An omalies, such as a th e positive cor relation between magn itude of an in cen tive an d respon se rates in some con texts an d a n egative cor relation in oth er con texts an d b th
Trang 1ECONOM ICS, ECOL OGICS, AND M ECH ANICS:
T H E DYNAM ICS OF RESPONDING UNDER CONDIT IONS OF VAR YING M OT IVAT ION
PET ER R KI LLEEN ARI ZO N A STAT E U N I VERSI T Y
Th e mech an ics of beh avior developed by Killeen ( 1994) is exten ded to deal with deprivation an d satiation an d with recover y of arousal at th e begin n in g of session s Th e exten ded th eor y is validated again st satiation cur ves an d with in -session ch an ges in respon se rates An omalies, such as ( a) th e positive cor relation between magn itude of an in cen tive an d respon se rates in some con texts an d a
n egative cor relation in oth er con texts an d ( b) th e greater promin en ce of in cen tive effects wh en magn itude is varied with in th e session rath er th an between session s, are explain ed in ter ms of th e basic in terplay of drive an d in cen tive motivation Th e models are applied to data from closed econ - omies in wh ich ch an ges of satiation levels play a key role in deter min in g th e ch an ges in beh avior Relaxation of various assumption s leads to closed-for m models for respon se rates an d deman d fun c- tion s in th ese con texts, on es th at sh ow reason able accord with th e data an d rein force argumen ts for
un it price as a con trollin g variable Th e cen tral role of deprivation level in th is treatmen t distin guish es it from econ omic models It is argued th at tradition al experimen ts sh ould be redesign ed to reveal basic prin ciples, th at ecologic experimen ts sh ould be redesign ed to test th e applicability of
-th ose prin ciples in more n atural con texts, an d -th at beh avioral econ omics sh ould con sist of -th e application s of th ese prin ciples to econ omic con texts, n ot th e adoption of econ omic models as alter n atives to beh avioral an alysis.
Key words: econ omics, ecologics, mech an ics, deprivation , satiation , motivation , arousal, deman d fun ction s, drive, in cen tive, models, prin ciples
Th is paper compares th ree approach es to
th e prediction of beh avior th at is un der th e
con trol of in cen tives an d supported by
moti-vation al states of var yin g in ten sity Behavioral
economics frames beh avior as an exch an ge of
goods, an d motivation as th e optimization of
th e trade-offs required by th e con strain ts of
time an d experimen tal con text in order to
obtain th e best immediate or delay-discoun
t-ed package of goods Ecologics respects th e
n atural ecology of th e subject an d rejects th e
logic of th e marketplace an d th eoretician for
th at of an organ ism adapted by evolution ar y
fo r ce s to co m p le x n atu r al e n vir o n m e n ts
Ecologics frames beh avior as n ested sets of
systems or action patter n s, an d motivation as
regulation —th e defen se of setpoin ts with in
th ose system states Both of th ese approach es
are teleon omic or fun ction al, focusin g on
fi-n al causes, ofi-n outcomes: Th e ecofi-n omic
or-gan ism beh aves so as to optimize packages of
Th is research was supported by NSF Gran ts
IBN-9408022 an d BNS 9021562 It ben efited greatly from th e
reviewers’ commen ts, alth ough it is un likely th ey would
en dorse all of th e claims of th is version
Address cor respon den ce to Peter R Killeen ,
Depart-men t of Psych ology, Box 871104, Arizon a State Un
iver-sity, Tempe, Arizon a 85287-1104 ( E-mail: KILLEEN@
ASU.EDU)
goods, an d th e ecologic organ ism beh aves tomin imize deviation s from optimal setpoin ts
in its parameter space Mechanics focuses on
th e efficien t rath er th an th e fin al causes ofbeh avior, an d provides a set of for mal caus-es—a set of math ematical models—th at ex-pan ds simple assertion s of causal agen cy in tomore precise fun ction al relation s betweenvariables Th e mech an ical organ ism is n ot be-
h avin g to o p tim ize an yth in g; in cite m e n tmakes it active, satiation decreases its excit-ability, an d co-occur ren ce of particular re-spon ses with in cen tives in creases th e proba-bility of th ose respon ses Th e primar y goal of
th is paper is to develop th e mech an ics to th epoin t at wh ich it is applicable to th e experi-men tal con texts th at are favored by econ omic
in g, so th at arousal level ( A) is proportion al
Trang 2to rate of in citemen t ( R; a will be defin ed
below) :
But th ere are con strain ts Th ere is on ly so
much time available in wh ich to respon d (
Kil-leen ’s secon d prin ciple) , an d for a particular
target respon se to be differen tially excited by
an in cen tive, it must be paired with th at in
-cen tive; th ey must coreside in th e an imal’s
sh ort-ter m memor y ( th e th ird prin ciple) It is
on ly wh en effective con tin gen cies couple an
in cen tive with a respon se th at th e in cen tive
becomes a rein forcer Th ese th ree prin ciples
provided th e bases for models of th e beh avior
gen erated by various sch edules of rein
force-men t For in stan ce, th e th eor y predicts
re-spon se rates on in ter val sch edules to be
R 1 1/ a l
wh ere k is proportion al to th e maximal
attain able respon se rate, R is th e rate of rein
forcemen t, a is a key parameter wh ose mean
-in g will be developed below, an d lambda ( l)
is th e rate of decay of memor y for a respon se
Note th at with out th e subtrah en d, th is is
es-sen tially H er r n stein ’s h yperbola, wh ich h as
been demon strated to predict respon se rate
over a wide ran ge of con dition s ( see, e.g., de
Villiers & H er r n stein , 1976) Th e subtrah en d
comes in to play on ly at ver y h igh rates of
re-in forcemen t ( R 2 per mre-in ute) , wh ere an
in creasin g fraction of th e in cen tive bears on
th e prior con summator y respon se, stren gth
-en in g it rath er th an th e in str um-en tal
re-spon se Because th e subtrah en d is importan t
on ly un der ver y h igh rates of rein forcemen t,
it will be set to zero for th e rest of th is paper,
because th is simplifies an alysis an d in curs
on ly a small decrease in goodn ess of fit
T he Specifi c Activation of In cen tives
Th e parameter a, wh ich I h ave called th e
specific activation , is of greatest con cer n in
th is paper In H er r n stein ’s ( 1974) for
mula-tion , RO 5 1/ a was treated as th e rate of
re-in fo r ce m e n t availab le fr o m so u r ce s o th e r
th an th ose sch eduled by th e experimen ter
Th is in terpretation h as n ot been supported
by subsequen t research ( e.g., Bradsh aw,
Sza-badi, Ruddle, & Pears, 1983; Dougan &
McSween ey, 1985; McSween ey, 1978)
Ac-cordin gly, some in vestigators ( e.g., Bradsh aw,Ruddle, & Szabadi, 1981) h ave more agn os-
tically called th e parameter th e half-life stant, because respon se rate attain s h alf its maximal value wh en R equals RO
con-In earlier work on in cen tive motivation ,Kille e n , H an so n , an d O sb o r n e ( 1978)
sh owed th at each in cen tive delivered un der
con stan t con dition s will gen erate a total of a secon ds of beh avior It follows th at R in cen - tives will gen erate th e poten tial for aR sec-
on ds of respon din g, an d th ey called aR th e organ ism’s level of arousal Th e particular
for m of respon din g gen erated by th at arousaldepen ds on th e con tin gen cies th at deter min ejust wh at particular respon se will occur be-fore th e deliver y of th e in cen tive It is th iscouplin g of respon ses to in cen tives th at con -stitutes rein forcemen t Wh en th e couplin gapproach es its maximum ( 1.0) , as it does on
sh ort ratio sch edules, most of th e beh avior of
th e organ ism is con cen trated on th e targetrespon se Wh en th e couplin g is ver y weak, as
in sch edules of beh aviorin depen den t rein forcemen t, beh avior is diffuse an d drifts to-ward adjun ctive for ms But in all cases, th etotal amoun t of time spen t respon din g is afun ction of th e arousal level of th e organ ism,
-wh ich is a product of th e specific activation
of th e in cen tives ( a) an d th e rate of th eir liver y ( R) It is th ese con sideration s th at gave
de-rise to Equation 1
We may simplify Equation 2 by droppin gits subtrah en d, an d we may multiply its n u-
merator an d den omin ator by a to reveal
more clearly th e multiplicative in teraction
be-tween in cen tive factors summarized by a, an d rate of in citemen t, R:
kaR
aR 1 1 Equation 3 is h yperbolic in aR because of th e
n on lin earities in troduced by ceilin gs on spon se rate Wh en we are operatin g well be-low th ose ceilin gs, it reduces to th e simpleproportion al model, th e first prin ciple of th emech an ics Wh ereas Equation 2 emph asizes
re-th e relation of re-th is model to H er r n stein ’s h perbola, Equation 3 remin ds us of th e mul-
y-tiplicative relation between a an d R as th ey
con join tly deter min e arousal level an d spon se rate
re-Terminology It is worth an aside to clarify
Trang 3th e ter min ology used th rough out th is paper.
Th e above equation s were proposed as
equilibrium solution s for wh en th e beh avior un
-der study h as come to a steady state In ph
ys-ics th e study of systems at equilibrium is
called statics; an alogously, th e above
equa-tion s are part of a statics of beh avior Much
of th e recen t research in beh avior an alysis
con cer n s such asymptotic beh avior It derives
from a tradition of descriptive beh aviorism;
wh en ever a cumulative record is displayed or
a regression is fit th rough a scatter of data,
th e goal is description Th is is a first step
to-ward a more gen eral scien ce: ‘‘Galileo was
con cer n ed n ot with th e causes of motion but
in stead with its description Th e bran ch of
mech an ics h e reared is kn own as kinematics;
it is a math ematically descriptive accoun t of
m o tio n with o u t co n ce r n fo r its cau se s’’
( Frautsch i, O len ick, Apostol, & Goodstein ,
1986, p 114) It follows in th e Pyth agorean
tradition th at ‘‘approach ed ph en omen a in
ter ms of order an d was satisfied to discover
an exact math ematical description ’’ ( Westfall,
1971, p 1) Th ere are man y examples of such
a tradition in psych ology today, in cludin g
de-scriptive statistics, th e laws of psych oph ysics,
an d th e origin al match in g law
Th e study of forces th at cause objects to
move is called dynamics; dyn amics con stitutes
‘‘a th eor y of th e causes of motion ’’ ( Frautsch i
et al., 1986, p 114) Beh avior is th e motion
of organ isms, an d th e study of ch an ges in
be-h avior as a fun ction of motivation , lear n in g,
an d oth er causal factors con stitutes a dyn
am-ics of beh avior Examples in th e beh avioral
literature are provided by H iga, Wyn n e, an d
Staddon ( 1991) , Staddon ( 1988) , an d
Myer-son an d Miezin ( 1980) ; Mar r ( 1992) provides
an over view A framework th at embraces all
of th e above special cases is called a mechanics.
Th is ter m does n ot n owadays refer to h
ypo-th etical in ter n al mech an ical lin kages; such
mach in er y is th e vestige of th e Cartesian
tra-dition in wh ich Newton labored wh en h e
be-gan to establish th e moder n scien ce of
me-ch an ics Th at meme-ch an ical tradition sough t to
provide causal explan ation s of ph en omen a,
alth ough such causes were often n ar rowly
con str ued as material causes in volvin g th e
motion s of particles or aggregation s of matter
un derlyin g th e ph en omen a It was on e of
Newton ’s ch ief disappoin tmen ts th at h e was
n ever able to provide such a ‘‘mech an ical’’
substrate for forces such as gravity, an d h e
fi-n ally repudiated kfi-n owledge of such h
ypo-th etical causes in h is famous ‘‘h ypoypo-th eses n onfin go,’’ offerin g in stead a precise math emat-ical description of th e effects of th ose forces
H is dyn amical th eor y recon ciled ‘‘th e tion of math ematical description , represen t-
traded by Galileo, with th e tradition of mech an cal ph ilosoph y, represen ted by Descartes’’( Westfall, 1971, p 159)
i-As is th e case in ph ysics, in beh avior an
al-ysis th e ter m mechanics is someth in g of an
at-avism; but in both cases, it may be in terpreted
as an emph asis on th e an alysis of complexresultan ts in to th eir con stituen t forces, as afocus on causal rath er th an statistical expla-
n ation s, an d on math ematical rath er th anmech an ical lin kages between cause an d ef-fect It is in th ose sen ses, on es common to
th e beh avior-an alytic tradition , th at it is used
h ere It embraces molecular models such asmelioration , but n ot teleological models such
as th ose predicated upon optimization It in
-volves th e th eoretical con str ucts of value an d drive Th eoretical con str ucts are as n ecessar y
for a scien ce of beh avior as th ey are for an yoth er scien ce ( Williams, 1986) ; th is was rec-ogn ized by Skin n er th rough out h is career, be-gin n in g with h is argumen t for th e gen eric n a-ture of th e con cepts stimulus an d respon se( Skin n er, 1935) , th rough h is defen se of drive
as a con str uct th at can make a th eor y of
be-h avior more parsimon ious overall ( Skin n er,1938) , to h is fin al writin gs Th e issue, as Skin -
n er an d oth ers ( Feigl, 1950; Meeh l, 1995)
h ave stated, is n ot wh eth er such con str uctsare h ypoth etical, but wh eth er th ey pay th eirway in th e cost-ben efit ratio of con str ucts toprediction s Th is article requires a loan of th ereader’s patien ce as th ese con str ucts are de-veloped an d deployed, in th e h ope th at th e
th eor y will in th e en d be judged a worth wh ilecon tribution to th e experimen tal an d th eo-retical an alysis of beh avior
Open Versu s Closed Econ omies
O n e of th e key con dition s th at is assumed
to be con stan t in Killeen ’s ( 1994) mech an ics,but th at varies substan tially in th e real world,
is th e value of th e in cen tive to th e organ ism
Th is value depen ds both on th e in trin sicqualities of th e in cen tive—wh at H ull an d h is
studen ts den oted by K an d called tivation—an d th e h un ger, th irst, or ‘‘drive’’ of
Trang 4incentive-mo-Fig 1 A revision of th e figure drawn by H ursh ( 1980) , sh owin g th e differen ces in patter n s of respon se rates of mon keys un der open an d closed econ omies, as
a fun ction of th e in ter rein forcemen t in ter val on
variable-in ter val sch edules Th e cur ves are drawn by Equation 89 See H ursh ( 1978) for procedural details an d origin al data.
th e organ ism, wh ich th ey den oted by D ( e.g.,
H ull, 1950; Spen ce, 1956) Much of th e early
research on th ese factors was an essen tially
qualitative an alysis of th e differen tial role
th ey played in motivation Th e presen t con
-cer n is th e developmen t of a quan titative
an alysis, on e th at proceeds by expan din g th e
sin gle parameter a ( th e specific activation of
an in cen tive) in to compon en ts akin to K an d
D H ere th ese con str ucts are developed out
of th e already-establish ed statics ( Equation s 1
th rough 3) an d provide th e motivation al
‘‘causes’’ th at tran sfor m it in to a dyn amics
All of th e data an alyzed un der th e origin al
for mulation of th e mech an ics were derived
from an imals at h igh levels of deprivation ,
wh ich often requires supplemen tar y feedin g
in th e h ome cages But beh avioral econ omists
h ave argued th at such con dition s provide a
restricted, perh aps even an omalous,
perspec-tive on beh avior, an d th at our an alysis will
h ave more ecological validity to th e exten t
th at we per mit our subjects to ear n th eir
com-plete daily ration un der th e con strain ts of th e
sch edule we study, in th e process often
per-mittin g th em to approach ad libitum
reple-tion by th e en d of th e ( exten ded) daily
ses-sion Th e tradition al procedure h as been
called an open economy because th e subject is
main tain ed by food an d water extrin sic to th e
sch edule con tin gen cies; th e latter ar ran
ge-men t h as been called a closed economy Collier,
Joh n son , H ill, an d Kaufman ( 1986) ch
ris-ten ed th e tradition al open -econ omy
proce-dure th e refinement paradigm, ‘‘developed in
classic ph ysics, first en un ciated for an imals by
Th or n dike ( 1911, pp 25–29) an d per fected
by Skin n er ( 1938) , H ull ( 1943) , th eir
stu-den ts, an d th eir con temporaries’’ ( Collier et
al., p 113) Because postsession feedin g is
on e of th e least importan t distin ction s
be-tween open an d closed econ omies, because
description of th e procedure as an econ omy
con stitutes a commitmen t to a particular
ex-plan ator y framework, an d because th e refin
e-men t paradigm is th e ideal con text in wh ich
to refin e basic prin ciples, th eir ter m is
uti-lized th rough out th is paper
A n umber of research ers h ave adopted th e
econ omic an alysis of sch edule effects, with
th eir design s often in volvin g n ovel sch edules
of rein forcemen t H ursh ( e.g., H ursh , 1984)
h as sh own th at th e ver y type of fun ction s an
-alyzed by Killeen ( 1994) look quite differen t
-2 an d 3, but increasing markedly in a closed
econ omy Figure 1 sh ows th ose data ( derivedfrom H ursh , 1978) Th is con stitutes a serious
th reat to beh avioral mech an ics an d to all oth
-er th eories th at en tail th e H -er r n stein h yp-er-bola H ursh argued th at ‘‘It is th e econ omicsystem wh ich produced th e differen t results’’( 1980, p 223) But just wh at was it about th edifferen t systems th at made th e differen ce?
yper-H ursh ’s explan ation is in ter ms of elasticity of demand ‘‘In th e closed econ omy with n o sub-
stitutable food outside th e session , deman d
was inelastic; in th e open econ omy with con
-stan t food in take ar ran ged by th e
experi-men ter, deman d was elastic’’ ( H ursh , 1980, p.
233) Elastic goods are th ose such as luxuriesfor wh ich in creases in price causes decreases
in willin gn ess to work for th em or in th e
amoun t th at will be paid for th em ( demand) ;
in elastic goods are th ose such as basic n eedsfor wh ich moderate in creases in cost h ave lit-tle margin al effect on deman d; customers willpay wh at th ey h ave to to main tain con sump-tion ( Kooros, 1965; Lea, 1978) Elasticity ismeasured as th e proportion al ch an ge in de-
Trang 5m an d th at r e su lts fr o m a p r o p o r tio n al
ch an ge in price For th e closed econ omy, as
th e rein forcemen t rate decreases ( movin g to
th e righ t on th e x axis of Figure 1) , price in
-creases ( an imals get less food per respon se)
an d th ere is a con comitan t in crease in
re-spon se rates Th e flat fun ction s for th e open
econ omy suggest an elasticity n ear un ity, as
sh ould be th e case: If you can get it after th e
session for free, you sh ouldn ’t work h arder
for it wh en prices go up ( Th e proper x axis
for th e econ omic an alysis is un it
price—respon ses per un it of rein forcer—wh ich is h igh
ly cor related with mean time between rein
-fo r ce r s at m o st r e sp o n se r ate s At lo w
respon se rates on in ter val sch edules, h
owev-er, price is positively cor related with respon se
rate Strictly speakin g, th is latter depen den cy
makes econ omic an alyses in appropriate for
in ter val sch edules, because ‘‘In order to
de-duce th e sh ape of th e deman d for a con
sum-er good, th e first assumption on e sh ould
make is [ th at] n o in dividual buyer h as an y
appreciable in fluen ce on th e market price;
n amely, th e price is fixed’’ Kooros, 1965, pp
51–52.)
Beh avioral econ omics provides an in
terest-in g perspective terest-in a field terest-in wh ich th e data
are rich an d complicated an d th e poten tial
for bridgin g to an oth er disciplin e is so clear
But is it th e righ t perspective? Does respon
d-in g con stitute a cost—do an imals meter key
pecks th e way h uman s do pen n ies? Do th ey
an ticipate en d-of-session feedin gs? Just wh y
sh ould th e rates un der th e closed econ omy
gen erally be lower th an th ose un der th e open
econ omy, if in th e latter case an imals can
ban k on a postsession feedin g? Wh y sh ould
rates fall to n ear zero for th e variable-in ter val
( VI) 20-s sch edule in th e closed econ omy in
con trast with th e open econ omy? H ow are
th ese effects predicted from econ omic th
eo-r y? Elasticity migh t desceo-ribe, but can n ot
ex-plain , th ese differen ces; n or h ave econ omists
explain ed wh y elasticity itself sh ould var y con
-tin uously with price, as is usually th e case for
beh avioral data A simpler h ypoth esis can
ex-plain th e differen ces in th e data un der th ese
two experimen tal paradigms: In th e closed
econ omy th e subjects are closer to satiation
more of th e time, especially at small VI values;
subjects from th e open econ omy, bein g h un
-grier, respon d at a h igh er rate To for malize
th is treatmen t requires an expan sion of th e
mech an ics to h an dle deprivation an d in cen tive motivation
-H U NGER
Wh ere does deprivation level en ter th e sic prin ciples of rein forcemen t? Th e primar yeffect will be on th e specific activation asso-
ba-ciated with an in cen tive: Th e value of a in
Equation 1 will decrease with satiation Th elevel of in citemen t th at a small ban an a pelletwill provide to a satiated mon key will be less
th an th at provided to a h un gr y on e.1 Th ecloser an an imal is to its n atural rate of in take
un der ad libitum feedin g, th e smaller a
sh ould be Similarly, th e in citemen t from asmall ban an a pellet will be less th an th at from
a large ban an a pellet Th erefore, th e
param-eter a must be expan ded from a sin gle free
parameter to a product of th e organ ism’s
h un ger an d th e value of th e in cen tive in leviatin g h un ger To be con crete, let us th in k
al-of th e h un ger drive in th e simplest ter ms:Con sider th e metabolic system to be a vessel
th at stores a fin ite amoun t of food an d
util-izes it at a con stan t metabolic rate M Th e
con text per mits th e organ ism to acquire n ew
food of average magn itude m at th e rate of R
( see th e Appen dix for a review of th e con stan ts an d th eir dimen sion s) Depen din g on
-th e recen t h istor y of depletion an d repletion ,
th ere will be more or less food in store To
be precise, we would n eed to deal with a cade of storage devices ( i.e., th e mouth , th estomach , th e bloodstream, th e adipose tis-sue) , each with th eir own release rates; dif-feren t types of food will affect th ese differ-
cas-en tly Bulky food may fill th e mouth an dstomach but do little to alleviate deep h un -ger, wh ereas sugars may immediately releasestored glucose in to th e bloodstream wh ileleavin g th e stomach relatively empty We will
n ot con fron t th ose details h ere: Th in k inter ms of th e stomach ( or crop) an d somestan dard food such as th ose typically used asrein forcers In th is simplest in stan tiation , th e
d e ficit is th e e m p tin e ss o f th e sto m ach
1 Secon dar y motivation al effects on all th e parameters are likely For in stan ce, a weakly motivated organ ism migh t take lon ger to complete a respon se, lowerin g th e ceilin gs on respon se rate ( see, e.g., McDowell & Wood,
1984, an d Equation 39 below) But th is paper focuses on
th e primar y motivation al effects, wh ose locus of action is
on th e parameter a.
Trang 6Ch an ges in th e deficit will depen d on th e
bal-an ce between th e rates of emptyin g th e
stom-ach ( depletion ) an d of fillin g it ( repletion )
over time In th e case in wh ich both th e in put
rate ( mR) an d th e output rate ( M) are con
-stan t over th e in ter val t, th e deficit at time t,
d t, is
d 5 d 1 ( M 2 mR ) t, t 0 ( 4)
wh ere d0den otes th e in itial deprivation level
Bou n dary Con dition s
It is worth a con crete discussion h ere of
two of th e variables ( d0 an d M) in Equation
4, because th ey recur th rough out th e paper
an d will often be set to fixed values In an
open econ omy, th e experimen ter migh t
de-prive th e organ ism for several days, but n o
matter h ow deprived, an imals can eat on ly
un til th eir stomach s are full In th ese cases
th e in itial deficit d0 takes th e value of th e
maximum capacity of th e stomach For rats,
th e typical maximum meal size is about 4 g
( see, e.g., Joh n son & Collier, 1989, 1991) For
an imals such as pigeon s with a crop or mon
-keys with ch eek pouch es, a meal can be much
more substan tial Th is is also th e case for rats
wh en th eir en viron men t per mits th em to
h o ar d T Re e se an d H o ge n so n ( 1962)
sh owed th at for deprivation times over 24 h r,
pigeon s will con sume approximately 10% of
th eir free-feedin g weigh ts Zeigler, Green ,
an d Leh rer ( 1971) foun d th at in th e course
of an h our, 10 Wh ite Car n eaux th at h ad been
deprived to 80% of th eir ad libitum weigh ts
con sumed 40 g of mixed grain on th e
average; th is is con sisten t with Reese an d H ogen
-son ’s estimate of d0
In closed econ omies in wh ich in itial
depri-vation times are min imal, d0will be small an d
may usually be set to zero Un der th ese con
-dition s deprivation will grow with time sin ce
th e last meal ( t) accordin g to Equation 4 un
-til h un ger motivation exceeds th e th resh old,
at wh ich poin t an oth er meal will be in itiated
Pigeon s of typical size require between 0.5
an d 1 g/ h r to main tain th eir weigh ts between
80% an d 100% of ad libitum, an d th e
re-quiremen ts for rats also fall with in th at ran ge
Th ese values for M are sufficien tly smaller
th an th e rates of repletion in typical ( open
econ omy) experimen ts th at on e may set M 5
0, as is don e in all of th e subsequen t an alyses
in th is paper
Drive Versu s Defi cit
Wh at is th e relation between th e h un ger
drive h t an d deficit d t? Th e simplest model
makes h un ger proportion al to deficit, h t 5
gd t, so th at from Equation 4
h 5 g[ d 1 ( M 2 mR ) t] t 0 ( 5)Alter n ate models of th is basic process are pos-sible Equation 5 is similar to a regulator ymodel proposed by Ettin ger an d Staddon( 1983) Town sen d ( 1992) explored a dyn am-
ic motivation al system th at, in place of tion 5, h ad motivation grow as a fun ction of
Equa-th e deviation between Equa-th e cur ren t tion al level an d th e ideal, with a th resh old
motiva-th at motivation must exceed before respon
d-in g will be d-in itiated Solution of such a modelleads to motivation th at grows expon en tiallywith time, rath er th an lin early:
1, th e subject will con tin ue respon din g even
wh en satiated ( Morgan , 1974) , eith er becausecon dition in g h as created some beh avioralmomen tum or because th e drive is also main -tain ed by oth er deprivation s ( e.g., dilute su-crose solution s will assuage both h un ger an d
th irst) In th e lin ear model, th resh old effectsare absorbed in to th e deficit parameters
Th e expon en tial model h as some face lidity, in th at in trospection suggests th at th eexigen cy of h un ger seems to grow moresteeply th an lin ear with deprivation time It iscon sisten t with con trol-systems an alyses ofmotivation al systems ( e.g., McFarlan d, 1971;Toates, 1980) Serious studen ts of th ese issueswill fin d an excellen t review of th e cur ren tstate of research on appetite an d its n eural
va-an d beh avioral bases in Legg va-an d Booth( 1994)
Yet an oth er model of h un ger would h ave itgrow sigmoidally with deprivation , approach -
in g a ceilin g at th e h igh est levels of tion Such a model is outlin ed in th e Appen -dix; its application did n ot improve an y of th e
depriva-an alyses, depriva-an d so it is n ot pursued h ere.Equation s 5 an d 6 sh ow th at wh en an an i-mal becomes satiated ( wh en th e in itial deficit
Trang 7is replaced an d depletion is just balan ced by
repletion ) , h t falls below th resh old, drivin g
motivation to zero an d car r yin g respon se rate
alon g with it Food-motivated beh avior ceases,
preven tin g overin dulgen ce th at would drive
h un ger levels to a n egative value Con tin gen
-cies of rein forcemen t th at require con
sump-tion for access to oth er in cen tives, h owever,
could drive h tto a n egative value In th is case,
respon se rates are depressed below free base
rates ( Allison , 1981, 1993) , requirin g exter n al
force or th e passage of time to overcome th at
in h ibition
Aggregatin g Over a Session
For th e lin ear model, th e average drive
lev-el over th e course of a session of durationtsess
is given by Equation 5, with t 5 tsess/ 2 ( see
th e Appen dix) Un der th e expon en tial drive
model, th e situation is more complicated If
session duration is con stan t, th e average drive
level is given by Equation 6, with t 5 t9, some
un defin ed fraction of tsess In employin g th e
expon en tial model, on e may set t9 to some
arbitrar y value ( e.g., tsess/ 2) an d let th e
re-main in g parameters adjust th emselves to th at
con strain t
Econ omic T ran slation
In econ omic parlan ce, d0is th e debt, mR is
th e wage, an d M is th e cost of doin g busin ess.
O n ratio sch edules th e rate of rein forcemen t
R is an in verse fun ction of th e ratio size ( n) ,
or price, an d n/ m is th e un it price M, th e
rate of utilization of food by a free-feedin g
organ ism, is th e coordin ate of th e ideal, or
bliss poin t, alon g th e food con sumption axis
It could be separated in to fixed cost or
over-h ead ( basal metabolic rate) , an d production
cost ( respon se effort) Basal metabolic rate
con stitutes th e major cost of foragin g an d
th us con stitutes a sign ifican t ‘‘sun k cost’’ to
an y en deavor: O n ce stan din g, it doesn ’t
re-quire much more en ergy to do an yth in g
( Th is distin ction implies flat optima for
mod-els of foragin g th at maximize calories gain ed
per calories of effort expen ded; more precise
feedback is provided by optimizin g calories
gain ed over time expen ded.)
Th e parameter g represen ts th e cost of
de-viation s from th e ideal, an d eg provides on e
in dex of th e elasticity of deman d If g is large
( an d th us eg 1) , th e an imal is ver y sen sitive
to deviation s from th e ideal rate of repletion ,
an d deman d is said to be in elastic If g is
small ( an d th us egø 1), then changes in price
elicit on ly min imal beh avioral adjustmen ts;deman d for th e commodity approach es un it
elasticity If g is n egative ( an d th us eg , 1) ,
an imals will work less for a commodity as itsprice in creases, an d deman d is said to be elas-tic Th is occurs in th e presen ce of substitutes,
as wh en food is available for respon din g onoth er levers ( Joh n son & Collier, 1987) Th is
in terpretation of elasticity differs from th at of
th e econ omists, because th eirs refers to man d as a fun ction of price but does n ot takedeprivation levels in to accoun t Econ omicmodels are design ed to map population ef-fects, n ot biological on es Saturation of th emarket is treated with differen t models th an
de-e lasticity ‘‘Dde-e cr de-e asin g m ar gin al u tility o fgoods’’ captures some of th e idea of satiation ,but is usually con str ued with out referen ce to
th e cur ren t deficit
Th e presen t approach predicts th at th eecon omists’ measure of elasticity will ch an gewith price, because on ratio sch edules th e
rate of rein forcemen t, R, wh ich appears in
th e righ t sides of Equation s 5 an d 6, equals
m/ n, th e reciprocal of un it price Motivation
varies with price because th at affects th e rate
of repletion In deed, H ursh , Raslear, man , an d Black ( 1989) foun d elasticity tovar y as a lin ear fun ction of un it price But th is
Bau-is n ot because g h as ch an ged; our measure
of elasticity, eg, may stay con stan t over ch an ges
in motivation because we h ave moved th econ trollin g variables in to our in depen den tvariables ( Equation s 5 an d 6) , an d th erefore
do n ot n eed to let our th eoretical con stan tsvar y with our in depen den t variables
Ecologic T ran slation
M is th e setpoin t repletion rate th at an
i-mals will defen d Equation 4 provides a sure of deviation from th at setpoin t Defen se
mea-of th e setpoin t is equivalen t to an imals’ temptin g to min imize th at deviation , th at is,set th e derivative to zero Th e force of th isequilibration is given by g In con trol-systemsparlan ce, g represen ts th e regulator y gain , orrestorin g force Man y differen t ar ran gemen ts
at-of con tin gen cies will gen erate man y differen tcon stellation s of beh avior, all of wh ich h ave
on ly on e th in g in common an d predictable;
th e absolute value of Equation 4 will be min imized Th is approach th erefore is like th e
Trang 8-Fig 2 Respon se rates un der ch ain ed sch edules for pigeon s receivin g differen t duration s of access to th e
h opper durin g exten ded session s ( Fisch er & Fan tin o, 1968) Th e data represen ted by filled symbols come from
th e ter min al lin k, an d th ose by open symbols from th e
in itial lin k Th e cur ves are drawn by Equation s 3 an d 7,
an d represen t per for man ce for 2-s ( in verted trian gles) , 6-s ( trian gles) , 10-s ( squares) , an d 14-s ( circles) access to food.
H am ilto n ian ap p r o ach to m e ch an ics, in
wh ich all of th e laws of mech an ics may be
derived from min imization of a sin gle
differ-en tial equation called th e action It is th e core
assumption of regulator y approach es to
be-h avioral econ omics sucbe-h as Allison ’s ( 1983)
Th e cur ren t approach also recogn izes th e
boun dar y con dition s to th is min imization :
Th e ch an ges in motivation will n ot be
re-vealed in beh avior un til th ey cross a th resh old
for action , an d th ey will n ot con tin ue on ce
th e capacity of th e organ ism is saturated
An Application of the Basic M odel
to Satiation Cu rves
H ow does drive level in teract with magn
i-tude or quality of th e in cen tive? Th e simplest
assumption is multiplicative: Absen t eith er
drive or a viable in cen tive, th e specific
activation a must be zero We may call th e in cen
-tive variable v Th en a t 5 vh t Th e value of an
in cen tive will n ot gen erally be proportion al
to its magn itude, alth ough a lin ear relation
may be an adequate approximation if th e
ran ge of variation is small
In accord with th e above an alysis, for th e
lin ear drive model we expan d th e specific
ac-tivation to
a 5 vh 5 v g[ d 1 ( M 2 mR ) t] , t t 0 ( 7)
wh ere ( M 2 mR) is th e balan ce between
de-pletion an d rede-pletion , an d its multiplication
by t gives th e cumulative effects of th at
bal-an ce Th is equation h as replaced a as a sin gle
free parameter with a th ree-parameter
mod-el: value v, th e in itial deficit d0, an d th e
pletion rate M ( For th e lin ear model th e
de-viation -cost parameter g is redun dan t with
th e value parameter v an d may be absorbed
in to it or simply set to 1.0.) Equation 7 may
th en be in serted in to Equation 3 to predict
r e sp o n se r ate s o f an im als u n d e r in te r val
sch edules wh en deprivation levels var y
Fisch er an d Fan tin o ( 1968) provided th e
data aroun d wh ich th e lin ear model was
de-veloped Th ey deprived pigeon s to 80% of
th eir ad libitum weigh ts, an d train ed th em to
respon d on ch ain ed VI 45 VI 45 sch edules,
e xte n d in g th e se ssio n s u n til r e sp o n d in g
ceased Th e rein forcer con sisted of access to
a h opper of mixed grain for 2, 6, 10, or 14 s
Figure 2 sh ows th e resultin g satiation cur ves
in th e ter min al lin ks of th e ch ain an d in th e
in itial lin ks Alth ough th e data th emselves
sh ow rath er un excitin g mon oton ic decreaseswith n umber of feedin gs, th e model provides
a ration al fit to th em Th e first step was toestimate th e amoun t of food obtain ed un der
th e differen t con dition s, because amoun tcon sumed is n ot proportion al to h opper du-ration Fortun ately, Epstein ( 1981) publish ed
a useful graph givin g th e amoun t con sumedfrom a h opper of th e design used in th isstudy For th ese h opper duration s th e regres-sion gave th e amoun ts as 0.13, 0.28, 0.35, an d0.36 g of mixed grain 2I used th ose n umbers
as estimates of m.
Th e pigeon s’ weigh ts were reduced to 80%
of th eir free-feedin g weigh ts To optimize th e
goodn ess of fit, I set th e parameter k in
Equa-tion 3 to 200 respon ses per min ute for th eter min al lin k an d 64 respon ses per min ute
for th e in itial lin k Th e in itial deprivation d0took a value of 57 g Th e value parameter v
was 1.5 s per rein forcemen t Th e expon en tialdrive model provides a comparable fit to
th ese data Given th e n ecessar y tion s, th e fit of th e model to th e data is per-
approxima-2 For Leh igh Valley feeders th e n umber of grams eaten approximates a lin ear fun ction of h opper duration , with
a slope of 0.06 g/ s an d an in tercept of 0.2 g ( Epstein , 1985) Pigeon s feedin g ad libitum are less efficien t, with typical eatin g episodes lastin g 7 s, durin g wh ich 0.33 g are con sumed ( H en derson , Fort, Rash otte, & H en der- son , 1992)
Trang 9Fig 3 With in session satiation effects sh own for gen eral activity as measured by a stabilimeter, an d for lever pressin g Th e data are averaged over two session s in
-wh ich 4 rats were given two 45-mg pellets for th e first respon se 30 s after th e previous rein forcemen t ( FI 30)
Th e cur ves are drawn by Equation 89.
h aps acceptable, alth ough respon din g in th e
in itial lin ks decreased at a faster rate th an
predicted, especially for th e 14s h opper con
-d itio n ( Le n -d e n m an n , Mye r s, & Fan tin o ,
1982, foun d a similar h ypersen sitivity in th e
in itial lin ks in respon se to variation s in
duration of rein forcemen t, as did Nevin , Man
-dell, & Yaren sky, 1981, in respon se to
satia-tion ) It may be th at in all cases decreased
motivation h as its primar y effects on pausin g,
an d on ce an an imal h as begun to respon d, it
con tin ues un til rein forcemen t If th is is th e
case, th en pausin g will occur primarily in th e
initial links, with animals responding
through-out the terminal links Segmenting responding
will thus put the greatest leverage of motivation
on the earliest segments ( See Williams, Ploog,
& Bell, 1995, for further analyses of these
chain-schedule effects.)
We can write th e above models in a more
con den sed for m Set th e metabolic rate M to
0, th e magn itude of th e in cen tive m to 1, an d
let th e gain parameter g be absorbed in to v;
th en write Equation 3 as
kR
R 1 1/ [ v( d 2 Rt) ]0
Th is equation reiterates th e above
descrip-tion s, but also provides quan titative
predic-tion s: Because of satiapredic-tion effects, respon se
rate is a quadratic fun ction of rein forcemen t
rate Un der con dition s of large in itial deficit
( d0) relative to repletion ( Rt) , th e paren th
et-ical expression is essen tially con stan t an d can
be absorbed by v, wh ich retur n s to us our
sim-ple Equation 3 ( or 39, below) Th e H er r n stein
h yperbola is th us valid primarily for session s
of sh ort duration or low rate of rein
force-men t, wh ere th e in itial deficit outweigh s th e
cumulative repletion But satiation effects
grow with t, an d become domin an t later in a
session
If on e is in terested in estimatin g th e
pa-rameters in H er r n stein ’s h yperbola, th en it is
better to use data from early in a session in
wh ich repletion ( Rt) is low relative to in itial
deficit ( d0) , or from sh ort session s, so th at th e
den omin ator is relatively con stan t Better yet,
use Equation 8 at th e cost of on e addition al
parameter ( d0) an d predict th e complete
fun ction
Note th at th e adden d 1/ [ v( d02 Rt) ] in th e
den omin ator was in terpreted by H er r n stein
as RO, th e value of rein forcemen t for oth er( n on target) respon ses H e an d Lovelan d pre-dicted th at wh en an imals were n ot deprived
of th e primar y rein forcer, th ese oth er implicitrein forcers sh ould seem to grow in relative
value, th us in creasin g th e value of RO( H er r n stein & Lovelan d, 1972) Th eir data sh owed
-th is to be -th e case; h owever, our in tion is more straigh tfor ward: Wh en an imals
terpreta-are n ot greatly deprived, d0 will by defin ition
be small, an d th us 1/ [ v( d0 2 Rt) ] ( th eir RO)will be cor respon din gly large
Th e expon en tial-drive model is n ecessar yfor some of th e data on satiation In th at case,Equation 8 may be rewritten as
kR
R 1 1/ ( vh ) t with drive level h tan expon en tial fun ction ofdeficit ( Equation 6) rath er th an a lin ear fun c-tion ( Equation 5) In an un publish ed exper-imen t, Lewis Bizo an d I delivered two 45-mgpellets to rats immediately after a lever press
on a fixedin ter val ( FI) 30s sch edule Gen eral activity was con cur ren tly measured with
-a st-abilimeter Figure 3 sh ows th e declin e ingen eral activity an d lever pressin g as a fun c-tion of th e n umber of trials Equation 89 drewboth cur ves Th e motivation al parameters ( g
5 0.3 g2 1 an d d0 5 4 g) were th e same for
both respon ses, wh ereas th e remain in g rameters were un dercon strain ed by th e data
Trang 10pa-Fig 4 Data from McSween ey et al ( 1990) , sh owin g with in -session war m-up an d satiation effects in rats Th e cur ve is drawn by Equation 3, with Equation 7 repre- sen tin g th e satiation effects an d Equation 9 th e war m-up effects.
Th e lever-press data are flatter because
ceil-in gs on respon se rate compress th e top en d
of th e fun ction Th e key poin t is th at
Equa-tion 8, wh ich predicts a lin ear or con
cave-down decrease in respon din g, could n ot h ave
fit th e con cave-up time course of satiation as
measured by gen eral activity
Equation 89 also drew th e cur ves th rough
th e data in Figure 1 In both econ omies d0
took th e value of 140 rein forcers an d k was
5,500 respon ses per h our; for th e open econ
-omy, g 5 0.10, an d for th e closed econ omy g
5 0.07 Th e key differen ce between th e
cur ves is th e degree of repletion per mitted
with in th e session For th e closed econ omy
th e session duration was 6,000 s, so th at tsess/
2 is 3,000 s, an d th e average session deficit
( th e coefficien t of g in Equation 6) is 140 2
R 3 3,000 Th e fixed duration of th e closed
econ omy per mitted differen tial satiation as a
fun ction of rate of rein forcemen t ( R) For
th e open econ omy th e session en ded after
180 rein forcemen ts, so tsess/ 2 is 90/ R s, an d
th e average session deficit is 140 2 R 3 90/
R; th at is, a con stan t 50 g Ter min atin g
ses-sion s after a fixed n umber of rein forcers, or
in gen eral keepin g session duration
propor-tion al to in ter rein forcemen t in ter val ( 1/ R) ,
con fers a con stan t average level of
motiva-tion Th is is th e key differen ce between th e
experimen tal paradigms; it is ‘‘th e econ omic
system wh ich produced th e differen t results’’
sh own in Figure 1 It did so by lettin g th e
an imals differen tially satiate in on e case but
n ot in th e oth er
Th e amoun t of food con sumed in th ese
an d th e Fisch er an d Fan tin o ( 1968) session s
was two to five times th e amoun t con sumed
in a typical session Is th ere eviden ce for th e
decrease in respon din g durin g operan t
ses-sion s of more typical duration ? Th an ks to
McSween ey an d h er colleagues, th ere is n ow
ample eviden ce of with in -session satiation
ef-fects ( see McSween ey & Roll, 1993, for a
re-view) But h er data also sh ow with in -session
war m-up effects, so we must digress to a
model of th ose
WARM-U PSome of th e first eviden ce for with in -ses-
sion effects from McSween ey’s laborator y
came from a study con ducted to test th e
ef-fects of postsession feedin g on rats th at were
required to press a lever for Noyes pellets or,
in a differen t con dition , to press a key forsweeten ed con den sed milk ( McSween ey, H at-field, & Allen , 1990) Alth ough n o effects ofpostsession feedin g were foun d, a remarkablepatter n of rate ch an ges with in th e session wasdiscovered ( see Figure 4) Respon se rates in -creased th rough th e first 20 min of th e ses-sion an d decreased th ereafter, an d th e pat-
te r n was vir tu ally id e n tical fo r th e tworespon ses an d rein forcers
Th e decrease in rates may be attributed tosatiation of th e kin d seen in th e previous fig-ures To wh at do we attribute th e in crease inrates? Killeen an d h is colleagues ( Killeen , inpress; Killeen et al., 1978) h ave described sim-ilar in creases in rates wh en an imals are first
in troduced to a sch edule of periodic rein forcemen t, an d attributed th em to th e cu-mulation of arousal Such war m-up plays alarge role in beh avior main tain ed by aversivestimuli an d a lesser but still measurable role
in beh avior main tain ed by relief from h un ger In troduction to th e ch amber itself be-comes a con dition ed rein forcer an d th ere-fore a con dition ed exciter If th ere were n oloss of th is arousal between session s, even tu-ally each session would begin with rates at
-th eir asymptotic level But -th e an imals calmdown between session s For th e presen t pur-poses, assume th is between -session s loss iscomplete ( see Killeen , in press, for a more
Trang 11Fig 5 Data from McSween ey an d Joh n son ( 1994) ,
sh owin g with in -session war m-up an d satiation effects Th e pigeon s were removed from th e ch amber for periods of
3 to 30 min an d th en were rein troduced to it Th e data are averaged over subjects an d duration s of in ter mission ;
th e cur ves are drawn by Equation s 3, 7, an d 9.
gen eral treatmen t) ; th en arousal sh ould
ac-cr ue as
2at
A 5 aR( 1 2 e ) , ( 9)
wh ere a is th e rate of th e decay of arousal,
usually takin g a value aroun d 6 min2 1 (
Kil-leen , in press; KilKil-leen et al., 1978) , an d t is
th e time in to th e session As t grows large, th is
reduces to A 5 aR Th is sh ould look familiar:
It is Equation 1 ( th e first prin ciple of th e
me-ch an ics) an d a key compon en t of Equation 3
Note th at Equation 9 predicts th e time course
of war m-up to be in depen den t of th e rate of
rein forcemen t; R merely sets th e asymptote.
To accoun t for th e data of McSween ey et
al ( 1990) , we replace a in Equation 9 ( a
mod-el of war m-up) with its expan sion by Equation
7 ( a model of satiation effects) an d in sert th is
in place of aR in Equation 3 ( a model of
ceil-in gs on respon se rates) We may fix d0an d M
at th eir stan dard values of 4 g an d 0 g/ s
Th en solvin g for scale parameter k 5 7
re-spon ses per secon d, value parameter v 5 11.5
s per rein forcemen t, an d decay rate a 5 1/ 9
min utes, min imizes th e sum of squares
devi-ation from th e data Figure 4 sh ows th e
pre-diction s with th e lin ear h un ger model (
Equa-tion 7) with th ese parameter values; th e
expon en tial h un ger model provides an
equiv-alen t fit to th e data, as it does to th ose from
th e n ext study
A recen t experimen t of McSween ey an d
Joh n son ( 1994) rein forces th is in terpretation
of th e biton icity bein g due to war m-up an d
satiation In th is study th e auth ors rein forced
pigeon s’ peckin g on a VI 60-s sch edule with
5 s access to mixed grain After 50 min th ey
were removed from th e ch amber an d th en
retur n ed after 3, 10, or 30 min O ur in
ter-pretation of th e ascen din g limb as bein g due
to war m-up en tails th at th ere sh ould also be
a war m-up wh en th e subjects are rein
tro-duced to th e ch amber If pigeon s are
de-tain ed with in ch amber, we expect a similar
but less pron oun ced war mup effect For lon
-ger duration s of in ter r uption , th ere sh ould
also be a sligh t in crease in h un ger
motiva-tion Figure 5 sh ows th e data from
Mc-Sween ey an d Joh n son ’s first experimen t, with
th e cur ves sh owin g respon se rates in 5-min
bin s before an d after th e in ter mission s,
av-eraged over subjects an d duration s of in
ter-mission I set k 5 240 respon ses per min ute
an d d 5 22 g; th e latter less th an typical, but
th ese were small birds main tain ed at 85% an dgiven 5-s feeder access per meal Th e timecon stan t for war m-up was 1/ a 5 6.5 min , an d
value of v was 0.15 s per rein forcemen t In
th eir secon d experimen t th e birds were n otremoved from th e ch amber, an d th e postin -ter mission war m-up was reduced
In an oth er study, McSween ey ( 1992) variedrates of rein forcemen t for lever pressin g an dmeasured rats’ respon se rates th rough out th esession As expected, th e decreases in ratesdurin g th e last h alf of th e session were great-est un der th e h igh est rates of rein forcemen t,
wh ere satiation occurs most quickly Th efun ction s look similar to th ose sh own in Fig-ures 4 an d 5, an d th e above model provides
an excellen t fit to th em McSween ey also ted th e data usin g rate of rein forcemen t as
plot-th e x axis for data from differen t portion s of
th e session —first 5 min , th e th ird 5 min , th e9th min , an d th e 12th min Alth ough th esmall database en tails ir regularity in th e data,Figure 6 makes an importan t poin t: Th e
sh ape of th e H er r n stein h yperbola depen ds
on wh ich portion of th e session th e data arecollected from In particular, th e decrease inrespon se rates at th e h igh est rate of rein force-men t in th e latter part of th e session is n otpredicted by H er r n stein ’s model A decrease
in respon din g at ver y h igh rates is predicted
by Equation 2, but for reason s oth er th an tiation , an d th at equation can n ot predict th e
Trang 12sa-Fig 6 Data from McSween ey ( 1992) , sh owin g respon se rate as a fun ction of rate of rein forcemen t, with 5-min segmen ts of th e session as th e parameter Th e cur ves are drawn by Equation s 3, 7, an d 9.
obser ved with in -session ch an ges th at are due
to satiation ( th e use of Equation 2 in con cert
with th e satiation an d war m-up models does
in gen eral provide a sligh tly better fit to th e
data, as on e would expect) In fittin g th e
presen t model, I give th e in itial deficit an d
metabolic rate th eir stan dard assign men ts: d0
5 4 g, M 5 0 Th e remain in g parameters
were assign ed values th at min imized th e sum
of squares deviation between th eor y an d data,
an d th e cur ves were drawn th rough th e data
sh own in Figure 6: 1/ a 5 10 min , v 5 11.5 s
per rein forcemen t, an d k 5 72 respon ses per
min ute Equation 8 provides an
almost-equiv-alen t fit, but overpredicts th e rate in th e first
pan el because it does n ot allow for war m-up
Figure 6 provides a strikin g picture of th e
impact th at such with in -session satiation can
h ave on our overall models of beh avior Th e
top left pan el sh ows respon se rates from th e
first 5 min of each sch edule, displayin g th efor m th at Catan ia an d Reyn olds ( 1968) madefamous an d th at H er r n stein made epon ymic
Bu t as th e se ssio n p r o gr e sse s, th e fo r m
ch an ges: At all rates of rein forcemen t greater
th an or equal to on e per min ute, respon serates dropped, an d un der a VI 15-s sch edule
th ey dropped precipitously
Effects of session duration an d satiationsimilar to th ose sh own above were foun d byDougan , Kuh , an d Vin k ( 1993) an d O sbor n e( 1977) Satiation an d war m-up effects can besubstan tial, an d th e mech an ics of beh aviorprovides a framework with in wh ich to derivemodels of th em Both th e presen tation of in -cen tives an d th eir removal often affect an i-mals on ly after a lag; th us, we h ave war m-upeffects wh en session s start, cool-down or ex-tin ction effects wh en in cen tives cease, an d re-spon din g th rough satiation in well-practiced
Trang 13subjects All may be assimilated in mech an
is-tic models of beh avior Th e fin al issue th at
must be addressed before mech an ics can
be-gin to stan d as an alter n ative to econ omic
an d ecologic an alyses is th e relation between
th e amoun t of an in cen tive an d its value
MAGNIT U DE O F INCENT IVES
Wh ereas an imals typically ch oose larger
amoun ts of food over smaller amoun ts ( see,
e.g., Bon em & Crossman , 1988; Collier, Joh n
-son , & Morgan , 1992; Killeen , Cate, & Tr un g,
1993) , respon se rates often ch an ge little or
n ot at all as a fun ction of th e magn itude of
th e in cen tive Wh y sh ould th is be? In part,
th e an swer depen ds on th e fact th at th e
re-in forcre-in g value of an re-in cen tive is n ot
propor-tion al to its size In th e case in wh ich
mag-n itude is mamag-n ipulated by var yimag-n g duratiomag-n of
th e in cen tive, th e reason s for th is are obvious:
Th e secon d, th ird, an d nth in stan ts of con
-sumption are n ot con tiguous with th e
re-spon se th at brough t th em about; th ey are
separated from it by n 2 1 prior in stan ts of
con sumption ( Killeen , 1985) th at block th eir
effectiven ess Th e last in stan ts of a lon
g-du-ration reward con stitute a delayed reward
Th ose later in stan ts of con sumption in
creas-in gly recreas-in force n ot th e prior operan t
respon ses but rath er th e immediately prior con
-summator y respon ses Assume th at each of
th e in stan ts of con summator y activity in
terpolated between a respon se an d th e last in
-stan t of con summator y activity will block th at
latter’s effectiven ess by a con stan t proportion ,
n Th en it follows th at th e effectiven ess of an
in cen tive sh ould in crease as an expon en tial
in tegral fun ction of its duration :
2nm
v 5 v ( 1 2 e m ` ) , ( 10)
wh ere v m expan ds th e value of an in cen tive
from a con stan t v to a fun ction of its duration
or magn itude ( m) ; v`is th e value of an
arbi-trarily lon g duration of th at in cen tive, an d n
is th e rate of discoun tin g th e in cen tive as a
fun ction of its duration Value ( v m) refers to
th e psych ological/ beh avioral magn itude of
an in cen tive wh ose ph ysical magn itude ( m)
may be measured in grams, secon ds, or
mil-ligrams per kilogram Incentive motivation
re-fers to th e evaluative or in stigatin g
effective-n ess of th e ieffective-n ceeffective-n tive th at depeeffective-n ds oeffective-n its value
in th e con text, as represen ted by equation ssuch as Equation 8
Equation 10 embodies th e maxim of gin ally decreasin g utility’’ of in cen tives ( as afun ction of th eir duration , n ot, as often used
‘‘mar-in econ omic parlan ce, as a fun ction of n ber of rein forcers) If n is small, th e relation
um-is approximately proportion al; if n um-is large,
in creasin g duration adds ver y little value leen ( 1985) foun d th at Equation 10 with nbetween 0.25 an d 0.75 s2 1 fit man y of th e
Kil-ch oice data h e reviewed For th e represen tive value of n 5 1/ 2, th e value of 3 s of h op-per access h as attain ed 78% of th e maximum
ta-possible ( v`) Studies th at man ipulate lon gerduration s are operatin g with in a ver y restrict-
ed ran ge
Th is model of th e ch an ge in value with
ch an ges in th e duration of an in cen tive may
be combin ed with Equation s 7 an d 8 to dict per for man ce wh en th e duration of an in -cen tive is varied Wh en th e value of an in cen -tive is man ipulated by ch an gin g its qualityrath er th an by ch an gin g its duration , someutility fun ction oth er th an Equation 10 ( e.g.,
pre-a power fun ction or pre-a logpre-arith mic fun ction )may be more appropriate Wh en , for in -stan ce, a dr ug level or sucrose con cen tration
is man ipulated, a plausible model is v m 5 mn,
an d th e value of th e deficit th e an imal is
at-temptin g to satisfy If in itial deficit d0is large
or repletion time t is sh ort or th e rate of pletion mR is small, th e satiation effects will
re-be buffered by d0 an d n et in cen tive effects( in creasin g respon se rates with in creasin g
magn itude) will be foun d Con versely, if d0issmall an d repletion is moderate or large, as
is typical of closed econ omies, th e satiationeffect will domin ate, an d respon se rates willdecrease as a fun ction of magn itude Th e de-pen den ce of th e sign of th e cor relation be-tween magn itude an d respon se rate—positive
in th e realm of small in cen tives, n egative in
th e realm in wh ich satiation effects
domi-n ate—is sh owdomi-n idomi-n a study by Collier adomi-n d ers ( 1961) , wh o foun d positive covariation of