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.     

Residence time and choice in concurrent foraging schedules

Five pigeons were trained on a concurrent-schedule analogue of the “some patches are empty” procedure. Two concurrently available alternatives were arranged on a single response key and were signaled by red and green keylights. A subject could travel between these alternatives by responding on a second yellow “switching” key. Following a changeover to a patch, there was a probability (p) that a single reinforcer would be available on that alternative for a response after a time determined by the value of λ, a probability of reinforcement per second. The overall scheduling of reinforcers on the two alternatives was arranged nonindependently, and the available alternative was switched after each reinforcer. In Part 1 of the experiment, the probabilities of reinforcement, ρ_red and ρ_green, were equal on the two alternatives, and the arranged arrival rates of reinforcers, λ_red and λ_green, were varied across conditions. In Part 2, the reinforcer arrival times were arranged to be equal, and the reinforcer probabilities were varied across conditions. In Part 3, both parameters were varied. The results replicated those seen in studies that have investigated time allocation in a single patch: Both response and time allocation to an alternative increased with decreasing values of λ and with increasing values of ρ, and residence times were consistently greater than those that would maximize obtained reinforcer rates. Furthermore, both response- and time-allocation ratios undermatched mean reinforcer-arrival time and reinforcer-frequency ratios.     

A quantitative analysis of extreme choice

Six homing pigeons were trained on a variety of concurrent variable-interval schedules in a switching-key procedure. Unlike previous work, reinforcer ratios of up to 160 to 1 and concurrent extinction variable-interval schedules were arranged in order to investigate choice when reinforcer-frequency outcomes were extremely different. The data obtained over 11 conditions were initially analyzed according to the generalized matching law, which fitted the data well. The generalized matching law was then fitted only to conditions in which the reinforcer ratios were between 1 to 10 and 10 to 1. The deviations of choice measures from the other four more extreme reinforcer-ratio conditions were significantly more towards equal choice than predicted by this second generalized matching fit. A contingency-discriminability model, which predicts such deviations, described the data more effectively than did the generalized matching law, and also correctly predicted the maintenance of responding on both alternatives when one was associated with extinction.     

Behavior-dependent reinforcer-rate changes in concurrent schedules: A further analysis

Six pigeons were trained on concurrent variable-interval schedules in three different procedures. The first procedure was a standard concurrent schedule, and the relative reinforcer frequency for responding was varied. The second was a schedule in which a relative left-key response rate (over a fixed period of time) exceeding .75 produced, in the next identical time period a higher reinforcer rate on the right key. If this criterion was not exceeded, equal reinforcer rates were arranged on the two keys in this period. This was the dependent procedure. In the third (independent) procedure, the periods of higher right-key reinforcer rates occurred with the same probability as in the second procedure, but occurred independently of behavior. In the second and third procedures, the fixed-time period (window) was varied from 5 s to 60 s, and to 240 s in the second procedure only. Performance on the two keys was similar in the concurrent and independent procedures. The procedure used in the dependent conditions generally affected performance when the windows were shorter than about 30 s. Models of performance that assume that subjects do not discriminate changes in local relative reinforcer rates cannot account for the data. Moreover, existing models are inherently unable to account for the effects of contingencies of reinforcement between responding on one alternative and gaining reinforcers on another that are arranged or that emerge as a result of time allocated to alternative schedules. Undermatching on concurrent variable-interval schedules may result from such emergent contingencies.     

Stimulus effects on concurrent performance in transition

Six experimentally naive pigeons were exposed to concurrent variable-interval variable-interval schedules in a three-key procedure in which food reinforcement followed pecks on the side keys and pecks on the center key served as changeover responses. In Phase 1, 3 birds were exposed to 20 combinations of five variable-interval values, with each variable-interval value consistently associated with a different color on the side keys. Another 3 pigeons were exposed to the same 20 conditions, but with a more standard procedure that used a nondifferential discriminative stimulus on the two side keys throughout all conditions. In Phase 2, the differential and nondifferential stimulus conditions were reversed for each pigeon. Each condition lasted for one 5-hr session and one subsequent 1-hr session. In the last 14 conditions of each phase, the presence of differential discriminative stimuli decreased the time necessary for differential responding to develop and increased the sensitivity of behavior to reinforcement distribution in the 1st hr of training; during the last hours of training in each condition, however, the effects of the differential discriminative stimuli could not be distinguished from the effects of reinforcement distribution per se. These results show the importance of studying transitions in behavior as well as final performance. They may also be relevant to discrepancies in the results of previous experiments that have used nonhuman and human subjects.     

Strict and random alternation in concurrent variable-interval schedules

Six pigeons responded on pairs of concurrent variable-interval schedules with, in different parts, four different arrangements of alternation between schedules. Following a single switching-key response, alternation was either strict or random, and the alternative presented after a switch (the postswitch alternative) was either signaled by the location of the switching key or unsignaled. Generalized-matching analyses showed little difference in behavior among the different alternation arrangements, except the usual finding of lower sensitivity of response allocation than time allocation was eliminated by arranging random alternation. Patterns of interchangeover times were similar for all arrangements except signaled random alternation. Differences in behavior preceding the different postswitch alternatives were found in the signaled random alternation procedure. Preference was biased towards the color of the signaled postswitch alternative and showed increased sensitivity when the postswitch alternative was to be the one with the higher reinforcer rate. Interchangeover times were substantially shorter when the postswitch alternative was signaled to be different from the current alternative than when it was signaled to be the same. However, when separate reinforcer ratios were calculated for the different postswitch alternatives, those effects were eliminated or greatly reduced. We suggest that, although behavior is indeed influenced by the postswitch alternative, the mechanism is indirect. That is, the distributions of reinforcers between alternatives obtained before each postswitch alternative differ when those alternatives are signaled, and those distributions are discriminated, but the same relations between choice and relative reinforcement hold irrespective of which postswitch alternative is signaled.     

Development and maintenance of choice in a dynamic environment

Four pigeons were exposed to a concurrent procedure similar to that used by Davison, Baum, and colleagues (e.g., Davison & Baum, 2000, 2006) in which seven components were arranged in a mixed schedule, and each programmed a different left∶right reinforcer ratio (1∶27, 1∶9, 1∶3, 1∶1, 3∶1, 9∶1, 27∶1). Components within each session were presented randomly, lasted for 10 reinforcers each, and were separated by 10-s blackouts. These conditions were in effect for 100 sessions. When data were aggregated over Sessions 16-50, the present results were similar to those reported by Davison, Baum, and colleagues: (a) preference adjusted rapidly (i.e., sensitivity to reinforcement increased) within components; (b) preference for a given alternative increased with successive reinforcers delivered via that alternative (continuations), but was substantially attenuated following a reinforcer on the other alternative (a discontinuation); and (c) food deliveries produced preference pulses (immediate, local, increases in preference for the just-reinforced alternative). The same analyses were conducted across 10-session blocks for Sessions 1-100. In general, the basic structure of choice revealed by analyses of data from Sessions 16-50 was preserved at a smaller level of aggregation (10 sessions), and it developed rapidly (within the first 10 sessions). Some characteristics of choice, however, changed systematically across sessions. For example, effects of successive reinforcers within a component tended to increase across sessions, as did the magnitude and length of the preference pulses. Thus, models of choice under these conditions may need to take into account variations in behavior allocation that are not captured completely when data are aggregated over large numbers of sessions.     

Choice performance in several concurrent key-peck treadle-press reinforcement schedules

Five pigeons were exposed to several concurrent variable-interval food reinforcement schedules. For three subjects, one component of the schedule required a key-pecking response, the other a treadle-pressing response. For the other two subjects, both schedule components required treadle-pressing responses. The relative probability of reinforcement associated with the manipulanda was varied from 0 to 1.0 in 13 experimental conditions for the Key-Treadle subjects and nine conditions for the Treadle-Treadle subjects. The results indicated that the logarithms of relative time spent responding, and the logarithms of relative number of responses emitted on a manipulandum, approximated direct linear functions of logarithms of the relative frequencies of reinforcement associated with that manipulandum. No systematic bias in favor of time spent key pecking over time spent treadle pressing was apparent for the Key-Treadle subjects. All subjects exhibited undermatching, in that the ratios of time and response allocation at the alternatives systematically differed from the ratios of reinforcers obtained from the alternatives in the direction of indifference. Key pecking appeared to have no special link to food beyond treadle pressing or what would be expected on the basis of the reinforcement dependencies alone.     

Reporting contingencies of reinforcement in concurrent schedules

Five pigeons were trained on concurrent variable-interval schedules in which two intensities of yellow light served as discriminative stimuli in a switching-key procedure. A conditional discrimination involving a simultaneous choice between red and green keys followed every reinforcer obtained from both alternatives. A response to the red side key was occasionally reinforced if the prior reinforcer had been obtained from the bright alternative, and a response to the green side key was occasionally reinforced if the prior reinforcer had been obtained from the dim alternative. Measures of the discriminability between the concurrent-schedule alternatives were obtained by varying the reinforcer ratio for correct red and correct green responses across conditions in two parts. Part 1 arranged equal rates of reinforcement in the concurrent schedule, and Part 2 provided a 9:1 concurrent-schedule reinforcer ratio. Part 3 arranged a 1:9 reinforcer ratio in the conditional discrimination, and the concurrent-schedule reinforcer ratio was varied across conditions. Varying the conditional discrimination reinforcer ratio did not affect response allocation in the concurrent schedule, but varying the concurrent-schedule reinforcer ratio did affect conditional discrimination performance. These effects were incompatible with a contingency-discriminability model of concurrent-schedule performance (Davison & Jenkins, 1985), which implies a constant discriminability parameter that is independent of the obtained reinforcer ratio. However, a more detailed analysis of conditional discrimination performance showed that the discriminability between the concurrent-schedule alternatives decreased with time since changing over to an alternative. This effect, combined with aspects of the temporal distribution of reinforcers obtained in the concurrent schedules, qualitatively predicted the molar results and identified the conditions that operate whenever contingency discriminability remains constant.     

Variation, repetition, and choice

Experiment 1 investigated the controlling properties of variability contingencies on choice between repeated and variable responding. Pigeons were exposed to concurrent-chains schedules with two alternatives. In the REPEAT alternative, reinforcers in the terminal link depended on a single sequence of four responses. In the VARY alternative, a response sequence in the terminal link was reinforced only if it differed from the n previous sequences (lag criterion). The REPEAT contingency generated low, constant levels of sequence variation whereas the VARY contingency produced levels of sequence variation that increased with the lag criterion. Preference for the REPEAT alternative tended to increase directly with the degree of variation required for reinforcement. Experiment 2 examined the potential confounding effects in Experiment 1 of immediacy of reinforcement by yoking the interreinforcer intervals in the REPEAT alternative to those in the VARY alternative. Again, preference for REPEAT was a function of the lag criterion. Choice between varying and repeating behavior is discussed with respect to obtained behavioral variability, probability of reinforcement, delay of reinforcement, and switching within a sequence.     

Matching and maximizing with concurrent ratio-interval schedules.

Animals exposed to standard concurrent variable-ratio variable-interval schedules could maximize overall reinforcement rate if, in responding, they showed a strong response bias toward the variable-ratio schedule. Tests with the standard schedules have failed to find such a bias and have been widely cited as evidence against maximization as an explanation of animal choice behavior. However, those experiments were confounded in that the value of leisure (behavior other than the instrumental response) partially offsets the value of reinforcement. The present experiment provides another such test using a concurrent procedure in which the confounding effects of leisure were mostly eliminated while the critical aspects of the concurrent variable-ratio variable-interval contingency were maintained: Responding in one component advanced only its ratio schedule while responding in the other component advanced both ratio schedules. The bias toward the latter component predicted by maximization theory was found.     

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.     

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.     

Choice and segmented interreinforcement intervals

Pigeons were trained on a two-key concurrent schedule, where food reinforcers on one key were arranged by a simple variable-interval schedule and on the other key by a chain variable-interval variable-interval schedule. When the initial link of the chain was in effect, the pigeons tended to respond more on the simple variable-interval schedule, and hence less on the chain, than would be expected from a comparison of both the local and overall rates of reinforcement of the two schedules. When the terminal link of the chain was in effect, the pigeons responded more on the chain than would be expected from a comparison of the rates of reinforcement of the schedules then in effect. Overall responding on the chain was not proportional to overall reinforcement on the chain but rather was a by-product of responding during initial- and terminal-link phases.     

Contrast and induction in multiple schedules of discrete-trial concurrent reinforcement

Three pigeons were exposed to two-key discrete-trial concurrent schedules of reinforcement. Red and white key colors alternated irregularly and the assignment of reinforcers depended on key color. The red-key schedules were held constant, with the scheduled relative frequency of reinforcement for left-key pecks set at 0.75, while the white-key schedules varied. When the location of white-key reinforcement was changed from one side to the other, while its overall frequency was constant, red-key choices shifted in the same direction as white-key choices, an induction effect. When the overall frequency of white-key reinforcement was changed while its location remained constant, red key choices shifted in a direction opposite to white-key choices, a contrast effect. Both induction and contrast effects were clearer when the overall frequency of red-key reinforcement was reduced. These data demonstrate that the allocation of responding may exhibit schedule interaction effects similar to those commonly reported for response rate.     

Dynamical concurrent schedules

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

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, experience, and the generalized matching law

Five pigeons were exposed to different pairs of concurrent variable-interval, variable-interval schedules on nine experimental conditions of 30 sessions each. For every session, the parameters of the generalized matching equation were computed for the first five, six, seven, eight, and nine experimental conditions. The exponent a, both for response and time distribution, tended to decrease with increases in number of experimental conditions and to increase with number of sessions per condition, but values of k (bias) varied unsystematically. When the subjects were exposed to five new pairs of schedules, with 55 sessions per condition, the findings were confirmed. Data from the literature on the generalized matching law suggest that the variability of exponent values may be explained in part by the use of naive or experienced subjects in different investigations and by the variability in number of experimental conditions and in number of sessions per condition.     

Maximizing versus matching on concurrent variable-interval schedules

Maximization and matching predictions were examined for a time-based analogue of the concurrent variable-interval variable-ratio schedule. One alternative was a variable interval whose time base operated relatively independent of the schedule chosen, and the other was a discontinuous variable interval for which timing progressed only when selected. Pigeons switched between schedules by pecking a changeover key. The maximization hypothesis predicts that subjects will show a bias toward the discontinuous variable interval and undermatching; however the obtained results conformed closely to the predictions of the matching law. Finally, a quantitative comparison was made of the bias and sensitivity estimates obtained in published concurrent variable-interval variable-ratio analogue studies. Results indicated that only the ratio-based analogue of the concurrent variable interval variable ratio studied by Green, Rachlin, and Hanson (1983) produced significant bias toward the variable-ratio alternative and undermatching, as predicted by reinforcement maximization.     

Substitution effects in a generalized token economy with pigeons

Pigeons made repeated choices between earning and exchanging reinforcer‐specific tokens (green tokens exchangeable for food, red tokens exchangeable for water) and reinforcer‐general tokens (white tokens exchangeable for food or water) in a closed token economy. Food and green food tokens could be earned on one panel; water and red water tokens could be earned on a second panel; white generalized tokens could be earned on either panel. Responses on one key produced tokens according to a fixed‐ratio schedule, whereas responses on a second key produced exchange periods, during which all previously earned tokens could be exchanged for the appropriate commodity. Most conditions were conducted in a closed economy, and pigeons distributed their token allocation in ways that permitted food and water consumption. When the price of all tokens was equal and low, most pigeons preferred the generalized tokens. When token‐production prices were manipulated, pigeons reduced production of the tokens that increased in price while increasing production of the generalized tokens that remained at a fixed price. The latter is consistent with a substitution effect: Generalized tokens increased and were exchanged for the more expensive reinforcer. When food and water were made freely available outside the session, token production and exchange was sharply reduced but was not eliminated, even in conditions when it no longer produced tokens. The results join with other recent data in showing sustained generalized functions of token reinforcers, and demonstrate the utility of token‐economic methods for assessing demand for and substitution among multiple commodities in a laboratory context.