Behavioral momentum theory fails to account for the effects of reinforcement rate on resurgence

The behavioral‐momentum model of resurgence predicts reinforcer rates within a resurgence preparation should have three effects on target behavior. First, higher reinforcer rates in baseline (Phase 1) produce more persistent target behavior during extinction plus alternative reinforcement. Second, higher rate alternative reinforcement during Phase 2 generates greater disruption of target responding during extinction. Finally, higher rates of either reinforcement source should produce greater responding when alternative reinforcement is suspended in Phase 3. Recent empirical reports have produced mixed results in terms of these predictions. Thus, the present experiment further examined reinforcer‐rate effects on persistence and resurgence. Rats pressed target levers for high‐rate or low‐rate variable‐interval food during Phase 1. In Phase 2, target‐lever pressing was extinguished, an alternative nose‐poke became available, and nose‐poking produced either high‐rate variable‐interval, low‐rate variable‐interval, or no (an extinction control) alternative reinforcement. Alternative reinforcement was suspended in Phase 3. For groups that received no alternative reinforcement, target‐lever pressing was less persistent following high‐rate than low‐rate Phase‐1 reinforcement. Target behavior was more persistent with low‐rate alternative reinforcement than with high‐rate alternative reinforcement or extinction alone. Finally, no differences in Phase‐3 responding were observed for groups that received either high‐rate or low‐rate alternative reinforcement, and resurgence occurred only following high‐rate alternative reinforcement. These findings are inconsistent with the momentum‐based model of resurgence. We conclude this model mischaracterizes the effects of reinforcer rates on persistence and resurgence of operant behavior.     

A COMPUTATIONAL THEORY OF SELECTION BY CONSEQUENCES APPLIED TO CONCURRENT SCHEDULES

Virtual organisms animated by a computational theory of selection by consequences responded on symmetrical and asymmetrical concurrent schedules of reinforcement. The theory instantiated Darwinian principles of selection, reproduction, and mutation such that a population of potential behaviors evolved under the selection pressure exerted by reinforcement from the environment. The virtual organisms' steady‐state behavior was well described by the power function matching equation, and the parameters of the equation behaved in ways that were consistent with findings from experiments with live organisms. Together with previous research on single‐alternative schedules (McDowell, 2004; McDowell & Caron, 2007) these results indicate that the equations of matching theory are emergent properties of the evolutionary dynamics of selection by consequences.     

Stimulus–reinforcer relations established during training determine resistance to extinction and relapse via reinstatement

The baseline rate of a reinforced target response decreases with the availability of response‐independent sources of alternative reinforcement; however, resistance to disruption and relapse increases. Because many behavioral treatments for problem behavior include response‐dependent reinforcement of alternative behavior, the present study assessed whether response‐dependent alternative reinforcement also decreases baseline response rates but increases resistance to extinction and relapse. We reinforced target responding at equal rates across two components of a multiple schedule with pigeons. We compared resistance to extinction and relapse via reinstatement of (1) a target response trained concurrently with a reinforced alternative response in one component with (2) a target response trained either concurrently or in separate components from the alternative response across conditions. Target response rates trained alone in baseline were higher but resistance to extinction and relapse via reinstatement tests were greater after training concurrently with the alternative response. In another assessment, training target and alternative responding together, but separating them during extinction and reinstatement tests, produced equal resistance to extinction and relapse. Together, these findings are consistent with behavioral momentum theory—operant response–reinforcer relations determined baseline response rates but Pavlovian stimulus–reinforcer relations established during training determined resistance to extinction and relapse. These findings imply that reinforcing alternative behavior to treat problem behavior could initially reduce rates but increase persistence.     

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.     

Reinforcer magnitude (sucrose concentration) and the matching law theory of response strength

This experiment investigated the relationship between reinforcer magnitude (sucrose concentration) and response rate. The purpose was to evaluate the behavior of two parameters of an equation that predicts absolute response rate as a function of reinforcement rate and two free parameters. According to Herrnstein's (1970) theory of reinforced behavior, one parameter of this "response-strength equation" measures the efficacy of the reinforcer maintaining responding and the other parameter measures motoric components of response rate, such as response duration. Seven rats served as subjects. Experimental sessions consisted of a series of five different variable-interval schedules of reinforcement, each in effect for 5 minutes. Within each session, obtained reinforcement rates varied over more than a 30-fold range, from about 20 per hour to 700 per hour. The reinforcer was sucrose solution, and, between sessions, its concentration was varied from 0.0 to 0.64 molar (0 to 21.9%). For sucrose concentrations of 0.16 to 0.64 m, response rate was a negatively accelerated function of reinforcement rate. Increases in sucrose concentration increased response rates maintained by low but not high reinforcement rates. This pattern of changes corresponds to a change in the reinforcement-efficacy parameter of the response-strength equation. In contrast, the motor-performance parameter did not change as a function of sucrose concentration. These findings are inconsistent with the results of a similar study (Bradshaw, Szabadi, & Bevan, 1978) but support Herrnstein's theory of reinforced behavior.     

Experience with dynamic reinforcement rates decreases resistance to extinction

The ability of organisms to detect reinforcer‐rate changes in choice preparations is positively related to two factors: the magnitude of the change in rate and the frequency with which rates change. Gallistel (2012) suggested similar rate‐detection processes are responsible for decreases in responding during operant extinction. Although effects of magnitude of change in reinforcer rate on resistance to extinction are well known (e.g., the partial‐reinforcement‐extinction effect), effects of frequency of changes in rate prior to extinction are unknown. Thus, the present experiments examined whether frequency of changes in baseline reinforcer rates impacts resistance to extinction. Pigeons pecked keys for variable‐interval food under conditions where reinforcer rates were stable and where they changed within and between sessions. Overall reinforcer rates between conditions were controlled. In Experiment 1, resistance to extinction was lower following exposure to dynamic reinforcement schedules than to static schedules. Experiment 2 showed that resistance to presession feeding, a disruptor that should not involve change‐detection processes, was unaffected by baseline‐schedule dynamics. These findings are consistent with the suggestion that change detection contributes to extinction. We discuss implications of change‐detection processes for extinction of simple and discriminated operant behavior and relate these processes to the behavioral‐momentum based approach to understanding extinction.     

Behavioral momentum and resistance to extinction across repeated extinction tests

The present experiments assessed whether resistance to extinction of pigeons' key pecking decreased across repeated extinction tests. An additional impetus for this research was to determine how the quantitative framework provided by behavioral momentum theory might be used to describe any such changes across tests. Pigeons pecked keys in two‐component multiple schedules (one component associated with a higher reinforcer rate and the other with a lower rate) in which baseline and extinction conditions alternated. In Experiment 1, baseline and extinction conditions alternated every session, and, in Experiment 2, these conditions lasted for 10 and 7 sessions, respectively. Resistance to extinction decreased across successive extinction conditions in both experiments. Fits of the behavioral‐momentum based model of extinction to the data returned uncertain results in Experiment 1 but implicated both generalization decrement and response–reinforcer contingency termination as the possible mechanisms responsible for behavior change in Experiment 2. Thus, these data suggest that experimental manipulations that affect discrimination of changes in reinforcement contingencies may influence resistance to extinction by modulating the disruptive impacts of removing reinforcers from the experimental context and of suspending response–reinforcer contingencies.     

Effects of signaled and unsignaled alternative reinforcement on persistence and relapse in children and pigeons

Three experiments explored the impact of different reinforcer rates for alternative behavior (DRA) on the suppression and post‐DRA relapse of target behavior, and the persistence of alternative behavior. All experiments arranged baseline, intervention with extinction of target behavior concurrently with DRA, and post‐treatment tests of resurgence or reinstatement, in two‐ or three‐component multiple schedules. Experiment 1, with pigeons, arranged high or low baseline reinforcer rates; both rich and lean DRA schedules reduced target behavior to low levels. When DRA was discontinued, the magnitude of relapse depended on both baseline reinforcer rate and the rate of DRA. Experiment 2, with children exhibiting problem behaviors, arranged an intermediate baseline reinforcer rate and rich or lean signaled DRA. During treatment, both rich and lean DRA rapidly reduced problem behavior to low levels, but post‐treatment relapse was generally greater in the DRA‐rich than the DRA‐lean component. Experiment 3, with pigeons, repeated the low‐baseline condition of Experiment 1 with signaled DRA as in Experiment 2. Target behavior decreased to intermediate levels in both DRA‐rich and DRA‐lean components. Relapse, when it occurred, was directly related to DRA reinforcer rate as in Experiment 2. The post‐treatment persistence of alternative behavior was greater in the DRA‐rich component in Experiment 1, whereas it was the same or greater in the signaled‐DRA‐lean component in Experiments 2 and 3. Thus, infrequent signaled DRA may be optimal for effective clinical treatment.     

Resurgence and alternative‐reinforcer magnitude

Resurgence is defined as an increase in the frequency of a previously reinforced target response when an alternative source of reinforcement is suspended. Despite an extensive body of research examining factors that affect resurgence, the effects of alternative‐reinforcer magnitude have not been examined. Thus, the present experiments aimed to fill this gap in the literature. In Experiment 1, rats pressed levers for single‐pellet reinforcers during Phase 1. In Phase 2, target‐lever pressing was extinguished, and alternative‐lever pressing produced either five‐pellet, one‐pellet, or no alternative reinforcement. In Phase 3, alternative reinforcement was suspended to test for resurgence. Five‐pellet alternative reinforcement produced faster elimination and greater resurgence of target‐lever pressing than one‐pellet alternative reinforcement. In Experiment 2, effects of decreasing alternative‐reinforcer magnitude on resurgence were examined. Rats pressed levers and pulled chains for six‐pellet reinforcers during Phases 1 and 2, respectively. In Phase 3, alternative reinforcement was decreased to three pellets for one group, one pellet for a second group, and suspended altogether for a third group. Shifting from six‐pellet to one‐pellet alternative reinforcement produced as much resurgence as suspending alternative reinforcement altogether, while shifting from six pellets to three pellets did not produce resurgence. These results suggest that alternative‐reinforcer magnitude has effects on elimination and resurgence of target behavior that are similar to those of alternative‐reinforcer rate. Thus, both suppression of target behavior during alternative reinforcement and resurgence when conditions of alternative reinforcement are altered may be related to variables that affect the value of the alternative‐reinforcement source.     

Melioration revisited: a systematic replication of Vaughan (1981)

Organisms that behave so as to forfeit a relatively higher overall rate of reinforcement in favor of a relatively lower rate are said to engage in suboptimal choice. Suboptimal choice has been linked with maladaptive behavior in humans. Melioration theory offers one explanatory framework for suboptimal choice. Melioration theory suggests behavior is controlled by differences in local reinforcer rates between alternatives. Vaughan (1981) arranged two experimental conditions in which maximizing the overall rate of reinforcement required behavior that was compatible, or incompatible, with melioration. Vaughan found pigeons allocated more time to a locally richer alternative even when doing so resulted in suboptimal choice. However, Vaughan did not show whether these effects could systematically reverse and did not provide within‐session data to show that choice across short time spans remains under the control of differences in local reinforcer rates. The present study used pigeons to replicate and extend Vaughan's findings. We investigated shifts in overall‐ and within‐session choice across repeated conditions, according to arranged local contingencies. Behavior systematically followed changes in local contingencies for most pigeons. Within‐session data suggests that, providing differences in local reinforcer rates are discriminated, pigeons will allocate more time to a locally richer alternative, even if this leads to suboptimal choice. These findings facilitate the more confident use of similar procedures that investigate how melioration contributes to suboptimal choice.     

Reinforcer pathology II: Reward magnitude,reward delay,and demand for alcohol collectively relate to college students' alcohol related problems

The reinforcer pathologies model of addiction posits that two characteristic patterns of operant behavior characterize addiction. Specifically, individuals suffering from addiction have elevated levels of behavioral economic demand for their substances of abuse and have an elevated tendency to devalue delayed rewards (reflected in high delay discounting rates). Prior research has demonstrated that these behavioral economic markers are significant predictors of many of college students' alcohol-related problems. Delay discounting, however, is a complex behavioral performance likely undergirded by multiple behavioral processes. Emerging analytical approaches have isolated the role of participants' sensitivity to changes in reinforcer magnitude and changes in reinforcer delay. The current study uses these analytic approaches to compare participants' discounting of money versus alcohol, and to build regression models that leverage these new insights to predict a wider range of college students' alcohol related problems. Using these techniques, we were able to 1) demonstrate that individuals differed in their sensitivity to magnitudes of alcohol versus money, but not sensitivity to delays to those commodities and 2) that we could use our behavioral economic measures to predict a range of students' alcohol related problems.     

Contrast and reallocation of extraneous reinforcers between multiple-schedule components

Four pigeons responded in components of multiple schedules in which two responses were available and reinforced with food. Pecks on the left key (“main” key) were reinforced at a constant rate in one component and at a rate that varied over conditions in the other component. When reinforcer rate was varied, behavioral contrast occurred in the constant component. On the right key (“extra” key), five variable-interval schedules and one variable-ratio schedule, presented conjointly, arranged reinforcers for responses in all conditions. These conjoint schedules were common to both multiple-schedule components—rather than unique to particular components—and reinforcers from these schedules could therefore be arranged in one component and obtained during the other component. In this way, the additional reinforcers were analogous to the “extraneous” reinforcers thought to maintain behavior other than pecking in conventional multiple schedules. Response rate on the extra key did not change systematically over conditions in the constant component, and in the varied component extra responding was inversely related to main-key reinforcement. All subjects obtained more extra-key reinforcers in whichever component arranged fewer main-key reinforcers. Consistent with the theory that reallocation of extraneous reinforcers may cause behavioral contrast, absolute reinforcer rate for the extra key in the constant component was low in conditions that produced positive contrast on the main key and high in those that produced negative contrast. Also consistent with this theory, behavioral contrast was reduced in two conditions that canceled extra-key reinforcers that had been arranged but not obtained at the end of components. Thus, a constraint on reallocation markedly reduced the extent of contrast.     

THE DYNAMICS OF THE LAW OF EFFECT: A COMPARISON OF MODELS

Dynamical models based on three steady‐state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two‐component functions law‐of‐effect equations performed better than models based on Herrnstein's (1970) and Davison and Hunter's (1976) equations. Navakatikyan's model successfully described the behavioral dynamics in schedules with negative‐slope feedback functions, concurrent variable‐ratio schedules, Vaughan's (1981) melioration experiment, and experiments that arranged equal, and constant‐ratio unequal, local reinforcer rates.     

Parent‐conducted rapid assessment of attention types for the treatment of attention‐maintained problem behavior

When praise is not a reinforcer for alternative behavior in the treatment of attention‐maintained problem behavior, further pretreatment assessments are warranted to develop an effective treatment. The current study reports a replication of the pretreatment rapid assessment of attention types (RAAT) procedures, implemented by the parents of a 19‐year‐old female with attention‐maintained problem behavior. After administering staff and parent‐conducted RAATs, a parent‐implemented treatment, (a) produced clinically significant decreases in problem behavior, and (b) confirmed that the RAAT identified an attention‐type that served as a reinforcer for appropriate alternative behavior. This study extends the findings of Strohmeier et al. by reporting results of a parent‐conducted RAAT and treatment evaluation. The findings highlight the practical importance of pretreatment assessment of attention‐types, with emphasis on caregiver involvement, to develop effective treatments for attention‐maintained problem behavior.     

Effects of reinforcer consumption and magnitude on response rates during noncontingent reinforcement

Results of previous research on the effects of noncontingent reinforcement (NCR) have been inconsistent when magnitude of reinforcement was manipulated. We attempted to clarify the influence of NCR magnitude by including additional controls. In Study 1, we examined the effects of reinforcer consumption time by comparing the same magnitude of NCR when session time was and was not corrected to account for reinforcer consumption. Lower response rates were observed when session time was not corrected, indicating that reinforcer consumption can suppress response rates. In Study 2, we first selected varying reinforcer magnitudes (small, medium, and large) on the basis of corrected response rates observed during a contingent reinforcement condition and then compared the effects of these magnitudes during NCR. One participant exhibited lower response rates when large-magnitude reinforcers were delivered; the other ceased responding altogether even when small-magnitude reinforcers were delivered. We also compared the effects of the same NCR magnitude (medium) during 10-min and 30-min sessions. Lower response rates were observed during 30-min sessions, indicating that the number of reinforcers consumed across a session can have the same effect as the number consumed per reinforcer delivery. These findings indicate that, even when response rate is corrected to account for reinforcer consumption, larger magnitudes of NCR (defined on either a per-delivery or per-session basis) result in lower response rates than do smaller magnitudes.     

Accumulated reinforcers increase academic responding and suppress problem behavior for students with Attention‐Deficit Hyperactivity Disorder

We compared rates of academic responses and problem behavior during mathematics with distributed and accumulated reinforcer arrangements for 3 students with Attention‐Deficit Hyperactivity Disorder who engaged in chronic, severe problem behavior. All 3 students engaged in more academic responding and less problem behavior when reinforcers accumulated throughout the session, relative to conditions in which reinforcers were distributed throughout the session or withheld completely. We then conducted concurrent‐chain analyses to evaluate student preference for the reinforcer arrangements. Two students preferred distributed reinforcers, even though this arrangement continued to produce problem behavior. One student preferred accumulated reinforcers. Our data replicate previous findings regarding the efficacy of accumulated‐reinforcer arrangements, but suggest that students do not always prefer the most efficacious reinforcer arrangement.     

Zebrafish choice behavior is sensitive to reinforcer rate,immediacy, and magnitude ratios

Behavioral flexibility has, in part, been defined by choice behavior changing as a function of changes in reinforcer payoffs. We examined whether the generalized matching law quantitatively described changes in choice behavior in zebrafish when relative reinforcer rates, delays/immediacy, and magnitudes changed between two alternatives across conditions. Choice was sensitive to each of the three reinforcer properties. Sensitivity estimates to changes in relative reinforcer rates were greater when 2 variable-interval schedules were arranged independently between alternatives (Experiment 1a) than when a single schedule pseudorandomly arranged reinforcers between alternatives (Experiment 1b). Sensitivity estimates for changes in relative reinforcer immediacy (Experiment 2) and magnitude (Experiment 3) were similar but lower than estimates for reinforcer rates. These differences in sensitivity estimates are consistent with studies examining other species, suggesting flexibility in zebrafish choice behavior in the face of changes in payoff as described by the generalized matching law.     

Resurgence Following Higher or Lower Quality Alternative Reinforcement

Resurgence is a temporary increase in a previously suppressed target behavior following a worsening in reinforcement conditions. Previous studies have examined how higher rates or magnitudes of alternative reinforcement affect suppression of the target behavior and subsequent resurgence. However, there has been no investigation of the effects of higher versus lower qualities of alternative reinforcement on resurgence. Using a three-phase resurgence preparation with rats, the present experiments examined the effects of an alternative reinforcer that was of higher (Experiment 1) or lower (Experiment 2) quality than the reinforcer that had previously maintained the target behavior. The results of both experiments showed greater reductions in target behavior with a higher quality alternative reinforcer and larger increases in target responding when a higher quality alternative reinforcer was removed. Along with prior findings with higher rates and magnitudes of alternative reinforcement, these findings suggest that variations in reinforcer dimensions that increase the efficacy of alternative reinforcement also tend to increase resurgence when alternative reinforcement is removed. The results are discussed in terms of the resurgence as choice in context model and in terms of potential clinical implications.