Comparison of Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model in a successive temporal bisection task

The present research tested the generality of the "context effect" previously reported in experiments using temporal double bisection tasks [e.g., Arantes, J., Machado, A. Context effects in a temporal discrimination task: Further tests of the Scalar Expectancy Theory and Learning-to-Time models. J. Exp. Anal. Behav., in press]. Pigeons learned two temporal discriminations in which all the stimuli appear successively: 1s (red) vs. 4s (green) and 4s (blue) vs. 16s (yellow). Then, two tests were conducted to compare predictions of two timing models, Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model. In one test, two psychometric functions were obtained by presenting pigeons with intermediate signal durations (1-4s and 4-16s). Results were mixed. In the critical test, pigeons were exposed to signals ranging from 1 to 16s and followed by the green or the blue key. Whereas SET predicted that the relative response rate to each of these keys should be independent of the signal duration, LeT predicted that the relative response rate to the green key (compared with the blue key) should increase with the signal duration. Results were consistent with LeT's predictions, showing that the context effect is obtained even when subjects do not need to make a choice between two keys presented simultaneously.     

Context effect in a temporal bisection task with the choice keys available during the sample

In a symbolic matching to sample task, six pigeons learned to associate different sample durations with different comparison stimuli. On “Short” trials, choice of Red and Green keylight comparisons were reinforced following 3-s and 9-s samples, respectively; on “Long” trials, Blue and Yellow keylight comparisons were reinforced following 9-s and 27-s samples, respectively. In contrast with previous studies, the comparison keys were available during the samples. After the temporal discriminations were learned, new pairs of comparison keys were presented and the preference for each was assessed during 27-s samples. One pair in particular, Green and Blue, was critical because it tested the predictions of two timing models, Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model. The results showed that preference for Green increased during the sample, a result consistent with LeT but not with SET. Other test results, however, were predicted by neither model.     

Evidence that pigeons represent both time and number on a logarithmic scale

Pigeons were presented with trials that always began with presentation of a houselight that lasted for 1–16 s. Red and green side keys were presented immediately after the houselight went off. A peck on the red key was reinforced if the houselight duration was 8 s or shorter, and a peck on the green key was reinforced if the houselight duration was 9 s or longer. Plots of asymptotic performance as a function of houselight duration showed bow-shaped curves with higher accuracy at the ends of the scale than in the middle. Training to bisect a scale containing houselight durations of 2–32 s yielded a performance curve that superimposed on the 1–16 s curve. Both curves showed two important asymmetries around the midpoint: pigeons were more accurate at 9 and 10 s than at 7 and 8 s but were more accurate at 1–4 s than at 13–16 s. These findings closely resembled those found in a similar study of number scale bisection [Roberts, W.A., 2005. How do pigeons represent numbers? Studies of number scale bisection. Behav. Process. 69, 33–43]. Theoretical predictions from associative and confusion models showed a good match to the obtained data if it was assumed that time and number scales were logarithmic and that generalization or confusion curves were constant but not if it was assumed that scales were linear and that generalization or confusion curves were scalar.     

Temporal discrimination in a long operant chamber

Pigeons were placed in a long chamber equipped with one key and feeder at each end side and one key and houselight at the middle. To obtain food the birds had to choose one side key after a short signal and the other side key after a long signal. The signals consisted of the illumination of the center key and the houselight and were initiated by a peck at the center key. The chamber had sensitive floor panels that enabled us to measure the location of the bird during the signals. In Experiment 1, after the birds learned the discrimination we reversed the assignment of keys to signals. In Experiment 2, we examined performance on two pairs of discriminations holding the same ratio. In Experiment 3, after the pigeons learned to discriminate two signals, we changed the duration of the long signal. The results showed that (a) the birds' motion during the signal was highly stereotypical, i.e. the birds moved to the short side, waited a few seconds, and then departed to, and stayed on the long side; (b) this motion pattern predicted the results of generalization tests with novel durations; (c) the mean of the times of departure from the short side approached its steady state values quicker than the standard deviation and consequently superposition of behavioral measures became stronger with training; (d) only the duration of the short signal influenced significantly the moment the birds departed from the short side; finally (e) the times of arrival at and departure from the short side were positively correlated, but the times of arrival and residence at the short side were negatively correlated.     

How do pigeons represent numbers?: Studies of number scale bisection

Pigeons' bisection of two number scales, 1-16 and 2-32, was examined in two experiments. In Experiment 1, pigeons learned to choose different comparison keys following 1 or 16 key pecks and 2 or 32 key pecks and then were tested with intermediate numbers of key pecks on nonreinforced probe trials. Psychophysical curves that plotted choice of the large number key against number of pecks showed superposition of the two number scales and indifference between the two keys at the geometric means of each scale. The same procedures were used in Experiment 2, but pigeons were trained to bisect each scale at its arithmetic mean. Two asymmetries appeared in curves that plotted discrimination performance against number: near the midpoints of the scales, accuracy was higher for high numbers than for low numbers, but this relationship reversed at the ends of the scales, with low numbers discriminated more accurately than high numbers. An associative model that assumed stimulus generalization between numbers was used to predict the findings of these two experiments. The model showed a good qualitative fit to the obtained data when it was assumed that number was represented on a log scale and generalization was constant at all numbers but not when it was assumed that number was represented on a linear scale and generalization was scalar.     

The effects of cue competition on timing in pigeons

We studied the effects of cue competition on timing in both overshadowing and blocking operant procedures with pigeons. A white center key delivered reward when pecked 30 s after a red or green sidekey was presented and 10 s after presentation of the alternate color on the other sidekey. In Experiment 1, key presentations were concurrent during training trials for overshadow-condition pigeons, while side key presentations were separated across training trials for control birds. In Experiment 2, half of the birds (Blocking group) were given pre-exposure trials to either the 10-s or 30-s sidekey condition. Both blocking-condition and control birds were then given trials of concurrent side key presentations. Peak time curves were compared between experimental and control conditions. The results showed blocking of timing accuracy of a long (30-s) stimulus by a short (10-s) stimulus, but no evidence for overshadowing of timing accuracy.     

Representation of time intervals in a double bisection task: Relative or absolute?

We examined if the representation of time intervals in a temporal discrimination task is based not only on their absolute but also on their relative durations. Six pigeons learned two temporal discriminations. In the first, red and green choices were correct following 2-s and 8-s samples, respectively. In the second, vertical and horizontal bar choices were correct following 4-s and 16-s samples, respectively. In a previous study [Zentall, T.R., Weaver, J.E., Clement, T.S., 2004. Pigeons group time intervals according to their relative duration. Psychon. Bull. Rev. 11, 113-117.], tests with 4-s samples and red/green comparisons revealed a bias for red, whereas tests with 8-s samples with vertical/horizontal comparisons revealed a bias for horizontal. These results were interpreted in terms of relative encoding of sample durations. We attempted to replicate this finding but instead of testing with only 4-s or 8-s samples, we tested with several other sample durations to obtain a psychometric function. Results were inconsistent with the relative encoding hypothesis.     

Serial conditional discrimination and temporal bisection in rats selectively lesioned in the dentate gyrus

In positive serial conditional discrimination, animals respond during a target stimulus when it is preceded by a feature stimulus, but they do not respond when the same target stimulus is presented alone. Moreover, the feature and target stimuli are separated from each other by an empty interval. The present work aimed to investigate if two durations (4 or 16 s) of the same feature stimulus (light) could modulate the operant responses of rats to different levers (A and B) during a 5-s target stimulus (tone). In the present study, lever A was associated with the 4-s light, and lever B was associated with the 16-s light. A 5-s empty interval was included between the light and the tone. In the same training procedure, the rats were also presented with the 5-s tone without the preceding light stimuli. In these trials, the responses were not reinforced. We evaluated the hippocampal involvement of these behavioral processes by selectively lesioning the dentate gyrus with colchicine. Once trained, the rats were submitted to a test using probe trials without reinforcement. They were presented with intermediate durations of the feature stimulus (light) to obtain a temporal bisection curve recorded during the exposure to the target stimuli. The rats from both groups learned to respond with high rates during tones preceded by light and with low rates during tones presented alone, which indicated acquisition of the serial conditional discrimination. The rats were able to discriminate between the 4- and 16-s lights by correctly choosing lever A or B. In the test, the temporal bisection curves from both experimental groups showed a bisection point at the arithmetic mean between 4 and 16 s. Such processes were not impaired by the dentate gyrus lesion. Thus, our results showed that different durations of a feature stimulus could result in conditional properties. However, this processing did not appear to depend on the dentate gyrus alone.     

Associative symmetry and stimulus-class formation by pigeons: The role of non-reinforced baseline relations

Two experiments tested the assumption of Urcuioli's (2008) theory of pigeons’ equivalence-class formation that consistent non-reinforcement of certain stimulus combinations in successive matching juxtaposed with consistent reinforcement of other combinations generates stimulus classes containing the elements of the reinforced combinations. In Experiment 1, pigeons were concurrently trained on symbolic (AB) and two identity (AA and BB) successive tasks in which half of all identity trials ended in non-reinforcement but all AB trials were reinforced, contingent upon either responding or not responding to the comparisons. Subsequent symmetry (BA) probe trials showed evidence of symmetry in one of four pigeons. In Experiment 2, pigeons learned three pair-comparison tasks in which left versus right spatial choices were reinforced after the various sample-comparison combinations comprising AB, AA, and BB conditional discriminations. Non-differentially reinforced BA probe trials following acquisition showed some indication of symmetrical choice responding. The overall results contradict the theoretical predictions derived from Urcuioli (2008) and those from Experiment 2 challenge other stimulus-class analyses as well.     

Differential resurgence and response elimination

Resurgence refers to the transient recovery of previously reinforced, but presently not reinforced, responding when more recently reinforced responding is extinguished. The primary purpose of our research was to determine how differential resurgence results from the procedures used to eliminate that responding. There were three conditions in each of five experiments. In Condition 1, key pecking by pigeons was maintained under a two-component multiple variable-interval (VI) 30-s VI 30-s schedule. In Condition 2, this pecking was eliminated in different ways across components. In Condition 3, extinction was in effect for all responses, and resurgence of key pecking was compared across components. These three conditions were repeated for most pigeons, and the procedures used to eliminate responding in Condition 2 varied across experiments. In Experiment 1, there was greater resurgence, and an earlier onset of it, after a differential-reinforcement-of-other-behavior (DRO) schedule than after a VI schedule was correlated with pecking an alternative key. Experiments 2 and 3 showed that the differential resurgence in Experiment 1 probably was not due to conditional stimulus control or the periodicity of food delivery, respectively. In Experiment 4, there was no systematic difference in resurgence after either a DRO schedule or a VI schedule correlated with treadle pressing. In Experiment 5, there was greater resurgence, and/or an earlier onset of it, after a VI schedule correlated with treadle pressing than after a VI schedule correlated with pecking an alternative key. Taken together, the results showed that the reinforcement of an alternative key-peck response was the most effective means of reducing subsequent key-peck resurgence. The relation of these results to an understanding of resurgence is discussed.     

Applications of timing theories to a peak procedure

This article describes applications of scalar expectancy theory (SET), learning-to-time theory (LeT), and Packet theory to data from a peak procedure. Twelve rats were trained in a multiple cued-interval procedure with two fixed intervals (60 and 120 s) signaled by houselight and white noise. Twenty-five percent of the cycles were nonfood cycles, which were 360 s long and had no reinforcement. Mean and individual response rates on nonfood cycles were fitted with explicit solutions of SET, LeT and Packet theory. Applications of the three timing theories were compared in terms of goodness of fit and complexity.     

The effects of concurrent task and gap events on peak time in the peak procedure

The effect of a concurrent task on timing performance of pigeons was investigated with the peak interval procedure. Birds were trained to peck a side key on a discrete-trial schedule that included reinforced fixed-interval (FI) 30-s trials and nonreinforced extended probe trials. Then, in separate sessions, birds were trained to peck a 6-s center key for food. In a subsequent test phase, the FI procedure was in effect along with dual-task probe test trials. On those test trials, the 6-s center key (task cue) was presented at 3, 9, or 15s after probe trial onset. During another test phase, a 6-s gap (the FI keylight was extinguished) was presented at 3, 9, or 15s after probe trial onset. Peak time increased with center key time of onset, and was greater under task than gap conditions. Moreover, peak time under task conditions exceeded values predicted by stop and reset clock mechanisms. These results are at variance with current attentional accounts of timing behavior in dual-task conditions, and suggest a role of nontemporal factors in the control of timing behavior.     

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.     

Spatial serial conditioning maintained with minimal temporal contingency

Two experiments used a spatial serial conditioning paradigm to assess the effectiveness of spatially informative conditioned stimuli in eliciting tracking behavior in pigeons. The experimental paradigm consisted of the simultaneous presentation of 2 key lights (CS2 and CTRL), followed by another key light (CS1), followed by food (the unconditioned stimulus or US). CS2 and CTRL were presented in 2 of 3 possible locations, randomly assigned; CS1 was always presented in the same location as CS2. CS2 was designed to signal the spatial, but not the temporal locus of CS1; CS1 signaled the temporal locus of the US. In experiment 1, differential pecking on CS2 was observed even when CS2 was present throughout the interval between consecutive presentations of CS1, but only in a minority of pigeons; prevalence of differential pecking was enhanced when CS2 duration was halved. A control condition verified that pecking on CS2 was not due to temporal proximity between CS2 and US. Experiment 2 demonstrated the reversibility of spatial conditioning between CS2 and CTRL. Asymptotic performance never involved tracking CTRL more than CS2 for any of 16 pigeons. It is inferred that pigeons learned the spatial association between CS2 and CS1, and that temporal contingency facilitated its expression as tracking behavior.     

Reaction times identify a Pavlovian component in a two-choice discrimination

Six pigeons discriminated on discrete trials between two colors. In Experiment 1, two luminous spots were both either blue or green and the reinforced responses were “peck left” for blue and “peck right” for green. In Experiment 2, the hue of a center spot controlled subsequent choice pecks to left or right. In both experiments response bias was manipulated in two ways. During stimulus frequency (“SF”) sessions correct responses brought food on 40% of trials; in “imbalanced” blocks of sessions one hue appeared on 80% of trials and the other on 20%. During reinforcement probability (“RNF”) sessions the hues appeared equally often, but in imbalanced blocks the hues signaled different reinforcement probabilities, either 64% or 16%. In “balanced” control blocks the hues appeared equally often and were both reinforced at 40%. The experiments gave similar results. When bias was computed from choice percentages the imbalanced conditions yielded substantial response bias, and the amount of bias was about the same under RNF and SF treatments. However, reaction times (RTs) gave a different outcome. RNF imbalance slowed responses directed at the less reinforced stimulus, but SF imbalance had little RT effect (Experiment 1) or no effect (Experiment 2). These results suggest that choice was controlled by an instrumental stimulus-response-reinforcement association, whereas RTs were controlled by a Pavlovian stimulus-reinforcement association.     

An investigation of colour discrimination with horses (Equus caballus)

The ability of four horses (Equus caballus) to discriminate coloured (three shades of blue, green, red, and yellow) from grey (neutral density) stimuli, produced by back projected lighting filters, was investigated in a two response forced-choice procedure. Pushes of the lever in front of a coloured screen were occasionally reinforced, pushes of the lever in front of a grey screen were never reinforced. Each colour shade was randomly paired with a grey that was brighter, one that was dimmer, and one that approximately matched the colour in terms of brightness. Each horse experienced the colours in a different order, a new colour was started after 85% correct responses over five consecutive sessions or if accuracy showed no trend over sessions. All horses reached the 85% correct with blue versus grey, three horses did so with both yellow and green versus grey. All were above chance with red versus grey but none reached criterion. Further analysis showed the wavelengths of the green stimuli used overlapped with the yellow. The results are consistent with histological and behavioural studies that suggest that horses are dichromatic. They differ from some earlier data in that they indicate horses can discriminate yellow and blue, but that they may have deficiencies in discriminating red and green.     

Rats (Rattus norvegicus) and pigeons (Columbia livia) are sensitive to the distance to food,but only rats request more food when distance increases

Three experiments investigated foraging by rats and pigeons. In Experiment 1, each response on a manipulandum delivered food to a cup, with the distance between the manipulandum and the cup varying across conditions. The number of responses made before traveling to collect and eat the food increased with distance for rats, but not for pigeons. In Experiment 2, two manipulanda were placed at different distances from a fixed food source; both pigeons and rats preferentially used the manipulandum closest to the food source. Experiment 3 was a systematic replication of Experiment 1 with pigeons. In different conditions, each peck on the left key increased the upcoming hopper duration by 0.5, 1.5 or 2.5 s. Completing a ratio requirement on the right key of 1, 4, 8, 16 or 32 pecks, depending on the condition, then produced the food hopper for a duration that depended on the number of prior left pecks. As the ratio requirement increased on the right key, pigeons responded more on the left key and earned more food. Overall, the results replicate previous research, underlining similarities and differences between these species. The results are discussed in terms of optimal foraging, reinforcer sensitivity and delay discounting.     

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.