JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

PAUSING UNDER VARIABLE-RATIO SCHEDULES:INTERACTION OF REINFORCER MAGNITUDE,VARIABLE-RATIO SIZE, AND LOWEST RATIO

HENRY SCHLINGER, ELBERT BLAKELY, AND THOMAS KACZOR

WESTERN MICHIGAN UNIVERSITY

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-saccess to grain. Postreinforcement pausing and the rates of responding following the pause (run rates)in each component were measured as a function of variable-ratio size and the size of the lowest ratioin the configuration of ratios comprising each schedule. In one group of subjects, variable-ratio sizewas varied while the size of the lowest ratio was held constant. In a second group, the size of thelowest ratio was varied while variable-ratio size was held constant. For all subjects, the mean durationof postreinforcement pausing increased in the 2-s component but not in the 8-s component. Postrein-forcement pauses increased with increases in variable-ratio size (Group 1) and with increases in thelowest ratio (Group 2). In both groups, run rates were slightly higher in the 8-s component than inthe 2-s component. Run rates decreased slightly as variable-ratio size increased, but were unaffectedby increases in the size of the lowest ratio. These results suggest that variable-ratio size, the size ofthe lowest ratio, and reinforcer magnitude interact to determine the duration of postreinforcementpauses.Key words: postreinforcement pause, variable-ratio schedule, lowest ratio, reinforcer magnitude, run

rate, key peck, pigeons

Research on postreinforcement pauses(PRPs) under fixed-ratio (FR) schedules hasshown that PRPs are directly related to FRsize (e.g., Felton & Lyon, 1966) and inverselyrelated to reinforcer magnitude (e.g., Powell,1969) and food deprivation (Sidman & Steb-bins, 1954). Moreover, the effects of FR sizeand reinforcer magnitude have been shown tointeract. Powell (1969) exposed pigeons to FRschedules of different sizes that programmed2.5-s and 4-s access to grain. The resultsshowed that PRPs increased more rapidly withFR size when 2.5 s of grain was programmedthan when 4 s of grain was available.

Studies have shown that PRPs undervariable-ratio (VR) schedules are also a func-tion of ratio size and reinforcer magnitude (e.g.,Blakely & Schlinger, 1988; Priddle-Higson,Lowe, & Harzem, 1976). Using pigeons,Blakely and Schlinger demonstrated thatbriefer access to mixed grain produced in-creases in PRPs as VR size increased. Priddle-Higson et al. showed with rats that higherconcentrations of a milk solution increasedPRPs as VR size increased. In these studies,VR size varied together with the size of thelowest ratio in the distribution of ratios com-

Correspondence and requests for reprints should be ad-dressed to Henry Schlinger, Department of Psychology,Western New England College, Springfield, Massachu-setts 011 19.

prising each VR schedule. (VR schedules arecomposed of a sequence of ratios in an irreg-ular order.) Thus, it was unclear whether theeffects were due to increases in VR size, in-creases in the lowest ratio, or some combina-tion of the two variables. Results from theBlakely and Schlinger study suggested that thelowest ratio can affect PRPs. Postreinforce-ment pausing under VR 70 schedules wasmeasured as a function of reinforcer magni-tude. When the distribution of individual ra-tios included a ratio of one, PRPs were briefand unaffected by reinforcer magnitude. Whenthe distribution did not include a ratio of one(the lowest ratio was seven), PRPs increased,as did the differences in PRPs due to differ-ences in reinforcer magnitude. Although it ap-peared that changes in the lowest ratio wereresponsible for the effects, the conclusion wastentative because the other ratio values in theVR distributions were not identical and couldhave contributed to the effect. Thus, the extentto which the effects of reinforcer magnitudeon PRPs depends on VR size, the size of thelowest ratio, or some combination of the twois unknown.The present study was carried out to inves-

tigate the role of these previously confoundedvariables and to replicate prior work (e.g.,Blakely & Schlinger, 1988). The effects onPRPs of reinforcer magnitude were evaluatedin two groups. In Group 1, VR size was varied

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Table 1The individual ratios of each schedule for Groups 1 and 2.

Schedule Individual ratios

Group 1VR 20 10 12 14 16 18 22 24 26 28 30VR 50 10 18 24 34 44 54 64 74 84 94VR 80 10 24 40 56 72 88 104 120 136 150VR 110 10 33 55 77 99 121 143 165 187 210

Group 2VR 30 1 14 18 23 27 31 36 42 47 61VR 30 4 14 18 23 27 31 36 42 47 58VR 30 7 14 18 23 27 31 36 42 47 55VR 30 10 14 18 23 27 31 36 42 47 52

while the lowest ratio was held constant. InGroup 2, the size of the lowest ratio was variedwhile VR size was held constant. In additionto PRPs, run rates (the rates of respondingfollowing the PRP) were collected to providea more complete profile of the interaction ofreinforcer magnitude, VR size, and the size ofthe lowest ratio.

METHOD

SubjectsSix female White Carneau pigeons served

as subjects. Birds were maintained at approx-imately 80% of their free-feeding weights andwere individually housed with unlimited ac-cess to water and grit in a constantly illumi-nated room. Both groups comprised 3 birdseach (P5 10, P20, and P5 in Group 1 andP3005, P137, and P99 in Group 2). All birdshad previous exposure to VR schedules.Apparatus

Sessions were conducted in three three-keychambers measuring 38 cm high, 41 cm wide,and 40 cm long. Only the right key (BRS/LVE) on the intelligence panel of each cham-ber was used. The key, which could be trans-illuminated red or green by an IEE projector,was 11 cm from the side wall and 25 cm abovethe floor and could be operated with a forceof 0.2 N. A 6-cm by 6-cm aperture, centeredon the front wall 10 cm from the floor, per-mitted feeding from the grain hopper. Whenraised, the hopper was illuminated with a 7-Wbulb and provided access to mixed grain. Thekeylight was not illuminated when access tograin was available. Ambient illumination was

provided by a 7-W houselight centrally locatedon the ceiling of each chamber. A Grason-Stadler white noise generator (Model 901 B)provided masking noise through a speakermounted on the back wall of each chamber.An exhaust fan mounted behind the intelli-gence panel ventilated each chamber. A PDP-8A® minicomputer (Digital Equipment Cor-poration), equipped with SUPERSKED®software (State Systems, Inc.) and relay inter-facing, scheduled experimental events and col-lected data.

ProcedureBirds were exposed to multiple (mult) VR

VR schedules in which the VR values in thetwo components were always equal. Either 2-sor 8-s access to grain was available in eachcomponent. Within each experimental condi-tion, the keylight was red during one of thecomponents and green during the other. TheVR schedules were composed of 10 individualratios presented in random order within blocksof 10 reinforcers. The initial schedule com-ponent of each session was also determined atrandom. Thereafter, components alternatedafter every 10 reinforcers, and sessions ter-minated after two exposures to each compo-nent (i.e., 40 trials).

Subjects in Group 1 were exposed to multVR 20 VR 20, mult VR 50 VR 50, mult VR80 VR 80, and mult VR 110 VR 110 sched-ules. The lowest ratio was always 10. Theindividual ratios of each VR schedule approx-imated an arithmetic progression (see Table1); some individual ratios were adjusted to givethe appropriate VR size. Each bird receivedall mult schedules in a different order acrossconditions. The key color correlated with 2-s

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access to grain, which was unchanged acrossconditions, was red for 1 bird (P5 10) and greenfor the other 2 (P20 and P5).

Birds in Group 2 were exposed to four multVR 30 VR 30 schedules. In one mult VR 30VR 30 schedule, the lowest ratio in both sched-ule components was 1; in the other three multschedules, the lowest ratios were 4, 7, and 10,respectively. Each distribution of individualratios approximated an arithmetic progression(see Table 1), although the largest ratio wasadjusted such that the VR size was always 30.Each bird was exposed to all four mult sched-ules in a different order; thus, the size of thelowest ratio was varied across conditions. Thekey color associated with 2-s access to grainwas red for Bird P137 and green for BirdsP3005 and P99.

In both groups, mean PRPs and run rates(PRP and reinforcer durations were excludedfrom run times) were recorded in each sched-ule component. Conditions for both groupswere changed after a minimum of 10 sessionswith no visible trend in PRPs over the last fivesessions.

RESULTSFigure 1 shows mean PRPs under both

components for all birds in Group 1 (leftpanels) and Group 2 (right panels). In general,PRPs in the 2-s reinforcer component in-creased systematically with VR size for sub-jects in Group 1. For Subject P5, mean PRPswere higher in the VR 50 condition than inthe VR80 or VR 110 conditions. When theyoccurred, increases in PRPs in the 8-s com-ponent were smaller. For subjects in Group 2,PRPs in the 2-s component increased as thesize of the lowest ratio increased. The largestincrease occurred generally between the firsttwo conditions. No consistent increases in PRPsoccurred in the 8-s reinforcer component.

Figure 2 shows mean run rates under eachcomponent for all birds in Group 1 (left panels)and Group 2 (right panels). For subjects inGroup 1, run rates were higher in the com-ponent with 8-s reinforcer for all birds exceptP510 under the VR 20 condition. In general,run rates decreased slightly with increases inVR size under both components, although thiseffect was greater for the 2-s than for the 8-scomponent. No consistent differences in runrates due to increases in the lowest ratio were

observed for subjects in Group 2, although runrates were generally higher in the componentwith the 8-s reinforcer.

DISCUSSIONResults showed that the duration of PRPs

was inversely related to reinforcer magnitude.These findings are consistent with previousinvestigations of pigeons responding under FRschedules (Powell, 1969) and VR schedules(Blakely & Schlinger, 1988). In Group 1, dif-ferences in PRPs produced by different rein-forcer magnitudes increased with VR size.These differences resulted largely from in-creases in PRPs in the 2-s reinforcer compo-nent. Similar effects of varying VR size werereported in previous research with pigeons(Blakely & Schlinger, 1988) and rats (Priddle-Higson et al., 1976), although in these studiesVR size and the size of the lowest ratio variedin the same direction. In Group 2, VR sizedid not vary and differences in PRPs as afunction of reinforcer magnitude became largerwith increases in the lowest ratio. Again, thesedifferences resulted primarily from increasesin PRPs in the 2-s reinforcer component.Hence, the results of Groups 1 and 2 suggestthat VR size and the size of the lowest ratiocan interact independently with reinforcermagnitude to determine PRPs, and that thechanges in PRPs reported in previous research(e.g., Blakely & Schlinger, 1988; Priddle-Hig-son et al., 1976) were likely due to both vari-ables.The present results and those of previous

work on VR schedules (e.g., Blakely & Schlin-ger, 1988; Priddle-Higson et al., 1976) maybe understood in terms of Mazur's (1982) mo-lecular analysis of performance under ratioschedules. Mazur suggested that the momen-tary probability of responding under ratioschedules is determined by a subject's prox-imity in time to the next reinforcer. With ratioschedules, proximity to a reinforcer is tanta-mount to the number of responses remainingto that reinforcer. In particular, the probabilityof responding should be inversely related toreinforcer proximity, and the duration of PRPsshould therefore be directly related to reinforc-er proximity.

In Group 1, reinforcer proximity (i.e., thenumber of responses remaining to the nextreinforcer) was varied for all individual ratios

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HENRY SCHLINGER et al.

except the lowest (see Table 1). Thus, thenumber of responses remaining to the nextreinforcer after any given response increasedas VR size increased from VR 20 to VR 110.Reinforcer proximity was manipulated inGroup 2 by varying the size of the lowest ratio.All other individual ratios (except the highest)were the same across conditions. Consistentwith predictions based on Mazur's (1982) for-mulation, the duration of PRPs in both groupswas directly related to variations in reinforcerproximity. The present results add to Mazur'sanalysis by showing that, with essentiallyequivalent VR schedules, increasing the sizeof the lowest ratio can increase the durationof PRPs. Mazur (1983) has also reported sim-ilar effects of manipulating the lowest ratio.When the initial FR component of a mixed-ratio (MR) schedule was relatively short (i.e.,FR 2, FR 4, or FR 8), PRPs were brief relativeto comparable FR schedules.

Mazur's analysis of ratio schedule perfor-mance may also help to explain observed dif-ferences in run rates. In Group 1, increases inVR size produced small, albeit systematic, de-creases in run rates (Figure 2, left panels),which is similar to other findings with ratioschedules (e.g., Mazur, 1983). In contrast, theresults from Group 2 showed no consistentrelation between run rates and the lowest ratio(Figure 2, right panels). In Group 1, prox-imity to reinforcement was varied only for re-sponses after Response 10. In fact, VR sizewas incremented by increasing the size of in-dividual ratios other than the lowest ratio (seeTable 1). According to Mazur's model, rein-forcer proximity not only affects the proba-bility of responding after the completion of aratio, but also the probability of respondingwithin a ratio run (Mazur, 1983). Thus, wemay assume that observed decreases in runrates in Group 1 were due to increases inwithin-ratio pausing produced by varying in-dividual ratios in the VR configuration. InGroup 2, proximity to reinforcement did notgenerally vary for responses after Response 10and, consequently, run rates were unaffected.Although decreasing the lowest ratio decreasedrun rates in previous research (Blakely &Schlinger, 1988), no such effect was observedin the present study, perhaps because the rel-atively low VR size (i.e., VR 30) workedagainst long within-ratio pauses.These results as well as those from other

studies suggest that VR size and the size ofthe lowest ratio may interact. Postreinforce-ment pauses have been shown to increase withVR size when the lowest ratio was larger thanone (e.g., Group 1 of the present study; Prid-dle-Higson et al., 1976), but not when thelowest ratio was one (Crossman, Bonem, &Phelps, 1987; Ferster & Skinner, 1957). Takentogether, these findings suggest that when aVR schedule includes even a single ratio ofone, the effects of VR size on PRPs are atten-uated. Interestingly, the differential effects ofunequal reinforcer magnitudes were also at-tenuated under VR schedules with a lowestratio of one (e.g., Group 2 of the present study;Blakely & Schlinger, 1988). Therefore, theeffects of both VR size and reinforcer mag-nitude on PRPs appear to depend on the sizeof the lowest ratio. Whether the effects of thelowest ratio also depend on VR size is as yetunknown.The present results do show, however, that

the effects of VR size and the size of the lowestratio depend on reinforcer magnitude. Recallthat PRPs in the 2-s reinforcer componentwere more sensitive than those in the 8-s com-ponent to increases in both VR size and thesize of the lowest ratio. Specifically, varyingVR size (Group 1) and the size of the lowestratio (Group 2) systematically increased PRPduration only in the 2-s reinforcer component.Similar differences have also been observed inprevious research with pigeons responding un-der VR schedules (Blakely & Schlinger, 1988)and FR schedules (Powell, 1969). Thus, itseems that the effects on PRPs of such pow-erful variables as VR size and the size of thelowest ratio may be either potentiated or at-tenuated by varying reinforcer magnitude.

In conclusion, the present results show thatthe duration of PRPs under VR schedules de-pends not only on VR size, but also on the sizeof the lowest ratio, both of which are manip-ulated by varying different aspects of reinforc-er proximity. That the size of the lowest ratiois a factor has implications for PRPs underother ratio schedules that require a variablenumber of responses. For example, Mazur(1983) showed that PRPs were relatively in-sensitive to random-ratio (RR) size where ra-tios of one are always possible, although theirdensity probably decreases as responses perreinforcer increases. The occasional ratio ofone may account for PRP insensitivity to RR

PAUSING UNDER VARIABLE-RATIO SCHEDULES 139

size. Moreover, quantitative comparisons ofPRPs under FR schedules with those that re-quire a variable number of responses (i.e., MR,RR, and VR schedules) must consider the sizeof the lowest ratio in the latter. If the size ofthe lowest ratio is small, PRPs may be briefand unaffected by average ratio size, and PRPswill differ considerably from those under FRschedules. If the size of the lowest ratio varieswith average ratio size, both variables maycombine to increase PRPs, which will there-fore resemble those under FR schedules.Studying the interaction of average ratio sizeand the size of the lowest ratio should providea more complete profile of the quantitativeinteraction of the two variables and permitmore accurate predictions of PRPs under var-ious schedules.

REFERENCESBlakely, E., & Schlinger, H. (1988). Determinants of

pausing under variable-ratio schedules: Reinforcermagnitude, ratio size, and schedule configuration. Jour-nal of the Experimental Analysis of Behavior, 50, 65-73.

Crossman, E. K., Bonem, E. J., & Phelps, B. J. (1987).

A comparison of response patterns on fixed-, variable-,and random-ratio schedules. Journal ofthe ExperimentalAnalysis of Behavior, 48, 395-406.

Felton, M., & Lyon, D. 0. (1966). The post-reinforce-ment pause. Journal of the Experimental Analysis of Be-havior, 9, 131-134.

Ferster, C. B., & Skinner, B. F. (1957). Schedules ofreinforcement. New York: Appleton-Century-Crofts.

Mazur, J. E. (1982). A molecular approach to ratioschedule performance. In M. L. Commons, R. J.Herrnstein, & H. Rachlin (Eds.), Quantitative analysesof behavior: Vol. 2. Matching and maximizing accounts(pp. 79-110). Cambridge, MA: Ballinger.

Mazur, J. E. (1983). Steady-state performance on fixed-,mixed-, and random-ratio schedules. Journal of the Ex-perimental Analysis of Behavior, 39, 293-307.

Powell, R. W. (1969). The effect of reinforcement mag-nitude upon responding under fixed-ratio schedules.Journal of the Experimental Analysis of Behavior, 12,605-608.

Priddle-Higson, P. J., Lowe, C. F., & Harzem, P. (1976).Aftereffects of reinforcement on variable-ratio sched-ules. Journal of the Experimental Analysis of Behavior,25, 347-354.

Sidman, M., & Stebbins, W. C. (1954). Satiation effectsunder fixed-ratio schedules of reinforcement. Journalof Comparative and Physiological Psychology, 47, 114-116.

Received October 18, 1988Final acceptance June 13, 1989