95

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2002, 78, 95–116 NUMBER 1 (JULY)

FROM MOLECULAR TO MOLAR:A PARADIGM SHIFT IN BEHAVIOR ANALYSIS

WILLIAM M. BAUM

UNIVERSITY OF CALIFORNIA–DAVIS

A paradigm clash is occurring within behavior analysis. In the older paradigm, the molecular view,behavior consists of momentary or discrete responses that constitute instances of classes. Variationin response rate reflects variation in the strength or probability of the response class. The newerparadigm, the molar view, sees behavior as composed of activities that take up varying amounts oftime. Whereas the molecular view takes response rate and choice to be ‘‘derived’’ measures andhence abstractions, the molar view takes response rate and choice to be concrete temporally ex-tended behavioral allocations and regards momentary ‘‘responses’’ as abstractions. Research findingsthat point to variation in tempo, asymmetry in concurrent performance, and paradoxical resistanceto change are readily interpretable when seen in the light of reinforcement and stimulus control ofextended behavioral allocations or activities. Seen in the light of the ontological distinction betweenclasses and individuals, extended behavioral allocations, like species in evolutionary taxonomy, con-stitute individuals, entities that change without changing their identity. Seeing allocations as individ-uals implies that less extended activities constitute parts of larger wholes rather than instances ofclasses. Both laboratory research and everyday behavior are explained plausibly in the light of con-crete extended activities and their nesting. The molecular view, because it requires discrete responsesand contiguous events, relies on hypothetical stimuli and consequences to account for the samephenomena. One may prefer the molar view on grounds of elegance, integrative power, and plau-sibility.

Key words: resistance to change, individual, class, concrete/abstract, molar, molecular, atomism

No man is an Iland, intire of it selfe; every manis a peece of the Continent, a part of the maine;if a Clod bee washed away by the Sea, Europeis the lesse . . . any mans death diminishes me,because I am involved in Mankinde; And there-fore never send to know for whom the belltolls; It tolls for thee.

John Donne (1572–1631)

Every scientific paradigm includes bothepistemological claims—claims about knowl-edge, such as what it is and how it is ob-tained—and ontological claims—claims as towhat we are to know about (Kuhn, 1970). Inparadigm clashes, ontological claims oftenmatter most. In the Ptolemaic view of the uni-verse, the planets, like other heavenly bodies,revolve around the earth. Their irregularmovements in the sky were explained withthe use of epicycles, circles within the circularorbits around the earth. In the modern view,the sun, moon, and planets constitute a solarsystem. The concept of epicycle makes sensein one paradigm but is absent from the other.The concept of solar system exists in the oth-

I thank Michael Ghiselin and Howard Rachlin for help-ful comments on an earlier draft of this paper.

Correspondence should be addressed to William M.Baum, 1095 Market, #217, San Francisco, California94103 (e-mail: wmbaum@ucdavis.edu).

er paradigm but is absent from the first. Nei-ther concept is wrong. Each makes sensewithin one paradigm but is nonsense in theother. That is why, in contrast to theoreticaldisputes, paradigm clashes cannot be settledby data. Any particular set of data may bemeaningful to one paradigm and meaning-less to another or may have different inter-pretations according to different paradigms.The interpretations will be ‘‘incommensu-rate’’—that is, each will make sense only with-in its paradigm (Kuhn, 1970).

The purpose of this paper is to describeand support a paradigm that has developedwithin behavior analysis over about the last 30years. I will call it the molar view, because mo-lar carries the connotation of aggregation orextendedness, and the molar view is based onthe concept of aggregated and extended pat-terns of behavior. Its roots may be traced backto the 1960s, but it became clearly visible inthe 1970s (e.g., Baum, 1973; Rachlin, 1976),and it was articulated explicitly in the 1980sand 1990s (e.g., Baum, 1997; Chiesa, 1994;Lee, 1983; Rachlin, 1994, 2000). Like the he-liocentric view of the solar system, the molarbehavior-analytic view clashes with an olderparadigm (Baum, 2001; Dinsmoor, 2001;Hineline, 2001), which I will call the molec-

96 WILLIAM M. BAUM

ular view, because it is based on an atomismof discrete events at moments in time. I willfocus on the contrasting ontological claimsmade by the molar and molecular views, eventhough they also clash on epistemologicalgrounds (e.g., the uses of cumulative recordsvs. digital counters), because the ontologicalclash, though more fundamental, is less ob-vious.

THE MOLECULAR VIEW

In the 19th century, many psychologistssought to put psychology on a sound scientif-ic basis by focusing on the association ofideas, sensations, and movements. Theseunits of consciousness were conceived of asdiscrete events that could be ‘‘hooked’’ to-gether or associated according to certainprinciples. Chief among these principles wasthe law of contiguity, which stated that twoevents that occurred close together in time(i.e., in temporal contiguity) would tend torecur together. In particular, if the idea offood happened to follow closely upon theidea of a musical tone, then when the idea ofthe tone recurred, the idea of the food wouldrecur. This seemed a way to account for boththe stream of consciousness and for the build-up of complex ideas from simpler ideas, asmolecules are built up from atoms.

Although the association of ideas becameless popular in the 20th century, the originalatomism persisted in the concepts of stimulusand response. A stimulus was a discrete eventin the environment, and a response was a dis-crete event in behavior. The principle of as-sociation by contiguity persisted in the con-cept of the conditional reflex.

In a classic paper, ‘‘The Generic Nature ofthe Concepts of Stimulus and Response,’’Skinner (1935/1961) attempted to create def-initions of stimulus and response that wouldserve as the basis for a science of behavior.One can hardly overstate the importance ofthis paper to the development of behavioranalysis. Skinner proposed a solution to theproblem of particularity that plagues behav-ior analysis as it does any science: If eachevent (stimulus or response) is unique, howdoes one achieve the reproducibility requiredfor scientific study? His answer was that astimulus or a response was not a unitary eventbut was a class of unitary events. Although

any particular event might be described withgreat precision, the goal for defining a stim-ulus or response, as a class, was to specify theclass’s defining properties. The lever press,for example, would consist of the class of acts,all of which achieved the necessary move-ment of the lever. The nondefining proper-ties could be ignored or could serve as themeans for further differentiation. One wouldknow if one’s defining properties were cor-rect by the consistency of one’s results whenthe class is so defined—that is, in ‘‘smoothcurves for secondary processes’’ (p. 366),what he was later to call functional relations.In this way, Skinner made possible a scienceof behavior—that is, behavior, as opposed tophysiology or consciousness.

Skinner’s stimulus and response, however,were classes of discrete events, the same sortof events as the previous century’s ideas, sit-uated at moments in time and explained bycontiguity between events in time. A reflexfor Skinner (1935/1961) was a correlationbetween two classes, meaning that when amember of the stimulus (as class) occurred,it would be followed by a member of the re-sponse (as class). Conditional reflexes werecreated by the repeated contiguity of mem-bers of the two classes. Later, he treated thelaw of effect in similar fashion: The response(as class) was strengthened by repeated con-tiguity between its members and the mem-bers of the reinforcer (as stimulus class).

Skinner (1938) equated response strengthto probability. He proposed to measure prob-ability as response rate. He saw response rateas an expression of response probability orstrength, often writing as if this were the truedependent variable (Skinner, 1938, 1950,1953/1961, 1957/1961). Response ratewould be the outcome of probability actingmoment to moment, as if at every moment aprobability gate determined whether a re-sponse would occur just then or not. Changesin response rate were an outcome of changesin response strength, possibly acting locally,as in the fixed-interval scallop (Ferster &Skinner, 1957). Stimulus control occurred asa result of modulating response strength, asif in the presence of a discriminative stimulusthe probability gate became more or less lib-eral in its moment-to-moment decisions.

97MOLECULAR TO MOLAR

A MOLAR VIEW

In 1969, Baum and Rachlin proposed a dif-ferent view of response rate. We drew on T.F. Gilbert’s (1958) suggestion that responseslike lever presses and key pecks might occurin bouts at a constant rate, which he calledthe tempo of responding. Variation in re-sponse rate, in this molar view, would resultfrom variation in the duration of bouts andthe pauses between bouts (e.g., Shull, Gay-nor, & Grimes, 2001). The time spent re-sponding (T) at the tempo (k) would deter-mine the number of responses (N): N 5 kT.If S is the duration of the sample (usually thesession duration), then response rate (B) isgiven by

kTB 5 . (1)

S

We suggested that behavior might be thoughtof as divided among activities that lasted forperiods of time (i.e., bouts). Taking time asthe universal scale of behavior, we proposedthat the dependent variable be thought of astime spent responding (T 5 N/k) or propor-tion of time spent responding:

T N5 . (2)

S kS

Accordingly, we wrote of choice as time allo-cation, the allocation of time among contin-uous activities, and we characterized thematching law as a matching of relative timespent in an activity to relative reinforcementobtained from that activity. The idea was ex-tended to other changes in responding, suchas behavioral contrast (White, 1978).

The elaboration of this idea is the para-digm that I am calling the molar view of be-havior. Whereas the central ontological claimof the molecular view is that behavior consistsof discrete responses, the central ontologicalclaim of the molar view is that behavior con-sists of temporally extended patterns of ac-tion. I shall call these activities. Besides theconcept of an activity, the molar view is basedalso on the concept of nesting, the idea thatevery activity (e.g., playing baseball) is com-posed of parts (batting) that are themselvesactivities. I shall focus first on activities anddiscuss nesting later.

Historically, the notion of reproducible dis-crete events, whether ideas or responses, al-

lowed a scientific approach to the subjectmatter. The concept of discrete response al-lowed quantification. Skinner’s (1938) prep-aration, based as it was on the reflex, en-couraged researchers to think of the responseas momentary, as an event without duration.Skinner even set out one of his requirementsfor a response to study that it should be briefand easily repeated, because these propertieswould allow rate to vary over a wide range. Aconcept like the delay-of-reinforcement gra-dient depends on the idea that the responseoccurs at a certain point in time from whichdelay is measured. The concept of contiguityitself depends on the idea that two discreteevents (e.g., response and reinforcer) markthe beginning and end of such a delay, theduration of which, for perfect contiguity,should be zero.

The notion of activity takes for granted thepossibility of quantification, extending it be-yond discrete responses and contiguity. Thekey difference lies in the recognition that ac-tivities take up time. In an earlier paper, Iargued that the reinforcement relation mightbe thought of as a correlation (Baum, 1973).In the molar view, an activity like lever press-ing, extending in time, is seen as accompaniedby the reinforcers it produces. Many reinforc-ers may be involved, and consequences, be-ing extended like activities, often consist ofchanges in reinforcer rate or changes in re-inforcer magnitude. The idea that reinforcersaccompany an activity might be misinterpret-ed to mean that delay is irrelevant, a claimthat apparently would be easy to refute by ex-perimentation. As in other paradigm clashes,however, in the molecular–molar clash thephenomena observed are simply seen in dif-ferent terms. A procedure that arranges fooddelivery to immediately follow depressions ofa lever arranges a strong correlation betweenlever pressing and rate of food delivery. Aprocedure that arranges food deliveries tofollow responses at some delay arranges alesser correlation, because the food deliveriesmay fail to accompany the activity. To effectchanges in behavior, strong correlations workbest; to maintain activities already occurringfrequently, weak correlations may suffice(Baum, 1973).

The point might seem trivial, until we turnto other types of activity. Had Skinner chosento study wheel running instead of lever press-

98 WILLIAM M. BAUM

ing, his situation would have been different.Experimenters often measure wheel runningin revolutions or quarter-revolutions, butthese are artifices aimed at creating discreteresponses where none are apparent. Premack(1965, 1971) instead proposed time as themeasure. If we turn this reasoning onto activ-ities like lever pressing, we see that discreteresponses like lever presses are an outcomeof instrumentation. ‘‘Responses’’ are momen-tary events (usually switch closures) contrivedby the apparatus (e.g., lever or key). Theirmomentary character is only an artifact of theuse of electrical switches. As a thermometer,whether stuck into a bowl of ice cream or apile of cow manure, indicates only the tem-perature, regardless of the stuff it is stuckinto, so a lever, when stuck into the activityof a rat, indicates only rate of switch closure,regardless of what sort of activity it is stuckinto.

When I was a graduate student, laboratorypractice dictated that one attach a lever orkey to a pulse former, a device that wouldgenerate a uniform pulse on each operationof the lever or key. Laboratory lore claimedthis was essential to keep the subjects fromholding the switch. I tested this claim by omit-ting the pulse formers in an experiment onconcurrent schedules (Baum, 1976). I mea-sured both number of lever presses (switchoperations) and time that the lever was de-pressed. The measures turned out to beequivalent, because the activity continued toresult in jiggling of the lever, producing manyswitch operations. Even though the durationof the operations varied, the average was con-sistent enough that time and number ofpresses could be interchanged, as in Equation2. Just as a rat’s jiggling of a lever operates itat certain points in the jiggling, a pecking keyoperates only at a certain point in the move-ment of a pigeon’s head. When Pear (1985)arranged a system for keeping continuoustrack of the position of a pigeon’s head, keypecking appeared as cyclic motion, a waveform.

Two simple arguments might persuade oneto think about behavior in terms of activitiesrather than discrete responses: (a) Momen-tary events are abstractions and (b) reinforce-ment operates by selection. The first, that mo-mentary events cannot be observed, but onlyinferred, was argued in an earlier paper

(Baum, 1997). I shall recapitulate briefly.Suppose I show you a snapshot of a rat withits paw on a lever, and I ask you, ‘‘Is the ratpressing the lever?’’ You will have to reply, ‘‘Idon’t know. I have to see what comes next.’’You won’t know until you see the whole (ex-tended) lever press. In other words, youwould never be able to tell from a momentarypicture of the behavior what behavior was oc-curring at that moment. Only after the wholepattern unfolded would you be able to lookback and infer that at that moment the ratwas pressing the lever. The momentary re-sponse is never observable at the moment. Itis always inferred afterwards. Like instanta-neous velocity in physics, instantaneous be-havior cannot be measured at the moment itis supposed to have occurred but must be in-ferred from a more extended pattern. Thatis why it might fairly be called an abstraction.That is why one may argue that it is impossi-ble to reinforce a momentary response; onecan only reinforce some activity with someduration.

The second argument is that reinforce-ment consists of selection. Possibly Ashby(1954) was the first to recognize the parallelbetween reinforcement and natural selection.Campbell (1956) spelled out the idea that re-inforcement is a type of selection, and R. M.Gilbert (1970) and Staddon and Simmelhag(1971) elaborated it further. Skinner (1981)himself proposed it eventually. The essentialpoint is that behavior varies as do genotypeswithin a population of organisms. As differ-ential reproductive success increases some ge-notypes while decreasing others, so differen-tial reinforcement increases some behavioralvariants while decreasing others. This paral-lel, however, requires competition among var-iants, in the sense that the increase of onevariant necessitates the decrease of others.With genotypes, this occurs because the sizeof the population tends to remain constant atthe carrying capacity of the environment(i.e., the number of organisms that the re-sources of the environment can maintain).For behavior, the competition requires thatthe total of behavior in any period of timeshould, like the carrying capacity, remainconstant. In other words, it requires that be-havior take up time, and presumably that allthe behavior that occurs in a time period takeup all the time. Just as the limit to a biological

99MOLECULAR TO MOLAR

population necessitates that if longer neckedgiraffes increase in frequency then shorternecked giraffes must decrease in frequency,so the temporal limit to behavior necessitatesthat if pecks at the left key increase in fre-quency then pecks at the right key must de-crease in frequency. At the least, the idea thatreinforcement is a kind of selection requiresthat discrete responses must have duration.Add to that the possibility that the so-calledresponses may vary in duration, and you havegranted that behavior consists of activities.The so-called response becomes indistin-guishable from a bout of an activity.

Someone wedded to the molecular viewmight reply in a number of different ways.One might reject the analogy to natural se-lection altogether and stick with momentaryresponses. One might insist that in any timeperiod greater and lesser amounts of behav-ior may occur. The molarist might reply thatsacrificing the elegance of selection is a highcost to pay for the sake of keeping to mo-mentary responses.

STRENGTH VERSUSALLOCATION

The difference between the molar and mo-lecular views may be seen in their differentguiding metaphors. Whereas the molecularview relies on the idea of strength, the molarview relies on the idea of allocation. Thesedifferent ideas depend on the different on-tological claims of the two paradigms.

In the molecular view, reinforcers strength-en behavior. They do this by following im-mediately upon or soon after a bit of behav-ior, a response. The underlying assumption ofa central role for contiguity in time entailsthe ontological claims of the molecular view,because contiguity exists at or around a cer-tain moment in time. For two events to becontiguous, to occur close to the same mo-ment, they must either be momentary orhave distinct beginnings and ends. For a re-sponse to be followed immediately by a re-inforcer, the response and the reinforcermust be discrete events. Thus, the contiguity-based notion of reinforcement espoused bythe molecular view entails the ontologicalclaim that behavior consists of discrete events.

Strength cannot attach to a single instanceof a discrete unit, because each of those is

unique. Therefore, in the molecular view,strength attaches to the class and is inferredfrom the number of members of the classthat occur in any given time period (i.e., fromthe calculated rate). A rat may press a lever30 times per minute or twice per minute. Imay drive to work seven times per week oronce per week. A reinforcer may follow eachoccurrence of a discrete unit, but only someoccurrences need be followed by reinforcersfor the rate of occurrence of members of theclass to be maintained—that is, reinforce-ment may be intermittent. The more oftenmembers of the class are reinforced, thegreater the strength of the class.

In contrast, the guiding metaphor of themolar view is allocation. If the molecular viewlikens behavior to picking numbers out of ahat, the molar view likens behavior to cuttingup a pie. Choice is time allocation (Baum &Rachlin, 1969). All behavior entails choice.All behavior entails time allocation. To be-have is to allocate time among a set of activ-ities. Such an allocation is a behavioral pat-tern. If a pigeon spends 60% of its timepecking at one response key, 30% of its timepecking at another, and 10% of its time inother, unmeasured activities, that is the pat-tern of its behavior while in the experiment.If a person spends 47% of his or her recrea-tional time watching television, 40% reading,10% walking, and 3% going to movies, thatis a pattern of recreational behavior. Suchpatterns or allocations are necessarily extend-ed in time.

Because every activity itself is composed ofother activities—that is, because every activityis a whole constituted of parts—every activityitself contains an allocation of behavior. Inthis sense we may say that every activity is abehavioral allocation. The pigeon’s allocationin the experiment may be called its experi-mental activity, and the allocation of recrea-tional time may be called the person’s recre-ational activity. We shall discuss this furtherwhen we take up the concept of nesting.

In the molar view, the appearance that be-havior might be composed of discrete unitsarises because activities often occur in epi-sodes or bouts. Task completion providesmany examples: completion of a fixed-ratiorun, of a house, of writing a paper, of readinga book. In the laboratory, the training of re-sponse chains originated to try to model such

100 WILLIAM M. BAUM

extended units. In the molecular view, the se-quence is thought to terminate at least someof the time with a reinforcer and to be heldtogether with conditional reinforcers alongthe way to ultimate reinforcement. In the mo-lar view, an activity like building a house en-tails a pattern of activities such as pouring thefoundation, framing the structure, insulating,putting in windows and doors, and finishingthe interior. House construction seems like aunit only because it is labeled as such, as onemay call an episode of napping a nap or about of walking a walk. To a building con-tractor, construction of one house wouldseem more like an episode of building thana discrete unit. Against the molecular view,one might argue that behavioral chains some-times bear little resemblance to extended be-havior in the real world. Is it plausible to treatobtaining a bachelor’s degree as a behavioralchain? Except for repetitive sequences likethose of the assembly line, real-life sequenceslike building a house or baking a cake rarelyfollow a rigid order. Even the fixed-orderchain of the laboratory (e.g., chain fixed in-terval fixed ratio) may be seen as a sequenceof activities (fixed-interval activity, then fixed-ratio activity), and if some activities are main-tained better than others, that is a matter tobe studied. Completion of any task may beseen as an episode of an activity. Even activi-ties that usually end in a certain way, such assearch, last for varied durations; sooner or lat-er the forager encounters prey, sooner or lat-er one finds a parking space.

In particular, the molar view holds that theso-called response is an episode of an activity.Grant that pecks and presses take up timeand that the time taken up by each cycle ofactivity—of body motion back and forth or upand down—takes up about the same amountof time (Baum, 1976; Pear, 1985), and thenEquation 2 illustrates how switch operations(N ) are convertible to time and how thattime may be considered relative to the total(T). In other words, rate of pecking or press-ing is equivalent to an allocation—relativetime spent pecking or pressing. Even if count-ing responses is convenient, from the molarviewpoint a response rate is a relative time inthe activity.

In the molar view, discrete behavioral unitsare not only illusory but often are simply im-possible. As Baum and Rachlin (1969) argued

before, many activities lack any natural unit.What is the discrete unit of watching televi-sion, reading, sleeping, or driving a car? Ap-plied behavior analysts recognize this whenthey set goals such as increasing time on task.Even in the laboratory, activities like wheelrunning and lever holding lack any nonarbi-trary unit. Such activities, for which the mo-lecular view must invent ‘‘responses,’’ readilylend themselves to the idea of allocation.

THREE EXAMPLES OFMOLAR EXPLANATION

Although the conflict between two para-digms cannot be resolved by data, the powerof a paradigm may be seen in its ability tointerpret various phenomena of the labora-tory. Three examples of the power of the mo-lar view appear in its ability to treat (a) vari-ation in tempo, (b) asymmetrical concurrentperformances, and (c) resistance to change.

Variation in Tempo

Herrnstein’s (1970, 1974) formulation ofthe matching law relied on response rate. Heexpressed it in the form

B r1 15 , (3)n nB rO Oi i

i51 i51

which states that the relative response rate ofany of n alternative responses matches therelative reinforcement obtained from those nalternative responses. Herrnstein (1970) fur-ther supposed that the sum total of behavior(the denominator on the left side of Equa-tion 3) was a constant. On this assumption,Equation 3 is rewritten as

r1B 5 k , (4)1 r 1 r1 O

where rO represents all reinforcement ob-tained from alternatives other than Alterna-tive 1, and k represents the sum total of be-havior expressed in the response units of B1.

In keeping with the notion of time alloca-tion that Baum and Rachlin (1969) put for-ward, however, the constant k in Equation 4may be reinterpreted as the tempo of the ac-tivity defining B1. It equals the response ratethat would occur if all behavior were allocat-ed to Alternative 1—that is, the response rate

101MOLECULAR TO MOLAR

if all the time were spent in Activity 1, some-times called the asymptotic response rate.Substituting Equation 1 into Equation 4 al-lows one to rewrite Equation 4 to have pro-portion of time spent in Activity 1 matchingproportion of reinforcement obtained fromActivity 1.

One seeming challenge to Equation 4arose from research by McDowell and asso-ciates (e.g., Dallery, McDowell, & Lancaster,2000) that cast doubt on Herrnstein’s as-sumption of constancy of k. They found thatseveral operations, such as varying depriva-tion or reinforcer magnitude, result in differ-ent values of k when the response (of B1) re-mains ostensibly the same. McDowell offeredequations that predicted variation in asymp-totic response rate, but at the cost of assum-ing discrete responses of invariant duration(e.g., McDowell, 1987). How might one ex-plain variation in k while retaining the molarview?

One may interpret McDowell’s findings asshowing that the operations that vary k affectthe tempo of responding, perhaps by affect-ing response topography. If k increases withincreasing magnitude of reinforcement, thatmight be because the increased magnituderesults in more vigorous responding, whichresults in less time per response. The highertempo of the activity would result in moreswitch closures counted in the same amountof time. Thus the observation of varying k isreadily accommodated by the molar view.

Asymmetrical Concurrent PerformancesAnother challenge to the matching law is

the observation that behavior at two choicealternatives may differ qualitatively. The two-alternative version, expressed as

B r1 15 , (5)B r2 2

may be thought of as derived by taking theratio of Equation 3 to the similar equationwritten for Alternative 2. Such a derivationwould be justified only if k were equal for thetwo alternatives. Suppose that the topographyof the two responses differed, resulting in adifference in tempo (k). For example, sup-pose that one alternative was reinforced ac-cording to a variable-interval (VI) scheduleand the other was reinforced according to avariable-ratio (VR) schedule (e.g., Baum &

Aparicio, 1999; Herrnstein & Heyman, 1979).If the tempo on the VR alternative were high-er, the same amount of time spent at that al-ternative would result in more responsescounted (i.e., more switch operations) therethan if that time were spent at the VI alter-native. Relative ‘‘responses’’ would deviatefrom matching.

The generalized matching law has beenused to estimate such deviations from match-ing:

sB r1 15 b , (6)1 2B r2 2

where b is a proportionate bias that is inde-pendent of the rates of reinforcement, r1 andr2, and s is the sensitivity to variation in theratio of reinforcement. If b and s both equal1.0, the strict matching of Equation 5 occurs.When deviations from strict matching occur,they are usually estimated as values of b ands different from 1.0. If the tempos of B1 andB2 differed, one would expect a value of bdifferent from 1.0, favoring the VR (e.g.,Baum & Aparicio, 1999; Herrnstein & Hey-man, 1979).

A stronger challenge to the matching lawarises from the observation that a differencein topography or tempo may affect s (Baum,Schwendiman, & Bell, 1999). Equation 6 isusually fitted to behavior and reinforcer ra-tios in its logarithmic form,

B r1 1log 5 s log 1 log b, (7)B r2 2

because this form is symmetrical around theindifference point (behavior and reinforcerratios both equal to 1.0) and because, beinglinear, it is easier to fit. The equation is fittedto behavior ratios determined for several re-inforcer ratios to both sides of equality (i.e.,sometimes making Alternative 1 richer, some-times making Alternative 2 richer) on the as-sumption that parameters s and b remain in-dependent of variation in the reinforcerratio. Baum et al. found that when pigeonswere exposed to pairs of concurrent VI sched-ules long enough for performance to remainstable over a substantial sample, the behaviorratios deviated systematically from Equation7. On closer examination, a simple pattern ofbehavior appeared: Responding occurred al-most exclusively on the rich alternative, in-

102 WILLIAM M. BAUM

Fig. 1. Apparent deviations from matching explained by the fix-and-sample pattern. Left: The top graph showsapparent undermatching. Close examination reveals systematic deviation from the fitted line (the generalized match-ing law). The bottom graph shows the same data fitted with the two lines predicted by fix and sample. Right: aninstance of apparent overmatching, with systematic deviation from the generalized matching law. The bottom graphshows the data fitted with the two lines predicted by fix and sample, eliminating the systematic deviation.

terrupted only by brief visits to the lean al-ternative. This pattern, which we called ‘‘fixand sample,’’ predicted two lines, each withslope s equal to 1.0 but with different bias b,depending on whether Alternative 1 or Alter-native 2 was the lean alternative (Houston &McNamara, 1981). We found that the two-linemodel, with the same number of parametersas the one-line model, fitted the data betterand with no systematic deviations.

Figure 1 illustrates the finding. The two leftgraphs show the behavior ratios from Pigeon

973, fitted with one line (top) and with twolines (bottom). A casual look at the top graphwould lead one to conclude that the resultswere typical of such experiments: a good fitto Equation 7 with a moderate amount of un-dermatching (s 5 0.8). Closer inspection re-veals that, going from left to right, the datapoints first lie above the line, then below theline, then above again, and then below again.Not only is the two-line fit better, but also thevariation in choice appears to conform close-ly to the assumed slopes of 1.0. Indeed, the

103MOLECULAR TO MOLAR

undermatching shown in the top graph is ex-plained by the inappropriate fitting of oneline to data better described by two.

The two right graphs in Figure 1 demon-strate a similar explanation for an example ofapparent overmatching. They show behaviorratios from Pigeon 490 in the Baum–Rachlin(1969) experiment, fitted with one line andwith two. Again the two-line fit (bottom)shows less systematic deviation, again theslopes of 1.0 seem appropriate, and again theapparent deviation of slope s from 1.0 may beexplained as the result of inappropriate fit-ting of one line to data better described bytwo.

Although the two-line fits in Figure 1 bothshow biases that explain the deviations of sfrom 1.0, these biases differ from the bias bin Equations 6 and 7. Whereas the usual biasis assumed to be independent of reinforcerratio, the biases in the two-line model dependon the reinforcer ratio, because they dependon which is the leaner alternative. In the un-dermatching example, the bias favoredwhichever was the lean alternative. In theovermatching example, the bias favoredwhichever was the rich alternative. The over-matching example shows standard positionbias too; that is why the vertical crossover oc-curs at a reinforcer ratio less than 1.0.

The results shown in Figure 1 support theidea that behavior at the rich alternative andbehavior at the lean alternative constitute dif-ferent activities that, in turn, comprise partsof a more extended pattern (i.e., the fix-and-sample activity) involving both alternatives.Behavior at the rich alternative consists ofstaying there—fixing—whereas behavior atthe lean alternative consists of brief visiting—sampling. In the undermatching example,the pigeons pecked at two keys, but visits tothe lean key nearly always consisted of singleisolated pecks. To explain the apparent biasin favor of the lean alternative, one need onlyassume that less time was spent per peck atthat key. For example, a pigeon stationed infront of the rich key would ‘‘travel’’ to thelean key by stretching its neck toward the key,and in that position, make a brief exploratorypeck. Measured as time spent, a number ofpecks at the lean key would represent lesstime than the same number of pecks at therich key, and counting them equally wouldoverestimate the time spent at the lean alter-

native. In other words, if the subscripts inEquation 7 were reinterpreted to mean richand lean, rather than left and right, then thebias would differ from 1.0 only because thetime per peck differed, just as the earlier dis-cussion suggested for concurrent VI VRschedules.

In the overmatching example, Baum andRachlin (1969) measured only time spent ontwo sides of a chamber; there were no re-sponse keys. We observed informally that thepigeons would station themselves near themiddle of the chamber and move rapidlyback and forth. Whereas behavior on the richside consisted of standing or dancing, a visitto the lean side consisted of stepping overthere, waiting out the signaled changeoverdelay (COD), and then either running to thefeeder on the lean side or immediately hop-ping back again to the rich side. Under suchcircumstances, the visits to the lean side con-stituted brief episodes of an activity (i.e., sam-pling) different from that at the rich side (fix-ing). One need only assume that ourprocedure underestimated the time spent pervisit to the lean side to explain the apparentbiases in the lower right graph in Figure 1.In particular, we excluded time spent duringthe COD from our calculations, on theground that it was signaled timeout from theexperiment. Had we included that time, wewould have had to decide how to allocate itbetween the two sides. Owing to prematurechangeovers to the lean side, most of thechangeover time was probably spent on thelean side. Limitations of our electromechan-ical equipment prevented us from solving thisproblem.

The important point made by Figure 1,however, is that such instances of under-matching and overmatching may be readilyexplained by adopting the molar view, be-cause it allows choice between the rich andlean alternatives to be seen as time allocationbetween two different activities. The molec-ular view presumably would explain Figure 1as the aggregation of many discrete responsesmade at the two alternatives, combined withassumptions about the reinforcement ofswitching and delay gradients. A molaristmight judge the account logically correct, butwould regard it as implausible and inelegant,illustrating once again that a paradigm clash

104 WILLIAM M. BAUM

is resolved by such considerations rather thanby data (Kuhn, 1970).

Activities, Stimulus Control, andResistance to Change

A seeming challenge for the molar viewcomes from research and theory about be-havioral momentum, a recent reexpression ofthe notion of response strength (Nevin, 1974,1992; Nevin & Grace, 2000). The experi-ments show that persistence of responding(resistance to change) depends on prior rateof reinforcement. The molar interpretationof the results, which eschews responsestrength, stems from a molar view of rein-forcement and stimulus control.

In an earlier paper (Baum, 1973), I arguedthat, just as behavior is extended, so too areconsequences extended. As response rate isreal (i.e., to be known about), so rate of re-inforcement and rate of punishment are real.The molar analogue to contiguity is correla-tion—that is, correlation between extendedactivities and extended consequences. If I for-get to add baking powder when I’m makinga cake, the result is disappointing, but mycake baking generally pays off well and ismaintained by its high rate of mainly goodconsequences. In the molar view, reinforce-ment is like starting and stoking a fire. Spe-cial materials and care get the fire going, andthrowing on fuel every now and then keepsthe fire going.

McDowell’s experiments on variation in k(e.g., Dallery et al., 2000) and experimentson asymmetrical concurrent performancessupport the idea that behavior consists of ex-tended allocations or activities. Reinforce-ment and punishment may change the timespent in an activity (i.e., allocation), but alsomay change the allocation among the partsand even the parts themselves. This latterkind might be called change in topography,referring roughly to the way an activity isdone. Whatever the change, the molar viewattributes it to differential extended conse-quences.

Once we move away from the atomism ofdiscrete responses, we should expect that theway we talk about reinforcement and stimuluscontrol will change too, even if only in subtleways. In the molecular view, for example,‘‘continuous’’ reinforcement is often con-trasted with ‘‘intermittent’’ reinforcement.

One may question whether the notions of in-termittent and continuous reinforcementhave any meaning in relation to extended ac-tivities. In the molar view, reinforcers coin-cide with various parts of the activity in vari-ous forms. What matters is the aggregate ofconsequences that the activity (allocation)produces relative to other activities (alloca-tions) over time. In the simplified environ-ment of the laboratory, concurrent schedulesarrange that a pattern of choice (an alloca-tion) produces a rate of reinforcement(Baum, 1981). As with choice patterns of self-control, in which impulsive behavior is im-mediately reinforced and self-control pays offbetter only in the long run, even though themore extended choice pattern would pro-duce more reinforcers in the long run, localreinforcement contingencies may prevent thechoice pattern (allocation) from evolving to-ward the maximum possible (Rachlin, 1995,2000; Vaughan & Miller, 1984). An experi-ment by Heyman and Tanz (1995), however,showed that providing signals allowed chang-es in reinforcer rate to reinforce changes inchoice pattern (allocation). They arrangedthat when pigeons’ choice over a sample ofresponses deviated toward a more extreme al-location than would be expected from thematching law (Equation 5), relative reinforce-ment would remain unchanged, but that theoverall reinforcer rate would increase and alight would come on. They found that devi-ations from matching were reinforced by thechanges in overall reinforcer rate.

The molar concept of reinforcement alsoimplies a molar concept of stimulus control.In the experiment by Heyman and Tanz(1995), the light signaled a relation betweenan extended pattern (an allocation) and anincrease in reinforcer rate. In the molecularview, a discriminative stimulus signals thatsome responses may be intermittently rein-forced, and its presence increases the proba-bility of the response. In the molar view, adiscriminative stimulus signals more frequentreinforcement of one activity or allocationthan another, and its presence increases thetime spent in that activity. Reinforcers that oc-cur in the presence of the stimulus plus thepresence of the activity or allocation increasethe control of the stimulus over that activityor allocation.

In the molar view, a response rate, whether

105MOLECULAR TO MOLAR

measured in experiments in which the activ-ities consist of repetitive motions like keypecks or lever presses (e.g., White, 1985) orused to measure general activity (Buzzard &Hake, 1984), is equivalent to an allocation, apattern of behavior, an activity. We have seenthat experiments on variation in k and asym-metrical concurrent performances may be in-terpreted as changes in response rate result-ing from changes in extended patterns ofresponding. Heyman and Tanz’s (1995) ex-periment embodies the molar idea of stimu-lus control, in which control over extendedpatterns of responding entails control overresponse rate and choice. If extended pat-terns of behavior (activities or allocations)may be reinforced and controlled by discrim-inative stimuli, then we should expect that re-sponse rates are both reinforceable and sub-ject to stimulus control.

We may apply these expanded notions ofreinforcement and stimulus control to exper-iments on behavioral momentum and resis-tance to change (Nevin, 1974, 1992; Nevin &Grace, 2000). In a typical experiment, pi-geons are exposed to a multiple schedulecomposed of two components, each consist-ing of a VI schedule of food reinforcementfor pecking at a response key. One VI is rich-er than the other and thus maintains a higherrate of key pecking. Once the two rates of keypecking have stabilized, a variety of differentoperations may be used to disrupt the re-sponding; the usual ones are prefeeding,food presentations during timeout periodsbetween components, and extinction. Thetypical result is that response rate decreasesin both components, but by a larger propor-tion in the component with fewer reinforcers.For prefeeding and food presentations be-tween components, the decreases in responserate might be interpreted as the result of adecrease in magnitude of programmed (VI)reinforcement relative to background rein-forcement. In terms of Equation 4, these op-erations would decrease rate of pecking byincreasing rO. How Equation 4 might accountfor the difference in rate of extinction is lessclear, but one might suppose that higherrates of key pecking, once established, tendto persist longer in the absence of reinforce-ment. Nevin, Tota, Torquato, and Shull(1990) reported an experiment, however,that undermined such seemingly straightfor-

ward explanations. Pigeons were exposed, asusual, to a multiple schedule, one in whichthe same VI schedule occurred in both com-ponents. In one component, however, it wasthe only schedule present, whereas in theother component, a second schedule rein-forcing pecks on a second key (Experiment2) or delivering food independently of be-havior (Experiment 1) was paired with theconstant schedule. Although the overall rateof reinforcement was lower in the single-VIcomponent, the response rate there was high-er than the response rate on the same key inthe component with the concurrent VI (aswould be expected; Rachlin & Baum, 1972).The crucial result was that, comparing the re-sponse rates on the constant-schedule keyduring extinction, the lower response rate de-creased more slowly than the higher responserate.

Nevin (1992) interpreted this result andthe earlier experiments to mean that rein-forcement builds behavioral momentum: Themore reinforcement, the more momentum;the more momentum, the less the responseis susceptible to disruption. To maintain thistheory, however, he had to distinguish be-tween what he called operant and respondentaspects of the components. The difficulty wasthat pecks at the constant-VI key were rein-forced at the same rate in both components;the extra reinforcers that made the differ-ence in resistance to change were associatedwith the second key or some other behavior,and how reinforcement of other behaviorcould increase a response’s momentum wasunclear. Nevin concluded that, because theoverall reinforcer rate was higher in the two-VI component, the momentum of all behav-ior in a component must depend on all thereinforcers in that component. The associa-tion of reinforcers for other behavior with thecomponent’s stimulus constituted a respon-dent or Pavlovian aspect to determining mo-mentum.

The ideas of reinforcement and stimuluscontrol of extended patterns of behavior (al-locations) open the way to a different inter-pretation of experiments on resistance tochange. In a multiple schedule, we may sup-pose that if the contingencies of reinforce-ment differ from component to component,they will generate different allocations of be-havior in the presence of the different dis-

106 WILLIAM M. BAUM

criminative stimuli. All the reinforcers in acomponent serve to reinforce the allocationoccurring there, and the stimulus enjoinsthat allocation. The more reinforcement, themore the stimulus enjoins the allocation. Ina multiple schedule with two different VIschedules in two components, the higher re-inforcer rate will be associated with the allo-cation that generates (i.e., is equivalent to)the higher response rate, stimulus controlwill be stronger over that allocation, and thatstimulus will sustain that allocation longer asit disintegrates (i.e., transforms into someother allocation including little or no peck-ing) during extinction. As the experimentsshow, the higher rate allocation will take lon-ger to disintegrate than the lower rate allo-cation. In Nevin et al.’s (1990) crucial exper-iment, different allocations occur in theone-VI component and in the two-VI com-ponent. The allocation in the one-VI com-ponent entails a higher response rate on theconstant-VI key, but that allocation is less re-inforced. The allocation in the two-VI com-ponent entails responding on both keys andis more reinforced. Because stimulus controlis stronger over the two-VI allocation, thatone disintegrates more slowly during extinc-tion. Hence the response rate on the con-stant-VI key falls more slowly in the two-VIcomponent.

Although this explanation of variation inresistance to change bears some similarity toNevin’s explanation, it has advantages. First,it is arguably simpler. It requires no appeal toseparate operant and respondent aspects, be-cause it invokes only the idea that stimuluscontrol depends on rate of reinforcement.Second, it requires only an expansion of theconcepts of stimulus control and reinforce-ment to apply to extended patterns of behav-ior, instead of the introduction of new con-cepts, such as behavioral momentum andmass (Nevin & Grace, 2000). These concepts,borrowed by analogy from Newtonian me-chanics, seem particularly unlikely to explainthe dynamics of behavior, because mechanicsoffers only nonhistorical immediate causes(Aristotle’s efficient causes; Rachlin, 1995).In the molar view, reinforcement is a processof selection, resembling natural selection—an entirely different sort of causation andfundamentally historical (Baum & Heath,1992; Baum & Mitchell, 2000; Skinner, 1981).

IDEAL RESPONSE CLASSESVERSUS CONCRETE

BEHAVIORAL PATTERNS

The concept of behavioral momentum,like the concept of response strength, flowsfrom the molecular, atomistic view of behav-ior. Momentum, like strength, is consideredthe possession of a class, the members ofwhich are momentary responses. Skinner’s(1935/1961, 1938) operant, for example, wasa class with discrete responses as members,and when its strength was high its membersoccurred at a high rate. His ill-fated idea ofthe reflex reserve depended on just such anotion of strength, and Nevin’s notion of mo-mentum—the contemporary equivalent ofthe reflex reserve—similarly depends for itsdefinition on the idea of response class. Inthe molecular view, one supposedly specifiesthe ideal properties required for membershipin the class (e.g., a certain force, a certainextent, etc.). Any lever press or key peck thatpossesses the ideal properties may be record-ed. To estimate response rate, one counts anumber of instances and divides by the timeinterval during which they were counted. Anincrease or decrease in response rate reflectsan increase or decrease in strength or mo-mentum of the class. The more the membersof the class are reinforced, the more is theclass’s strength. That response rates on inter-val schedules fall short of those on ratioschedules, for example, is explained by thedifferential reinforcement of long inter-response times (IRTs) in interval schedules,the IRT being considered another propertyof the response or instance (Ferster & Skin-ner, 1957; Morse, 1966). Reinforcement thenselectively strengthens different responseclasses. The high rates on ratio schedules areattributed to the absence of differential re-inforcement of IRTs. In this view, responserate always remains an abstraction, becausethe concrete particulars are the responses,the class instances.

In the molar view, an activity occupies moretime or less time, depending on the condi-tions of reinforcement. No notion of strengthor momentum enters the picture. When be-havior is seen as composed of continuous ac-tivities or extended patterns (i.e., alloca-tions), response rate is no longer anexpression of strength or momentum. A re-

107MOLECULAR TO MOLAR

sponse rate, as an allocation, is seen as con-crete.

Increases or decreases in rate of key peck-ing may or may not indicate increases or de-creases in the time spent pecking. The ex-amples of varying k (tempo), asymmetricalconcurrent performances, and varying resis-tance to change show that at least two possi-bilities exist. First, response rate may increaseor decrease because the mix of activitieschanges to include more or less time spentin the repetitive activity, as implied by Equa-tion 4 (cf. Shull et al., 2001). Second, re-sponse rate may increase or decrease becausethe repetitive activity itself (its topography)changes. The difference in response rates be-tween ratio and interval schedules arises be-cause the schedules reinforce different pat-terns of responding—that is, differentactivities. Interval schedules differentially re-inforce activities that result in lower rates ofkey operation, whereas ratio schedules differ-entially reinforce activities that result in highrates of key operation (Baum, 1981). Acrossthe low range of reinforcer rates, as reinforc-er rate increases across VI schedules (i.e., asthe average interval gets shorter), responserate increases and levels off, as Equation 4would predict, but when the VI schedule be-comes brief enough, it begins to function likea ratio schedule, and response rate increasesup to the same level as for a comparable VR(Baum, 1993). The increase across the lowrange of reinforcer rates represents an in-crease in time spent in low-tempo key peck-ing, whereas the increase across the highrange of reinforcer rates represents an in-crease in time spent in high-tempo key peck-ing (Baum, 1981, 1993).

Class Versus Individual

This difference between the molecular andmolar views—the difference between re-sponse strength and behavioral allocation—corresponds to the ontological distinction be-tween class and individual (Ghiselin, 1997;Hull, 1988). The molecular view, as laid outby Skinner (1935/1961), relied on the notionof operant classes. A class is defined by spec-ifying a list of properties or rules of member-ship (e.g., all actions that depress the lever).Classes are abstract in the sense that one canonly talk about them, not point to them ormeasure them. Their abstract nature appears

also in the lack of any requirement that theyhave members or that such members exist(e.g., human beings who can leap over tallbuildings in a single bound). Useful classeshave members, which, unless they are otherclasses (a possibility we will ignore here), con-stitute concrete particulars—concrete in thesense that one can point to them or at leastobserve them, and particular in the sensethat each is just one thing. So, although op-erant classes are abstract, responses (instanc-es) would be considered concrete (Skinner,1935/1961).

Besides being members of classes, concreteparticulars are individuals (see Ghiselin,1997, and Hull, 1988, for longer explana-tions). An individual is a cohesive whole thatis situated in space and time—a historical en-tity. That is, an individual (e.g., B. F. Skinner)has a location, a beginning, and potentiallyan end. Individuals have no instances (e.g.,B. F. Skinner is who he is and has no instanc-es). Individuals cannot be defined except byostension (i.e., by pointing; e.g., that is my catthere). Individuals have parts (left leg, rightleg, liver, and heart), rather than instances.The quote from John Donne at the begin-ning expresses well the relation of part towhole; as a clod is part of Europe, so any manis a part of mankind. Classes cannot do any-thing; only individuals can do things (e.g., catcannot walk into the room, whereas my catcan).

In particular, whereas individuals canchange, classes cannot change. B. F. Skinnerchanged from boyhood to adulthood, but hewas still the same individual, B. F. Skinner. Aclass remains fixed because it is defined byfixed properties or rules. If the properties orrules change, we only have a new class. Theonly change associated with a class is in thenumber of its instances. Were we to discoveran individual able to leap tall buildings in asingle bound, that class would no longer beempty. Mathematical sets cannot change evenin this way, because adding or subtracting el-ements from a set creates a new set.

Any science that deals with change, wheth-er phylogenetic change, developmentalchange, or behavioral change, requires enti-ties that can change and yet retain their iden-tity (e.g., Homo sapiens, my cat, or my diet),because only such entities provide historicalcontinuity. In other words, because only in-

108 WILLIAM M. BAUM

dividuals can change and yet maintain histor-ical continuity, such a science must deal withindividuals. Although individual usuallymeans individual organism in everyday dis-course, philosophers mean something moregeneral. Organisms exemplify cohesivewholes, but so too do activities or allocations.Just as an organism is made up of a liver, kid-neys, brain, and the like, functioning togeth-er to produce results in the environment, sotoo an utterance (e.g., ‘‘I need help with thisproblem’’) is made up of sounds that func-tion together to produce results in the envi-ronment. The various parts of the whole arethemselves individuals (e.g., the liver or theuttered word ‘‘help’’); all individuals are com-posed of other individuals. This point will beimportant when we discuss the nesting of ac-tivities.

By way of example, we may compare themolecular and molar accounts of differentialreinforcement (‘‘shaping’’). Skinner (1935/1961) recognized that reinforcement of a cer-tain class of responses generates responsesthat may actually lie outside the reinforcedclass. He called this process induction (see alsoSegal, 1972). Induction is essential for shap-ing novel behavior, because the new inducedresponses may be reinforced. To do this, onedefines a new class for reinforcement, onethat excludes some of the old members. Re-inforcement of this new class leads to induc-tion of further new responses, which allowsdefinition of another new class, and so on,until some target class is reached.

One challenge for this molecular accountof shaping is that reinforcement may induceundesirable behavior, sometimes called ad-junctive or interim behavior (Staddon & Sim-melhag, 1971). The problem is that such be-havior interferes with the process of shaping(Breland & Breland, 1961; Segal, 1972) andfalls outside the reinforced classes. Conse-quently, the molecular view treats it as a sep-arate type, distinct from operant behaviorand with rules of its own.

The molar view of shaping instead incor-porates induced behavior into the account.The process begins, not with a response class,but with an allocation of activities (an individ-ual). Some activities (parts) are reinforced.The allocation changes, the parts reinforcedchange, and the allocation changes further.Induced activities may enter the allocation at

any stage; they become new parts. The end-point of the process (if any) will be a stableallocation maintained by stable reinforce-ment contingencies.

Although the idea that particular discreteresponses are instances of a class remainscommon (e.g., in textbooks), the molecularview allows at least one other possibility.Glenn, Ellis, and Greenspoon (1992) pro-posed that the aggregate of particular occur-rences be thought of as analogous to a pop-ulation of organisms. As each individualorganism is a part of the population, so eachparticular discrete unit is a part of a behav-ioral population, rather than an instance of aclass. Thus, one could redefine an operant asa behavioral population, which would be anindividual rather than a class. Response ratethen would correspond to the size of the pop-ulation. Such a population would constitutean individual, but different from an activityor allocation, because its parts would be dis-crete responses (Glenn & Field, 1994). Theirproposal illustrates that the molecular viewcannot be said to entail the concept of re-sponse class in the way that it can be said toentail discrete units.

During the 1960s and 1970s, Skinner’s no-tion of the operant as a class came in for crit-ical discussion (e.g., Schick, 1971; Segal,1972; Staddon, 1973). The main problem washow to deal with the induction of new behav-ior. Catania (1973) proposed a solution thatresembles the proposal by Glenn et al.(1992). He suggested distinguishing betweenthe descriptive operant and the functionaloperant—that is, between the operant asspecified by class properties and the operantas the pattern of behavior that actually resultsfrom reinforcement. Catania’s suggestionoverlooks, however, that the functional oper-ant constitutes a different ontological kind,one that eludes definition by a list of prop-erties. It overlooks that, in moving from de-scriptive operant to functional operant, onealso moves from class to individual. The func-tional operant, which Catania represented bydrawing frequency distributions, correspondsto a population of responses, but the respons-es no longer can be seen as instances of aclass, because now they are parts of a whole—whatever unspecified responses occur afterreinforcement. They could be seen (in themolar view) as parts of an extended behav-

109MOLECULAR TO MOLAR

ioral allocation, an individual. That allocationis both engendered by and maintained by thereinforcement it produces. Like Glenn et al.,however, Catania based his idea on discreteresponses. In their related discussion, Glennet al. argued,

In the ontological sense, an operant is . . . anentity—a unit, an extant individual. . . . It iscomposed of a population of behavioral oc-currences that are distributed over time, eachoccurrence having a unique spatiotemporallocation. The operant can evolve (as only op-erants and species can but organisms and re-sponses cannot). (p. 1333)

The main difference between this and themolar view is its implicit reliance on discreteresponses (‘‘occurrences’’). If one added thepoint that the occurrences take up time, in-troducing an analogue to the carrying capac-ity (limited size of a biological population),and one added that the occurrences werebouts of extended activities, the concept ofbehavioral population would become almostthe same as the concept of allocation. Onefurther concept, implied by the analogy to bi-ological evolution, is the idea that activitiesare nested, that every activity (allocation) iscomposed of parts that are other activities.

Species and ActivitiesAs Individuals

Another way to understand the concrete-ness of behavioral allocations, activities, andresponse rates is by comparison to evolution-ary theory. Glenn et al. (1992) were drawingon Ghiselin’s (1981, 1997) argument thatspecies are not classes but individuals. Thatis, the relation of an organism to its speciesis not the relation of instance to class, but therelation of part to whole. As before, the wordindividual here refers to an integrated entitythat may change through time. As before, incontrast to a class, an individual is situated intime and space (i.e., has a beginning andend) and has parts but no instances (e.g., B.F. Skinner). An organism is an individual, ofcourse, but, Ghiselin explains, so too is a spe-cies. A species is an individual composed ofthe organisms that make it up, in the sameway as John Donne noted that every man isa part of mankind. All the individual birds inthe Galapagos Islands that make up the spe-cies Geospiza fortis are parts of that whole. Se-lection may change a species through time,

particularly if the environment changes, butthe species remains the same individual, justas a person who grows and ages remains thesame individual. The existence of a speciesthrough time is referred to as its lineage. Alineage is an extended temporal entity inmuch the same way that a pattern of behavioris an extended temporal entity.

Ghiselin’s point was at first controversialamong biologists, but gradually gained accep-tance. Now, even its critics acknowledge that‘‘Only a few biologists and (bio)philosophershave resisted [it]’’ (Mahner & Bunge, 1997,p. 254).

Like a species, an allocation of behavior—an activity—is an individual. It is an entitywith a beginning and an end, integrated byits function; that is, by its effects in the envi-ronment. Just as taking away an organism’sleg changes its functioning, so taking awaypart of a behavioral pattern changes its envi-ronmental effects. Forget to add baking pow-der to a cake mix, and the result may be in-edible. A particular cake baking, however, ispart of a more extended allocation of bakingor cooking, including both successful and un-successful attempts and all their various out-comes.

This illustrates another parallel betweenextended activities and species: their similarparticipation in larger individuals. Commonancestry unites species into more extendedindividuals at the level of genus. Genera uniteinto still larger individuals, and so on, rightup to phylum and, finally, life (Ghiselin,1997). Although individuals at these varioustaxonomic levels may be more or less extend-ed, no matter how large or small they still areindividuals. Homo sapiens, as a species in thegenus Homo, is a part of the genus, just as theother species in that genus are parts of it.Geospiza fortis is one species of Darwin’s finch-es. It, Geospiza scandens, and several other spe-cies make up the genus Geospiza. In relationto the genus, the species are parts of a whole,not instances of a class.

NESTING OFACTIVITIES

Activities, like species, are parts of more ex-tended activities. Getting to work each daymay be part of working each day. Workingeach day may be part of holding a job. Hold-

110 WILLIAM M. BAUM

Fig. 2. One person’s hypothetical activity patterns. Left: pattern of life activities, showing time divided amonghealth and maintenance (i.e., personal satisfaction), gaining resources (e.g., job), relationships (e.g., friends), andreproduction (e.g., family). Middle: pattern of health and maintenance nested within the life activities, showing timedivided among medical (e.g., visits to practitioners), eating, personal hygiene, and recreation. Right: pattern ofrecreation nested within health and maintenance, showing time divided among watching television, reading, movies,and walking (i.e., exercise). All of these patterns constitute individuals, because they change without changing theiridentity.

ing a job may be part of making a living. Mak-ing a living may be part of gaining resources.Gaining resources may end with retirement,and all such parts may make up a whole,which we could call a lifetime lived (Baum,1995, 1997; Rachlin, 1994).

The converse holds, too: Activities and spe-cies are made up of parts consisting of lessextended individuals. A species may be com-posed of several populations. A populationmay be composed of several demes. Demes,populations, and species all are composed oforganisms, which are composed of organs,which are composed of cells, and so on. Forthe purposes of evolutionary theory, onestops at the smallest individual that mayevolve—a deme, a population, or a species.An activity like getting to work may be com-posed of parts like starting the car, driving tothe highway, driving on the highway, drivingto the campus, hunting for a parking place,and walking to the office. Driving on thehighway has parts like adjusting speed, switch-ing lanes, scanning for police cars, and swear-ing at other drivers. And so on, for each part.Some least extended activity exists for theanalysis of behavior, as it does for evolution-ary theory, defined by its usefulness and,probably, by its likelihood of evolving. Highlypracticed and stereotyped activities like shift-ing gears in a car change rarely; they attractlittle interest as targets of modification,whereas driving speed may change signifi-cantly and is a frequent target of attempts atmodification (e.g., ‘‘speed kills’’).

The Molar View of Ever yday Life

We may illustrate the conceptual power ofthe idea of nested activities with a hypotheti-cal example. Liz is a married woman in her40s, who lives in a city, works selling retire-ment plans for a mutual fund company, andhas an 18-year-old son who still lives at home.As I suggested in earlier papers (Baum, 1995,1997), her life may be divided into four basicactivities: personal satisfaction (i.e., healthand maintenance), job (i.e., gaining resourc-es), relationships, and family (i.e., reproduc-tion). The left graph in Figure 2 shows thepattern of these activities at this point in Liz’slife. Leaving out the 9 hr she spends sleepingeach night, we see that she spends about 35hr (33%) per week in personal satisfaction,36 hr (34%) in gaining resources, 24 hr(23%) in making and maintaining relation-ships, and 10 hr (10%) in family activities.The allocation was different 10 or 15 yearsearlier, when her son was young and she wascaring for her husband’s children from pre-vious marriages. As an individual, the activityhas changed and will change again over thecourse of Liz’s life, but it will remain the sameindividual, the pattern of Liz’s life. All fourof the activities shown in the left graph maybe analyzed in more detail and seen to becomposed of other activities. For example,Liz’s family activities consist of occasionallycaring for her husband’s grandchildren andprimarily of caring for her son: feeding him,cleaning up after him, advising him, and in-

111MOLECULAR TO MOLAR

terfering in his life sufficiently to make himrebellious.

The middle graph in Figure 2 shows thetime Liz spends in personal satisfaction de-composed into parts. She spends about 3 hr(8%) per week seeing medical practitioners,10 hr (29%) eating, 7 hr (20%) in personalhygiene, and 15 hr (43%) in recreation. Thisallocation also is an individual, subject tochange, and is nested within or incorporatedinto the more extended allocation of Liz’s lifeactivities. Each of the activities composing theactivity of personal satisfaction also is an in-dividual and is itself composed of individuals.The right graph in Figure 2 shows Liz’s rec-reational activities broken into parts. Shespends about 7 hr (47%) per week watchingtelevision, 6 hr (40%) reading, 0.5 hr (3%)watching movies, and 1.5 hr (10%) walkingfor exercise. This allocation of recreationalactivity constitutes an individual and is part ofLiz’s personal satisfaction and, because ofthat, is part of Liz’s life activity. Each of theparts of Liz’s recreational activities could befurther decomposed into parts that alsowould be individuals (Baum, 1995, 1997).

In contrast, the molecular view invites oneto view life as a time line of discrete events,one following another—a behavioral stream(e.g., Schoenfeld & Farmer, 1970). To themolarist, such a characterization, though pos-sible, appears impoverished and to resemblelittle the way people actually talk about theirlives (i.e., inelegant and low on external va-lidity).

Figure 2 implies that one might go into anyamount of detail about Liz’s activities. Whereshould subdividing stop, and how does onedefine the parts? Answers would depend onthe purpose of the analysis, whether it betherapeutic intervention, basic research, orsomething else. The issues involved are ad-dressed most directly in the context of labo-ratory research.

Applications in the Laborator y

As a laboratory example, we may consideractivities like key pecking and lever pressing.A pigeon’s food peck, when examined in de-tail, constitutes an individual with parts: for-ward head motion, eye closing, opening ofthe beak, head withdrawal, closing of thebeak, eye opening (Ploog & Zeigler, 1997;Smith, 1974). It is a stereotyped pattern that

researchers almost never seek to change, al-though other sorts of pecks, containing dif-ferent parts, exist, such as water-reinforcedpecks and exploratory pecks ( Jenkins &Moore, 1973; Schwartz & Williams, 1972; Wo-lin, 1948/1968). A similar, though more var-ied, list of motions might be made for a rat’slever press. Key pecks or lever presses may beparts of key pecking or lever pressing rein-forced, say, on a VI schedule. Key pecking orlever pressing on two different keys or leversmay be parts of an allocation of behavior be-tween two sources of reinforcement (Ploog &Zeigler, 1997). We usually measure the re-sponding on one of the keys or levers as aresponse rate. We measure the allocation aschoice or relative response rate.

In contrast, the molecular view sees choiceor concurrent performance as consisting ofoccurrences of two responses, each at a cer-tain rate. The response rates may be com-pared by calculating some relative measure(proportion or ratio) but such a measure isseen as only a summary or as ‘‘derived’’ (Ca-tania, 1981; Herrnstein, 1961). At least oneresearcher has suggested that relative mea-sures, as derived, should be viewed with sus-picion and that response rate is the only truemeasure of behavior (Catania, 1981). Thelimitations of such a view become apparentwhen we consider a specific example.

Alsop and Elliffe (1988) exposed 6 pigeonsto over 30 pairs of concurrent VI schedules,varying both relative and overall rate of re-inforcement. I reanalyzed their data bygrouping them according to five levels of re-inforcer ratio (r): 0.12, 0.25, 1.0, 4.0, and 8.0.Within each group, the obtained reinforcerratios varied a bit, but the variation fromgroup to group was larger than the variationwithin a group (although to achieve this, fiveconditions with aberrant reinforcer ratios outof 186 were omitted—one each for 3 pigeonsand two for 1 pigeon). For each reinforcerratio, overall reinforcer rate varied fromabout 10 to about 400 reinforcers per hour.Figure 3 shows the average results, whichwere representative of the results for the in-dividual birds.

The top graph in Figure 3 shows the totalrate of pecking at the two keys as a functionof the overall reinforcer rate. The curve rep-resents the least squares fit of Equation 4 (rO5 9.44; k 5 94.6). The only unusual feature

112 WILLIAM M. BAUM

Fig. 3. A study of concurrent schedules that illustratesthe concept of nested patterns. Top: combined rate ofkey pecking on two concurrent VI schedules as a functionof overall rate of reinforcement. The different symbolsrepresent different levels of reinforcer ratio (r). Thecurve represents the least squares fit of Equation 4 to allthe points. Middle: relative responding at the two alter-natives as a pattern nested within the pattern of overallrate of key pecking. The horizontal lines represent theaverage behavior ratio at each level of reinforcer ratio.Behavior ratio varies, as would be expected, across rein-

←

forcer ratio, but is independent of overall rate of rein-forcement. Bottom: the fix-and-sample pattern nestedwithin the pattern of relative responding. The bottomfive horizontal lines indicate the averages of probabilityof visiting the nonpreferred alternative, p(N), across thelevels of reinforcer ratio. The smaller the relative rein-forcement for visiting the nonpreferred alternative, thelower the probability of visiting it. Hence, the symbols forr equal to 0.12 and 8.0 (circles and diamonds) show thelowest p(N), and the symbols for r equal to 1.0 (triangles)show the highest p(N). The uppermost horizontal lineshows the average number of pecks per visit at the non-preferred alternative (Nppv; right vertical axis). The av-erage duration of a visit to the nonpreferred alternativeremained approximately constant at eight pecks, consis-tent with the fix-and-sample pattern. All variables aretransformed to Base 2 logarithms.

of this analysis is that pecks at the two keyswere combined, whereas usually Equation 4would apply to pecks at a single key. Recallingthat Equation 4 describes choice betweenschedule-reinforced activity and other back-ground activities, we see that choice betweenkey pecking and other activities followed theorderly pattern expected from the matchinglaw. That the various sets of symbols all over-lap each other shows that reinforcer ratio hadno effect on this choice pattern.

The middle graph in Figure 3 shows thatthe overall key pecking contained within itanother regular pattern. Here the ratio ofpecks at the two keys is plotted against overallreinforcer rate. As in the top graph, the dif-ferent symbols represent data from the dif-ferent reinforcer ratios from the two keys. Ahorizontal line, corresponding to the averagepeck ratio, is drawn through each set of sym-bols to allow assessment of trend. As overallreinforcer rate varied, each reinforcer ratiomaintained a certain peck ratio, which re-mained approximately invariant across over-all reinforcer rate. In other words, regardlessof the overall rate of reinforcement, the be-havior ratio remained about the same foreach reinforcer ratio, in accordance with thegeneralized matching law (Equation 7).

The bottom graph in Figure 3 shows that,on still closer examination, a pattern existswithin the behavior ratios, the activity that Iearlier called fix and sample (Baum et al.,1999). To see whether such a pattern waspresent, I calculated for each behavior ratiothe average number of pecks in a visit to thenonpreferred key and the probability of leav-

113MOLECULAR TO MOLAR

ing the preferred key to visit the nonpre-ferred key (number of visits to the nonpre-ferred key divided by number of pecks at thepreferred key). The fix-and-sample patternwould be revealed by invariant visits to thenonpreferred key combined with variationonly in the probability of visiting the nonpre-ferred key. For convenience, both probabilityof visiting the nonpreferred key [p(N)] andnumber of pecks per visit to the nonpre-ferred key (Nppv) are shown in the samegraph; p(N) is represented on the left verticalaxis, and Nppv is represented on the rightvertical axis. The five lower sets of symbolsshow that p(N), like the behavior ratio, dif-fered across reinforcer ratios, but remainedapproximately invariant for each reinforcerratio as overall reinforcer rate varied. Eachreinforcer ratio produced a certain, roughlyinvariant, probability of a visit to the nonpre-ferred alternative. The horizontal lines showthe averages. As would be expected from theresults of Baum et al. (1999), the lowest prob-abilities of visiting the nonpreferred key oc-curred for the strongest preferences, gener-ated by the most extreme reinforcer ratios (8and 0.12). The two intermediate reinforcerratios (4 and 0.25) produced intermediatep(N), and the 1:1 reinforcer ratio, which pro-duced the weakest preferences, produced thehighest probabilities of visiting the nonpre-ferred side. The higher the relative reinforce-ment for the nonpreferred key, the higherthe frequency of visiting the nonpreferredkey. The uppermost sets of symbols show thatNppv, the visit duration to the nonpreferredkey, remained invariant with respect to bothoverall reinforcer rate and reinforcer ratio.Independence from overall reinforcer rate isshown by the adherence of the points to thehorizontal line representing the average.That the different symbols all lie on top ofone another shows independence from thereinforcer ratio. Visits to the nonpreferredside, regardless of rate or distribution of re-inforcement, always lasted about eight pecks(i.e., 23; see right vertical axis), presumablylong enough to outlast the 2-s COD. Regard-less of the behavior ratio, the same activity ofbriefly visiting (i.e., sampling) the nonpre-ferred key held; only the probability of visit-ing changed to produce the different behav-ior ratios shown in the middle graph.

Figure 3 shows how activities or patterns

may be nested within each other. Nested with-in the pattern of overall responding to thekeys (top graph) was a pattern of allocationof the overall responding between the keys,measured by the behavior ratio (middlegraph). Nested within the behavior ratio wasa pattern of visitation at the two keys, a pat-tern of fixing on the preferred alternativeand briefly sampling the nonpreferred alter-native with a frequency depending on the re-inforcer ratio (bottom graph). In the molarview, all of these patterns constitute alloca-tions—between pecking and background ac-tivities (top graph), between pecking left andpecking right (middle graph), and betweenfixing and sampling (bottom graph).

CONCLUSION

An activity, like a species, is an individual,a concrete particular with parts, not a classwith instances. Contrary to 19th- and early20th-century thinking, the concrete particu-lars of behavior need not be momentary ordiscrete, but extend through time as parts ofbehavioral patterns (activities or allocations)over minutes, hours, days, or years. Like spe-cies, they only need to have a beginning andpotentially an end. This recognition changesthe notions of reinforcement and stimuluscontrol, but only moderately. Instead ofthinking of reinforcement as a sort of ‘‘mo-ment of truth’’ (e.g., Ferster & Skinner, 1957;Skinner, 1948), defined by contiguity with amomentary response, we may think of rein-forcement as a cumulative effect, as selectionthrough time (Skinner, 1981; Staddon, 1973),shaping patterns of behavior (activities) inlineages. Because reinforcement operates onthe activity as a whole, we are relieved of anyneed to imagine that the parts are all sepa-rately reinforced. Behavioral chains, for ex-ample, need not be held together with imag-ined conditional reinforcers, because they arereinforced as a whole (Baum, 1973; Rachlin,1991). Avoidance need not be explained withimagined stimuli and reinforcers (Baum,1973, 2001). We understand the behavior ofa species in relation to the climate and re-sources available in its evolutionary environ-ment. Similarly, instead of thinking of stimu-lus control as changing the probability of aresponse, we may think of discriminative stim-uli as setting the context in which certain ac-

114 WILLIAM M. BAUM

tivities or patterns are reinforced and wax inthe time that they occupy. Making these ex-tensions, we increase our ability to explaindisparate phenomena, such as variation in as-ymptotic response rate (k), asymmetrical con-current performances (Figure 1), resistanceto change, and the relations among analysesat various levels of generality (Figures 2 and3; Hineline, 2001).

Questions remain, of course. If an activityis an individual, how should we think aboutits coherence? Ghiselin (1997) explains thatorganisms have a special cohesiveness thatspecies and other taxa lack; an organismfunctions as an integrated whole. The partsof a species may be less crucial than those ofan organism, but a species has coherence be-cause it is defined as a reproductive unit, re-productively isolated from other such units(Mayr, 1970) and because the parts of thespecies share common ancestry (i.e., areparts of the same lineage). Higher taxa, fromgenus on up, have coherence only because ofcommon ancestry. In analogy to biologicaltaxa, the parts of an activity share commonancestry—are parts of the same lineage—be-cause they result from the same history of se-lection (reinforcement). The various parts ofthe activity we call ‘‘holding a job’’ coherebecause they share a common function (gain-ing resources) and a common history of se-lection (reinforcement) among variants thatfunctioned better and worse. Activities maybecome extinct in the same way as species, bya loss of functionality of the whole. The endof an unrewarding marriage (an activity) isthe end of an individual, like the extinctionof a species. Further evidence of coherencein the parts of an activity may be found incommon variation in the face of change inenvironmental factors (Herrnstein, 1977).Food deprivation, for example, changes timeallocation to a host of food-related activities.A more complete answer to the question ofcoherence awaits further research.

Although the research discussed here sug-gests advantages to the molar view over themolecular, deciding between the two para-digms depends, not on data, but on satisfac-tory interpretation of data. No one shoulddoubt that molecular accounts of concurrentperformance are possible. The advantages tothe molar view lie in its ability to integrateexperimental results, in its promotion of

quantitative theory, and in its applicability toeveryday life. The results of Alsop and Elliffe(1988; Figure 3) illustrate the way the molarview both integrates results at various levelsof analysis and fits them into a quantitativeframework. The hypothetical example of Liz(Figure 2) illustrates the power of the molarview to apply to everyday concepts like ‘‘hold-ing a job’’ or ‘‘recreation’’ (see Rachlin, 1994,for further discussion). Taking our cue fromanother historical science, evolutionary biol-ogy, we see that extendedness of allocationsor activities in no way excludes them fromconcreteness. On the contrary, I have arguedthat the discrete events of the molecular vieware abstractions (see Baum, 1997, for furtherdiscussion). Although someone committed tothe molecular view might disagree, I have ar-gued that on these grounds of plausibility, ex-planatory power, and elegance the molar viewis the superior paradigm.

REFERENCES

Alsop, B., & Elliffe, D. (1988). Concurrent-schedule per-formance: Effects of relative and overall reinforcerrate. Journal of the Experimental Analysis of Behavior, 49,21–36.

Ashby, W. R. (1954). Design for a brain. London: Chap-man & Hall.

Baum, W. M. (1973). The correlation-based law of effect.Journal of the Experimental Analysis of Behavior, 20, 137–153.

Baum, W. M. (1976). Time-based and count-based mea-surement of preference. Journal of the ExperimentalAnalysis of Behavior, 26, 27–35.

Baum, W. M. (1981). Optimization and the matchinglaw as accounts of instrumental behavior. Journal of theExperimental Analysis of Behavior, 36, 387–403.

Baum, W. M. (1993). Performances on ratio and intervalschedules of reinforcement: Data and theory. Journalof the Experimental Analysis of Behavior, 59, 245–264.

Baum, W. M. (1995). Introduction to molar behavioranalysis. Mexican Journal of Behavior Analysis, 21, 7–25.

Baum, W. M. (1997). The trouble with time. In L. J.Hayes & P. M. Ghezzi (Eds.), Investigations in behavioralepistemology (pp. 47–59). Reno, NV: Context Press.

Baum, W. M. (2001). Molar versus molecular as a para-digm clash. Journal of the Experimental Analysis of Behav-ior, 75, 338–341.

Baum, W. M., & Aparicio, C. F. (1999). Optimality andconcurrent variable-interval variable-ratio schedules.Journal of the Experimental Analysis of Behavior, 71, 75–89.

Baum, W. M., & Heath, J. L. (1992). Behavioral expla-nations and intentional explanations in psychology.American Psychologist, 47, 1312–1317.

Baum, W. M., & Mitchell, S. H. (2000). Newton and Dar-win: Can this marriage be saved? Behavioral and BrainSciences, 23, 91–92.

115MOLECULAR TO MOLAR

Baum, W. M., & Rachlin, H. C. (1969). Choice as timeallocation. Journal of the Experimental Analysis of Behav-ior, 12, 861–874.

Baum, W. M., Schwendiman, J. W., & Bell, K. E. (1999).Choice, contingency discrimination, and foraging the-ory. Journal of the Experimental Analysis of Behavior, 71,355–373.

Breland, K., & Breland, M. (1961). The misbehavior oforganisms. American Psychologist, 16, 681–684.

Buzzard, J. H., & Hake, D. F. (1984). Stimulus controlof schedule-induced activity in pigeons during multi-ple schedules. Journal of the Experimental Analysis of Be-havior, 42, 191–209.

Campbell, D. T. (1956). Adaptive behavior from randomresponse. Behavioral Science, 1, 105–110.

Catania, A. C. (1973). The concept of the operant in theanalysis of behavior. Behaviorism, 1, 103–115.

Catania, A. C. (1981). The flight from experimentalanalysis. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe(Eds.), Quantification of steady-state operant behavior (pp.49–64). Amsterdam: Elsevier North-Holland.

Chiesa, M. (1994). Radical behaviorism: The philosophy andthe science. Boston: Authors Cooperative.

Dallery, J., McDowell, J. J, & Lancaster, J. S. (2000). Fal-sification of matching theory’s account of single-alter-native responding: Herrnstein’s k varies with sucroseconcentration. Journal of the Experimental Analysis of Be-havior, 73, 23–43.

Dinsmoor, J. A. (2001). Stimuli inevitably generated bybehavior that avoids electric shock are inherently re-inforcing. Journal of the Experimental Analysis of Behavior,75, 311–333.

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

Ghiselin, M. T. (1981). Categories, life, and thinking.Behavioral and Brain Sciences, 4, 269–313.

Ghiselin, M. T. (1997). Metaphysics and the origin of species.Albany: State University of New York Press.

Gilbert, R. M. (1970). Psychology and biology. The Ca-nadian Psychologist, 11, 221–238.

Gilbert, T. F. (1958). Fundamental dimensional prop-erties of the operant. Psychological Review, 65, 272–285.

Glenn, S. S., Ellis, J., & Greenspoon, J. (1992). On therevolutionary nature of the operant as a unit of be-havioral selection. American Psychologist, 47, 1329–1336.

Glenn, S. S., & Field, D. P. (1994). Functions of the en-vironment in behavioral evolution. The Behavior Ana-lyst, 17, 241–259.

Herrnstein, R. J. (1961). Relative and absolute strengthof response as a function of frequency of reinforce-ment. Journal of the Experimental Analysis of Behavior, 4,267–272.

Herrnstein, R. J. (1970). On the law of effect. Journal ofthe Experimental Analysis of Behavior, 13, 243–266.

Herrnstein, R. J. (1974). Formal properties of thematching law. Journal of the Experimental Analysis of Be-havior, 21, 159–164.

Herrnstein, R. J. (1977). The evolution of behaviorism.American Psychologist, 32, 593–603.

Herrnstein, R. J., & Heyman, G. M. (1979). Is matchingcompatible with reinforcement maximization on con-current variable interval, variable ratio? Journal of theExperimental Analysis of Behavior, 31, 209–223.

Heyman, G. M., & Tanz, L. (1995). How to teach a pi-

geon to maximize overall reinforcement rate. Journalof the Experimental Analysis of Behavior, 64, 277–297.

Hineline, P. N. (2001). Beyond the molar-molecular dis-tinction: We need multiscaled analyses. Journal of theExperimental Analysis of Behavior, 75, 342–347.

Houston, A. I., & McNamara, J. (1981). How to maxi-mize reward rate on two varable-interval paradigms.Journal of the Experimental Analysis of Behavior, 35, 367–396.

Hull, D. L. (1988). Science as a process: An evolutionaryaccount of the social and conceptual development of science.Chicago: University of Chicago Press.

Jenkins, H. M., & Moore, B. R. (1973). The form of theauto-shaped response with food or water reinforcers.Journal of the Experimental Analysis of Behavior, 20, 163–181.

Kuhn, T. S. (1970). The structure of scientific revolutions(2nd ed.). Chicago: University of Chicago Press.

Lee, V. L. (1983). Behavior as a constituent of conduct.Behaviorism, 11, 199–224.

Mahner, M., & Bunge, M. (1997). Foundations of biophi-losophy. Berlin: Springer-Verlag.

Mayr, E. (1970). Populations, species, and evolution. Cam-bridge, MA: Harvard University Press.

McDowell, J. J. (1987). A mathematical theory of rein-forcer value and its application to reinforcement de-lay in simple schedules. In M. L. Commons, J. E. Ma-zur, J. A. Nevin, & H. Rachlin (Eds.), Quantitativeanalyses of behavior: Vol. 5. The effect of delay and of in-tervening events on reinforcement value (pp. 77–105).Hillsdale, NJ: Erlbaum.

Morse, W. H. (1966). Intermittent reinforcement. In W.K. Honig (Ed.), Operant behavior: Areas of research andapplication (pp. 52–108). New York: Appleton-Centu-ry-Crofts.

Nevin, J. A. (1974). Response strength in multiple sched-ules. Journal of the Experimental Analysis of Behavior, 21,389–408.

Nevin, J. A. (1992). An integrative model for the studyof behavioral momentum. Journal of the ExperimentalAnalysis of Behavior, 57, 301–316.

Nevin, J. A., & Grace, R. C. (2000). Behavioral momen-tum and the law of effect. Behavioral and Brain Sciences,23, 73–130.

Nevin, J. A., Tota, M. E., Torquato, R. D., & Shull, R. L.(1990). Alternative reinforcement increases resis-tance to change: Pavlovian or operant contingencies?Journal of the Experimental Analysis of Behavior, 53, 359–379.

Pear, J. J. (1985). Spatiotemporal patterns of behaviorproduced by variable-interval schedules of reinforce-ment. Journal of the Experimental Analysis of Behavior, 44,217–231.

Ploog, B. O., & Zeigler, H. P. (1997). Key-peck proba-bility and topography in a concurrent variable-intervalvariable-interval schedule with food and water rein-forcers. Journal of the Experimental Analysis of Behavior,67, 109–129.

Premack, D. (1965). Reinforcement theory. In D. Levine(Ed.), Nebraska symposium on motivation (pp. 123–180).Lincoln: University of Nebraska Press.

Premack, D. (1971). Catching up with common sense,or two sides of a generalization: Reinforcement andpunishment. In R. Glaser (Ed.), The nature of reinforce-ment (pp. 121–150). New York: Academic Press.

116 WILLIAM M. BAUM

Rachlin, H. (1976). Behavior and learning. San Francisco:Freeman.

Rachlin, H. (1991). Introduction to modern behaviorism(3rd ed.). New York: Freeman.

Rachlin, H. (1994). Behavior and mind: The roots of modernpsychology. New York: Oxford University Press.

Rachlin, H. (1995). Self-control: Beyond commitment.Behavioral and Brain Sciences, 18, 109–159.

Rachlin, H. (2000). The science of self-control. Cambridge,MA: Harvard University Press.

Rachlin, H., & Baum, W. M. (1972). Effects of alternativereinforcement: Does the source matter? Journal of theExperimental Analysis of Behavior, 18, 231–241.

Schick, K. (1971). Operants. Journal of the ExperimentalAnalysis of Behavior, 15, 413–423.

Schoenfeld, W. N., & Farmer, J. (1970). Reinforcementschedules and the ‘‘behavior stream.’’ In W. N.Schoenfeld (Ed.), The theory of reinforcement schedules(pp. 215–245). New York: Appleton-Century-Crofts.

Schwartz, B., & Williams, D. R. (1972). Two differentkinds of key peck in the pigeon: Some properties ofresponses maintained by negative and positive re-sponse-reinforcer contingencies. Journal of the Experi-mental Analysis of Behavior, 18, 201–216.

Segal, E. F. (1972). Induction and the provenance ofoperants. In R. M. Gilbert & J. R. Millenson (Eds.),Reinforcement: Behavioral analyses (pp. 1–34). New York:Academic.

Shull, R. L., Gaynor, S. T., & Grimes, J. A. (2001). Re-sponse rate viewed as engagement bouts: Effects ofrelative reinforcement and schedule type. Journal ofthe Experimental Analysis of Behavior, 75, 247–274.

Skinner, B. F. (1938). The behavior of organisms. New York:Appleton-Century-Crofts.

Skinner, B. F. (1948). ‘‘Superstition’’ in the pigeon. Jour-nal of Experimental Psychology, 38, 168–172.

Skinner, B. F. (1950). Are theories of learning necessary?Psychological Review, 57, 193–216.

Skinner, B. F. (1961). The analysis of behavior. In Cu-mulative record (Enlarged ed., pp. 70–76). New York:

Appleton-Century-Crofts. (Original work published1953)

Skinner, B. F. (1961). The experimental analysis of be-havior. In Cumulative record (Enlarged ed., pp. 100–131). New York: Appleton-Century-Crofts. (Originalwork published 1957)

Skinner, B. F. (1961). The generic nature of the con-cepts of stimulus and response. In Cumulative record(Enlarged ed., pp. 347–366). New York: Appleton-Century-Crofts. (Original work published 1935)

Skinner, B. F. (1981). Selection by consequences. Science,213, 501–504.

Smith, R. F. (1974). Topography of the food-reinforcedkey peck and the source of 30-millisecond interres-ponse times. Journal of the Experimental Analysis of Be-havior, 21, 541–551.

Staddon, J. E. R. (1973). On the notion of cause, withapplications to behaviorism. Behaviorism, 1, 25–63.

Staddon, J. E. R., & Simmelhag, V. (1971). The ‘‘super-stition’’ experiment: A re-examination of its implica-tions for the principles of adaptive behavior. Psycholog-ical Review, 78, 3–43.

Vaughan, W., Jr., & Miller, H. L., Jr. (1984). Optimizationversus response-strength accounts of behavior. Journalof the Experimental Analysis of Behavior, 42, 337–348.

White, K. G. (1978). Behavioral contrast as differentialtime allocation. Journal of the Experimental Analysis ofBehavior, 29, 151–160.

White, K. G. (1985). Interresponse-time analysis of stim-ulus control in multiple schedules. Journal of the Ex-perimental Analysis of Behavior, 43, 331–339.

Wolin, B. R. (1968). Difference in manner of pecking akey between pigeons reinforced with food and withwater. In A. C. Catania (Ed.), Contemporary research inoperant behavior (p. 286). Glenview, IL: Scott, Fores-man. (Original work published 1948)

Received May 18, 2001Final acceptance March 12, 2002