching law equation within the same individuals responding for qualitatively different consummatory reinforcers (i.e., water and sucrose solution) found similar asymptotic response rates (k). The present study compared these parameters within subjects responding on levers for consummatory and nonconsummatory reinforcers. Male Wistar rats responded on a lever in a running wheel on a series of tandem FR 1 VI schedules for either 0.1 ml of a 15%sucrose solution or the opportunity to run for 15 sec. Herrnstein's hyperbola was fit to response and reinforcement rates from each session. Results showed that k values were significantly higher for sucrose than for wheel-running reinforcement. On average, R; was lower for sucrose than for wheel-running reinforcement, though not significantly lower. The results of the present study appear to violate the assumption of the constancy of kin Herrnstein's matching law analysis.In Equation 2, B I is the response rate on the single alternative, R I is the reinforcement rate obtained from that alternative, and k and R; are estimated parameters. Specifically, k refers to the asymptotic rate ofresponding (i.e., the maximal response rate), whereas R; is the rate of rein- forcement associated with one halfthe asymptotic rate ofresponding. R, describes how quickly the response rate rises toward asymptote as the reinforcement rate increases, and, at one half the asymptotic response rate (k/2), the value of R; can be estimated because R I and R; are equivalent.Although there is only a single experimenter-arranged source of reinforcement, Herrnstein (1970Herrnstein ( ,1974 assumed that responding for this reinforcement represented the choice between responding for the arranged source and responding for all other sources of reinforcement in the context. In other words, responding on the arranged source ofreinforcement is a function ofthe rate of reinforcement from that alternative, relative to the rate of reinforcement for any behavior other than responding for the arranged reinforcement (e.g., sniffing, grooming, exploring). Accordingly, R; in Equation 1 represents the rate of reinforcement from all sources ofreinforcement in the context, other than that arranged by the experimenter. The parameter k represents both responding (B I) maintained by the arranged source of reinforcement (R I) and responding (Be) maintained by the uncontrolled (i.e., extraneous) sources of reinforcement in the context (R e ) .

Differences in responding for sucrose and wheel-running reinforcement: Excitatory stimulus effects or inhibitory after-effects?

“…The particular importance of these results is that they imply that the difference in response rate asymptotes observed by Belke (1998) for the same reinforcers used in the present study was a function of differences in the efficacy ofthese reinforcers for generating responding rather than differences in satiation or fatigue. Additional evidence consistent with this conclusion comes from research suggesting that fatigue does not contribute substantially to long pauses following wheel running.…”

“…Also, data from the 4 rats that demonstrated higher response rate asymptotes for sucrose in Belke's (1998) study were included in the present study. These 4 animals were maintained under identical conditions and exposed to an experimental procedure similar to that used in this study, but at an earlier date.…”

Local Response Rates on Variable-Ratio Schedules of Wheel-Running Reinforcement are Relatively Invariant Compared to Sucrose

“…Reinforcement rates were calculated based on the time spent responding, exclusive of PRP duration. Belke (1998Belke ( , 2000b subsequently replicated this, finding that response rates plotted as a function of reinforcement rates took the form of a rectangular hyperbola.…”

“…Note that the order of presentation of sucrose and wheel-running reinforcement was not counterbalanced. This raises the possibility of an order effect; however, previous studies using these reinforcers (Belke 1998(Belke , 2010 in which orders were counterbalanced showed no systematic differences between orders.…”

“…Local, rather than overall, response rates were the focus of the investigation, as local rates more accurately reflect changes in the reinforcing efficacy of wheel running. Wheel running generates much longer PRPs than conventional reinforcers (Belke 1998(Belke , 2000bBelke et al 2006), and PRPs are subject to different determinants than are local response rates (Belke 2004). Together, these factors result in overall response rates that are less informative about the reinforcing efficacy of wheel running.…”