Digitized by the Internet Archive
in 2015

https://archive.org/details/optinnalallocatioOOmoth

OPTIMAL ALLOCATION OF BEHAVIOR:
RATIO SCHEDULES

by

Mary Susan Motheral

Department of Psychology
Duke University

Date:

Approved:

Dissertation submitted in partial fulfillment of
the requirements for the degree of Doctor
of Philosophy in the Department of
Psychology in the Graduate School
of Duke University

1982

ABSTRACT
(Psychology -Experimental)

OPTIMAL ALLOCATION OF BEHAVIOR:
RATIO SCHEDULES

by

Mary Susan Motheral

Department of Psychology
Duke University-
Date:

Approved:

An abstract of a dissertation submitted in partial
fulfillment of the requirements for the degree
of Doctor of Philosophy in the Department of
Psychology in the Graduate School of
Duke University

1982

ABSTRACT

OPTIMAL ALLOCATION OF BEHAVIOR:
RATIO SCHEDULES
by

Mary Susan Motheral

During 1-hour sessions, rats were exposed to baseline sessions
allowing free access to dippers of milk, and to contingency sessions
requiring lever presses to obtain each dipper of milk. Contingency ses-
sions employed ratio sched\iles requiring from 1 to 160 lever presses for
each dipper of m.ilk. Ratio value was varied in a parametric mxanner in
order to determine whether ratio behavior can be characterized as an
optimal allocation of behavioral resources. The first two experiments
developed a means for reliably mapping behavior over ratio values
(response functions) by looking at the effects on behavior of number of
sessions at each ratio value and of ratio sequence. The results show that
most adjustment in behavior to change in ratio value occurs during the
first session of exposure to a new ratio value. Thus, many sessions of
exposure to each ratio value are not necessary to obtain replicable data.
Except at the highest ratio value investigated (i. e. , ratio 160), no

iii

differences were obtained in the overall response rates with fixed- and
variable- ratio schedules.

The third experiment used the procedure developed in Experiments
1 and 2 to look at the effects on ratio behavior of the opportunity to run in
a wheel and of variation in deprivation body weight. The form of ratio
response functions depends on the set of activities available and is inde-
pendent of the rate of food intake during free baseline conditions. The
results suggest that the minimum- deviation model provides a good quali-
tative and quantitative account of ratio- schedule behavior.

iv

ACKNOWLEDGMENTS

So many people have helped along the way that it is impossible to
thank them all. A few to whom I am grateful:

John Staddon, for lively discussions (and great arguments!), for help
in clarifying the nature of facts, and for introducing me to
microeconomics, evolutionary biology and all sorts of other
good stuff;

Friends, faculty and staff in the Psychology Department at D\ike and
elsewhere, who helped me survive the pitfalls of icy
North Carolina roads and all sorts of other harrowing (and also
wonderful) experiences --especially Edna Bissette. Amby Peach and the
members of Staddon 's lab;

Economists at Duke and Texas A&M, who have shown much patience
with a sometimes muddled psychologist;

My parents, who offered encouragement and support--even when they
could not imagine a daughter with a Ph. D. ;

My grandparents, who believed in education.

To Eula, who encouraged my curiosity and my independence.

M. S. M.

V

I

i

ABSTRACT iii

ACKNOWLEDGMENTS v

LIST OF TABLES viii

LIST OF FIGURES ix

GENERAL INTRODUCTION 1

EXPERIMENT 1: EFFECTS ON RATIO RESPONSE
, FUNCTIONS OF RATIO SEQUENCE AND NUMBER

OF SESSIONS AT EACH RATIO VALUE 9

Method

Subjects

Apparatus

Procedure
Results
Discussion

EXPERIMENT 2: EFFECTS ON RATIO RESPONSE
FUNCTIONS OF ONE SESSION AT EACH SCHEDULE

VALUE AND OF FIXED- AND VARIABLE -RATIO

SCHEDULES 26

Method 27

Subjects 27

Apparatus 27

Procedure 27

Results 3 1

Effects of One Session at Each Schedule Value 31

Effects of Fixed- and Variable- Ratio Schedules 39

Discussion 44

Effects of One Session at Each Schedule Value 44

Effects of Fixed- and Variable- Ratio Schedules 46

10
10
10
11
15
23

vi

EXPERIMENT 3: EFFECTS ON RATIO RESPONSE
FUNCTIONS OF THE OPPORTUNITY TO RUN IN A
WHEEL AND OF VARIATION IN DEPRIVATION
BODY WEIGHT 50

Method . 55

Subjects 55

Apparatus 56

Procedure 56

Results 60

Behavioral Outcomes for Whole Sessions 60

Behavior within Sessions 72

Discussion 78

Behavioral Outcomes for Whole Sessions 78

Behavior within Sessions 85

APPENDIX A: RESPONSE FUNCTION DATA FOR INDIVIDUALS

DURING EXPERIMENT 1 89

APPENDIX B: RESPONSE FUNCTION DATA FOR INDIVIDUALS

DURING EXPERIMENT 2 91

APPENDIX C: MATHEMATICS OF THE MINIMUM -DEVIATION

MODEL 93

APPENDIX D: PARAMETER ESTIMATION TECHNIQUE 97

APPENDIX E: INDIVIDUAL AND GROUP AVERAGE RESPONSE

FUNCTIONS FOR EXPERIMENT 3 100

APPENDIX F: ESTIMATED PARAMETER VALUES OF

MINIMUM- DEVIATION MODEL FOR EACH

SUBJECT DURING EACH CONDITION OF

EXPERIMENT 3 104

REFERENCES .105

vii

LIST OF TABLES

Table Page
1. Conditions of Experiment 1 13

2. Linear Regression Results Comparing Lever-Press

Rates Across Conditions of Experiment 1 19

3, Linear Regression Results for Rate of Adjustment to

Schedule Change in Experiment 1 22

4. Response Requirements for Variable Ratio Schedules:

Number of Lever Presses for Each Dipper of Milk 29

5. Linear Regression Analyses for Experiment 2 36

6, Conditions of Experiment 3 58

7, Linear R.egression P>.esults Comparing the Effects on

Lever- Press Rates of the Running Wheel and Change

in Deprivation Body Weight in Experiment 3 66

viii

LIST OF FIGURES

Figure ' Page

1. Regvilatory options on ratio schedules. 2

2. Linear ratio response functions. 5

3. Bitonic ratio response function. 7

4. Average response functions across conditions in

Experiment 1. 16

5. Group average response functions for successive parts

of Experiment 2. 32

6. Response functions for subject HR2 during each ascending

sequence of Condition 1, Experiment 2. 34

7. Group average distributions of interresponse times

(IRT's) in Experiment 2. 38

8. Response functions for FR and VR schedules in

Experiment 2, 41

9. IRT distributions for FR and VR schedules in Experi-

ment 2, 42

10. Micros true ture of behavior with FR and VR schedules

in Experiment 2. 43

11. Response functions predicted by minimimi- deviation

model. 52

12. Demand curves and lever-press functions predicted by

the minimum- deviation model, 54

IX

13. Group average response functions for Experiment 3. 61

14. Group average demand curves and lever-press functions

for Experiment 3, 63

15. Demand curves for individual subjects in Experiment 3. 65

16. Estimated parameter values of the minimum- deviation

model for individual data in Experiment 3. 68

17. Group average obtained data and parameter- estimated

response functions for Experiment 3. 70

18. Interactions between competitive activity and ratio

behavior in Experiment 3. '71

19. Group average response functions within successive

thirds (20-min periods) of sessions in Experiment 3. 74

20. Proportions of lever presses within successive sixths

(10-min periods) of sessions in Experiment 3. 75

21. Interactions between wheel turns and ratio behavior

within sessions of Condition 3 in Experiment 3. 77

X

GENERAL INTRODUCTION

A reinforcement schedule prescribes a feedback relationship
between the rates of (or proportion of time taken up by) two behaviors,
an instrumental response and a contingent response or reinforcer. For
a hungry rat, the contingent response might be eating a food pellet while
the instrumental response might be pressing a lever. For example, a
fixed-ratio reinforcement schedule allows access to the contingent
response after some number of instrumental responses equal to the ratio
value, e.g., five lever presses for each pellet of food (fixed ratio five;
FR5). The feedback relationship between the instrumental and contingent
responses is called a "schedule ftinction" (Baum, 1973; Staddon, 1979).
Within a two-dimensional behavior space where each axis corresponds to
the rate of one activity (i.e., instrumental and contingent behaviors), the
schedule f\inction for a fixed-ratio schedule is linear with zero intercept,
as shown by the solid line from the origin in Figure 1.

When an animal is exposed to a reinforcement schedule, the distri-
bution of behavior is limited in two ways: by session time and by the
reinforcement schedule (Premack, 1965, 1971; Timberlake & Allison,
1974). In order to determine the effects of reinforcement schedules on

1

3

distributions of behavior, it is necessary to compare behavior obtained
with and without the schedule, all else equal. Given free opportunity to
press a lever and eat pellets of food in the absence of a schedule, a hun-
gry rat might show a free baseline distribution of behavior such as point
in Figure 1, i.e., a high rate of eating (contingent response, R) and
a low rate of lever pressing (instrumental response, P).

The free baseline distribution of behavior can be thought of as the
set point of a behavioral regulatory system (cf. Staddon, 1980; Timber -
lake, 1980). As a set point, the baseline distribution of behavior repre-
sents the preferred distribution of behavior in the absence of a schedule;
hence the baseline distribution should limit the possible effects on behav-
ior of reinforcement schedxiles. For example, with the baseline distribu-
tion of behavior and the ratio schedule shown in Figure 1, an animal coxild:

1. Perfectly regulate the baseline level of activity R (vertical
dashed line in Figure 1) and increase activity P from p^ to p^;

2. Perfectly regulate the baseline level of activity P (horizontal
dashed line in Figure 1) and allow activity R to fall from r to

3. Make some compromise between decreases in R and increases
in P relative to the baseline distribution and, thus, let ratio
behavior fall between points (ri,pQ) and (rQ,pj^) on the ratio
schedule function in Figure 1.

Published data show that schedule behavior is typically a compromise:

In the case of the hungry rat required to press a lever to obtain pellets of

food, for example, a large increase in lever pressing might be traded for

a small decrease in the rate of eating pellets, relative to baseline (cf.

4

Timberlake, 1980). In terms of behavioral regxilation, the less that an
activity deviates from the baseline level, the better that activity is regu-
lated. Thus, for the hungry rat, food intake is generally well regulated
while lever pressing is poorly regiilated.

Since distributions of behavior are limited by the schedule function,
schedule value is one factor which determines the amount of change in
behavior from the baseline distribution. For ratio schediales, a change
in the ratio value (e.g., number of lever presses required for each pellet)
changes the slope of the ratio schedule ftinction. The pattern of behavior
obtained as the ratio value varies is termed a "ratio response fiinction"
(or labor supply curve; cf. Battalio, Kagel, & Green, 1979; Staddon,
1979).

The simplest regulatory r\ile applied to ratio schedule behavior is
the linear response function (cf. Allison, Miller, & Wozny, 1979; Staddon,
1979, 1980). Figure 2 shows two linear ratio response fxmctions originat-
ing from the baseline distribution of behavior at B . With the linear
^ o

response function, as the ratio value increases, decreases in the contin-
gent response are accompanied by constant proportional increases in the
instriomental response. The slope of the linear response function pro-
vides a measure of the degree of regulation of the contingent response
over ratio values --the greater the absolute value of the slope, the greater
the degree to which the contingent response is regxilated (Staddon, 1980;
Timberlake, 1980).

<

5

i
i

LU

1 2 3 4 5
CONTINGENT RESPONSE RATE

(ARBITRARY UNITS)

Figure 2. Linear ratio response functions.

i

i

6

The major problem with the linear regulatory rule is that published
data are in only partial agreement. Ratio response functions do tend to
be linear with a negative slope over relatively low ratio values. However,
at high ratio values, the slope of response f\inctions changes to positive;
ratio response functions are bitonic over the full range of ratio values
(cf. Barofsky & Hurwitz, 1968; Hogan & Roper, 1978; Hursh, 1980;
Kelsey & Allison, 1976; Staddon, 1979; Timberlake, 1980). Figure 3
shows an idealized example of a bitonic response function: Rate of instru-
mental responding increases over low ratio values and decreases over
high ratio values.

Economic models of schedule behavior provide the major alternative
to the linear regulatory rtile. Several quantitative models of behavior on
single schedules have been proposed (cf. Houston & McFarland, 1980;
Lea, 1981; Rachlin & Burkhard, 1978; Staddon, 1979). The models
assume that animals behave so as to maximize value, allocating time (and
other resources) between alternative, available activities based on pref-
erences and limited by the constraints of the environment, the session
time limit, and the reinforcement schedule function. Total activity can
be classified into three categories of behavior: instrumental, contingent,
and "other" behavior which is competitive with schedxile behavior (leisure
activity to an economist; cf. Graham, 1980; Walsh, 1970). The models
assume that trade-offs between spending time in different activities
depend, primarily, on the substitution relations between activities, i.e..

CONTINGENT RESPONSE RATE

Figure 3. Bitonic ratio response function.

8

the amount of one behavior that an animal is willing to give up or accept in
order to obtain more of another behavior (cf. Graham, 1980). Within the
economic models, the concept of regulation takes a form more complex
than in the linear models since, by the time -allocation constraint, regula-
tion of any one activity depends on trade-offs between time spent in at
least two other classes of behavior. Because of the time constraint, how-
ever, response functions can be projected into the two-dimensional space
of Figures 1-3. Economic models predict ratio response functions which
are in agreement with most published data.

The present research seeks to begin testing the economic models of
single-schedule behavior. These models differ in how they define pref-
erences, but the key assTomptions are encompassed by the minimum-
deviation model (Staddon, 1979; see individual papers for discussion of
this point). Hence, the minimum- deviation model is used for quantifying
predictions in the present report. The primary dependent variable is the
response function. Since there is no standard procedure for reliably
mapping response functions, a suitable procedure is developed in Experi-
ments 1 ctnd 2. Experiment 3 then uses this procedure to test two pre-
dictions of the minimum -deviation model. The results suggest that eco-
nomic models provide a useful approach to the study of schedule behavior.

EXPERIMENT 1
EFFECTS ON RATIO RESPONSE FUNCTIONS OF =
RATIO SEQUENCE AND NUMBER OF SESSIONS
AT EACH RATIO VALUE

Ratio -sched\ile response fiinctions provide a good place to begin
j investigation of the economic models because most published studies of
single -schedule behavior are of ratio behavior (for review, see Hogan &
Roper, 1978). There are two major procedural variables required in
mapping a response function: the amount of exposure to each schediile
value and the sequence of different schedxile values. Published ratio
studies show wide variation in the criteria used for changing schedule
value (cf. Mazur, 1975; Teitelbaum, 1957). Since most ratio response
f\inctions are bitonic in form over a wide range of ratio values, schedule -
change criteria do not appear to have much effect on the general form of
ratio response functions. However, the procedure may influence quanti-
tative properties of behavior. For example, several ratio studies report
differences in absolute rates of schedule behavior across successive
determinations of response functions (cf. Kanarek & Collier, 1979;
Powell, 1968; Reynolds, 1958). No data are available on the effects of

9

10

number of sessions at each schedule value. Before attempting tests of the
economic models, it therefore seems prudent to check out the effects of
procedural variables. Experiment 1 begins this procedural analysis by-
looking at the effects on ratio response functions of ratio sequence and
number of sessions at each ratio schedule value.

Method

Subjects

Four naive, 6-month-old, female, Long-Evans hooded rats (Rl, R2,
R3, and R4) were housed individually in 24-hr light. Subjects were given
ad lib. access to standard lab chow and maintained on 22 -hr water depriva-
tion by gi-vring each animal access to water for 1 hr following each daily
session.

Apparatus

Experimental sessions were conducted in a standard Skinner box for
rats measuring 30.8 cm (1) x 23.2 cm (w) x 15.5 cm (h). A Gerbrand's
retractable lever and a Gerbrand's dipper feeder (. 1 cc cup) were attached
from behind one end wall. The lever was mounted to the left of the dipper.
When retracted, the lever was flush with the wall. The midpoint of the
lever was 4 cm from the floor and 6. 3 cm from the outside wall. Effective
lever presses were accompanied by the click of a feedback relay. The
dipper cup opening was recessed 1 cm behind the wall, elevated 2 cm
from the floor and located 5. 5 cm from the nearest outside wall, A

11

photocell and a standard #1819 bulb (recessed 1 cm) were placed on oppos-
ing sides of the dipper cup (2 cm above the cup opening) so that the beam
of light to the photocell was interrupted when a rat's head was at the dipper
cup. The midpoint of the lever and the dipper cup was separated by 11.4
cm. The plexiglass chamber was located within a wooden chamber mea-
suring 79 cm (1) X 60 cm (w) x 60 cm (h) which contained an exhaust fan,
a speaker for white noise, and a 15 w houselight. The houselight was
mounted on the wall of the wooden chamber behind and above the lever and
dipper.

Electromechanical apparatus for controlling experimental sessions
and recording data was located in another room. Cumulative records,
and session totals of lever presses, dippers of milk, session time, and
time spent operating the photocell during dipper availability were recorded
daily.

Procedure

When available, the . 1 cc dipper cup was filled with a solution of
half evaporated milk and half water. There were two types of sessions:
baseline and contingency. During baseline sessions, the lever and dippers
of milk were freely available; the lever was in the extended position for
the whole session, and, with each initial activation of the photocell, the
dipper cup rose for 3 sec. After each 3 -sec period of access to milk, the
dipper dropped to its resting position in the milk reservoir. In order for
the dipper to rise again for 3 sec, the rat was required to stop

12

interrupting and then to reinterrupt the beam of light to the photocell.
The procedure of requiring the subject to operate the photocell in order
for the dipper to rise is the minimum requirement necessary to ensure
that subjects receive full access to each dipper of milk. This procedure
also has the advantage of maintaining the same reference units for milk
consumption during baseline and contingency sessions.

During contingency sessions, the rats had to press the lever to
obtain dippers of milk. Contingency sessions began with the lever in the
extended position. When the subject completed the number of lever
presses required by the ratio schedule, the lever retracted, and, follow-
ing the next break in the photocell light, the dipper rose for 3 sec. After
3 sec, the dipper returned to the resting position and the lever was,
extended to begin the cycle again. This contingency procedure is a recip-
rocal contingency between the number of lever presses and the number of
operations of the dipper (Allison, 1971), Fixed-ratio (FR) schedules were
used in all cases, i.e., subjects pressed the lever a fixed number of
times for access to each dipper of milk (e.g., five lever presses for each
dipper; FR5).

As shown in Table 1, Experiment 1 consisted of three conditions.
During successive conditions, subjects were exposed to 5, 12, and 4
sessions at each schedvile value. The three conditions controlled for the
effects of number of sessions at each ratio value by counterbalancing the
order of exposure to number of sessions (i.e., low, high, low). During

13

Table 1

Conditions of Experiment 1

Condition

Number of
sessions at
each value

Subjects

Type of
sequence

Schedule values

1

5

All

Ascending

Baseline, FR 1, 5,
10, 20, 40, 50, 70,
90, 110, 130, 150

All

Descending

FR 80, 40, 10, 5, 1

2

12

All

Ascending

Baseline, FR 1, 5,
20, 40, 60, 90,
120, 150

R2, R3,
R4

Descending

FR 90, 40, 20, 5,
1, Baseline

3

4

R3, R4

Ascending

Baseline, FR 1, 5,
10, 20, 40, 80, 160

14

Conditions 1 and 2 (5 and 12 sessions at each value), an ascending
sequence of ratio values was followed by a descending sequence. Condi-
tion 3 consisted of an ascending sequence. An ascending sequence of ratio
values began with baseline sessions, followed by sessions of FR 1 and
progressively increasing ratio values. A descending sequence began with
the last ratio value of an ascending sequence, followed by progressively
decreasing ratio values.

During the first baseline sessions, the experimenter (MSM) placed
each individual rat in the apparatus for successive daily sessions until the
animal reliably obtained dippers of milk, for one (R4) to three (R2) ses-
sions. After this period of exposure to the dipper, all animals reliably
made full use of dipper availability time, operating the photocell for the
full 3 -sec period. The procedure for ratio contingencies was similar:
Each rat was placed in the apparatus for successive daily sessions of FR 1
until the animal reliably pressed the lever and obtained dippers of milk.
All subjects met this criterion by the third session of exposure to FRl.
Initial sessions of baseline and FRl are excluded from the present report.

All sessions were 1-hr long, dipper time included. If a dipper was
available at the time the session clock timed out, however, the session
was extended until the dipper dropped to the resting position. One conse-
quence of the session time limitation is that session rates of lever press-
ing include lever presses from partially completed ratios. Thus, obtained
ratios of lever press to dipper rates often slightly exceed the actual mean
ratio values.

15

Onset and offset of the houselight, and extension and retraction of
the lever, signalled the beginning and end of a session. Dipper and lever -
press rates were computed with respect to total session time (1 hr). All
average data in Experiment 1 were taken from the last three sessions at
each ratio value.

Except for breaks between conditions, the experiment was generally
conducted 7 days a week, at approximately the same time each day. The
total duration of the experiment (including breaks) was approximately 1.25
years. Subject Rl died during the descending sequence of Condition 2;
subject R2 died during Condition 3. Data from partially completed
sequences of ratio values are omitted from the present report.

Resxilts

Response functions v/ere always bitonic. Figure 4 shows this result
in the average data for the ascending sequences of Experiment 1: Average
data for all four subjects during Conditions 1 and 2 (5 and 12 sessions at
each value) are in the upper panel; average data for the two subjects
exposed to all three conditions (R3 and R4; 4 sessions at each value during
Condition 3) are in the lower panel. During baseline sessions, rates of
dippers of milk were high while lever-press rates were low, if not zero;
hence baseline behavior is shown below the FR 1 schedule in the figure.

Across successive conditions (hence with greater experience), rates
of lever presses and dippers of milk increased at most schedule values so
that response ftanctions tended to move outward from the origin. In

16

DIPPERS OF MILK PER MINUTE

Figure 4, Average response functions across conditions in Experi-
ment 1. Top panel: group average data from Conditions 1 and 2. Lower
panel: average data for subjects R3 and R4 for Conditions 1, 2, and 3.

17

Figure 4, outward movement of response functions between successive con
ditions is clear both in the group average data comparing Conditions 1 and
2 (5 and 12 sessions at each value) and in the average data for R3 and R4
comparing Conditions 1, 2, and 3 (5, 12, and 4 sessions at each value).

Quantitative properties of response functions also varied with ratio
sequence. In particxilar, the slope of response functions tended to be
lower over the declining limb (i. e. , baseline through the ratio value
resulting in the maxim\im rate of lever pressing) during descending
sequences than during ascending sequences. This result is clear in six
out of seven possible comparisons of ascending and descending sequences
in Conditions 1 and 2. (Not shown but see Appendix A, which gives
response function data for individuals in Experiment 1.)

One way to quantify the outward movement of response functions
obtained in Experiment 1 (cf. Figure 4) is to use linear regression analy-
sis to predict behavior from one condition to the next. I assume that, over
ratio values, lever -press rates in Condition M are a linear function of
lever-press rates in Condition M-1, i.e., use behavior in Condition M-1
as a linear predictor of behavior in Condition M. Thus, over ratio values
(N), the model is Y=AX+B where X equals the lever-press rate at sched-
ule FRN during Condition M-1 and Y equals the lever -press rate at sched-
lole FRN during Condition M. With linear regression analysis, the degree

of prediction of behavior from one condition to the next is shown by the

2

coefficient of determination (r ); systematic change in (or recovery of)

18

behavior across conditions and error are indicated by the slope and inter-
cept values, respectively. Perfect recovery of behavior from one condi-

2

tion to the next would yield an r equal to 1.0, a slope equal to 1.0, and
an intercept equal to 0.0. A slope value greater (less) than 1.0 implies
a proportionally higher (lower) rate of lever pressing at all schedule
values during the predicted condition. Since lever press and dipper rates
were linked by ratio schedxiles (except during baseline sessions), the
value of the slope has the same implications for dippers of milk as for
lever presses; hence schedule behavior can be said to change between con-
ditions in the proportion indicated by the slope.

Table 2 shows linear regression results for data on the outward
movement of response functions across successive conditions of Experi-
ment 1. Data for group average behavior are in the upper panel; data for
individuals are in the lower panel. Regressions were based on all sched-
ule values repeated between as'cending sequences of the relevant conditions
(e.g., seven points for comparison of Conditions 1 and 2; see Table 1).
Over all sets of data analyzed, lever -press rates ranged from zero (base-
line) to 181 per minute (R2 at FR90 during Condition 2; see Appendix A).
Regression results for group -average data between conditions (upper
portion of Table 2) suggest proportional increases in lever-press rates
across successive conditions, i.e., slope greater than 1.0. The linear
rtile accounted for an average of 97. 1% of the variance in average behavior
obtained across conditions. Thus, on average, outward movement of

19

Table 2

Linear Regression Results Comparing Lever-Press Rates Across
Conditions of Experiment 1 (Prediction of Condition
(N+1) Using Behavior Obtained in Condition (N))

Predicted

Slope

Intercept

2

Data

condition

(A)

(B)

r

I. Averages

over animals

All subjects

2

1. 36

- .37 .

. 986

R3 and R4, only

2

1. 39

-2. 13

.939

3

1.21

.89

.987

n. Individual data

Rl

2

1. 04

4. 65

. 963

R2

2

1.85

9.22

. 806

R3

2

1. 38

6. 82

. 773

3

1. 33

-1.53

. 927

R4

2

1. 12

2. 34

. 943

3

1. 08

4.47

. 995

ma

^■BHHHHHHBBmaiiiBiHH

! 20

I
I

I response functions between conditions was characterized by proportional

I increases in behavior at all schedule values.

i

j Regression resiilts for individuals (lower panel of Table 2) show that

I

I . . .

, subjects differed in the amount of proportional increase in behavior across

successive conditions. For example, from Condition 1 to Condition 2, rat
' R2 showed a substantial proportional increase in schedxile behavior (i.e.,
slope = 1.85) while Rl showed good recovery of behavior between condi-
tions (slope = 1.04).

All subjects showed rapid adjustment of behavior to change in sched-
ule value, with most change in behavior occurring during the first session
of exposure to each schedule value. Regression analyses, similar to
those used to look at change in response functions between conditions, can
be used to show this. To look at the rate of behavioral adjustment to

i
i

schedule change, two assumptions are necessary. First, I assume that
average behavior at each ratio value (i.e., average over last three ses-

i
i

! sions) provides an estimate of total behavioral adjustment to the schedule

i

value. Second, I assume that, over ratio values, average lever -press
rate over the last three sessions is a linear fimction of lever-press rate
obtained during the first session of exposure to each ratio value. Thus,
estimates of behavioral adjustment to schedule change used the linear

r
i

I regression model of Y = AX + B where X equals the lever -press rate during

1

i the first session at sched\ile FRN and Y equals average lever-press rate

I

i during the last three sessions at schedule FRN, over all schedule values

i

i
i

21

(N) within each condition. The slope and intercept values retain the pre-
vious implications (i.e., as measures of systematic change and error).
However, the coefficient of determination provides an estimate of the

amount of behavioral adjustment accomplished during the first session of

2

exposure to each schediile value. For example, an r value of .5 implies

that an average of 50% of the adjustment in behavior to a change in ratio

value occurs during the first session of exposure to the ratio value. The

2

higher the value or r , the faster the rate of behavioral adjustment to
change in experimental conditions.

Table 3 shows regression res\alts on behavioral adjustment for each
subject using all schedule values within each condition (i.e., including
baseline; see Table 1 for number of schedule values in each condition).
The range of lever-press rates is the same as those used to predict
behavior between conditions (i.e., 0 to 181 per min) . Two effects are
clear. First, even during Condition 1, all subjects adjusted rapidly to
sched\ile change, with an average of 75. 2% of adjustment occurring during
the first session of exposure to schediile values. Second, the rate of
adjustment to schedule change increased across successive conditions for
three of four subjects (R2, R3, and R4). Over all subjects and conditions,
an average of 81. 2% of behavioral adjustment to schedule change was
accomplished during the first session of exposure to ratio values.

22

Table 3

Linear Regression Results for Rate of Adjustment to Schedule Change
in Experiment 1 (Prediction of Average Lever Press Rate During
Last Three Sessions Using Lever-Press Rates Obtained
During the First Session at Each Schedule
Value Within Each Condition)

Subject

Condition

Slope

(A)

Intercept
(B)

2

r

Rl

1

1. 00

4. 65

.879

2^

.81

11. 03

. 770

R2

1

.65

6. 00

. 714

2

.93

4. 11

. 834

R3

1

.76

4. 33

. 752

2

.85

3. 91

. 922

3

1. 30

-6. 74

. 931

R4

1

.75

17.61

. 663

2

.86

4. 12

. 759

3

1. 04

.97

. 983

Ascending sequence only.

23

Discus sion

The data of Experiment 1 replicate the majority of previous results
showing the general bitonic form of ratio response functions (cf. Staddon,
1979). However, the data suggest that the procedure of Experiment 1
(several sessions at each ratio value with infrequent redetermination of
points) is not suitable for testing economic models of single- sched\ile
behavior. First, absolute response rates were not generally replicable
between determinations. Second, although behavior changed in an orderly
way between determinations (e, g. , outward movement of response func-
tions; cf. Figure 4), the length of time required for the three conditions
of Experiment 1 meant that subjects were nearing (or had reached) the
end of the normal rat life span (i. e. , approximately 2 years) by the end
of the experiment. Although laziness and taste-aversion learning have
been investigated in dead rats amd pigeons (Gamzu, 1974; Kalat, 1973),
morbidity does impose severe limitations on generality.

Several sessions of exposure to each schedule value do not appear
to aid--or much affect- -either the recovery of response functions between
determinations or the rate of behavioral adjustment to change in experi-
mental conditions. In Experiment 1, an average of 81% of behavioral
adjustment was accomplished during the first session of exposure to
schedule values. These results are surprising since standard experi-
mental practice dictates that subjects be exposed to several sessions at
each schedule value. However, several previous studies report similar

24

findings on rate of behavioral adjustment. For example, with runway
behavior in rats, almost all change in latency to traverse a runway occurs
by the second trial following a change in either the number of hours of
deprivation (Hillman, Hiinter, & Kimble, 1953) or the magnitude of reward
(Crespi, 1944; Zeaman, 1949). Similar effects also occur when pigeons
are required to peck a key on random-ratio schedules with and without
delivery of free food; i.e., an average of 62% of behavioral adjustment is
accomplished during the first session of exposure to a new set of condi-
tions (Thistle, 1981). Thus, the data suggest that several sessions of
exposure to each schediile value are not necessary to obtain stable data at
each schedule value. Perhaps several sessions at each value actually
interfere with--or, at least, are not required for--reliable mapping of
response functions. Experiment 2 explores this possibility.

Since outward movement of response fiinctions was obtained with 12
sessions at each value in Condition 2 and with 4 sessions at each value in
Condition 3, it is clear that outward movement was not due to the number
of sessions at each ratio value. However, body weight change and indi-
vidual experience both provide possible explanations. For example, since
the deprivation condition restricted water intake, body weight could have
changed throughout the experiment. Change in weight is a plausible factor
since rats tend to gain weight with age under normal, free -feeding condi-
tions; increased milk intake during experimental sessions might have off-
set the tendency of rats to show decreases in food intake and in body

25

weight under conditions of restricted water intake (cf. Adolf, 1947;
Levitsky, 1970). Alternatively, differences between individuals in the
amotont of proportional increase in schedule behavior across successive
conditions (cf. lower panel of Table 2) suggest that outward movement
depended more on individual experience than on any one factor general to
all subjects.

EXPERIMENT 2
EFFECTS ON RATIO RESPONSE FUNCTIONS OF ONE
SESSION AT EACH SCHEDULE VALUE AND OF
FIXED- AND VARIABLE -RATIO SCHEDULES

The data of Experiment 1 demonstrated several problems with the
standard procedure (i.e., running several sessions at each ratio -schediile
value) as a means of testing economic models of single -schedule behavior.
However, the rapidity of behavioral adjustment to change in experimental
conditions in Experiment 1 suggests an alternative procedure for mapping
ratio response functions: one session at each ratio value (per determina-
tion of a response function) with frequent redetermination of points.
Experiment 2 develops this alternative by looking at response functions
obtained using repeated ascending sequences of ratio values in Condition 1,
and alternating between ascending and descending sequences of ratio values
in Condition 2. The effects of fixed (FR) and variable (VR) ratio schedules
are also investigated.

Change in body weight in Experiment 1 could not be ruled out as a
factor influencing the change in response fiinctions obtained between deter-
minations (i.e., outward movement; cf. Figure 4). In Experiment 2, any

26

27

possible effects of weight change were avoided by controlling deprivation
body weight rather than hours of water deprivation.

Method

Subjects

Four naive, 5-month -old, female, Long-Evans hooded rats (HRl,
HR2, HR3, and HR4) were housed individually in 24-hr light. The rats
were given ad lib. access to water in their home cages and maintained at
80% of ad lib. weight (average 80% weight was 218 g) by feeding the animals
appropriate amounts of standard lab chow immediately following each
daily session. Subjects were deprived to 80% of ad lib, weight for 2 weeks
prior to beginning the experiment.

Apparatus

The apparatus was the same as in Experiment 1. In addition to the
data recorded in Experiment 1, cumulative time between the end of a dip-
per and the next lever press (postreinforcement pause time) and lever
availability time were recorded for each session. During selected ses-
sions, the occurrence and time (l/l6 sec resolution) of each lever press
and dipper of milk was recorded on paper tape for later computer analysis.

Procedure

As in Experiment 1, all sessions were 1 -hr long, and the . 1 cc
dipper cup was filled with a solution of half evaporated milk and half water.
During baseline sessions, subjects were given free access to the lever

and to dippers of milk by interrupting the photocell light. During contin-
gency sessions, subjects were required to press the lever according to
ratio schedules to obtain dippers of milk. Two animals were randomly
assigned to fixed-ratio schedules (FR: HRl and HR2) and two to variable -
ratio schedules (VR: HR3 andPIR4).

Six (VR) or seven (FR) schedule values were employed: FRl, FR
or VR 5, 10, 20, 40, 80, and 160. The response requirements for each
VR value were generated by a Fleshier and Hoffman (1962) series
(rounded to the nearest whole number and randomized). The number of
different response requirements on the VR schedules ranged from 20
values (VR5) to 5 values (VR160). The same sets of VR values were used
throughout and are given in Table 4.

The experiment consisted of two conditions. In Condition 1,
ascending sequences of schedule values, with one session at each value,
were repeated until replicable response functions were obtained, with a
minimum of five successive sequences. Each ascending sequence began
with a free baseline session, followed by progressively increasing ratio
values (FRl or VR5 through FR or VR 160). Condition 1 ended when no
systematic trend was observed in response functions over at least two
determinations, a total of five (HRl, HR3, and HR4) or six (HR2) ascend-
ing sequences.

Condition 2 investigated the effects of ascending and descending
sequences of schedule values. The last ratio value of the last ascending

29

Table 4

Response Requirements for Variable Ratio Sched\iles
Nximber of Lever Presses for Each Dipper of Milk
(Arbitrary Starting Point)

Variable ratio value

Response

interval VR5 VRIO VR20 VR40 VR80 VR160

1

2

1

3

2

64

417

2

1

17

30

12

13

112

3

1

3

19

42

85

17

4

3

40

11

76

4

196

5

7

1

8

132

153

58

6

13

6

13

24

23

7

19

15

80

7

35

8

3

2

17

32

111

9

7

7

4

17

48

10

4

3

23

56

264

11

5

9

26

12

1

6

9

13

10

11

5

14

2

21

52

15

3

5

15

16

5

26

35

17

1

10

1

18

2

13

41

19

8

1

2

20

3

4

6

30

sequence of Condition 1 (FR or VR 160) was followed by a descending
sequence of ratio values (FR or VR 80), progressively decreasing through
baseline sessions). Ascending (A) and descending (D) sequences alter-
nated thereafter for a total of six sequences (i. e. , D A D A D A).

As in Experiment 1, during the first baseline and contingency ses-
sions, subjects were simply placed in the apparatus for a 1 -hr session
with the appropriate contingency in effect. All subjects reliably operated
the dipper by interrupting the photocell light during the first baseline
session. However, only rat HR4 reliably pressed the lever during the
first session of exposure to the ratio contingency (VR5); other subjects
received extra sessions at FRl or VR5 until they actively pressed the
lever and obtained dippers of milk (2 sessions for HR3; 4 sessions for
HRl and HR2). These extra sessions are excluded from the present
report. If a subject did not earn any dippers of milk (i. e. , complete one
lever press and dipper cycle) at a ratio value during Condition 1, then
higher ratio values were omitted from that sequence; the subject began
the next ascending sequence during the next session (a baseline session).

Dipper and lever-press rates were computed with respect to total
session time unless otherwise noted. The experiment was generally con-
ducted 7 days a week, at approximately the same time each day.

31

Results

Effects of One Session at
Each Schedule Value

Response fiinctions were always bitonic, and, with experience,
schedule behavior increased at all ratio values so that response functions
moved outward from the origin. These effects are shown in Figure 5,
which presents group average response functions for four successive parts
of Experiment 2 (i.e., the first, second, and average of the last two
ascending sequences of Condition 1, and the average of the last three
sequences of Condition 2), Effects were similar for all individuals unless
otherwise noted (see Appendix B, which gives individual data underlying
average response functions shown in Figure 5).

In Experiment 2, movement of response functions outward from the
origin occurred gradually between successive determinations. Response
functions also showed recovery between successive determinations (at
least in the short-run) within a relatively short period of time. Thus,
during the first and second ascending sequences of Condition 1, lever-
press rates were approximately constant over ratio values; response func-
tions moved outward from the origin between the first and second
sequences, but behavior remained relatively undifferentiated over ratio
values (see Figure 5 and Appendix B). By the third or fourth (depending
upon subject) ascending sequence of Condition 1 (cf, average for Condition
1 in Figure 5), behavior was differentiated over ratio values so that
response functions showed a clear maximum at ratio 40 (FR20 for rat HRl;

32

UJ

M
2:

021
LU
Q-

CO
LU

LU

q:

CL

LlJ
hJ

EXPERIMENT 2

CONDITION 1

ence
uence

DIPPERS OF MILK PER MINUTE

Figure 5. Group average response fxinctions for successive parts
of Experiment 2,

33

see Appendix B) . Response fiinctions also began to show periods of
recoverability between determinations (i.e., local stability, see below),
i.e., after approximately 3 or 4 weeks of experience in Experiment 2.

r Following the third or fourth ascending sequence of Condition 1,
systematic outward movement of response functions ceased and was
replaced either by good recovery of response functions from one deter-
mination to the next, or by change in behavior which was specific to indi-
viduals. The time course of the transition from outward movement to
stable, recoverable response functions varied between individuals: rats
HR 1 and HR4 showed highly recoverable behavior between Conditions 1
and 2; rats HR2 and HR3 showed periods of recoverable response f\inctions
punctuated by behavioral change (i.e., locally stable behavior intermixed
with outward movement of response fiinctions) from the third ascending
sequence of Condition 1 until the last half of Condition 2. Outward move-
ment of average response functions between Conditions 1 and 2 (cf.
Figure 5) was due, primarily, to changes in the behavior of HR2 and HR3,
By the end of Experiment 2, outward movement of response functions had
essentially ceased for all subjects.

The procedure of one session at each schedule value with frequent
redetermination of points allowed for focusing-in on stability of response
functions as well as for tracking change. This sensitive monitoring of
behavioral stability and change is illustrated in Figure 6, which shows
response functions for rat HR2 during each of the ascending sequences of

34

Figure 6. Response functions for subject HR2 during each ascend-
ing sequence of Condition 1, Experiment 2, Sequences with good recovery
of previous response functions are shown with the same symbol.

35

Condition 1 (six sequences for this subject). Each point represents data
from one daily session. Response fiinctions for HR2 were locally stable
(i.e., recoverable between at least two determinations) during sequences
three and four, and during sequences five and six; there was an abrupt
change in behavior between sequences four and five. When response
functions were locally stable, they were highly replicable.

There were no systematic differences in ascending and descending
response functions in Condition 2 (not shown, but see regressions, below)

As in Experiment 1, a quantitative estimate of recovery of behavior
between conditions is given by using the linear regression model Y=AX+B
where, over all ratio values (N), X equals lever -press rate at schedule
FRN in Condition M-1 (the condition used as a predictor), and Y equals
lever -press rate at schedule FRN in Condition M (the predicted condition)
For example, estimate the change in schedule behavior from Condition 1
to Condition 2 by using lever -press rates in Condition 1 to predict lever -
press rates in Condition 2. As before, the values of the coefficient of
determination, slope, and intercept indicate predictability, systematic
change, and error, respectively. Regression analyses are appropriate
for showing several effects in the data of Experiment 2.

Regression restilts for the data of Experiment 2 are given in Table
5, which is divided into four sections. Over all regressions, lever -press
rates ranged from zero (baseline) to approximately 125 per minute (rat
HR2 at FR40 during Condition 2; see Appendix B) . Data in the first two

36

Table 5

Linear Regression Analyses for Experiment 2

Subject Slope Intercept r

(A) (B)

I.

Local stability of behavior during Condition 1. (Pr
rates during last sequence using lever press rates
sequence of ratio values in Condition 1, )

edict lever
from next-

press
to-last

HRl .90 .05
HR2 .92 .46
HR3 1. 07 1. 30
HR4 .99 .85

. 760
.980
.920
.931

n.

Ascending versus descending sequences during Condition 2.
(Predict average descending lever press rates using average
ascending rates. )

HRl . 803 2. 54
HR2 .936 3.93
HR3 1.04 .75
HR4 1.06 -1.29

.976
. 948
.933
.979

in.

Change in group average response functions across
Experiment 2. (Predict average lever press rates
using behavior obtained in Condition 1.)

conditions in
in Condition 2

1.36 1.30

.931

IV.

Change in individual response functions across
Experiment 2. (Predict individual level press
using behavior obtained in Condition 1.)

conditions in

rates in Condition 2

HRl 1.09 1.96
HR2 1. 57 7.17
HR3 1.41 8.88
HR4 1.02 1.00

.979
.795
6.92
.989

I

37

sections of Table 5 show that during periods of locally stable response

fiinctions (e.g., last two sequences of Condition 1; section I of table), and

between ascending and descending sequences (section II), lever -press

rates were highly recoverable between determinations. Thus, slope and

intercept values were close to 1.0 and 0.0, respectively, and, in seven of
2

eight cases, r values were greater than .93. Regression results in
sections III and IV show that, on average, lever -press rates increased
proportionally across Conditions 1 and 2 (i.e., slope greater than 1.0;
section III), and that this proportional increase in average behavior was
due, primarily, to changes in the behavior of rats HR2 and HR3 (i.e.,
slope greater than 1.0 for these animals; good recovery of behavior for
rats HRl and HR4 between Conditions 1 and 2; section IV; see also
Appendix B) .

Change and stability of response functions across successive deter-
minations in Experiment 2 were associated with change and stability in the
distributions of times between successive lever presses (interresponse
times; IRT's). IRT distributions provide a measure of the rate at which
rats pressed the lever while they were pressing. Figure 7 shows two sets
of IRT distributions for rat HRl, The top panel shows IRT distributions
at one ratio value (FRIO) during successive parts of Experiment 2 (i.e.,
the first, second, and average of the last two sequences of Condition 1,
and the average of the last two sequences of Condition 2); the lower panel
shows IRT distributions obtained at three ratio values (FRIO, FR40, and

38

2 4 6 a 10

TIME (1/16 SECOND)

Figure 7. Group average distributions of inter respons e times
(IRT's) in Experiment 2. Proportions do not add to 1. 0 because IRT's
greater than 10/16 sec are excluded. Top panel: IRT distribution dur-
ing successive parts of Experiment 2. Lower panel: average IRT distri-
butions at three ratio values in Condition 2 of Experiment 2,

39

FR160; averaged over the last two determinations at each ratio value in
Condition 2) .

Early in training, when response functions were changing across
successive determinations, IRT distributions varied both over ratio
values and across successive determinations of behavior at each ratio
value. Over ratio values, IRT's varied inversely with ratio value so that
animals pressed the lever faster at high ratio values than at low ratio
values (e.g., mode of distribution at shorter time for high ratio values
than for low; not shown). With experience across successive determina-
tions, the mode of IRT distributions shifted to shorter times and the pro-
portion of IRT's at the mode increased (cf. top panel of Figure 7). The
transition to recoverable response functions (following the third ascending
sequence for HRl) was accompanied by IRT distributions which were
rem2.rkably constant both between determinations at each ratio value (e.g. ,
averages for Conditions 1 and 2 in top panel of Figure 7) and between dif-
ferent ratio values (lower panel of Figure 7). Thus, change and stability
of response functions were associated with change and stability of IRT
distributions. By the end of Experiment 2, response functions and IRT
distributions were recoverable for all subjects.

Effects of Fixed- and Variable -Ratio Schedules

The only possible systematic difference between response functions
obtained with fixea (FR) and variable (VR) ratio schedixles was at the
highest ratio value investigated, i.e., slightly higher average rates of

40

lever presses and dippers of milk at VR160 than at FR160. This effect is
shown in Figure 8, which gives response functions for each subject, aver-
aged over the last three sequences of Condition 2 (see Appendix B). Large
individual differences are clear, especially in the effects of FR schedules.

Although subjects showed slight differences in the modal value of
IRT distributions for lever pressing (i.e., mode at either 4/l6 or 5/l6
sec), there were no essential differences in IRT distributions obtained
with FR and VR schedules. This effect is shown in Figure 9, which com-
pares IRT distributions for the four subjects. Data were taken from the
last two determinations of FRIO (rats HR 1 and HR2) or of VRIO (rats HR3
and HR4) in Condition 2.

Similarities in response functions and IRT distributions obtained
with FR and VR schediiles did not carry over into the microstructure of
behavior (i.e., the distributions of behavior in time) obtained with the two
types of ratio schediiles. Thus, FR and VR schedules had differential
effects on: the mean amount of time spent pausing following each dipper
of milk (i. e. , time between the end of dipper and the next lever press);
the total amount of time spent pausing per session; and the "r\inning rate"
of lever pressing following the pause (i.e., total lever presses divided by
the time not spent pausing or drinking milk). Figure 10 shows each of
these measures of the distribution of behavior in time as a function of
ratio value, averaged for the two FR (HRl and HR2) and for the two VR
(HR3 and HR4) subjects over the last three sequences of Condition 2,

41

FR = Solid
• HRl

1 2 3 4 5 6

DIPPERS OF MILK PER MINUTE

Figure 8. Response functi ons for FR 3.iid VR schediiles in
Experiment 2.

42

FR= Solid

TIME (1/16 SECOND)

Figure 9. IRT distributions for FR and VR schedules in Experi-
ment 2. Proportions do not add to 1, 0 because IRT's greater than 9/16
sec are excluded.

43

] 5 10 20 40 80 160

RATIO VALUE

Figure 10. Micro structure of behavior with FR and VR schedules
in Experiment 2. (Since the response which ends the pause also results
in retraction of the lever, rtmning rate of lever pressing approaches
infinity at FRl and is omitted in the figure. )

44

The top panel of Figure 10 shows that, over ratio values, mean
pause time was approximately constant at all VR values, and was constant
at FR values of 80 or less. Although pause time was always longer with
FR schedules, the difference in mean pause for FR and VR was not great
over the range of constant values. The middle panel of Figure 10 shows
that less total time was spent pausing with VR sched\iles and that, with
both types of ratio schedules, total amount of time spent pausing
decreased with increases in ratio value.

At most ratio values, running rates of lever pressing were higher
on FR than on VR schedxiles, as shown in the bottom panel of Figure 10.
Thus, FR subjects tended to press the lever at a higher rate following the
pause.

Discussion

Effects of One Session at
Each Schedule Value

The procedures of Experiments 1 and 2 both produced bitonic

response functions which moved outward from the origin with experience

so that schedule behavior increased proportionally at all ratio values (cf.

Figures 4 and 5, and Tables 2 and 5). However, the data suggest that the

procedure of Experiment 2 has several advantages over the procedure of

Experiment 1 as a means of reliably mapping ratio response functions.

First, the procedure of Experiment 2 produced recoverable response

functions faster than the procedure of Experiment 1: In Experiment 2,

response functions began to show good recovery between determinations
after only 3 or 4 weeks of experience (i.e., local stability; cf. Figure 6).
At the end of Experiment 2 {i.e., after approximately 3 months of exper-
ience), recovery of behavior between determinations was as good as, or
better than, after a year of experience in Experiment 1. Second, since
response functions are redetermined frequently, the procedure of Experi-
ment 2 is flexible enough to monitor even a changing baseline effectively
(cf. Figure 6). Third, in contrast to the results of Experiment 1,
ascending and descending sequences of ratio values did not differentially
affect response functions in Experiment 2. The procedure of Experiment 2
provides an effective means of reliably mapping ratio response fiinctions
and, thus, is highly suited for testing the economic models of single -
schedule behavior.

The change in the deprivation condition between Experiments 1
(water deprivation) and 2 (food deprivation) limits the generality of
comparisons. However, since the same type of outward movement of
response fiinctions was obtained with and without direct control over body
weight in the two experiments, the data suggest that body weight was not
the critical factor underlying observed changes. Instead, data from both
experiments show that response functions stabilize at different rates for
different subjects (cf. Appendices A and B). Thus, the data point to indi-
vidual experience as fxondamental in determining outward movement of
response functions.

46

In Experiment 2, change in behavior between conditions was asso-
ciated with Tonderlying change in the distributions of times between succes-
sive lever presses (interresponse times; IRT's): With experience, all
subjects pressed the lever faster while they were pressing. These results
replicate previous findings for FR schedules (Gott & Weiss, 1972) and
extend them to VR sched'oles.

Recovery of response functions between determinations was asso-
ciated with recovery of IRT distributions. By the end of Experiment 2,
IRT distributions were remarkably constant between determinations of
behavior at each ratio value and across different ratio values (cf. Figure
7). Constancy of IRT distributions implies that, for each subject, the
amount of time spent lever pressing was simply proportional to lever -
press rate at each ratio value. Thus, amo\int of time spent pressing the
lever was bitonic over ratio values for all subjects.

Effects of Fixed- and Variable -Ratio Schedules

Response functions for FR and VR schedules were essentially the
same, except at ratio 160 (cf. Figure 8). Distributions of the times
between successive lever presses (IRT distributions) were also the same
for FR and VR schediiles (cf. Figure 9). Differences in the effects of FR
and VR showed up in differential allocation of behavior in time: FR and
VR subjects took "breaks" from lever pressing at different times. FR
subjects took a relatively longer break following each dipper of milk (i.e.,
longer mean pause) and less break time following the pause (i.e., higher

47

rionning rate of lever pressing; see Figure 10). The present results for
FR and VR are not strong since the large individual differences in response
fimctions obtained in Experiment 2 may have masked a smaller effect of
the type of ratio schedule (cf. Figure 8). Nevertheless, these results are
interesting for two reasons.

First, current economic models of single -schedizle behavior derive
predictions using molar schediile functions, without regard to molecular
properties of schedules or behavior. Although the molecular properties
of FR and VR schedules are quite different (i.e., the number of responses
required for each dipper of milk is constant for each FR value and varies
from dipper to dipper for VR sched\iles), molar schedule functions for FR
and VR are equivalent when behavior is averaged over a long enough time
period; i.e., both types of schedules impose a proportional relationship
between the rates of lever presses and dippers of milk. Thus, predictions
of current economic models are consistent with the results of Experiment
2, i.e., equivalent response functions for FR and VR schedules (at least
over most of the range; cf. Rachlin & Burkhard, 1978; Staddon, 1979).

Second, with the exception of ratio 160, the absence of differences
in lever-press rates for FR and VR schedules is counter to laboratory
lore, which suggests that animals always show higher rates of instrumen-
tal responding on VR schedules. There is no good evidence to decide the
case. While there are reports of higher instrumental response rates on
VR than on FR in rats with multiple (Sherman & Thomas, 1968) and

48

exchange (Webbe St Malagodi, 1978) schedules, the only available report
of single -schedxile behavior used pigeons and one, high ratio value (i.e.,
FR and VR 360; Ferster & Skinner, 1957).

In contrast to published data, the results of Experiment 2 suggest
that, with single ratio schediiles, rates of instr\imental responding may be
equivalent for FR and VR schedules, except at high ratio values. Differ-
ences in response rates on FR and VR schedules are typically attributed
to differences in the time spent pausing following each reinforcement (e.g.
dipper of milk). The general idea is that longer pause times on FR sched-
xoles lead to lower overall session rates of schedule behavior. However,
in Experiment 2, pause time was relatively constant at all VR values and
at FR values of 80 or less (for a similar result with FR schedules in
pigeons, see Powell, 1968), and the difference between pause times on
FR and VR was not large at ratio values of 80 or less. Additionally, over
most ratio values in Experiment 2, longer pause time on FR was compen-
sated for by higher running rates of lever pressing following the pause.
It is possible that the sharp increase in pause time at FR160 (cf. Figure
10) did lead to lower overall rates of schediile behavior at FR160. Future
research should look at the effects on response functions of FR and VR
schedxiles within subjects to see whether the two types of ratio schedules
do, in fact, have similar behavioral effects at relatively low ratio values
and dissimilar effects at high ratio values.

In summary, data in Experiment 2 on the equivalence of FR and VR

49

response functions provide some initial support for the economic models.
The most important result of Experiment 2 is the suggestion that the pro-
cedure of one session at each schedule value (with frequent redetermina-
tion of points) provides an effective method for reliably mapping ratio
response functions. Experiment 3 uses the basic procedure of Experi-
ment 2 to test two major predictions of the economic models of single -
schedule behavior.

KXPERIMENT 3
EFFECTS ON RATIO RESPONSE FUNCTIONS OF THE
OPPORTUNITY TO RUN IN A WHEEL AND OF
VARIATION IN DEPRIVATION BODY WEIGHT

Economic models of single -schedule behavior assume that animals
allocate time between different activities so as to maximize value (Houston
& McFarland, 1980; Lea, 1981; Rachlin & Burkhard, 1978; Staddon, 1979).
These models differ in how they define value (i.e., statement of the
objective function), but the key assumptions are encompassed by the
minimum -deviation model (Staddon, 1979; see individual papers for further
discussion of this point). As a result, the minimum -deviation model is
used for quantifying predictions in Experiment 3.

In the minimum -deviation model, the value of each activity is
defined by two parameters: the free baseline rate, and the cost of devia-
tions in the activity from the baseline rate (see Appendix C for further
explanation of the model, and Staddon, 1979). The two value parameters
are independent. Cost of deviation parameters scale the substitution rela-
tions between activities, and determine the form of response fxinctions
predicted for a given type of schedule (cf. Rachlin 8z Burkhard, 1978;

50

51

Staddon, 1979). The distribution of baseline behavior, on the other hand,
identifies the point of highest value in the behavior space but does not
influence the substitution relations between activities. Thus, the base-
line distribution determines the location of the predicted response function.

Experiment 3 tests two predictions of the minimum -deviation model
for ratio response functions. The effect of the cost of" deviations from
baseline is studied by manipulating the set of non -schedule, competitive
activities available: Ratio response functions are compared with and with-
out a running wheel available, a highly preferred activity for most rats
(cf, Motheral & Staddon, in press; Reid Se Staddon, in press; Staddon &
Ayres, 1975). The effect of the baseline distribution of behavior is
investigated by comparing ratio response functions obtained at two depri-
vation body weights (80% and 98% of ad lib. weight), a manipxilation which
should change the free baseline rate of eating.

Figure 11 shows response fiinctions predicted by the minimum-
deviation model for the two cases of interest in Experiment 3. The top
panel compares predictions with a change only in the cost of deviations in
competitive activity { ^ )', the bottom panel shows the effects of a change
only in the baseline rate of the contingent response (r; see Appendix C for
derivation). Competitive activity has a graded effect over ratio values
with the largest effect at high values. Thus, an increase in the cost of
deviations in competitive activity (from ^ = .0004 to ^ = .0025) results
in increasing suppression of schedule behavior with ratio value; the form

52

CO
J—
M

bJ
h-
•<
QC

P-

-<
C3C
h-
M

ca

CO
UJ

CO

o
co

01

LiJ

0::

I—

CO
M

SOLID 6 = .0004
DASHED 3 = .00 25

SOLID r = 6
DASHED r = 3

2 4 6

CONTINGENT RESPONSES
CARBITRARY RATE UNITS:)

Figure 11. Response functions predicted by minimum -deviation
model. Top panel: variation in the cost of deviations in competitive
activity ( ^ = • 0004 and . 0025, oL = . 0001, p = 0, r = 6). Bottom panel:
variation in the baseline rate of the contingent response (r = 6 and 3,
^ = . 0004, = . 0001, p = 0).

53

of the response fxinction changes so that the peak occurs at a lower ratio
value. In contrast, change in the baseline rate of the contingent response
(r = 3 versus r = 6) shifts the location of the predicted response function
in the behavior space without affecting the form.

Predicted behavior shown in Figure 11 can be viewed in two other
infornaative ways which are depicted in Figure 12. Recent applications of
economic ideas to ratio -schedule behavior have made much use of demand
curves for the contingent response, i.e., the rate of the contingent
response as a fxanction of ratio value (cf. Hursh, 1980; Lea, 1978). The
elasticity of a demand curve is defined as the proportional change in the
rate of the contingent response divided by proportional change in ratio
value (price), and is equal-to the slope of the demand curve in log-log
coordinates (for discussion in economics, see Graham, 1980; Varian,
1978; Walsh, 1970). The top panel of Figure 12 shows predicted data
from Figure 11 plotted in terms of demand curves for the contingent
response in log-log coordinates. Increase in the cost of deviations in com-
petitive activity (left side) results in suppression of the contingent
response which increases proportionally with ratio value. A decrease in
the baseline rate of the contingent response (right side) results in a con-
stant proportional decrease in demand for the contingent response over
ratio values. Thus, in the minimum -deviation model, demand elasticity
depends on the relative cost of deviations in competitive activity and is
independent of the baseline rate of the contingent response.

54

COMPETITIVE ACTIVITY

< 19 c

03
2
O
a.
yj

LU
CE

a

o
o

Solid i}3 0004
Dashed ^ = 0025

CONTINGENT RESPONSE

Solid 6
Dashed r a 3

B I 5 la 2B 48 80 169 B 1

RATIO VALUE

10 22 49 38 169

ratio 40

SQ 189 153 53 199

INSTRUMENTAL RESPONSE RATE

Figure 12. Demand curves and lever-press functions predicted by
the minimum- deviation model. Parameter values are the same as in
Figure 11.

liniliiiiiiiiniintTiftniiiimHfgiTniirwiiiiTfMiHiif I—"

55

The lower panel of Figure 12 compares rates of instrumental
responding shown in the predictions of Figure 11. Instrumental response
rates for the relevant comparisons are plotted against one another. For
example, take instrumental response rates at ratio 5 and plot the rate
predicted when = .0025 as a function of the rate predicted when
^ = . 0004. These comparisons are simply another way to show that
change in the cost of deviations in competitive activity has a differential
effect on instriomental response rate depending upon ratio value (i.e.,
non- symmetric, bow in function shown on the left side of the figure) while
change in the baseline rate of the contingent response has the same pro-
portional effect on instrumental responding at all ratio values (i.e., linear
function on right side; see Appendix C for derivation).

Thus, Experiment 3 tests two predictions of the minimimi -deviation
model by comparing ratio response functions obtained with and without a
running wheel and at two deprivation body weights. In addition to looking
at qualitative predictions shown in Figures 11 and 12, parameters of the
minimum -deviation model are estimated. We also look at the relationship
between rates of wheel turns and dippers of milk over schedule values,
and at changes in behavior within sessions.

Method

Subjects

The subjects were the same female. Long -Evans hooded rats used
in Experiment 2 (HRl, HR2, HR3, and HR4), approximately 8 months old

56

at the beginning of Experiment 3. Subjects had never run in a wheel. The
rats were housed individually in 24-hr light and given ad lib. access to
water in the home cages. Deprivation body weights (average 80% of ad
lib. was 218 g; average 98% was 268 g) were maintained by feeding the
animals appropriate amo\ints of standard lab chow following each daily
session. Subjects were maintained at 80% of ad lib. weight except in
Condition 5.

Apparatus

The apparatus was the same as in Elxperiments 1 and 2 except that
a sliding door and a running wheel (12. 5 cm wide, 35. 5 cm in diameter)
were added to the wall adjacent to the dipper wall. The sliding door could
be positioned to allow or restrict access to the running wheel.

In addition to data recorded in Experiment 2, half turns of the wheel
were recorded during each session of Condition 3.

Procedure

Aa in Experiments 1 and 2, all sessions were 1 -hr long (dipper time
included), and there were two types of sessions: free baseline and con-
tingency. When available, the . 1 cc dipper cup was filled with a solution
of half evaporated milk and half water. During baseline sessions, sub-
jects were given free access to the lever, and to dippers of milk by
operating the photocell. During contingency sessions, subjects were
required to press the lever on ratio schedules (FR for HRl and HR2, VR

1

57

for HR3 and HR4 as in Experiment Z) for access to dippers of milk. FR
and VR schedxile values were the same as in Experiment 2 (i.e., FRl, FR
or VR 5, 10, 20, 40, 80, and 160). With the exception of Condition 2,
each schedule was in effect for one session per determination of a response
function .

Experiment 3 consisted of six conditions, listed in Table 6. The
effects of the rxxnning wheel on response functions was studied in two ways;
by alternating between daily sessions without and with the wheel available
(four sessions at each ratio value; Condition 2), and by comparing behavior
obtained when the wheel was never available (Conditions 1 and 4) with
behavior obtained when the wheel was available during every session
(Condition 3). The effects of food deprivation were investigated by com-
paring behavior obtained at 80% (Conditions 4 and 6) and at 98% (Condition
5) of ad lib. weight.

Condition 1. Data for this condition were taken from the last three
sequences of ratio values in Condition 2 of Experiment 2 (i.e., ascending,
descending, ascending). Subjects were maintained at 80% of ad lib. weight
and the wheel was not available.

Condition 2, Immediately following Condition 1, all subjects were
exposed to five baseline sessions with the riinning wheel available during
each session. After this period of adaptation, each subject was exposed
to an ascending sequence of ratio values with each ratio in effect for four
sessions. The four sessions at each value alternated between one -session

58

Table 6
Conditions of Experiment 3

Sequences of schedule
values (in order

Condition Description of occurrence)

1

80% weight, no wheel

A,

D,

2

80% weight, alternation

no wheel and wheel available,
four sessions at each
schedule value

A

3

80% weight, wheel available
during every session

A,

A,

D,

A

4

80% weight, no wheel

A,

D,

A

5

98% weight, no wheel

A,

A,

D,

A

6

80% weight, no wheel

A,

A,

A

A = ascending; D = descending.

59

determinations of behavior without and with the wheel available. Thus,
four baseline sessions --no wheel, wheel available, no wheel, wheel
available --were followed by four sessions of FR 1 or VR5 and progressively-
increasing ratio values. Data reported for this condition represent aver-
ages over the two sessions with, or two sessions without, the wheel at
each ratio value. The first five baseline sessions with the wheel available
are excluded from the present report.

Condition 3. Immediately following Condition 2, subjects were
exposed to four sequences of ratio values (i.e., ascending, ascending,
descending, ascending) with one session at each schedule value and the
wheel available during every session. Average data were taken from the
last three sequences of schediale values.

Condition 4. The wheel was never available. Three baseline ses-
sions were followed by three series of ratio values (ascending, descending,
ascending) with one session at each value. Extra baseline sessions ?.re
excluded. Reported average data were taken from all three sequences of
schedvile values.

Condition 5. Immediately following Condition 4, all subjects were
fed increased amounts of lab chow xintil each animal reached approxi-
mately 98% of the original ad lib. weight. Over 5 to 9 days, subjects
gained an average of 50 g. Three baseline sessions were followed by four
sequences of ratio values (i.e., ascending, ascending, descending,
ascending) with one session at each value. Reported average data are

60

taken from the last three sequences of schedule values.

Condition 6. Following Condition 5, subjects were reduced to 80%
of the original ad lib. weight over a period of from 7 to 10 days. Subjects
were then exposed to three ascending sequences of ratio values with one
session at each value. Averages are taken from the last two sequences of
value s .

Results

Behavioral Outcomes for
Whole Sessions

Response fxinctions. Figure 13 shows group average response func-
tions obtained with and without the running wheel (Conditions 1, 2, 3, and
4; left side), and at 80% and 98% of ad lib, weight in the absence of the
wheel (Conditions 4, 5, and 6; right side). With the opport-unity to run in
the wheel, schediile behavior was suppressed at all ratio values and the
form of ratio response fianctions changed so that the peak occurred at a
lower ratio value. (A secondary effect of the wheel was to lower baseline
rates of dippers of milk slightly.) The major effect of the change in
deprivation weight was to shift the response functions in the behavior space
without affecting the form. Average response fvmctions were never per-
fectly replicable between determinations, but the patterns of effects were
consistent nevertheless. Similar results were obtained for all subjects
(see below, and also Appendix E which gives response f;inction data for
group averages and individuals).

61

3inNiw y3d S3ss3yd mil

bJ
h-
ZD

z:

M

CL

_1
M

Ll.
O

in
on
lij

Cl
CL
M

4} eg

CO

C

0)

a

W

o

CO

C

O
•i-i
■w

y
d

a;

c

o

§^

^ CD

a u
p —

O TJ

. c

CO ;i:

c
o
U

o o

nJ

> CO o

CQ

u

TJ

C
•i-i

0)
C!

C!
O

U

un

c
o

J?

Q <u

CO

o

1— ( 1^5

^3 TJ

cfl <j 5
^ a. TJ

M O a
m O
U

TJ

5 S ^

•t: u ^

'73

C!
O

U

O ™

o o

TJ

c
o
U

60

TJ

CO

03
■i-i

o
•t-i
TJ

C
■1-1

c

TJ

0)

cn

(TJ
TJ

DO .. ^

fi CO O

OJ ^ C30

••H C

f-t O CD

■» -Xj a; ^

« U O TJ

62

Demand curves for dippers of milk and lever -press functions.
Demand elasticity of dipper rate depended on the set of activities avail-
able but was relatively independent of the baseline rate of dippers of milk.
These effects are shown in the top panel of Figure 14, which gives group
average demand curves for dippers of milk (averaged over the relevant
comparison conditions; see legend) in log -log coordinates. The difference
in demand curves obtained with and without the wheel (left side) increased
proportionally with ratio value. Change in body weight (right side) resiilted
in an approximately constant proportional difference in obtained demand
curves .

The lower panel of Figure 14 compares average lever -press rates
with and without the wheel available (left side) and at the two body weights
(right side). The opportunity to r\m in the wheel had a clearly non-
symmetric effect on lever -press rates over ratio values, with the largest
effect at high ratio values. Deprivation change resulted in an approxi-
mately proportional change in lever -press rates from baseline through
ratio 40, with a slight bow at ratio values of 80 and 160. The "bow"
resulted, primarily, from the increase in average schediile behavior at
high ratio values obtained across Conditions 4 and 6 (see Figure 13 and
Appendix E) .

The differential effects of the running wheel and deprivation body
weight were especially clear in the data on demand curves and lever -
press rates for individual subjects. Individual demand curves for dippers

63

WHEEL EFFECTS DEPRIVATION EFFECTS

lac c

B I 5 19 22 48 89 )6a S 1 5 19 22 49 89 168

RATIO VALUE

LEVER PRESS RATE

Figure 14. Group average demand curves and lever-press functions
for Experiment 3. Averages for wheel effects (left side) were taken from
no wheel Conditions 1, 2, and 4, and from wheel available Conditions 2
and 3. Averages for deprivation effects were taken from 80% of ad lib,
weight in Conditions 4 and 6, and from 98% of ad lib. weight in Condition 5,
FRl is the average of two animals only (HRl and HR2).

64

of milk are shown in Figure 15 (data averaged over all relevant conditions).
In all cases, the opportunity to run in the wheel resulted in increasing
suppression of demand curves with ratio value; change in deprivation
resxilted in a constant proportional change in behavior over ratio values.

Linear regression analysis, used in Experiments 1 and 2 to compare
lever -press rates between conditions, can be used here to illustrate the
differential effects on lever -press rates of the wheel and deprivation
change. Regression results for average individual behavior are given in
Table 7 using the model Y = AX + B. For analysis of wheel effects
(Section I), X eqxaals lever -press rate for each individual subject in the
absence of the wheel (average of Conditions 1, 2, and 4) and Y equals
lever -press rate with the wheel available (average of Conditions 2 and 3).
For analysis of body weight effects (Section 11), X equals lever -press rate
at 80% (average of Conditions 4 and 6) and Y equals lever -press rate at
98% of ad lib. weight (average of Condition 5).

Regression resTolts show, for individuals, the same effects presented
graphically for group average behavior in Figure 14. Slope values were
always less than 1.0, indicating lowered rates of lever pressing with the
wheel available and at 98% weight. The non-symmetric effect of the run-
ning wheel on lever-press rates over ratio values shows up in the regres-
sion results as poor prediction of behavior, i.e., average deviation
(absolute value) of intercept from zero = 6.06, average r = . 395. Pro-
portional change in schedxile behavior between deprivation conditions comes

65

WHEEL EFFECTS

DEPRIVATION EFFECTS

hi
H
D
Z
H
Z

q:
III

Q.

)i
J

H
Z

U-

o

(0

hi
CL

a.

H

2

lap

2 -

SOLID sax UaGHT

DASHED 3& UEICHT

HR2

HR3

HR4

5 18 29 48

tea >

5 la 28 48 88 168

RATIO SCHEDULE VALUE

Figure 15. Demand curves for individual subjects in Experiment 3.
Averages are from the same conditions as in Figure 14. Data from base-
line sessions are omitted.

66

Table 7

Linear Regression Resiilts Comparing the Elffects on Lever
Press Rates of the Running Wheel and Change
in Deprivation Body Weight in Experiment 3

2

Subject Slope Intercept r

(A) (B)

I. Wheel effects. (Predict wheel availability using data from no wheel
conditions. )

HRl . 52 - .29 . 719

HR2 . 10 7.03 . 183

HR3 . 12 8. 09 . 286

HR4 . 33 8.83 . 391

II, Deprivation effects. (Predict 98% of ad lib weight using data from
80% conditions. )

HRl . 59 -1. 11 . 996

HR2 . 50 .18 .874

HR3 . 30 4.46 .840

HR4 .47 - . 59 . 874

67

through as a change in the value of the slope (average = ,47) with good

prediction of behavior, i.e., average deviation of intercept from zero =
2

1.59, average r = .896.

Parameter estimates. Parameters of the minimum-deviation model
were estimated using a non-linear regression procedure (see Appendix D
for explanation of the technique). Four parameters were estimated: the
baseline rates of lever pressing (p) and of dippers of milk (r), and the

relative costs of deviations from baseline in competitive activity ( |^ =

2/2, ,2,2
b /c ) and in lever pressing ( = a /c ). Estimates of p were not reli-
ably different from zero (see Appendix D). Figure 16 shows estimated
values of the other three parameter s - -r, ^ , and (tC - -for individxial sub-
jects during each of the no wheel and wheel available comparison condi-
tions (Conditions 1, 2, 3, and 4; top panel), and for each of the 80% and
98% deprivation comparison conditions (Conditions 4, 5, and 6; lower
panel), (Note scale differences for the three parameters. Obtained para-
meter values, as well as coefficients of determination comparing obtained
and parameter-estimated response functions, are given in Appendix F, )

The opportxinity to run in the wheel had two primary effects on esti-
mated parameter values: The cost of deviations in competitive activity

) generally increased; baseline rates of the contingent response (dippers
of milk; r) generally decreased. In contrast, the increase in body weight
from 80% to 98% of ad lib. had one major effect: The baseline rate of dip-
pers of milk (r) showed strong decreases in all cases. On average.

68

<
>

LU
<

<

Q

LU

I—
LU

0

a

WHEEL EFFECTS

8

2-

X

° X

o

.90
.14

.10

.051- •
I

.05-

NW-no

wheel

WA=» wheel
avaibbie

NW WA

NW WA

WA

DEPRIVATION EFFECTS

8

6.

.10

a .05.

.05

30

98

i

• HRl

XHR2
oHR3
AHR4

98

CONDITION

^8

Figure 16. Estimated parameter values of the minimum -deviation
model for individual data in Experiment 3. Parameter values for r (base-
line rate of the contingent response, dippers of milk), ^ (cost of devia-
tions in competitive activity), and cK. (cost of deviations in the instrumental
response of lever pressing; see also Appendix F).

69

parameter-estimated response fxinctions accounted for 88% of the variance
in obtained data for individuals (see Appendix F).

The value of the parameter which scales deviations in the instru-
mental response of lever pressing ( oC ) was generally lov/er than the value
of the parameter which scales deviations in competitive activity { ^ ; see
Appendix F). Thus, estimated parameter values suggest that, even in the
absence of the r\inning wheel, competing activity exerted more influence
over sched\ile behavior than did the instr\miental response of lever press-
ing.

Figure 17 compares obtained and parameter-estimated response
fionctions for wheel effects (upper panel) and for deprivation effects (lower
panel; averages over animals and relevant conditions in each case).
Obtained and parameter-estimated response functions were of the same
general form. Estimated functions accounted for an average of 87% of the
variance in average data. The primary systematic difference between
obtained and parameter-estimated functions was at high ratio values where
estimated f\anctions tended to predict higher rates of schedule behavior
than actually obtained.

Running in the wheel and time available for competitive activity. The
top panel of Figure 18 shows obtained rates of wheel turns and dippers of
milk over ratio values for each subject during Condition 3. Rates of wheel
turns were negatively related to dipper rates over ratio values (hence a
positive relation between wheel turns and ratio value). Milk intake had a

70

DIPPERS OF MILK PER MINUTE

Figure 17. Group average obtained data and parameter- estimated
response functions for Experiment 3. Estimated parameter values for
wheel effects--no wheel: r = 5. 55, ^ = . 0083, o(. = wheel available:
r = 4. 93, |6 = .08, 0^ = .0044. Deprivation effects--80%: r = 5.63,
^ = .0065, c< = 0; 98%: r = 3. 48, ^ = .0131, o< = 0.

71

? 60r

o >

■ * I I I 1-

1 2 3 4 5 6

DIPPERS OF MILK PER MINUTE

Figure 18. Interactions between competitive activity and ratio
behavior in Experiment 3. Top panel: wheel turns per minute in Condi-
tion 3 over rates of dippers of milk for individual subjects. Lower panel:
average obtained and parameter-estimated time available for competitive
activity over rates of dippers of milk (same data base as in Figure 17),
Computation of time available assumed that dippers lasted 3 sec and lever
presses lasted 5/16 sec (see Figure 9).

72

stronger suppressive effect on running than running had on milk intake:
When compared with average baseline rates when dippers of milk and wheel
turns were both available, wheel turn rate was 100% higher in the near-
absence of milk (i.e., at ratio 160) while dipper rate was only 22% higher
in the absence of the wheel (average of all relevant comparison conditions;
see Appendix E).

Estimates of time available for competitive activity, when the wheel
was available in Conditions 2 and 3 and using parameter-estimated values
of dippers of milk and lever presses (see response functions in Figure 17),
are shown in the lower panel of Figure 18. Obtained and parameter -
estimated ftmctions of time available for competitive activity showed the
same form over dipper rates (hence also ratio values). Running in the
wheel never filled all available time, but the pattern of wheel turns was
similar to the pattern of time available for competitive activity over dipper
rates.

Behavior within Sessions

In Experiment 1, most adjustment to schedule change occurred dur-
ing the first session of exposure to each schedule value. After a period of
adaptation in Experiment 2, response f\inctions were highly replicable with
the procedure of one session at each schedule value. These data imply
that either animals anticipated the schedule value in effect (an unlikely
-prospect) or that behavior changed within sessions. Thus, it is of interest
to look at patterns of behavior within sessions. Data on within - s e s s ion

73

behavior were averaged over all four subjects and taken from the last two
determinations at each ratio value during Conditions 1, 4, and 5, and from
the last determination during Conditions 3 and 6. (Thus, data on within -
session behavior do not cumulate to session average values presented pre-
viously. )

Figure 19 shows group average response functions obtained during
successive thirds of sessions (i.e., 20-min periods) in four conditions of
Experiment 3: 80% weight in the absence of the wheel (Conditions 1 and 4;
left side), 80% weight with the wheel available (Condition 3; top right), and
98% weight (Condition 5; lower right). Response fTonctions were bitonic
throughout sessions and retained the same relative differences between
conditions, as observed in behavior sumnned over whole sessions (e.g.,
peak at ratio 40 in the absence of the wheel and at ratio 20 in the presence
of the wheel). However, schedule behavior decreased with session time
so that response functions were not the same form throughout. Resxilts
were similar for all subjects.

Figure 20 shows three comparisons of proportions of lever presses
within successive 10-minute periods of sessions. Since lever pressing
was proportional to dippers of milk at each ratio value, data plotted for
lever pressing are equally indicative of change in dippers of milk.

Changes in response functions within sessions resulted from a
tendency, in the absence of the wheel, for schedule behavior to decline
more slowly within sessions at intermediate ratio values (e.g., ratio 40)

DIPPERS OF MILK PER MINUTE

Figure 19. Group average response functions within successive
thirds (20-min periods) of sessions in Experiment 3.

75

* Condition 4

•^Condition 6

lO 20 30 40 50 60

MINUTES CF SESSION

Figure 20. Proportions of lever presses within successive sixths
(10-min periods) of sessions in Experiment 3.

76

than at low or high ratio values (e.g., ratio 5 or 80). This effect is shown
in the top panel of Figure 20, which compares within -session change in
behavior at three ratio values (ratios 5, 40, and 80) during Condition 4.

The middle panel of Figure 20 compares average behavior within
sessions during three different determinations of ratio 40 at 80% weight in
the absence of the wheel (i.e., Conditions 1, 4, and 6). After some
experience, change in behavior within sessions was remarkably constant
between redeterminations at the same ratio value.

The lower panel of Figure 20 compares v/ithin-ses sion behavior
obtained at 80% ad lib. weight in the absence of the wheel (Condition 4)
with behavior obtained when the running wheel was available (Condition 3)
and at increased body weight (i.e., 98% weight during Condition 5). The
rate of decline in lever pressing within sessions was relatively independent
of body weight and, instead, depended on whether the running wheel was
present.

Figure 21 looks at interactions between schedule behavior and wheel
turns at three ratio values (ratios 5, 4Q, and 160) in Condition 3 when the
wheel was available during every session. Lever pressing declined with
increasing rapidity with increases in ratio value (e.g., greater proportion
of lever presses in first 10 minutes at ratio 40 than at ratio 5). The rela-
tionship between rates of wheel turns and lever presses was clearly nega-
tive: If lever pressing was high within a 10 -minute period, then wheel
turns were low (and vice versa).

77

Figure 21. Interactions between wheel turns and ratio behavior
within sessions of Condition 3 in Experiment 3.

78

Discussion

Behavioral Outcomes for
Whole Sessions

When analyzed in terms of behavioral outcomes for whole sessions,
the results of Experiment 3 provide strong qualitative and quantitative
support for the minimum- deviation model (Staddon, 1979). Qualitative
support derives from comparison of predicted and obtained response func-
tions, demand -curves, and lever-press functions (cf. Figures 11-15).
Quantitative support derives from estimated parameter values which gen-
erally changed between conditions in the ways assumed in making predic-
tions, and which acco\inted for a high proportion of the variance in obtained
data (see Figure 16 and Appendix F). Overall, the match between data and
theory suggests that ratio behavior can be characterized as an optimal
allocation of behavioral resources between schedule and non-schedule
(competitive or leisure) activities.

The effects on ratio behavior of the opportunity to run in the wheel
varied with ratio value, while the effects of deprivation weight were inde-
pendent of ratio value. Thus, the form of ratio response f\anctions (and
demand curves) depended on the set of activities available while the loca-
tion of the response function (amd demand curve) depended, primarily, on
the baseline rate of the contingent response (dippers of milk). These
results on the independent effects of the rujining wheel and deprivation body
weight lend credence to the assumption, in the minimum- deviation model,
that at least two parameters are required in describing preferences: the

79

baseline rate ajid the cost of deviations from baseline rate in each activity.

The major discrepancy between assumptions used in making predic-
tions and behavior obtained in Experiment 3 was that, in addition to chang-
ing the form of obtained response functions, the opportunity to run in the
wheel also acted to suppress baseline rates of dippers of milk. In the
minimum- deviation model, there is no necessary relation between the
baseline rate of schedule behavior and the relative cost of deviations in
(or relative value of) activities which are competitive with schedule behav-
ior. However, this effect can be xinderstood in terms of time allocation:
The presence of the running wheel probably resulted in an increase in the
amoTint of time spent in competitive activity, leaving less time available
for obtaining milk during baseline sessions. These results do not contra-
dict the model; instead, they point to a limitation.

Response functions derived from parameter estimates were the same
general form as obtained data (cf. Figure 16) and accoTonted for a high
percentage of the variance in obtained data (cf. Appendix F). The only
systematic difference between obtained and parameter-estimated response
functions was at high ratio values where predictions tended to exceed
obtained rates of schedule behavior. This systematic difference could
have resulted from several factors. For example, non-linear estimation
is not an exact method, and it is possible that differences between obtained
and predicted data at high ratio values was an artifact of the relatively
narrow range of dipper rates over the high ratio values (cf. Appendix E).

80

Alternatively, it is possible that either the parameters scaling the costs
of deviations are not constant over the full range of dipper rates, or that
a related model (with different specification of preferences; cf. Rachlin &
Burkhard, 1978) would account for more of the variance in the data.

In contrast to recent suggestions (e. g. , Hursh, 1980), the data of
Experiment 3 show that demand elasticity for milk (i. e. , the slope of the
demand curve in log-log coordinates; cf. Figures 14 and 15) was the result
of interactions between available activities rather than deriving from any
property of the contingent response (the "reinforcer" ) per se. These data
on the determinants of the demand elasticity of milk are actually somewhat
coTinter-intuitive: With commodities such as food intake which are essen-
tial to physiological well-being, common ideas suggest that the more of
the commodity an animal chooses under free conditions, the better the
commodity should be regulated (i. e. , the lower the demand elasticity)
\inder schedule conditions.

The problem with common ideas is that they implicitly assume the
depletion/ repletion model of motivation, i. e. , the idea that animals eat
(for example) when depleted of food and cease eating when no longer
depleted. Although rarely stated directly, the depletion/repletion model
of motivation assumes the existence of an absolute level of food intake (for
example) at which satiation occurs, i. e. , that satiation is a fixed charac-
teristic of an animal consuming a given type of food. The data of Experi-
ment 3 challenge the validity of the depletion/repletion model by suggesting

81

that observed rate of eating is a joint function of the amoxint of deprivation
for food (i. e. , body weight), the set of alternative available activities,
and the effective environmental constraints (i. e. , the session time limit
and the form and value of the schedule function).

The present research is not alone in recent challenges to the
depletion/ repletion model (cf. Collier, 1980; Levitsky, Faust, & Glassman,
1976; Peck, 1978). However, the theory and data help to clarify the dis-
tinction between the empirical definition of satiation (i. e. , cessation of an
activity) and implicit connotations of the term. Clarification is aided
because the present approach explicitly distinguishes between the prefer-
ences of the animal and the constraints of the environment.

Given the fundamental constraint on session time, the baseline rate
of each activity is equal to the satiation value of the activity by empirical
definition since no more than the baseline rate of the activity will be chosen
in the absence of a significant chajige in either the animal (e. g. , depriva-
tion change) or the environment (e. g. , change in the session time, limit or
the set of activities available). The data show that satiation values of
each activity are relative: All animals ate more during baseline sessions
in the absence of the wheel than in the presence of the wheel, and ran
more in the absence of milk than in the presence of free milk. In these
comparisons, there is no reason to suppose, for example, that some abso-
lute "satiation" level for milk changed substantially with the presence or
absence of the running wheel, i. e. , that animals were h-ungrier in some

82

sense in the absence of the wheel. Instead, empirical levels of satiation
during baseline sessions can be understood as an adaptation to environ-
mental limitations on time available. Several researchers (e. g. , Collier,
1980; Peck, 1978) have suggested that body weight is a strategy of adapta-
tion; the present results suggest that eating rate is also a strategy of
adaptation.

If we take the economic ideas literally, then we see that observed
behavior always represents preferences subject to constraint. Thus, the
idea that baseline rates of behavior represent satiation values can be
extended to behavior at any ratio value. The only difference is that, for
ratio values, there are two effective constraints (i. e. , time plus the
schedule) rather than one (i. e. , the session time limit).

Food rate (i. e. , dippers of milk) was less suppressed by running
than running was suppressed by food. These results imply, simply, that
food was a more highly valued commodity to the food- deprived rats in
Experiment 3 than was rtinning in a wheel, an idea which accords well with
intuition. These data on interactions between activities are also in accord
with recent investigations into inhibitory interactions between activities
(Reid &: Staddon, in press).

The negative relationship between rates of wheel turns and dippers
of milk obtained over ratio values (cf. upper panel of Figure 18) supports
the basic assumption, in the minimum- deviation model, of competitive
interactions between activities for limited time resources. The model can

83

also account for the form of the relationship between wheel turns and dip-
pers (i. e. , time available for competitive activity in the lower panel of
Figure 18)» These data replicate in form (although not in detail) the type
of interactions obtained between wheel turns and food deliveries with fixed
time schedules (reported in Staddon, 1977). Thus, the data suggest the
generality of the form of interactions between competitive activities and
schedule behavior on different types of schedules.

Collier and his associates (e. g. , Collier, 1980; Collier, Hirsch, &
Hamlin, 1972) and Hursh (1980) have suggested that fundamental differ-
ences exist between schedule behavior obtained during short (e. g. , 1-
hour) and long (e, g. , 24-hour) sessions. The typical finding is that
schedule behavior shows lower demand elasticity (i. e. , better regulation
of food intake over ratio values) during long sessions than during short
sessions. The results of Experiment 3 suggest that these differences
between long and short sessions may be due to differential effects of com-
petitive activity: In contrast to recent suggestions (e.g. , Collier, 1980),
competitive activity may be a more important determinant of schedule
behavior during short sessions than during long sessions.

Nevin (e, g. , 1979) has suggested that response strength can best be
interpreted as resistance to change in instrumental responding. Within
this scheme, resistance to change is identified with the change in the
logarithm of rate of instrumental responding over levels of a disturbance
variable such as free reinforcers or sessions of extinction. The basic

84

idea is that, the higher the reinforcement rate, the greater the resistance
to change in instrumental responding. The results of Experiment 3 sug-
gest that, in the analysis of resistance to change, the focus on one class
of behavior may be misplaced. For ratio sched\iles (at least), change in
lever-press rates between conditions depends on interactions between
schedule ajid non- schedule behavior rather than on any one property of the
reinforcer or of the instrumental response.

Timberlake and Wozny (1979) and Allison (1981) both suggested
criticisms of the minimum- deviation model, but there are problems with
each of these acco\ints. Timberlake and "Wozny (1979) compared predic-
tions of several models using data on wheel running and eating which was
taken from free baseline sessions and two ratio values. Parameters were
estimated with data from the baseline session and one ratio value, and
used to predict behavior at the second ratio value. The minimum- deviation
model fared relatively poorly. However, Timberlake and Wozny' s criti-
cisms are not well founded for at least two reasons. First, there is the
problem of sample size: Two points may be sufficient to show an excep-
tionally reliable behavioral effect, but they are not sufficient to estimate
parameter values reliably using a non-linear regression technique.
Second, Timberlake and Wozny did not consider the effects of competitive
activity on schedule behavior.

Allison (1981) recognized that the minimum- deviation model cannot
accoTint for behavior obtained with a ratio procedure frequently used by

85

Collier and his colleagues (e.g.. Collier, Hirsch, & Hamlin, 1972), i.e.,
the requirement of a fixed number of instrumental responses for each
meal (i. e. , period of eating) rather than for a fixed portion of food, as in
the standard procedure. Allison is correct, but the criticism is mis-
guided. Since predictions of the economic models of single -schedule
behavior depend on a schedule function which is fixed in form and value,
predictions for behavior in the Collier procedure are beyond the proper
range of application of current economic models. The form of the sched-
\ile function is fixed in the Collier procedure (and the same as standard
ratio schedules), but, since the animal controls the amount of food con-
sumed during each meal, the animal also controls the effective ratio value
in terms of instrumental responses per gram of food obtained, for
example. Although response functions obtained with a meal as outcome
are similar to those obtained with a single pellet as outcome, animals do
not strictly minimize the n\miber of instrumental responses performed for
each xinit of contingent activity. Data from the Collier procedure point out
a limitation of current economic models of single -schedule behavior.

Behavior within Sessions

The minimum- deviation model caji account for the gross features of
response functions obtained within sessions since effects were similar to
those obtained in behavioral outcomes for whole sessions (e. g. , bitonic
response functions with peak at ratio 20 when the wheel was available; cf.
Figures 13 and 19). However, the model cannot account for obtained

86

changes in the form and location of response functions within sessions:
The minimum -deviation model is static as opposed to dynamic, and is
therefore limited to predicting behavioral outcomes rather than behavioral
processes. Rather than contradicting the foundations of the model, data
on within -session change in behavior point out one limitation of the
minimum -deviation model.

Within-session decline in schedule behavior has been reported pre-
viously for rats, pigeons andmonkeys exposed to interval schedules and FRl
(Collier, 1959; Collier & Myers, 1961: Collier & Siskel, 1959; Collier &
Willis, 1961; Premack, Collier, & Roberts, 1957; Schrier, 1965; and in
unpublished data from our laboratory), and is implicit in "satiation"
curves (cf. McCleery, 1975; Skinner, 1932a, 1932b; Stellar & Hill, 1952).
Thus, within-session decline in schedule behavior appears to be a general
phenomenon. Similarities in the rate of decline in schedxile behavior at
80% cLnd 98% of ad lib. weight in Experiment 3 replicate previous resiilts on
the effects of deprivation (Collier & Willis, 1961). Unforttmately, no
published studies have looked at within-session change in behavior over
the full range of schedule values or at the effects of a running wheel.

Recovery of within-session decline in behavior across successive
determinations of each ratio value (cf. Figure 20) was rather remarkable
and suggests, at the very least, that the dynamic process controlling
within-session change in behavior is highly reliable. There are several
dynamic process hypotheses which might accovmt for observed data. One

87

possibility is the classic idea of satiation, i. e. , the idea that the more
food (for example) that an animal has obtained within a session, the less
likely the animal will be to work for more food. Within each ratio value,
schedule behavior did decline as more food was obtained. However, the
satiation hypothesis implies that lever pressing should have declined most
rapidly at the highest rate of food intake (i. e, , the lowest ratio value) and
least rapidly at the lowest rate of food intake (i. e. , highest ratio value).
The data clearly contradict predictions of the satiation hypothesis and,
thus, suggest that the depletion/repletion model of motivation is no more
appropriate for analysis of within- session behavior than it is for analysis
of behavioral outcomes for whole sessions.

Another possibility is to apply the idea of response strength as
resistance to change to obtained changes in behavior within sessions
(after Nevin, 1979). The response strength hypothesis implies effects
opposite to those of the satiation hypothesis ever ratio values, i. e. ,
greater constancy of behavior within sessions at low ratio values than at
high ratio values. Although the response strength prediction for change
within sessions was supported by data obtained when the wheel was avail-
able, it was clearly contradicted by data at each of the deprivation body
weights in the absence of the wheel.

Thus, the data on within- session change in schedule behavior cannot
easily be explained by the satiation hypothesis or by the response-strength
hypothesis. A third approach arises simply from consideration of the

88

factors which appeared to determine within- session change in behavior in
Experiment 3: The rate of decline in schedule behavior within sessions
was independent of body weight and, instead, depended on the set of com-
petitive activities available and on the ratio value. Thus, the variables
of importance to within- session change appear to be the same ones which
are important in understanding behavioral outcomes for whole sessions
the economic variables of preferences and constraints. However, the
mode of interaction of these variables appears to differ in the two cases,
as well it should in describing am outcome and a process. Precise model-
ing of behavior within sessions is beyond the scope of the present paper,
but the type of model required would probably take a form akin to that
used by Hinson (e. g. , Hinson & Staddon, 1981) in the analysis of choice
between concurrently available reinforcement schedules.

In summary, the minimum- deviation model (Staddon, 1979) provides
a good qualitative and quantitative account of the determinants of ratio
schedule behavior when behavior is analyzed in terms of outcomes for
whole sessions. Data on within- session change in behavior show that the
rule which describes behavioral outcomes (e.g., minimum deviation) may
not, and in fact need not, accurately describe the behavioral processes
which are responsible for obtained outcomes.

APPENDIX A

RESPONSE FUNCTION DATA FOR INDIVIDUALS DURING
EXPERIMENT 1 (Rates Per Minute of Dippers of Milk
(D) and Lever Presses (LP))

Condition 1: Ascending Sequence

Rl R2 R3 R4

Schedule

value D LP D LP D LP D LP

Baseline

1. 98

0

1.

93

0

4.

48

•

1

3.

77

. 2

FR 1

2.43

2.5

2.

13

2. 2

2.

50

2.

6

3.

00

3. 1

5

2.43

12.9

1.

80

9. 3

2.

65

13.

7

2.

95

17. 0

10

2. 37

24. 9

1.

57

16.4

2.

83

29.

0

2.

68

28. 6

Ct\J

2. 35

48. 7

1.

43

7 Q d

7

07

41

"X

7

7 n

4.4.

4U

2. 82

115. 6

1.

08

±^ 1

1

D J

A7

o

7

S 4.

cn
3U

2. 78

142. 3

•

63

Ji . 7

•

73

7

7 n

117 n

f U

2.43

173. 9

•

40

Co , 0

D 0

AA

1

1

i .

An

1 1 A n

1. 78

163.2

18

1 A 7

•

7

7 1

7
1

•

7 0

1 DA 7

1 1

1 1 U

1.13

126.2

•

08

Q Q

7 . 7

•

VJ 3

L
D .

C

1 •

1 1 A n

1 1 O . VJ

1

i jU

1. 02

133. 8

03

7

n

•

A

Ort . O

1 C A

1 OU

.67

101. 1

»

03

A. %

i u

■2

•

A7

Q A
7 -J. D

Condition 1 :

Descending Sequence

FR 1

4. 22

7.0

2.

13

2. 2

2.

73

2.

8

3.

17

3. 7

5

3.98

21. 7

2.

10

10. 9

1.

93

9.

8

2.

28

13. 1

10

3. 05

31. 7

2.

05

21.4

1.

95

19.

7

2.

08

22. 8

40

3. 03

124.6

1.

25

51. 0

•

95

38.

8

1.

57

64.4

80

1. 83

148. 9

•

68

56.6

38

32.

8

1.

00

80. 5

Condition 2:

Ascending Sequence

Baseline

4. 82

0

3.

27

0

3.

53

•

2

3.

32

1.0

FR 1

3.40

5.9

2.

70

2.7

2.

63

2.

7

2.

48

2. 5

5

3. 62

19. 6

2.

50

12. 9

2.

52

12.

7

2.

72

15.4

20

3. 60

73.4

2.

77

56. 2

3.

23

65.

4

3.

00

62. 0

40

3. 17

128. 7

2.

25

90. 8

2.

25

90.

5

2.

87

116. 7

60

2. 58

157. 5

1.

43

87. 2

1.

77

107.

3

2.

15

131. 1

90

1.98

181.4

68

62. 7

•

83

76.

2

1.

13

103. 0

120

1. 12

135.4

48

58. 5

•

42

49.

2

•

85

102. 0

150

. 57

85. 3

•

23

36.6

•

15

23.

3

«

70

107. 0

89

I

1

90

Condition 2: Descending Sequence

Rl R2 R3 R4

Schedule

value D LP D LP D LP D LP

Baseline Died 4. 53

FR 1 3.78

5 3. 18

20 2. 28

40 1.63

80 . 78

Condition 3: Ascending Sequence

Baseline
FR 1
5
10
20
40
80
160

1

4.

72

0

5.

25

. 7

3.

8

3.

62

3. 9

4.

28

5. 5

16.

5

3.

85

19. 9

3.

72

21. 3

46.

8

2.

27

40. 5

3.

32

69. 3

66.

0

2.

32

93. 8

2.

63

107. 7

70. 7

•

98

88.4

1.

37

124. 9

d

5.

47

0

4.

33

.2

5.

33

5.6

4.

62

7.4

3.

42

17. 8

4.

12

25. 1

4.

05

41. 5

4.

07

44. 8

2.

97

60. 6

3.

55

75. 1

3.

38

136. 2

3.

10

128. 3

1.

28

103. 7

1.

92

156. 0

•

23

36. 2

•

95

152. 8

Died

APPENDIX B

RESPONSE FUNCTION DATA FOR INDIVIDUALS DURING
EXPERIMENT 2 (Rates Per Minute of Dippers of Milk
(D) and Lever Presses (LP))

Condition 1

First Ascending Sequence

HRl HR2 HR3 HR4

Schedule

value

D

LP

D

LP

D

LP

D

LP

Baseline

2.24

0

1.93

— — _____
. 3

3. 00

0

3. 31

. 2

FR 1

2. 12

2. 1

2. 64

2. 7

FR or VR 5

1. 73

9.0

3. 05

15. 5

2. 61

13. 6

1.90

9. 7

10

1. 36

14. 3

1.44

14. 5

2. 27

22. 8

2. 50

25. 5

20

. 53

10.9

. 20

4.2

1. 60

32. 7

1. 59

32. 5

40

.27

11. 1

. 07

3. 0

.07

3. 1

. 72

30. 2

80

. 17

13. 5

0

.5

. 03

2. 4

. 27

21 . 3

160

.02

4.5

0

1. 0

. 12

17. 2

Second Ascending Sequence

Baseline

3. 31

0

4. 02

0

3. 58

. 2

5. 07

. 3

FR 1

2. 86

3.4

. 4. 73

4.9

FR or VR 5

3. 01

15. 8

4.66

24. 1

3. 89

21 . 2

4.16

22. 8

10

2.99

31.4

2. 07

21. 2

1. 86

19. 3

3. 62

33. 8

20

1.21

22. 6

.91

18. 6

2. 07

42. 0

2. 15

43.9

40

.69

28. 2

. 16

6. 8

. 75

31. 7

1. 39

57. 2

80

. 30

24. 2

0

1.3

.43

33. 6

.44

36.4

160

.15

24.4

.05

10.4

.23

33.4

Averages, Last Two

Ascending Sequences

Baseline

4.43

0

4.92

. 1

3.96

0

4. 61

0

FR 1

3.65

4.4

4. 70

5.2

FR or VR 5

3. 60

20. 1

3. 83

20. 0

3. 56

19. 6

3. 55

20. 1

10

3.29

35. 1

3. 93

41. 3

3. 03

32. 1

3. 81

40. 1

20

2.29

47. 7

2. 98

61.9

2. 16

45. 0

3.49

77. 2

40

1. 11

45. 2

1. 78

72. 8

1. 51

62. 1

2.29

95.6

SO

. 38

31.2

. 56

45. 9

. 68

55. 5

1. 14

93. 2

160

.07

11.7

. 08

13. 6

. 08

12. 7

.49

75.1

91

92

Condition 2

Averages, Last Three Sequences (Ascending, Descending,
Ascending)

HRl HR2 HR3 HR4

Schedule

value D LP D LP D LP D LP

Baseline

5.

86

0

5.

52

•

5

4.

62

1

5.

25

•

1

FR 1

4.

57

4. 7

5.

31

5.

7

FR or VR 5

4.

18

24. 1

4.

61

25.

7

2.

89

16.

7

4.

51

25.

1

10

3.

46

37.6

4.

84

52.

7

3.

50

38.

0

3.

55

37.

9

20

2.

76

56. 3

4.

04

85.

4

2.

86

60.

1

3.

63

75.

7

40

1.

18

48.4

3.

01

124.

1

2.

66

107.

8

2.

42

98.

0

80

•

45

36.9

1.

43

116.

8

1.

11

91.

2

1.

20

96.

8

160

•

12

20. 1

•

35

56.

1

•

44

68.

8

•

54

84.

7

APPENDIX C

MATHEMATICS OF THE MINIMUM- DEVIATION MODEL

The objective function of the minimum -deviation model (Staddon,
1979) is the following quadratic utility function:

D^ = a^(P-p)^ + b^(Q-q)^ + c^(R-r)^ Eq. C. 1

where:

a, b, c = parameters scaling deviations in each class of behavior
from baseline (i. e. , costs of deviations);

p, q, r = baseline rates of the instrumental response, competitive
or leisure activity, and the contingent response;

P, Q, R = rates of instrumental, competitive and contingent
behavior under schedule conditions.

The effective constraints are those due to time:

P + Q + R = 1

(with, for purposes of substitution, p + q + r = 1) and to the schedule
function. For m equal to the ratio value, the ratio schedule function
is given by:

P = mR.

Solution is most easily obtained by substituting p = mR into the
objective function and the time allocation constraint, and applying
standard methods of Lagrangian multipliers to solve for the minimum.
With substitution, the Lagrangian is:

L(D^) = a^(mR-p)^ + b^(Q-q)^ + c^(R-r)^ - % (R(m+1)+Q-1). Eq. C. 2
Taking partial derivatives with respect to P, Q and ^yields

93

94

2 2
^L/3lR = 2a (mR-p)m + 2c (R-r) - A (m+1)

^L/3.Q = 2b^(Q-q) - X

^ L/9;L = 1-R(m+1) - Q.

With each equation set equal to zero, the equations can be solved to

yield a solution in R;

_ p(b^(in+l)+a^in) + r(b^(m+l)+c^)
^" 2 2 2 2 2 • Eq. C. 3

am + b (m+1) + c

This is the equation for the demand curve of the contingent response,

e. g. , the predicted rate of dippers of milk (R) obtained over ratio

values (m).

Since there are only two free parameters scaling deviations in

2

activities, one parameter can be eliminated by dividing through by c .

2 2 2 2

Letting = a /c and j2 = b /c , the demand curve becomes:

^_ p(Mm+l) H-oCm) + r(;g(m+lHl) Eq.C,4
o( m^ + ^ (m+1)^ + 1

The predicted value of P for given values of m and R can be

obtained by the schedule ftinction, i. e. , P = mR. Substituting

m = P/R into the demand equation (Eq. C.4) and rearranging yields the

predicted ratio response function:

R^( g + l)+P^(o( + |S) -.R(^(p+r)+r) -P(^(p+r) + o^p) + 2^RP=0. Eq. C. 5

The predicted effect on demand curves of variation in any one
parameter can be derived by holding all other parameters constant and
examining the effect on the ratio of R demanded in one case (R^) to R

95

demanded in a second case (R2)' For variation in the parameter r

(i. e. , the baseline rate of the contingent response), the ratio of R^/R^

can be written as follows since all parameters except r are constant:

(pX + r^Y)/Z pX + r^Y

where X, Y and Z are constants. If the baseline rate of the instrumental
response equals zero (i. e. , p = 0), then demand for R at the two values
of r is simply proportional;

R r

— i = _i . Eq. C. 7

Of course, if the rate of the contingent response changes in a propor-
tional manner, the rate of the instrumental response must also change
in the same proportion at each ratio value. Substituting the ratio
schedule function into Eq. C. 7 yields:

P. r„

_1 = _i . Eq. C. 8

P r
^2 2

Thus, if the baseline rate of the instrumental response is zero,, then the
minimum -deviation model predicts that a change in the baseline rate of
the contingent response (all other parameters constant) results in a
proportional change in the response function which is independent of
ratio value. (This assumption was used for predictions shown in
Figures 11 and 12 in the text. )

Alternatively, the effect on the demand curve of variation in

96

parameter ^ (i. e. , parameter scaling deviations in competitive, leisure
activities) is more complex. Rearranging the demand curve in terms of
^ yields:

R = ^ ("^+^) (P+^) +^pin + r ^ g
f/,m + ^ (m+l) + 1

Eq. C. 9 can then be rewritten in terms of R predicted under two values
of ^ ^ I' ^ 2^ other parameters constant:

R, ^ (^^(m+l)S + T)/(U+^^(m+l)')
^2 ( ^ ^{m^DS + T)/(U + ^ 2(^+1)^)

where S, T, and U are constants. Eq. C. 10 cannot be simplified further.
However, it is clear that the effects of ^ vary with the ratio value (m),
and that change in ^ has a larger effect, the larger the ratio value.

APPENDIX D
PARAMETER ESTIMATION TECHNIQUE

Parameter values of the minimurn. -deviation model (Staddon,
1979) were estimated using the SAS nonlinear regression program
(NUN) with, an equation similar to Eq. C. 3 but including parameters
representing the time taken up by each unit of each activity. With
assumptions about the time of activities, the session time constraint
becomes :

k^P + Q + k^R = 1
(with k^p + q + k^r = 1 for purposes of substitution) where

k^ = time for each unit of P, the instrumental response;
- k^ = time for each unit of R, the contingent response.
(No time parameter scales Q. Since the class of activity Q is not
measured, the units of Q and the time spent per unit of Q are functionally
indistinguishable. )

Given the time constraint and the ratio schedule function, solution
of the Lagrangian yields the following demand curve with parameters

defined as in Appendix C:

2 2 2 2 2

m(b k,(pk. +rk.,) + a p) + (b k (pk +rk )+c r)

R= — i i ^ i . Eq. D. 1

2 2 2,2 2
am + b (k^m+k^) + c

2 ,2,2
Dividing nimierator and denominator by c and letting = a /c

2 , 2

and I? = b /c yields:

97

I

98

R =

m( ^ k^(pk^+rk2)+o( p) + ( ^ k2(pk^+rk2)+r

Eq. D, 2

For parameter estimation, the value of k was set equal to the approxi-

mate mode of inter-lever press-time distributions, i. e. , . 375 (5/16)
sec (cf. Figure 7). Parameter k^ was set equal to the programmed
dipper availability time of 3 sec.

In estimating parameter values, the value of p was typically zero.
Tests of p = 0 were performed, in part, by eliminating p from Eq. C. 2:

and re-estimating parameter values. Elimination of p had no effect on
other parameter values. Consequently, the true value of p was assumed
to be zero, and Eq. D, 3 was used for estimating the parameter values
presented in the text.

Coefficients of determination were estimated by averaging the
linear correlation results (i. e. , resultant coefficients of determination)
for obtained and estimated rates of dippers of milk with those for obtained
and estimated lever press rates. Thus, reported coefficients of determ-
ination are a measure of the percentage of variance accounted for in
rates of lever presses and dippers of milk.

In estimating parameters, better fits to obtained data (i. e. ,
higher coefficients of determination) resulted from using the derivative

Eq. D. 3

99

method of the nonlinear regression program. In the few cases where
estimates of cC yielded negative values, better fits to obtained data
resulted from restricting parameter values to be equal to or greater
than zero. Consequently, parameter values were bounded to be positive
throughout. Use of data for each session during a condition reduced the
95% confidence intervals for parameter values, but had almost no effect
on estimated parameter values; hence, average response fxinction data
were used throughout (see Appendix E). Parameter estimates obtained
with a different nonlinear technique (program written by Dr. G. R.
Dwyer at Texas A&M University) resulted in equivalent estimated
parameter values.

APPENDIX E

INDIVIDUAL AND GROUP AVERAGE RESPONSE FUNCTIONS
FOR EXPERIMENT 3 (Rates Per Minute of Dippers of
Milk (D), Lever Presses (LP), and WTieel Turns
(WT), Condition 3; See Appendix B
for Condition 1 Data)

Condition 2: Alternation No Wheel, WTieel Available

No WTieel

HRl HR2 HR3 HR4

Schedule

value D LP D LP D LP D LP

Baseline

7.49

. 1

5.

72

.4

5.

84

.2

5.

13

. 1

FR 1

6.91

7.0

5.

71

8. 1

FR or VR

5

5. 13

29.9

4.

82

26.9

4.

88

29. 7

4.

03

23. 3

10

4.49

49. 2

5.

14

55. 3

4.

93

53. 7

4.

29

46. 0

20

3. 26

68. 3

5.

08

107. 7

3.

53

70. 5

2.

91

60. 5

40

1.68

68. 8

3.

53

145. 3

2.

47

98.8

2.

31

93.2

80

.63

48.6

1.

43

116.9

1.

08

88. 6

1.

15

94. 1

160

. 14

22. 5

•

04

7.4

•

40

62.4

•

42

70. 3

Wheel

Available

Baseline

6.43

. 1

3.

76

. 5

2.

97

. 1

4.

81

. 1

FR 1

6. 17

6.5

3.

79

5.6

FR or VR

5

3.99

23. 6

3.

09

17. 8

2.

10

12. 3

3.

30

18. 5

10

3.27

35. 8

3.

22

35. 8

1.

94

20. 5

2.

81

30.2

20

2. 06

43. 2

1.

95

40.9

•

99

20. 5

2.

48

51. 6

40

1. 37

56. 1

•

61

25.4

•

55

22. 5

1.

05

42.9

80

. 12

10. 0

*

06

4.9

•

17

14. 1

•

43

35.1

160

.02

4.2

•

01

1.4

•

05

7. 7

08

14. 3

100

101

Condition 3: Wheel Available During Every Session
Response Functions

HRl HR2 HR3 HR4

Schedule

value

D

LP

D

LP

D

LP

D

LP

Baseline

6.

64

.8

4.

08

. 3

6.

61

. 7

4. 54

.5

FR 1

5.

66

6.4

4.

06

5. 1

FR or VR 5

3.

96

23. 5

2.

25

14. 0

3.

90

23.1

4.21

23. 2

10

2.

48

27. 3

1.

72

19.4

2.

02

23.4

3.92

44. 1

20

1.

22

25. 7

1.

00

21.4

1.

21

25. 2

2. 57

52.2

40

•

36

14. 8

•

13

5.6

•

48

18. 6

.67

27. 1

80

•

11

9.6

•

05

4.8

•

13

10.4

.25

20. 5

160

«

04

2. 0

•

02

3. 1

•

09

12. 3

. 05

11.9

Wheel Turns

Baseline

10.9

16. 0

12. 3

8.9

FR 1

9.4

14.4

FR or VR 5

9.9

17. 5

15. 6

7.4

10

14.2

19.8

19. 5

7. 1

20

17.1

19.9

23. 2

7. 8

40

22. 5

26. 1

24. 1

14. 8

SO

25.4

26. 0

23. 0

17. 3

160

26. 7

26.9

27. 2

17. 1

Condition 4: 80% of ad lib. Weight, No Wheel

Baseline

7.

59

1.4

6.

52

.6

7.

23

.6

5.

99

. 3

FR 1

7.

40

8. 1

5.

65

7. 3

FR or VR 5

5.

94

34. 6

4.

69

29.4

5.

65

32,4

4.

36

24. 7

10

5.

05

55. 1

4.

85

48.9

5.

42

62.4

4.

65

52. 8

20

3.

58

75.2

4.

89

103. 3

4.

16

86, 5

3.

52

73. 5

40

1.

69

69.4

3.

28

135.9

2.

66

108. 5

1.

92

78. 1

80

58

46. 7

96

78. 0

1.

15

94. 8

•

71

57. 6

160

•

24

38. 8

•

21

49, 8

•

47

69.6

•

27

43.6

102

Condition 5: 98% of ad lib. Weight, No Wheel

HRl HR2 HR3

HR4

Schedule

value

D

D

D

T O

Baseline

5. 13

. 1

4.

00

.2

2.

78

.2

2

88

. 1

FR 1

4. 52

4.9

— •

74

4.6

£ rv. or V xv. D

J. Uft

i O. 1

3.

33

20. 3

2.

56

T A n
irt, U

2.

39

i. ~>, ->

1 n
1 u

■? Q c;

3.

15

35. 2

2.

51

2.

15

7 A 7

on

2.

73

57. 7

1.

67

"XA 7

2.

03

'il a O

A.C\

i .

1.

82

74. 9

•

97

J7. J

1.

05

A7 1

csu

i 7.

•

50

40. 6

35

7 Q 7

43

i. O . 7

•

14

22.9

•

18

74. 7

13

7 1 1

Condition 6 :

oU /o Ox

_ J 141-1

au 11 D.

Weight

:, No Wheel

Baseline

6.94

.1

5.

90

.2

5.

71

.1

5.

22

0

FR 1

6. 15

6. 8

6.

18

7.9

FR or VR 5

5. 53

32. 8

4.

71

28. 5

5.

28

29. 7

4.

56

25.4

10

5. 36

58.8

6.

06

67. 5

4.

77

54. 1

3.

79

42.9

20

3. 32

69. 7

4.

83

102. 8

5.

21

109. 1

3.

93

80. 8

40

2. 08

85. 1

3.

08

126, 5

3.

03

125. 2

2.

43

98.2

80

.49

39.8

1.

56

126. 1

1.

39

113. 0

1.

14

91.2

160

.16

26. 3

•

68

110. 1

•

49

79.4

•

44

74. 7

Group Averages

Condition 1

Schedule
value D

Baseline
FR 1**
FR or

5. 31
4.94

LP

. 1
5.2

Condition 2

Condition 3

no wheel wheel available
D LP D LP

D

LP

6. 05
6. 31

.2

7. 6

4. 52
4.98

.2

6. 1

5.47
4. 86

.6
5. 8

WT

12. 0
11.9

VR 5

4.09

23. 3

4.

71

27. 5

3.

12

18. 0

3.

58

20.9

12.6

10

3. 82

41. 3

4.

71

51. 0

2.

81

30. 6

2.

53

28. 5

15.1

20

3.41

71. 5

3.

69

76. 7

1.

87

39. 1

1.

50

31. -1

17. 1

40

2. 35

95.9

2.

49

101. 5

•

89

36. 7

•

41

16. 5

21.9

80

1.05

85. 7

1.

08

87. 0

•

19

16. 0

•

14

11.3

22.9

160

. 37

58. 0

•

25

40. 7

•

04

6. 8

•

05

7. 3

24. 5

103

Condition 4 Condition 5 Condition 6

Schedule

value

D

LP

D

LP

D

LP

Baseline

6. 87

. 7

3. 73

. 1

6. 09

. 1

FR 1**

6. 53

7.7

4. 13

4.8

6.17

7.4

FR or VR 5

5. 16

30. 3

2. 84

16.4

5. 02

29. 3

10

4.99

54.8

2. 70

31. 1

4.99

55. 8

20

4. 04

84. 6

2. 18

45. 5

4. 32

90. 6

40

2. 39

98, 0

1. 23

49.8

2. 66

108. 7

80

. 85

69. 3

.38

30. 8

1.15

92. 7

160

. 30

50. 5

.13

20. 4

.44

72. 6

=i«*FRl averages are for two animails only, HRl and HR2.

I

APPENDIX F

ESTIMATED PARAMETER VALUES OF MINIMUM- DE VIA TION
MODEL (r, ^ , o{ ) FOR EACH SUBJECT DURING EACH
CONDITION OF EXPERIMENT 3 (Coefficients of
Determination (r^) Measure Relationship Between
Obtained and Parameter-Estimated
Response Functions)

Subject Condition

HRl 1

2 no v/heel

wheel available

3
4
5
6

HR2

HR3

HR4

r

r2

5.26

.0317

0

. 847

7. 26

. 0541

0

. 822

6.76

. 8996

. 0033

. 577

6.42

.1095

. 0267

.731

7. 51

. 0301

. 0003

.907

4.90

.0908

0

. 754

6. 51

. 0110

. 0007

.890

1 5.22

2 no wheel 5. 49
wheel available 3.62

3 4. 19

4 5. 59

5 3. 73

6 5. 84

1 3.76

2 no wheel 5.57
wheel available 2.91

3 6.62

4 6.23

5 2.78

6 5.48

1 4.75

2 no wheel 4. 74
wheel available 4. 59

3 4. 58

4 5. 55

5 2.70

6 4. 84

104

.0037 0 .951

0 .0004 .875

0 .0023 .908

.1426 .0308 .659

0 .0005 .944

.0043 .0003 .910

.0022 .0002 .966

.0027 0 .912

.0067 0 .980

.0403 .0021 .817

.0955 .0351 .906

.0018 0 .845

.0044 .0008 .970

0 .0004 .978

.0051 0 .971

.0068 0 .965

.0401 0 .776

0 .0022 .935

.0117 0 .929

.0070 .0001 .936

.0048 0 .973

I REFERENCES

i

i Adolf, E. F. Urges to eat and drink in rats. American Journal of
! Physiology. 1947, 151. 110-125.

i Allison, J, Microbehavioral features of nutritive and nonnutritive

drinking in rats. Journal of Comparative and Physiological
I Psychology. 1971, 408-417.

Allison, J. Paired baseline performance as a behavioral ideal.

Journal of the Ebcperimental Analysis of Behavior, 1981, 35, 355-
366.

I

I Allison, J. , Miller, M. , & Wozny, M. Conservation in behavior,
j Journal of Experimental Psychology; General, 1979, 108, 4-34.

!

Barofsky, I. , & Hurwitz, D. Within ratio responding during fixed ratio
performance. Psychonomic Science, 1968, 1_1_, 263-264.

i

!

I Battalio, R. C. , Kagel, J. H. , & Green, L. Labor supply behavior of
i cinimal workers: Towards an experimental analysis. Research in

j Experimental Economics, 1979, 1_, 231-253.

j

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

Collier, G. The loci of reinforcement. American Psychologist, 1959,
14. 398. (Abstract)

Collier, G. Body weight loss as a measure of motivation in h\anger and
thirst. Annals of the New York Academy of Sciences. 1969, 157,
594-609.

Collier, G. H. An ecological analysis of motivation. In F. M. Toates
& T. R. Halliday (Eds.), Analysis of motivational processes.
New York: Academic Press, 1980.

105

106

Collier, G. , Hirsch, E, , & Hamlin, P. H. The ecological determinajits
of reinforcement in the rat. Physiology and Behavior, 1972,
705-716.

Collier, G. , & Myers, L. The loci of reinforcement. Journal of
Experimental Psychology, 1961, 61 , 57-66.

Collier, G. , & Siskel, M, , Jr. Performance as a joint function of
amount of reinforcement and inter -reinforcement interval.
Journal of Experimental Psychology, 1959, 57, 115-120.

Collier, G. , & Willis, F. N. Deprivation and reinforcement. Journal
of Experimental Psychology. 1961, 62^ 377-384.

Crespi, L, P. Amount of reinforcement and level of performance.
Psychological Review. 1944, 51_, 341-357.

Ferster, C. B. , Sc Skinner, B. F. Schedules of reinforcement.
New York: Appleton-Century-Crofts, 1957.

Gamzu, E. R. Learned laziness in dead pigeons. The "Worm Rionner's
Digest. 1974, 16_, 86-87.

Gott, C. T. , & Weiss, B. The development of fixed-ratio performance
imder the influence of ribonucleic acid. Journal of the Experimental
Analysis of Behavior. 1972, 1_8^ 481-497.

Graham, D. A. Microeconomics: The analysis of choice. Lexington,
Mass.: D. C. Heath, 1980.

Greenwood, M. R. C. , Quartermain, D. , Johnson, P. R. , Cruce,
J. A. F. , & Hirsch, J. Food-motivated behavior in genetically
obese and hypothalamic -hyp erphagic rats and mice. Physiology
and Behavior, 1974, ly, 687-692.

Hillman, B. , Hunter, W. S. , k Kimble, G. A. The effect of drive
level on the maze performance of the white rat. Journal of
Comparative and Physiological Psychology, 1953, 46_, 87-89.

Hinson, J. M, , & Staddon, J. E. R. Maximizing on interval

schedules. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe (Eds.),
Quantification of steady- state operant behaviour. Amsterdam:
Elsevier /North Holland Biomedical Press, 1981.

107

Hogan, J, A. , & Roper, T. J. A comparison of the properties of
different reinforcers. In J. S. Rosenblatt, R, A. Hinde, C.
Beer, & M. C. Busnel (Eds.), Advances in the study of
behavior (Vol, 8), New York: Academic Press, 1978.

Houston, A. I. , & McFarland, D. J. Behavioural resilience and its
relation to demaind. In J. E, R. Staddon (Ed.), Limits to action:
The allocation of individual behavior. New York: Academic
Press, 1980.

Hursh, S. R. Economic concepts for the analysis of behavior. Journal
of the Experimental Analysis of Behavior, 1980, 34_, 219-238.

Kalat, J. W. Taste-aversion learning in dead rats. The "Worm
Runner's Digest, 1973, 15_, 59-30.

Kanarek, R. B., Sc Collier, G. Patterns of eating as a fimction of the
cost of the meal. Physiology and Behavior, 1979, 23_, 141-145,

Kelsey, J, E. , & Allison, J. Fixed -ratio lever pressing by VMH

rats: Work vs. accessibility of sucrose reward. Physiology and
Behavior. 1976, rT, 749-754.

Lea, S. E, G, The psychology ajid economics of demand.
Psychological Bulletin, 1978, 85_, 441-466.

Lea, S. E, G. Concurrent fixed-ratio schedules for different

reinforcers: A general theory. In C, M. Bradshaw, E. Szabadi,
&t C, F, Lowe (Eds.), Quantification of steady- state operant
behavior. Amsterdam: Elsevier /North Holland Biomedical
Press, 1981.

Levitsky, D. A. Feeding patterns of rats in response to fasts and
changes in environmental conditions. Physiology and Behavior,
1970, i, 291-300.

Levitsky, D, A, , Faust, I. , h Classman, M. The ingestion of food
ajid the recovery of body weight following fasting in the naive rat.
Physiology and Behavior. 1976, 12, 575-580.

McCleery, R. H. On satiation curves. Animal Behavior. 1977, 25.
1005-1015.

Mazur, J. E. The matching law and quantifications related to
Premack's principle. Journal of Experimental Psychology:
Animal Behavior Processes, 1975, 1_, 374-386.

108

Motheral, M. S. , & Staddon, J. E, R. Behavioral competition on

periodic food schedules. Journal of the Experimental Analysis of
Behavior, in press.

Nevin, J. A, Reinforcement schedules and response strength. In
M. D. Zeiler &£ P. Harzem (Eds,), Advances in the analysis of
behavior; Reinforcement and the organization of behavior (Vol. 1).
New York: John Wiley smd Sons, 1979.

Peck, J. W. Rats defend different body weights depending on palatability
and accessibility of their food. Journal of Comparative and
Physiological Psychology. 1978, 2L 555-570.

Powell, R. W. The effect of small sequential changes in fixed-ratio
size upon the post-reinforcement pause. Journal of the
Experimental Analysis of Behavior. 1968, _11_, 589-593,

Premack, D. Reinforcement theory. In D. Levine (Ed. ), Nebraska
Symposium on Motivation (Vol. 13). Lincoln: University of
Nebraska Press, 1965.

Premack, D. Catching up with common sense or two sides of a

generalization: Reinforcement and punishment. In R. Glaser
(Ed,), The nature of reinforcement. New York: Academic Press,
1971,

Premack, D. , Collier, G., & Roberts, C. L. Frequency of light

contingent bar pressing as a function of the amount of deprivation
for light. American Psychologist. 1957, 12^ 411. (Abstract)

Rachlin, H. , 8c Burkhard, B, The temporal triangle: Response

substitution in instrumental conditioning. Psychological Review,
1978, 85^ 22-47.

Reid, A. K. , & Staddon, J. E. R. Schedule induced drinking:

Elicitation, atnticipation or behavioral interaction. Journal of the
Experimental Analysis of Behavior, in press.

Reynolds, R. W. The relationship between stimulation voltage and rate
of hypothalamic stimulation in the rat. Journal of Consulting and
Clinical Psychology. 1958, Sl_, 193-198.

Schrier, A. M. Response rates of monkeys (macaca mTolatta) under
varying conditions of sucrose reinforcement. Journal of
Comparative and Physiological Psychology, 1965, 59, 378-384.

109

Sherman, J. A. , &r Thomas, J. R. Some factors controlling

preference between fixed-ratio and variable-ratio schedules of
reinforcement. Journal of the Experimental Analysis of Behavior,
1968, 11^ 689-702.

Skinner, B. F. Drive and reflex strength. Journal of General
Psychology. 1932, 6_, 22-37. (a)

Skinner, B. F. Drive and reflex strength, II. Journal of General
Psychology. 1932, 6^ 38-48. (b)

Staddon, J. E. R. Schedule -induced behavior. In W. K, Honig &i
J. E, R. Staddon (Eds.), Handbook of operant behavior.
Englewood Cliffs, N. J. : Prentice-Hall, 1977.

Staddon, J. E. R. Operant behavior as adaptation to constraint.

Journal of Experimental Psychology; General, 1979, 108. 48-67.

Staddon, J. E. R, Obesity and the operant regulation of feeding. In

F. M. Toates 8r T. R. Halliday (Eds. ), The analysis of motivational
processes. New York: Academic Press, 1980.

Staddon, J. E, R. , & Ayres, S. L, Sequential and temporal properties
of behavior induced by a schediile of periodic food delivery.
Behaviour. 1975, 54, 26-49.

Stellar, E. , &c Hill, J. H. The rat's rate of drinking as a function of
water deprivation. Journal of Comparative and Physiological
Psychology. 1952, 45, 96-102.

Teitelbaum, P. Random auid food-directed activity in hyperphagic and
normal rats. Journal of Comparative and Physiological Psychology,
1957, 50, 486-490.

Thistle, P. D. Essays in labor supply. Unpublished doctoral disserta-
tion, Texas A & M University, 1981.

Timberlake, W. A molar equilibrium theory of learned performance.
In G. H. Bower (Ed.), The psychology of learning and motivation
(Vol. 14). New York: Academic Press, 1980.

Timberlake, W. , & Allison, J. Response deprivation: An empirical
approach to instrumental performance. Psychological Review,
1974, 81_, 146-164.

110

Timberlake, W. , & Wozny, M. Reversibility of reinforcement

between eating and running by schedule changes: A comparison
of hypotheses and models. Animal Learning and Behavior. 1979,
7, 461-469.

Varian, H, R. Microeconomic analysis. New York: W. W, Norton
&t Co. , Inc. , 1978.

Walsh, V, C. Introduction to contemporary microeconomics.
New York: McGraw-Hill, 1970.

Webbe, F, M, , & Malagodi, E. F. Second-order schedule of token
reinforcement: Comparisons of performance under fixed-ratio
and variable- ratio exchange schedules. Journal of the
Experimental Analysis of Behavior, 1978, 30, 219-224.

Zeaman, D. Response latency as a function of amotmt of reinforce-
ment. Journal of Experimental Psychology, 1949, 39, 466-483.

I

BIOGRAPHY

Mary Susan Motheral

July 1, 1952, in Fort "Worth, Texas

A.B,, Grinnell College, Psychology, 1974
Ph.D., Duke University, Experimental Psychology

National Research Service Award, postdoctoral

fellowship from Public Health Service, 1981
Graduate Research Award, D\ake University, 1977
Graduate Fellowships, Duke University, 1974-1979
Member of scientific honor society, Sigma Xi
Associate to The Behavioral and Brain Sciences

Publications and Papers Presented:

Motheral, M. S. Ideal versus real worlds: Bliss points, time allocation
and curve fitting. The Behavioral and Brain Sciences, 1981, 4, 400.

Motheral, M, S. and Staddon, J. E. R. Behavioral competition on

periodic food schedxiles. Journal of the Experimental Analysis of
Behavior, in press.

Motheral, M. S. and Staddon, J, E. R. Research on the economics of
behavior. Paper presented at the meetings of the Southwestern
Psychological As sociation, Houston, Texas, 1981.

Motheral, M. S. and Staddon, J. E. R. Optimal allocation of behavior:
Ratio and interval sched\iles. Invited address presented at the meet-
ing of the Association for Behavior Analysis, Dearborn, Michigan,
1980.

Staddon, J. E. R. and Motheral, S. Response independence, matching
and maximizing: A reply to Heyman. Psychological Review, 1979,
86, 501-505.

Name:

Born:

Education:

Honors:

111

112

Staddon, J. E. R, and Motheral, S. On matching and nnaximizing in

operant choice experiments. Psychological Review, 1978, 85, 436-
444.