Temporal constraint on choice: Sensitivity and bias in multiple schedules

Choosing a future from a murky past: A generalization-based model of behavior

Remembering the past appears critical in allowing organisms to detect order in an environment, and hence to behave in accordance with likely future events. Yet the shortcomings of remembering and perceiving typically mean that the remembered past differs from the actual past, and hence that behavior does not perfectly track the structure of the environment. Here, we outline how the process of generalization might be used to understand differences between what an organism does, and the structure of the past and potential structure of the environment. We explore how different sources of generalization - both from within the same stimulus situation, and from different stimulus situations - might be modeled quantitatively, and how predictions made by this modeling approach are supported by research. Finally, we discuss how generalization from multiple stimulus situations, longer-term experience, and from stimulus situations in the past that are not identical to the stimulus situation in the present, might contribute to our understanding of how an organism's experience translates into behavior.

Relative reinforcer rates determine pigeons' attention allocation when separately trained stimuli are presented together

Previous research suggests that organisms allocate more attention to stimuli associated with higher reinforcer rates. This finding has been replicated several times when stimuli are trained together as compounds, but not in other procedures. Thus, the generality of the relation between relative reinforcer rates and divided attention is not well established. Therefore, we investigated whether relative reinforcer rates determine attention allocation when stimuli are trained separately and then encountered together. Pigeons learned to associate two colors and two frequencies of key light on/off alternation with a left or right comparison key in a symbolic 0-s delayed matching-to-sample task. Across conditions, we varied the probability of reinforcement associated with each stimulus dimension during training. After training, we introduced test trials in which a color and flash-frequency stimulus were presented simultaneously. During sample-stimulus presentation in test trials, all pigeons preferred the stimulus associated with the higher reinforcer rate, suggesting that more attention was allocated to that stimulus. Interestingly, such attention allocation did not result in preference for the comparison that matched that stimulus. Instead, all pigeons preferred the comparison that was physically closer to the stimulus associated with the higher reinforcer rate, suggesting that comparison choice was controlled by the location of that stimulus. Nevertheless, overall, our results provide the first evidence that relative reinforcer rates determine divided attention between separately trained stimuli and thus demonstrate the generality of the relation between relative reinforcement and attention allocation. We suggest several avenues for future research to establish further the generality of this relation.

Response strength in extreme multiple schedules

Four pigeons were trained in a series of two-component multiple schedules. Reinforcers were scheduled with random-interval schedules. The ratio of arranged reinforcer rates in the two components was varied over 4 log units, a much wider range than previously studied. When performance appeared stable, prefeeding tests were conducted to assess resistance to change. Contrary to the generalized matching law, logarithms of response ratios in the two components were not a linear function of log reinforcer ratios, implying a failure of parameter invariance. Over a 2 log unit range, the function appeared linear and indicated undermatching, but in conditions with more extreme reinforcer ratios, approximate matching was observed. A model suggested by McLean (1991), originally for local contrast, predicts these changes in sensitivity to reinforcer ratios somewhat better than models by Herrnstein (1970) and by Williams and Wixted (1986). Prefeeding tests of resistance to change were conducted at each reinforcer ratio, and relative resistance to change was also a nonlinear function of log reinforcer ratios, again contrary to conclusions from previous work. Instead, the function suggests that resistance to change in a component may be determined partly by the rate of reinforcement and partly by the ratio of reinforcers to responses.

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 cent to 35.0 cent 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.

Successive independence of multiple-schedule component performances

In three experiments, pigeons' responses were reinforced on two keys in each component of a series of multiple-schedule conditions. In each series, concurrent variable-interval schedules were constant in one component and were varied over conditions in the other component. In the first experiment both components arranged the same, constant total number of reinforcers, in the second the two components arranged constant but different totals, and in the third experiment the total was varied in one component and remained constant in the other. Relative reinforcer rate during the varied component was manipulated over conditions in all three experiments. In all these experiments, response and time allocation in the constant component were invariant when reinforcer ratios varied in the other component, demonstrating independence of behavior allocation in a multiple-schedule component from the relative reinforcer rate for the same alternatives in another component. In the two experiments which maintained constant reinforcer totals in components, sensitivity to reinforcement in the multiple schedules was the same as that in the concurrent schedules arranged during the varied component, with multiple-schedule bias in the experiment in which the totals were unequal.

Resistance to change and the law of effect

Three experiments using multiple schedules of reinforcement explored the implications of resistance-to-change findings for the response-reinforcer relation described by the law of effect, using both steady-state responding and responding recorded in the first few sessions of conditions. In Experiment 1, when response-independent reinforcement was increased during a third component, response rate in Components 1 and 2 decreased. This response-rate reduction was proportionately greater in a component in which reinforcer magnitude was small (2-s access to wheat) than in the component in which it was large (6-s access to wheat). However, when reinforcer rates in the two components were varied together in Experiments 2 and 3, response-rate change was the same regardless of the magnitude of reinforcers used in the two components, so that sensitivity of response rates to reinforcer rates (Experiment 2) and of response-rate ratios to reinforcer-rate ratios (Experiment 3) was unaffected by the magnitude of the reinforcers. Therefore, the principles determining resistance to change, described by behavioral momentum theory, seem not to apply when the source of behavior change is the variation of reinforcement contingencies that maintain the behavior. The use of extinction as a manipulation to study resistance to change is questioned.

A quantitative analysis of chain-schedule performance

Six pigeons were trained with a chain variable-interval variable-interval schedule on the left key and with reinforcers available on the right key on a single variable-interval schedule arranged concurrently with both links of the chain. All three schedules were separately and systematically varied over a wide range of mean intervals. During these manipulations, the obtained reinforcer rates on constant arranged schedules also frequently changed systematically. Increasing reinforcer rates in Link 2 of the chain increased response rates in both links and decreased response rates in the variable-interval schedule concurrently available with Link 2. Increasing Link-1 reinforcer rates increased Link-1 response rates and decreased Link-2 response rates. Increasing reinforcer rates on the right-key schedule decreased response rates in Link 1 of the chain but did not affect the rate in Link 2. The results extend and amplify previous analyses of chain-schedule performance and help define the effects that a quantitative model must describe. However, the complexity of the results, and the fact that constant arranged reinforcer schedules did not necessarily lead to constant obtained reinforcer rates, precluded a quantitative analysis.

Resistance to reinforcement change in multiple and concurrent schedules assessed in transition and at steady state

Behavioral momentum theory relates resistance to change of responding in a multiple-schedule component to the total reinforcement obtained in that component, regardless of how the reinforcers are produced. Four pigeons responded in a series of multiple-schedule conditions in which a variable-interval 40-s schedule arranged reinforcers for pecking in one component and a variable-interval 360-s schedule arranged them in the other. In addition, responses on a second key were reinforced according to variable-interval schedules that were equal in the two components. In different parts of the experiment, responding was disrupted by changing the rate of reinforcement on the second key or by delivering response-independent food during a blackout separating the two components. Consistent with momentum theory, responding on the first key in Part 1 changed more in the component with the lower reinforcement total when it was disrupted by changes in the rate of reinforcement on the second key. However, responding on the second key changed more in the component with the higher reinforcement total. In Parts 2 and 3, responding was disrupted with free food presented during intercomponent blackouts, with extinction (Part 2) or variable-interval 80-s reinforcement (Part 3) arranged on the second key. Here, resistance to change was greater for the component with greater overall reinforcement. Failures of momentum theory to predict short-term differences in resistance to change occurred with disruptors that caused greater change between steady states for the richer component. Consistency of effects across disruptors may yet be found if short-term effects of disruptors are assessed relative to the extent of change observed after prolonged exposure.

Contrast and reallocation of extraneous reinforcers as a function of component duration and baseline rate of reinforcement

Four pigeons responded on multiple schedules arranged on a "main" key in a two-key experimental chamber. A constant schedule component was alternated with another component that was varied over conditions. On an extra response key, conjoint schedules of reinforcement that operated in both components were arranged concurrently with the multiple schedule on the main key. On the main key, changes in reinforcement rate in the varied component were inversely related to changes in response rates in the constant component (behavioral contrast). On the extra key, some reinforcers were reallocated between components, depending on the schedules in effect on the main key in the varied component. In the varied component, the obtained rates of reinforcement on the extra key were inversely related to main-key reinforcement rate. In the constant component, extra-key reinforcer rates were positively related to main-key reinforcer rates obtained in the varied component, and were not a function of response rates on the extra key. In two comparisons, the rate at which components alternated and the value of the main-key schedule in the constant component were varied. Consistent with earlier work, long components reduced the extent of contrast. Reductions in contrast as a function of component duration were accompanied by similar reductions in the extent of reinforcer reallocation on the extra key. In the second comparison, lowering the rate of reinforcement in the constant component increased the rate at which extra-key reinforcers were obtained, reduced the extent of reinforcer reallocation, and reduced contrast. Overall, the results are consistent with the suggestion that some contrast effects are due to the changes in extraneous reinforcement during the constant component, and that manipulations of component duration, and manipulations of the rate of reinforcement in the constant component, affect contrast because they influence the extent of extraneous reinforcer real-location.

Local contrast in behavior allocation during multiple-schedule components

Allocation of responses between two keys was studied during two alternating multiple-schedule components. Responses were recorded in successive quarters of each component. Variable-interval reinforcer schedules on the two keys were constant throughout the experiment for one (constant) component and were varied over conditions on one key for the other, producing changes in reinforcer ratios for the varied component. Behavior allocation for the first quarter of the constant component was inversely related to varied-component reinforcer ratios, a form of local contrast, but this relationship was not observed later in the component. During the first quarter of the varied component, slopes of matching lines were high and decreased later in the component. It is argued that this form of local contrast cannot be explained in terms of reallocation of extraneous reinforcers between components, and that the matching law for concurrent operants does not capture some sources of control over behavior allocation. A simple extension of the matching law is offered that adequately describes behavior changes during both components. A version of this formulation can predict contrast effects in absolute response rates.

Interresponse-time analysis of stimulus control in multiple schedules

Interresponse-time distributions were recorded in two components of multiple variable-interval schedules that were varied over several conditions. Values of the exponent for power functions relating ratios of interresponse times emitted per opportunity to ratios of reinforcers obtained in the two components varied with interresponse-time class interval. The exponent (sensitivity to reinforcement) afforded a measure of stimulus control exerted by the discriminative stimuli. Exponents were near zero for short interresponse times, consistent with previous conclusions that responses following short interresponse times are controlled by response-produced or proprioceptive stimuli. Values of exponents increased with longer interresponse times, indicating strong control by exteroceptive stimuli over responses following interresponse times of approximately one second or longer.

Quantitative analysis

Quantitative analysis permits the isolation of invariant relations in the study of behavior. The parameters of these relations can serve as higher-order dependent variables in more extensive analyses. These points are illustrated by reference to quantitative descriptions of performance maintained by concurrent schedules, multiple schedules, and signal-detection procedures. Such quantitative descriptions of empirical data may be derived from mathematical theories, which in turn can lead to novel empirical analyses so long as their terms refer to behavioral and environmental events. Thus, quantitative analysis is an integral aspect of the experimental analysis of behavior.

Behavioral contrast for key pecking as a function of component duration when only one component varies

Pigeons pecked keys for food reinforcers delivered by multiple variable-interval 2-min variable-interval 2-min schedules. Positive behavioral contrast was created by changing one component to extinction; negative contrast was achieved by changing one component to a variable-interval 15-s schedule. The duration of each component was varied independently of the other from 5 to 960 s. The size of positive contrast was greatest when the extinction component was 30 or 60 s long. It did not change significantly with changes in the duration of the variable-interval 2-min component. The absolute size of negative contrast decreased with increases in the duration of the variable-interval 2-min component. It did not change significantly with changes in the duration of the variable-interval 15-s component. These results show that the size of contrast is determined primarily by the duration of the component that provides the less favorable conditions of reinforcement. These results are not predicted by current theories.

Momentary maximizing in concurrent schedules with a minimum interchangeover interval

Eight pigeons were trained on concurrent variable-interval variable-interval schedules with a minimum interchangeover time programmed as a consequence of changeovers. In Experiment 1 the reinforcement schedules remained constant while the minimum interchangeover time varied from 0 to 200 s. Relative response rates and relative time deviated from relative reinforcement rates toward indifference with long minimum interchangeover times. In Experiment 2 different reinforcement ratios were scheduled in successive experimental conditions with the minimum interchangeover time constant at 0, 2, 10, or 120 s. The exponent of the generalized matching equation was close to 1.0 when the minimum interchangeover time was 0 s (the typical procedure for concurrent schedules without a changeover delay) and decreased as that duration was increased. The data support the momentary maximizing theory and contradict molar maximizing theories and the melioration theory.

Superimposition of response-independent reinforcement

Studies that have superimposed response-independent reinforcement (or reinforcers scheduled by contingencies placed on the absence of responding) upon conventional response-dependent schedules are reviewed. In general, providing alternative sources of reinforcement reduced response rates below the levels observed when alternative reinforcement was absent. However, response-rate elevation was sometimes found, particularly when rates of superimposed response-independent reinforcement were low. Superimposition of schedules providing reinforcers contingent on the absence of responding usually produced more severe response-rate decrements than superimposition of response-independent reinforcement. A variant of Herrnstein's equation, which assumes that some of the alternative reinforcers function as if they were delivered by baseline response-dependent source of reinforcement, is in qualitative agreement with the overall body of results obtained, and can predict both increases and decreases in response rate as resulting from superimposed reinforcers.

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.

Closed-economy multiple-schedule performance: Effects of deprivation and session duration

Three pigeons responded for food reinforcement on multiple variable-interval schedules in which the total consumption of food was entirely determined by the subjects' interaction with the schedules (a closed economy). The finding of overmatching, where response allocation between components is more extreme than the distribution of reinforcers, was reconfirmed. Generalized-matching sensitivity decreased from overmatching to undermatching values typical of conventional multiple schedules when food deprivation was increased by decreasing session duration, but not when deprivation was increased by decreasing overall reinforcer rate. Sensitivity also increased from undermatching to overmatching as session duration increased from 100 min to 24 hr, while deprivation was held constant by decreasing overall reinforcer rate. These results can be understood in terms of increases in the value of extraneous reinforcers relative to food reinforcers as deprivation decreases or as the economy for extraneous reinforcers becomes more closed. However, no published quantitative expression of the effects of extraneous reinforcers is entirely consistent with the results.

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.

On the effects of food deprivation and component reinforcer rates on multiple-schedule performance

Six pigeons were used to investigate the effects of varying body weight and component reinforcer rates in two-component multiple variable-interval variable-interval schedules. In Parts 1 and 3 of the experiment, unequal component reinforcer rates were arranged, and body weights were respectively increased and decreased. At 80% ad lib weight, response-rate ratios were closer to unity than reinforcer-rate ratios, but at 100% or more of ad lib weight, response-rate ratios generally equaled reinforcer-rate ratios. In Part 2, component reinforcer-rate ratios were varied over five conditions with the subjects maintained at 100% or more of their ad lib weights, and response-rate ratios matched reinforcer-rate ratios. The data thus support the empirical finding that response allocation in multiple schedules is a function of deprivation. Although this qualitative result is predicted by three models of multiple-schedule performance, only a model that assumes no direct component interaction adequately describes the data.

Remembering: the role of extraneous reinforcement

In two experiments, pigeons' responding on an extraneous task was explicitly reinforced during delayed matching-to-sample trials. In Experiment 1, red or green sample stimuli were followed by retention intervals of 0.2, 1, 4, or 12 sec, during which pecks to a white center key were reinforced with 2.5-sec access to wheat according to extinction, variable-interval 30-sec, and variable-interval 15-sec schedules in different conditions. A proportion of .2, .5, .7, or .9 of subsequent red or green choice responses that matched the sample were reinforced with 3-sec access to wheat. The result was that increasing center key reinforcement, or reducing reinforcer probability, lowered overall accuracy. Initial discriminability fell, but with no change in the rate of forgetting. In Experiment 2, initial discriminability was affected by extraneous reinforcers that were contingent on center key pecking, but not by noncontingent reinforcers. A plausible conclusion is that initial discriminability decreases when reinforcers strengthen competing behaviors.

Investigating the devaluation explanation for negative anticipatory contrast

This study addressed whether negative anticipatory contrast results in a decrease in the value of the low-valued substance. Rats responded in training conditions designed to produce negative contrast. They then responded in test sessions in which the low-valued substance from the training sessions was the reinforcer for an operant response. Despite the finding of contrast in the training conditions, the low-valued substance was a more effective reinforcer early in testing after training conditions in which it had been followed by access to the high-valued substance than after training conditions in which it had not. The findings question the devaluation explanation for contrast but may be similar to other findings of reversals of "preference."

Interresponse times and the structure of choice

This paper presents some analyses of available data on interresponse-time emission on concurrent variable-interval schedules arranged either continuously or as discrete components, and in which either reinforcer rates or magnitudes were varied. Ratios of frequencies of interresponse times in a series of temporal bins varied in their sensitivity to reinforcement: Sensitivity values were least for interresponse times around 0.2-0.4s, were higher in the region 0-0.2s, and were highest at values greater than 0.4s. Relative frequencies of interresponse times were greatest around 0.2-1.6s. As a result, time allocation to alternatives were mainly determined by IRTs between 0.8 and 6.4s, and least by IRTs less than 0.8s. If inter-bout times reflect time allocation to unmeasured responses, then time spent emitting unmeasured behavior may be the main constituent of time allocation on concurrent schedules. An analysis of log survivor plots supported this suggestion, and further suggested that a full understanding of time allocation in choice requires accepting that unmeasured responses do not result from a unitary process, but from many disparate contributing processes. These other behaviors can be revealed through Gaussian log-normal analyses of interresponse-time distributions.

Arousal, changeover responses, and preference in concurrent schedules

Pigeons were trained on multiple schedules that provided concurrent reinforcement in each of two components. In Experiment 1, one component consisted of a variable-interval (VI) 40-s schedule presented with a VI 20-s schedule, and the other a VI 40-s schedule presented with a VI 80-s schedule. After extended training, probe tests measured preference between the stimuli associated with the two 40-s schedules. Probe tests replicated the results of Belke (1992) that showed preference for the 40-s schedule that had been paired with the 80-s schedule. In a second condition, the overall reinforcer rate provided by the two components was equated by adding a signaled VI schedule to the component with the lower reinforcer rate. Probe results were unchanged. In Experiment 2, pigeons were trained on alternating concurrent VI 30-s VI 60-s schedules. One schedule provided 2-s access to food and the other provided 6-s access. The larger reinforcer magnitude produced higher response rates and was preferred on probe trials. Rate of changeover responding, however, did not differ as a function of reinforcer magnitude. The present results demonstrate that preference on probe trials is not a simple reflection of the pattern of changeover behavior established during training.

Reinforcement context and resistance to change

Eight pigeons responded in a multiple variable-interval (VI) schedule in which a constant component always delivered 40rft/h, and an alternated component was either rich (200rft/h) or lean (6.67rft/h) in different conditions. Four tests of resistance to change were conducted in each condition: prefeeding, full extinction, constant-component-only extinction, and response-independent food. Resistance to both prefeeding and full extinction in the constant component varied inversely with the reinforcement rate in the alternated component, but resistance to response-independent food did not. The extinction and response-independent food results were consistent with [J. Exp. Psychol.: Anim. Behav. Proc. 25 (1999) 256] behavioral momentum model. Maintaining reinforcement in the alternated component increased resistance to extinction in the constant component, as predicted by the behavioral momentum model but not accounts of multiple-schedule performance based on [J. Exp. Anal. Behav. 13 (1970) 243] equation. Overall, the momentum model gave a good account of the results with the exception of the prefeeding data. Possible ways to reconcile the prefeeding results with behavioral momentum theory are considered.

Behavioral contrast redux

Behavioral contrast is defined as a change in response rate during a stimulus associated with a constant reinforcement schedule, in inverse relation to the rates of reinforcement in the surrounding stimulus conditions. Contrast has at least two functionally separable components: local contrast, which occurs after component transition, and molar contrast. Local contrast contributes to molar contrast under some conditions, but not generally. Molar contrast is due primarily to anticipatory contrast. However, anticipatory contrast with respect to response rate has been shown to be inversely related to stimulus preference, which challenges the widely held view that contrast effects reflect changes in stimulus value owing to the reinforcement context. More recent data demonstrate that the inverse relation between response rate and preference with respect to anticipatory contrast is due to Pavlovian contingencies embedded in anticipatory contrast procedures. When those contingencies are weakened, anticipatory contrast and stimulus preference are positively related, thus reaffirming the view that the reinforcing effectiveness of a constant schedule is inversely related to the value of the context of reinforcement in which it occurs. The underlying basis of how the context of reinforcement controls reinforcement value remains uncertain, although clear parallels exist between contrast and the effects of contingency in both Pavlovian and operant conditioning.

Psychophysics of remembering

We present a new model of remembering in the context of conditional discrimination. For procedures such as delayed matching to sample, the effect of the sample stimuli at the time of remembering is represented by a pair of Thurstonian (normal) distributions of effective stimulus values. The critical assumption of the model is that, based on prior experience, each effective stimulus value is associated with a ratio of reinforcers obtained for previous correct choices of the comparison stimuli. That ratio determines the choice that is made on the basis of the matching law. The standard deviations of the distributions are assumed to increase with increasing retention-interval duration, and the distance between their means is assumed to be a function of other factors that influence overall difficulty of the discrimination. It is a behavioral model in that choice is determined by its reinforcement history. The model predicts that the biasing effects of the reinforcer differential increase with decreasing discriminability and with increasing retention-interval duration. Data from several conditions using a delayed matching-to-sample procedure with pigeons support the predictions.

Action at a temporal distance: Component transition as the relational basis for successive discrimination

In a successive discrimination, red and green hues signaled component variable-interval schedules. The exponent of the power function relating ratios of responses in the red and green components to ratios of reinforcers provided a reinforcement-free measure of discrimination or stimulus control. Responses were recorded in successive 10-s subintervals of the 50-s components. The power-function exponent decreased systematically with increasing time since component transition in most conditions of five experiments. This reduction was not influenced by the absolute rate of reinforcement, consistent with the interpretation of the exponent as a measure of stimulus control. A reduction in the overall level of stimulus control by increasing the duration of response-produced keylight offset did not influence the decrease in discrimination with increasing time since component transition. The results support the conclusion that discriminative responding in successive discriminations is governed by several sources of stimulus control including delayed control by component transition.

Shortcomings of the behavioral competition theory of contrast: Reanalysis of McLean (1992)

McLean (1992) presented significant data showing that the occurrence of behavioral contrast in a multiple schedule was correlated with shifts in the frequency of reinforcers from a second source between components of the schedule, and interpreted his results as showing that contrast was due to changes in the degree of response competition within the constant component of the multiple schedule. Reanalysis of his data shows that there was an effect of reinforcement in the alternative component of the schedule independent of the shifts in reinforcers between components. Thus, the effect of relative rate of reinforcement cannot be ascribed, at least entirely, to the mechanisms proposed by the behavioral competition theory of contrast.

Successive independence and behavioral contrast in a closed economy

Two pigeons had access to multiple concurrent schedules of reinforcement for 24 hours per day in their home cages. The variable-interval schedules comprising the multiple concurrent schedules were varied across 16 conditions. In three sets of conditions, one schedule was varied while its concurrent alternative and the concurrent schedules in the other component were held constant. Behavioral contrast was observed; that is, as the rate of reinforcement arranged by the varied schedule decreased, response rates on the constant schedules typically increased. These conditions formed part of two larger sets of conditions in which the concurrent schedules in one multiple-schedule component remained constant while the concurrent schedules in the other component were varied. Successive independence was found, in that behavior allocation during the constant component did not vary as a function of the reinforcer ratios in the varied component. Successive independence between components in multiple concurrent schedules is a robust result that occurs in closed economies and under conditions that promote behavioral contrast.

Delayed and current stimulus control in successive discriminations

In a successive discrimination in which successively alternating red and green hues signaled component variable-interval schedules, sensitivity of the ratio of responses in the two components to variation in the component reinforcer ratio decreased systematically during the course of the component. This decrease in stimulus control or discrimination over the course of the component was shown to be the result of delayed control of responding during the component by the stimulus transition between components. When the red-green stimulus transition was altered by interpolating a white stimulus at the end of each 60-s component, discrimination at the beginning of the component (measured by the power-function exponent for sensitivity to reinforcement) was reduced. Conditions with the white stimulus inserted in other quarters of the component indicated that the current discriminative stimulus exerts control over responding throughout the component, whereas during about the first half of the component, response differentials are influenced by the transition between discriminative stimuli.

Effects of reinforcement context on choice

Two experiments investigated the effects of successive reinforcement contexts on choice. In the first, concurrent variable-interval schedules of primary reinforcement operated during the initial links of concurrent chains. The rate of this reinforcement arranged by the concurrent schedules was decreased across conditions: When it was higher than the terminal-link rate, preference for the higher frequency initial-link schedule increased relative to baseline. (During baseline, a standard concurrent-schedule procedure was in effect). When the initial-link reinforcement rate was lower than the terminal-link rate, preference converged toward indifference. In the second experiment, a chain schedule was available on a third key while a concurrent schedule was in effect on the side keys. When the terminal link of the chain schedule was produced, the side keys became inoperative. Availability of the chain schedule did not affect choice between the concurrent schedules. These results show that only when successive reinforcement contexts are produced by choice responding do those successive contexts affect choice in concurrent schedules.

Effects of response-allocation constraints on multiple-schedule performance

Four pigeons were trained on multiple variable-interval schedules in which components alternated after a fixed number of responses had been emitted. In Part 1, each component change occurred after 20 responses; in Part 2, the number was 40; and in Part 3, the number of responses before change was 10. Component reinforcer rates were varied over five experimental conditions in each of Parts 1 to 3. Component response rates decreased as the specified number of responses per component was increased. However, the relation between component response-rate ratios and component reinforcer-rate ratios was independent of the specified number of responses per component, and was similar to that found when components alternate after fixed time periods. In the fourth part of the experiment, the results from Parts 1 to 3 were systematically replicated by keeping the component reinforcer rates constant, but different, while the number of responses that produced component alternation was varied from 5 to 60 responses. The results showed that multiple-schedule performance under component-response-number constraint is similar to that under conventional component-duration constraint. They further suggest that multiple-schedule response rates are controlled by component reinforcer rates and not by principles of maximizing overall reinforcer rates or meliorating component reinforcer rates.

Rapid determinations of preference in multiple concurrent-chain schedules

With concurrent chains arranged for a pigeon's key pecks, pecks on two concurrently available initial-link keys (left and right) respectively produce separately operating terminal links (A and B). Preferences for terminal link A over terminal link B are usually calculated as deviations of relative initial-link response rates (left divided by total pecks) from those during baseline conditions, when A equals B. Baseline preferences, however, are often variable and typically are determined indirectly (e.g., with unequal A and B, reversing left-right assignments of A and B over sessions and estimating the baseline from differences between the relative rates generated). Multiple concurrent-chain schedules, with components each consisting of a pair of concurrent chains, speed the determination of preferences by arranging A and B and their reversal within sessions. In two experiments illustrating the feasibility of this procedure, one component operated with circles projected on initial-link keys and the other with pluses; when left and right initial-link pecks respectively produced terminal links A and B in one component, they produced B and A in the other. Even as the baselines fluctuated, preference was observable within sessions as the difference between relative initial-link response rates in the two components. The first experiment demonstrated the rapid development of preferences when terminal links A and B consisted of fixed-interval 15-s and 30-s schedules. The second demonstrated the sensitivity of the procedure to preference for a fixed-interval 30-s schedule operating for pecks on either of two keys (free choice) over its operating for pecks on only a single key (forced choice).

Conjoint control of performance in conditional discriminations by successive and simultaneous stimuli

In a conditional discrimination, reinforcement of pigeons' responses to pairs of simultaneously presented wavelength stimuli depended on the orientation of white lines superimposed on the wavelengths. Over different conditions in Experiment 1, three wavelength differences were combined with two differences between successively presented line orientations. Measures of stimulus discriminability increased with increases in the difference between both orientation and wavelength stimuli. Conditional-discrimination performance was thus conjointly determined by stimulus disparity in the successive and simultaneous discriminations. In Experiment 2, ratios of rates of reinforcement contingent upon the two categories of correct responses were varied over several conditions for difficult and easy discriminations. Ratios of responses to wavelength pairs were sensitive to variations in the reinforcement ratio to a greater extent for the more difficult orientation discrimination than for the easier orientation discrimination. Performance in the conditional discrimination was therefore determined by the interacting effects of stimulus disparity and the relative rates of reinforcement contingent upon the two correct choices. It was concluded that the effect of temporally distant reinforcement on behavior in a prevailing schedule component is attenuated to an extent that depends on similarity of stimuli that delineate the successive components.

An equation for behavioral contrast

Pigeons were trained on a three-component multiple schedule in which the rates of reinforcement in the various components were systematically varied. Response rates were described by an equation that posits that the response-strengthening effects of reinforcement are inversely related to the context of reinforcement in which it occurs, and that the context is calculated as the weighted average of the various sources of reinforcement in the situation. The quality of fits was comparable to that found with previous quantitative analyses of concurrent schedules, especially for relative response rates, with over 90% of the variance accounted for in every case. As with previous research, reinforcements in the component that was to follow received greater weights in determining the context than did reinforcements in the preceding component.

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.

Temporal proximity and reinforcement sensitivity in multiple schedules

Distributions of reinforcers between two components of multiple variable-interval schedules were varied over a number of conditions. Sensitivity to reinforcement, measured by the exponent of the power function relating ratios of responses in the two components to ratios of reinforcers obtained in the components, did not differ between conditions with 15-s or 60-s component durations. The failure to demonstrate the "short-component effect," where sensitivity is high for short components, was consistent with reanalysis of previous data. With 60-s components, sensitivity to reinforcement decreased systematically with time since component alternation, and was higher in the first 15-s subinterval of the 60-s component than for the component whose total duration was 15 s. Varying component duration and sampling behavior at different times since component transition may not be equivalent ways of examining the effects of average temporal distance between components.