Behavioural Processes 70 (2005) 51–61

Demarcated response sequences and generalised matching

Susan M. Schneidera,∗, Michael Davisonb

a Department of Psychology, Florida International University, Miami, FL 33199, USAb Department of Psychology, University of Auckland, Private Bag 92019, Auckland, New Zealand

Received 6 October 2004; received in revised form 31 March 2005; accepted 23 April 2005

Abstract

The generalised matching law was applied for the first time to sequences of responses. Pigeons responded on dependentlyarranged two-operandum concurrent schedules in which all four possible two-response sequences on these operanda weredemarcated and reinforced. Reinforcer rates for the sequences were varied over a wide range, including extinction. Sequencesof responses, rather than individual responses, followed the generalised matching law. We compared single-sensitivity andmultiple-sensitivity versions of the generalised matching law. The multiple sensitivities were not significantly different fromeach other, so the single-sensitivity model provided the more efficient fit. As in previous research, responding was biased againstthe emission of sequences that required changeovers.© 2005 Elsevier B.V. All rights reserved.

Keywords:Response sequences; Generalised matching law; Natapoff equation; Anti-changeover bias; Concurrent schedules; Pecking; Pigeons

1

eacsmpMtd

f

se-ntlyencee se-ftnc-encetiosons.theratiosalosed

chis-

0

. Introduction

Demarcated response sequences are ubiquitous inveryday life, and therefore, in choice: For example,n oft-repeated series of behaviours under stimulusontrol allows a wild bird to drink at its favouriteource. The generalised matching law is arguably ourost successful quantitative model for choice, ap-lying across a host of variables (e.g.,Davison andcCarthy, 1988; Mazur, 1991). As of yet, however,

he generalised matching law has not been applied toemarcated sequences.

∗ Corresponding author. Tel.: +1 3053481230;ax: +1 3053483879.

E-mail address:schneids@fiu.edu (S.M. Schneider).

In one paradigm, free-operant two-responsequences on left and right operanda are intermittereinforced, with the second member of each sequsignalled in some way. Four possible two-responsquences result: left–left (LL), left–right (LR), right–le(RL), and right–right (RR). If these sequences futioned as behavioural units, the ratios of the sequdistributions would be expected to match the raof the corresponding sequence reinforcer distributiOn the other hand, if reinforcers acted only onlast response in each sequence, then responsewould follow reinforcer ratios for those individuresponses—standard “response matching” as oppto “sequence matching”.

Stubbs et al. (1987)used pigeons trained on sua procedure, with a 1-s blackout following the em

376-6357/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.beproc.2005.04.005

52 S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61

sion of unreinforced sequences. They investigated bothtwo- and three-response sequences, varying the relativefrequency of reinforcers for sequences starting or end-ing in left-key responses and, in the three-response se-quences, also when the second response was a left-keyresponse. They did not independently vary the rein-forcer rates for each of the sequences. They plotted therelative frequencies of sequences with left responses asthe first, second, and last response as a function of theobtained relative frequency of reinforcement for suchsequences, and showed that the emissions of each ofthese sequences roughly followed strict matching. Intheir second experiment, they independently varied thereinforcer rates in two conditions for each of the fourresponse combinations in two-response sequences, butalways kept the left–left (LL) sequence under extinc-tion. They showed that right–right (RR) sequences oc-curred more often, and RL sequences less often, thanpredicted by matching, with LR sequences showingstrict matching (see their Fig. 10.6).

These were groundbreaking experiments, but theysuffered from two drawbacks. First, the range of rein-forcer contingencies was limited: In all but two condi-tions, all members of one particular set of sequences(e.g., LL and RL) were reinforced at the same rate,and the reinforcer rate for that set of sequences versusone other set was varied. Second, only strict match-ing was assessed. Without more quantified information,our understanding of sequence matching remains lim-ited. For example, when interresponse times are short,w pre-f theya .g.,N al.,2 irs overb notq

lyu omesl re-m dD ntera r-a tingi st tod

The generalised matching law for two (i, j) alterna-tives (Baum, 1974) is written(

Bi

Bj

)= bij

(Ri

Rj

)a

,

or, in logarithmic form,

logBi

Bj

= a logRi

Rj

+ logbij, (1)

whereB refers to responses emitted, andR to rein-forcers obtained, on the two alternatives. The parameterb, inherent bias, measures a constant proportional pref-erence for one alternative over the other. If, for example,Behaviouri requires more force than Behaviourj, thenwhen reinforcer ratios are varied,bij will be less than1.0. The parametera is sensitivity to reinforcement,which measures the change in response ratios as a pro-portion of changes in reinforcer ratios. The usual valueof sensitivity for concurrent variable-interval (VI) VIschedules is between 0.8 and 1.0 (Baum, 1979).

The generalised matching law has been applied tochoice between more than two reinforced responses byinvestigating all pairwise ratios. Such an analysis oftenassumes (and finds) that preference between any twoalternatives is independent of the reinforcer frequencyfor other alternatives (the Constant Ratio Rule,Luce,1959; seeDavison and Hunter, 1976for empirical sup-port). Even assuming adherence to this rule, differentsensitivities may be required for each pair of behaviours(see, e.g.,Davison and McCarthy, 1994). We will refert liedtm

cd ands onsec idedi in-c rce-m orityod testt

e expect sequences without changeovers to beerred over sequences with changeovers becausere less effortful, less time-consuming, or both (eeuringer, 1992; Neuringer et al., 2001; Reid et001; Stubbs et al., 1987). Stubbs et al. with thehort IRTs found evidence for such an anti-changeias using this sequence paradigm, but it wasuantified.

Indeed, thestrict matching relation is inherentnable to quantify a constant preference for sequences over others. Thegeneralisedmatchingaw (Baum, 1974), however, allows such a measu

ent through its bias parameter (e.g.,Beautrais anavison, 1977; Davison and Ferguson, 1978; Hund Davison, 1982). The wide applicability of genelised matching offers an additional reason for tes

t on sequence data. The current paper is the firo so.

o this version of the generalised matching law appo more than two alternatives as themultiple-sensitivityodel.An alternative approach to the analysis ofn> 2

hoice was suggested byNatapoff (1970). Natapoff’serivation was mathematical rather than empirical,imple assumptions of symmetry in response, resphangeover effort, and consequence value provts theoretical basis. His strict-matching approachluded neither biases nor sensitivities to reinfoent, although both are necessary to fit the majf concurrent-schedule data (Baum, 1974, 1979). Theata collected in the present experiment allow us to

he following extension of Natapoff’s model.Natapoff’s equation forn alternatives was:

Bi

n√

BiBjBk . . . Bn

= Ri

n√

RiRjRk . . . Rn

.

S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61 53

We suggest that Natapoff’s equation can be generalisedby adding sensitivity and bias terms in the followingway:

Bi

(BiBjBk . . . Bn)1/n

= bi

(bibjbk . . . bn)1/n

Rai

(RiRjRk . . . Rn)a/n, (2)

where the bias parameters,bi , are measures of the un-known reinforcer or response parameters that, whenheld constant throughout an experiment, affect prefer-ences for any alternative. Thebi values have no absolutemeaning: It is the values ofbi /bj , etc., that constitutethe biases between alternatives. Eq.(2) is the gener-alised matching law forn> 2 alternative choice, as canbe shown by considering two-alternative choice. Thisis accomplished by looking at theith values in the nu-merators and theith andjth values in the denominators,squaring, and cancelling terms. From such algebraicmanipulation of Eq.(2), or from a direct applicationof Eq. (2) to two alternatives, we obtain the standardform of generalised matching Eq.(1), to which Eq.(2)reduces.

Thus, while Eq.(2) ostensibly states that preferencebetween one alternative and the aggregate of allother alternatives is a function ofall reinforcer ratesobtained, it reduces to Eq.(1), implying that preferencebetween pairs of alternatives is independent of all otherreinforcer rates—the Constant Ratio Rule, as indeedw ch,p hats yp mt ach.W ym

ityg ntifyb sensit .g.,L cerr ces,w hatt ues-t oicew ofs

2. Materials and methods

2.1. Subjects

Six individually housed homing pigeons, num-bered 111–116, were maintained at approximately85%± 15 g of their free-feeding body weights. Waterand grit were available 24 h a day. All subjects except114 had participated in several foraging experimentsusing concurrent schedules.

2.2. Apparatus

One wall of the pigeons’ home cages was fitted witha response panel. The cages were 380 mm× 380 mm× 380 mm, and contained a wooden perch, set 70 mmabove the grid floor and 110 mm from the responsepanel. The three keys were 20 mm in diameter, can-tered 100 mm apart, and 205 mm above the level of theperch. Only the left and centre keys, which could beilluminated by red or green lights, were used; the cen-tre key will accordingly be referred to as the right key.The physical right key remained dark with no sched-uled consequences for pecking throughout. Pecks ex-ceeding about 0.1N operated the keys. The top of the50 mm× 50 mm food hopper aperture was 100 mm be-neath the middle of the centre key.

The apparatus was controlled and data recordedby an IBMR-compatible computer running Med-PCR

hardware and software, remote from the home cages.T .

2

2ed-

u ly ona cedo eys.T t ofe geonsp us-i thep ,w ardt

di-t eys

as assumed by Natapoff. Following this approareference inn> 2 alternative choice assumes tensitivity to reinforcement (a) is the same for everairwise alternative—the major difference fro

he standard generalised matching law approe refer to this version as thesingle-sensitivitodel.Application of these single- and multiple-sensitiv

eneralised matching models enabled us to quaias between sequences and ascertain whether

ivity is the same for different pairs of sequences (eL/RR, LL/RL). We arranged independent reinforates for each of the four two-response sequenith sufficiently varied experimental conditions so t

hese two models could be compared. The basic qion is thus: Can we account for performance in chith more than two alternatives with a single valueensitivity to reinforcement?

-

he time of occurrence of all events was recorded

.3. Procedure

.3.1. Preliminary trainingThe pigeons’ previous training on foraging sch

les had encouraged them to respond repeatedsingle key. Thus, initial sequence training reinfornly two-peck LR or RL sequences on the lighted khese were followed by reinforcement or a blackouqual duration as sequence demarcators. Some piecked during blackouts, however, so we stopped

ng blackouts: The last 16 training sessions usedrocedure described under Section2.3.2. Pigeon 114hich had a different history, joined the study tow

he beginning of Condition 1.Throughout all training and experimental con

ions, sessions began with the left and right k

54 S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61

Table 1Scheduled sequence relative reinforcer probabilities and number ofsessions

Condition LL LR RL RR Sessions

1 0.25 0.25 0.25 0.25 38a

2 0.25 0.45 0.05 0.25 253 0.10 0 0 0.90 274 0.45 0.25 0.25 0.05 265 0 0.90 0.10 0 306 0.25 0.05 0.45 0.25 247 0.45 0.45 0.05 0.05 268 0.90 0 0 0.10 269 0 0.50 0.50 0 32

10 0.45 0.45 0.05 0.05 3111 0 0.10 0.90 0 2312 0.45 0.05 0.45 0.05 3413 0.05 0.25 0.25 0.45 3514 0.50 0 0 0.50 3715 0.05 0.05 0.45 0.45 4416 0.25 0.45 0.05 0.25 44

a Twenty-one for Pigeon 114, which started the experiment late.

illuminated green, and ended in blackout after either45 min had elapsed or 90 reinforcers had been deliv-ered, whichever came first. Reinforcers were 2.5-s ac-cess to wheat, and during this period the key lights wereextinguished and the hopper illuminated. Pigeons wereexposed in numerical order to the experimental con-tingencies over the course of each morning, and post-feeding if necessary took place within an hour after thelast pigeon’s session. Sessions were conducted withinan hour of the same time each day, 7 days per week.

2.3.2. Experimental conditionsTwo-response sequences were emitted in free-

operant fashion, and demarcated as follows: The firstpeck on either key changed the colour for both fromgreen to red, and the second changed it back to green.The overall probability of reinforcement per secondwas set at 0.033 (VI 30 s), and when reinforcers werearranged, they were allocated to the various sequencesas shown inTable 1by partitioning the computer’s ran-dom number output.

Stability criteria were applied to each of the four se-quences: Beginning with the 10th session, monotonictrends in the sessional totals of each sequence were as-sessed over blocks of three consecutive sessions. Whensuch trends were absent on five not necessarily con-secutive overlapping three-session blocks for all foursequences, the criteria were met (i.e., sequence totals

could not be steadily increasing or decreasing). Thesecriteria were supplemented by visual inspection fortrends that defeated the purpose of the criteria throughtheir non-monotonic nature. The minimum number ofsessions in each condition was thus 16; the actual num-bers were higher, as shown inTable 1. All pigeons werekept running in each condition until all had met thesecriteria.

3. Results

The Appendix A shows the absolute numbersof sequences emitted and reinforcers obtained foreach pigeon over the last five sessions of each ofthe 16 experimental conditions.Fig. 1 is a standardgeneralised-matching analysis based on the individualresponses emitted. Strict matching is indicated by thedotted 45◦ line.

Conditions in Experiment 1 fell into two categories:those where the sequence matching and individual-response matching predictions were the same, andthose where they were different. The figure showsthat response matching occurred only in those caseswhere the response-matching outcome was the sameas the sequence-matching outcome (filled circles; e.g.,the 90%/10% LL/RR condition 8 and conditions 1,3, 4, 9, 13, and 14). When the sequence matchingand response matching predictions were not the same,response matching did not occur. For the conditionss ot re-s onser rvedl . Ane Se-q d Rr manym con-d 15),r ointsa weres rapht erec onsem

ingm asedm

hown as open circles, sequence matching but nponse matching predicted a 50%/50% L/R respatio (conditions 2, 5, 6, 11, and 16)—and the obseog response ratios were correspondingly close to 0xample would be the 90%/10% LR/RL condition:uence matching predicts equal numbers of L anesponses, whereas response matching predictsore R than L responses. For the remaining fouritions (open triangles, conditions 7, 10, 12, andesponse matching also did not occur, and the pre near where they would be expected to beequence-matching occurring (see below). The ghus shows that the L/R response distributions wonsistent with sequence matching, not with respatching.We used the two different generalised match

odels to evaluate the degree of sequence-batching.

S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61 55

Fig. 1. Response matching results for all pigeons. The log L/R re-sponse ratios are plotted as a function of obtained log L/R reinforcerratios. Conditions shown by filled circles offer the same predictionfor both sequence and response matching. Unfilled circles offer dif-ferent predictions, with the sequence-matching prediction being alog ratio of 0. Unfilled triangles are for other contradictory predic-tions. The straight lines were fitted by the method of least squares.The dotted line indicates strict matching.

3.1. Multiple-sensitivity model

Eq. (1) (to which Eq.(2) reduces) was fitted usingthe standard generalised matching law technique of lin-ear regression. The four sequences were combined inthe six possible sequence ratios, and one regressionfor each of these six ratios was fitted. Only one se-quence ratio was fitted for those conditions where onlytwo sequences were reinforced. A minimum of threebias parameters needed to be fitted, with the other threecalculated from them: The bias parameterbLL/RL , forexample, is the product of the bias parametersbLL/LRandbLR/RL. (Note that this is mathematically true, but

because of empirical error variance the fitted and cal-culated values could and sometimes did differ.) Thismodel thus requires nine free parameters: six sensitiv-ity parameters—one for each sequence pairing—andthree bias parameters.

Within each bird, the fitted sensitivity parametervalues were similar across most sequence pairings. AFriedman non-parametric analysis of variance on thesix sensitivity values accordingly produced no signifi-cant differences across pairings (χ2(3, 5) = 3.4,p> .05);further, no systematic deviations were noted. Thus,only the average sensitivity value for each bird is shownin Table 2(with the standard error), along with the biasvalues and the assessments of the fits.

All six pigeons’ performances showed some biasesfavouring sequences with no changeovers. Ab valueof one indicates the presence of no bias. Bias valuesfor sequences without versus with changeovers (e.g.,bLL/RL ) were greater than 1 in 23 of 24 cases (p< .05on a binomial test). (To see this fromTable 2, inversionof thebRL/RR andbLR/RR bias values is necessary.)

3.2. Single-sensitivity model

For this model, linear regression could not beused. The equations were fitted simultaneously to thedata from all 16 conditions using Corel QuattroPro’soptimisation procedure to find the best-fitting param-eter values: The squares of the differences betweenthe predicted and obtained log sequence ratios werem re fita nes ourf

rf ted toc eree ivitym cho werer y thet

le-s uset thes ass fora for

inimised. The same three bias parameters wes for the multiple-sensitivity model. With only oensitivity parameter, this model required only free parameters.

The results are graphed inFig. 2, where data foour of the six possible sequence pairs are presenover the range of relations. In general, the fits wxcellent. Inspection showed that the single-sensitodel fit all conditions well, including those in whinly two of the four possible response sequenceseinforced. The sensitivities and biases produced bwo models were similar.

The fits were not as good as for the multipensitivity model, as would be expected becahis model uses more free parameters thaningle-sensitivity model; but the difference wmall. The single-sensitivity model accountedn average of 89% variance, compared to 91%

56 S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61Ta

ble

2G

ener

alis

edm

atch

ing

law

para

met

ers

for

sing

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and

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tiple

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odel

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Sen

sitiv

ity(a

)B

ias

(b)

Bird

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t(S

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RLR

/RL

RL/

RR

LL/R

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022)

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1.55

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rage

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−207

−172

Note

:The

Mul

tLL/

RL,

LL/R

R,a

ndLR

/RR

bias

valu

esw

ere

calc

ulat

edra

ther

than

fitte

d(s

eete

xt),

and

the

VAC

and

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valu

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the multiple-sensitivity model. A comparison of thesingle-sensitivity and multiple-sensitivity modelsusing the Akaike information criterion (which takesthe different numbers of free parameters into account;seeDavison and McCarthy, 1988; Shull, 1991) showedthat the former was always the more efficient descriptorof the data (Table 2; lower numbers are better).

Statistical tests revealed the same anti-changeoverbias pattern as for the multiple-sensitivity model:Bias values for sequences without compared to withchangeovers were greater than 1 in 22 of 24 cases(p< .05 on a binomial test).

4. Discussion

In this experiment response sequences were con-currently reinforced at different rates, and the se-quences, rather than single responses, obeyed the gen-eralised matching law. Two principal results were ob-tained from analyses by both the single- and multiple-sensitivity generalised matching models forn> 2 alter-natives. First, both models fitted the obtained sequence-emission data excellently for all subjects, supportingthe Constant Ratio Rule for response sequences. Sec-ond, the birds’ performances showed significant biasesagainst emitting sequences requiring changeovers.

We found no significant differences in sensitivityto reinforcement across response sequence pairing, sothe single-sensitivity version appears to be entirely sat-i e-r ast r alls ple-s

eds eans ome-w ulep sm sesi imet omee Foris oret k. As n

sfactory. Accordingly, the Akaike information crition confirmed that the single-sensitivity model whe more efficient descriptor of the present data foubjects. However, in some applications the multiensitivity model might still be useful.

Although two of our six subjects producequence-allocation sensitivities over 0.80, the mensitivity value across subjects averaged 0.70, shat lower than usual for concurrent VI VI schederformance (Baum, 1979). These lower sensitivitieight result from the requirement for two respon

tself: Of necessity, two responses will take more to emit than a single response of the same type. Svidence in the literature supports this possibility.

nstance,Davison and Ferguson (1978)found lowerensitivities to reinforcement in pigeons for the mime-consuming lever-press compared to a key-pecimilar result was reported byBeautrais and Daviso

S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61 57

Fig. 2. Sequence matching results for all pigeons. The log of each sequence ratio is plotted against the corresponding obtained log sequencereinforcer ratio. The straight lines were fitted by an optimiser minimizing the sum of the squares of the differences, using the single-sensitivityversion of the generalised matching law. Parameter values and the total variance accounted for are given inTable 2. The dotted line indicatesstrict matching.

(1977)using second-order schedules: When the first-order fixed-ratio requirements were smaller, sensitivityto reinforcement was higher (also seeSumpter et al.,1998). Differential effort also existed, but the availableevidence fails to support effort as a variable affecting re-inforcement rate sensitivity in this context (e.g.,Hunterand Davison, 1982, who found independence; but cf.

Sumpter et al., 1998). In any event, a reanalysis of theStubbs et al. (1987)two-response sequence data us-ing multiple-sensitivity generalised matching producedsensitivities that averaged higher than those reportedhere (mean of 0.77).

Anti-changeover bias was a clearcut finding: Thedata reported byStubbs et al. (1987)showed a bias

58 S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61

toward emitting RR responses over RL responses, andour reanalysis of their data found bias values and pat-terns similar to ours. Thus, despite different reinforcerdistributions and Stubbs’ et al.’s required minimumpost-sequence delay, the results from both studiessupport the general finding that sequences withoutchangeovers (e.g., LL) are preferred over those thatrequire a changeover (e.g., LR). Because changeoversrequire travel between the response alternatives withinthe sequence, they entail both more time and moreeffort. Biases against greater response duration andeffort have been shown (e.g.,Beautrais and Davison,1977; Davison and Ferguson, 1978; Hunter and Davi-son, 1982). Accordingly, because sequences requiringchangeovers take longer to emit, the delay to reinforce-ment for the first response in such sequences is longerthan is the case for sequences without changeovers.

These considerations bear on the question ofwhether reinforcing sequences of responses producessequence units, a question extensively discussed byStubbs et al. (1987). If, through reinforcement, a se-quence of responses becomes a behavioural unit, theimplication is that the sequence itself will be affectedby reinforcer-rate changes. This occurred:Fig. 2showsthat generalised matching applied to sequence units (in-cluding sequences with changeovers) in the same wayas it does to single responses. Thus, after sufficienttraining, first responses under delayed reinforcementin two-responsedemarcatedsequences appear to havecome under as much reinforcer control as did secondr edi-

ate reinforcement. Sequences behaved like units in thisrespect.Shimp (1979)concluded pragmatically that “ifa set of functional relations is more nearly invariant, issimpler, and is more coherent when expressed in termsof one behaviour than in terms of another, then the firstbehaviour better qualifies as an analytical unit” (p. 263;also seeIversen, 1991; Stubbs et al., 1987).

In summary, demarcated two-response sequencedata exhibited sequence matching, and were fit bytwo related choice models. We generalisedNatapoff’s(1970) equation to obtain the prediction that asingle-sensitivity should suffice for application ofthe generalised matching law. Statistical analysis ofthe multiple-sensitivity generalised matching lawresults confirmed this prediction. The Akaike criterionresults verified that this version was preferable to themultiple-sensitivity form of the generalised matchinglaw for the present data.

Acknowledgements

We thank the members of the Auckland laboratoryfor their help in running this experiment, and Mick Sib-ley for his care of the animals. We also thank DouglasElliffe and David Schaal for their helpful comments.

Appendix A

TA e sequ eft, and Lefta

C

RR

P30 824 96711 66

19 07 9

1037 81

esponses that were occasionally followed by imm

able A1bsolute sequence and reinforcer distributions: LL, LR, etc., arnd Right, sequences

ondition Responses

LL LR RL

igeon 1111 2037 1483 14152 3689 2355 1463 1262 119 4444 4171 692 23465 422 3087 8446 2375 341 22657 2824 1900 2668 4633 86 1049 665 1657 1822

10 4214 1783 21411 943 577 3790

SeeTable A1.

ences of responses on, and reinforcers obtained for, Left and L

Reinforcers

LL LR RL RR

41 84 90 103 855 101 147 15 890 32 0 0 37201 176 80 102 100 0 350 46 071 97 17 162 829 153 156 17 154 351 0 0 3448 0 170 179 084 166 163 20 197 0 42 348 0

S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61 59

Table A1 (Continued)

Condition Responses Reinforcers

LL LR RL RR LL LR RL RR

12 4171 283 2351 542 174 13 161 1613 1072 1710 1670 3554 24 77 103 16414 2831 240 326 3173 190 0 0 20115 682 142 2465 3411 18 18 159 16116 1692 1445 323 1368 88 161 14 75

Pigeon 1121 3654 1558 1520 3348 110 101 103 832 4324 3300 222 2395 100 184 21 1023 1080 545 6 7885 48 0 0 3684 6271 1557 971 1344 169 97 96 215 1778 3860 758 220 0 385 35 06 2454 1297 2005 3109 89 17 191 1037 5703 2229 625 664 178 180 24 208 6037 88 548 1918 351 0 0 419 5957 1709 1503 783 0 207 193 0

10 7146 2646 623 869 160 173 10 1911 647 2143 3541 1127 0 38 372 012 4992 584 1944 1970 179 26 179 1313 3151 1476 1219 4114 14 99 105 16414 4774 53 145 4099 213 0 0 20915 1810 485 2737 4895 16 14 174 18916 3999 2510 994 3394 100 203 23 85

Pigeon 1131 1761 1820 1451 2842 94 80 94 1052 2308 3190 376 1980 108 181 16 853 964 35 12 6452 49 0 0 3764 3730 2135 1491 610 169 91 96 175 79 5572 935 93 0 364 39 06 1865 818 2500 2337 83 18 148 1097 2916 3810 307 785 155 165 22 218 4290 178 38 978 388 0 0 349 85 3728 2557 84 0 190 216 0

10 2921 3471 327 995 170 179 18 1811 124 848 3935 51 0 52 345 012 2879 184 3108 570 170 13 167 1913 306 1837 1889 3127 14 112 93 16214 3289 56 23 3075 202 0 0 20515 642 288 3006 2934 27 13 193 18616 1818 3158 428 2477 90 189 17 104

Pigeon 1141 2526 1342 1499 2875 85 93 95 1022 2596 2471 419 2544 101 179 9 1033 1190 361 24 5202 38 0 0 3504 3633 1504 1851 1522 186 83 98 175 438 2495 900 1161 0 379 34 06 2332 584 1987 2236 105 17 168 907 3430 1840 390 937 160 160 19 198 4699 642 110 1678 359 0 0 369 313 1934 3617 157 0 202 190 0

10 4205 2422 251 618 201 165 14 2011 223 1098 4448 27 0 42 338 0

60 S.M. Schneider, M. Davison / Behavioural Processes 70 (2005) 51–61

Table A1 (Continued)

Condition Responses Reinforcers

LL LR RL RR LL LR RL RR

12 3447 573 3185 1198 201 16 194 2213 823 1608 2485 3209 17 83 103 16114 4127 257 46 3364 194 0 0 23415 917 475 2773 3954 25 19 183 17216 2799 2427 424 2645 99 182 18 93

Pigeon 1151 1751 2863 1287 2674 94 94 95 1062 3234 2820 280 2688 97 190 18 963 1438 2031 8 5342 44 0 0 3644 3520 2238 2134 799 146 97 105 195 126 5033 866 126 0 347 40 06 1840 955 1886 2384 77 22 166 887 2369 3475 276 898 171 188 16 178 5020 500 44 2107 359 0 0 489 50 4267 1741 86 0 206 177 0

10 2830 3467 253 411 151 166 18 811 54 2771 2642 69 0 43 360 012 3182 272 2431 1105 156 21 164 1313 588 2495 1364 3398 21 89 109 18514 3478 1465 40 4440 213 0 0 20515 739 629 1709 3443 22 24 160 15116 1921 3605 271 2276 109 190 14 98

Pigeon 1161 5083 1912 1350 4449 93 103 89 1102 3140 2767 709 3140 107 150 14 953 955 1502 149 8843 42 0 0 3734 3314 3083 1081 1278 174 112 90 365 801 6169 1268 599 0 366 48 06 3323 672 3178 3831 108 17 180 977 5423 3604 1306 1584 146 179 27 228 7589 36 465 2600 384 0 0 539 679 3774 3412 576 0 197 226 0

10 4493 3896 1085 1128 176 161 23 2211 1292 1740 5899 204 0 44 355 012 4397 1302 4033 782 196 19 169 813 760 2441 2669 5034 12 97 99 20014 4758 723 175 6691 200 0 0 19615 1185 861 3687 5596 19 31 167 18316 2275 3608 1343 4092 95 187 30 100

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