CHOICE BETWEEN CONCURRENT SCHEDULES' RONALD L. MENLOVE2, MARILYNNE MOFFITT, AND CHARLES P. SHIMP

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1 JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 1973, 19, NUMBER 2 (MARCH) CHOICE BETWEEN CONCURRENT SCHEDULES' RONALD L. MENLOVE2, MARILYNNE MOFFITT, AND CHARLES P. SHIMP UNIVERSITY OF UTAH Six pigeons pecked for food in three-key experiment. A subject t ny time could choose the left or right key nd receive reinforcement ccording to one to-key concurrent vrible-intervl vrible-intervl schedule of reinforcement, or it could peck the center key. A peck on the center key rrnged the complementry to-key concurrent vrible-intervl vrible-intervl schedule on the left nd right keys. The to different to-key concurrent schedules rrnged reinforcements concurrently nd ere signlled by to different colors of key lights. Choice behvior in the presence of given color conformed to the usul reltionship in to-key concurrent schedules: the reltive frequency of responding on key pproximtely equlled the reltive frequency of reinforcement on tht key. Preference for to-key concurrent schedule, hich s equivlent to preference for color, s mesured by the percentge of ll responses on the left nd right keys in the presence of tht color: this percentge pproximtely equlled the percentge of ll reinforcements tht ere delivered in the presence of tht color. Thus, choice beteen concurrent schedules conforms pproximtely to the sme reltionship s does choice beteen lterntives in single concurrent schedule. A pigeon chooses beteen the to lterntives in to-key concurrent vrible-intervl vrible-intervl (conc VI VI) schedule in such fshion tht the reltive frequency of responses on key tends to equl the reltive frequency of reinforcement for responses on tht key (Herrnstein, 1961). An experimentl prdigm for the study of choice behvior in more complex concurrent schedules is concurrent schedule, ech component of hich is itself concurrent schedule. Behvior in such complex concurrent schedule s described by Shimp (1971), ho rrnged one-key concurrent schedule of reinforcement for to clsses of interresponse times on ech of to keys. Thus, there ere four clsses of opernts: shorter nd longer interresponse times on the left nd right keys. It s found tht the reltive frequency of responses on key pproximtely equlled the reltive frequency of reinforcement for responses on tht key. Choice of key s equiv- 'This reserch s supported in prt by NIMH grnt nd by Reserch Felloship rded to Mrilynne Moffitt by the University Reserch Committee of the University of Uth. Reprints my be obtined from C. Shimp, Center for Advnced Study in the Behviorl Sciences, 22 Junipero Serr Blvd., Stnford, Cliforni 'No t the University of Delre. lent to choice of concurrent schedule (of reinforcement for to clsses of interresponse times). Therefore, the mtching behvior obtined there shoed tht in one prticulr context, choice beteen concurrent schedules obeyed the sme reltionship s does choice beteen the to lterntives ithin conventionl to-key concurrent schedule. In ddition, interresponse times ere distributed ithin prticulr concurrent schedule of reinforcement for to interresponse times in the sme y s they ould hve been hd there not lso been second concurrent schedule of reinforcement for to interresponse times rrnged concurrently. Thus, in the context of tht experiment, behvior in one concurrent schedule s not ffected by the presence of second concurrent schedule rrnged concurrently. The present experiment further investigted the nture of behvior controlled by compound concurrent schedules of reinforcement in hich ech component is itself concurrent schedule. Here, there ere to to-key concurrent schedules of reinforcement insted of to one-key concurrent schedules of reinforcement for to clsses of interresponse times. At ny time, one of the to to-key concurrent schedules of reinforcement s rrnged on the left nd right keys of three- 331

2 332 RONALD L. MENLOVE et l. key experimentl chmber. Responding on center key rrnged the other to-key concurrent schedule on the left nd right keys. The to different to-key concurrent schedules of reinforcement ere signlled by to different colors of keylights nd ere complementry in the sense tht if the probbility of reinforcement on the left key s p in the presence of red, it s 1-p in the presence of green. To questions ere sked corresponding to the to results obtined by Shimp (1971). First, re choices distributed beteen the to tokey concurrent schedules in the sme y s choices re distributed beteen the to lterntives of single to-key concurrent schedule? Second, re choices distributed beteen keys in single to-key concurrent schedule s they ould be if there ere not second to-key concurrent schedule rrnged concurrently? METHOD Subjects Six mle White Crneux pigeons ere mintined t pproximtely 8%7o of their free-feeding body eights. Three of the six pigeons (Subjects 4, 5, nd 6) ere experimentlly nive: the others (Subjects 1, 2, nd 3) hd served in n experiment on probbilistic discrimintion lerning tht tised tilted lines for stimuli (Shimp, 1973). Apprtus The experimentl chmber s Lehigl Vlley Electronics three-key pigeon chmber. Colors nd vrious tilted lines could be mde to pper on ech trnslucent key. Electromechnicl rely equipment, including punched-pper tpe reder, rrnged the stimuli nd reinforcements nd counted responses. The punched-pper tpes ere generted on PDP 12 lbortory computer. Procedure Reinforcements ere rrnged for pecks on the left nd right keys by single VI schedule tht determined the distribution of interreinforcement intervls nd by rndom mechnism tht ssigned ech reinforcement to one of four different clsses of responses: peck on the left or right key hen ll the keys ere red nd peck on the left or right key hen ll the keys ere green. A peck on the center key chnged the color of ll three keys nd complemented, i.e., reversed, the probbilities of reinforcement on the left nd right keys. For exmple, if ll three keys ere red nd the reltive frequencies of reinforcement ere.8 nd.2 on the left nd right keys, respectively, peck on the center key chnged the color of the keys to green nd chnged the probbilities of reinforcement on the left nd right keys to.2 nd.8, respectively. A horizontl line nd verticl line ere superimposed on red or green on the center key to further discriminte the center key from the side keys. The center key in the present experiment s nlogous to the sitching key in procedure used by Findley (1958). In the Findley procedure, either one of to VI schedules of reinforcement s rrnged t ny moment on single min key nd bird could sitch beteen the to schedules (ech signlled by different color) by responding on second, or sitching key. In the present experiment, one of to to-key conc VI VI schedules s rrnged t ny moment on the side keys nd bird could sitch beteen the to to-key conc VI VI schedules (ech signlled by different color) by responding on the center key. VI schedule. The distribution of interreinforcement intervls s rrnged by single, constnt-probbility, VI schedule. The constnt probbility tht reinforcement ould be rrnged s.2 every 3 sec so tht the verge scheduled interreinforcement intervl s 15 sec. Ordinrily, hen reinforcement is rrnged by finite punclhed tpe, the probbility of rrnging reinforcement depends on the time since the lst reinforcement, even in constnt-probbility, VI schedule. In suclh cses, the probbility of ssigning reinforcement equls 1. t some mximum post-reinforcement time. Here, this difficulty s voided by progrmming the schedule ith n electronic timer nd Bernoulli-trils genertor (see Shimp nd Whetley, 1971). Once the VI schedule rrnged reinforcement, the electronic timer stopped. The reinforcementselection mechnism described belo s employed just once for every interreinforcement intervl rrnged by the VI schedule. Reinforcement-selection mechnism. At the beginning of session nd fter every reinforcement, reinforcement-selection mechnism determined to hiclh one of the four re-

3 CHOICE BETWEEN CONCURRENT SCHEDULES 333 sponse clsses the next reinforcement ould be ssigned. Once the next reinforcement s ssigned to prticulr response clss, reinforcements could not be ssigned to ny other clss until the VI schedule rrnged reinforcement, the orgnism emitted response belonging to the pproprite clss, nd reinforcement s collected. The schedule of reinforcement used here my be vieed s vrition of schedule in hich reinforcements re rrnged by single VI schedule nd rndom selection mechnism tht probbilisticlly ssigns ech reinforcement to one of four response lterntives. This procedure s used by Shimp (1971) hen he rrnged concurrent schedule of reinforcement for to interresponse times on ech of to keys. Hoever, disdvntge of this procedure is tht the obtined reltive frequency of reinforcement for response lterntive often devites from the progrmmed probbility of reinforcement for tht response lterntive. Therefore, this generl procedure to rrnge reinforcements s modified here so tht the obtined reltive frequency of reinforcement for ech response clss exctly equlled the progrmmed probbility of reinforcement for tht response clss. There ere 1 reinforcements in ech dy's session. Ech reinforcement s ssigned to one of the four clsses of reinforced responses by punched-pper tpe contining sequence of codes tht determined hich response clss ould be reinforced on ech of the 1 trils. For ech session, there s different tpe for ech of the six birds. Ho these tpes ere generted by the computer is conceptully identicl to the folloing method. Consider n urn contining 1 blls, ech mrked "red-left", "red-right", "greenleft", or "green-right". Thus, ech bll corresponded to one of the four clsses of reinforced responses. The proportion of blls of ech type exctly equlled the desired proportion of reinforcements for the corresponding clss of responses. A bll s rndomly selected from the urn, nd its corresponding response clss s noted. This response clss then occupied the first loction in sequence of 1. Then, second bll s rndomly selected from the remining 99 blls nd this response clss then occupied the second loction in the sequence of 1. Smpling s "ithout replcement": selected bll s not returned to the urn nd so could not be resmpled. This process continued until ll 1 blls ere selected nd sequence of length 1 s obtined. Finlly, the sequence of reinforcements for the four response clsses s rerrnged. The contents of loctions 1, 11, 21,..., 91, 2, 12, 22,..., 92, 3, 13, 23,..., 1 of the originl list ere plced in loctions 1, 2, 3,..., 1 in the second list. After ll 1 ssigned reinforcements ere rerrnged in the second list, they ere punched out on pper tpe. In summry, ech punched tpe contined the exct desired proportions for ech of the four ctegories, yet the sequence of reinforcing events presumbly ppered to pigeon to be rndom sequence. Chngeover delys. There ere to different dely contingencies in effect. Ech s 1 sec in durtion. The first contingency s for response on one side key fter response on the other side key. Such response is defined here s chngeover response. The second dely contingency s for response on side key folloing response on the center key, hich is defined here s sitching response. The chngeover dely procedure s the sme s tht often used in to-key conc VI VI schedules of reinforcement (e.g., see Herrnstein, 1961). In the present experiment, chngeover, tht is the first response on side key fter response on the other side key, strted 1-sec chngeover dely. A subsequent response on the sme key s folloed by reinforcement, provided tht the 1-sec chngeover dely hd timed out nd provided tht reinforcement s vilble for tht prticulr response clss. Therefore, response on one of the to side keys could not be reinforced if tht response folloed response on the other side key. The chngeover-dely procedure prevented the reinforcement of chngeovers nd seprted responses on one side key in the presence of given color from reinforcements rrnged for responses on the other side key in the presence of the sme color. The dely procedure initited by sitching response s the sme s tht used in the kind of concurrent schedule developed by Findley (1958). A sitching response, tht is peck on the center key, strted 1-sec dely. A subsequent response on side key s reinforced provided the I-sec sitching dely hd timed out nd provided reinforcement s vilble for tht prticulr response clss.

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6 336 RONALD L. MENLOVE et l. Notice tht the first response on side key fter sitching response could be reinforced. This procedure seprted sitching responses from reinforcements for side-key responses. It lso seprted responses in the presence of one color from reinforcements for responses in the presence of the other color. Experimentl conditions. Tble 1 provides to types of informtion bout the experimentl conditions: the probbilities of reinforcement for responses in the presence of red keys nd in the presence of green keys (columns 3 nd 4) nd the probbilities of reinforcement for responses on the left key in the presence of either red or green keys (columns 1 nd 2). (Note tht for given bird in given condition, columns 1 nd 2 sum to unity, nd columns 3 nd 4 lso sum to unity.) As shon in Tble 1, Condition 1 s the sme for ll six birds; hoever, Conditions 2 through 8 for Birds 1, 2, nd 3 ere different from Conditions 2 through 8 for Birds 4, 5, nd 6. The purpose of hving different sets of experimentl conditions for the to groups of birds s simply to enble the completion of the experiment in less time thn if ech bird hd experienced ech condition. The folloing is n exmple of ho the number of reinforcements for ech response clss my be obtined from the probbilities shon in Tble 1. For Bird 1 in Condition 2, the probbility of reinforcement for responses in the presence of red keys s.5 (see column 3). Therefore, 5 of the 1 reinforcements ere for responses on the left or right keys in the presence of red keys nd 5 of the 1 reinforcements ere for responses on the left or right keys in the presence of green keys. When the keys ere red, the probbility of reinforcement for responses on the left key s.2 (see column 1) nd the probbility of reinforcement for responses on the right key s 1. minus.2, or.8. Tht is, hen the keys ere red, 27% of the 5 reinforcements or 1 reinforcements, ere ssigned for responses on the left key nd 8% of the 5 reinforcements, or 4 reinforcements, ere ssigned for responses on the right key. Tble 1 shos tht in ny one condition, either the probbility of reinforcement for responses in the presence of red keys s equl to.5, or the probbility of reinforcement for responses on the left key in the presence of either color s equl to.5. Tht is, either columns 3 nd 4 re.5, or columns 1 nd 2 re.5. Other contingencies. A brief blckout of pproximtely.3 sec folloed ech response nd provided the pigeons ith visul response feedbck. Also, the houselight nd keylights ere drkened during reinforcement, hich consisted of 1.75-sec ccess to mixed grin. Summry nd discussion of procedure. At ny time, subject could respond on the left or right key nd receive reinforcement ccording to concurrent schedule in hich interreinforcement intervls ere rrnged by single VI schedule nd in hich reinforcements ere rrnged for responses on the left nd right keys in pseudo-rndom fshion. The sequence of reinforcements s restricted so tht the obtined reltive frequency of reinforcement for response clss equlled the corresponding progrmmed probbility of reinforcement. At ny time, subject lso could respond on the center key nd thereby rrnge concurrent schedule of reinforcement in hich the probbilities of reinforcement on the left nd right keys ere reversed. These to complementry concurrent schedules ere signlled by different colors. The method used here to rrnge to-key concurrent schedule is different from the older, trditionl method. According to trdition, conc VI VI schedule is rrnged by to seprte VI schedules. Ech runs until it ssigns reinforcement, then it lone stops until tht reinforcement is collected. Such schedule is different in number of ys from tht used here. First, the successive left-right positions of reinforcement in to-key concurrent schedule re independent ith the present method, heres there is no gurnteed independence hen to seprte VI schedules re used (see Moffitt nd Shimp, 1971). Second, the reltive frequency of reinforcement for n lterntive is experimentlly controlled ith the present method: unlike the usul rrngement, there is no dy-to-dy vrition in the obtined reltive frequency of reinforcement. Third, sitching responses re essentil ith the present method. Tht is, if n niml never sitched, it sooner or lter ould go into extinction. With the trditionl method of rrnging concurrent schedule, sitching is encourged becuse the probbility of reinforcement increses on one lterntive hile n orgnism responds on nother, but sitch-

7 CHOICE BETWEEN CONCURRENT SCHEDULES 337 ing is not essentil. Unfortuntely, sitching behvior mintined by the trditionl tokey concurrent sclhedule remins lrgely unknon, but sitching hs been described in gret detil for the method used in the present experiment (Menlove, 1972). The sclhedule used lhere is ppropritely clled, by nlogy ith otlher schedules of reinforcement (Anger, 1954; Slhimp, 1973b), kind of syntlhetic conc VI VI sclhedule, i.e., schedule of reinforcement for concuirrent responding tht duplictes some but not ll of the properties of conc VI VI sclhedule, nd in hich the reltive frequency of reinforcement for response clss is experimentlly controlled, rther thn dependent upon belhvior. Any of the differences beteen the to ys of rrnging concurrent schedule might produce differences in behvior. Hoever, vilble dt suggest the to methods re equivlent itlh regrd to the reltionship beteen I.c U..8 BIRD I * BIRD 2 x.6 the reltive frequency of responding in component nd such reinforcement prmeters s: the reltive frequency of reinforcement in tht component (compre Herrnstein, 1961, ith Menlove, 1972, Experiment III in Shimp, 1966, nd Stubbs nd Pliskoff, 1969), nd; the reltive immedicy of reinforcement in tht component (compre Chung nd Herrnstein, 1967, itlh Herbert, 197). Corresponding reltionships lso hold for one-key concurrent schedules rrnged botlh ys (compre Stddon, 1968, itlh Slhimp, 1968 nd Moffitt nd Shimp, 1971). Perlhps the to metlhods produce the sme reltionslhips becuse the mjor difference beteen them rises only hen subject persists in responding to one lterntive for reltively long time; only then do the to procedures differ drmticlly. Hoever, subjects on both kinds of concurrent schedule tend to sitch reltively often, i.e., every fe seconds, so tht the mjor difference beteen BIRD 3, clj.62 >- :.8 IRD 4 ; / BIRD e. z.f4 [i X / 31: D ~~~~ *,8 *./ ~~BIRD6/ I. ~ PROBABILITY OF REINFORCEMENT ON THE LEFT KEY WHEN THE KEYS WERE A PARTICULAR COLOR Fig. 1. Reltive frequency of responses on the left key hen the keys ere prticulr color plotted ginst the probbility of reinforcement for responses on the left key hen the keys ere tht color. For exmple, the frequency of responses on the left key hen the keys ere red divided by the totl frequency of responses on the left nd right keys hen the keys ere red plotted ginst the frequency of reinforcement for responses on the left key hen the keys ere red divided by the totl frequency of reinforcement for responses on the left nd right keys hen the keys ere red. Ech pnel shos the dt for n individul subject. Open circles represent dt obtined hen the keys ere red; dots represent dt obtined hen the keys ere green. The digonl line in ech pnel represents the mtching function.

8 338 RONALD L. MENLOVE et l. the methods my not come in contct ith behvior. In ny event, on the bsis of vilble dt, one my tenttively ssume tht the reltionships obtined in the present experiment beteen reltive responding nd reltive reinforcement ould be the sme if the to-key concurrent schedules ere rrnged by seprte VI schedules. The present procedure is equivlent to tht used by Shimp (1971) in terms of the extent to hich subject hd ccess to the four reinforced response clsses. In the present experiment, subject hd equl ccess to the to response clsses reinforced by the prticulr concurrent schedule momentrily rrnged for the responses on the left nd right keys, but subject could emit response belonging to one of the other to reinforced clsses only by first mking n intermedite sitching response on the center key. In the schedule used by Shimp (1971), there s concurrent schedule of reinforcement for to interresponse times rrnged on eclh of to keys. The choice of key in tht schedule s choice of concurrent schedule nd s conceptully equivlent to the sitclhing response in the present experiment. In prticulr, in the erlier experiments, subject t ny time hd equl ccess to the to clsses of responses (interresponse times) reinforced on prticulr key, i.e., the next response could terminte either shorter or longer interresponse time on tht key, but the subject could terminte n interresponse time belonging to one of the other to reinforced response clsses only by mking n intermedite sitching response on the other key. This sitching response initited n interresponse time on the other key, hich then could terminte either during the clss of shorter or longer interresponse times on tht key. In short, in both Shimp (1971) nd the present experiment, subject hd to emit sitclhing response, hich s never itself reinforced, in order to pss from one concurrent schedule to the other. Both in Shimp (1971) nd the present experiment, preference for concurrent schedule s mesured by the number of responses mintined by tht concurrent schedule divided by the totl number of responses mintined by both concurrent schedules. In the previous experiment, this mesure ment tht the totl number of shorter nd longer interresponse times on one key s divided by the totl number of shorter nd longer interresponse times on both keys. Here, the totl number of responses on the left nd right keys hen the keys ere one color s divided by the totl number of responses on the left nd right keys hen the keys ere both colors. The ltter demonintor is simply the totl number of responses on the left nd right keys. In both Shimp (1971) nd the present experiment, ht re here clled sitching responses ere not included in these computtions mesuring preference beteen concurrent schedules. RESULTS Columns 5 to 8 in Tble 1 sho the frequencies of ech of the four response clsses verged over the lst three dys of ech condition. All of the figures presented here re bsed on the informtion in Tble 1. Figures 1 through 4 present dt from the conditions in hich the probbility of reinforcement for responses on the left key hen the keys ere red s vried. Therefore, the -W, >: WI >1 -c LU- -O PROBABILITY OF REINFORCEMENT ON THE LEFT KEY WHEN THE KEYS WERE A PARTICULAR COLOR Fig. 2. Reltive frequency of responses on the left key hen the keys ere prticulr color plotted ginst the probbility of reinforcement for responses on the left key hen the keys ere tht color. Circles represent dt verged over Birds 1, 2, nd 3; tringles represent dt verged over Birds 4, 5, nd 6. Open forms indicte dt obtined hen the keys ere red; filled forms indicte dt obtined hen the keys ere green. The solid digonl line represents the mtching function. The dshed line is lest-squres best-fitting stright line. The prmeters nd stndrd error of estinmte for the best-fitting line re given t the top of the figure.

9 CHOICE BETWEEN CONCURRENT SCHEDULES 339 I.u v y U).8 BIRD I BIRD 2 BIRD o o. ~~~~~~~~~ IL.8 BIRD 4 BIRD 5 BIRD ~~~~ -J ) PROBABILITY OF REINFORCEMENT ON THE LEFT KEY WHEN THE KEYS WERE RED Fig. 3. Reltive frequency of responses on red side keys plotted ginst the probbility of reinforcement for responses on the left key hen the keys ere red. Tht is, the frequency of responses on the left nd right keys hen the keys ere red divided by the totl frequency of responses on the left nd right keys plotted ginst the frequency of reinforcements for responses on the left key hen the keys ere red divided by the totl frequency of reinforcements for responses on the left nd right keys hen the keys ere red. Ech pnel shos the dt for n individul subject. The horizontl line in ech pnel represents the mtching function beteen reltive frequency of responses on red side keys nd probbility of reinforcement for responses on red side keys. probbility of reinforcement for responses on the left key hen the keys ere green lso s vried becuse it s complementry to the probbility of reinforcement for responses on the left key hen the keys ere red. In ech of these conditions, hlf of the reinforcements ere for responses in the presence of red keys nd hlf ere for responses in the presence of green keys. In short, Figures I to 4 present dt from conditions for hich columns 1 nd 2 in Tble 1 re.5. Figures 1 nd 2 sho the reltive frequency of responses on the left key hen the keys ere red s function of the probbility of reinforcement for responses on the left key hen the keys ere red (open circles). They lso sho the reltive frequency of responses on the left key hen the keys ere green s function of the probbility of reinforcement for responses on the left key hen the keys ere green (filled circles). The reltive frequency of responses on the left key hen the keys ere prticulr color s computed by dividing the number of responses on the left key hen the keys ere tht color by the totl number of responses on either the left or right key hen the keys ere tht color. The solid lines in Figures 1 nd 2 represent the mtching function nd the dshed line in Figure 2 is the lest-squres best-fitting stright line. Figure 1 shos the individul dt nd Figure 2 shos the verged dt for Birds 1, 2, nd 3, nd for Birds 4, 5, nd 6. (It ill be reclled tht these to sets of birds experienced different experimentl conditions.) Figure 1 shos tht the individul dt points tended to cluster ner the mtchingline: of the 6 points, lmost one hlf re ithin.5 of the mtching-line, over to thirds re ithin.1, nd nerly ll re ithin.2. Hoever, Figure 1 lso shos slight but systemtic devition from the mtch-

10 34 RONALD L. MENLOVE et l. ing-line: for ll but Bird 1, the empiricl points corresponding to vlues belo.5 on the X-xis tended to be someht too high nd the points corresponding to vlues bove.5 on the X-xis tended to be someht too lo. In short, the dt points tended slightly to undershoot the mtching-line. This Systemtic undershooting cn be seen clerly in the verged dt shon in Figure 2. Hoever, the bsolute devitions from mtching typiclly re smll in botlh Figure 1 nd Figure 2 nd so the dt cn be roughly summrized s follos: the reltive frequency of responses on the left key in the presence of color pproximtely equlled the probbility of reinforcement for responses on the left key in the presence of tht color, hen hlf of the reinforcements ere rrnged for responses in the presence of ech color. Figures 3 nd 4 sho the reltive frequency of responses on red side keys s function of the probbility of reinforcement for responses on the left key hen the keys ere red. The dependent vrible in Figures 3 nd 4 s computed by dividing the totl number of responses on the left nd right keys hen the keys ere red by the totl number of responses on the left nd right keys hen the keys ere red nd hen the keys ere green. Figures 3 nd 4 revel reltionship pproximting the mtching reltionship. Tht is, subject responded on red nd green side keys pproximtely eqully often over the conditions in hich reinforcements ere rrnged eqully often for responses on red nd green keys. This reltionship did not depend on the y in hich reinforcements ere distributed beteen the left nd right keys hen the keys ere prticulr color. Figures 5 to 8 represent dt from the conditions in hich the proportion of reinforcements rrnged for responses in the presence of prticulr color s vried but the probbility of reinforcement for responses on the left key hen the keys ere prticulr color s.5. Tht is, Figures 5 to 8 present dt from conditions for hich columns 3 nd 4 in Tble 1 s.5. Figures 5 nd 6 sho the reltive frequency of responses on red side keys s function of the probbility of reinforcement for responses on red side keys. The reltive frequency of responses on red side keys s computed the sme y s in Figures 3 nd 4. The individul dt points in Figure 5 cluster ner the mtching-line, nd the best-fitting striglht line in Figure 6 lso flls close to the mtching-line. Thus, the reltive frequency of ll responses tht ere in the presence of red keys pproximtely equlled the reltive frequency of ll reinforcements tht ere delivered for responses in the presence of red keys. Figures 7 nd 8 slho the reltive frequency of responses on the left key lhen the keys ere prticulr color s function of the proportion of reinforcements tht ere delivered for responses in the presence of tht color. The reltive frequency of responses on the left key hen the keys ere prticulr color s computed in the sme y s in Figures 1 nd 2. It ill be reclled tht over the conditions for hich dt pper in Figures 7 nd 8, the probbility of reinforcement on the left key hen the keys ere prticulr color s.5. Figure 7 revels tendency for individul dt points to fll ner the lhorizontl mtchingline t.5. The devitions from this line ere gretest for Birds 1, 4, nd 5, btut even for these birds, the mtching-line is bout s good C') (I) WLY z cy I. I I I I y= x.8 lyx=.22.6 *jk1 -v- -o n ' PROBABILITY OF REINFORCEMENT ON THE LEFT KEY WHEN THE KEYS WERE RED Fig. 4. Reltive frequency of responses on red side keys plotted ginst the probbility of reinforcement for responses on the left key hen the keys ere red. Circles represent dt verged over Birds 1, 2, nd 3; tringles represent dt verged over Birds 4, 5, nd 6. The solid horizontl line represents the mntching function betveen reltive frequency of responses on red side keys nd probbility of reinforcement for responses on red side keys. The dshed line is lestsqures best-fitting stright line. The prmneters nd stndrd error of estimte for the best-fitting line re given t the top of the figure.

11 CHOICE BETWEEN CONCURRENT SCHEDULES BIRD I BIRD 2 BIRD UJ6 4 ~~~~~~~~~~.8 BDB 4 BIRD 5 BIRD 6 U A....,....,.. LL.4 L&J Co) PROBABILITY OF REINFORCEMENT ON RED SIDE KEYS Fig. 5. Reltive frequency of responses on red side keys plotted ginst the probbility of reinforcement for responses on red side keys. Tht is, the frequency of responses on the left nd right keys hen the keys ere red divided by the totl frequency of responses on the left nd right keys plotted ginst the frequency of reinforcements for responses on the left nd right keys hen the keys ere red divided by the totl frequency of reinforcements for responses on the left nd right keys. Ech pnel shos the dt for n individul subject. The digonl line in ech pnel represents the iiitching function. summry of the dt s ny stright line could be. Figure 8 shos tht the verged dt ere described quite ell by best-fitting stright line tht pproximted the mtching-line. Thus, Figures 7 nd 8 revel tht subject responded pproximtely eqully often on the left nd right keys in the presence of color over the conditions in hich reinforcements ere rrnged eqully often for responses on the left nd right keys in the presence of tht color. This reltionship did not depend on the proportion of reinforcements delivered for responses in the presence of prticulr color. The frequency of the sitching response, i.e., responses on the center key, re not reported hlere, s they did not seem to depend in ny orderly y on the vrious reinforcement probbilities mnipulted here. DISCUSSION To questions ere sked regrding the present results. First, does choice beteen to to-key concurrent schedules conform to the mtching reltionship, s does choice beteen lterntives ithin single to-key concurrent schedule? Second, does choice beteen lterntives ithin single to-key concurrent schedule conform to the mtching reltionship, s it ould if there ere no second to-key concurrent schedule? These questions re the nlogues of to questions sked by Shimp (1971) lho, s noted bove, found tht the nser to ech s ffirmtive ithin the context of to-key schedule in hiclh there s one-key concurrent schedule of reinforcement for to interresponse times rrnged on ech key. First, consider choice beteen concurrent schedules. Figures 5 nd 6 shoed tht the proportion of ll responses tht ere in the presence of prticulr color closely pproximted the proportion of ll reinforcements tht ere delivered for responses in the presence of tht color. There s one-to-one correspondence beteen colors nd to-key conc VI VI schedules, so tht this mtching reltionship describing preference beteen colors lso

12 342 RONALD L. MENLOVE et l. describes preference beteen concurrent schedules. Thus, choice beteen concurrent schedules conformed to the sme mtching reltionship s does choice beteen components in concurrent sclhedule. This result corresponds to tht obtined previously by Slhimp (1971), here the proportion of ll responses tht ere mintined by one conc VI VI schedule (for to interresponse times) pproximtely equlled the proportion of ll reinforcements tht ere obtined by responses mintined by tht concurrent sclhedule. Figures 3 nd 4 in the present pper sho tht this mtching reltionship describing preference beteen concurrent sclhedules did not depend on the y in hlich responses nd reinforcements ere distributed beteen the left nd right keys in either to-key concurrent schedule. The corresponding result s obtined by Shimp (1971), ho found tht the mtching reltionship describing preference beteen one-key concurrent schedules of reinforcement for to interresponse times did not depend on the y in hiclh responses nd reinforcements ere distributed beteen the shorter nd the longer interresponse times in either one-key concurrent sclhedule. Hoever, 6 y cr -U) s z c o C) J c :r I PROBABILITY OF REINFORCEMENT ON RED SIDE KEYS Fig. 6. Reltive frequency of responses on red side keys plotted ginst the probbility of reinforcement for responses on red side keys. Circles represent dt verged over Birds 1, 2, nd 3; tringles represent dt verged over Birds 4, 5, nd 6. The solid digonl line represents the mtching function. The dshed line is lest-squres best-fitting stright line. The prmeters nd stndrd error of estimte for the bestfitting line re given t the top of the figure. note tht Figures 3 nd 4 in the present experiment, nd the corresponding figures in Shimp (1971), sho this independence only for vlue of.5 on the y-xis. The generlity of this independence for other vlues is unknon. No consider the second question, tht deling ith choice beteen the to lterntives in to-key concurrent schedule. The present Figures 1 nd 2 slho tht the reltive frequency of responses on key in the presence of prticulr color pproximtely equlled the probbility of reinforcement for responses on tht key in the presence of tht color. Thus, choice beteen lterntives in to-key concurrent schedule s pproximtely the sme here s it ould hve been hd there been no second to-key concurrent schedule. The smll but systemtic devition from mtching in Figures 1 nd 2 my be ttributble to the fct tht the to-key concurrent sclhedules corresponding to red nd green ere complementry. Any generliztion of response tendencies, for htever reson, from one concurrent schedule to the other might therefore hve tended to produce the slight undershooting obtined here. In the previous experiment by Shimp (1971), the to concurrent schedules ere the sme, not complementry, nd no undershooting s obtined there. In this erlier experiment, the reltive frequency of occurrence of n interresponse time in onekey concurrent schedule of reinforcement for to interresponse times depended on the corresponding probbility of reinforcement in the sme y s it ould hve hd there been no second one-key concurrent schedule of reinforcement for to interresponse times. Figures 7 nd 8 in the present pper sho tht the mtching reltionship describing preference beteen lterntives in to-key concurrent schedule did not depend on the y in hich responses nd reinforcements ere distributed beteen the to to-key concurrent schedules. The corresponding result s obtined by Shimp (1971). Notice tht this result, like the one in Figures 3 nd 4, s obtined only for y-xis vlue of.5, nd my not hold for other vlues. The present results, hen compred to those obtined by Slhimp (1971), provide evidence for certin degree of equivlence beteen choices nd interresponse times. In both experiments, complex concurrent schedule of re-

13 CHOICE BETWEEN CONCURRENT SCHEDULES U.~.8 BIRD I BIRD 2 BIRD 3 8 A ~~~~~ ' 2 ~' PROBABILITY OF REINFORCEMENT ON RED SIDE KEYS Fig. 7. Reltive frequency of responses on the left key hen the keys ere prticulr color plotted ginst the probbility of reinforcement for responses on the left nd right keys hen the keys ere tht color. For exmple, the frequency of responses on the left key hen the keys ere red divided by the totl frequency of responses on the left nd right keys hen the keys ere red plotted ginst the frequency of reinforcement for responses on the left nd right keys hen the keys ere red divided by the totl frequency of reinforcements for responses on the left nd right keys. Ech pnel shos the dt for n individul subject. Open circles represent dt obtined hen the keys ere red; dots represent dt obtined hen the keys ere green. The horizontl line in ech pnel represents the mtching function beteen reltive frequency of responses on the left key hen the keys ere prticulr color nd probbility of reinforcement for responses on the left key hen the keys ere tht color. inforcement s studied. Ech component of the concurrent schedule in both experiments s itself concurrent schedule. In the previous experiment, the lterntives ithin component concurrent schedule ere shorter or longer interresponse times on single key, nd in the present experiment the lterntives ere choices beteen left or right keys. In both instnces, preference beteen concurrent schedules conformed to mtching reltionslhip nd behvior in concurrent schedule s, in certin limited ys described in detil bove, independent of the presence of second concurrent schedule. This specific functionl equivlence beteen one-key concurrent schedules for interresponse times nd to-key concurrent schedules for choices is in ddition to severl other specific ys in hich choices nd interresponse times re equivlent. For exmple, it is knon tht in one-key conc VI VI schedule for to interresponse times, the reltive frequency of occurrence of n interresponse time pproximtely equls the reltive reciprocl of its length, so long s the to interresponse times re reinforced eqully often nd the overll density of reinforcement is sufficiently high (Shimp, 1969, 197). This mtching reltionship is precisely the sme s tht hich describes the reltion beteen choice behvior nd delys of reinforcement in to-key conc VI VI schedules (Chung nd Herrnstein, 1967; Herbert, 197). Furthermore, Moffitt nd Shimp (1971) found tht the y in hich the reltive frequency of n interresponse time depends on the corresponding reltive frequency of reinforcement is the sme, regrdless of hether ech interresponse time is rrnged on seprte key, or both interresponse times re rrnged on single key.

14 344 RONALD L. MENLOVE et l. I- 1., I } (/3 y= x (no r 8 = 52_ ~~e~~~ W 4r : c O C.6, j O z PROBABILITY OF REINFORCEMENT ON RED SIDE KEYS Fig. 8. Reltive frequency of responses on the left keey hen the keys ere prticulr color plotted ginst the probbility of reinforcement for responses on the left nd right keys hen the keys ere tht color. Circles represent dt verged over Birds 1, 2, nd 3; tringles represent dt verged over Birds 4, 5, nd 6. Open forms represent dt obtined hen the keys ere red; filled forms represent dt obtined hen the keys ere green. The solid horizontl line represents the mtching function beteen reltive frequency of responses on the left key hen the keys ere prticulr color nd probbility of reinforcement for responses on the left key hen the keys ere tht color. The dshed line is lest-squres best-fitting stright line. The prmeters nd stndrd error of estimte for the best-fitting line re given t the top of the figure. A complex concurrent schedule in hich the components re themselves concurrent schedules is only one of mny possible kinds of complex concurrent schedules tht could be devised. Indeed, it lredy is knon tht the mtching reltionship pplies to choice behvior in concurrent schedule, one component of hich is VI schedule nd the other component of hichl is multiple VI VI schedule (Pliskoff, Shull, nd Gollub, 1968). The full extent to hich multiple nd concurrent schedules my be combined hile preserving reltionships such s mtching remins for future reserchl to determine. REFERENCES Anger, D. The effect upon simple niml behvior of different frequencies of reinforcemlent. Report PLR- 33, Office of the Surgeon Generl, Chung, S. -H. nd Herrnstein, R. J. Choice nd dely of reinforcement. Journl of the Experimentl Anlysis of Behvior, 1967, 1, Findley, J. D. Preference nd sitching under concurrent scheduling. Journl of the Experimentl Anlysis of Behvior, 1958, 1, Herbert, E. W. To-key concurrent responding: Response-reinforcement dependencies nd blckouts. Journl of the Experimentl Anlysis of Behvior, 197, 14, Herrnstein, R. J. Reltive nd bsolute strength of response s function of frequency of reinforcement. Journl of the Experimentl Anlysis of Behvior, 1961, 4, Menlove, R. L. Locl ptterns of responding mintined by concurrent nd multiple schedules. Unpublished doctorl disserttion, University of Uth, Moffitt, M. nd Shimp, C. P. To-key concurrent pced vrible-intervl pced vrible-intervl schedules of reinforcement. Journl of the Experimentl Anlysis of Behvior, 1971, 16, Pliskoff, S. S., Shull, R. L., nd Gollub, L. R. The reltion beteen response rtes nd reinforcement rtes in multiple schedule. Journl of the Experimentl Anlysis of Behvior, 1968, 11, Shimp, C. P. Probbilisticlly reinforced choice behvior in pigeons. Journl of the Experimentl Anlysis of Behvior, 1966, 9, Shimp, C. P. Mgnitude nd frequency of reinforcement nd frequency of interresponse timiies. Journl of the Experimentl Anlysis of Behvior, 1968, 11, Shimp, C. P. The concurrent reinforcenment of to interresponse timiies: the reltive frequcnicy of n interiresponse timiie equls its reltive hrmiionic length. Journl of the Experimentl Anlysis of Behvior, 1969, 12, Shimp, C. P. The concurrent reinforcement of to interresponse times: bsolute rte of reinforcement. Journl of the Experimentl Anlysis of Behvior, 197, 13, 1-8. Shimp, C. P. The reinforcement of four interresponse times in to-lterntive sitution. Jouirnl of the Experimentl Anlysis of Behvior, 1971, 16, Shimiip, C. P. Probbilistic discrinmintion lerning in the pigeon. Journl of Experitmientl Psychology, (in press) (). Shimp, C. P. Synthetic vrible-intervl schedules of reinforcement. Jotirtnl of the Experimentl Anlysis of Behvior, (in press) (b). Shimp, C. P. nd Whetley, K. L. Mtching to reltive reiniforcement frequency in multiple schedules ith short component durtion. Journl of the Experimentl Anlysis of Behvior, 1971, 15, Stddon, J. E. R. Spced responding nd choice: preliminry nlysis. Journl of the Experimentl Anlysis of Behvior, 1968, 11, Stubbs, D. A. nd Pliskoff, S. S. Concurrent responding ith fixed reltive rte of reinforcement. Journl of the Experimentl Anlysis of Behvior, 1969, 12, Received 1 My (Finl Acceptnce 12 September 1972.)