Preference and resistance to change with constant-duration schedule components

Previous research on preference between variable-interval terminal links in concurrent chains has most often used variable-duration terminal links ending with a single reinforcer. By contrast, most research on resistance to change in multiple schedules has used constant-duration components that include variable numbers of reinforcers in each presentation. Grace and Nevin (1997) examined both preference and resistance in variable-duration components; here, preference and resistance were examined in constant-duration components. Reinforcer rates were varied across eight conditions, and a generalized-matching-law analysis showed that initial-link preference strongly over-matched terminal-link reinforcer ratios. In multiple schedules, baseline response rates were unaffected by reinforcer rates, but resistance to intercomponent food, to extinction, and to intercomponent food plus extinction was greater in the richer component. The between-component difference in resistance to change exhibited additive effects for the three resistance tests, and was systematically related to reinforcer ratios. However, resistance was less sensitive to reinforcer ratios than was preference. Resistance to intercomponent food and to intercomponent food plus extinction was more sensitive to reinforcer ratios in the present study than in Grace and Nevin (1997). Thus, relative to variable-duration components, constant-duration components increased the sensitivity of both preference and relative resistance, supporting the proposition that these are independent and convergent measures of the effects of a history of reinforcement.     

Dynamical concurrent schedules

Previous work on the matching law has predominantly focused on the molar effects of the contingency by examining only one reinforcer ratio for extended periods. Responses are distributed as a function of reinforcer ratios under these static conditions. But the outcome under a dynamic condition in which reinforcer ratios change continuously has not been determined. The present study implemented concurrent variable-interval schedules that changed continuously across a fixed 5-min trial. The schedules were reciprocally interlocked. The variable interval for one key changed continuously from a variable-interval 15-s to a variable-interval 480-s, while the schedule for the other key changed from a variable-interval 480-s to a variable-interval 15-s. This dynamical concurrent schedule shifted behavior in the direction of matching response ratios to reinforcer ratios. Sensitivities derived from the generalized matching law were approximately 0.62, the mean absolute bias was approximately 0.11, and r2s were approximately 0.86. It was concluded that choice behavior can come to adapt to reinforcer ratios that change continuously over a relatively short time and that this change does not require extensive experience with a fixed reinforcer ratio. The results were seen as supportive of the view that all behavior constitutes choice.     

An integrative model for the study of behavioral momentum.

Behavioral momentum is the product of response rate and resistance to change. The data on relative resistance to change are summarized for pigeons responding on single-key two-component multiple schedules, in the initial links of two-key multiple chained schedules, and in equivalent components of two-key serial schedules. For single-key procedures, the ratio of resistance to change in two schedule components is shown to depend on the ratio of reinforcer rates obtained in the presence of the component stimuli. For two-key procedures, the ratio of resistance to change in equivalent components is shown to depend on the ratio of reinforcer rates correlated with key locations. A model based on stimulus-reinforcer contingencies that combines the reinforcer rates in schedule components summed over key locations and reinforcer rates correlated with key locations summed over components, each expressed relative to the session average reinforcer rate, gives a good account of the data. An extension of the relative law of effect for multiple schedules fails to provide a complete account of resistance to change, but both approaches are needed for a comprehensive understanding of behavioral momentum.     

Concurrent variable-interval variable-ratio schedules can provide only weak evidence for matching

Herrnstein and Heyman (1979) showed that when pigeons' pecking is reinforced on concurrent variable-interval variable-ratio schedules, (1) their behavior ratios match the ratio of the schedules' reinforcer frequencies, and (2) there is more responding on the variable interval. Since maximizing the reinforcement rate would require responding more on the variable ratio, these results were presented as establishing the primacy of matching over maximizing. In the present report, different ratios of behavior were simulated on a computer to see how they would affect reinforcement rates on these concurrent schedules. Over a wide range of experimenter-specified choice ratios, matching obtained — a result suggesting that changes in choice allocation produced changes in reinforcer frequencies that correspond to the matching outcome. Matching also occurred at arbitrarily selected choice ratios when reinforcement rates were algebraically determined by each schedule's reinforcement-feedback function. Additionally, three birds were exposed to concurrent variable-interval variable-ratio schedules contingent on key pecking in which hopper durations were varied in some conditions to produce experimenter-specified choice ratios. Matching generally obtained between choice ratios and reinforcer-frequency ratios at these different choice ratios. By suggesting that reinforcer frequencies track choice on this procedure, instead of vice versa, this outcome questions whether matching-as-outcome was due to matching-as-process in the Herrnstein and Heyman study.     

Sensitivity of time allocation to an overall reinforcer rate feedback function in concurrent interval schedules

Six pigeons were trained on concurrent variable-interval schedules in which feedback functions arranged that the overall reinforcer rate either (a) was independent of preference, (b) decreased with increasing absolute preference, or (c) increased with increasing absolute preference. In Experiment 1, the reinforcer rate in an interreinforcement interval was determined by the absolute time-allocation ratio in the previous interval. When arranged reinforcer ratios were varied, there was no evidence of control over preference by overall reinforcer rate. In Experiment 2, the feedback function arranged that reinforcer rates were an inverse function of absolute preference, and window durations were fixed times. In Phase 1, using schedules that provided a four-to-one reinforcer ratio, the window duration was decreased from 20 s to 5 s over four conditions. Then, in Phases 2 and 3, the arranged reinforcer ratios were varied. In Phase 2, the reinforcer rate in the current 5-s time window was determined by preference in the previous 5-s window, and in Phase 3, the window durations were 20 s. Again, there was no indication of control by obtained overall reinforcer rate. These data call into question theories that suggest that the process underlying matching is one of maximizing overall reinforcer rates, or that preference in concurrent aperiodic schedules is controlled to any extent by overall reinforcer rate. They also question the notion that concurrent-schedule preference is controlled by molecular maximizing.     

Variable-ratio versus variable-interval schedules: response rate, resistance to change, and preference

Two experiments asked whether resistance to change depended on variable-ratio as opposed to variable-interval contingencies of reinforcement and the different response rates they establish. In Experiment 1, pigeons were trained on multiple random-ratio random-interval schedules with equated reinforcer rates. Baseline response rates were disrupted by intercomponent food, extinction, and prefeeding. Resistance to change relative to baseline was greater in the interval component, and the difference was correlated with the extent to which baseline response rates were higher in the ratio component. In Experiment 2, pigeons were trained on multiple variable-ratio variable-interval schedules in one half of each session and on concurrent chains in the other half in which the terminal links corresponded to the multiple-schedule components. The schedules were varied over six conditions, including two with equated reinforcer rates. In concurrent chains, preference strongly overmatched the ratio of obtained reinforcer rates. In multiple schedules, relative resistance to response-independent food during intercomponent intervals, extinction, and intercomponent food plus extinction depended on the ratio of obtained reinforcer rates but was less sensitive than was preference. When reinforcer rates were similar, both preference and relative resistance were greater for the variable-interval schedule, and the differences were correlated with the extent to which baseline response rates were higher on the variable-ratio schedule, confirming the results of Experiment 1. These results demonstrate that resistance to change and preference depend in part on response rate as well as obtained reinforcer rate, and challenge the independence of resistance to change and preference with respect to response rate proposed by behavioral momentum theory.     

Concurrent-schedule performance: Effects of relative and overall reinforcer rate

Six pigeons were trained to respond on two keys, each of which provided reinforcers on an arithmetic variable-interval schedule. These concurrent schedules ran nonindependently with a 2-s changeover delay. Six sets of conditions were conducted. Within each set of conditions the ratio of reinforcers available on the two alternatives was varied, but the arranged overall reinforcer rate remained constant. Each set of conditions used a different overall reinforcer rate, ranging from 0.22 reinforcers per minute to 10 reinforcers per minute. The generalized matching law fit the data from each set of conditions, but sensitivity to reinforcer frequency (a) decreased as the overall reinforcer rate decreased for both time allocation and response allocation based analyses of the data. Overall response rates did not vary with changes in relative reinforcer rate, but decreased with decreases in overall reinforcer rate. Changeover rates varied as a function of both relative and overall reinforcer rates. However, as explanations based on changeover rate seem unable to deal with the changes in generalized matching sensitivity, discrimination accounts of choice may offer a more promising interpretation.     

The effects of reinforcer magnitude in the preceding and upcoming ratios on between‐ratio pausing in multiple,mixed, and single fixed‐ratio schedules

Hens responded under multiple fixed‐ratio schedules with equal response requirements and either a 1‐s or a 6‐s reinforcer. Upcoming reinforcer size was indicated by key color. Components were presented in a quasirandom series so that all four component transitions occurred. Postreinforcement pauses were affected by the upcoming and preceding reinforcer size, with longer pauses after large reinforcers followed by small reinforcers than when followed by large ones, and longer pauses after small reinforcers that were followed by small reinforcers rather than large ones. Pauses increased with fixed‐ratio size and the effects of reinforcer size were larger the larger the ratio. When reinforcer size was not signaled—mixed fixed‐ratio schedules—pauses were shorter after small than after large reinforcers. Signalling the upcoming reinforcer attenuated the effect of the previous reinforcer size on pause duration when small was followed by small and when either small or large by large, but enhanced the effect when large was followed by small. There was no effect of reinforcer size on pause duration when single fixed‐ratio schedules were arranged. The effects of reinforcer size on pauses depends on the size and range of the fixed ratios as well as the exact procedures used in the study.     

Choice and amount of reinforcement in rats

Rats were exposed to concurrent-chains schedules in which the terminal links were equal, fixed-interval (FI) schedules terminating in one or a varying number of food pellets. In most rats, choice proportions for the larger reinforcer increased with increases in reinforcer amount (e.g., from one to five food pellets). When log response ratios were plotted against log reinforcer amount ratios, the results indicated that the effects of reinforcer amount depended on the length of fixed-interval terminal links, by showing that rats undermatched their response ratios to reinforcer amount ratios with the shorter terminal links (FI 5 s, Experiment 1), whereas they overmatched with the longer terminal links (FI 20 s, Experiment 2). These results demonstrated that the manipulation of FI terminal-link schedules affected the sensitivity of choice to reinforcer amount, and are consistent with the previous findings that choice proportions for the larger of two reinforcers (one vs three food pellets) increased with increases in the length of FI terminal-link schedules.     

Determination of a behavioral transfer function: White-noise analysis of session-to-session response-ratio dynamics on concurrent VI VI schedules

Six pigeons were exposed to concurrent variable-interval schedules in which the programmed reinforcer ratios changed from session to session according to a pseudorandom binary sequence. This procedure corresponded to the stochastic identification paradigm (“white-noise experiment”) of systems theory and enabled the relation between log response ratios in the current session and log reinforcer ratios in all previous sessions to be determined. Such dynamic relations are called linear transfer functions. Both nonparametric and parametric representations of these, in the form of “impulse-response functions,” were determined for each bird. The session-to-session response ratios resulting from the session-to-session pseudorandom binary variations in reinforcer ratios were well predicted by the impulse-response functions identified for each pigeon. The impulse-response functions were well fitted by a second-order dynamic model involving only two parameters: a time constant and a gain. The mean time constant was 0.67 sessions, implying that the effects of abrupt changes in log reinforcer ratios should be 96% complete within about five sessions. The mean gain was 0.53, which was surprisingly low inasmuch as it should equal the sensitivity to reinforcement ratio observed under steady-state conditions. The same six pigeons were subjected to a similar experiment 10 months following the first. Despite individual differences in impulse-response functions between birds within each experiment, the impulse-response functions determined from the two experiments were essentially the same.     

Performance in continuously available multiple schedules

Three pigeons were given continuous access in their home cages to food reinforcement on two-component multiple variable-interval variable-interval schedules. The reinforcer rates in the two components were varied over seven experimental conditions, and a partial replication over five conditions was arranged one year later. When component reinforcer rates were unequal, ratios of component response rates were more extreme than ratios of obtained component reinforcer rates, a result which in a generalized-matching analysis is termed overmatching. This finding contrasts sharply with results obtained when multiple schedules are arranged in shorter sessions, in which performance is characterized by undermatching when subjects are deprived of food, and by matching, or equality between component response- and reinforcer-rate ratios, when deprivation is minimal. More molecular data obtained in two subsequent conditions suggested that this finding did not reflect local fluctuations or asymmetries in deprivation. Theories of multiple-schedule performance that predict that matching cannot be exceeded are disconfirmed by the present results.     

Resistance To Change As A Function Of Stimulus-reinforcer And Location-reinforcer Contingencies

Pigeons responded on two keys in each component of a multiple concurrent schedule. In one series of conditions the distribution of reinforcers between keys within one component was varied so as to produce changes in ratios of reinforcer totals for key locations when summed across components. In a second series, reinforcer allocation between components was varied so as to produce changes in ratios of reinforcer totals for components, summed across key locations. In each condition, resistance to change was assessed by presenting response-independent reinforcers during intercomponent blackouts and (for the first series) by extinction of responding on both keys in both components. Resistance to change for response totals within a component was always greater for the component with the larger total reinforcer rate. However, resistance to change for response totals at a key location was not a positive function of total reinforcement for pecking that key; indeed, relative resistance to extinction for the two locations showed a weak negative relation to ratios of reinforcer totals for key location. These results confirm the determination of resistance to change by stimulus—reinforcer contingencies.     

Choice between repleting/depleting patches: A concurrent-schedule procedure

Six pigeons responded on two concurrently available keys that defined patches with the following characteristics. Reinforcer stores repleted on a patch as a linear function of time when the bird had last responded to the other patch, or else did not replete. Repletion schedules thus timed only when the bird was absent from the patch. Reinforcer stores on a patch could be depleted and reinforcers obtained, again as a linear function of time, when the bird responded on a key. Depletion schedules thus timed only when the birds were present at a patch. Experiment 1 investigated changing relative depletion rates when repletion rates were constant and equal (Part 1) and changing relative repletion rates when the depletion rates were constant and equal (Part 2). Response- and time-allocation ratios conformed to a generalized matching relation with obtained reinforcer ratios, and there appeared to be no control by the size of the reinforcer stores. In Experiment 2, absolute depletion rates were varied with a pair of unequal repletion rates (Part 3), and absolute repletion rates were varied with a pair of unequal depletion rates (Part 4). Dwell times in the patches were not affected by either variation. Melioration theory predicted the results of Experiment 1 quite closely but erroneously predicted changing dwell times in Experiment 2. Molar maximization theory did not accurately predict the results of either experiment.     

Pavlovian contingencies and resistance to change in a multiple schedule

According to theoretical accounts of behavioral momentum, the Pavlovian stimulus—reinforcer contingency determines resistance to change. To assess this prediction, 8 pigeons were exposed to an unsignaled delay-of-reinforcement schedule (a tandem variable-interval fixed-time schedule), a signaled delay-of-reinforcement schedule (a chain variable-interval fixed-time schedule), and an immediate, zero-delay schedule of reinforcement in a three-component multiple schedule. The unsignaled delay and signaled delay schedules employed equal fixed-time delays, with the only difference being a stimulus change in the signaled delay schedule. Overall rates of reinforcement were equated for the three schedules. The Pavlovian contingency was identical for the unsignaled and immediate schedules, and response—reinforcer contiguity was degraded for the unsignaled schedule. Results from two disruption procedures (prefeeding subjects prior to experimental sessions and adding a variable-time schedule to timeout periods separating baseline components) demonstrated that response—reinforcer contiguity does play a role in determining resistance to change. The results from the extinction manipulation were not as clear. Responding in the unsignaled delay component was consistently less resistant to change than was responding in both the immediate and presignaled segments of the signaled delay components, contrary to the view that Pavlovian contingencies determine resistance to change. Probe tests further supported the resistance-to-change results, indicating consistency between resistance to change and preference, both of which are putative measures of response strength.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

Temporal constraint on choice: Sensitivity and bias in multiple schedules

In multiple schedules of reinforcement, ratios of responses in successive components are relatively insensitive to ratios of obtained reinforcers. An analysis is proposed that attributes changes in absolute response rates to concurrent interactions between programmed reinforcement and extraneous reinforcement in other components. The analysis predicts that ratios of responses in successive components vary with reinforcer ratios, qualified by a term describing the reinforcement context, that is, programmed and extraneous reinforcers. Two main predictions from the analysis were confirmed in an experiment in which pigeons' responses were reinforced in the components of a multiple schedule and analog extraneous reinforcement was scheduled for an alternative response in each component. Sensitivity of response and time ratios to reinforcer ratios in the multiple schedules varied as a function of the rate of extraneous reinforcers. Bias towards responding in one component of the multiple schedule varied as an inverse function of the ratios of extraneous reinforcer rate in the two components. The data from this and previous studies of multiple-concurrent performance were accurately predicted by our analysis and supported our contention that the allocation of behavior in multiple-schedule components depends on the relative values of concurrently-available reinforcers within each component.     

Relative reinforcer rates and magnitudes do not control concurrent choice independently

One assumption of the matching approach to choice is that different independent variables control choice independently of each other. We tested this assumption for reinforcer rate and magnitude in an extensive parametric experiment. Five pigeons responded for food reinforcement on switching-key concurrent variable-interval variable-interval schedules. Across conditions, the ratios of reinforcer rates and of reinforcer magnitudes on the two alternatives were both manipulated. Control by each independent variable, as measured by generalized-matching sensitivity, changed significantly with the ratio of the other independent variable. Analyses taking the model-comparison approach, which weighs improvement in goodness-of-fit against increasing number of free parameters, were inconclusive. These analyses compared a model assuming constant sensitivity to magnitude across all reinforcer-rate ratios with two alternative models. One of those alternatives allowed sensitivity to magnitude to vary freely across reinforcer-rate ratios, and was less efficient than the common-sensitivity model for all pigeons, according to the Schwarz-Bayes information criterion. The second alternative model constrained sensitivity to magnitude to be equal for pairs of reinforcer-rate ratios that deviated from unity by proportionately equal amounts but in opposite directions. This model was more efficient than the common-magnitude-sensitivity model for 2 of the pigeons, but not for the other 3. An analysis of variance, carried out independently of the generalized-matching analysis, also showed a significant interaction between the effects of reinforcer rate and reinforcer magnitude on choice. On balance, these results suggest that the assumption of independence inherent in the matching approach cannot be maintained. Relative reinforcer rates and magnitudes do not control choice independently.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.