ANALYSIS OF BEHAVIOR NUMBER I A COMPARISON OF RATIO …

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

A COMPARISON OF RATIO ANDINTERVAL REINFORCEMENT SCHEDULES WITHCOMPARABLE INTERREINFORCEMENT TIMES

GEORGE W. CAPEHART, DAVID A. ECKERMAN,MARILYN GUILKEY, AND RICHARD L. SHULL

UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL AND AT GREENSBORO

Pigeons were trained to peck keys on fixed-ratio and fixed-interval schedules of food rein-forcement. Both schedules produced a pattern of behavior characterized as pause and run,but the relation of pausing to time between reinforcers differed for the two schedules evenwhen mean time between reinforcers was the same. Pausing in the fixed ratio occupied lessof the time between reinforcers for shorter interreinforcer times. For two of three birds, therelation was reversed at longer interreinforcer times. As an interreinforcer time elapsed,there was an increasing tendency to return to responding for the fixed interval, but aroughly constant tendency to return to responding for the fixed-ratio schedule. In Experi-inent 1 these observations were made for both single-reinforcement schedules and multipleschedules of fixed-ratio and fixed-interval reinforcement. In Experiment 2 the observationswere extended to a comparison of fixed-ratio versus variable-interval reinforcement sched-ules, where the distribution of interreinforcement times in the variable interval approxi-Iiated that for the fixed ratio.Key words: fixed-ratio schedule of reinforcement, fixed-interval schedule of reinforce-

ment, variable-interval schedule of reinforcement, postreinforcement pause, proximity,delay of reinforcement, pigeons

Fixed-ratio (FR) reinforcement schedules ar-range reinforcer presentation to follow eachNth response regardless of time. Fixed-interval(FI) reinforcement schedules arrange reinforcerpresentation to follow the first response occur-ring after some point in time, regardless ofthe number of previous responses. In manycases both FR and Fl schedules generate simi-lar patterns of behavior: after a reinforcer thereis a pause in responding, followed by a transi-tion period in which rate of responding accel-erates, followed, in turn, by a terminal run ofresponses at a more constant rate.Do the same variables affect the duration of

the pause on FR and Fl schedules? Schneider

Experiment 1 was conducted at the University ofNorth Carolina at Chapel Hill and was supported bygrants from the University Research Council of theUniversity of North Carolina at Chapel Hill and bytraining grant MH-14269 from the National Instituteof Mental Health, Public Health Service. The authorswish to thank Rebecca Carpenter for preparation of thefigures. Experiment 2 was conducted by Marilyn Guil-key and Richard L. Shull at the University of NorthCarolina at Greensboro and was supported by NSFGrant BNS76-04317. Reprints may be obtained fromDavid A. Eckerman or Richard L. Shull, Department ofPsychology, University of North Carolina, Chapel Hill,North Carolina 27514 or Greensboro, North Carolina27412.

61

(1969), Shull, Guilkey, and Witty (1972), andNeuringer and Schneider (1968) have shownthat the pause in FI occupies a roughly con-stant proportion of the time between rein-forcers (the interreinforcer time, IRfT) asIRfT is varied over a wide range. Similarly,Felton, and Lyon (1966) and Powell (1968) haveshown that the pause increases as the FRvalue increases. Since increased IRfT is a con-sequence of increased FR value, could theIRfT be the variable accounting for increasedFR pausing as it seems to be in the FI pausing?Killeen (1969) and Nevin (1973, p. 208) haveproposed that the pause may be directly relatedto the IRfT for both FR and Fl schedules.Nevin based his proposal on an analysis ofdata obtained in a study by Berryman andNevin (1962) comparing FR, Fl, and interlock-ing schedules of reinforcement for bar pressingby rats. At the values used, pausing occupiedroughly half the IRfT for both FR and Fl.Killeen based his proposal on finding approxi-mately equal pausing for FR and on a sched-ule in which a yoked "interval" bird was pro-vided a reinforcer for the first peck after thetime when its yoked FR bird obtained a rein-forcer.The proposal above is simple, and therefore

appealing, but it is unlikely that pausing is

1980, 34, 61-76 NUMBER I (JULY)

GEORGE W. CAPEHART et al.

comparably controlled by IRfT in FR and Flschedules because pausing has a different re-lation to reinforcement in each case. This in-equivalence may be stated in many ways. Sincelong pauses in Fl terminate nearer the rein-forcer, long pausing may be differentially re-inforced by the brief delay of reinforcement(or short work time) that follows the end ofthe pause. FR pauses, in contrast, always ter-minate a constant number of responses-andtherefore, presumably, a constant time-awayfrom the reinforcer, and neither long nor shortpauses are differentially reinforced. Expressedanother way, short pauses in FR yield higherreinforcers/hour and may thereby be differen-tially reinforced. However, pausing has littleto do with determining reinforcers per hourin FI, and therefore should not be differen-tially reinforced by this characteristic. Regard-less of the relative merits of these expressionsof the inequivalence, its presence suggests thepossibility of inequivalent relations betweenpausing and IRfT for FR and FI. Further,FR pausing (or pausing in other scheduleswhere duration and work time are indepen-dent) seems to be more sensitive than Fl paus-ing to changes in a variety of conditions (e.g.,shock punishment, deprivation, reinforceramount, objects controlling adjunctive behav-ior, differential reinforcement of pause dura-tion-see Shull and Guilkey, 1976, for a reviewof these effects). This differential sensitivitysuggests that FR and FI pausing might be dif-ferently related to IRfT. This suggesion issupported by the work of Crossman, Heaps,Nunes, and Alferink (1974) who demonstratedthat pausing differs for "work times" filledwith FR responses and yoked "work times"when food is provided at the end of a fixedtime regardless of intervening responding. In-asmuch as FR and Fl produce different behav-ior during the terminal run, then, differencesin pausing might be expected.Even though there is reason to question the

equivalent relation of pausing to IRfT in FRand FI schedules, there is no direct comparisonavailable to assess these issues. In the presentexperiment we provide direct evidence regard-ing the relation between pausing and IRfTfor FR and FI schedules having similar IRfT's.In Experiment 1 the comparison was madebetween behavior generated by FR schedulesand Fl schedules where the IRfT was adjustedto equal the mean IRfT under FR. The rela-

tion was observed both in single schedules andin multiple schedules where a daily contrastmight be drawn between FR and Fl for indi-vidual subjects and where interactions betweenthe schedules might be observed. Since thesefixed schedules are very common and the ear-lier assertions were made regarding them, theeffect of IRfT on responding was evaluated forthese simple schedules first.

In Experiment 2 we compared behavior gen-erated by FR schedules and Fl schedules hav-ing a distribution of IRfT's comparable tothat obtained under the FR schedule.

EXPERIMENT 1METHOD

SubjectsThree male White Carneaux pigeons (627,

628, 945) with experimental histories on vari-ous interval-reinforcement schedules with key-peck responding were maintained at approxi-mately 75% of their free-feeding weights. Allwere approximately 3 years old at the begin-ning of the experiment.

ApparatusA two-key operant-conditioning chamber for

pigeons was used. The chamber measured 30.5cm (height) by 27.9 cm (width) by 30.5 cm(length). Three walls were natural finish a'lu-minum; one 27,9- by 30.5-cm wall was anodizedblack aluminum; and the floor was wire mesh.Two pecking keys (18 N) were mounted behind2.2-cm diameter holes cut 7.6 cm apart andcentered at a height of 18.6 cm in the blackanodized wall. A screen that could be trans-illuminated with a white horizontal line on ablack background or with a green circle wasmounted .6 cm behind the keys. A feederopening was centered below and between thekeys, 8.9 cm above the floor. During the rein-forcement cycle (3-sec access to mixed grain),the keylight and houselight were extinguished,and the hopper was illuminated. In this ex-periment only the left key was used. Maskingsound was provided by the ventilation fan andby white noise. Standard electromechanical ap-paratus and recording equipment were locatedin an adjacent room.

Proce.dureSingle schedule conditions. In the first ex-

perimental condition (see Table 1), birds were

62

RATIO COMPARED TO INTERVAL SCHEDULES

Table 1Sequence of Reinforcement Schedules

Scheduk value (No. ofsessions)Condition Scheduk B627 B628 B945

1 FRx 100 (41) 50(36) 100(18)2 FIy 114a(22) 43(23) 147(22)3 mult FRFI FR100 FR50 FR100

A FI74(12) FI Ab(28) FI A(41)B FI100(20) Fl Hb(43) FI H(34)C FI120(14) Fl A(24) Fl A(41)D F1240(19)

4 FRx 100(29) 50(18) 100(30)5 Fly 276(14) 32(22) 251(19)6 FRx 50(21) 100(49) 50(15)7 Fly 50(17) 94(16) 22(9)8 mult FRFI FR50 FR100 FR50

Fl A(21) FI A(22) FI A(32)9 FRx 50(26) 100(20) 50(21)10 Fly 46(14) 133(46) 21(44)11 FRx 65(120) 95(52) 85(59)12 FIy 67(23) 122(24) 60(27)13 FRx 65(22) 95(24) 85(47)14 FIy 86(19) 100(22) 86(19)

aValues for FI schedules. are seconds.bFI A indicates the Fl value was the arithmetic mean of the prior day FR interreinforcement times. Fl H indicates the Fl

value was the harmonic mean.

exposed to either FR 50 (B628) or FR 100(B627, B945) reinforcer schedules. The key wasilluminated with a horizontal white linethroughout these sessions, except that the keywas dark during reinforcer presentations. Dailysessions lasted for 50 reinforcers or 120 min,whichever occurred first. When performancestabilized, the condition was changed to a FIschedule. The criterion for stability in a condi-tion required that for 5 consecutive sessionsthere was no consistent trend and that thedaily values were between the minimum andmaximum values obtained earlier in that con-dition. The Fl value was chosen to equal thearithmetic mean of the IRfT's for the last fiveFR sessions (the first five IRfTs of these ses-sions were excluded from this average). Dur-ing FI sessions the key was illuminated greenexcept during reinforcer presentations when itwas dark. When performance stabilized (cri-terion as above), a multiple FR-Fl schedulewas arranged, as described below. Subse-quently, the original FR schedule was againarranged (Condition 4), a new FI value wasdetermined and arranged (Condition 5), andso on until observations had been made ateach of three FR values (replications at twoof these values) and at "matching" FI values.The third FR value was intermediate be-

tween FR 50 and FR 100. Its value was selectedfor each bird so that 50 reinforcers would beearned consistently in 120 min. This value wasthen taken as the third FR. The values were:B627, FR 65; B628, FR 95; B945, FR 85.Multiple schedule conditions. In experimen-

tal Conditions 3 and 8, sessions were arrangedin which FR and Fl schedules were alternatedevery five reinforcers. During FR componentsthe key was illuminated with the horizontalbar; during FI components the key was il-luminated with the green circle. Each sessionlasted for 50 reinforcers or 120 min, whicheveroccurred first. Whether a session started withthe FR or the FI component was determinedby a scrambled sequence. The FR scheduleswere either FR 50 or FR 100 (see Table 1).For most multiple-schedule sessions, the Flwas adjusted daily so that it matched the IRfTfor the FR schedule in the prior session (theexception for B627 is described below). Themanner of matching was either by setting theFl equal to the arithmetic mean or the har-monic mean IRfT (the first five FR IRfTswere excluded from this average). Table 1indicates for which sessions the two methodswere used. As performance under this sched-ule stabilized, the FI value changed less fromsession to session, approaching a truly fixed

63


FI. For the multiple schedule of Condition3 for B627, however, the FR was only mar-ginally maintained, and IRfTs were incon-sistent. The Fl value was therefore adjustedevery several sessions instead of daily.

RESULTSAll statistics in this report are based on data

pooled over the last five days of a condition.Conclusions, therefore, apply to data pooledin this fashion.

120

100 /

/80 FR:Y-.72x-20/r

BIRD 627

6060 / ~~~~~FlY=.14x+17_

r2 =.79340 / ,2- 7

20

/ pF Y=.40x+ 12D °2 S / r2.855w/n 0 / BIRD 628a. j ,,/ o- FR Fl CONDITIONz / a o INITIAL

//< >- /ZFR:Y'.34x-3 * ° MULTr2'937 * 0 REPLICATION

/20 / 7 FR:Y'.54x-5.'

/ .9 ~~r2 .983/

,Fl Y=.26x +I1240_-=.85o

BIRD 94520 .

20

50 100 150 200 250 300MEDIAN INTER-REINF. TIME (SEC)

Fig. 1. Time spent pausing in each fixed-interval andfixed-ratio schedule. Median values were used from thelast five sessions exposure to each schedule, both forinitial exposure and replication. Interreinforcementtimes are given in seconds. The nmedian pause value isshown for each schedule over the median interrein-forcement time for that schedule, for median pause tothe fifth response following each reinforcer. In eachcase higher interreinforcement time indicates higherschedule value (see Table 1). A line fit by least-squaresmethod is shown for each bird for ratio and intervalschedules drawn from all conditions.

Comparison of PausingPausing for both FR and FI reinforcer sched-

ules increased as IRfT increased (Figure 1).For both schedules the pause generally occu-pied about half the IRfT. At the short IRfTs,however, FR pausing always fell below Flpausing, emphasizing a difference between thetwo schedules. Further, at long IRfTs the rela-tion was reversed for two of the three birds(B627 and B945), with FI pausing falling be-low FR pausing. The values for B627 andB945 fall noticeably below half the IRfT. Theyrepresent values from the first few FI condi-tions, where training with the Fl closely fol-lowed training with the large FR. It will laterbe argued that contrast with this FR shortenedthe FI pausing in these cases.

In Figure 1, the median pause to the fifthresponse is shown. Pause to the fifth responsewas used to minimize inclusions of occasionalshort pauses where pausing continued afterthe first one or two responses (Gollub, 1964).Data for pause to the first response, however,show the same effects. Data are not available tomeasure the "breakpoint" from pausing to re-sponding (Schneider, 1969), though pause tothe fifth response probably approximates thisvalue. The median pause was chosen as themeasure of central tendency for these some-what skewed distributions.While comparison of median pause (Figure

1) emphasizes a subtle differences between ratioand interval pausing, comparison of the dis-tribution of pauses (Figure 2) over the IRfTemphasizes more major differences. Figure 2presents a transformation of the frequencydistributions of pausing that shows the propor-tion of pauses greater than a particular valueof time. The slope of this functionrepresentsthe conditional probability of a pause termi-nation for each time in the IRfT. The propor-tions are shown as logarithms, since the log is:(a) a decreasing linear function of time whenthis probability is constant across time; (b) aconcave-down function when there is an in-creasing probability of pause termination; and(c) a convex function (with limit at slope ofzero) when there is a decreasing probability ofpause termination. A selection of three single-schedule and the two multiple-schedule FRpause distributions and their matching Flpause distributions are shown for each birdin Figure 2. The single-schedule functions

64


BIRD 945

1.0

Q0 >

04

0.204I100 (MULT)98 (MULT)100 (MULT)

02 -

i1.008 -\

J 0.6 - FR 6

0.4 -

02 F

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0.4

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0.4I_\Q2I

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0.4FR 50Fl 32

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I l l

80 100 120 0

FR IOORs F1 251

FR 100 (MULT)Fl 80 (MULT)

%\ FR85R\' Fl 86

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II

II

I

20 40 60 80 100 120 0

FR 50(MULT)Fl 29 (MULT)

RATIO--- INTERVAL

20 40 60 80 100 120 140 160

TIME SINCE REINFORCEMENT (SEC)Fig. 2. Logarithm of the proportion of pauses to the fifth response greater than any particular time. Functions

are shown for one determination at each fixed-ratio value and for the fixed interval paired with that schedule.Data were taken from the last five sessions at a determination. For functions derived from the second determina-tion at a particular ratio value, an "R" is shown following the ratio value.

were chosen as the FR with longest IRfT, nation was roughly constant across time forsmallest IRfT, and one intermediate IRfT the FR schedules; i.e., the functions for FR in(the final condition). Figure 2 are roughly linear. In some cases theThe conditional probability of pause termi- functions are linear only after a brief delay.

I

liJ

ILi

Ct

cnu

aC

2

C

F-

C

a

Ca

ar

65

!A

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The conditional probability of pause termi-nation increased across time for the Fl sched-ules. That is, the functions for FI in Figure 2are concave down. This changing probabilityof pause termination is thus different from themore nearly constant probability seen for FR.For the long IRfT condition for birds 627 and945 (the condition producing median pausingconsiderably shorter than half the IRfT), theFl functions are exceptional and are quiteclose to linear. Again, then, these are deviantconditions.The conditional probability of pause termi-

nation was roughly constant across time for theFR schedules, but gradually increased for theFI schedules. To assess the concavity of thefunctions of Figure 2, each triplet of successivedata points was inspected for each function,starting with the longest time since reinforce-ment having a value of 1.0. Since the verticalaxes are scored logarithmically, each propor-tion was converted to its logarithm. Then, foreach successive triplet the first and third valueswere averaged, and the middle value was com-

pared to this average. When the middle valuewas higher, the triplet was judged to be con-cave. Table 2 shows the percent of triplets thatwere concave for the ratio and interval func-tions. For each bird the interval functionsshowed a higher percent of concave tripletsthan did the ratio functions. Further, the av-erage deviation from linearity was less positiveor negative (showing overall convexity) for theratio functions, while it was more positive(showing overall. concavity) for the intervalfunctions. When pairs of functions are com-

pared (ratio vs. interval), the average deviationfor the interval function exceeds that for theratio function for all pairs. Several evalua-tions, therefore, confirm that pause termi-nation increases in probability as the IRfTelapses in interval, but not in ratio schedules.

In addition to representing the probabilitiesof terminating the pause, these functions alsoindicate the variability in pausing. For exam-ple, the median values (shown in Figure 1) aswell as the interquartile range values can bedetermined easily from the functions in Figure2 by finding the pause time on the x-axis cor-responding to a particular percentile point onthe cumulative distribution.

Comparison of RespondingOnce initiated, responding occurred at a

higher rate (the running rate) in FR than inFl schedules (see Figure 3). For both schedulesrunning rate either remained constant or de-creased as IRfT increased.Running rates are shown both for respond-

ing after the first response and for respondingafter the fifth response. By comparing theserates a judgment may be made regarding the"break-run" characteristics of responding be-tween the first and fifth response. For bothFl and FR, running rate was typically higherwhere measured from the fifth response, show-ing that the rate from the first to fifth response

was somewhat lower than thereafter. The dif-ference between the two measures of runningrate was about equal for the two schedules,however, and did not change systematicallyacross IRfT for either FI or FR. Thus, the

Table 2Concavity of Ratio and Interval Functions of Figures 2 and 5

Fixed ratios IntevalsNo. Prop. No. Prop.

Bird tripets concave Dev. a tripkts concave Dev.EXPERIMENT 1

627 57 .47 - .139 35 .80 .073628 52 .54 .002 43 .86 .044945 57 .56 -.078 47 .79 .037

Overall 166 .52 -.074 125 .82 .050

EXPERIMENT 2P5 35 .57 .013 10 1.00 .130DD1 9 .89 .431 4 1.00 .529MG2 39 .64 .009 11 .91 .099MG11 47 .53 .009 14 .93 .045

Overall 130 .60 .039 39 .95 .045

'Mean deviation between midvalue (In) of triplet and linear interpolated midvalue (In) of triplet.

66


"break-run" pattern was similar for both FRand Fl, and the break-run pattern did notchange systematically for either schedule acrossIRft.

For Fl the pause in a particular intervaland the time spent responding in that interval(work time) are negatively correlated becauseof the properties of the schedule. For FR, how-over, no correlation is forced between pauseand run time, and, indeed, no relation wasfound when mean run time was plotted for anumber of pause-time categories. The ratiorun was completed about as quickly followingshort as following long pauses. This impliesthat the IRfT distributions for FR shouldparallel the pause distributions shown for FRin Figure 2. Again, this implication was con-firmed by comparing such plots.

Multiple-Schedule InteractionsSince five successive reinforcers were earned

under one component-reinforcer schedule be-fore stimulus and contingency were switchedto the alternate component, transient effects onpausing or on running rate might be observedas differences between the successive five IRfTsin a component. For Fl no consistent transienteffects were observed for either pausing orrunning rate. For FR there was a consistenteffect observed for pausing, but not for run-ning rate. The first IRfT of an FR componentincluded a somewhat longer pause than thesecond IRfT (about 8% more of the IRfTwas spent in pausing). There was, therefore, asmall transient multiple-schedule interactioneffect on FR pausing.

DISCUSSIONOur initial goal was to determine if paus-

ing was comparably controlled by time-since-reinforcement on FR and FI schedules of rein-forcement. The answer seems to be no. Thoughaverage pause was directly related to the IRfTfor each type of schedule, the pause occupieda smaller proportion of time for short FR'sthan for comparably short FI's. For two ofthree birds, the function relating pause toIRfT was of lower slope for FI than for FR.Crossman et al. (1974, Experiment II) alsoreport that pausing occupied an increasinglygreater proportion of the time between rein-forcers for larger FR than for "interval" sched-ules with comparable IRfTs. In the presentprocedure the comparison was between FR

and FI. In the Crossman et al. (1974) proce-dure, the comparison was between FR and aschedule where the IRfT of a ratio was takento set the IRfT for a subsequent interval. Thatsimilar effects were observed emphasizes thegenerality of this difference. Experiment 2will add further to this generality. Since thefunctions relating pause to IRfT crossed fortwo of the birds in the present study, therewas a mid-range where average pause was sim-ilar for FR and FI. Prior suggestions of com-parability between FR and FI pausing mayhave been based on data from this mid-range(Killeen, 1969; Nevin, 1973).Even when average pause durations were

similar for FR and FI schedules, however, thedistribution of pauses in time differed for thetwo schedules. For FR the probability of pausetermination was relatively constant acrosstime; for Fl this probability increased acrosstime. Because this constancy for FR schedules

20

1.0

a 2.0z0w0 1.0

w0.

wcnz 4.000.

z 3.0

2.0

1.0

-BIRD 627

- ~s"3---=t-

- BIRD 628to - --0

- 18-1,_

BIRD 945

_\\I,&\

INITIAL REPLICATION MULTRATIO 0 0 aINTERVAL * a °

\

--\--

40 80 120 160 200 240 280INTER-REINE TIME (SEC)

Fig. 3. Median running rate of responding for thelast five sessions are shown for each fixed-interval andfixed-ratio condition (initial exposure, replication, andmultiple schedule) over the median interreinforcementtime for those sessions. In each case, higher interrein-forcement time indicates higher schedule value (seeTable 1). For each condition both rate of respondingfollowing the first response and following the fifth re-sponse is shown if these measures differed. Rate fromthe fifth response is always the higher value.

67


was at least as apparent at the shorter FR val-ues as at the larger FR values, it is unlikelyto be due to "ratio strain" or some other in-stability in ratio performance at high values.

It seems, therefore, that we must give up thesimple hypothesis that the average pause issimply controlled by average time between re-inforcers and is therefore comparable betweenFl and FR's. Perhaps, however, the averagepause is controlled by some characteristic ofthe distribution of IRfTs other than the av-erage. Because the time between reinforcers isfixed for FI but varies for FR, the differencein the average pause seen here may reflect thisdifference in variability of the times betweenreinforcers. Yet, the direction of the differencebetween average FR and Fl pauses is incon-sistent with this proposal. Catania and Reyn-olds (1968) note that when two interval sched-ules producing a similar number of reinforcersper hour are compared, the one having thegreater frequency of short intervals (and thusthe greater variability) will ordinarily gener-ate the shorter mean pause. In the presentstudy, however, the larger FR schedules pro-duced longer average pauses for two of threebirds than did comparable Fl schedules. Whenthese ratio and interval schedules were com-pared, therefore, the schedule containing morevariable IRfT's (and more short times) pro-duced longer pauses. This last issue is morethoroughly addressed in Experiment 2, andsuggestions regarding why pausing differs forratio and interval schedules are presented inthe General Discussion.

Before completing discussion of Experiment1, we want to note that the observed inter-action between the FR and FI components ofthe multiple schedule supports the proposalthat FR's were less supportive of initiatingresponding than were comparable Fl's. Thatis, at the start of the FR component, pausingwas long-a transient contrast effect compa-rable to that seen when changing from a high-reinforcement-density to a low-reinforcement-density component (e.g., Nevin 8c Shettleworth,1966). This interaction was quite small. Sinceaverage IRfTs were equated and stimuli werevery distinct, there was little reason to expectinteraction effects at all, however.A similar interaction might have operated

even when the schedules were studied in isola-tion. When the FR 100 was studied first (Birds627 and 945), the pause and IRfT obtained

for the replication of FR 100 were much largerthan in the initial observations. This resultis consistent with the possibility that the largeFR, following exposure to Fl schedules, suffersa lowering of the tendency to initiate re-sponding.

For all three birds of this study, FI pausingoccupied a decreasing proportion of the IRfTas this time increased. In some previous studiesthe average pause has occupied a constant pro-portion of the interval (Schneider, 1969; Shull,1971), but in others the average pause has oc-cupied a decreasing proportion, as in the pres-ent study (Lowe, Harzem, 8c Spencer, 1979).The present results, then, are within the rangeof previous findings. It might be emphasizedthat the slope of the function relating pausingto IRfT is not lowered by the very long FlIRfT's found in Condition 4 for Bird 627 andBird 945, since in one case this point falls onthe line of best fit (B627) and in the other itfalls above this line (B945). Even in the firstdetermination of the long FI (Condition 1 forthese two birds), the pausing fell close to thisline of lower slope.

If FI pausing was affected by a history ofexposure to FR schedules, this may limit thegenerality of the present result. Perhaps thislimit is real as regards average pause values.That the same form of pause distribution hasbeen found even for birds that had no historyof training on ratio schedules (Shull & Brown-stein, 1975), however, suggests that the differ-ence between FR and Fl pause distributionsis not limited by this aspect of the single-subject design. Further, an across-group com-parison of FR and Fl performances wouldcontain its own limitations.

EXPERIMENT 2FR and FI schedules differ in many ways,

but they also have some features in common.The issue being considered here is whetherone common feature, namely the fact that re-inforcers are distributed in time in relationto the last reinforcer, is sufficient to accountfor pausing on both kinds of schedules. Ex-periment 1 ruled out the possibility that theaverage IRfT is a sufficient predictor of theaverage pause. Experiment 2 evaluates the roleof variability in the distribution of IRfT's indetermining the distribution of pauses.One way that variability could operate is by

68


affecting the local density of reinforcers at dif-ferent times since the last reinforcer; that is,the number of reinforcers received duringsome small time band divided by the amountof time spent in that time band. On Fl sched-ules almost all the reinforcers occur within arelatively small band of time after the end ofthe FI, and so the local density of reinforcersis high right after the end of the Fl and lowor zero at other times. On FR schedules, incontrast, reinforcers are more widely distrib-uted in time. In fact, as a function of timesince the last reinforcer, the local density ofreinforcers remains zero for a while, then in-creases for a brief period, and then remainsfairly constant over much of the range ofIRfTs. (These local densities can be inferredfrom the pause-distribution data for FR sched-ules as presented in Figure 2. Since the vari-ability in run times is small relative to thevariability in pausing, the distribution ofIRfTs closely resembles the distribution ofpauses on FR schedules except that it is shiftedtoward longer times by an amount equal tothe run time.)On interval schedules, the response rate at

a particular time since the last reinforcer iscorrelated with the local density of reinforcersat that time (Catania 8c Reynolds, 1968). Per-haps the tendency to resume responding aftera pause on FR and FI schedules is similarlycontrolled. The continuously increasing prob-ability of a pause termination on Fl schedulesand the relatively constant probability afteran initial rise on FR schedules (Figure 2) areconsistent with this interpretation.

If local densities of reinforcement at differ-ent times since the last reinforcer controlledthe probability of a pause termination simi-larly on ratio and interval schedules, it shouldbe possible to generate an FR-like distributionof pauses by using a variable-interval (VI)schedule that provides a similar distribution ofIRfTs. The procedure of Experiment 2 wasmuch like that of Experiment 1 except that aVI schedule, approximating the distributionof IRfTs obtained on an FR schedule, wassubstituted for the Fl schedule in the com-parison.

METHODSubjectsThe subjects were three adult male and one

adult female domestic pigeons maintained at

about 80% of their free-feeding weights. Theyhad had extensive prior experience with fixed-ratio schedules of food reinforcement.

ApparatusA sound-attenuating shell enclosed the ex-

perimental cubicle measuring 31 cm by 37 cmby 36 cm. White noise in the chamber and aventilating fan helped mask extraneous noises.One wall of the chamber contained a rectangu-lar opening for presenting mixed grain, cen-tered 10 cm above the floor. To the right ofthe feeder opening, 25 cm above the floor, wasa 2.5-cm diameter translucent response keythat required a minimum of .2 N to operate.Key closures of sufficient force produced abrief click from a relay mounted behind thekey and also operated appropriate control andrecording circuits constructed of standard elec-tromechanical equipment. The key could betransilluminated with different colored lights.A lamp (GE #1829) centered near the top ofthe front wall provided low-level general il-lumination.The reinforcer consisted of four sec access to

mixed grain, during which the response keyand the houselight were darkened and thefeeder opening illuminated.

ProcedureBecause of their extensive previous training,

no special pretraining was needed. Each pigeonwas trained initially on a fixed-ratio fifty (FR50) schedule for 35 sessions, then on a VIschedule for 33 sessions, and then, after someconditions unrelated to the present study, onthe FR 50 again for 24 sessions. The VI sched-ule reinforced the first response after an inter-val of time elapsed since the last reinforcer.It was constructed separately for each bird toprovide about the same local densities of rein-forcement at different times since the last re-inforcer as had been obtained on the initialFR 50 schedule. This was accomplished by firstconstructing a cumulative frequency distribu-tion of the IRfTs obtained during the last fivesessions of the initial FR 50 schedule. Next,beginning with the fifth percentile, IRfTs weremarked off corresponding to consecutive decilesof the cumulative distribution. Finally, the tenintervals so generated for each bird were mixedwith respect to duration and programmed asa repeating series. These series are presentedin Table 3 for each bird.

69


Table 3The 10 intervals (sec) of the yoked interreinforcer time (VI)schedule of Experiment 2 (rank ordered).

FR 50 FR 100 FR 70Bird Bird Bird

DD1 P5 MG2 MG11 DDI P5 MG2 MG11

12 19 25 26 24 49 55 4812 21 31 30 26 54 67 6413 23 33 33 28 59 75 7513 25 36 35 29 63 80 8313 27 39 38 31 67 87 9114 28 40 40 32 71 94 10514 29 42 43 34 76 107 11815 31 45 47 35 83 117 13517 35 49 54 39 96 141 16820 43 57 74 45 180 216 216

This same sequence of FR, VI, and FR was

repeated with the FR set at 100 (at 70 forBird MGI 1). These schedules were studied for40, 20, and 20 consecutive sessions, respec-

tively. The VI schedule for this series was

constructed as described above except that thereference FR schedule was, of course, larger.For all conditions the key color was white

between reinforcers. Sessions were conducteddaily and terminated after the end of the six-tieth reinforcer. The chamber was dark be-fore the start and after the end of the session.

RESULTSThe pause in Experiment 2 was measured to

the first response after each reinforcer, ratherthan to the fifth response as in Experiment 1.The median pause increased as a function ofthe median IRfT for the FR and the yoked-VIschedules (see Figure 4). At the FR 50 com-parison, the median pause was similar for theFR and yoked-VI schedule; at the larger FRcomparison, the median pause was longer on

the FR schedule for all but Bird DD-1.Figure 5 shows the proportion of pauses

longer than any particular value of time sincethe last reinforcer. The vertical axis is scaledlogarithmically and the horizontal axis scaledin seconds since the last reinforcer. For the FRschedules these functions are often reasonablydescribed as straight-line, decreasing after an

initial horizontal segment. For the yoked-VIschedules, in contrast, the functions are usuallycontinuously concave downward. These pat-terns are most clear for Bird P-5 and leastclear for Bird DD-1, whose average pauses were

by far the shortest of the four birds. As de-scribed earlier, the probability of terminating

the pause as a function of elapsed time sincethe last reinforcer can be derived from thesefunctions. For the FR schedules that probabil-ity was low after the reinforcer, increased overa brief period, and then remained fairly con-stant for the rest of the IRfT. For the yoked-VIschedules, in contrast, the probability of ter-minating the pause usually increased continu-ously as a function of elapsed time. Althougha number of experimental manipulations in-tervened between the two determinations ofthe FR schedules, both determinations pro-duced similar functions. Table 2 presents thepercent of successive triplets of points showingconcavity for the functions of Figure 5 (seeExperiment 1 for a detailed description ofthis measure). As for Experiment 1, the inter-

30 -

20

DD I

10 -

0

Z M10 /w

wcflQ

10 MGz

1030-------------

20-MGI I 0

a FIXED RATIO10 0 YOKED INTERVAL

II 1I

20 40 60 80 100INTER-REINF. TIME (SEC)

Fig. 4. The median pause is plotted over the medianinterreinforcer interval for the first determination ofeach of the two FR schedules and for the correspond-ing yoked VI schedules. The medians were derivedfrom frequency distributions compiled over the last300 reinforcers of each condition (the last five sessions).

70


INITIAL FR

YOKED INTERVAL

.---- REPLICATION FR

I I I I I °l0.: I\ ,10 20 30 40 50 60 70 10 20 30 40

TIME SINCE REINFORCEMENT (SEC)

Fig. 5. The proportion of pauses longer than t-sec is plotted over seconds since the last reinforcer for bothdeterminations of each of the two FR schedules and for the corresponding yoked VI schedules. The verticalaxis is scaled logarithmically so that a linear decrease signifies a constant probability of pause termination (seetext). The distributions were made from the last 300 pauses of each condition (the last five sessions).

val functions showed a greater percentage ofconcave triplets for each bird (though thevalues are very close for bird DDl). For noneof the individual pairs did the proportions ofconcave triplets for an FR schedule exceedthat for its yoked interval schedule. Further,the average deviation for the interval func-tions exceeds that for the ratio functions foreach bird. This direction of difference heldfor each schedule pair except for two com-

parisons for DDI. Again, therefore, the point-

by-point analysis of the functions confirms thatinterval functions showed more concavity thandid ratio functions. Again, variability in paus-ing may be determined from these cumulativefrequency distributions.Response rates after the end of the pause

(running rates) decreased with the medianIRfT for both the FR and the yoked-VI sched-ules (see Figure 6). For a particular IRfT, therunning rates were higher for the FR thanfor the yoked-VI schedules.

FR 1001.0

08

0.6

71

0.8

0.6

0.4

0.2

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FR VI ferences in the way FR and FI schedules con-DD I * o trol pause termination seem to be due to some-

thing other than differences in the distributionP5 * ^ of IRfTs.

MG2 a 0

MGII * O

I I I I I I20 40 60 80 10INTER-REINF. TI ME (SEC)

Fig. 6. The mean response rate after the end of thepause is plotted over the median interreinforcer inter-val for the first determination of each of the two FRschedules and for the corresponding VI schedules. Theresponse rates were calculated from response and timetotals accumulated over the last five sessions of eachcondition. The interreinforcer interval value is themedian of the last 300 intervals.

DISCUSSIONExperiment 2 compared performance on

FR and VI schedules, whereas Experiment 1

compared performance on FR and Fl sched-ules. Nevertheless, the salient results of the twoexperiments were quite similar. First, the func-tions relating average pause and average IRfTwere steeper for the FR schedules than forthe corresponding interval schedules (see Cross-man et al., 1974, for similar results). Secondly,the probability of a pause termination was

fairly constant over much of the IRfT forFR schedules, but usually increased continu-ously for the corresponding interval schedules.This difference occurred in Experiment 2 de-spite the fact that the FR and yoked-VIschedule arranged similar local densities ofreinforcement at different times since the lastreinforcer. It is possible, of course, that a

more exact yoking procedure than used herewould have yielded a closer correspondencebetween the pause distributions for the FRand yoked-VI schedules. However, the highdegree of similarity between the pause distri-butions for the Fl and yoked-VI schedulesmakes this possibility unlikely. Thus, the dif-

GENERAL DISCUSSION

The question addressed by these experimentsis whether FR schedules and Fl or VI sched-ules control the postreinforcement pause com-parably when these schedules generate similarIRfTs. Such an outcome would result if, forexample, time since the last reinforcer actedlike a stimulus to induce responding as afunction of (a) the relative frequency of rein-forcers previously associated with that timeand (b) the similarity (proximity) of that timeto other times previously associated with rein-forcers. The present data, however, along withthose reported previously by Crossman et al.(1974), suggest that FR schedules and Fl orVI schedules do not control pausing similarlyeven when the IRfTs are similar.The data are consistent with an alternative

account that emphasizes the time or responsecount remaining after the end of the pause.This variable could be viewed as a delay ofreinforcement that follows the transition frompausing to terminal responding or a response-cost per reinforcer variable. There is no con-sensus yet on how these variables control re-sponding and pausing. Precedent does exist forthe view (cf. Shull, 1979, for an extended dis-cussion) that increasing delays of reinforce-ment, or increasing response cost, decrease theprobability during any small time interval ofinitiating terminal responding-i.e., respond-ing directed toward the scheduled reinforcer(Staddon & Simmelhag, 1971). (This is one wayof stating that response strength is negativelyrelated to the delay of reinforcement, or theresponse cost per reinforcer, associated withthe response.) Thus, the duration of the pausewould represent the number of consecutivesmall intervals during which terminal respond-ing was not initiated, plus any additional timefollowing the initiation of terminal respond-ing until the first recorded terminal response.This latter time might include such activitiesas moving into position in front of the keyafter a commitment to peck.

Because of the probabilistic nature of theprocess, the number of consecutive small in-tervals without a transition to terminal be-

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havior would vary under constant scheduleconditions, and so pauses would vary. On theaverage, however, conditions that raise orlower the probability of initiating terminal be-havior at all pause times will correspondinglyshorten or lengthen the pause. As just men-tioned, the delay of reinforcement followingthe initiation of terminal behavior (or theamount of terminal responding during thatperiod) may be one such condition.Changing size of an FR schedule directly

alters the response count per reinforcer andindirectly alters the time that follows thetransition to terminal responding. Thus, therelation between the average postreinforce-ment pause and the FR size might be an in-stance of a more general relation betweendelay of reinforcement or response cost andthe probability of initiating terminal behav-ior. The pause distribution data from FRschedules provide additional support for thisview. With a ratio contingency the averageamount of time or work until reinforcementis the same regardless of pause time, and sothese variables cannot differentially reinforceresponding at different pause times. Thus, ifthe delay of reinforcement or amount of ter-minal responding is the primary controllingvariable, the initiation of terminal behaviorshould be independent of elapsed pause time.Except at the shortest pause time, the cumula-tive distributions for FR schedules (Figures 2and 5) show this expected independence: thefunctions are roughly linear over most of theobserved range. The period of rising probabil-ity over the shortest pause times might repre-sent time after the initiation of terminal be-havior until an effective key peck occurs.Data from response-initiated, fixed-interval

schedules (RIFI or chain FR one FI schedules)provide additional support. Since the FI doesnot begin until a specific response is madeafter the last reinforcer, the remaining timeafter the end of the postreinforcement pause isindependent of pause time, much as responsecount and remaining time is independent ofthe pause on FR schedules. It is significant,therefore, that the probability of terminatingthe pause on RIFI seems to be independentof pause time, except for an initial rise, ason FR schedules (Shull, 1979). Further, theaverage pause is an increasing function of theFl that begins after the end of the pause(Chung & Neuringer, 1967; Shull, 1970, 1979).

On FI schedules, as on FR schedules, someamount of time and behavior intervenes be-tween the end of the pause and contact withthe next reinforcer. This remaining time ofresponding could control the probability ofinitiating terminal behavior on Fl schedulesin much the same way as on FR and RIFIschedules. Unlike FR and RIFI schedules,however, time and work until reinforcementare decreasing functions of the pause on FIschedules, approaching zero when the pauseexceeds the Fl.Although this negative correlation compli-

cates the analysis of Fl schedules, two ap-proaches appear workable. The first is basedon the assumption that pause time acts as astimulus to differentially control the prob-ability of initiating terminal behavior becauseof past differential associations between pausetimes and the delays that followed. The sec-ond is based on the opposite assumption thatpast associations between pause times and thedelays that follow are ineffective in generat-ing differential control by elapsed pause time,but that the differing delays merely enter intoan equilibrium equation. We will present eachof these possibilities in turn.Of the two the first approach is the more

conventional (cf. Dews, 1962, 1970; Gibbon,1977). The idea, simply, is that in the course ofadjusting to the Fl schedule the subject ini-tiates terminal responding at different pausetimes and experiences the different delays as-sociated with the different initiation times.Thus, if pause time is susceptible to differ-ential reinforcement, the probability of ini-tiating terminal behavior should increase asa function of pause time. The concave down-ward functions for FI (in Figure 2) andyoked-VI schedules (in Figure 5) show thatthe probability of initiating key pecking didincrease with pause time. Such an observationis consistent with this temporal discriminationaccount.That the average pause increased as a func-

tion of the FI is also consistent with thistemporal discrimination approach. Changingthe Fl would cause a corresponding changein the remaining time or responding followingany given pause time, and so the probabilityof initiating terminal behavior during anysmall interval during the pause should changeinversely with the Fl. The average pause, then,would vary directly with the FI. A more

73


exact prediction would require a more pre-cise description of the relation between delayand the probability of initiating terminal be-havior. If, for example, that relation is in-variant when all time intervals are expressedrelative to the Fl duration (cf. Dews, 1969;Gibbon, 1977; Killeen, 1975), the averagepause would vary as a constant proportion ofthe Fl. That the present pauses did not occupya constant proportion does not contradict thisaccount, but does imply that delay may notbe described as merely a proportion of the Fl.The second account of Fl pausing is also

able to accommodate the available data. Thebasic idea is that previously experienced delaysof reinforcement following the initiation ofterminal behavior establish a probability ofinitiating terminal behavior that is indepen-dent of pause time. Differential associationsbetween pause times and the remaining delaysuntil reinforcement are not considered toestablish a temporal discrimination based onelapsed pause time.To develop this approach it is necessary to

derive an equilibrium solution since the pre-viously experienced delays on Fl schedules aredetermined jointly by the FI duration and bythe duration of previous pauses. In words,when pauses are longer than the equilibriumvalue, the ensuing short delays will uniformlyraise the probability of initiating terminal be-havior, and so will cause the average pause toshorten. Correspondingly, if the pauses areshorter than the equilibrium value, the ensu-ing long delays will lower the probability ofinitiating terminal behavior and so will causethe average pause to lengthen. When pausesequal the equilibrium value, the ensuing de-lays will generate a probability level that will,on the average, generate the same pause dura-tions again. We say "on the average" becausethe assumed probabilistic nature of the processwill generate variability.With some simplifying assumptions, an il-

lustrative symbolic expression for the equilib-rium value can be developed.

1. The probability of initiating terminalbehavior during any small subinterval is pro-portional to the reciprocal of previously ex-perienced delays-until-reinforcement followingthe initiation of terminal behavior. The no-tion that reward value or response strengthis reciprocally related to the delay of reinforce-ment seems a reasonable first approximation

(Chung & Herrnstein, 1967; Baum & Rachlin,1969). Symbolically,

p=a De

where p is the probability of initiating termi-nal behavior during any small subinterval, Derepresents previously experienced delays, anda is a proportionality constant.

2. Since the probability of initiating termi-nal behavior is assumed to be independent ofpause time,

t tP = -= -D6 = dDp ae (1)

where P is the average pause, t is the durationof the small subinterval over which the prob-ability is determined, and b is the ratio of thetwo constants, t and a. The linear relationbetween pause and previously experienced de-lays, implied by this expression is almost cer-tainly an oversimplification, but is at leastqualitatively consistent with data from re-sponse-initiated Fl schedules (Chung 8c Neu-ringer, 1967; Shull, 1970).

3. For Fl schedules previously experienceddelays are the times remaining after the endof the pause, so that when the pause is lessthan or equal to the Fl duration,

De = I- P

where I is the Fl and Pe is the duration ofprevious pauses.

4. At equilibrium previous pauses generatedelays that maintain the same average pauseagain so that P = Pe. Thus, substituting intoequation 1 and solving for P gives the equilib-rium value thusly,

P = b(I-Pe)and at equilibrium,

P = b(I - P)

solving for P,b

P b+ 1I

This equilibrium solution shows the pause tovary proportionally with the Fl, or the inter-reinforcer interval, even though the control-ling variable was assumed to be the absoluteduration of previously experienced delays fol-lowing the initiation of terminal behavior.While the temporal discrimination account re-

74

RATIO COMPARED TO INTERVAL SCHEDULES 75

lies on a Weber-law-like mechanism to render"relative time" as the effective stimulus di-mension, the second account is able to accountfor the relation between relative time andpausing by absolute duration of the delay.A major problem for this nontemporal dis-

crimination approach is to reconcile the as-sumption of independence between initiationprobability and pause time with the obviouslyincreasing functions relating key peck prob-ability with pause time shown for Fl and VIschedules in Figures 2 and 5. One possible so-lution is based on the idea expressed earlierthat some time may intervene between theinitiation of terminal behavior and the firstrecorded terminal response. Recall the sugges-tion that the rising probability of a key peckover early pause times for FR schedules mightrepresent unmeasured terminal behavior time(that i.e., time from the initiation of terminalbehavior until an appropriately directed andsufficiently forceful key peck). Contingencies in-herent in FR schedules (and in response-ini-tiated FI schedules) could operate to keep thistime short; any time spent in unmeasured ter-minal behavior before key pecking lengthensthe terminal behavior time and terminal re-sponding per reinforcer. On Fl schedules, incontrast, as long as terminal behavior is ini-tiated well before the end of the FI, time spentin unmeasured terminal behavior before aneffective key peck has little effect on theamount of terminal behavior time or respond-ing per reinforcer. Consequently, this timecould reasonably be expected to be longer andmore variable. If so, this period of unmeasuredterminal behavior could produce the down-ward concavity in the cumulative distributions.If a sequence of unmeasured activities endswith a measured response, the probability ofobserving the measured response may increasewith time even if the probability of terminat-ing each member of the sequence is indepen-dent of time (McGill, 1963; McGill & Gibbon,1965). That running rates are higher on FRthan Fl schedules (cf. Figures 3 and 6) is gen-erally consistent with the idea that FR sched-ules more strongly select measured over un-measured terminal behavior than Fl schedules.

REFERENCESBaum, W. M., & Rachlin, H. Choice as time alloca-

tion. Journal of the Experimental Analysis of Be-havior, 1969, 12, 861-874.

Berryman, R., & Nevin, J. A. Interlocking schedules ofreinforcement. Journal of the Experimental Analysisof Behavior, 1962, 5, 213-223.

Catania, A. C., & Reynolds, G. S. A quantitative analy-sis of responding maintained by interval schedulesof reinforcement. Journal of the Experimental Anal-ysis of Behavior, 1968, 11, 327-383.

Chung, S. H., & Herrnstein, R. J. Choice and delay ofreinforcement. Journal of the Experimental Analysisof Behavior, 1967, 10, 67-74.

Chung, S. H., & Neuringer, A. J. Control of respondingby a percentage reinforcement schedule. Psycho-nomic Science, 1967, 8, 25-26.

Crossman, H. K., Heaps, R. S., Nunes, D. L., & Alferink,L. A. The effects of number of responses on pauselength with temporal variables controlled. Jour-nal of the Experimental Analysis of Behavior, 1974,22, 115-120.

Dews, P. B. The effect of multiple SA periods on re-sponding on a fixed-interval schedule. Journal ofthe Experimental Analysis of Behavior, 1962, 5,369-374.

Dews, P. B. Studies on responding under fixed-intervalschedules of reinforcement: The effects on the pat-tern of responding of changes on requirements atreinforcement. Journal of the Experimental Analy-sis of Behavior, 1969, 12, 191-199.

Dews, P. B. The theory of fixed-interval responding.In W. N. Schoenfeld (Ed.), The theory of reinforce-inent schedules. New York: Appleton-Century-Crofts,1970.

Felton, M., & Lyon, D. 0. The post-reinforcementpause. Journal of the Experimental Analysis of Be-havior, 1966, 9, 131-134.

Gibbon, J. Scalar expectancy theory and Weber's Lawin animal timing. Psychological Review, 1977, 84,279-325.

Gollub, L. R. The relations among measures of per-formance of fixed-interval schedules. Journal of theExperimental Analysis of Behavior, 1964, 7, 337-343.

Killeen, P. Reinforcement frequency and contingencyas factors in fixed-ratio behavior. Journal of the Ex-perimental Analysis of Behavior, 1969, 12, 391-395.

Killeen, P. On the temporal control of behavior. Psy-chological Review, 1975, 82, 89-115.

Lowe, C. F., Harzem, P., & Spencer, P. T. Temporalcontrol of behavior and the power law. Journal ofthe Experimental Analysis of Behavior, 1979, 31,333-343.

McGill, W. J. Stochastic latency mechanisms. In R. D.Luce, R. R. Bush, & E. Galanter (Eds.), Handbookof mathematical psychology (Vol. 1). New York:Wiley, 1963.

McGill, W. J., & Gibbon, J. The general-gamma dis-tribution and reaction times. Journal of Mathemati-cal Psychology, 1965, 2, 1-18.

Neuringer, A. J., & Schneider, B. A. Separating the ef-fects of interreinforcement time and number of in-terreinforcement responses. Journal of ExperimentalAnalysis of Behavior, 1968, 11, 661-667.

Nevin, J. A. The maintenance of behavior. In J. A.Nevin and G. S. Reynolds (Eds.), The study of be-havior: Learning, motivation, emotion, and instinct.Glenview, Ill.: Scott, Foresman, 1973.

Nevin, J. A., & Shettleworth, S. J. An analysis of con-

76 GEORGE W. CAPEHART et al.

trast effects in multiple schedules. Journal of theExperimental Analysis of Behavior, 1966, 9, 305-315.

Powell, R. The effect of small sequential changes infixed-ratio size upon the post-reinforcement pause.Journal of the Experimental Analysis of Behavior,1968, 11, 589-593.

Schneider, B. A. A two-state analysis of fixed-intervalresponding in the pigeon. Journal of the Experimen-tal Analysis of Behavior, 1969, 12, 667-687.

Shull, R. L. A response-initiated fixed-interval sched-ule of reinforcement. Journal of the ExperimentalAnalysis of Behavior, 1970, 13, 13-15.

Shull, R. L. Sequential patterns in post-reinforcementpauses on fixed-interval schedules of food. Journal ofthe Experimental Analysis of Behavior, 1971, 15,221-231.

Shull, R. L. The postreinforcement pause: Some im-plications for the correlational law of effect. InM. D. Zeiler & P. D. Harzem (Eds.), Advances inanalysis of behaviour, Vol. 1: Reinforcement and the

organization of behaviour. Chichester, England: Wi-ley, 1979.

Shull, R. L., & Brownstein, A. J. The relative proxim-ity principle and the postreinforcement pause. Bul-letin of the Psychonomic Society, 1975, 5, 129-131.

Shull, R. L., & Guilkey, M. Food deliveries during thepause of fixed-interval schedules. Journal of theExperimental Analysis of Behavior, 1976, 26, 415-423.

Shull, R. L., Guilkey, M., & Witty, W. Changing theresponse unit from a single peck to a fixed numberof pecks in fixed-interval schedules. Journal of theExperimental Analysis of Behavior, 1972, 17, 193-200.

Staddon, J. E. R., & Simmelhag, V. L. The "supersti-tion" experiment: A reexamination of its implica-tions for the principles of adaptive behavior. Psy-chological Review, 1971, 78, 3-43.

Received March 22,1979Final acceptance November 16, 1979

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