The present study compared four prominent models of delay discounting: a one-parameter exponential decay, a one-parameter hyperbola (Mazur, 1987), a two-parameter hyperboloid in which the denominator is raised to a power (Green and Myerson, 2004), and a two-parameter hyperbola in which delay is raised to a power (Rachlin, 2006). Sixty-four college undergraduates made choices between hypothetical monetary rewards, one immediate and one delayed, and the fit of the four models to their data was assessed. All four equations accounted for a large proportion of the variance at both the group and the individual levels, but the exponents of both two-parameter models were significantly less than 1.0 at the group level, and frequently so at the individual level. Taken together, these results strongly suggest that more than one parameter is needed to accurately describe delay discounting by humans. Notably, both the Rachlin and the Green and Myerson models accounted for more than 99% of the variance at the group level and for 96% of the variance in the median individual. Because both models provide such good descriptions of the data, model selection will need to be based on other grounds.

The interresponse-time structures of pigeon key pecking were examined under variable-ratio, variableinterval, and variable-interval plus linear feedback schedules. Whereas the variable-ratio and variableinterval plus linear feedback schedules generally resulted in a distinct group of short interresponse times and a broad distribution of longer interresponse times, the variable-interval schedules generally showed a much more continuous distribution of interresponse times. The results were taken to indicate that a log survivor analysis or double exponential fit of interresponse times may not be universally applicable to the task of demonstrating that operant behavior can be dichotomized into bouts of engagement and periods of disengagement.Key words: interresponse time, variable-ratio, variable-interval, yoked schedules, Shull machine, key peck, pigeonsIn the past, the conceptualization of behavior as two-state (Gilbert, 1958) has not enjoyed widespread research interest because of the difficulty in validly dichotomizing the behavior stream into visits and nonvisits by simply specifying some specific interresponse time (IRT) duration as a criterion. The split between within-visit IRTs and visit-initiation IRTs is unlikely to be at the same value across individuals, or even within an individual across procedures.Shull, Gaynor, and Grimes (2001) described one possible solution for resolving the categorization problem. They displayed the total distribution of obtained IRTs as a survivor plot with a logarithmically scaled y axis. In this semilogarithmic plot, the slope between any two points on the x axis is an indicator of the relative decrease in the frequency of the IRTs per opportunity between those points. If a single exponential decay governed the occurrence of all responding, then the IRT distribution would appear as a single straight line. If, on the other hand, behavior occurred in short bouts of responding separated by longer delays, then the short IRTs governed by one exponential decay process would result in an initial steep slope, while the longer delays between response bouts characterized by a different exponential would be spread across a broad range of values and would generate a second shallower slope.Shull and his colleagues (Shull et al., 2001) found that the log survivor plots of the output of their explicitly two-state emulator had two relatively straight lines intersecting at an angle less than 180u, or had a ''broken-stick'' appearance, such that the function and therefore the two classes of behavior were easily dichotomized by simple inspection. Figure 1 provides example log survivor plots of the output of Shull's model. The ratio of the within-visit response rate to the between-visit response rate and the probability of disengaging are given above each frame. The columns of frames illustrate how increasing the relative value of the probability of entering the engaged state, p(V), with respect to the probability of a response during a visit, p(R), (i.e., larger ratios of within-visit to the be...

BackgroundOperant hyperactivity, the emission of reinforced responses at an inordinately high rate, has been reported in children with ADHD and in the Spontaneously Hypertensive Rat (SHR), the most widely studied animal model of ADHD. The SHR emits behavior at hyperactive levels, relative to a normoactive strain, only when such behavior is seldom reinforced. Because of its dependence on rate of reinforcement, operant hyperactivity appears to be driven primarily by incentive motivation, not motoric capacity. This claim was evaluated in the present study using a novel strategy, based on the organization of behavior in bouts of reinforced responses separated by pauses.MethodMale SHR, Wistar-Kyoto (WKY) and Wistar rats (WIS) were exposed each to a multiple variable-interval schedule of sucrose reinforcement (12, 24, 48, 96, and 192 s) between post-natal days (PND) 48 and 93. Responding in each schedule was examined in two epochs, PND 58-62 and 89-93. Parameters of response-reinforcement functions (Herrnstein's hyperbola) and bout-organized behavior were estimated in each epoch.ResultsSHR emitted higher response rates than WKY and WIS, but only when rate of reinforcement was low (fewer than 2 reinforcers per minute), and particularly in the second epoch. Estimates of Herrnstein's hyperbola parameters suggested the primacy of motivational over motoric factors driving the response-rate differential. Across epochs and schedules, a more detailed analysis of response bouts by SHR revealed that these were shorter than those by WKY, but more frequent than those by WKY and WIS. Differences in bout length subsided between epochs, but differences in bout-initiation rate were exacerbated. These results were interpreted in light of robust evidence linking changes in bout-organization parameters and experimental manipulations of motivation and response-reinforcement contingency.ConclusionsOperant hyperactivity in SHR was confirmed. Although incentive motivation appears to play an important role in operant hyperactivity and motoric capacity cannot be ruled out as a factor, response-bout patterns suggest that operant hyperactivity is primarily driven by steeper delay-of-reinforcement gradients. Convergence of this conclusion with theoretical accounts of ADHD and with free-operant performance in children with ADHD supports the use of SHR as an animal model of ADHD.

Rationale The ability to withhold reinforced responses—behavioral inhibition—is impaired in various psychiatric conditions including Attention Deficit Hyperactivity Disorder (ADHD). Methodological and analytical limitations have constrained our understanding of the effects of pharmacological and environmental factors on behavioral inhibition. Objectives To determine the effects of acute methylphenidate (MPH) administration and rearing conditions (isolated vs. pair-housed) on behavioral inhibition in adult rats. Methods Inhibitory capacity was evaluated using two response-withholding tasks, differential reinforcement of low rates (DRL) and fixed minimum interval (FMI) schedules of reinforcement. Both tasks made sugar pellets contingent on intervals longer than 6 s between consecutive responses. Inferences on inhibitory and timing capacities were drawn from the distribution of withholding times (interresponse times, or IRTs). Results MPH increased the number of intervals produced in both tasks. Estimates of behavioral inhibition increased with MPH dose in FMI and with social isolation in DRL. Nonetheless, burst responding in DRL and the divergence of DRL data relative to past studies, among other limitations, undermined the reliability of DRL data as the basis for inferences on behavioral inhibition. Conclusions Inhibitory capacity was more precisely estimated from FMI than from DRL performance. Based on FMI data, MPH, but not a socially enriched environment, appears to improve inhibitory capacity. The highest dose of MPH tested, 8 mg/kg, did not reduce inhibitory capacity but reduced the responsiveness to waiting contingencies. These results support the use of the FMI schedule, complemented with appropriate analytic techniques, for the assessment of behavioral inhibition in animal models.

BackgroundDeficient operant extinction has been hypothesized to be constitutive of ADHD dysfunction. In order to elucidate the behavioral mechanisms underlying this deficit, the performance of an animal model of ADHD, the spontaneously hypertensive rat (SHR), was compared against the performance of a control strain, the Wistar-Kyoto rat (WKY) during extinction.MethodFollowing extensive training of lever pressing under variable interval schedules of food reinforcement (reported previously), SHR and WKY rats were exposed to two sessions of extinction training. Extinction data was analyzed using the Dynamic Bi-Exponential Refractory Model (DBERM) of operant performance. DBERM assumes that operant responses are organized in bouts separated by pauses; during extinction, bouts may decline across multiple dimensions, including frequency and length. DBERM parameters were estimated using hierarchical Bayesian modeling.ResultsSHR responded more than WKY during the first extinction session. DBERM parameter estimates revealed that, at the onset of extinction, SHR produced more response bouts than WKY. Over the course of extinction, response bouts progressively shortened for WKY but not for SHR.ConclusionsBased on prior findings on the sensitivity of DBERM parameters to motivational and schedule manipulations, present data suggests that (1) more frequent response bouts in SHR are likely related to greater incentive motivation, and (2) the persistent length of bouts in SHR are likely related to a slower updating of the response-outcome association. Overall, these findings suggest specific motivational and learning deficits that may explain ADHD-related impairments in operant performance.