Peak shift as a function of multiple schedules of reinforcement

Pigeons were trained to respond to two stimuli on the wavelength continuum, 550 nm and 570 nm, each correlated with an independent schedule of reinforcement. The multiple schedule component in effect during 550 nm (S1) was always a variable-interval 1-min. During the 570-nm stimulus (S2) the second component of the schedule was either variable-interval 30-sec, 1-min, 2-min, 5-min, or extinction for different groups of birds. Generalization gradients were obtained after this training, with the following results: (1) response rate to S1 during training was related to the reinforcement frequency associated with S2; the distribution of responding during generalization testing was a function of the schedules of reinforcement used during training and the response rates they produced. Decreases in the relative frequency of reinforcement correlated with S2 resulted in increases in the distribution shift of responses away from S2 during generalization testing.     

Performance in concurrent fixed-interval schedules

Six pigeons were trained on a variety of concurrent fixed-interval fixed-interval schedules. Matching between response or time ratios and ratios of obtained numbers of reinforcements was found for eight of 12 schedules studied. Cumulative records showed both typical burst-and-break patterns and also atypical response patterns in which response rate was constant between reinforcements on a schedule. Matching occurred only when the same pattern was present on both concurrent schedules. When different response patterns were generated by the two schedules, the pigeons consistently emitted fewer responses to the shorter fixed-interval than required by matching.     

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.     

Choice between concurrent schedules

Six pigeons pecked for food in a three-key experiment. A subject at any time could choose the left or right key and receive reinforcement according to one two-key concurrent variable-interval variable-interval schedule of reinforcement, or it could peck the center key. A peck on the center key arranged the complementary two-key concurrent variable-interval variable-interval schedule on the left and right keys. The two different two-key concurrent schedules arranged reinforcements concurrently and were signalled by two different colors of key lights. Choice behavior in the presence of a given color conformed to the usual relationship in two-key concurrent schedules: the relative frequency of responding on a key approximately equalled the relative frequency of reinforcement on that key. Preference for a two-key concurrent schedule, which was equivalent to preference for a color, was measured by the percentage of all responses on the left and right keys in the presence of that color: this percentage approximately equalled the percentage of all reinforcements that were delivered in the presence of that color. Thus, choice between concurrent schedules conforms approximately to the same relationship as does choice between alternatives in a single concurrent schedule.     

Income maximizing in concurrent interval-ratio schedules

Three mice chose between concurrent variable-ratio variable-interval schedules to produce a warm air stream while they were housed in a cold chamber. Across conditions, the duration of the warm air stream was varied between 10 and 80 s and was equal for both schedules. Preference for the VI schedule covaried with reinforcer duration as predicted by maximizing accounts of choice.     

Matching in concurrent variable-interval avoidance schedules

After pretraining with multiple variable-interval avoidance schedules, two rats were exposed to a series of concurrent variable-interval avoidance schedules. Responses on two levers cancelled delivery of electric shocks arranged according to two independent variable-interval schedules. The ratio of responses and time spent on the two levers approximately matched the ratio of shocks avoided on each. Matching to the number of shocks received was not obtained. Concurrent variable-interval avoidance can therefore be added to the group of positive and negative reinforcement schedules that can be expressed in the quantitative framework of the matching law.     

Inhibitory stimulus control in concurrent schedules

Six pigeons were exposed to two keys, a main key and a changeover key. Pecking the main key was reinforced on a variable-interval 5-min schedule when the key was blue and never reinforced when the key displayed a vertical line on a blue background. Each peck on the changeover key changed the stimulus displayed on the main key. Each subject was given two generalization tests, consisting of presentations on the main key of six orientations of the line on the blue background, with no reinforcements being given. In one test changeover-key pecks changed the stimulus; in the other test the changeover key was covered and the experimenter controlled stimulus changes. Both responses to the six stimuli and time spent in the presence of the stimuli gave U-shaped gradients when the changeover key was operative. With most subjects, absolute rates of responding to each stimulus produced unsystematic gradients, whether or not the changeover key was operative.     

Preference in concurrent variable-interval fixed-ratio schedules

Five pigeons were trained on concurrent variable-interval fixed-ratio schedules in three experiments. Experiment 1 used two variable-interval schedules and one fixed-ratio schedule, and the ratio requirement was varied. Using the generalized matching law, sensitivity to reinforcement was close to 1.0, but performance was biased toward the variable-interval schedule with the lower reinforcement rate. In Experiment 2, which used one variable-interval and one fixed-ratio schedule, the interval schedule was varied. All birds showed sensitivities to reinforcement of less than 1.0 and of less than the values obtained in Experiment 1. The performance was also biased toward the fixed-ratio schedule. Because the generalized matching law could not account for the differences in the data from Experiments 1 and 2, an extension of this law was suggested and successfully tested in Experiment 3. The proposed dual-sensitivity model was also shown to clarify some previously reported results.     

Timeout from concurrent schedules.

Response-contingent timeouts of equal duration and frequency were added to both alternatives of unequal concurrent schedules of reinforcement. For each of 4 pigeons in Experiment 1, relative response rates generally became less extreme as the frequency of timeout increased. In Experiment 2, relative response rates consistently approached indifference as the duration of timeout was increased. Variation in time allocation was less consistent in both experiments. Absolute response rates did not vary with the timeout contingency in either experiment. In a third experiment, neither measure of choice varied systematically when the duration of a postreinforcement blackout was varied. In contrast to the present results, preference has been shown to vary directly with the parameters of shock delivery in related procedures. The pattern of results in the first two experiments follows that obtained with other manipulations of the overall rate of reinforcement in concurrent schedules. The results of the third experiment suggest that an intertrial interval following reinforcement is not a critical feature of the overall rate of reinforcement.     

Variable-time reinforcement in multiple and concurrent schedules

Experiment I examined the role of a reduced rate of responding in the occurrence of behavioral contrast. Four rats and a pigeon were exposed to a two-component multiple schedule in which one component was always a variable-interval schedule. The second component was, at different times, either a variable-time schedule in which food was delivered independently of responding, or extinction. Both extinction and the variable-time schedule reduced the rate of responding in the second component. Behavioral contrast was observed, however, only when extinction was scheduled in the second component. Experiment II examined preference, as measured by time allocation in concurrent schedules for a variable-interval schedule relative to a variable-time schedule. Two rats displayed a lack of preference between the two schedules. The results of these experiments support a preference interpretation of behavioral contrast, which holds that behavioral contrast is the result of the introduction of a less-preferred condition in one component of a multiple schedule.     

Signalled reinforcement in multiple and concurrent schedules

Five pigeons were exposed to multiple and concurrent variable-interval, variable-interval reinforcement schedules in which reinforcement availability in one component was never signalled. During certain phases of the experiment, reinforcement availability in the other component was signalled. Behavioral contrast was observed in seven of eight instances when reinforcement availability in the multiple schedules was signalled. Under the concurrent schedules in which reinforcement availability was signalled, the subjects did not always allocate more time to (prefer) the component containing non-signalled reinforcement, as would be predicted by an account of behavioral contrast holding that contrast results from the introduction of a less-preferred condition in one component of a multiple schedule.     

Response and time allocation in concurrent second-order schedules

Six pigeons were trained on two-key concurrent variable-interval schedules in which the required response was the completion of a fixed number of key pecks. When the required number of pecks was equal on the two keys, response- and time-allocation ratios under-matched obtained reinforcement rate ratios. A similar result was found when the required number of pecks was unequal, except that performance, measured in response terms, was biased to the shorter required number of pecks and was less sensitive to reinforcement-rate changes. No such differences were found in the data on time spent responding. When the variable-interval schedules were kept constant and the required numbers of pecks were systematically varied, response ratios changed inversely with the ratio of the required number of pecks, but time-allocation ratios varied directly with the same independent variable. Thus, on response measures, pigeons “prefer” the schedule with the smaller peck requirement, but on time measures they “prefer” the schedule with the larger peck requirement. This finding is inconsistent with a commonsense notion of choice, which sees response and time-allocation measures as equivalent.     

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.     

Maximizing and matching on concurrent ratio schedules

Pigeons on concurrent variable-ratio variable-ratio schedules usually, though not always, maximize reinforcements per response. When the ratios are equal, maximization implies no particular distribution of responses to the two alternatives. When the ratios are unequal, maximization calls for exclusive preference for the smaller ratio. Responding conformed to these requirements for maximizing, which are further shown to be consistent with the conception of reinforcement implicit in the matching law governing relative responding in concurrent interval schedules.     

Peak shift in honey bee olfactory learning

If animals are trained with two similar stimuli such that one is rewarding (S+) and one punishing (S?), then following training animals show a greatest preference not for the S+, but for a novel stimulus that is slightly more different from the S? than the S+ is. This peak shift phenomenon has been widely reported for vertebrates and has recently been demonstrated for bumblebees and honey bees. To explore the nature of peak shift in invertebrates further, here we examined the properties of peak shift in honey bees trained in a free-flight olfactory learning assay. Hexanal and heptanol were mixed in different ratios to create a continuum of odour stimuli. Bees were trained to artificial flowers such that one odour mixture was rewarded with 2 molar sucrose (S+), and one punished with distasteful quinine (S?). After training, bees were given a non-rewarded preference test with five different mixtures of hexanal and heptanol. Following training bees’ maximal preference was for an odour mixture slightly more distinct from the S? than the trained S+. This effect was not seen if bees were initially trained with two distinct odours, replicating the classic features of peak shift reported for vertebrates. We propose a conceptual model of how peak shift might occur in honey bees. We argue that peak shift does not require any higher level of processing than the known olfactory learning circuitry of the bee brain and suggest that peak shift is a very general feature of discrimination learning.     

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.     

Reinforcement of eye movement with concurrent schedules

Human macrosaccadic eye movements to two areas of a four-dial display were conditioned by concurrent variable-interval schedules of signals. Reinforcers (signals) were delivered to the two right-hand dials on one schedule and to the two left-hand dials on another, independent schedule. The use of a changeover delay between crossover eye movements and reinforcement had the effect of changing the pattern of scanning from fixating four dials in succession or in a Z-shaped pattern to scanning vertically the dials on either side with fewer crossovers. In the presence of a changeover delay, subjects matched relative eye-movement rates and relative reinforcement rates on each schedule. Rate of crossover eye movements, with a changeover delay in effect, was also inversely related to the difference in reinforcements arranged by the concurrent schedules. The results suggest that for stimuli whose critical components are arranged spatially, conditioned eye movements play an important part in selective stimulus control.     

Optimal behavior and concurrent variable interval schedules

Behavior maintained with 2-component concurrent variable interval schedules of reinforcement (CONC VIVI) is described well by the matching law. Deviations from matching behavior have been handled by adding free parameters to the matching law equation. With CONC VIVI schedules there are infinitely many solutions to the matching law equation at each value of the procedural parameters. However, at each value of the procedural parameters, only one combination of durations of intervals spent in each VI component (dwell times) yields the combined maximum reinforcement rate. The equations that yield the optimal dwell times solution for CONC VIVI schedules are mathematically incompatible with the matching law. Optimal performance and matching coincide only when the parameter values of the two VI components are equal. It seems reasonable to use optimal behavior to assess performance in these schedules. Researchers have not compared optimal and empirical performances in CONC VIVI possibly because the equations for optimal dwell times (ODT) can be solved only numerically. We present a table of ODT for a wide range of VIs and changeover delays. We also derive a function m that can be used to compare matching data and the matching behavior predictions of optimization. We prove that 0.5<m<1.003502, and we describe some of the more nteresting properties of the function.     

Performance in concurrent interval schedules: a systematic replication

Five pigeons were trained on a variety of concurrent interval schedules that arranged reinforcements at either fixed or variable times after the last reinforcement. Two measures were obtained: the number of responses on each schedule, and the time spent responding on each schedule. Ratios of response rates on the two schedules did not equal ratios of reinforcement rates when both schedules were variable nor when one was variable and the other fixed. Ratios of times spent responding approximately equalled ratios of reinforcement rates when both schedules were variable, but did not do so when one was fixed.     

Sensitivity to reinforcement in concurrent arithmetic and exponential schedules

The generalized matching law states that the logarithm of the ratio of responses emitted or time spent responding in concurrent variable-interval schedules is a linear function of the logarithm of the ratio of reinforcements obtained. The slope of this relation, sensitivity to reinforcement, varies about 1.0 but has been shown to be different when obtained in different laboratories. The present paper analyzed the results from 18 experiments on concurrent variable-interval schedule performance and showed that response-allocation sensitivity to reinforcement was significantly smaller when arithmetic, rather than exponential, progressions were used to produce variable-interval schedules. There were no differences in time-allocation sensitivity between the two methods of constructing variable-interval schedules. Since the two laboratories have consistently used different methods for constructing variable-interval schedules, the differences in obtained sensitivities to reinforcement are explained. The reanalysis suggests that animals may be sensitive to differences in the distribution of reinforcements in time.