A

epasWai©

K

1

elpdacfftsofssamt

0d

Behavioural Processes 73 (2006) 187–198

Molecular order in concurrent response sequences

Susan M. Schneider a,∗, Michael Davison b

a Department of Psychology, Florida International University, Miami, FL 33199, United Statesb Department of Psychology, University of Auckland City Campus, Private Bag 92019, Auckland, New Zealand

Received 14 July 2005; received in revised form 9 May 2006; accepted 12 May 2006

bstract

We studied the order of emission of concurrently reinforced free-operant two-response sequences such as left–left (LL) and left–right (LR). Thend of each sequence was demarcated by stimulus change. The use of demarcated sequences of responses, as opposed to individual responses,rovides an expanded set of distinct, temporally ordered behaviour pairings to investigate (e.g., LL followed by LL, LL followed by LR, etc.); it iss well a real-life analogue. A sequential analysis of new and existing rat and pigeon data revealed patterns in both overall and post-reinforcer-onlyequence emission order. These patterns were consistent across species and individuals, and they followed higher-order organising principles.

e describe sequence non-repetition, last-response repetition, and the proportion and post-reinforcer effects, and relate them to existing molar

nd molecular behaviour principles. Beyond their immediate implications, our results illustrate the value of sequential analysis as a tool for thenvestigation of molar-molecular behavioural relations.

2006 Elsevier B.V. All rights reserved.

ility;

dp

druDrmiIeafi

r

eywords: Response sequences; Sequential analysis; Molar-molecular; Probab

. Introduction

Researchers have identified many orderly behaviour–nvironment relations, many of which apply over relativelyonger-term (“molar”) aggregation scales such as single or multi-le sessions. An example is the generalised matching law, whichescribes the steady-state relation between obtained responsend reinforcer ratios in the concurrent schedules used to studyhoice. (In a concurrent schedule, two or more schedules of rein-orcement operate simultaneously, and the behaver can alternatereely between them.) A continuing research question concernshe degree to which molar relations like this one result fromhorter-term “molecular”-level causal control (e.g., that foundn a minute-to-minute basis). Heyman (1979), for example,ound no evidence for sequential dependencies in response emis-ion order in a standard concurrent variable-interval (VI) VIchedule, but others have (e.g., Silberberg et al., 1978, both with

nd without changeover delays). Silberberg et al. suggested thatolecular control was primary. Williams (1991) countered that

he literature offered sufficient data to support the existence of

∗ Corresponding author. Tel.: +1 3053481230; fax: +1 3053483879.E-mail address: schneids@fiu.edu (S.M. Schneider).

dycCsrm

376-6357/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.beproc.2006.05.008

Concurrent schedules; Pigeons; Rats

irect molar control producing matching to the molar reinforcerrobabilities.

In recent years, molar choice theorising has continued toevelop (e.g., Davison and Nevin, 1999), but at the same timeesearch demonstrating molecular order in concurrent sched-les has become progressively more convincing. For example,avison and Baum (2000) and Landon and Davison (2001)

eported molecular order in concurrent schedules with reinforce-ent probability ratios that changed up to seven times a session:

ndividual reinforcers produced predictable, repeatable effects.ncreasingly, it appears that molar matching may after all bexplicable from more molecular mechanisms of control: Baronnd Perone (2001) considered that “the balance has tipped inavor of [this] interpretation” (p. 359). Molecular order remainsnsufficiently understood, however.

The concurrent-schedules paradigm using two individual-esponse behavioural units such as left and right keypecks hasominated the study of choice, and has been locally anal-sed using the various forms of conditional probability forhangeovers (e.g., MacDonall, 2000) and Markov models (e.g.,

leaveland, 1999; also see Silberberg et al., 1978). However,

tudying more than two behavioural units creates more tempo-ally ordered behavioural possibilities, and thus the basis forore comprehensive analyses. The basic procedure entails dif-

1 aviou

fpr

daStltatdta

s(ptCobLcft1p1tt

pRtAssifR2oa1ttaLqf

sttt

trra

sdrulwmtamoltfdhtStwsft

a(dotaas

2

2

Si1(fPe5

2

88 S.M. Schneider, M. Davison / Beh

erentially reinforcing the concurrent production of the fourossible two-response sequences: left–left (LL), left–right (LR),ight–left (RL), and right–right (RR).

In a seminal study, Stubbs et al. (1987) utilised this proce-ure with pigeons on dependently arranged VI schedules, with1-s blackout after unreinforced sequences to demarcate them.equence emissions increased or decreased following the con-

ingencies, and could be approximated by the strict matchingaw (see Schneider and Davison, 2005, for a reanalysis usinghe generalised matching law). At a molecular level, Stubbs etl. performed a conditional probability analysis on data fromwo experimental conditions and found indications of sequentialependencies. They did not, however, compare their probabili-ies with those expected based on chance concatenation of thectual sequence distributions.

A sequential analysis method that is based on the actualequence distributions is described in Bakeman and Gottman1986); it is frequently employed in applied and comparativesychology (e.g., Justice et al., 2002; Walker and Fell, 2001),hough seldom in the present context (but see Richardson andlark, 1976). In a Lag-1 analysis, the behavioural emissionrder is examined. The observed frequencies of each possi-le ordered behaviour pairing (e.g., LL sequence followed byR sequence) are compared with the frequencies expected byhance, based on the actual behaviour distributions—a straight-orward application of probability theory. The differences canhen be converted to z-scores and analysed statistically. Any Lag-

sequential dependencies may themselves depend upon theirositions in longer sequences (e.g., Cleaveland, 1999; Iversen,986, 1991), which can also be analysed using this method. Theemporal intervals between the events are irrelevant in this par-icular analysis.

To take a simplified example: in a 100-sequence sample, sup-ose there are 25 emissions each of the four sequences (LL, LR,L, and RR). Suppose also that each sequence type is emit-

ed as a block, with the 25 LLs followed by the 25 LRs, etc.random distribution of sequences would predict that each

equence would precede and follow itself and all the otherequences equally often: roughly 6 times each. That is, look-ng at the 25 instances of LL in the sample, LL would beollowed by LL about 6 times; LR 6 times; RL 6 times; andR 6 times. Obviously, the example data are far otherwise, with4 LL–LL ordered sequence pairings, 1 LL–LR, and no LL–RLsr LL–RRs. What we shall call the sequential probability ratiosre the (observed − expected)/expected frequency ratios for the6 sequence pairings. Given random sequence-emission order,he observed − expected difference should be close to 0, and soherefore should the ratio. Instead, the values for this examplere 3.0 for LL–LL, −0.83 for LL–LR, and −1.0 for LL–RL andL–RR. In the analysis of the actual data, each observed fre-uency was also converted into a z-score, based on the expectedrequency (see Appendix A).

The same analysis can be performed for the reinforced

equences only and those sequences that immediately followedhem. Because these post-reinforcer sequential probability pat-erns turned out markedly different from the overall patterns inhe present data set, the overall sequential probability ratios were

hs

ral Processes 73 (2006) 187–198

hen recalculated for all data sets with the reinforced sequencesemoved as leading sequences in the sequence pairings (but stillemaining as following sequences). All overall sequential prob-bility data exclude the post-reinforcer data.

Schneider and Morris (1992) were the first to utilise thisequential analysis method on concurrent-schedule sequenceata. Rats were the subjects, and the required minimum inter-esponse time (IRT) was substantially longer (4–7 s) than thatsed by Stubbs et al. Delays this long make sequences lessikely to function as coherent units, and indeed, respondingas intermediate between matching of sequences as units andatching only of the final responses in the sequences to rela-

ive reinforcers (standard response matching). For the sequentialnalysis, as described above, probability theory allowed deter-ination of the expected-from-chance number of occurrences

f a sequence followed by any other sequence (e.g., LL fol-owed by LR). If the sequences were emitted in random order,he differences between the observed and expected-from-chancerequencies would be small. Alternatively, sequential depen-encies might occur: some sequences might follow others atigher-than-chance or lower-than-chance frequencies, showinghat the emission of sequences was under sequential control.chneider and Morris (1992) found nonrandom patterns of this

ype for their two-response sequences; moreover, these patternsere consistent across individuals. However, a post-reinforcer

equential analysis of the sort described above was not per-ormed, and the overall sequential probability analysis includedhe post-reinforcer data.

In the current study, we reanalysed the rat data of Schneidernd Morris (1992) and the pigeon data of Schneider and Davison2005), which shared the same basic concurrent-sequence proce-ure; Schneider and Davison (2005) performed a molar analysisnly. We augmented these studies by running and analysing addi-ional conditions with rats, with different overall reinforcer ratesnd different minimum IRTs. We looked for sequential patternsnd higher-level sequential-order principles, and we made cross-pecies comparisons to test for generality.

. Materials and methods

.1. Subjects

The new data were acquired in three phases (see Table 1).ubjects for each phase were four individually housed, exper-

mentally naive Sprague–Dawley rats, designated 1A throughD (Phase 1), 2A through 2D (Phase 2), and 3A through 3DPhase 3). They were maintained at about 85% of their free-eeding weights, with water available in their home cages. Inhase 1, rats were males 3–4 months old at the beginning of thexperiment. Phase 2 rats were 2-month-old females; Phase 3,-month-old males.

.2. Apparatus

Two standard Lafayette two-lever operant chambers withouselights were used. Fans in the outer sound-attenuatinghells provided both ventilation and masking noise. Food pel-

S.M. Schneider, M. Davison / Behaviou

Table 1Scheduled sequence relative reinforcer probabilities minimum temporal spacing,and VI values

Condition LL LR RL RR Minimumspacing (s)

VI (s)

Phase 11 0.45 0.45 0.05 0.05 – 602 0.05 0.05 0.45 0.45 – 453 0.45 0.45 0.05 0.05 – 304 0.05 0.05 0.45 0.45 – 60

Phase 25 0.90 0 0 0.10 – 606 0.50 0 0 0.50 – 607 0.05 0.05 0.45 0.45 – 608 0.90 0 0 0.10 – 60

Phase 39 0.45 0.45 0.05 0.05 2 4510 0.05 0.05 0.45 0.45 1 5511 0.45 0.45 0.05 0.05 0 60

lawtl

2ofwsssabc

2

ihss

eeawtaapatV

ris(n

r1oeoHaPm

pasedta

ccb2ttiitoae32s

eri

3

eosf(c

12 0.05 0.05 0.45 0.45 2 45

ets (45 mg) were delivered in a food receptacle centered 20 mmbove the floor on the main panel. The two levers on either sideere at a height of 70 mm and a 125 mm center-to-center dis-

ance. A minimum force of 0.16 N was required to activate theevers, producing a clicking feedback sound.

In Phase 1, the apparatus was controlled remotely by VIC0® and Commodore 64® computers using BASIC. Becausef the limitations of these computers, sequence emission orderor the sequential probability analyses of Conditions 3 and 4as displayed onscreen and recorded by hand once every nine

essions from the 20th session on. Four hundred consecutiveequences were recorded from the beginning and middle of theseessions, starting at about 5 min into the session. For Phases 2nd 3, the same apparatus was controlled and all data recordedy MedPC® hardware and software and an IBM®-compatibleomputer.

.3. Procedure

For all phases, demarcation of the rats’ L and R responsesnto two-response sequences was accomplished by blinking theouselight off for about 0.15 s after the second response in eachequence. Thus, a response stream of L–L–R–L became an LLequence followed by an RL sequence.

Table 1 summarises the main elements of the procedure forach phase. Our reinforcement probability sets replicated sev-ral of those used in the previous work with pigeons (Schneidernd Davison, 2005; also see Schneider and Morris, 1992), ande also included replications across phases. Throughout, as in

he previous work, a VI schedule ran until reinforcement avail-bility. One of the four two-response sequences was then chosenccording to the probabilities shown in the table, the first com-

letion of the selected sequence was followed by reinforcement,nd a new VI interval was selected. For example, in Condi-ion 1, the LL sequence was chosen 45% of the time. After theI interval ended, the first completion of an LL sequence was

rqrt

ral Processes 73 (2006) 187–198 189

einforced (even if it had been initiated prior to the end of thenterval). This method of scheduling is known as “dependent”cheduling, because each reinforcer is held until it is received.“Independent” scheduling makes reinforcers for different alter-atives available independently of each other.)

In Phase 1, randomly generated inter-reinforcer intervalsanged from 1 s to twice the VI schedule value minus 1 s (e.g.,–119 s for VI 60 s). Dividing the computer’s random numberutput into suitable fields set up the reinforcer probabilities forach sequence. In Phases 2 and 3, VI values were selected with-ut replacement from a list of 20 based on the Fleshler andoffman (1962) progression. Sequences to be reinforced were

lso chosen probabilistically from a list without replacement. Inhase 3, the VI schedules were chosen to maintain an approxi-ately equal reinforcer rate across conditions.In Phase 3, a minimum IRT was required. To facilitate appro-

riately spaced responding in the 1- and 2-s spacing conditions,timeout contingency operated: IRTs shorter than the required

pacing incurred a 4-s timeout accompanied by a blackout, andach response during the last 2 s of timeout extended the timeouturation by 2 s from the time of the response. The VI timer con-inued to run during timeout, and the first response after timeoutlways started a new sequence.

A minimum of 20 sessions was required for each rat in eachondition. Quantitative stability criteria were based on three suc-essive blocks of three sessions: the most extreme differenceetween the three-block medians had to be less than or equal to0% of the nine-session average for the two response rates andhe four two-response sequence rates, respectively and simul-aneously. No noticeable trends were allowed over the 9 days,ncluding trends in changeover rate. In Phase 3, the same stabil-ty criteria applied to the left and right time-in response rates andhe four time-in sequence rates. However, for low-rate sequencesf three or fewer per min, differences of up to 20–25% wereccepted. The average number of sessions in each condition forach rat was about 30 for Phases 1 and 2, and for most of Phase. However, the first condition in Phase 3 (Condition 9), with its-s minimum IRT, required an average of about 80 sessions fortability.

Postfeeding took place shortly after the end of the last sessionach day. Sessions lasted 50 min (60 min in Phase 1), and wereun at about the same time each day, 5–7 days a week. Sessionsn Phases 2 and 3 began with a 30-s blackout period.

. Results

We performed a Lag-1 sequential analysis on this new andxisting concurrent sequence data set, using all occurrencesf the four two-response sequences across the last five ses-ions of each condition. That is, we compared the observedrequency of occurrence of one sequence followed by anotheran ordered sequence pairing) to the frequency expected byhance (Bakeman and Gottman, 1986; see Appendix A). The

atio of the difference between the observed and expected fre-uencies to the expected frequency is the sequential probabilityatio ((Obs − Exp)/Exp), and the sets of these positive or nega-ive values across the different ordered sequence pairings are the

190 S.M. Schneider, M. Davison / Behavioural Processes 73 (2006) 187–198

Fig. 1. Overall Lag-1 sequential probability ratios for each pigeon in the sample condition. The frequency expected by chance was based on the actual distributiono sequep aviso

sw

3

mIcrdfdaL

3

rtqRcnter

f sequences for each pigeon. Positive ratios indicate more occurrences of thatairing is at the top of each panel. (Data from Condition 15 of Schneider and D

equential probability patterns. With four sequence types, thereere 16 ordered sequence pairings.

.1. Schneider and Davison (2005) pigeon data

This study consisted of 16 conditions of concurrent reinforce-ent for demarcated two-response sequences with no minimum

RT; the conditions covered a range of sequence reinforcementontingency combinations. The base schedule was VI 30-s, andeinforcement was arranged dependently for each sequence asescribed in Section 2 (see Schneider and Davison, 2005, for

urther details). Six pigeons participated. The molar analysisescribed in that paper revealed sequence matching with a biasgainst sequences with changeovers (e.g., LL was preferred overR).

ec

1

nce pairing in that order than expected by chance. The leading sequence in then, 2005.)

.1.1. Overall sequential probabilityFig. 1 shows the overall sequential probability results for a

epresentative condition (15): the patterns of difference betweenhe observed and expected-from-chance sequence pairing fre-uencies as represented by the sequential probability ratios.atios near zero are at chance levels; thus, departures fromhance levels are evident. Ratios with high absolute values wereot uncommon, so we set a scale limit of ±1.0; values greaterhan 0.5 were usually significant. (Note based on the z-scorequation in Appendix A that the significance level for a givenatio value varied depending on the particular observed and

xpected values. A ratio value of 0.4 was significant in someases but not in others.)

Moreover, the positive or negative values for each of the6 sequence pairings were often identical across individuals.

S.M. Schneider, M. Davison / Behaviou

Table 2Schneider and Davison (2005) Overall sequential probability consistency

3 same 4 same 5 same 6 same χ2

Expected from chance: 5 7.5 3 0.5

Condition1 1 5 10 0 16.1a

2 1 5 3 7 16.1a

3 2 5 4 5 11.34 1 5 5 5 16.1a

5 4 2 4 6 18.3a

6 2 4 2 8 15.5a

7 3 1 5 7 27.1a

8 4 1 10 1 21.9a

9 0 5 2 9 21.9a

10 1 3 5 7 26.5a

11 0 2 7 7 40.5a

12 1 3 3 9 26.5a

13 4 6 2 4 2.314 1 8 3 4 6.715 3 2 4 7 20.9a

16 2 5 6 3 11.3

Number out of 16 sequential probability patterns per condition showing statedlevels of consistency across the six pigeons.“3 same”: three pigeons produced positive overall sequential probability ratios(greater than chance), and three, negative (less than chance). “4 same”: fourpigeons all produced either positive or negative values, and the other two, theopposite. “5 same”: five pigeons all produced either positive or negative values,and the sixth, the opposite. “6 same”: unanimous positive or negative values.

wχ

Tadpfafitbtbor5ftp

scetcirLoL

od−oz

rl

3fs(sR

3sar

3pt(ppic

3

fipteeclr

epaFLpaspo

a Statistically significant. Note that the “5 same” and “6 same” categoriesere combined for the χ2 analysis. For d.f. = 2, with Bonferroni correction,2crit = 12.73, p < .05.

able 2 summarises the degree to which the six pigeons’ over-ll sequential probability ratios were consistently in the sameirection – positive or negative – for each of the 16 sequenceairings across all 16 conditions. From Fig. 1 for Condition 15,or example, the LL–LL sequence pairing produced five neg-tive ratios and only one (slightly) positive, putting it in theve-same/one-different category. The LL–LR pairing fell into

he three same/three different category. LL-RL and LL–RR wereoth in the unanimous six-same category, and so on. As shown inhe table, consistency was often significantly greater than chanceased on a χ2 analysis. For conditions that were replicationsr reversals of each other, these sequential probability patternseplicated or reversed. That is, for condition reversals (such as%/5%/45%/45% and 45%/45%/5%/5% LL/LR/RL/RR rein-orcement probability), R was substituted for L and L for R, sohat a negative LL–RR sequential pattern in one condition wasredictably a negative RR–LL pattern in its reversal condition.

The magnitude of the differences from chance levels wasubstantial. As discussed above, we calculated the z-scoresorresponding to the observed and expected frequencies ofach sequence pairing. Across conditions, 70% (1069/1536) ofhe pigeons’ z-scores were significant (study-wide Bonferroni-orrected significance level z-score of 4.26, p < .05). As anllustration of the actual sequence-pairing frequencies, for a rep-

esentative pigeon in one condition, the expected number ofL–RL sequence pairings was 585, while the actual numberbserved was 4, a floor effect frequently found in this study. ForR–RL, the expected frequency was 379 and the observed 916,

aRrb

ral Processes 73 (2006) 187–198 191

ut of a possible maximum of 1303 (the number of RLs in thisatabase)—a ceiling effect. The corresponding z-scores were24.6 and 28.0, respectively, larger than the average magnitude

f 10.9 but not atypical, and well below the highest-magnitude-score of 54.8.

Perusal of these overall sequential probability patternsevealed several higher-order regularities. In all cases, chanceevels are 50%.

.1.1.1. Sequence non-repetition. In conditions in which allour sequences were reinforced with nonzero probability, aequence was less likely than chance to be immediately repeated206 of 240 cases: 86%). The exceptions were almost exclu-ively repetitions that did not include changeovers (LL–LL orR–RR).

.1.1.2. Last-response repetition. For the remaining orderedequence pairings (i.e., those involving two different sequences),new sequence was likelier than chance to begin with the last

esponse of the previous one (839 of 1152 cases: 73%).

.1.1.3. Proportion effect. When the scheduled reinforcer pro-ortions for two sequences added to greater than 90% (or lesshan 10%), they were more (or less) likely to follow each otheronly one set each of the most extreme per condition). For exam-le, in one condition, LL and LR both had scheduled reinforcerroportions of 45%, so the LL–LR and LR–LL sequence pair-ngs would be expected to occur more often than expected byhance (183 of 240 cases: 76%).

.1.2. Post-reinforcer sequential probabilityAs described above, a sequential analysis was also performed

or the reinforced sequences only and those sequences thatmmediately followed them. We found very different sequentialrobability patterns from this post-reinforcer analysis: as men-ioned above, reinforcer delivery markedly altered the sequencemission order. The most frequently reinforced and frequentlymitted sequence tended to be the only sequence more likely thanhance to be emitted immediately after reinforcement, regard-ess of which sequence had been reinforced (the “combinedule”).

Because the post-reinforcer pattern was thus a function ofach individual’s obtained sequence distributions, not all theigeons produced the same pattern (in contrast to the over-ll sequential probability results). In the condition graphed inigs. 1 and 2, the scheduled reinforcement probabilities forL/LR/RL/RR were 5%/5%/45%/45%. In this condition, fiveigeons evinced the anti-changeover bias noted in the molarnalysis of Schneider and Davison, and produced more RRequences than any other. Fig. 2 shows that their post-reinforceratterns were identical: after a reinforcer delivery, they emittednly RR at greater-than-chance levels. One pigeon (113) with

very low molar anti-changeover bias parameter emitted moreLs than RRs; it accordingly favored RL instead of RR after

einforcer deliveries, still following the combined rule. As cane seen from the figure, the combined rule was thus followed by

192 S.M. Schneider, M. Davison / Behavioural Processes 73 (2006) 187–198

F e samd Posite from

as

ffopwaodtfat

tr(mTidtsda

ig. 2. Post-reinforcer Lag-1 sequential probability ratios for each pigeon in thistribution of following sequences was the overall distribution in the database.xpected by chance. The reinforced sequence is at the top of each panel. (Data

ll six pigeons in all 96 cases except two (for the LL–LR leadingequence-following sequence pairing).

Just as for the overall sequential probability, the differencesrom chance were often large. For this condition, for example,or the five birds that favored it, RR constituted 50% on averagef all sequences emitted. The expected chance post-reinforcerroportion of RR sequences compared to all sequences emittedould thus also be expected to be 50%. However, the actual

verage RR post-reinforcer proportion was 92%, a differencef 42% (for the individual birds, χ2 = 67.8–192.1, N = 292–386,.f. = 1, p < .01 with Bonferroni correction; all post-reinforcer χ2

ests for both species were performed with the appropriate Bon-erroni correction, and all had 1 d.f.). The corresponding aver-ge differences in overall and post-reinforcer proportion in thewo conditions with reinforcement contingencies that reversed

fe

r

ple condition. Only reinforced sequences were the leading sequences. Chanceive ratios indicate more occurrences of that sequence pairing in that order thanCondition 15 of Schneider and Davison, 2005.)

his one (i.e., 45%/45%/5%/5%) was similar at 40% and 36%,espectively (individual χ2 = 38.1–166.4, N = 272–393, p < .01).These results are for the 11 of 12 cases that followed a one-odal-sequence post-reinforcer rule like the combined rule.)his molecular post-reinforcer order applied right from the start:

n the first condition, for the five pigeons that followed stan-ard one-modal-sequence rules, the average difference betweenhe overall and the post-reinforcer proportions for the favoredequence was 36% (individual χ2 = 27.7–346.1, N = 201–345,.f. = 1, p < .01). These results were typical across conditions,nd limited mainly by ceiling effects. Appendix A provides

urther information about the magnitude of the post-reinforcerffects.

The data most often followed the combined rule, but closelyelated alternate rules sometimes applied instead (Fig. 3; e.g.,

S.M. Schneider, M. Davison / Behavioural Processes 73 (2006) 187–198 193

Fig. 3. Post-reinforcer rule categorisation for the pigeons across all conditions.Srt

tsslp

3

3

rtctf

Plt

TE“

P

111111

NNss

Table 4Overall sequential probability consistency

2 same 3 same 4 same χ2

Expected from chance: 6 8 2

Conditiona

Phase 1, Condition 3 1 6 9 6.7Condition 4 1 5 10 6.7Phase 2, Condition 5 0 1 15 9.6b

Condition 6 0 0 16 9.6b

Condition 7 0 4 12 9.6b

Condition 8 0 1 15 9.6b

Phase 3, Condition 9 (2-s delay) 0 9 7 9.6b

Condition 10 (1-s delay) 0 5 11 9.6b

Condition 12 (2-s delay) 6 6 4 0

Number out of 16 sequential probability patterns per Condition showing statedlevels of consistency across the four rats.“2 same”: two rats produced positive values and two, negative. “3 same”: threerats all produced either positive or negative values, and the fourth, the opposite.“4 same”: unanimous positive or negative values.

a Phase 3, Condition 11 (0-s delay) is excluded because only three rats partic-i

a

arsr1ano

atc(fPd

ee text for description of the combined rule and the closely related alternateules. The mixed category includes cases that did not follow these rules consis-ently enough to be categorised as either.

he most-frequently emitted but not most-frequently reinforcedequence was the only greater-than-chance post-reinforcerequence in some cases). To show how closely the data fol-owed these rules, Table 3 lists the number of exceptions to theatterns predicted by the best-fitting rule.

.2. New rat data

.2.1. Overall sequential probabilityFig. 4 presents overall sequential probability results for a

epresentative condition, showing consistency similar to that forhe pigeons. Table 4 verifies the consistency similarities acrossonditions. The χ2 results would have been even stronger hadhe three-same and four-same columns not had to be combinedor the analysis.

In Phase 1 (only two sequential probability conditions) andhase 2, the overall sequential probability patterns, once estab-

ished, did not change much across conditions. The patterns ofhe temporal spacing conditions (Phase 3) varied more. Over-

able 3xperiment 1 Post-reinforcer sequential probability consistency in adherence torules”

igeon 0 or 1 2 3 or more

11 9 4 312 14 2 013 13 2 114 15 1 015 16 0 016 12 1 3

umber of conditions with 0–1, 2, or 3+ exceptions to best-fitting pattern.ote: Eight possible exceptions maximum for the 10 conditions in which all four

equences were reinforced; four exceptions maximum for the six two-reinforced-equence conditions.

iAc

rrs31a

3

mttft

pated: due to time constraints, Rat 3D was not exposed to this condition.b Statistically significant. Note that 3 and 4 same were combined for the χ2

nalysis. For d.f. = 1, with Bonferroni correction, χ2crit = 8.71, p < .05.

ll sequential probability patterns nonetheless replicated andeversed across conditions within each phase, except for the 0-spacing Phase 3 condition (Condition 11). Only within-phaseeplications were successful. For rats 3A and 3D, the Condition0 sequential probability patterns reversed those of Condition 9s expected even though their molar sequence distributions didot reverse, showing that the former does not necessarily dependn the latter.

The significance of the individual departures from chance wasgain ascertained using z-scores. In Phase 2, 86% (220/256) ofhe ratios met significance (p < .05, Bonferroni-corrected criti-al z-score = 3.79). The average z-score in this phase was 11.3with a high of 33.7), very similar to that for the pigeons. Asor Fig. 1, ratio values greater than 0.5 were usually significant.hases 1 (see Section 2) and 3 (2-s minimum IRT) had smalleratabases. For Phase 3’s Conditions 10 and 11 (1- and 0-s min-mum IRT), however, 60% of the z-scores reached significance.s was the case for the pigeons, ceiling and floor effects were

ommon.Sequence non-repetition applied to the rat data with a success

ate similar to that for the pigeons (95 of 108 cases: 88%). Last-esponse repetition was found not to apply to the two availableessions of Phase 1, and was not expected to pertain in Phase, with its temporal spacing. In Phase 2, it described 169 of the92 cases (88%). The “proportion effect” defined above did notpply.

.2.2. Post-reinforcer sequential probabilityThe combined post-reinforcer rule was again found to be the

ost common organising principle that described the data, and

he magnitude of the differences from chance was the same ashat for the pigeons. In Phase 2, Condition 6 (50%/50% LL/RR),or example, LL was emitted with a 47% average proportion forhe three rats that followed the combined rule, making it the most

194 S.M. Schneider, M. Davison / Behavioural Processes 73 (2006) 187–198

Fig. 4. Overall Lag-1 sequential probability ratios for each rat in Phase 2, Condition 8. The frequency expected by chance was based on the actual distribution ofs e paii

flftχ

ta9cN

Ecicfs4

15d

ftwptoectr

equences for each rat. Positive ratios indicate more occurrences of that sequencs at the top of each panel.

requently reinforced and emitted sequence. (The fourth rat fol-owed a different rule.) The post-reinforcer proportion averageor LL was 89%, however. This difference of 42% replicatedhe corresponding pigeon results for that condition (individual2 = 68.2–96.1, N = 188–204, p < 0.01). For Phase 2, Condi-

ions 5 and 8 (90%/10% LL/RR), LL predominated with a 72%verage across the eight cases. Its post-reinforcer average was7%, replicating the comparable pigeon ceiling effect for thatondition (average difference 25%, individual χ2 = 11.3–76.8,= 146–230, p < .01).Indeed, all such results were similar to those for the pigeons.

ven with its reduced database, for the six (of eight possible)ases in Phase 1 where the number of reinforced sequencesn the recorded portion of the session was at least 15, four

ases followed the standard combined rule, and one, an alternateorm. For these five, the average difference between the favoredequence percentage and its expected-from-chance level was4% (individual χ2 = 13.4–22.9, N = 14–47, p < .01). All Phase

cp

c

ring in that order than expected by chance. The leading sequence in the pairing

sequence reinforcement sets were of the 45%/45%/5%/5% or%/5%/45%/45% LL/LR/RL/RR category, so the pigeon resultsescribed above provide direct comparisons.

Finally, the temporal spacing in Phase 3 resulted in lower-requency sequence pairings. Of the 11 (of 15 possible) cases inhis phase that demonstrated post-reinforcer regularities, thereere more variations on the combined rule than in the otherhases (e.g., three cases followed the combined rule, but withwo sequences predominating after reinforcement rather thanne—also seen occasionally in the pigeon data). Nonetheless,ight cases offered one modal sequence – most following theombined rule – with an average difference of 25% betweenhe expected and observed proportions of the preferred post-einforcer sequence (and again, most were statistically signifi-

ant). Thus, the post-reinforcer effect occurred despite the tem-oral spacing.

Consistent with Schneider and Morris’s (1992) results, molarhoice proportions in the three phases changed in the predicted

aviou

fmm

3

tsTca(Bint(

MsTtrtdpip

4

bcratasirsba

srSmsrp

qsa

frfaaaiqoh

4

wbceecaWpetiiirmosTigtoatftrtw2

ondifc1

S.M. Schneider, M. Davison / Beh

ashion as a function of changes in the sequence reinforce-ent contingencies: results were intermediate between sequenceatching and response-level matching.

.3. Rat data from Schneider and Morris (1992)

The Schneider and Morris (1992) data were newly subjectedo the overall and post-reinforcer sequential probability analy-es performed here in order to test the generality of our results.he overall sequential probability results were comparable inonsistency and magnitude, and the higher-level regularitiesgain applied: of the 32 testable cases in their two experimentsone condition each), 94% followed sequence non-repetition.ecause the Schneider and Morris experiments used 4–7-s spac-

ng, last-response repetition was not expected to apply, and didot. The proportion effect that had previously applied strictlyo the pigeons, however, was followed in all 16 possible caseschance level of 50%).

Finally, the post-reinforcer effect described Schneider andorris’s data as well as it did our own. Two sessions of stable

equence emission order data were available, with four rats each.wo sequence distributions were equal across the four sequence

ypes, and thus no test of the pattern was possible. Five of theemaining six cases followed the standard combined rule. Forheir Experiment 2, Condition 3 (5%/5%/45%/45%), the averageifference between the expected and observed favored-sequenceercentages was 40%, very similar to the results above. Exper-ment 1’s less extreme 32.5%/32.5%/17.5%/17.5% distributionroduced, as expected, a lower average difference of 28%.

. Discussion

Sequential analysis enables the comparison of observedehaviour emission order patterns with those expected byhance. The use of concurrently reinforced demarcated two-esponse sequences makes 16 ordered sequence pairings avail-ble for analysis in this manner, enabling a microscopic inves-igation of molecular patterning. We performed a sequentialnalysis on new data and on data from two previously publishedtudies that used this procedure; sequence reinforcer probabil-ty, minimum IRT, and overall reinforcer rate were varied, andesults from two species were compared. The sequential analy-es revealed that sequences were not emitted in random order,ut in orderly patterns that were similar across individuals andcross species.

Most individual overall sequential probability ratios departedignificantly from chance. The patterns of positive or negativeatios were similar across individuals with the same histories.everal higher-order regularities occurred in the patterns, theost widely applicable of which was sequence non-repetition:

equences were less likely than chance to be immediatelyepeated. The requirement of a minimum IRT affected theseatterns and higher-order regularities.

The post-reinforcer-only sequential probability patterns wereuite different from the overall patterns: regardless of whichequence had been reinforced, the only sequence likely to occurfter reinforcement was the most frequent and most often rein-

(rrd

ral Processes 73 (2006) 187–198 195

orced in the data set. This “rule” (or one of several closelyelated “rules”) was consistent across species, sequence rein-orcement conditions, histories, and temporal spacing. Thisppears to be a new finding. Such findings may offer usefulpplications to human behaviour under comparable conditions;fter all, much human behaviour can be considered sequentialn nature, and occurring under concurrent schedules of conse-uences. Neuringer (e.g., 1994) has found that related effectsf sequence variability and repetition appear to be similar forumans and nonhumans.

.1. Sources of local order

Across species and conditions in which all four sequencesere reinforced, sequences were less likely than chance toe repeated—even when one sequence predominated. With nohangeover delay in the no-minimum-IRT conditions, how-ver, the sequences themselves may have occasionally becomentrained in adventitiously reinforced chains, thus potentiallyausing the well-known increase in changeovers (e.g., Shahannd Lattal, 1998; Shull and Pliskoff, 1967; Temple et al., 1995;illiams and Bell, 1999). Could the non-repetition effect sim-

ly reflect this adventitious increase? This seems unlikely. Forxample, the presence of four different sequence units decreasedhe automatic high reinforcement rate for occasionally chang-ng over to a lower-reinforcement-probability behaviour, seenn standard two-response studies (Dreyfus et al., 1982). Thats, with just left and right responses reinforced in a concur-ent VI VI procedure, lengthy responding on one alternativeeans that the first changeover will likely be reinforced. With

ur four-sequence procedure, changeovers only to the reinforcedequence would be reinforced; other changeovers would not be.he existence of the non-repetition effect in the studies requir-

ng minimum IRTs is suggestive corroboration that more isoing on here. So is the existence of the effect across most ofhe varied sequence reinforcer probability conditions: the effectccurred for sequences with both high and low reinforcer prob-bilities. Finally, the effect occurred as often for the rats withheir leaner VI schedule of VI 60s, compared to the VI 30s usedor the pigeons. Other aspects of our procedure, most likelyhe dependent scheduling, appear to have caused sequence non-epetition—an interesting effect at a more molar level. In effect,he animals learned that excessive perseveration on one sequenceas not an efficient strategy under this paradigm (cf. Neuringer,004).

Sequence non-repetition and the post-reinforcer effect wereur most robust pattern regularities, but, as would be expected,either effect is universal: different contingencies naturally pro-uce different molecular as well as molar order. In a studyn which pigeons’ four-keypeck sequence variability was rein-orced, the percentage of post-reinforcer sequences that met theontingency was lower than for other sequences (Neuringer,992); repetition of recently emitted sequences occurred instead

also see Neuringer et al., 2001). This difference from our post-einforcer effect might be explained, however, by the differentequirement for maximising reinforcement probability: to pro-uce a sequence differing from the last three emitted (also see

1 aviou

Nr(Wlerbehe

sSlitearBt

itc1owctttpdmoopISrwm

dash

4

ib(w

ssmifswsctD

4

SmpahfsssrsitisnI1mra

rtmirTstmebu

ifs

96 S.M. Schneider, M. Davison / Beh

euringer, 1991). More closely related to our study is the two-esponse concurrent-schedule work of Davison and colleaguese.g., Davison and Baum, 2000; Landon and Davison, 2001).

ith just two behaviours in this paradigm, the just-reinforcedeft or right response was most likely to be immediately repeated,ven if it had the lower reinforcement probability of the twoesponses. However, when the reinforcement probability distri-ution was highly skewed, something like our post-reinforcerffect occurred, as the higher-reinforcement-probability andigher-rate response predominated after all reinforcement deliv-ries.

Past research with concurrent schedules has revealedtrong effects of changeover delays on local responding (e.g.,ilberberg et al., 1978; also see Navarick, 1979), and molecu-

ar order has thus occasionally been considered an uninterest-ng product of procedural structure. The results analysed hereranscend procedural structure for the most part, however: forxample, sequence non-repetition and the post-reinforcer effectpplied regardless of the presence or lack of a minimum IRTequirement (note that we used no changeover delays as such).ut what about the possibility that molecular order is an unin-

eresting product of history?Carryover effects were strong for the overall sequential order:

ndividuals with a common history produced similar sequen-ial probability patterns and, once established, they sometimeshanged only in small ways (see also Machado, 1994; Williams,991). Accordingly, only within-experiment or within-phaseverall sequential probability patterns replicated and reversedith the sequence reinforcement contingencies, which may indi-

ate that they depend on history. The mechanisms producinghese patterns were robust enough, however, to produce consis-ency across individuals. And the consistent sequential regulari-ies across experiments and species (e.g., the non-repetition andost-reinforcer effects) further testify to the existence of pre-ictable and ahistorical effects of controlling variables at thisolecular level. Perhaps the initial conditions determine which

f several sets of likely molecular regularities will occur. Allf our rats were experimentally naive, and each of the three rathases began with a different condition and used different rats.n support, the only overall sequential probability patterns inchneider and Morris (1992) that replicated our patterns for cor-esponding reinforcement conditions were from rats that startedith the same reinforcement probability set and shared a nonzeroinimum IRT.We suggest that molecular order thus transcended initial con-

itions to a large extent. Those carryover effects that did occurre of interest in themselves, and of potential application. Indeed,equential analysis offers a new and useful way to investigateistorical effects.

.2. Behavioural units

The molar analyses of these data showed sequence match-

ng (Schneider and Davison, 2005) or results intermediateetween individual-response matching and sequence matchingSchneider and Morris, 1992; the present data). However, evenhen reinforcement produced what might be considered full

(1N1

ral Processes 73 (2006) 187–198

equence units at the molar level, as in Schneider and Davi-on’s results, our molecular analysis showed that they were notonolithic ones in which all the subsidiary behaviours remained

dentical (cf. Hawkes and Shimp, 1975). For example, we per-ormed a latency analysis of Schneider and Davison’s data thathowed differing patterns. Still, most intrasequence latenciesere shorter than the corresponding intersequence latencies,

upporting the idea of sequences as units. The strength andonsistency of the post-reinforcer effect and the overall sequen-ial probability patterns are also suggestive (see Schneider andavison, 2005, for further discussion).

.3. The question of mechanism

Order was present at many temporal levels in these data.everal of our molecular regularities may contribute to theatching found in the molar analyses (e.g., the proportion and

ost-reinforcer effects). However, they may not be enough toccount for matching—and they could theoretically themselvesave been a function of more direct molar control. Relatedly, weound that a short latency after a high-reinforcement-probabilityequence was more likely to lead to a switch to a differentequence, and a long latency to lead to sequence repetition (alsoee Cleaveland, 1999), contrasting with the equal repetition/non-epetition latencies expected by chance. This result is con-istent with a matching mechanism like momentary maximis-ng (Shimp, 1966). So is the post-reinforcer effect, in whichhe favored post-reinforcer sequence generally has the highestmmediate probability of reinforcement. This effect precluded atraight contiguity effect, in that sequences just reinforced wereot more likely than chance to be immediately repeated (cf.versen and Mogensen, 1988; Morgan, 1974; Neuringer, 1991,992). Highly molecular contiguity effects like the changeover-inimising last-response repetition effect did occur. The car-

yover in the overall sequential probability patterns offers yetnother level of temporal order.

The sequential dependencies that occurred even in sequencesequiring long temporal spacing sometimes reflected effects ofhe molar sequence contingencies without any corresponding

olar adjustments: recall that two Phase-3 rats showed changesn sequence emission order consistent with those for the otherats, but without showing the expected changes in molar order.hus, in some situations, the molecular measures may be moreensitive to molar contingencies than are molar measures. Buthis sensitivity could, of course, be mediated through molar or

olecular mechanisms. Even if an analysis showed that oneffect generally preceded the other as behaviour gradually sta-ilised over sessions, the temporal level of control would remainncertain. Our data do not allow any conclusions.

We can only agree with Stubbs et al. (1987), who noted, “Its more likely that there is multiple control produced by the dif-erent sets of dependencies and contingencies, with the differentources of control shifting somewhat from situation to situation”

pp. 220–221; also see Baron and Derenne, 2000; Cleaveland,999; Heyman and Tanz, 1995; Machado, 1994; Morgan, 1974;euringer, 1992; Silberberg and Williams, 1974; Stubbs et al.,986; Williams, 1991). This poses quite a challenge, but not an

aviou

ieA

teif

A

AatS

A

fp

scbopdsns

z

wsb

tTwr

Gsocdneb

(a

mosothprtera

votev

R

B

B

B

B

C

D

D

D

F

H

H

H

I

I

I

S.M. Schneider, M. Davison / Beh

nsoluble one. The more we look, the more order we find (see,.g., the 1992 special issue of the Journal of the Experimentalnalysis of Behavior on behaviour dynamics).

So, what is controlling what, and when? Different levels ofemporal control may compete or coexist. Only by continuing tolucidate molecular order as well as molar, and experimentallysolating its sources of control, will we be able to answer thisundamental question.

cknowledgements

Phase 1 was run at St. Olaf College, and Phases 2 and 3 atuburn University; we thank the Auburn undergraduate research

ssistants who helped run this research. Finally, we appreciatehe helpful comments provided by Douglas Elliffe and Davidchaal.

ppendix A. Sequential analysis

This analysis was performed separately for each individual,or each condition. The last five sessions in each condition sup-lied each data set.

For the overall sequential probability (with the reinforcedequences removed as leading sequences), the expected-from-hance frequencies of each sequence pairing were determinedy multiplying the frequency of each leading sequence by thatf itself, and then, in turn, of each of the other sequences. Eachroduct was divided by the total number of sequences in theatabase. To correct for those sequence emissions that endedessions and could not be followed by another sequence, theumber of sessions was subtracted from the total number ofequences, giving the corrected total.

The formula for the z-scores was

= Obs − Exp√Exp

(1 − Exp

Tot

) ,

here Obs and Exp are the observed and expected-from-chanceequence pairing frequencies and Tot is the corrected total num-er of sequences (see Bakeman and Gottman, 1997).

The determination of the post-reinforcer sequential probabili-ies included only the reinforced sequences as leading sequences.he expected sequence proportions of the following sequencesere based on the sequence proportions in the database. In other

espects, the equations were identical.In the most recent edition of their book, Bakeman and

ottman (1997) now generally recommend the log-linearequential analysis method over the method reported here. Theriginal method (Bakeman and Gottman, 1986), however, is stillonsidered valid and useful. In our view, the theoretically-basedata analysis winnowing provided by the log-linear approach isot yet appropriate for our application, given our lack of knowl-dge about sequential patterning. We have as yet insufficient

asis to devise a plausible, empirically supported theory.

For overall sequential probability, all omnibus testsBakeman and Gottman, 1997, p. 118) were significant forll conditions in all of our studies, not surprising given the

J

L

ral Processes 73 (2006) 187–198 197

agnitudes of the z-scores. Bakeman and Gottman’s new rec-mmendations for minimum data set sizes in order to justifytatistical significance testing are low enough that even most ofur post-reinforcer sequential probability data sets would exceedhem. Had we chosen to present those z-scores, many wouldave been significant. Even when the expected and observedost-reinforcer frequencies were low, the sequential probabilityatio in these cases still often appears to represent operation ofhe normal controlling variables, evident from comparison withxpected patterns and from consistency across individuals. Byetaining these data, tests of consistency, replication/reversal,nd rule-following were more conservative.

z-scores increase with an increase in the number of obser-ations, as can be seen in a comparison of the rat and pigeonverall sequential probability results. Their high magnitudes andhe frequent ceiling and floor effects, however, corroborate thextent by which they exceeded the Bonferonni-corrected criticalalues.

eferences

akeman, R., Gottman, J.M., 1986. Observing Interaction: An Introductionto Sequential Analysis. Cambridge University Press, Cambridge.

akeman, R., Gottman, J.M., 1997. Observing Interaction: An Introductionto Sequential Analysis, 2nd ed. Cambridge University Press, Cambridge.

aron, A., Derenne, A., 2000. Progressive-ratio schedules: effects of laterschedule requirements on earlier performances. J. Exp. Anal. Behav. 73,291–304.

aron, A., Perone, M., 2001. Explaining avoidance: two factors are still betterthan one. J. Exp. Anal. Behav. 75, 357–361.

leaveland, J.M., 1999. Interresponse-time sensitivity during discrete-trial andfree-operant concurrent variable-interval schedules. J. Exp. Anal. Behav.72, 317–339.

avison, M., Baum, W.M., 2000. Choice in a variable environment: everyreinforcer counts. J. Exp. Anal. Behav. 74, 1–24.

avison, M., Nevin, J.A., 1999. Stimuli, reinforcers, and behavior: an inte-gration. J. Exp. Anal. Behav. 71, 439–482.

reyfus, L.R., Dorman, L.G., Fetterman, J.G., Stubbs, D.A., 1982. An invari-ant relation between changing over and reinforcement. J. Exp. Anal.Behav. 38, 327–338.

leshler, M., Hoffman, H.S., 1962. A progression for generating variable-interval schedules. J. Exp. Anal. Behav. 5, 529–530.

awkes, L., Shimp, C.P., 1975. Reinforcement of behavioral patterns: shapinga scallop. J. Exp. Anal. Behav. 23, 3–16.

eyman, G.M., 1979. A Markov model description of changeover probabil-ities on concurrent variable-interval schedules. J. Exp. Anal. Behav. 31,41–51.

eyman, G.M., Tanz, L., 1995. How to teach a pigeon to maximize overallreinforcement rate. J. Exp. Anal. Behav. 64, 277–297.

versen, I.H., 1986. Time allocation, sequential, and kinematic analyses ofbehaviors controlled by an aperiodic reinforcement schedule. Psychol.Rec. 36, 239–255.

versen, I.H., 1991. Methods of analyzing behavior patterns. In: Iversen, I.H.,Lattal, K.A. (Eds.), Techniques in the Behavioral and Neural Sciences,vol. 6: Experimental Analysis of Behavior (Part 2). Elsevier, Amsterdam,pp. 193–241.

versen, I.H., Mogensen, J., 1988. A multipurpose vertical holeboard withautomated recording of spatial and temporal visit patterns for rodents. J.Neurosci. Meth. 25, 251–263.

ustice, L.M., Weber, S.E., Ezell, H.K., Bakeman, R., 2002. A sequentialanalysis of children’s responsiveness to parental print references duringshared book-reading interactions. Am. J. Speech Lang. Path. 11, 30–40.

andon, J., Davison, M., 2001. Reinforcer-ratio variation and its effects onrate of adaptation. J. Exp. Anal. Behav. 75, 207–234.

1 aviou

M

M

M

N

N

NN

N

R

S

S

S

S

S

S

S

S

S

T

W

98 S.M. Schneider, M. Davison / Beh

acDonall, J.S., 2000. Synthesizing concurrent interval performances. J. Exp.Anal. Behav. 74, 189–206.

achado, A., 1994. Polymorphic response patterns under frequency-dependent selection. Anim. Learn. Behav. 22, 53–71.

organ, M.J., 1974. Effects of random reinforcement sequences. J. Exp.Psychol. Anim. Behav. Process 22, 301–310.

avarick, D.J., 1979. Free-operant choice behavior: a molecular analysis. J.Exp. Anal. Behav. 32, 213–232.

euringer, A., 1991. Operant variability and repetition as functions of inter-response time. J. Exp. Psychol. Anim. Behav. Process 17, 3–12.

euringer, A., 1992. Choosing to vary and repeat. Psychol. Sci. 4, 246–250.euringer, A., 2004. Reinforced variability in animals and people: implica-

tions for adaptive action. Am. Psychol. 59, 891–906.euringer, A., Kornell, N., Olufs, M., 2001. Stability and variability in extinc-

tion. J. Exp. Psychol. Anim. Behav. Process 27, 79–94.ichardson, W.K., Clark, D.B., 1976. A comparison of the keypeck and

treadle-press operants in the pigeon: differential-reinforcement-of-low-rateschedule of reinforcement. J. Exp. Anal. Behav. 26, 237–256.

chneider, S.M., Davison, M., 2005. Demarcated response sequences and thegeneralised matching law. Behav. Proc. 70, 51–61.

chneider, S.M., Morris, E.K., 1992. Sequences of spaced responses: behav-

ioral units and the role of contiguity. J. Exp. Anal. Behav. 58, 537–555.

hahan, T.A., Lattal, K.A., 1998. On the functions of the changeover delay.J. Exp. Anal. Behav. 69, 141–160.

himp, C.P., 1966. Probabilistically reinforced choice behavior in pigeons. J.Exp. Anal. Behav. 9, 443–455.

W

W

ral Processes 73 (2006) 187–198

hull, R.L., Pliskoff, S.S., 1967. Changeover delay and concurrent schedules:some effects on relative performance measures. J. Exp. Anal. Behav. 10,517–527.

ilberberg, A., Hamilton, B., Ziriax, J.M., Casey, J., 1978. The structure ofchoice. J. Exp. Psychol. Anim. Behav. Process 4, 368–398.

ilberberg, A., Williams, D.R., 1974. Choice behavior on discrete trials: ademonstration of the occurrence of a response strategy. J. Exp. Anal.Behav. 21, 315–322.

tubbs, D.A., Dreyfus, L.R., Fetterman, J.G., Dorman, L.G., 1986. Choicewith a fixed requirement for food, and the generality of the matchingrelation. J. Exp. Anal. Behav. 45, 333–349.

tubbs, D.A., Fetterman, J.G., Dreyfus, L.R., 1987. Concurrent reinforcementof response sequences. In: Commons, M.L., Mazur, J.E., Nevin, J.A.,Rachlin, H. (Eds.), Quantitative Analyses of Behavior: vol. 5. The Effectsof Delay and of Intervening Events on Reinforcement Value. Erlbaum,Hillsdale, NJ, pp. 205–224.

emple, W., Scown, J.M., Foster, T.M., 1995. Changeover delay andconcurrent-schedule performance in domestic hens. J. Exp. Anal. Behav.63, 71–95.

alker, K.A., Fell, R.D., 2001. Courtship roles of male and female Europeanearwigs, Forficula auricularia L. (Dermaptera: Forficulidae), and sexual

use of forceps. J. Insect Behav. 14, 1–17.

illiams, B.A., 1991. Choice as a function of local versus molar reinforce-ment contingencies. J. Exp. Anal. Behav. 56, 455–473.

illiams, B.A., Bell, M.C., 1999. Preference after training with differentialchangeover delays. J. Exp. Anal. Behav. 71, 45–55.