Confirmation of linear system theory prediction: Rate of change of Herrnstein's kappa as a function of response-force requirement

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes (¢/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's κ were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) κ increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of κ was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of κ was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's κ.     

Feedback functions, optimization, and the relation of response rate to reinforcer rate

The present experiment arranged a series of inverted U-shaped feedback functions relating reinforcer rate to response rate to test whether responding was consistent with an optimization account or with a one-to-one relation of response rate to reinforcer rate such as linear system theory's rate equation or Herrnstein's hyperbola. Reinforcer rate was arranged according to a quadratic equation with a maximum at a unique response rate. The experiment consisted of two phases, during which 6 Long Evans rats lever pressed for food. In the first phase of the experiment, the rats responded on six fixed-interval-plus-quadratic-feedback schedules, and in the second phase the rats responded on three variable-interval-plus-quadratic-feedback schedules. Responding in both phases was inconsistent with a one-to-one relation of response rate to reinforcer rate. Instead, different response rates were obtained at equivalent reinforcer rates. Responding did vary directly with the vertex of the feedback function in both phases, a finding consistent with optimization of reinforcer rate. The present results suggest that the feedback function relating reinforcer rate to response rate imposed by a reinforcement schedule can be an important determinant of behavior. Furthermore, the present experiment illustrates the benefit of arranging feedback functions to investigate assumptions about the variables that control schedule performance.     

Effects of adding a second reinforcement alternative: implications for Herrnstein's interpretation of r(e)

Herrnstein's hyperbola describes the relation between response rate and reinforcer rate on variable-interval (VI) schedules. According to Herrnstein's (1970) interpretation, the parameter r(e) represents the reinforcer rate extraneous to the alternative to which the equation is fitted (the target alternative). The hyperbola is based on an assumption that extraneous reinforcer rate remains constant with changes in reinforcer rate on the target alternative (the constant-r(e) assumption) and that matching with no bias and perfect sensitivity occurs between response and reinforcer ratios. In the present experiment, 12 rats pressed levers for food on a series of 10 VI schedules arranged on the target alternative. Across conditions, six VI values and extinction were arranged on a second alternative. Reinforcer rate on the second alternative, r2, negatively covaried with reinforcer rate on the target alternative for five of the six VI values on the second alternative, and significant degrees of bias and undermatching occurred in response ratios. Given covariation of reinforcer rate on the second and target alternatives, the constant-r(e) assumption can be maintained only by assuming that reinforcer rate from unmeasured background sources, rb, covaries with reinforcer rate on the second alternative such that their sum, r(e), remains constant. In a single-schedule arrangement, however, r(e) equals rb and thus rb is assumed to remain constant, forcing a conceptual inconsistency between single- and concurrent-schedule arrangements. Furthermore, although an alternative formulation of the hyperbola can account for variations in bias and sensitivity, the modified equation also is based on the constant-r(e) assumption and therefore suffers from the same logical problem as the hyperbola when reinforcer rate on the second alternative covaries with reinforcer rate on the target alternative.     

On the falsifiability of matching theory.

Herrnstein's matching theory requires the parameter, k, which appears in the single-alternative form of the matching equation, to remain invariant with respect to changes in reinforcement parameters like magnitude or immediacy. Recent experiments have disconfirmed matching theory by showing that the invariant-k requirement does not hold. However, the theory can be asserted in a purely algebraic form that does not require an invariant k and that is not disconfirmed by the recent findings. In addition, both the original and the purely algebraic versions of matching theory can be asserted in forms that allow for commonly observed deviations from matching (bias, undermatching, and overmatching). The recent finding of a variable k does not disconfirm these versions of matching theory either. As a consequence, matching remains a viable theory of behavior, the strength of which lies in its general conceptualization of all behavior as choice, and in its unified mathematical treatment of single- and multialternative environments.     

Discrete and contextual cue alterations eliminate the instrumental appetitive-to-aversive transfer impairment in phenytoin-treated rats

We have shown previously that the antiepileptic phenytoin impairs transfer in an instrumental learning task (Banks et al., 1999). The present study examined the effects of contextual alterations on appetitive-to-aversive transfer performance of rats treated with either phenytoin or tang. Adult rats were tested in tone-signaled appetitive and aversive instrumental tasks, where the animal bar-pressed to obtain a food reward (sugar pellet) or to avoid shock. Rats were trained on the appetitive task for 31 days. Beginning on the twenty-first day, rats were gavaged with either phenytoin or tang twice daily. Animals were then transferred to aversive training, with the phenytoin or tang treatment continuing throughout the 25 testing days. For some animals, contextual changes were introduced as they shifted from appetitive to aversive training, while for other animals these changes were not made. Phenytoin-treated rats that were presented with changes in context as they transferred from the appetitive to the aversive task learned the avoidance response to levels substantially higher than drug-treated rats not presented with the contextual changes. These results indicate that phenytoin impairs avoidance learning following transfer from the appetitive task, and that this impairment can be eliminated by introducing changes in context at the point of transfer. In the tang-treated control subjects, on the other hand, there was no improvement in transfer learning performance associated with the changes in contextual cues. This pattern of results suggests that contextual encoding processes in rats being trained in an instrumental appetitive-to-aversive paradigm are dramatically affected by phenytoin.     

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25¢ to 35.0¢ per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.     

All Behavior is choice: Revisiting an evolutionary theory's account of behavior on single schedules

The axiomatic principle that all behavior is choice was incorporated into a revised implementation of an evolutionary theory's account of behavior on single schedules. According to this implementation, target responding occurs in the context of background responding and reinforcement. In Phase 1 of the research, the target responding of artificial organisms (AOs) animated by the revised theory was found to be well described by an exponentiated hyperbola, the parameters of which varied as a function of the background reinforcement rate. In Phase 2, the effect of reinforcer magnitude on the target behavior of the AOs was studied. As in Phase 1, the AOs' behavior was well described by an exponentiated hyperbola, the parameters of which varied with both the target reinforcer magnitude and the background reinforcement rate. Evidence from experiments with live organisms was found to be consistent with the Phase-1 predictions of the revised theory. The Phase-2 predictions have not been tested. The revised implementation of the theory can be used to study the effects of superimposing punishment on single-schedule responding, and it may lead to the discovery of a function that relates response rate to both the rate and magnitude of reinforcement on single schedules.     

DEVELOPING FLUENCY AND ENDURANCE IN A CHILD DIAGNOSED WITH ATTENTION DEFICIT HYPERACTIVITY DISORDER

We examined the effect of a teaching method on skill fluency and on‐task endurance of a 9‐year‐old boy who had been diagnosed with attention deficit hyperactivity disorder. An academic task that occurred at low fluency during 10‐min baseline sessions was taught to fluency. When responding was not yet fluent, brief reversals to baseline showed that the learner's rate of responding decreased and that he did not spend entire sessions on task. However, once a fluency goal had been reached, responding remained fluent and he remained on task in the third reversal condition.