Choice and timing in concurrent chains: effects of initial-link duration

Theories of timing have been applied to choice between delayed rewards by assuming that delays are represented in memory and that subjects sample from memory when choosing between alternatives. To search for covariation in single-trial measures of performance that might confirm this assumption, we used a procedure that allowed for convergent measurement of choice and timing behavior. Four pigeons responded in a concurrent chains/peak procedure in which the terminal links were fixed-interval (FI) 8s and FI 16s, across conditions the duration of the initial-link schedule was either short or long, and one quarter of the terminal links lasted for 48 s and ended without reinforcer delivery. Preference for the FI 8-s alternative was stronger with shorter initial links, replicating the 'initial-link effect'. Responding on no-food trials was unaffected by initial-link duration, and aggregated across trials, was typical of the peak procedure: response distributions were approximately Gaussian, with modes near the FI schedule durations, and variance was greater for the FI 16-s terminal link. Analysis of local measures of initial-link performance (e.g., pause to begin responding, time spent responding, number and duration of visits to each alternative, etc.) found that the initial-link effect was associated with an increase in the number and duration of visits per cycle to the nonpreferred alternative. Regression analyses showed that local initial-link measures contributed relatively little additional variance in predicting performance on individual no-food trials beyond that accounted for by FI schedule. Our results provide no clear evidence that initial- and terminal-link responding in concurrent chains are mediated by a common representation of terminal-link delays.     

The role of terminal-link stimuli in concurrent-chain schedules: revisited using a behavioral-history procedure

A behavioral-history procedure was used to study the function of terminal-link stimuli as conditioned reinforcers in multiple concurrent-chain schedules of reinforcement. First, three pigeons were exposed to multiple concurrent-chain schedules in which the two multiple-schedule components were correlated with a blue and a white stimulus, respectively. In each component the initial links were equal independent variable-interval (VI) 15 s schedules. A fixed-interval (FI) 10 s schedule operated on the red key in one terminal link while extinction operated on the green key in the alternative terminal link. When large preferences for the red stimulus had been established, two tests were conducted. In the terminal-link test, under new initial-link stimuli--purple and brown--an FI 10 s schedule operated for both the red and green terminal-link stimuli. In the subsequent initial-link test, the blue and white initial-link stimuli were reintroduced, and, as in the terminal-link test, FI 10s operated for both the red and the green terminal-link stimuli. In the terminal-link test, the three pigeons showed no preference for the terminal links with the red stimulus, but showed clear and consistent preferences for the red stimulus when blue and white stimuli were reintroduced as initial-link stimuli in the initial-link test. This suggests that there are multiple sources of control over initial-link response allocation in concurrent-chains, including control by both terminal- and initial-link stimuli.     

Effects of unpredictable changes in initial-link duration on choice and timing

Four pigeons responded in a concurrent-chains procedure in which terminal-link schedules were fixed-interval (FI) 10 s and FI 20 s. Across sessions, the location of the shorter terminal-link changed according to a pseudorandom binary sequence. Each session, the variable-interval initial-link schedule value was sampled from a uniform distribution that ranged from 0.01 to 30 s. On some terminal links, food was withheld to obtain measures of temporal control. Terminal-link delays determined choice (log initial-link response ratios) and timing (start and stop times on no-food trials) measures, which stabilized within the 1st half of each session. Preference for the shorter terminal-link delay was a monotonically decreasing function of initial-link duration. There was no evidence of control by initial-link durations from previous sessions.     

Psychological distance to reward: equating the number of stimulus and response segments

Psychological distance to reward, or the segmentation effect, refers to the preference for a terminal link of a concurrent-chains schedule consisting of a simple reinforcement schedule (e.g. fixed interval [FI] 30s) relative to its chained-schedule counterpart (e.g. chained FI 15s FI 15s). This experiment was conducted to examine whether the segmentation effect is due to the number of terminal-link stimulus and response segments per se. Three pigeons pecked under a concurrent-chains schedule in which identical variable-interval (VI) schedules operated in the initial links. In each session, half the terminal-link entries followed one initial-link key and the other half followed the other initial-link key. The initial-link keys correlated with the different terminal links were manipulated across conditions. In the first three conditions, each terminal link contained a chained fixed-time (FT) FT schedule, and in the final three conditions, each terminal link contained a chained FI FI schedule. In each condition, in one terminal link (alternating), the order of two key colors correlated with the different schedule segments alternated across terminal-link entries, whereas in the other terminal link (constant), the order of two other key colors was identical for each entry. With the chained FT FT schedule terminal links, there was indifference between the alternating and constant terminal links within and across pigeons, as indexed by initial-link choice proportions. In addition, terminal-link response rates were relatively low. With the chained FI FI schedule terminal links, for each pigeon, there was relatively more preference for the alternating terminal link and terminal-link response rates increased relative to conditions with the chained FT FT schedule terminal links. These data suggest that the segmentation effect is not due simply to the number of terminal-link stimulus or response segments per se, but rather to a required period of responding during a stimulus segment that never is paired with reinforcement.     

Does the terminal-link effect depend on duration or reinforcement rate?

Preference in concurrent chains for the richer terminal-link schedule becomes more extreme as the schedule values increase with their ratio held constant, a result known as the terminal-link effect. We report two experiments that attempt to determine whether this effect is related to terminal-link duration or the overall rate of reinforcement. These variables have been confounded in prior studies, but can be separated by comparing variable-duration schedules that end after a single reinforcer has been earned, with constant-duration schedules during which a variable number of reinforcers may be earned. In Experiment 1, the terminal-link effect was obtained with variable-duration schedules when duration and overall reinforcement rate were manipulated, but not with constant-duration schedules when overall reinforcement rate was changed with duration held constant. In Experiment 2, the terminal-link effect was obtained with constant-duration schedules when duration was manipulated with overall reinforcement rate held constant. Taken together, these results show that the terminal-link effect depends on changes in terminal-link duration, not overall reinforcement rate (or equivalently, average time to reinforcement). This accords with the account of the terminal-link effect provided by the contextual choice model [J. Exp. Anal. Behav. 61 (1994) 113] but not delay-reduction theory [J. Exp. Anal. Behav. 12 (1969) 723].     

Rapid acquisition of preference in concurrent schedules: effects of reinforcement amount

Four pigeons were trained on concurrent variable-interval 30-s schedules. Relative reinforcer amounts arranged across the two alternatives were varied across sessions according to a pseudorandom binary sequence [cf., Hunter, I., Davison, M., 1985. Determination of a behavioral transfer function: white-noise analysis of session-to-session response-ratio dynamics on concurrent VI schedules. J. Exp. Anal. Behav. 43, 43-59]; the ratios (left/right) were either 1/7 or 7/1. Reinforcer amount was manipulated by varying the number of 1.2s hopper presentations. Sessions ended after 30 reinforcers (15 for each alternative). After approximately 30 sessions, response ratios for all pigeons began to track the changes in amount ratio (i.e., subjects' responding showed a moderate increase in sensitivity of responding to reinforcer amount). Characteristics of responding were similar to procedures in which reinforcer rate and immediacy have been manipulated, although sensitivity estimates for amount were lower than those previously obtained with rate and immediacy. This procedure may serve as a useful method for studying the effects of certain environmental manipulations (e.g., drug administration) on sensitivity to reinforcer amount.     

Comparing the generalized matching law and contingency discriminability model as accounts of concurrent schedule performance using residual meta-analysis

To compare the generalized matching law (Baum, W.M., 1974b. On two types of deviation from the matching law: bias and undermatching. J. Exp. Anal. Behav. 22, 231-242) and contingency discriminability model (Davison, M., Jenkins, P.E., 1985. Stimulus discriminability, contingency discriminability, and schedule performance. Anim. Learn. Behav. 13, 77-84) as accounts of concurrent schedule performance, we conducted a residual meta-analysis of response- and time-allocation data from 20 studies (n's=886 and 774, respectively). Both models were fitted to the individual-subject data from each study, and residuals were obtained. Polynomial regressions were then performed on the pooled residuals to determine whether systematic trends were present as a function of predicted values. For the contingency discriminability model, the cubic coefficients were positive and statistically significant for both response- and time-allocation data. By contrast, no statistically significant systematic trend was obtained in the residuals for the generalized matching law. These results suggest that the relationship between log response allocation and log reinforcer allocation does not deviate significantly from linearity over an approximate range of +1.25 to -1.25 log units, consistent with the generalized matching law. Although qualitative criteria are also important in comparing models of behavioral phenomena, residual meta-analysis provides a powerful quantitative methodology for model selection and should prove useful in future research.     

An application of the active time model to multiple concurrent variable-interval schedules

The current experiment investigates whether an active time model can account for anomalous results that have emerged from multiple schedule, concurrent variable-interval (VI) VI experiments. The model assumes that (1) during concurrent VI VI training pigeons learn a function that relates time since the most immediate response, i.e., active time, to changeover probabilities and (2) that molar preference is the result of an interaction between inter-response time frequencies and the learned active time changeover functions. Pigeons were trained under a concurrent VI 30-s VI 30-s schedule and a concurrent VI 60-s VI 60-s schedule. Probes were conducted in which VI 30-s and VI 60-s stimuli were paired. During these probes, birds allocated choices equally to the stimuli. The active time model accurately fit individual subject data. In contrast data were not fit by a variant of scalar expectancy theory proposed by Gibbon [Gibbon, J., 1995. Dynamics of time matching: arousal makes better seem worse. Psychon. Bull. Rev. 2, 208-215].     

Shifts in the psychophysical function in rats

The primary goal was to compare results from a free-operant procedure with pigeons [Machado, A., Guilhardi, P., 2000. Shifts in the psychometric function and their implications for models of timing. J. Exp. Anal. Behav. 74, 25-54, Experiment 2] with new results obtained with rats. The secondary goal was to compare the results of both experiments with dependent variables that were not used in the original publication. As in the original study with pigeons, rats were trained on a two-alternative free-operant psychophysical procedure in which left lever press responses were reinforced during the first and second quarters of a 60-s trial, and right lever press responses were reinforced during the third and fourth quarters of the trial. The quarters were reinforced according to four independent variable interval (VI) schedules of reinforcement. The VI duration was manipulated in each quarter, and shifts in the psychophysical functions that relate response rate with time since trial onset were measured. The results obtained with rats were consistent with those previously obtained with pigeons. In addition, results not originally reported were also consistent between rats and pigeons, and provided insights into the perception, memory, and decision processes in Scalar Expectancy Theory and Learning-to-Time Theory.     

Dishabituation with component transitions may contribute to the interactions observed during multiple schedules

Rates of responding by rats were usually higher during the variable interval (VI) 30-s component of a multiple VI 30-s fixed interval (FI) 30-s schedule than during the same component of a multiple VI 30-s VI 30-s schedule (Experiment 1). Response rates were also usually higher during the FI 30-s component of a multiple VI 30-s FI 30-s schedule than during the same component of a multiple FI 30-s FI 30-s schedule (Experiment 2). The differences in response rates were not observed when the components provided VI or FI 120-s schedules. These results were predicted by the idea that differences in habituation to the reinforcer between multiple schedules contribute to behavioral interactions, such as behavioral contrast. However, differences in habituation were not apparent in the within-session patterns of responding. Finding differences in response rates in both experiments violates widely-held assumptions about behavioral interactions, including that behavioral contrast does not occur for rats and that improving the conditions of reinforcement decreases, rather than increases, response rate in the alternative component.     

Segmentation and the pairing hypothesis

The effect of stimulus contiguity and response contingency on responding in chain schedules was examined in two experiments. In Experiment 1, four pigeons were trained on two simple three-link chain schedules that alternated within sessions. Initial links were correlated with a variable-interval 30s schedule, and middle and terminal links were correlated with interdependent variable-interval 30s variable-interval 30s schedules. The combined duration of the interdependent schedules summed to 60s. The two chains differed with respect to signaling of the schedule components: a two-stimulus chain had one stimulus paired with the initial link and one stimulus paired with both the middle and the terminal link, while a three-stimulus chain had a different stimulus paired with the each of the three links. The results showed that the two-stimulus chain maintained lower initial-link responding than the three-stimulus chain. In Experiment 2, four pigeons were exposed to three separate conditions, the two- and three-stimulus chains of Experiment 1 and a three-stimulus chain that had a 3s delay to terminal-link entry from the middle-link response that produced it. The two-stimulus chain maintained lower initial-link responding than the three-stimulus chain, as in Experiment 1, and a similar initial-link responding was maintained by the two-stimulus chain and the three-stimulus chain with the delay contingency. The results demonstrate that a stimulus noncontiguous with food can maintain responding that is sometimes greater than a stimulus contiguous with food, depending on the response contingency for terminal-link entry. The results are contrary to the pairing hypothesis of conditioned reinforcement.     

The effect of intruded events on peak time: the role of reinforcement history during the intruded event

Pigeons were studied in an extension of a study by Aum et al. [Aum, S., Brown, B.L., Hemmes, N.S. 2004. The effects of concurrent task and gap events on peak time in the peak procedure. Behav. Process. 65, 43-56] on timing behavior under a discrete-trial fixed-interval (FI) procedure during which 6-s intruded events were superimposed on peak-interval (PI) test trials. In Aum et al., one event consisted in termination of the timing cue (gap trial); the other was a stimulus in the presence of which subjects had been trained to respond under an independent random-interval (RI) schedule of reinforcement (concurrent task trial). Aum et al. found a disruption of timing on concurrent task trials that was greater than that on gap trials. The present study investigated history of reinforcement associated with intruded events as a possible explanation of this earlier finding. After training to peck a side key on a 30-s PI procedure, discrimination training was conducted on the center key in separate sessions; red or green 6-s stimuli were associated with RI 24s or EXT (extinction) schedules. During testing under the PI procedure, three types of intruded events were presented during probe trials--the stimulus associated with the RI (S+) or EXT (S-) schedule during discrimination training, or a gap (termination of the side-keylight). Intruded events occurred 3, 9, or 15s after PI trial onset. Effects of reinforcement history were revealed as substantial disruption of timing during the S+ event and relatively little disruption during the S- event. Intermediate effects were found for the gap event. Results indicate that postcue effects are at least partially responsible for the disruptive effects of the S+ event.     

Resistance to change varies inversely with reinforcement context

We report two experiments which test whether resistance to prefeeding and satiation for a variable-interval (VI) schedule that delivers a constant rate of reinforcement varies inversely with the reinforcement rate for an alternative schedule. In Experiment 1, eight pigeons responded in a multiple schedule in which the red key was always associated with a VI 90-s schedule and the green key with either a richer (VI 18s) or leaner (VI 540s) schedule in different conditions. After baseline training in each condition, prefeeding test sessions were conducted in which 10g, 20g, 30g, 40g, and 50g food were provided one-hour prior to test. Additional baseline training was given between each test session. In Experiment 2, two groups of pigeons responded in a multiple schedule similar to Experiment 1. After baseline training, pigeons were exposed to a 5-h satiation test session in which the VI 90-s schedule was available continuously. Test sessions were conducted when pigeons were maintained at 85%, 95%, and 85% of their body weights in an ABA design. Results of both experiments showed that responding in the VI 90-s schedule that alternated with a leaner schedule during baseline was more resistant to prefeeding and satiation. These data rule out alternative explanations for results of previous studies, and confirm that resistance to change varies inversely with reinforcement context.     

Upcoming food-pellet reinforcement alters rats' lever pressing for liquid sucrose delivered by a progressive-ratio schedule

The present study investigated whether rats' responding for liquid-sucrose reinforcement delivered by a progressive-ratio (PR) schedule would be altered by the addition of food-pellet reinforcement available subsequent to the PR schedule. In Experiment 1, six rats lever pressed for 1% sucrose reinforcers delivered by a PR 3 schedule. In Experiment 2, six rats lever pressed for 5% sucrose delivered by a PR 5 schedule. In both experiments, baseline sessions consisted of 40min of exposure to the PR schedule. In the first treatment condition, a 25-min period of food-pellet reinforcement, delivered by a random-interval 60-s schedule, immediately followed the initial 40min. In the second treatment condition, the 25-min period of food-pellet reinforcement became available when 10min elapsed without the subject completing a ratio on the PR schedule. Results from both experiments showed that upcoming food-pellet reinforcement increased the number of ratios subjects completed on the PR schedule. Portions of the present results represent a partial replication of results reported by Baron and Derenne [J. Exp. Anal. Behav. 73 (2000) 291], who used a similar procedure. They also augment a growing body of research on positive induction.     

The role of context in risky choice

Human choice behavior was assessed in a concurrent-chain schedule, where two equal initial links (IL) each led to a distinct terminal-link (TL). One TL was associated with a fixed ratio schedule of reinforcement, while the other was associated with a bi-valued mixed ratio schedule of reinforcement, whose arithmetic mean equaled the Fixed TL schedule. The fixed component (FR50; FR25; FR5) was arranged to be equal to the alternative mixed component in each condition (FR1/99; FR1/49; FR1/9), and choice behavior was measured by proportion of responses to each IL. In addition, the IL duration varied across conditions (VI 30 s; VI 15 s; FI 1 s). Preference for the mixed option was observed with longer durations (e.g., when IL = VI 30 s and TL = FR1/99). Participants were relatively indifferent in other conditions, though the results suggested a monotonic increase in preference as either durations or programmed efforts increased. It is concluded that both choice and the conditioned reinforcement value of the mixed option is contextually based, so that the value of a stimulus correlated with an immediate reward (i.e., FR 1) is enhanced the greater the temporal context in which the FR1 is embedded.     

Habituation contributes to the decline in wheel running within wheel-running reinforcement periods

Habituation appears to play a role in the decline in wheel running within an interval. Aoyama and McSweeney [Aoyama, K., McSweeney, F.K., 2001. Habituation contributes to within-session changes in free wheel running. J. Exp. Anal. Behav. 76, 289-302] showed that when a novel stimulus was presented during a 30-min interval, wheel-running rates following the stimulus increased to levels approximating those earlier in the interval. The present study sought to assess the role of habituation in the decline in running that occurs over a briefer interval. In two experiments, rats responded on fixed-interval 30-s schedules for the opportunity to run for 45 s. Forty reinforcers were completed in each session. In the first experiment, the brake and chamber lights were repeatedly activated and inactivated after 25 s of a reinforcement interval had elapsed to assess the effect on running within the remaining 20 s. Presentations of the brake/light stimulus occurred during nine randomly determined reinforcement intervals in a session. In the second experiment, a 110 dB tone was emitted after 25 s of the reinforcement interval. In both experiments, presentation of the stimulus produced an immediate decline in running that dissipated over sessions. No increase in running following the stimulus was observed in the first experiment until the stimulus-induced decline dissipated. In the second experiment, increases in running were observed following the tone in the first session as well as when data were averaged over several sessions. In general, the results concur with the assertion that habituation plays a role in the decline in wheel running that occurs within both long and short intervals.     

Extinguished operant responding shows stimulus specificity

The experiment tested for stimulus specificity in extinguished operant responding. Eight pigeons pecked keys for food reinforcers delivered by a variable interval (VI) 60-s schedule. The key was illuminated with red light during some sessions and white light during others. Then, responding was placed on extinction. During some sessions of extinction, the color of the key light remained constant throughout the session (red or white). During other sessions the color changed at 30 min into the session (red to white or white to red). Response rate increased after the change of key color in extinction. If it is assumed that key color is part of the stimulus to which subjects habituate, then these results are consistent with McSweeney and Swindell's [J. Gen. Psychol. 129 (2002) 364] suggestion that responding declines in extinction partly because subjects habituate to the stimuli that support conditioned responding. Habituation is relatively specific to the exact nature of the stimulus presented. Therefore, changes in the stimulus violate stimulus specificity and restore habituated responding. The results are also consistent with other theories that attribute extinction to a reduction of stimulus control [e.g., Psychol. Bull. 114 (1993) 80; J. Exp. Psychol.: Anim. Behav. Process. 16 (1990) 235], but considerations such as parsimony and testability favor the habituation hypothesis over these theories.     

Reinforcement context and resistance to change

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

A further application of the active time model to multiple concurrent variable-interval schedules

In this experiment we show that the active time model (ATM) accurately predicts probe data from multiple concurrent VI VI schedules. Subjects were trained under a concurrent VI 30-s VI 60-s and a concurrent VI 60-s VI 120-s schedule. Two types of unreinforced probes were then conducted. The first paired the two VI 60-s stimuli. These stimuli, while equivalent in their associated absolute rates of reinforcement, differed in their relative rates of reinforcement. The second probe paired the VI 30-s stimulus with the relatively rich VI 60-s stimulus. In contrast with the first probe, these stimuli differed in their absolute rates of reinforcement, while being similar in their relative rates. During the first set of probes, birds preferred the VI 60-s stimulus trained with the VI 120-s schedule. During the second set of probes, birds were indifferent to the two stimuli. These results are less extreme than others reported in the literature. Nonetheless, we found that ATM accurately fit individual subject data in both sets of probes. In contrast a variant of scalar expectancy theory did not fit the data at either the individual or group level.