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THE INTERACTION OF TEMPORAL GENERALIZATION GRADIENTS PREDICTS THECONTEXT EFFECT

ANA CATARINA VIEIRA DE CASTRO AND ARMANDO MACHADO

UNIVERSITY OF MINHO, PORTUGAL

In a temporal double bisection task, animals learn two discriminations. In the presence of Red andGreen keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforcedafter 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-ssamples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice betweenGreen and Blue, the probability of choosing Green increases with the sample duration–the contexteffect. In the present study we asked whether this effect could be predicted from the stimulusgeneralization gradients induced by the two basic discriminations. Six pigeons learned to peck Greenfollowing 4-s samples (S+) but not following 1-s samples (S2) and to peck Red following 4-s samples (S+)but not following 16-s samples (S2). Temporal generalization gradients for Green and Red were thenobtained. Finally, the pigeons were given a choice between Green and Red following sample durationsranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at theS2 duration, an intermediate value between the S2 and the S+ durations, and the maximum at the S+ aswell as more extreme durations; b) on choice trials, preference for Green over Red increased withsample duration, the context effect; and c) the two generalization gradients predicted the averagecontext effect well. The Learning-to-Time model accounts for the major trends in the data.

Key words: context effect, temporal generalization, temporal discrimination, quantitative model,Learning-to-Time model, key peck, pigeon

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With the aim of contrasting some models oftiming, Machado and Keen (1999) developedthe double bisection task, a modified versionof one of the most well-known proceduresused to study timing in animals and humans—the temporal bisection task. In a typicaltemporal bisection task, the subjects learn todiscriminate between two samples of differentdurations. For instance, a pigeon is presentedwith a sample light illuminated for either 1 or4 s and then with two comparison stimuli, aRed key and a Green key. The pigeon receivesfood if it pecks Red following 1-s samples andGreen following 4-s samples. After the discrim-ination is acquired the animal is presentedwith samples of intermediate durations andthe preference for one of the keys, say, Green,is assessed. It is commonly found that theproportion of responses to Green increases

with sample duration from about 0 to about 1,with the indifference point close to thegeometric mean of the two training durations(Catania, 1970; Church & Deluty, 1977; Fetter-man & Killeen, 1991; Platt & Davis, 1983;Stubbs, 1968; for summaries, see Gallistel,1990; Richelle & Lejeune, 1980; Shettleworth,1998).

In the double bisection procedure (seeFigure 1) the animals learn not one but twotemporal discriminations, which we call Type 1and Type 2. In the Type 1 discrimination theylearn to choose Red over Green after 1-ssamples and Green over Red after 4-s samples.In the Type 2 discrimination they learn tochoose Blue over Yellow after 4-s samples andYellow over Blue after 16-s samples. Next,generalization tests are conducted in whichnew pairs of comparisons are introducedfollowing different sample durations. Of crit-ical importance to contrast timing models arethe test trials on which Green and Blue arepresented together, for these two comparisonswere reinforced following the same sampleduration of 4 s.

Figure 2 shows the typical result of these testtrials: Preference for Green over Blue increas-es with sample duration (Machado & Keen,1999). This finding is called the context effectbecause, even though the choices of Green

The authors thank the students from the AnimalLearning and Behavior laboratory of the University ofMinho for their helpful comments on the paper. AnaCatarina Vieira de Castro was supported by a PhDfellowship and Armando Machado by a grant from thePortuguese Foundation for Science and Technology(FCT).

Address correspondence to Ana Catarina Vieira de Castroor Armando Machado at Escola de Psicologia, Universidade doMinho, 4710 Braga, Portugal (e-mail: [email protected] or [email protected]).

doi: 10.1901/jeab.2012.97-263

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2012, 97, 263–279 NUMBER 3 (MAY)

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and Blue were reinforced following the samesample duration, the context in which suchreinforcement occurred differed. ChoosingGreen was reinforced in a context in which ashorter sample signaled extinction for Green,whereas choosing Blue was reinforced in acontext in which a longer duration signaledextinction for Blue. As a series of studies usingdifferent versions of the double bisectionprocedure have shown, the context effect isquite robust and general (Arantes, 2008;Arantes & Machado, 2008; Machado & Aran-tes, 2006; Machado & Keen, 1999; Machado &Pata, 2005; Oliveira & Machado, 2008, 2009).

The context effect is theoretically importantbecause it differentiates timing models. Con-sider the leading model, Scalar ExpectancyTheory (SET; e.g., Church, 2003; Gibbon,1977; Gibbon, Church, & Meck, 1984). Accordingto SET’s standard account for temporal bisec-

Fig. 1. Structure of the two types of training trials in a double bisection task. On Type 1 trials, pecking red or green isreinforced after 1-s or 4-s samples, respectively. On Type 2 trials, pecking blue or yellow is reinforced following 4-s or 16-ssamples, respectively.

Fig. 2. Proportion of responses to Green, given achoice between Green and Blue, as a function of sampleduration. The Green and Blue comparisons had beenreinforced following 4-s samples (see Figure 1). The dataare from Machado and Keen (1999); N58 pigeons; thebars show the SEM.

264 ANA CATARINA VIEIRA DE CASTRO and ARMANDO MACHADO

tion (e.g., Gibbon, 1981, 1991), the animalrepresents the reinforced sample durations indistinct memory stores. Therefore, in thedouble bisection task, the animal forms fourstores, but only two are critical for the contexteffect, the store representing 4-s samples andassociated with the Green comparison and thestore representing 4-s samples associated withthe Blue comparison. Moreover, according toSET, the contents of each store dependexclusively on its corresponding sample dura-tion—they are context independent. Hence,the stores associated with Green and Blue willhave identical representations causing SET topredict that the preference for Green over Bluewill not vary with the sample duration. In short,because temporal memories are assumed con-text-independent, SET fails to predict thecontext effect.

In contrast with SET, the Learning-to-Timeor LeT model (Machado, 1997) or its newerversion (Machado, Malheiro & Erlhagen,2009) is a context-dependent timing model.It assumes that, in a temporal discriminationtask, the sample stimulus activates a set ofstates serially such that, on the average, theactive state at the end of the sample variesdirectly with the sample duration (see alsoKilleen & Fetterman, 1988). Moreover, eachstate is coupled with the comparison stimuliand the degree of the coupling changes withreinforcement and extinction. Reinforcementstrengthens and extinction weakens the cou-pling between the active state and the chosencomparison. Finally, the probability of choos-ing one or the other comparison depends ontwo factors, which state is active at the end ofthe sample (a function of sample duration)and which of the two couplings is stronger (afunction of the reinforcement contingen-cies). Because the couplings between theactive states and the comparisons depend onthe sample durations and on which compar-ison is reinforced and which is extinguishedfollowing each sample, the model is context-dependent.

Before we explain in greater detail how LeTaccounts for the context effect, we present aqualitative account of that effect that does notrely on a specific model. The account con-ceives of a simultaneous discrimination as twosuccessive discriminations operating simulta-neously. In the double bisection task, thismeans that pecking Green and Blue are

conceived of as operants controlled by twosample durations, an S+ and an S2. For Green,the S+ and S2 are the 4-s and 1-s samples,respectively; for Blue, the S+ and S2 are the 4-sand 16-s samples, respectively. In addition, theaccount assumes that choice between the twocomparison stimuli may be predicted from thegeneralization gradients induced by the dis-criminative training (Honig, 1962; Spence,1937).

Machado and Pata (2005) suggested that thecontext effect could be the result of a peak-shift-like phenomenon in the temporal do-main. Peak shift refers to a shift in the peak ofa generalization gradient after intradimen-sional discrimination training, a shift in thedirection opposite to the negative stimulus(S2). If we assume that the effect of the S2 isto shift the peak of the generalization gradientaway from S+ (Hanson, 1959; see also Bloom-field, 1967; Purtle, 1973; Spence, 1937), then,in the double bisection task, the gradient forGreen will have its maximum at a value greaterthan 4 s, whereas the gradient for Blue willhave its maximum at a value less than 4 s. Thenet effect of these two shifts is that thegradient for Blue will be above the gradientfor Green for durations less than 4 s, but thegradient for Green will be above the gradientfor Blue for durations greater than 4 s. Therelative positions of the two gradients couldexplain why preference for Green over Blueincreases with sample duration.

A few studies have examined peak shift inpostdiscrimination temporal-generalizationgradients. Mellgren, Mays, and Haddad(1983) with rats and Spetch and Cheng(1998) with pigeons obtained generalizationgradients resembling step functions (a highresponse rate in the presence of the S+ andhigher values, and the same low response ratein the presence of the S2 and lower values); nopeak shift was found. In Elsmore’s (1971)study, 2 pigeons showed a peak shift effect andthe other 2 responded approximately at thesame rate to the S+ and to the values on the farside of it. More recently, Russell and Kirkpa-trick (2007) found, with rats, gradients with aclear peak shift and gradients that peaked at aduration away from the S+ in the directionopposite the S2, but did not decrease signif-icantly for the remaining durations. Alsorecently, Bizo and McMahon (2007) reporteda reliable peak shift effect in humans. To

GENERALIZATION GRADIENTS AND THE CONTEXT EFFECT 265

summarize, the evidence for peak shift in thetemporal domain is mixed, with one studyreporting positive evidence, two studies re-porting negative evidence and two othersreporting, at least for some subjects, positiveevidence.

Peak shift, however, can be seen as a specialcase of the area shift phenomenon. An areashift occurs when more than 50% of the areaof the gradient lies on the side of S+ oppositethe S2 (Rilling, 1977; see e.g. Cheng, Spetch,& Johnston, 1997, for an area shift effect inthe spatial domain). It follows from thedefinition that whenever a peak shift occurs,an area shift also occurs, but the reverse is notnecessarily the case. In fact, whereas area shiftis reliably found in the temporal domainfollowing intradimensional discriminationtraining, including in all the studies reportedabove, peak shift does not always occur.Hence, in what follows we focus our attentionin the more general phenomenon of areashift.

The area shift account of the context effectwould work as follows. If we assume that a)because the choice of Green is extinguishedafter 1-s samples, the area of the gradient forGreen will be shifted to the right (i.e., towarddurations longer than 4 s); b) because choiceof Blue is extinguished after16-s samples, thearea of the gradient for Blue will be shifted tothe left (i.e., toward durations shorter than4 s); c) because of (a) and (b), the general-ization gradient for Green will be below thatfor Blue at 1 s, approximately equal to it at 4 s,and above it at 16 s; d) if choice following a t-ssample depends on the relative heights of thetwo gradients at t s, then the proportion ofGreen choices should increase with sample

duration, the context effect. According to thisaccount, the exact location of the peaks of thegradients is irrelevant.

The area shift hypothesis is consistent withhow the LeT model accounts for the contexteffect. We present the general argumentqualitatively and defer until the Discussion amore quantitative treatment (for additionaldetails, see Machado et al., 2009). Table 1helps to understand the argument. Let S1, S4,and S16 represent the behavioral states mostlikely to be active at the end of 1-s, 4-s and 16-ssamples, respectively. Initially, these states areequally coupled with the two critical compar-isons, the Green and Blue keys, and the degreeof the coupling is represented by the ‘‘+’’symbol in the table. During Type 1 trials,choices of Green will be reinforced after 4-ssamples and extinguished after 1-s samples.Hence, the coupling of S4 with Green willincrease to ‘‘++’’ but the coupling of S1 withGreen will decrease to ‘‘0’’. Similarly, duringType 2 trials, choices of Blue will be reinforcedafter 4-s samples and extinguished after 16-ssamples and consequently the coupling of S4with Blue will increase to ‘‘++’’ but thecoupling of S16 with Blue will decrease to‘‘0’’. Two consequences follow from thecoupling profiles acquired during training.First, if we run generalization tests by present-ing either the Green or the Blue key followingsamples ranging from 1 s to 16 s, then weshould obtain the two area-shifted generaliza-tion gradients mentioned above, a gradientshifted to the right (Green) and a gradientshifted to the left (Blue). Second, if the animalis given a choice between Green and Bluefollowing samples ranging from 1 s to 16 s,then it should prefer Blue following 1-ssamples, be indifferent following 4-s samples,and prefer Green following 16-s samples—thecontext effect.

The foregoing account also justifies thedesignation of a context effect. Although theanimal learns to respond to Green and Bluefollowing the same 4-s samples, the contextin which such learning takes place differs:Responses to Green are extinguished follow-ing 1-s samples, whereas responses to Blueare extinguished following 16-s samples.According to LeT, the difference in thelearning context explains why preferencefor Green over Blue increases with sampleduration.

Table 1

How couplings between the behavioral states and thechoice comparisons change during training, according toLeT.

Comparisonstimulus

Behavioral state

S1 S4 S16

Green + R 0 + R ++ +Blue + + R ++ + R 0

Note. S1, S4 and S16 represent the most likely activestates at the end of the 1-s, 4-s, and 16-s samples,respectively. The arrows show the direction of change.‘‘0’’, ‘‘+’’, and ‘‘++’’ stand for weak, moderate, and strongcouplings.


To summarize, the LeT model instantiatesthe area shift hypothesis. The coupling pro-files acquired during training induce area-shifted generalization gradients which com-bined produce the context effect.

The main purpose of the present study was totest directly this generalization-based accountof the context effect. To that end, we simplifiedthe double bisection task by retaining only theelements central to the account, the twooperants and their reinforcement contingen-cies—reinforcement after 4-s samples for bothoperants; extinction after 1-s samples for oneoperant; and extinction after 16-s samples forthe other operant. Specifically, in the new task,the pigeons started by learning one of the twobasic discriminations, to peck A after 4-ssamples, the S+, and not to peck A after 1-ssamples, the S2. Then, we varied the sampleduration from 1 to 16 s to obtain the temporalgeneralization gradient for pecking A. Next,the pigeons learned the second basic discrim-ination, to peck B after 4 s (S+), and not to peckB after 16 s (S2) and then we varied the sampleduration to obtain the gradient for pecking B.Finally, we presented the pigeons with samplesranging from 1 to 16 s and gave them a choicebetween the two operants, peck A and peck B.According to our hypothesis, the preference ofA over B should increase with sample duration,and, in addition, the two generalization gradi-ents, with their areas shifted in oppositedirections, should predict the preference data.

One potential difficulty with the task de-scribed above is that it involves successivechoice during the basic discriminations (e.g.,peck A following 4-s samples; do not peck Afollowing 1-s samples), but simultaneouschoice during the final test phase (peck A orB). The novelty of simultaneous choice duringthe final test phase could mask the effects ofthe generalization gradients induced by thetwo basic discriminations. To eliminate thispotential difficulty, we introduced a ‘‘dummy’’alternative during the basic discriminations.Specifically, after 1-s and 4-s samples, thepigeon was given a choice between pecking A(e.g., a Green key) and pecking a key with avertical bar. Choice of A was reinforced afterthe 4-s samples, but not after the 1-s samples,and choice of the vertical bar was neverreinforced. Similarly, after 4-s and 16-s sam-ples, the pigeon was given a choice betweenpecking B (e.g., a Red key) and pecking a key

with a vertical bar. Choice of B was reinforcedafter the 4-s samples, but not after the 16-ssamples, and again choice of the vertical barwas never reinforced. The ‘‘dummy’’ alterna-tive gave the pigeons experience with simulta-neous choice from the beginning of theexperiment.

METHOD

Subjects

Six adult pigeons (Columba livia) participat-ed in the experiment. The birds had previousexperience with the time-left procedure, butnot with matching-to-sample tasks. They weremaintained at 80% of their free-feeding bodyweights throughout the experiment and werehoused in individual home cages with waterand grit continuously available. A 13:11 hlight/dark cycle, beginning at 8:00 am, was ineffect in the pigeon colony.

Apparatus

Three identical Lehigh ValleyH operantchambers were used. Each chamber was34 cm high, 35 cm long and 31 cm wide. Thewalls and ceiling were made of aluminum andthe floor was wire mesh. The response panelcontained three circular keys, 2.5 cm indiameter, arranged in a horizontal row,22.5 cm above the floor, and 9 cm apart,center to center. The keys could be illuminat-ed with yellow, green and red lights and with avertical white bar on a dark background. Onthe back wall of the chamber, 4 cm below theceiling, a 7.5-W houselight provided generalillumination. Reinforcement consisted ofmixed grain delivered by a hopper that wasaccessible through a 635-cm opening, cen-tered on the response panel 8.5 cm above thefloor. A 7.5-W white light illuminated theopening whenever a reinforcer was available.An outer box enclosed the operant chamber.The box was equipped with a ventilation fanthat circulated air through the chamber andprovided masking noise. A personal computercontrolled all experimental events and record-ed the data.

Procedure

The pigeons learned two temporal discrim-inations, 1 s versus 4 s and 4 s versus 16 s,referred to as Type 1 and Type 2, respectively.


Half of the birds learned the Type 1 discrim-ination first and the Type 2 discriminationnext, whereas the other half learned thediscriminations in the opposite order. For 3pigeons (P170, P178, and P841) a Green keywas associated with the 4-s samples from Type1 trials and a Red key was associated with the 4-s samples from the Type 2 trials; for the other3 pigeons, the reverse assignment was in effect.However, for clarity we describe the procedureand the experimental results as if all of thebirds had learned the Type 1 discriminationfirst and had the Green key assigned to the 4-ssample of the Type 1 discrimination.

Table 2 summarizes the procedure. It con-sisted of three phases, one in which only theType 1 discrimination was trained, another inwhich only the Type 2 discrimination wastrained, and yet another in which both Type 1and Type 2 discriminations were trained. Inaddition, each phase consisted of three condi-tions: Training, during which the discrimina-tion was learned and all correct choices werereinforced; Pretesting, during which somecorrect choices were extinguished to adaptthe pigeons to the intermittent reinforcementthat would be in effect during the nextcondition; and Testing, during which newsample durations were introduced to obtain

the generalization gradients (Phases 1 and 2);or new sample durations and a new pair ofchoice keys, Green and Red, were introducedto examine the context effect (Phase 3).

Phase 1. The general structure of a Type-1Training Condition trial was as follows. After adark, 20-s ITI, the houselight was turned onand the center key was illuminated with yellowlight. After the sample duration elapsed (1 s or4 s) the center keylight was turned off and theside keys were illuminated, one with a greenlight and the other with a white vertical bar ona dark background. The two side keys re-mained illuminated for at least 6 s. If the S+, 4-ssample had been presented, the first peck at achoice key after 6 s turned all keylights and thehouselight off, and if the response was correct(pecking Green), it activated the food hopper.The hopper duration varied across birds from3 s to 9 s in order to maintain body weight withminimal extra session feeding. After food, theITI followed. If the response was incorrect(pecking the vertical bar), the ITI startedimmediately and the trial was repeated. If thebird made three consecutive errors, only theGreen key was presented (correction proce-dure). If the S2, 1-s sample had beenpresented, the side keys and the houselightwere turned off after the 6-s period regardless

Table 2

Comparison Stimuli, Sample duration, and the number of reinforced and non-reinforced trialsper session.

Phase Condition Comparison Stimuli

Sample duration (s)

1 2 4 8 16

Type 1 Training Bar Green 302 30+Pretesting Bar Green 302 24+,62Testing Bar Green 302 22 24+ 22 22

Type 2 Training Bar Red 30+ 302

Pretesting Bar Red 24+,62 302Testing Bar Red 22 22 24+ 22 302

Type 1 + Type 2(Combined)

Training Bar Green 202 20+Bar Red 20+ 202

Pretesting Bar Green 202 14+,62Bar Red 14+,62 202

Testing Bar Green 202 14+Bar Red 14+ 202Green* Red 62 62Green* Red 42 42 42Green** Red 62 62Green** Red 42 42 42

Note. N+ means that N trials per session were reinforced (provided the choice was correct) and N- means that N trialsper session were in extinction.

* For pigeons P890, P948, P178, and P841** For pigeons P170 and PG12


of the animal’s behavior and then the ITIstarted.

Learning was assessed by the relative re-sponse rate during the 6-s choice period, thatis, by the discrimination ratio ‘‘#S+/(#S+ +#S2)’’, where #S+ is the total number ofresponses to Green after the 4-s samples, and#S2 is the total number of responses to Greenafter the 1-s samples. Initially, the learningcriterion was set at a discrimination ratio of .85or above, excluding repeated trials, for fiveconsecutive sessions. For some subjects, thecriterion had to be reduced to .80 because theinitial criterion proved to be too hard to reach.

Sessions 1 to 12 consisted of 60 trials, 30 withthe S+ and 30 with the S2 (see first row ofTable 2). Within each set of 30 trials, 15 hadGreen on the left key and 15 had Green on theright key. However, as some birds continued topeck Green during the S2 trials, in subsequentsessions we increased the proportion of S2

trials: 20 S+ and 40 S2 trials for pigeons P170,P178, P890, and PG12, and 16 S+ and 44 S2

trials for pigeons P841 and P948. For the last 2pigeons we also reduced to 3 s the duration ofthe choice period in order to make theirchoice responses more contiguous with rein-forcement and extinction. Before advancing tothe next condition, though, all pigeons re-turned to the original session structure with 30S+ and 30 S2 trials and a 6-s choice period. TheTraining Condition lasted 42 sessions onaverage (range: 32 to 69).

In the Pretesting Condition (see second rowof Table 2), extinction trials were introduced.In addition to not ending with food, evenwhen a choice was correct, extinction trialsalso were not repeated when the choice wasincorrect. Sessions consisted of 60 trials, 30 S+

(24 reinforced and 6 unreinforced, 12 and 3for each left/right assignment, respectively)and 30 S2 (15 for each left/right assignment).Pretesting lasted until the learning criterionwas met (M 5 7 sessions; range: 5 to 12).

In the Testing Condition (see third row ofTable 2), each session consisted of 60 trials, 24S+ and 30 S2 (12 and 15 for each left/rightassignment, respectively) and 6 test trials. Ontest trials the sample duration equaled 2, 8 or16 s, and each sample was presented twice persession (once for each left/right assignment).If during any test session a bird’s discrimina-tion ratio decreased by more than .05 from itscriterion (either .85 or .80), the bird was

returned to training for at least two sessionsand until its performance met the criterionagain. Testing continued until 10 test sessionswere completed (M 5 12 sessions; range: 10 to19).

Phase 2. After the pigeons completed thethree conditions of Phase 1, they were exposedto exactly the same conditions but with theType 2 discrimination (see Table 2). Traininglasted from 16 to 53 sessions (M 5 30),Pretesting from 5 to 17 (M 5 7) and Testingfrom 12 to 26 (M 5 15).

Phase 3. Initially, the Type 1 and Type 2discriminations alternated across sessions for aminimum of five sessions and until thepigeons reached the criterion. Next, bothdiscriminations were presented within thesame session (see Table 2, ‘‘Type 1 + Type2’’). Each session consisted of 80 trials, 40 ofType 1 and 40 of Type 2. For each type, therewere 20 S+ and 20 S2 trials (10 for each left/right assignment). Training lasted from 6 to 31sessions (M 5 16).

During the Pretesting Condition, the sessionstructure remained the same except that a fewS+ trials were conducted in extinction (seeTable 2). Pretesting lasted from 5 to 18sessions (M 5 7).

During the Testing Condition, each sessionconsisted of 68 training trials and 12 test trialsfor a total of 80 trials. During the test trials,Green and Red were presented together forthe first time. In addition, the sample durationon test trials equaled 1 s or 16 s during the first6 sessions and 2 s, 4 s or 8 s during the nextnine sessions (see Table 2, 3rd and 4th rowsfrom bottom). Due to a programming error,for pigeons P170 and PG12, the sampledurations equaled 1 s and 8 s during the firstsix sessions and 2 s, 4 s and 16 s during thenext nine sessions (Table 2, last two rows).Each test trial was presented six times persession during the first six sessions, and fourtimes per session during the last nine sessions.

If during any test session a bird’s discrimi-nation ratio for Type 1 or Type 2 trialsdecreased by more than .05 from its currentcriterion (either .80 or .85), the bird returnedto training for at least two sessions and until itsperformance recovered. However, for pigeonsP948 and P841, testing disrupted the Type 1discrimination to such extent that the criteri-on had to be lowered. Pigeon P948 recoveredpartly and completed the tests with the


criterion set at .75 for the Type 1 discrimina-tion; for Type 2 trials, the criterion wasmaintained at .80. Pigeon P841 did not recoverthe Type 1 discrimination, even after 20sessions of Training and Pretesting. Becauseits ratio for Type 2 trials remained above .80and the ratio for Type 1 trials stabilizedaround .65, testing was resumed. The TestingCondition, with intercalated training sessionswhen required, lasted from 15 to 42 sessionsacross birds (M 5 22).

RESULTS

Training. By the 10th session of training 5 ofthe 6 pigeons were rarely pecking the key withthe vertical bar (fewer than two pecks persession on average); P841 was the exception,for this pigeon maintained some respondingto the vertical bar throughout the experiment(from 4.5 to 30.8 pecks per session).

All subjects learned the two basic discrimi-nations. They required a similar number ofsessions to learn the Type 1 and Type 2discriminations (M 5 35 and 37 sessions,respectively, t(5) 5 0.29, ns). And though thediscrimination learned in the second place(Type 1 for half of the pigeons and Type 2 forthe other half) required fewer sessions thanthe discrimination learned in the first place(M 5 30 and 42, respectively), the differencewas not statistically significant (t(5) 51.83, p 5.13). During the last five training sessions, thediscrimination ratio averaged .93 on Type 1trials (range: .84–.99) and .92 on Type 2 trials(range: .89–.97). When the two discrimina-tions were combined into the same session, theoverall discrimination ratio averaged .90(range: .82–.99).

The total number of sessions required tolearn the two discriminations (i.e., Type 1alone + Type 2 alone + Types 1 and 2combined) ranged from 93 to 158 (M 5118). This number is significantly higher thanthe number obtained in previous studies with asimultaneous double bisection procedure(e.g., 29 to 34 in Machado & Keen, 1999; 27to 65 in Machado & Pata, 2005; 26 to 45 inMachado & Arantes, 2006; 28 to 68 in Oliveira& Machado, 2008; and 26 to 38 in Oliveira &Machado, 2009). However, the number is closeto that obtained by Arantes (2008) with asuccessive double bisection procedure (M 5103, range: 51–133). These results (see also

Arantes & Grace, 2008) show that simulta-neous double bisection tasks are easier to learnthan successive ones, presumably becauselearning to not respond following an S2 iseasier if the same S2 is an S+ for responding onanother key.

Stimulus generalization testing. Figure 3 showsthe stimulus generalization gradients for thetwo temporal discriminations. The responserate on the Green or Red keys during the 6-schoice period is plotted against sample dura-tion. All pigeons exhibited similar generaliza-tion gradients: Response rate was lowest at theS2, intermediate between the S2 and the S+,and highest at the S+ and durations furtheraway from the S2. For pigeon P890, thegradient for Type 2 trials decreased for theshortest sample duration of 1 s.

Figure 4 shows that the average gradient wassimilar for the two discriminations. Responserate increased from the S2 to the S+ and thenit remained high (Type 1) or decreasedslightly (Type 2). A two-way repeated-measuresANOVA, with sample duration and type ofdiscrimination as factors revealed significanteffects of sample duration [F(4, 20) 5 38.95,p , .001], type of discrimination [F(1, 5) 515.10, p , .05], and their interaction [F(4, 20)5 59.72, p , .001].

To analyze the symmetry of the two general-ization gradients, we reflected the curve forType 2 trials around the line t 5 4. The bottompanel of Figure 4 shows the result. The(reflected) gradient for Type 2 trials was belowthe gradient for Type 1 trials, particularly at thegeometric means of the training durations (i.e.,t 5 2 s for Type 1 and t 5 8 s for Type 2) and atthe extreme durations on the opposite side ofS2 (t 5 16 s for Type 1 and t 5 1 s for Type 2). Atwo-way, repeated-measures ANOVA with sam-ple duration and type of discrimination asfactors revealed that all effects were significant(type of discrimination, F(1, 5) 5 15.10, p ,.05, sample duration, F(4, 20) 5 68.66, p ,.001, and their interaction F(4, 20) 5 6.17, p ,.005).

Paired t-tests conducted for the t 5 2 s, t 5 8 sand t 5 16 s samples (defined by the Type 1discrimination in the bottom panel of Figure 4)revealed a significant difference between re-sponse rate on t 5 2 s and t 5 16 s [t(5) 5 5.42,p , .05 and t(5) 5 3.66, p , .05, respectively];on t 5 8 s the difference approached signifi-cance [t(5) 5 2.27, p 5 .07].


Stimulus–response generalization testing. Thedata analysis from the choice tests addressesan important question: Does the context effecthold even when only two responses arereinforced, that is, when pecking Green andRed are reinforced following 4-s samples butnot following 1-s and 16-s samples, respective-ly? Figure 5 shows the individual and averageresults. The filled circles show that thepreference for Green—defined by the ratiobetween the total number of responses toGreen and the total number of responses toGreen plus Red—tended to increase with sam-ple duration. A repeated-measures ANOVArevealed a significant effect of sample dura-tion, F(4,20) 5 13.79, p , .001.

The filled circles in the bottom panel showthat, on the average, preference for Greenincreased monotonically from about .1 toabout .7, thus reproducing the context effectpreviously found with other variants of the

double bisection task (compare Figures 2 and5; see also, Arantes, 2008; Arantes andMachado, 2008; Machado and Arantes, 2006;Machado and Keen, 1999; Machado and Pata,2005; Oliveira and Machado, 2008, 2009).

The individual curves show some variabilityacross birds. Pigeons P890, P948 and P178displayed steep, monotonically increasing pref-erence functions; pigeon P841 also presenteda monotonically increasing function, but itnever exceeded .50; for pigeons PG12 andP170, preference for Green also tended toincrease with sample duration, although notmonotonically. Three subjects revealed astrong overall bias for one comparison, Greenin the case of PG12 and Red in the case ofP170 and P841.

The causes of the individual differences inthe strength of the context effect remainunclear. On the one hand, the relativelyweaker effect revealed by pigeon P841 could

Fig. 3. Generalization gradients obtained after the Type 1 (S+54s, S251s) and Type 2 (S+54s, S2516s)discriminations. Note the logarithmic scale on the x-axis.


be due to its poor discrimination between the1-s and 4-s samples during Phase 3, but thesame cannot be said of pigeons P170 and PG12because their discrimination ratios never fellbelow .80. On the other hand, pigeons P170and PG12 started the choice test with sampledurations of 1 s and 8 s, whereas the remainingpigeons started them with sample durations of1 s and 16 s, but it is unclear how thisdifference could explain the differences inthe strength of the context effect.

Another potential source of the individualdifferences may be the number of choice trialson which the pigeon pecked neither theGreen nor the Red keys. Table 3 shows thenumber of these ‘‘empty’’ trials, out of 36, foreach pigeon and sample duration. The num-ber of empty trials was particularly highfollowing the 8-s and 16-s samples. However,there was no clear relation between thatnumber and the preference for Green. Con-sider the 16-s samples: Of the 3 pigeons that

showed a strong preference for Green, 2 had alarge number of empty trials (P890 and P178)but 1 had only one empty trial (P948). Thecase was similar following 1-s samples. Spear-man’s rank-order correlations between thenumber of empty trials and the preferencefor Green were not statistically significant (seeTable 3, bottom lines).

Although variation in the number of emptytrials does not seem to account for thedifferences in the context effect, the largenumber of empty trials following some sampledurations raises an interpretative problemrelated to the measurement of preference.Consider the data for pigeon P170. The 33empty trials following the 16-s samples meanthat the pigeon responded on 3 trials only. Ontwo of them, it chose Green, and on one ofthem it chose Red, which suggests a prefer-ence for Green. However, preference forGreen measured by relative response rate wasonly .27 (see Figure 5) because response rateon Red was higher than on Green. Differencesin response rate may have contaminated thepreference measure.

This difficulty suggested a second way tomeasure preference. For each sample, wecounted the number of trials on which thepigeon pecked Green at least once (even if italso pecked Red) and then divided it by thetotal number of trials on which the pigeonpecked at least one key. This ‘‘all-or-none’’preference measure is not affected by differ-ences in response rate.

The unfilled circles in Figure 5 show the‘‘all-or-none’’ measure. It is clear that both

Fig. 4. Top panel. Average generalization gradientsobtained after the Type 1 (S+54s, S251s) and Type 2(S+54s, S2516s) discriminations. Bottom panel. Thegradient for Type 2 trials is reflected along the verticalline t54 (the inverted x-axis shows the original sampledurations). The bars show the SEM. Note the logarithmicscale on the x-axis.

Table 3

Number of empty trials (out of 36) following each sampleduration.

Pigeon

Sample duration

1 2 4 8 16

P170 0 0 1 13 33P178 21 7 0 11 22P841 0 0 0 7 4P890 18 24 1 26 30P948 2 1 0 6 1PG12 7 10 0 20 27Avg 8 7 0 14 20rs 2.03 .32 .42 .43 2.20p .48 .27 .20 .20 .35

Note. rs is Spearman’s rank-order correlation betweenthe number of empty trials and the preference for Green.p is the corresponding p-value under H0.


preference measures yielded similar results.The correlations between them were strongfor 4 pigeons (.91 # r 2 # .99 for P178, P841,P890, and P948), and moderate for theremaining 2 (.60 # r 2 # .75). The averagesof the two measures (see bottom panel) werepositively correlated (r 2 5 .97). We concludethat, with few exceptions, the two measures ofpreference were consistent and, therefore,

that relative response rate is a reliable measureof preference in the present task.

Predicting preference functions from stimulusgeneralization gradients. The major goal of thepresent study was to assess how well thecontext effect found in double bisection taskscould be predicted from the stimulus general-ization gradients. To that end we carried outthe following analysis. For each pigeon and

Fig. 5. The top panels show the individual functions relating preference for Green over Red to sample duration.Filled and unfilled circles correspond to different measures of preference, relative response rate or ‘‘all-or-none’’. Thebottom panel shows the average results. The vertical bars show the SEM. Note the logarithmic scale on the x-axis.


sample duration, we used the response ratesfrom Phases 1 and 2 displayed in Figure 3 tocompute the predicted preference for Green.Specifically, we divided the absolute responserate to Green by the sum of the absoluteresponse rates to Green and Red. Finally, weplotted the preference function predicted fromthe generalization gradients and compared it

with the preference function obtained duringthe choice test. Figure 6 shows the results.

All six predicted functions (unfilled circles)expressed the context effect: The preferencefor Green increased monotonically with sam-ple duration. In addition, for pigeons P890,P948, and P178, the predicted and obtainedfunctions were similar (r 2 5 .93, .90, and .85,

Fig. 6. Filled circles show the preference for Green obtained in the Testing Condition of Phase 3 with samplesranging from 1 to 16 seconds and Green and Red as comparisons. The unfilled circles show the preference for Greenpredicted from the gradients obtained during the stimulus generalization tests of Phases 1 and 2. The vertical bars showthe SEM. Note the logarithmic scale on the x-axis.


respectively); for pigeon P841 the two func-tions differed appreciably at 8- and 16-ssample durations (r2 5 .81); and for pigeonsP170 and PG12, they differed considerably(r 2 5 .54 and .27, respectively). Interestingly,the pigeons that showed the greatest overlapbetween the predicted and the obtainedpreference functions also showed the stron-gest context effect.

The average of the predicted functions (seebottom panel) increased monotonically fromabout .1 to .9. Although more extreme thanthe average of the obtained preference func-tions, it had approximately the same shape.The two average functions were stronglycorrelated (r 2 5 .93).

DISCUSSION

Six pigeons were exposed to a simplifiedversion of the temporal double bisection proce-dure. On Type 1 trials they learned to peck aGreen key following 4-s samples but not to peckit following 1-s samples; on Type 2 trials theylearned to peck a Red key following 4-s samplesbut not following 16-s samples. After eachdiscrimination was learned, a stimulus general-ization gradient was obtained by varying sampleduration from 1 to 16 s. Next, the two trial typeswere included in the same session and astimulus–response generalization test was con-ducted in which the samples ranged from 1 to16 s and the comparison stimuli were the Greenand Red keys. The study had two interrelatedgoals, to investigate whether the two temporalgeneralization gradients could predict the con-text effect that was expected to occur during thechoice trials, and to determine whether thegeneralization gradients as well as the contexteffect were consistent with the LeT model.

The choice test showed that, for 4 out of 6pigeons, preference for Green over Red in-creased monotonically with the sample dura-tion (Figure 5). For the other 2, the effect wasweaker but the overall positive trend wasobserved. The context effect was obtainedregardless of whether preference was assessedby relative response rate or by an ‘‘all-or-none’’measure that is not influenced by differences inresponse rate between the two keys. And inspite of considerable procedural changes, themagnitude of the average effect was similar tothat obtained in previous studies. Replicatingthe context effect in a situation where only two

responses were reinforced opened the possibil-ity to test a generalization-based account of it.

The results showed that the average contexteffect could be predicted from the generaliza-tion gradients. However, the accuracy of thepredictions varied across pigeons. For 3 ofthem (see Figure 6, left panels), the general-ization gradients predicted well not only thepositive trend, but also the specific values ofthe preference functions; for the other 3, thegradients predicted well only the positivetrend of the preference functions (Figure 6,right panels). The mismatches between thepredicted and observed function values re-vealed that the generalization gradients tend-ed to overestimate the strength of the contexteffect (cf. the slopes of the two functions in theright panels of Figure 6).

The reasons for the mismatches remainunclear. They could stem from generalizationdecrement because the stimulus conditionsduring the training and generalization trials(i.e., only one of the keys, Green or Red, waspresent) differed from the stimulus conditionsduring the choice trials (i.e., both the Greenand Red keys were present). Furthermore,some pigeons may have learned that thedistinctive combination of Green and Red keyssignaled extinction and, as a consequence,they did not respond on a large proportion ofchoice trials (Table 3). (The large number ofempty trials, particularly following the extremesample durations of 1 s and 16 s, may havebeen caused also by the preceding stimulusgeneralization tests, which also were conduct-ed in extinction.). A small number of non-empty trials could have distorted the measureof preference. However, note that there was nosignificant correlation between the number ofempty trials and the degree of preference forthe Green or Red keys. Also, how well thegeneralization gradients predicted the contexteffect did not seem to depend on how much thebasic discriminations were disrupted duringtesting. In any event, the nuisance of emptytrials may be reduced in future studies by using atwo-group design, with only one group exposedto generalization tests, and by using choice testswith partial but nondifferential reinforcement.

To account for the context effect in terms ofgeneralization gradients, we advanced onequalitative account relying on area shift, andone quantitative account based on the LeTmodel. We analyze them in this order.


Qualitative account. According to the areashift account, gradients obtained after intradi-mensional training are asymmetrical, display-ing a higher number of responses in the sideof S+ opposite the S2. Then, the area of thegeneralization gradient on Type 1 trials shouldbe shifted toward durations longer than 4 s,and the area of the generalization gradient onType 2 trials should be shifted toward dura-tions shorter than 4 s.

The generalization gradients obtained inPhases 1 and 2 matched these predictions. All12 gradients showed an area shift effect. Thegradient produced by pigeon P890 duringType 2 trials (see the top right panel inFigure 3), in contrast with the other gradients,showed a clear reduction in response rate forstimulus values moved away from the S+ in thedirection opposite to the S2. It is conceivablethat a closer spacing of the test stimuli in thevicinity of S+ (4 s) might have revealed a peakaround t 5 3 s. In the other 11 gradients,response rate increased as the stimulus dura-tion changed from the S2 to the S+, and thenit remained high as the stimulus durationcontinued to change past the S+ (see Figures 3and 4). The shape of these gradients resem-bles a step function, with a low response rate atthe S2, an intermediate response rate betweenthe S2 and the S+, and a high response rate atand past the S+. Because the gradients ob-tained in the present experiment revealed anarea shift effect and could predict the contexteffect, we conclude that the area shift accountworks well in explaining our findings.

The ‘‘opposed’’ generalization gradientsdisplayed in Figure 3 and in the top panel ofFigure 4 are similar to the gradients obtainedby Boneau and Honig (1964). These authorswere the first to examine generalizationgradients based upon conditional discrimina-tion training. As in the present study, theirpigeons learned two conditional discrimina-tions. When the response key was illuminatedwith a 550-nm light, a white vertical bar addedto the key was the S+ and the absence of thebar was the S2; when the response key wasilluminated with 570-nm light, the contingen-cies were reversed, the S+ and S2 were theabsence and presence of the bar, respectively.During generalization tests, the authors variedthe wavelength of the light from 540 to 580 nmwith either the bar present or with the barabsent. When the bar was present, the gener-

alization gradient was high at 540 and 550 nmand low at 570 and 580. When the bar wasabsent, the generalization gradient was low at540 and 550 nm, high at 570 nm, and lowagain at 580 nm. If we replace wavelength withsample duration and the presence/absence ofthe bar with Green/Red keylight color, then wecan conceive of the present study as extendingBoneau and Honig’s findings to the timingdomain. In both studies, the areas of the twogradients shifted in opposite directions and nopeak shift effect was observed.

A quantitative (and integrative) account: theLeT model. To see how well the LeT modelreproduces the major trends in the data, weran a simulation of the entire experiment,following the same phases and conditions asthe pigeons, and for a similar number ofsessions. Throughout, the model parametersremained constant and their values weresimilar to those used in previous studies(Machado et al., 2009).

The model behaves as follows. Consider aType 1 training trial. During the sample, thebehavioral states are activated serially—firststate 1, then state 2, etc. Each state remainsactive for l seconds, with l sampled at trialonset from a normal distribution with mean m5 1.0 s and standard deviation s 5 0.3 s. At theend of the sample one state is active, say, staten*. This state is coupled with the operantresponse (e.g., Green) and the degree of thecoupling, always between 0 and 1, is represent-ed by the variable WG(n*). When there is onlyone key, as during training and generalizationtrials1, WG(n*) yields the probability of emittinga response. (To keep the simulation simple andfocus on the shape of the predicted curves, wedid not attempt to model absolute responserate.) When a response occurs, WG(n*) changes,increasing if the response is reinforced (i.e.,DWG(n*) 5 b(1 2 WG(n*)) and decreasing ifthe response is extinguished (i.e., DWG(n*) 52aNWG(n*)), where b 5 0.2 and a 5 0.04 arelearning parameters.

In the present simulation, the coupling ofeach state was initialized at 0.8 (i.e., WG(n) 50.8, for n 5 1, 2, 3,…) ensuring that, duringthe first session, a response on the Green key

1 All training and generalization trials included also akey with a vertical bar. However, because pecks on that keywere never reinforced, and after the first few sessions thepigeons rarely pecked at it, the model ignores it.


was very likely to happen on each trial. After 40sessions, with reinforcement following 4-ssamples and extinction following 1-s samples,the WG(n) values changed and the result isthe curve with filled circles displayed in the toppanel of Figure 72. The early states, activemostly after the 1-s samples, lost their couplingwith Green, but subsequent states, activemostly after the 4-s samples, had their couplingstrengthened. The remaining states, almostnever active during Type 1 trials, retained theirinitial coupling of 0.8.

The simulation details for Type 2 trials werethe same except that a different vector,WR(n), coupled the states with the Red key.The curve with open circles shows how theWR(n) values changed with training fromtheir initial value of 0.8. The early states, activemostly after the 4-s samples, either retained orstrengthened their couplings with Red, where-as the states active mostly after the 16-s sampleslost most of their coupling.

The middle panel shows the generalizationgradients. Nothing in the model changedfrom training to testing. These gradientsreflect the coupling strengths (W) resultingfrom training. To illustrate, consider the curvefor Type 1 trials (filled circles). The gradient at1 s is close to zero because after 1-s samples a)the initial states (n 5 1 and 2) are the mostlikely to be active, and b) as the top panelshows, those states have close-to-zero couplingswith Green. The generalization gradientreaches its maximum at 4 s because after 4-ssamples the most active states are the interme-diate states (n 5 3 to 6), which are stronglycoupled with Green (see top panel). Theresponse probability at 2 s occurs because thestates most likely to be active after the 2-ssamples, States 2 and 3, have weak and strongcouplings with Green, respectively; the neteffect is an intermediate response probability.Finally, the gradient decreases slightly after 4sbecause the couplings of later states (n . 6),the states most likely to be active at the end of8-s and 16-s samples, are not as strong as thecoupling of the intermediate states.

The two generalization gradients are op-posed and both display an area shift. Thegradient for Green is low at 1 s and high at 4 sand longer samples. The gradient for Red islow at 16 s and high at 4 s and shorter samples.The gradients are similar to those produced by

Fig. 7. Results from the simulation of the LeT model(Machado et al., 2009). Top panel. Strength of thecouplings between the behavioral states and the operantresponses, Green and Red, at the end of the TrainingConditions of Phases 1 and 2 (see Table 2). Middle panel.Generalization gradients obtained dung the TestingConditions of Phases 1 and 2. Bottom panel. Preferencefor Green over Red obtained during the Testing Conditionof Phase 3. Note the logarithmic scale on the x-axis in themiddle and bottom panels.

2 The contribution of the Pretesting Condition (partialreinforcement) to the coupling strengths (W) is negligi-ble, thus, when the animal advances to testing, theresponse probabilities yielded by WG and WR wouldbasically be the same.


our pigeons except that the model predictssymmetric gradients that decrease for eithervery long (Green) or very short (Red) dura-tions. If the couplings had been initialized at alower value (e.g., .2 instead of .8) the decreasefor the extreme durations would have beenmore pronounced (see also Boneau & Honig,1964, Figure 2).3

On choice trials, the Green and Red keysoccur together. The model assumes that p, theprobability of choosing the Green key, is givenby the relative value of the couplings, that is, p5 WG(n*)/[WG(n*) + WR(n*)], where n* isthe active state at the end of the sample. Thebottom panel of Figure 7 shows the predictedpreference function: As the sample durationranges from 1 s to 16 s, preference for Greenincreases monotonically. The model predictsthe context effect and reproduces well thepigeons’ average preference function (com-pare the bottom panels of Figures 5 and 7).

In summary, the LeT model reproduced themajor trends in the data. The shape of thesimulated generalization gradients was consis-tent with the pigeons’ gradients. The majordiscrepancy was the symmetry of the gradients(predicted by LeT but not observed reliably inthe pigeons’ data) and the decrease inresponse strength for durations significantlyaway from the S+ and S2 (also predicted byLeT but rarely observed in the pigeons’ data).With respect to the context effect, the model’spreference function also was consistent withthe average of the pigeons’ preference func-tions. However, the individual differencesamong the pigeons are beyond the scope ofthe model.

The present study makes two significantcontributions to our understanding of tempo-ral control, one related to the LeT model andthe other to the broader subject of stimuluscontrol. Concerning LeT, in previous studieswith the double bisection task we showed thatthe model could predict the context effect, but

we had not tested directly the model’s accountof the effect, namely, that it depends on thecoupling profiles learned during training.Temporal generalization tests with the twooperants, pecking Green and pecking Red, areone way of revealing these coupling profilesand thereby of testing one of the model’shidden components. Because in LeT choiceproportions depend on the coupling profiles,the latter are more fundamental than theformer. Putting to test the model’s assump-tions about the coupling profiles is a signifi-cant advance over testing only the model’spredictions about choice proportions.

Concerning stimulus control, the presentstudy followed a strategy that proved fruitful inother domains, namely, to try to explainseemingly complex phenomena on the basisof stimulus generalization gradients and theirinteractions (e.g., transposition and peak shiftfrom excitatory and inhibitory gradients; seeHonig, 1962, Riley, 1968, and Rilling, 1977).One added benefit of this strategy is to bringto the forefront of timing research the conceptof temporalgeneralization gradient and high-light how little we know about it, its attributes,and the variables that affect it.

REFERENCES

Arantes, J. (2008). Comparison of Scalar ExpectancyTheory (SET) and the Learning to-Time (LeT) modelin a successive temporal bisection task. BehaviouralProcesses, 78, 269–278.

Arantes, J., & Grace, R. C. (2008). Failure to obtain valueenhancement by within-trial contrast in simultaneousand successive discriminations. Learning and Behavior,36, 1–11.

Arantes, J., & Machado, A. (2008). Context effects in atemporal discrimination task: Further tests of theScalar Expectancy Theory and Learning-to-Timemodels. Journal of the Experimental Analysis of Behavior,90, 33–51.

Bizo, L. A., & McMahon, C. V. (2007). Temporalgeneralization and peak shift in humans. Learningand Behavior, 35, 123–130.

Bloomfield, T. M. (1967). A peak shift on a line-tiltcontinuum. Journal of the Experimental Analysis ofBehavior, 10, 361–366.

Boneau, C. A., & Honig, W. K. (1964). Opposedgeneralization gradients based upon conditionaldiscrimination training. Journal of Experimental Psychol-ogy, 68, 89–93.

Catania, A. C. (1970). Reinforcement schedules and thepsychophysical judgments: a study of some temporalproperties of behavior. In W. N. Schoenfeld (Ed.), Thetheory of reinforcement schedules (pp. 1–42). New York:Appleton-Century-Crofts.

3 A different decision rule could solve the problem (butsee the gradient for Type 2 trials of pigeon P890 inFigure 3): Assume that WG(n) and WR(n) are notprobabilities but response strengths and that a responseoccurs only if its strength is above a threshold, H. If theinitial values of WG and WB are all greater than H, themodel predicts gradients that do not decrease at theextreme sample durations. This improved decision rulecosts one extra parameter, the threshold H, and it will notbe discussed further here.


Cheng, K., Spetch, M. L., & Johnston, M. (1997). Spatialpeak shift and generalization in pigeons. Journal ofExperimental Psychology: Animal Behavior Processes, 23,469–481.

Church, R. M. (2003). A concise introduction to scalartiming theory. In W. H. Meck (Ed.), Functional andneural mechanisms of interval timing (pp. 3–22). BocaRaton, FL: CRC Press.

Church, R. M., & Deluty, M. Z. (1977). Bisection oftemporal intervals. Journal of Experimental Psychology:Animal Behavior Processes, 3, 216–228.

Elsmore, T. F. (1971). Control of responding by stimulusduration. Journal of the Experimental Analysis of Behavior,16, 81–87.

Fetterman, J. G., & Killeen, P. R. (1991). Adjusting thepacemaker. Learning and Motivation, 22, 226–252.

Gallistel, C. R. (1990). The organization of learning. Cam-bridge, MA: Bradford Books/MIT Press.

Gibbon, J. (1977). Scalar expectancy theory and Weber’slaw in animal timing. Psychological Review, 84, 279–325.

Gibbon, J. (1981). On the form and location of thepsychometric bisection function for time. Journal ofMathematical Psychology, 24, 58–87.

Gibbon, J. (1991). Origins of scalar timing theory. Learningand Motivation, 22, 3–38.

Gibbon, J., Church, R. M., & Meck, W. H. (1984). Scalartiming in memory. In L. Allan, & J. Gibbon (Eds.),Timing and time perception (pp. 52–77). New York:Annals of the New York Academy of Sciences.

Hanson, H. M. (1959). Effects of discrimination trainingon stimulus generalization. Journal of ExperimentalPsychology, 58, 321–334.

Honig, W. K. (1962). Prediction of preference, transposi-tion, and transposition reversal from the generalizationgradient. Journal of Experimental Psychology, 64, 239–248.

Killeen, P. R., & Fetterman, J. G. (1988). A behavioraltheory of timing. Psychological Review, 95, 274–285.

Machado, A. (1997). Learning the temporal dynamics ofbehavior. Psychological Review, 104, 241–265.

Machado, A., & Arantes, J. (2006). Further tests of theScalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model in a temporal bisection task.Behavioural Processes, 72, 195–206.

Machado, A., & Keen, R. (1999). Learning to Time (LET)or Scalar Expectancy Theory (SET)? A critical testof two models of timing. Psychological Science, 10,285–290.

Machado, A., Malheiro, M. T., & Erlhagen, W. (2009).Learning to time: a perspective. Journal of theExperimental Analysis of Behavior, 92, 423–458.

Machado, A., & Pata, P. (2005). Testing the ScalarExpectancy Theory (SET) and the Learning to Timemodel (LeT) in a double bisection task. Learning andBehavior, 33, 111–122.

Mellgren, R. L., Mays, M. Z., & Haddad, N. F. (1983).Discrimination and generalization by rats of temporalstimuli lasting for minutes. Learning and Motivation,14, 75–91.

Oliveira, L., & Machado, A. (2008). The effect of sampleduration and cue on a double temporal discrimina-tion. Learning and Motivation, 39, 71–94.

Oliveira, L., & Machado, A. (2009). Context effect in atemporal bisection task with the choice keys availableduring the sample. Behavioural Processes, 81, 286–292.

Platt, J. R., & Davis, E. R. (1983). Bisection of temporalintervals by pigeons. Journal of Experimental Psychology:Animal Behavior Processes, 9, 160–170.

Purtle, R. B. (1973). Peak shift: a review. PsychologicalBulletin, 80, 408–421.

Richelle, M., & Lejeune, H. (1980). Time in animal behavior.New York: Pergamon.

Riley, D. A. (1968). Discrimination learning. Boston: Allyn &Bacon.

Rilling, M. (1977). Stimulus control and inhibitoryprocesses. In W. K. Honig. & J. E. R. Staddon (Eds.),Handbook of operant behavior (pp. 432–480). EnglewoodCliffs, NJ: Prentice Hall.

Russell, R., & Kirkpatrick, K. (2007). The role of temporalgeneralization in a temporal discrimination task.Behavioural Processes, 74, 115–125.

Shettleworth, S. J. (1998). Cognition, evolution, and behavior.New York: Oxford University Press.

Spence, K. W. (1937). The differential response of animalsto stimuli varying within a single dimension. Psycho-logical Review, 44, 430–444.

Spetch, M. L., & Cheng, K. (1998). A step function inpigeons’ temporal generalization in the peak shifttask. Animal Learning and Behavior, 26, 103–118.

Stubbs, D. A. (1968). The discrimination of stimulusduration by pigeons. Journal of the Experimental Analysisof Behavior, 11, 223–238.

Received: August 1, 2011Final Acceptance: March 7, 2012


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