Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Sensitivity to reinforcer duration in a self-control procedure

In a concurrent-chains procedure, pigeons' responses on left and right keys were followed by reinforcers of different durations at different delays following the choice responses. Three pairs of reinforcer delays were arranged in each session, and reinforcer durations were varied over conditions. In Experiment 1 reinforcer delays were unequal, and in Experiment 2 reinforcer delays were equal. In Experiment 1 preference reversal was demonstrated in that an immediate short reinforcer was chosen more frequently than a longer reinforcer delayed 6 s from the choice, whereas the longer reinforcer was chosen more frequently when delays to both reinforcers were lengthened. In both experiments, choice responding was more sensitive to variations in reinforcer duration at overall longer reinforcer delays than at overall shorter reinforcer delays, independently of whether fixed-interval or variable-interval schedules were arranged in the choice phase. We concluded that preference reversal results from a change in sensitivity of choice responding to ratios of reinforcer duration as the delays to both reinforcers are lengthened.     

Concurrent schedules: reinforcer magnitude effects

Five pigeons were trained on pairs of concurrent variable-interval schedules in a switching-key procedure. The arranged overall rate of reinforcement was constant in all conditions, and the reinforcer-magnitude ratios obtained from the two alternatives were varied over five levels. Each condition remained in effect for 65 sessions and the last 50 sessions of data from each condition were analyzed. At a molar level of analysis, preference was described well by a version of the generalized matching law, consistent with previous reports. More local analyses showed that recently obtained reinforcers had small measurable effects on current preference, with the most recently obtained reinforcer having a substantially larger effect. Larger reinforcers resulted in larger and longer preference pulses, and a small preference was maintained for the larger-magnitude alternative even after long inter-reinforcer intervals. These results are consistent with the notion that the variables controlling choice have both short- and long-term effects. Moreover, they suggest that control by reinforcer magnitude is exerted in a manner similar to control by reinforcer frequency. Lower sensitivities when reinforcer magnitude is varied are likely to be due to equal frequencies of different sized preference pulses, whereas higher sensitivities when reinforcer rates are varied might result from changes in the frequencies of different sized preference pulses.     

Choice in a variable environment: effects of unequal reinforcer distributions

Six pigeons were trained in a procedure in which sessions included seven unsignaled components, each offering two pecking keys, and each providing a potentially different reinforcer ratio between the two keys. Across conditions, various combinations of reinforcer ratios and reinforcer-magnitude ratios were used to create unequal reinforcer distributions between the two alternatives when averaged across a session. The results extended previous research using the same basic procedure that had included only reinforcer distributions symmetrical around 1:1. Data analyses suggested that the variables controlling choice operated at a number of levels: First, individual reinforcers had local effects on choice; second, sequences of successive reinforcers obtained at the same alternative (continuations) had cumulative effects; and, third, when these sequences themselves occurred with greater frequency, their effects further cumulated. A reinforcer obtained at the other alternative following a sequence of continuations (a discontinuation) had a large effect and apparently reset choice to levels approximating the sessional reinforcer ratio.     

Reinforcer-ratio variation and its effects on rate of adaptation

Six pigeons were trained in sessions that consisted of six or seven concurrent-schedule components, each of which could have a different reinforcer ratio arranged in it. The components were unsignaled and occurred in a random order separated by 10-s blackouts. The overall reinforcer rate arranged in each component was 2.22 reinforcers per minute. In Experiment 1, the range of reinforcer ratios in the seven components was varied from a condition in which the ratios were always 1:1, to a condition in which the ratios varied between concurrent variable-interval 27 s extinction (EXT) and concurrent extinction variable-interval 27 s (ratios of 1:EXT, 9:1, 3:1, 1:1, 1:3, 1:9, EXT:1). In Experiment 2, the range of reinforcer ratios was always 27:1 to 1:27, and the presence and absence of the intermediate reinforcer ratios used in Experiment 1 (9:1, 3:1, 1:1, 1:3, 1:9) were investigated. Log response-allocation ratios in components changed rapidly with increasing numbers of reinforcers in components, and Experiment 1 showed that sensitivity to reinforcement was usually higher when the range of reinforcer ratios was greater. When the range of reinforcer ratios was kept constant in Experiment 2, the presence or absence of less extreme reinforcer ratios had no clear effect on sensitivity. At a local level, individual reinforcers had predictable quantitative effects on response ratios: Successive same-alternative reinforcers in a component had rapidly diminishing effects in both experiments. Reinforcers obtained on the opposite alternative to one or more prior reinforcers always had large effects on preference, and these changes were greater when the range of reinforcer ratios was greater. The effects of such reinforcers in changing preference were enhanced, and produced clear preference reversals, when intermediate reinforcer ratios were absent in Experiment 2. Two processes, one local to reinforcers and one with a longer time course, may be necessary to account for these results.     

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.     

Concurrent-schedule performance in transition: changeover delays and signaled reinforcer ratios

Six pigeons were trained in experimental sessions that arranged six or seven components with various concurrent-schedule reinforcer ratios associated with each. The order of the components was determined randomly without replacement. Components lasted until the pigeons had received 10 reinforcers, and were separated by 10-s blackout periods. The component reinforcer ratios arranged in most conditions were 27:1, 9:1, 3:1, 1:1, 1:3, 1:9 and 1:27; in others, there were only six components, three of 27:1 and three of 1:27. In some conditions, each reinforcement ratio was signaled by a different red-yellow flash frequency, with the frequency perfectly correlated with the reinforcer ratio. Additionally, a changeover delay was arranged in some conditions, and no changeover delay in others. When component reinforcer ratios were signaled, sensitivity to reinforcement values increased from around 0.40 before the first reinforcer in a component to around 0.80 before the 10th reinforcer. When reinforcer ratios were not signaled, sensitivities typically increased from zero to around 0.40. Sensitivity to reinforcement was around 0.20 lower in no-changeover-delay conditions than in changeover-delay conditions, but increased in the former after exposure to changeover delays. Local analyses showed that preference was extreme towards the reinforced alternative for the first 25 s after reinforcement in changeover-delay conditions regardless of whether components were signaled or not. In no-changeover-delay conditions, preference following reinforcers was either absent, or, following exposure to changeover delays, small. Reinforcers have both local and long-term effects on preference. The former, but not the latter, is strongly affected by the presence of a changeover delay. Stimulus control may be more closely associated with longer-term, more molar, reinforcer effects.     

Choice in a variable environment: every reinforcer counts

Six pigeons were trained in sessions composed of seven components, each arranged with a different concurrent-schedule reinforcer ratio. These components occurred in an irregular order with equal frequency, separated by 10-s blackouts. No signals differentiated the different reinforcer ratios. Conditions lasted 50 sessions, and data were collected from the last 35 sessions. In Part 1, the arranged overall reinforcer rate was 2.22 reinforcers per minute. Over conditions, number of reinforcers per component was varied from 4 to 12. In Part 2, the overall reinforcer rate was six per minute, with both 4 and 12 reinforcers per component. Within components, log response-allocation ratios adjusted rapidly as more reinforcers were delivered in the component, and the slope of the choice relation (sensitivity) leveled off at moderately high levels after only about eight reinforcers. When the carryover from previous components was taken into account, the number of reinforcers in the components appeared to have no systematic effect on the speed at which behavior changed after a component started. Consequently, sensitivity values at each reinforcer delivery were superimposable. However, adjustment to changing reinforcer ratios was faster, and reached greater sensitivity values, when overall reinforcer rate was higher. Within a component, each successive reinforcer from the same alternative ("confirming") had a smaller effect than the one before, but single reinforcers from the other alternative ("disconfirming") always had a large effect. Choice in the prior component carried over into the next component, and its effects could be discerned even after five or six reinforcement and nonreinforcement is suggested.     

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.     

Discriminability and sensitivity to reinforcer magnitude in a detection task

Three pigeons discriminated between two sample stimuli (intensities of red light). The difficulty of the discrimination was varied over four levels. At each level, the relative reinforcer magnitude for the two correct responses was varied across conditions, and the reinforcer rates were equal. Within levels, discriminability between the sample stimuli did not change systematically as reinforcer magnitude varied. Across levels, the sensitivity of behavior to changes in the reinforcer-magnitude ratio decreased as the discriminability between the sample stimuli increased. Subsequent analysis showed that this relation was limited to performance following only one of the sample stimuli, the dim red light that remained constant across all conditions. Extant behavioral models of signal detection cannot easily accommodate these results.     

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

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

Component probability and component reinforcer rate as biasers of free-operant detection

Six pigeons were trained on multiple schedules whose components were concurrent variable-interval extinction and concurrent extinction variable-interval schedules. In Experiments 1a and 1b the stimuli signaling the components were two different light intensities, and in Experiments 2a and 2b they were two identical intensities. The components of the multiple schedule changed probabilistically after each reinforcer. In Experiments 1a and 2a, the probability of presenting the components was varied over five conditions and a replication. In Experiments 1b and 2b, the component probability was .5 and the component reinforcer rates were varied systematically over five conditions and a replication. The data, analyzed according to the Davison-Tustin behavioral detection model, confirmed that the discriminability of the stimuli signaling the components was high when the stimuli were different, and low when the stimuli were the same. Discriminability, measured by log d, was unaffected by component probability variation and by component reinforcer-rate variation. When discriminability was high, bias, or the response allocation between the two keys, was more strongly affected by variation of reinforcer rate within components than by variation of component probability, but the reverse was found when discriminability was low. The results suggest that free-operant detection performance is controlled by the rates of reinforcers in periods of time in which stimuli signal differential contingencies. These periods comprise the components when the component stimuli are discriminable, and comprise the total session when the components are indiscriminable. An extension of the Davison-Tustin behavioral detection model that incorporates these results is presented.     

Choosing among multiple alternatives: Relative and overall reinforcer rates

Choice behavior among two alternatives has been widely researched, but fewer studies have examined the effect of multiple (more than two) alternatives on choice. Two experiments investigated whether changing the overall reinforcer rate affected preference among three and four concurrently scheduled alternatives. Experiment 1 trained six pigeons on concurrent schedules with three alternatives available simultaneously. These alternatives arranged reinforcers in a ratio of 9:3:1 with the configuration counterbalanced across pigeons. The overall rate of reinforcement was varied across conditions. Preference between the pair of keys arranging the 9:3 reinforcer ratio was less extreme than the pair arranging the 3:1 reinforcer ratio regardless of overall reinforcer rate. This difference was attributable to the richer alternative receiving fewer responses per reinforcer than the other alternatives. Experiment 2 trained pigeons on concurrent schedules with four alternatives available simultaneously. These alternatives arranged reinforcers in a ratio of 8:4:2:1, and the overall reinforcer rate was varied. Next, two of the alternatives were put into extinction and the random interval duration was changed from 60 s to 5 s. The ratio of absolute response rates was independent of interval length across all conditions. In both experiments, an analysis of sequences of visits following each reinforcer showed that the pigeons typically made their first response to the richer alternative irrespective of which alternative was just reinforced. Performance on these three‐ and four‐alternative concurrent schedules is not easily extrapolated from corresponding research using two‐alternative concurrent schedules.     

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.     

Response–reinforcer dependency and resistance to change

The effects of the response–reinforcer dependency on resistance to change were studied in three experiments with rats. In Experiment 1, lever pressing produced reinforcers at similar rates after variable interreinforcer intervals in each component of a two‐component multiple schedule. Across conditions, in the fixed component, all reinforcers were response‐dependent; in the alternative component, the percentage of response‐dependent reinforcers was 100, 50 (i.e., 50% response‐dependent and 50% response‐independent) or 10% (i.e., 10% response‐dependent and 90% response‐independent). Resistance to extinction was greater in the alternative than in the fixed component when the dependency in the former was 10%, but was similar between components when this dependency was 100 or 50%. In Experiment 2, a three‐component multiple schedule was used. The dependency was 100% in one component and 10% in the other two. The 10% components differed on how reinforcers were programmed. In one component, as in Experiment 1, a reinforcer had to be collected before the scheduling of other response‐dependent or independent reinforcers. In the other component, response‐dependent and ‐independent reinforcers were programmed by superimposing a variable‐time schedule on an independent variable‐interval schedule. Regardless of the procedure used to program the dependency, resistance to extinction was greater in the 10% components than in the 100% component. These results were replicated in Experiment 3 in which, instead of extinction, VT schedules replaced the baseline schedules in each multiple‐schedule component during the test. We argue that the relative change in dependency from Baseline to Test, which is greater when baseline dependencies are high rather than low, could account for the differential resistance to change in the present experiments. The inconsistencies in results across the present and previous experiments suggest that the effects of dependency on resistance to change are not well understood. Additional systematic analyses are important to further understand the effects of the response–reinforcer relation on resistance to change and to the development of a more comprehensive theory of behavioral persistence.     

Choice in a variable environment: effects of blackout duration and extinction between components

Pigeons were trained in a procedure in which sessions included seven four- or 10-reinforcer components, each providing a different reinforcer ratio that ranged from 27:1 to 1:27. The components were arranged in random order, and no signals differentiated the component reinforcer ratios. Each condition lasted 50 sessions, and the data from the last 35 sessions were analyzed. Previous results using 10-s blackouts between components showed some carryover of preference from one component to the next, and this effect was investigated in Experiment 1 by varying blackout duration from 1 s to 120 s. The amount of carryover decreased monotonically as the blackout duration was lengthened. Preference also decreased between reinforcers within components, suggesting that preference change during blackout might follow the same function as preference change between reinforcers. Experiment 2 was designed to measure preference change between components more directly and to relate this to preference change during blackout. In two conditions a 60-s blackout occurred between components, and in two other conditions a 60-s period of unsignaled extinction occurred between components. Preference during the extinction period progressively fell toward indifference, and the level of preference following extinction was much the same as that following blackout. Although these results are consistent with Davison and Baum's (2000) theory of the effects of reinforcers on local preference, other findings suggest that theory is incomplete: After a sequence of reinforcers from one alternative, some residual preference remained after 60 s of extinction or blackout, indicating the possibility of an additional longer term accumulation of reinforcer effects than originally suggested.     

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.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Human symbolic matching-to-sample performance: Effects of reinforcer and sample-stimulus probabilities

Four experiments, each with 6 human subjects, varied the distribution of reinforcers for correct responses and the probability of sample-stimulus presentation in symbolic matching-to-sample procedures. Experiment 1 held the sample-stimulus probability constant and varied the ratio of reinforcers obtained for correct responses on the two alternatives across conditions. There was a positive relation between measures of response bias and the ratio of reinforcers. Experiment 2 held the ratio of reinforcers constant and varied the sample-stimulus probability across conditions. Unlike previous studies that used pigeons as subjects, there was a negative relation between bias and the ratio of sample-stimulus presentations. In Experiment 3, the sample-stimulus probability and the reinforcer ratio covaried across conditions. Response bias did not vary systematically across conditions. In Experiments 1 to 3, correct responses were reinforced intermittently. Experiment 4 used the same procedure as Experiment 3, but all correct responses now produced some scheduled consequence. There was a positive relation between response bias and the ratio of reinforcers. The results suggest that human performance in these tasks was controlled by both the relative frequency of reinforced responses and the relative frequency of nonreinforced responses.     

Choice between delayed reinforcers in an adjusting-delay schedule: The effects of absolute reinforcer size and deprivation level

Choice between two reinforcers differing in magnitude and delay was investigated in rats using an adjusting-delay discrete-trials schedule in which the two reinforcers were associated with two levers (A and B). The delay to Reinforcer A (the smaller reinforcer) was always 2 sec, whereas the delay to Reinforcer B was varied in accordance with the distribution of choices in successive blocks of trials. In Experiment 1, the mean delay to the large reinforcer during the last 5 of 60 training sessions was greater when the rats were maintained at 80% than when they were maintained at 90% of their free-feeding body weights. In Experiment 2, the delay to the larger reinforcer was greater when the two reinforcers consisted of one and two 45-mg food pellets than when they consisted of three and six pellets. The results are consistent with a model of “self-control” which posits hyperbolic relations between reinforcer value and reinforcer magnitude, and between reinforcer value and delay of reinforcement.