Performance in concurrent interval schedules

Four pigeons were trained under concurrent variable-interval variable-interval and fixed-interval variable-interval schedules in a two-key situation. Both response allocation and time allocation to the two schedules were measured when various reinforcement rates were arranged on each key. All animals showed an approximately constant proportional preference for the variable-interval schedule over the fixed-interval schedule. These results support Schneider's (1969) analysis of fixed-interval schedule performance.     

Preference for unsegmented interreinforcement intervals in concurrent chains

Five pigeons were trained under concurrent-chain schedules in which a pair of independent, concurrent variable-interval 60-s schedules were presented in the initial link and either both variable-interval or both fixed-interval schedules were presented in the terminal link. Except for the baseline, one of the terminal-link schedules was always a two-component chained schedule and the other was either a simple or a tandem schedule of equal mean interreinforcement interval. The values of the fixed-interval schedules were either 15 s or 60 s; that of the variable-interval schedules was always 60 s. A 1.5-s changeover delay operated during the initial link in some conditions. The pigeons preferred a simple or a tandem schedule to a chain. For the fixed-interval schedules, this preference was greater when the fixed interval was 60 s than when it was 15 s. For the variable-interval schedules, the preferences were less pronounced and occurred only when the changeover delay was in effect. For a given type of schedule and interreinforcement interval, similar preferences were obtained whether the nonchained schedule was a tandem or simple schedule. The changeover delay generally inflated preference and lowered the changeover rate, especially when the terminal-link schedules were either short (15 s) or aperiodic (variable-interval). The results were consistent with the notion that segmenting the interreinforcement interval of a schedule into a chain lowers the preference for it.     

Transfer tests of stimulus value in concurrent chains

We report two experiments that use transfer tests to investigate whether in concurrent chains the value of a terminal-link stimulus is affected by the alternate terminal link. In Experiment 1, two groups of pigeons were trained on multiple concurrent-chains schedules in which switching between the schedules was via pecking a changeover key. For one group, the terminal links were fixed-interval 8 s versus fixed-interval 16 s in one component and fixed-interval 16 s versus fixed-interval 32 s in the other component. For a second group, the terminal links were variable-interval 10 s versus variable-interval 20 s in one component and variable-interval 20 s versus variable-interval 40 s in the other. After sufficient baseline training had been given so that performances had stabilized, transfer tests were conducted in which the two chains with equal terminal-link schedules were presented together as a new concurrent pair. For 6 of the 7 subjects, initial-link responding changed fairly rapidly during the test in the manner predicted if the values of the terminal links were equal. In Experiment 2, pigeons were trained on multiple concurrent chains using a two-key procedure, and the terminal links were the same variable-interval schedules as in Experiment 1. After baseline training, transfer tests were conducted that assessed (a) the relative reinforcing strength of the terminal-link stimuli in a novel initial-link situation and (b) the relative ability of those stimuli to evoke responding. The data from the reinforcing strength test were consistent with those from Experiment 1, but those from the evocation strength test were not. Although this discrepancy shows that responding in transfer tests is not solely a function of stimulus value, the results from both experiments suggest, overall, that value is determined by the stimulus—reinforcer relation independently of the alternative terminal link.     

Resistance to change produced by access to fixed-delay versus variable-delay terminal links

Pigeons' responding was reinforced on a multiple schedule consisting of two two-link chain schedules presented in regular alternation. Responding in initial links (always variable-interval 60-s) produced a key-color change and access to a terminal link. The terminal link for one chain provided food after a fixed delay (fixed-interval or fixed-time); the terminal link for the other provided food after a variable delay (variable-interval or variable-time). The average duration of the terminal-link schedules was varied across conditions, but in every condition the arithmetic mean of the variable-delay terminal-link schedule was equal to the duration of the fixed delay. Response rates were higher in the initial links of the chains with the variable-delay terminal links. Response-decreasing operations (satiation, extinction) were used after performances reached asymptote. Response rates maintained by access to variable-delay terminal links tended to be more resistant to change than were rates maintained by access to fixed-delay terminal links. These results are consistent with the preference for variable- over fixed-interval terminal links observed with concurrent-chains schedules, suggesting (1) that immediacy of reinforcement influences the conditioned reinforcing potency of access to a terminal link and (2) that choice in concurrent chains and resistance of responding to change may be manifestations of the same effect of reinforcement.     

Conditioned reinforcement versus time to reinforcement in chain schedules.

Pigeons were trained on three-component chain schedules in which the initial component was either a fixed-interval or variable-interval schedule. The middle and terminal components were varied among fixed-interval fixed-interval, variable-interval variable-interval, and an interdependent variable-interval variable-interval schedule in which the sum of the durations of the two variable-interval components was always equal to the sum of the fixed-interval fixed-interval components. At issue was whether the response rate in the initial component was controlled by its time to primary reinforcement or by the temporal parameters of the stimulus correlated with the middle terminal link. The fixed-interval initial-link schedule maintained much lower response rates than the variable-interval initial-link schedule regardless of the schedules in the middle and terminal links. Nevertheless, the intervening schedules played some role: With fixed-interval schedules in the initial links, response rates were consistently highest with independent variable-interval schedules in the middle and terminal links and intermediate with the interdependent variable-interval schedules; these initial-link differences were predicted by the response rates in the middle link of the chain. With variable-interval schedules in the initial links, response rates were lowest with the fixed-interval fixed-interval schedules following the initial link and were not systematically different for the two types of variable-interval variable-interval schedules. The results suggest that time to reinforcement itself accounts for little if any variance in initial-link responding.     

DOES SENSITIVITY TO MAGNITUDE DEPEND ON THE TEMPORAL DISTRIBUTION OF REINFORCEMENT?

Our research addressed the question of whether sensitivity to relative reinforcer magnitude in concurrent chains depends on the distribution of reinforcer delays when the terminal-link schedules are equal. In Experiment 1, 12 pigeons responded in a two-component procedure. In both components, the initial links were concurrent variable-interval 40-s variable-interval 40-s, and the terminal links were both 20-s interval schedules in which responses were reinforced by either 4-s of grain in one, or 2-s of grain in the other. The only difference between the components was whether the terminal-link schedules were fixed interval or variable intervals. For all subjects, the relative rate of responding in the initial links for the terminal link that produced the 4-s reinforcer was greater when the terminal links were fixed-interval schedules than when they were variable-interval schedules. This result is contrary to the prediction of Grace's (1994) contextual choice model, but is consistent with both Mazur's (2001) hyperbolic value-added model and Killeen's (1985) incentive theory. In Experiment 2, 4 pigeons responded in a concurrent-chains procedure in which 4-s or 2-s reinforcers were provided independently of responding according to equal fixed-time or mixed-time schedules. Preference for the 4-s reinforcer increased as the variability of the intervals comprising the mixed-time schedules was decreased. Generalized-matching sensitivity of initial-link response allocation to relative reinforcer magnitude was proportional to the geometric mean of the terminal-link delays.     

The effects of terminal-link fixed-interval and variable-interval schedules on responding under concurrent chained schedules

Previous work using variable-interval schedules in the terminal links of concurrent chained schedules suggested that relative choice proportion in the initial links equalled relative rate of reinforcement in the terminal links. With fixed-interval terminal-link schedules, however, matching was not obtained. The present study held pairs of fixed-interval terminal-link schedules in a constant ratio but varied absolute sizes. Relative choice for the smaller terminal-link fixed-interval schedule was a negatively accelerated, increasing function of absolute size of the fixed-interval pairs. Matching was found only with the fixed-interval pair of 5 and 10 sec. When pairs of variable-interval schedules were arranged so that the harmonic mean of the intervals equalled the fixed-interval parameter values, relative choice functions were like those for fixed-interval schedules.     

Concurrent-chains schedules as a method to study choice between alcohol-associated conditioned reinforcers

An extensive body of research using concurrent-chains schedules of reinforcement has shown that choice for one of two differentially valued food-associated stimuli is dependent upon the overall temporal context in which those stimuli are embedded. The present experiments examined whether the concurrent chains procedure was useful for the study of behavior maintained by alcohol and alcohol-associated stimuli. In Experiment 1, rats responded on concurrent-chains schedules with equal variable-interval (VI) 10-s schedules in the initial links. Across conditions, fixed-interval schedules in the terminal links were varied to yield 1∶1, 9∶1, and 1∶9 ratios of alcohol delivery. Initial-link response rates reflected changes in terminal-link schedules, with greater relative responding in the rich terminal link. In Experiment 2, terminal-link schedules remained constant with a 9∶1 ratio of alcohol delivery rates while the length of two equal duration initial-link schedules was varied. Preference for the rich terminal link was less extreme when initial links were longer (i.e., the initial-link effect), as has been previously reported with food reinforcers. This result suggests that the conditioned reinforcing value of an alcohol-associated stimulus depends on the temporal context in which it is embedded. The concurrent-chains procedure and quantitative models of concurrent chains performance may provide a useful framework within which to study how contextual variables modulate preference for drug-associated conditioned reinforcers.     

Concurrent second-order schedules of reinforcement

Responses on one key (the main key) of a two-key chamber produced food according to a second-order variable-interval schedule with fixed-interval schedule components. A response on a second key (the changeover key) alternated colors on the main key and provided a second independent second-order variable-interval schedule with fixed-interval components. The fixed-interval component on one variable-interval schedule was held constant at 8 sec, while the fixed interval on the other variable-interval schedule was varied from 0 to 32 sec. Under some conditions, a brief stimulus terminated each fixed interval and generated fixed-interval patterns; in other conditions, the brief stimulus was omitted. Relative response rate and relative time deviated substantially from scheduled relative reinforcement rate and, to a lesser extent, from obtained relative reinforcement rate under both brief-stimulus and no-stimulus conditions. Matching was observed with equal components on both schedules; with unequal components, increasingly greater proportions of time and responses than the matching relation would predict were spent on the variable-interval schedule containing the shorter component. Preference for the shorter fixed interval was typically more extreme under brief-stimulus than under no-stimulus schedules. The results limit the extension of the matching relation typically observed under simple concurrent variable-interval schedules to concurrent second-order variable-interval schedules.     

On the relation between preference and resistance to change

Nevin (1979) noted that preference in concurrent chains and resistance to change in multiple schedules were correlated, in that both measures were affected similarly by variations in parameters of reinforcement such as rate, immediacy, and magnitude. To investigate the relationship between preference and resistance to change directly, we used a within-session procedure that arranged concurrent chains in one half of the session and a multiple schedule in the other half. The same variable-interval schedules served as terminal links in concurrent chains and as the components of the multiple schedule, and were signaled by the same stimuli. After performances had stabilized, responding in the multiple schedule was disrupted by delivering response-independent reinforcement during the blackout periods between components. Both preference in concurrent chains and relative resistance to change of multiple-schedule responding were well described as power functions of relative reinforcement rate, as predicted by current quantitative models (Grace, 1994; Nevin, 1992b). In addition, unsystematic variation in preference and resistance to change was positively correlated, which suggests that preference and resistance to change are independent measures of a single construct. That construct could be described as the learning that occurs regarding the prevailing conditions of reinforcement in a distinctive stimulus situation.     

Preference for fixed-interval schedules: effects of initial-link length

Six homing pigeons were trained on a variety of concurrent-chains schedules in which the initial links were equal variable-interval schedules and the terminal links were fixed-interval schedules. Both terminal-link and initial-link schedules were systematically varied. The results showed that preference for a particular terminal-link schedule combination was greater, the shorter the initial-link schedules. The data closely matched predictions from the model of choice suggested by Davison and Temple (1973), but did not match predictions from two other models. An alternative method for analyzing concurrent-chains performance by assuming that the schedule consists of both chained schedules and successive, discriminated components that comprise multiple schedules, was suggested.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Preference for simple interval schedules of reinforcement in concurrent chains: Effects of segmentation ratio

A concurrent-chains procedure was used to examine pigeons' preferences between segmented and unsegmented terminal-link schedules of reinforcement. During the initial link, a pair of independent, concurrent variable-interval 60-s schedules was in effect. In the terminal link, reinforcement was provided by a chain fixed-interval fixed-interval schedule on one key and by a simple fixed-interval schedule with an equal interreinforcement interval in the other. The relative duration between the first and second components (segmentation ratio) in the terminal-link chained schedule was systematically varied while the terminal-link duration was kept constant at either 15 s or 30 s in two sets of conditions. With few exceptions, the simple schedule was preferred to the chained schedule. Furthermore, this preference was inversely related to the size of the segmentation ratio in the segmented schedule. When the segmentation ratio was smaller than 1:1, preference was more extreme for a 30-s condition than for a 15-s condition. However, preference decreased more rapidly in conditions with the longer terminal-link duration when the ratio increased. Taken together, these results were consistent with previous findings concerning the effect of the terminal-link duration on choice between segmented and unsegmented schedules. In addition, the data suggested that segmentation ratio in a segmented schedule constitutes another potent factor influencing preference for the unsegmented schedule.     

Preference for mixed-interval versus fixed-interval schedules

Pigeons were trained on a two-link concurrent chain schedule in which responses on two keys were reinforced according to independent variable-interval schedules by the production of a change in key color. Further responses on the key on which the stimulus change had been produced gave a single food reinforcement and a return to concurrent variable-interval conditions. On one key the terminal link was a two-valued mixed-interval schedule, while on the other, the terminal link was a fixed-interval schedule. When the mixed-interval values were kept constant and the fixed-interval values varied, relative response rates in the initial concurrent links matched relative reinforcement rates in the terminal links when these were computed from cubic transformations of the reciprocals of the intervals comprising the terminal link schedules.     

Choice in transition: A comparison of melioration and the kinetic model

Transition-state choice behavior of pigeons was examined in two experiments designed to test predictions of melioration and the kinetic model. Both experiments began with an initial training condition during which subjects were maintained on concurrent variable-interval schedules. In Experiment 1, subjects were then exposed to concurrent variable-ratio schedules, whereas in Experiment 2, subjects were then exposed to concurrent extinction. Contrary to the predictions of melioration, but consistent with the kinetic model, acquisition of preference on concurrent variable-ratio schedules followed a negatively accelerated logistic trajectory, and preference remained stable in concurrent extinction. Predictions made by the kinetic model concerning rates of switching between alternatives were also supported.     

Preference for fixed-interval terminal links in a three-key concurrent chain schedule

Pigeons were trained on three-key concurrent chain schedules in which the initial links were variable-interval schedules and the terminal links were fixed-interval schedules. In the first experiment, the initial links were all equal and the terminal-link schedule on one key only was varied. In the second part of the experiment, the terminal-link schedules were all fixed, but different, and the initial-link schedule on one key was varied. Relative response rates in the initial links did not match either the relative arranged, nor the relative obtained, terminal-link reinforcement rates. The relations between independent and dependent variables in three-key concurrent chains were similar to, but not identical with, those found in two-key chains comprising the same schedule types.     

Control of human vigilance by concurrent schedules

Twenty four subjects were studied for ten 1-hr sessions to determine whether the human observer's visual monitoring of individual meters in a complex display can be differentially controlled by concurrent scheduling of signals. Subjects were divided into two main groups of 12 each. One group was given fixed-interval, variable-interval, and differential-reinforcement-of-low-rates schedules. The second group was given fixed-interval, fixed-ratio, and differential-reinforcement-of-low-rates schedules. Test subjects were instructed only to detect as many signals as possible. Results indicated that observing responses to the individual meters corresponded to the temporal patterns known to be associated with the schedules for the group given fixed-ratio instead of variable-interval as a component schedule. The group given the variable-interval schedule in the three-schedule combination tended to exhibit the same pattern of viewing across each of the three meters during any given session. However, subsequent testing was performed on two more subjects over 64 sessions, by adding initial feedback of signal detection results, and instructions concerning schedule construction. These results indicated that with knowledge of schedule construction and initial feedback of detection data, differentiated responding can be maintained efficiently over long periods of time by the combination including fixed-interval, variable-interval, and differential-reinforcement-of-low-rates schedules.     

Preference and resistance to change in concurrent variable-interval schedules

Pigeons were trained on a multiple schedule in which separate concurrent schedules were presented in the two components of the schedule. During one component, concurrent variable-interval 40-sec variable-interval 80-sec schedules operated. In the second component, concurrent variable-interval 40-sec variable-interval 20-sec schedules operated. After stable baseline performance was obtained in both components, extinction probe choice tests were presented to assess preference between the variable-interval 40-sec schedules from the two components. The variable-interval 40-sec schedule paired with the variable-interval 80-sec schedule was preferred over the variable-interval 40-sec schedule paired with the variable-interval 20-sec schedule. The subjects were also exposed to several resistance-to-change manipulations: (1) prefeeding prior to the experimental session, (2) a free-food schedule added to timeout periods separating components, and (3) extinction. The results indicated that preference and resistance to change do not necessarily covary.     

Preference for mixed-interval versus fixed-interval schedules: number of component intervals

Six pigeons were trained under a concurrent chains procedure so that preference for fixed-interval versus mixed-interval schedules with varying numbers of component intervals could be examined. The smallest and largest intervals in the terminal links were the same value as those used by Davison (1969). Relative choice in all cases approximated the relative means of the squares of the harmonic intervals to reinforcement in the terminal links, and no effect of number of component intervals was demonstrated. Mixed-interval versus fixed-interval choice could not be predicted from extant data on fixed-interval versus fixed-interval choice.     

Toward a quantitative theory of punishment

In two experiments, pigeons' key pecking for food on concurrent variable-interval schedules was punished with electric shock according to concurrent variable-interval punishment schedules. With unequal frequencies of food but equal rates of punishment associated with the two keys and at several intensities of shock, the response and time allocation of all six pigeons overmatched the obtained relative frequency of food. The overmatching was predicted by a subtractive model of the interaction between punishment and positive reinforcement but not by two alternative models. Increases in the k and r_e parameters of the generalized matching law could not account for the observed shifts in preference.