The effect of delay and intervening events on reinforcement value 9781315825502, 1315825503, 0898598001

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Volume V

QUANTITATIVE ANALYSES OF BEHAVIOR The Effect of Delay and of Intervening Events on Reinforcement Value

Edited by MICHAEL L. COMM ONS JAMES E. MAZUR JOHN A. NEVIN HOW ARD RACHLIN

\JD Psychology Press X

Taylor & Francis Croup

Q U A N T IT A T IV E ANALYSES OF BEHAVIOR

1.

M ichael L . C o m m o n s

B aum

5. U n k n o w n

M c C a rth y

2. J o h n A . N evin

6. S eth R o b e rts

9. H o w a r d

R a c h lin

10. A lia n R . W a g n e r

12. E d m u n d J . F a n tin o

13. J o h n G ib b o n

M c D o w e ll

E . P e n a -C o rre a l

16. T e lm o

18. A le x an d ra W . L o g u e E is e n b e r g e r H in elin e

19. J a y M o o re

2 2 . D e b ra J .

Spear

25. M a rk S. S n y d e rm an

28. K en n o n A . L a tta l A la n S tubbs

3. R o b e rt E p stein

7. M ichael C . D av iso n

11. G e o rg e A in slie

14. N u re y a A b a rc a 17. R ic h a rd

J.

20. M o n ica L . R o d rig u ez

23 . M ic h a e l W o o d f o r d 26. R ich a rd L . S hull

29. Ja m es E . M a z u r

4. W illiam

8. D ia n n e C .

24.

15. Ja c k J H e rrn s te in 21. R o b e rt P h ilip N .

27. L eon R. D reyfus

30. J . G re g o r F e tte rm a n

31. D.

QUANTITATIVE ANALYSES OF BEHAVIOR The Effect of Delay and of Intervening Events on Reinforcement Value Volume V Edited by MICHAEL L. C O M M O N S Harvard University JAMES E. M AZU R Harvard University JOHN A. NEVIN University of New Hampshire H O W A R D RACHLIN State University of New York Stony Brook

V p Psychology Press A

Taylor & Francis Group New York London

First Published by Lawrence Erlbaum Associates, Inc., Publishers 365 Broadway Hillsdale. New Jersey 07642 T ransferred to Digital Printing 2009 by Psychology Press 270 M adison Ave, N ew York NY 10016 27 C hurch Road, Hove, E ast Sussex, BN3 2FA Copyright © 1987 by Lawrence Erlbaum A ssociates, Inc. All rights reserved. No part of this book may be reproduced in any form, by photostat, m icroform , retrieval system , or any other m eans, without the prior written permission o f the publisher.

Library o f Congress C ataloging in Publication Data Library o f Congress Catalog Card Number: 81-2654 ISBN 0-89859-800-1 P ublisher’s Note T he publisher has gone to great lengths to ensure the quality o f this reprint but points out that som e im perfections in the original may be apparent.

Volumes in the QUANTITATIVE ANALYSES OF BEHAVIOR series:

• Volume I: DISCRIMINATIVE PROPERTIES OF REINFORCEMENT SCHEDULES. Edited by Michael L. Commons, Harvard University and John A. Nevin, University of New Hampshire • Volume II: MATCHING A N D M AXIM IZING ACCOUNTS. Edited by Michael L. Commons, Harvard University, Richard J. Herrnstein, Harvard University, and Howard Rachlin, State University o f New York, Stony Brook • Volume III: ACQUISITION. Edited by Michael L. Commons, Harvard University, Richard J. Herrnstein, Harvard University, and Allan R. Wagner, Yale University • Volume IV: DISCRIMINATION PROCESSES. Edited by Michael L. Commons, Har­ vard University, Richard J. Herrnstein, Harvard University, and Allan R. Wagner, Yale University • Volume V: THE EFFECT OF DELAY AN D OF INTERVENING EVENTS ON REIN­ FORCEMENT VALUE. Edited by Michael L. Commons, Harvard University, james E. Mazur, Harvard University, John A. Nevin, University of New Hampshire, and FHoward Rachlin, State University of New York, Stony Brook • Volume VI: FORAGING (in press). Edited by Michael L. Commons, Harvard U n i­ versity, Alejandro Kacelnik, Oxford University, and Sara ). Shettleworth, University of Toronto

All volumes available from LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS

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CONTENTS

About the Editors List of Contributors Preface— Michael L. Commons

I

STUDIES OF DELAY A N D CHOICE: MOLAR A N D MOLECULAR CONCEPTIONS OF CHOICE Chapter 1 Duration Comparison and the Perception of Time —J. Gregor Fetterman and Leon R. Dreyfus Chapter 2 Behavioral Models of Delayed Detection and Their Application to the Study of Memory — Dianne McCarthy and K. Geoffrey White Chapter 3 An Adjusting Procedure for Studying Delayed Reinforcement —lames E. Mazur

CONTENTS

II

SINGLE SCHEDULES Chapter 4 A Mathematical Theory of Reinforcer Value and its Application to Reinforcement Delay in Simple Schedules — /. I M cD ow ell Chapter 5 Considerations in the Experimental Analysis of Reinforcement Delay — Kennon A. Lattal

III

CONCURRENT SCHEDULES AND CONCURRENT-CHAIN SCHEDULES Chapter 6 Aversion With Only One Factor — Ceorge Ainslie Chapter 7 Appetitive and Aversive Schedule Preferences: Schedule Transitions as Intervening Events — Philip N. Hineline and Frank /. Sodetz Chapter 8 Choice and Punishment: A Local Analysis — W illiam Vaughan, )r. Chapter 9 Detention Time After Reinforcement: Effects Due to Delay of Reinforcement? — Richard L. Shull and D. /. Spear Chapter 10 Concurrent Reinforcement of Response Sequences — D. Alan Stubbs, ) . Gregor Fetterman, and Leon R. Dreyfus

CONTENTS

Chapter 11 The Analysis of Concurrent-Chain Performance — Michael C. Davison

IV

SELF-CONTROL Chapter 12 Quantification of Individual Differences in SelfControl — A W. Logue, Monica L. Rodriguez, Telmo E. Peha-Correal, and Benjamin C. Mauro Chapter 13 Effects of Prior Learning and Current Motivation on Self-Control — Robert Eisenberger and Fred A. Masterson Chapter 14 Prey Selection and Self-Control — Mark Snyderman Chapter 15 The Delay-Reduction Hypothesis: Extensions to Foraging and Three-Alternative Choice — Edmund Fantino, Nureya Abarca, and Roger Dunn

Author Index Subject Index

ABOUT THE EDITORS

M ic h a e l L a m p o r t C o m m o n s is a research associate in the D epartm ent o f Psychology and Social R elations at H arvard U niversity. He did his und erg rad u ­ ate w ork at the U niversity o f C alifo rn ia at B erkeley, and then at Los A ngeles, w here in 1965 he o btained a B .A . in m athem atics and p sychology. In 1967 he received his M .A . and in 1973 his P h .D . in psychology from C o lum bia U niver­ sity. B efore com ing to H arvard U niversity in 1977, he w as an assistant p rofessor at N orthern M ichigan U niversity. H e has co-edited Q uantitative A n a ly se s o f B ehavior: V olum e I, D iscrim in a tive P ro p erties o f R ein fo rc em e n t S chedules, V o l­ um e 11, M a tch in g a n d M a xim izin g A cco u n ts, V olum e HI, A cquisition, V olum e IV , D iscrim in a tive P ro cesses, and B e y o n d F o rm a l O perations: L ate-A dolescent a n d A d u lt C o g n itive D evelopm ent. His area o f research interest is the quantative analysis o f the c onstruction and the u n derstanding o f reality, especially as they affect decision p rocesses. T his includes the subarea o f utility , along w ith such topics as perception and k now ledge o f causal relations and o f v alue, and how it develops in infrahum ans and hum ans across the lifespan. J a m e s E . M a z u r received his B .A . from D artm outh C ollege in 1973 and his P h .D . from H arvard U niversity in 1977. H e has served on the editorial board o f the Jo u rn a l o f the E xp erim en ta l A n a ly sis o f B ehavior, and is cu rrently a c o n su lt­ ing ed ito r o f the Jo u rn a l o f E xp e rim e n ta l P sych o lo g y: A n im a l B eh a vio r P ro ­ cesses. H e has c o ntributed several articles to these and o th er jo u rn a ls, and is the author o f a recently published tex tb o o k , Learning a n d B ehavior. H e is now an associate p ro fesso r o f psychology at H arvard U niv ersity , w here he has taught since 1980. H is cu rren t research concerns how v ariab les, such as d elay , am ount, and probability o f rein fo rcem en t, influence choice. x

ABOUT THE EDITORS

xi

Joh n A n th on y N evin received his B .E . in m echanical engin eerin g from Yale U niversity in 1954 and his P h .D . in p sychology from C o lum bia U niversity in 1963. He taught at S w arthm ore C ollege from 1963 until 1968, and at C o lum bia U niversity from 1968 until 1972. H e served as an ed ito r o f the J o u rn a l o f the E xperim ental A n a ly sis o f B eh a v io r from 1979 to 1983 and c o -ed ito r o f Q u a n ­ titative A nalyses o f B ehavior: V olum e I, D iscrim inative P ro p erties o f R ein fo rc e ­ m ent Schedules. H is cu rren t research interests include schedules o f rein fo rce­ m ent, stim ulus c o n tro l, conditio n ed rein fo rcem en t, behavioral m om entum , anim al psychophysics, and nuclear d isarm am ent. H ow ard R ach lin received his B .E . in m echanical engineering from C ooper Union in 1956, his M .A . in p sychology from the N ew S chool for Social R e­ search in 1962, and his P h .D . in p sychology from H arvard U niversity in 1965. He taught at H arvard from 1965 until 1969. He is now a p rofessor o f p sychology at the State U niversity o f N ew Y ork at Stony B rook, w here he has been teaching since 1969. H is interests include self-co n tro l, the interaction o f econom ics and psychology, the m atching law , the psychology o f eating and drin k in g , and the philosophy o f p sychology.

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LIST OF CONTRIBUTORS

Nureya Abarca Department o f Psychology University o f California at San Diego Now at: Escuela de Psicologia Pontificia Universidad Catolica de Chile

Roger M. Dunn Department of Psychology University of California at San Diego Now at: Department o f Psychology San Diego State University Imperial Valley Campus

George Ainslie VA Medical Center and Jefferson Medical College

Robert Eisenberger Department of Psychology University o f Delaware

Michael C. Davison Department of Psychology The University of Auckland Leon R. Dreyfus Department o f Psychology University o f Maine Now at: Department of Psychology Loyola University

Edmund J. Fantino Department of Psychology University o f California at San Diego

John Gregor Fetterman Department of Psychology University of Maine Now at: Department of Psychology Norwich University

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LIST OF CONTRIBUTORS

Philip N. Hineline Department of Psychology Temple University Kennon A. Lattal Department of Psychology West Virginia University Alexandra W. Logue Department of Psychology State University o f New York at Stony Brook Fred A. Masterson Department of Psychology University of Delaware Benjamin C. Mauro Department of Psychology State University o f New York at Stony Brook Now at: Department of Psychology Temple University James E. Mazur Department of Psychology and Social Relations Harvard University Dianne C. McCarthy Department of Psychology The University o f Auckland Jack J McDowell Department o f Psychology Emory University Telmo E. Pena-Correal Department of Psychology State University of New York at Stony Brook Now at: Departamiento de Psicologfa Universidad de los Andes

Monica L. Rodriguez Department of Psychology State University of New York at Stony Brook Richard L. Shull Department o f Psychology The University of North Carolina Mark Snyderman Department of Psychology and Social Relations Harvard University Debra J. Spear Department o f Psychology The University of North Carolina Frank J. Sodetz Walter Reed Army Institute of Research Now at: United States Army Medical Component Armed Forces Research Institute of Medical Sciences D. Alan Stubbs Department of Psychology University of Maine William Vaughan, Jr. Department of Psychology and Social Relations Harvard University K. Geoffrey White Department of Psychology Victoria University Now at: Department of Psychology The University of Otago

PREFACE

T he study o f b eh av io r has consisted o f a nu m b er o f som ew hat separate traditions. O ne trad itio n , starting w ith T horndike and then continuing w ith S kinner, has analyzed experim entally the control o f b ehavior by events that o c cu r subsequent to it. A second trad itio n , starting w ith B echterev and Pavlov and c om ing dow n to the present through W atso n , H ull, S pence, and oth ers, has analyzed the control and transfer o f c ontrol by events that precede behavior. A fter the 1920s both approaches becam e m ore quantitative. In the e x p erim e n ­ tal analysis o f beh av io r, q uantifiable variables, such as the rate o f resp o n d in g , w ere used to rep resen t the behavioral outcom es. A t the sam e tim e, m ore e la b o ­ rate quantitative studies w ere carried out in the H ullian approach. Q uantifiable m easures, such as response p robability and latency, w ere introduced. In that period, and extending through the 1950s, m athem atical m odels w ere developed by H ull, S pence, E stes, B ush and M o steller, and L o g an , am ong others. B oth groups carried out som e param etric studies in the tradition o f p sychophysics. By the early 1960s m athem atical psychology had developed to the point w here it could deal w ith problem s from a nu m b er o f dom ains. In each dom ain , e xplicit m athem atical m odels w ere proposed for the processes by w hich perform ances were acquired and m aintained w ithin that dom ain. A lthough the m odels g e n er­ ated a num ber o f ex p erim en ts, they w ere o f lim ited generality. “ Q u antitative a n aly sis” now generally refers to the fact that theoretical issues are represented by quantitative m odels. An analysis is not a m atter o f fitting arbitrary functions to data points. R ath er, each param eter and variable in a set o f equations represents part o f a process that has both a th eoretical and an em pirical interpretation. Q uantitative an aly sis has forced researchers to represent explicitly their notions and to be econom ical in the nu m b er o f p aram eters that m ust be xv

XVI

PREFACE

estim ated. T he m atching law , a m odel o f m aintained perfo rm an ce, is one ex am ­ ple from the a n aly sis-o f-b eh av io r tradition. T he R e sc o rla -W a g n e r m odel o f acquisition processes is a second exam p le. T h ese m odels represent effects o f interactions o f environm ental and b ehavioral events. B ecause neither m odel requires o therw ise, the possibility exists that both the organism and the e n v iro n ­ m ent m odify each other. T he rules o f such interaction m ay be represented by an arithm etic that accounts for the results from a large class o f studies. T he m odels are designed to account for the m axim al am ount o f variance found in a num ber o f e xperim ental situ atio n s to w hich the processes d escribed by a given one o f those m odels apply. Som e p aram eter estim ates should be the sam e regardless o f the situation. T he a dequacy o f a m odel can be tested by exam ining how well that m odel fits the data o r by c o m paring ob tain ed data to the th e ­ oretically sim ulated values. T hese m ethods are to be co n trasted w ith the testing o f relatively sim ple hypotheses. B ecause the m odels can be quite com plex, how ever, only portions o f them are tested by single sets o f studies. A s in other areas o f science, looking for the gen erality o f a form ulation has m ade these m odels m ore testable. Independent routes o f verification are possible because o f the increased scope o f the m odels. T he volum es in the presen t series have been w ritten for behavioral scientists. T hose concerned with issues in the study o f how b e h av io r is a cquired and then allocated in various e n v iro n m en ts— b iologists, psy ch o lo g ists, econom ists, a n ­ thropologists, and o th er research ers, as w ell as g raduate students and advanced undergraduates in those a rea s— should find volum es in this series to be state-ofthe-art readers and reference w orks. T hey are also intended for use in sem inars. Each volum e o f the series exam ines a p articu lar topic that has been d iscussed at the annual S ym posium on Q uantitative A n alyses o f B ehavior held at H arvard U niversity. T he topic o f V olum e I w as the discrim ination o f schedules o f re in ­ forcem ent. It w as chosen because it represents an area that has been highly quantified through the a pplication o f psychophysical m ethods and analyses o f m aintained p erform ances. V olum e II explored m atching and m axim izing accounts o f the allocation o f behavior, an o th er area that has been hig h ly quantified. It explored the generality o f such form ulations and how they apply to anim al b eh av io r in both the field and the laboratory and to hum an b e h av io r in choice situations in econom ics. A cquisition m odels and data w ere considered in V olum e III. T h ese m odels dealt w ith the roles that vario u s events p lay in differen t c onditioning situations and how those events interact to produce c onditioning o r to retard it. A spects o f the conditioning situation w ere considered that g o beyond the sim ple notions o f tem poral c o ntiguity betw een the stim ulus to be c o nditioned and the u n c o n d i­ tioned stim ulus. V olum e IV presen ted studies o f discrim ination processes. H ow d isc rim in a ­ tions are acquired and the role o f various ev en ts w ithin the d iscrim ination situ a­ tion w ere considered.

PREFACE

X v ii

T his v o lu m e, V , ad dresses the topic o f how reinforcem ent value is affected by delay and intervening events. Self-control studies are also presented and discussed. V olum e VI w ill address issues in foraging. Included w ill be an ex am ination o f optim al-foraging theory and its a lte rn a tiv e s, as w ell as an exam ination o f how the detectibility o f prey controls the choice to pursue those prey. V olum e VII w ill address the biological determ in an ts o f rein fo rcem en t and m em ory. T entative future volum es will include V olum e V III, the topics o f w hich are pattern recognition and con cep ts in an im als, p eople, and m ach in es, V olum e IX, w hose topic will be econom ic approaches to hum an and anim al c h o ic e, and V olum e X , w hich will deal w ith stim ulus control. T he contents o f the presen t volum e w ere first p repared for and presented at the Fifth S ym posium on Q uantitative A n alyses o f B ehavior, held at H arvard U niver­ sity on June 6 and 7, 1982. S ubseq u en tly , a portion o f the ch ap ters has been revised, updated, and rearranged into the four topical parts found herein. T he sym posium ou t o f w hich th is fifth v olum e has arisen w as o rganized by M ichael L. C om m ons, R ichard J. H errn stein , Jam es E. M azur, John A. N evin, and H ow ard R achlin. T he sym posium w as supported in part by the S ociety for the Q uantitative A nalyses o f B ehavior, T h e D epartm ent o f P sychology and S o ­ cial R elations at H arvard U niversity, and by the D are A sso ciatio n , Inc. In 1982 local arran g em en ts w ere m ade by Patrice M . M iller and D ean G al­ lant, w ith assistance from T heodore L. A llen, M ichael A rm strong-R oche, B rian D. C abral, M ark C onstas, M artin N. D avidson, Patricia S. F rench, W ilson Fong, Jose G a b ilo n d o , and B enjam in Singer. For help in editing the chapters w e thank C harlotte M andell and W illiam V aughan, Jr. F o r help in review ing the chapters for stylistic and organizational im provem ents w e thank the sta ff o f the D are Institute. M ich a el L . C om m ons H a rva rd U niversity

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STUDIES OF DELAY A N D C H O IC E: M O LA R A N D M O LEC U LAR C O NC EPTIO NS OF CH O ICE

I

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Duration Comparison and the Perception of Time

J. G regor Fetterm an Leon R. D reyfus University of Maine at Orono

T he study o f tim e p erception has a long and varied history in psychology. R esearch on hum an tim e p erception has used a diverse group o f p rocedures and independent variables including the effects o f different stim uli on tim e ju d g ­ m ents, the psychophysics o f tim e, the d evelopm ent o f tim e percep tio n , the role o f cognitive and em otional factors on the experience o f tim e, ju d g m e n ts o f “ n orm al” and “ a b n o rm a l” subjects, the effects o f d ru g s, ju d g m e n ts o f sim ultaniety and su ccessio n , and the p erception o f rhythm (see for exam ple review s by B oring, 1942; D oob, 1971; F raisse, 1963, 1978, 1984; F ran k en h au ser, 1959; O m stein , 1969; W oodrow , 1951; and the b ibliography by E isler, L inde, T hroeng, L azar, E isler, & H ellstrom , 1980). A lthough less w ell studied, re ­ search on a n im a ls’ tim e percep tio n has alm ost as long a history as the hum an tim e p erception w ork. D iscussions o f the role o f tem poral variables in learning go back at least to Pavlov (1927), w ith references to the role o f tem poral factors appearing p eriodically in som e o f the o ld er anim al learning literature (e .g ., A nderson, 1932; C ow les & F inan, 1941; Sam s & T o lm an , 1935; S kinner, 1938). Interest in tim e perception in anim als stem s in part from the role that tem poral discrim inations are p resum ed to p lay in learning situ atio n s, w here tem poral regularities betw een b eh av io r and environm ental events m ay occur. F or ex am ­ ple, behavior un d er tem porally defined reinforcem ent schedules (e .g ., fixedinterval sch ed u les, free-operant avoidance sch ed u les, and d ifferential-reinforcem ent-of-low -rate (D R L ) schedules) suggests the p o ssibility that tem poral dis­ crim inations m ay be form ed and m ay contribute to p erfo rm an ce (see for e x am ple C hurch, 1978; G ib b o n , 1977; R ic h e lle & L ejune, 1980; S tad d o n , 1974). E xperi­ m ents on tim e percep tio n w ith anim als also perm it com parisons o f different species w ith differen t e volutionary and experiential histories. T he anim al studies c om plem ent research on hu m an s, a species w ith a history o f c ounting and using tim e pieces. 3

4

FETTERMAN AND DREYFUS

R esearch on a n im a ls’ tim e p erception falls un d er tw o general categories (S tubbs, 1979): pro ced u res related to the tim e-based schedules o f reinforcem ent such as D R L sch ed u les, fixed-interval sch ed u les, and the like ( e .g ., C atania, 1970; P latt, 1979), and psychophysical trials procedures like those used with hum ans (e .g ., C hurch & D eluty, 1977; S tubbs, 1968, 1979). W ith the D R L schedule, for exam p le, a response is reinforced only if it is delay ed from the previous response by a m inim um tim e; the b ehavior that resu lts from this tem ­ poral restriction on resp o n d in g suggests a tem poral d iscrim ination. W ith the psychophysical trials p ro c ed u re s, anim als m ay be train ed to m ake one response if the duration o f a stim ulus is short (2 sec for e x am p le), but to m ake a second response if the duration is long (for exam p le, 6 sec). A ccuracy is gen erally a function o f the relative d ifference betw een the tw o stim ulus durations ( e .g ., S tub bs, 1968). A lthough a diverse gro u p o f p rocedures have been used, all the m ethods used to study tim e p erception in anim als share a com m on feature. T his feature d is­ tinguishes the anim al m ethodology from the m ore com plex pro ced u res used to study hum an tim e perception. In all these procedures in the anim al tim ing liter­ ature, the c onsequences fo r resp o n d in g depend on a fixed tem poral criterion or cu to ff point. T he onset o f the interval is m arked by a specific ev en t, w hich m ight be the onset o f a stim u lu s, o r som e asp ect o f the a n im a l’s b ehavior. W ith fixedinterval schedules the interval typically begins w ith the end o f the prior re in ­ forcer; w ith D R L sch ed u les, the interval is begun w ith each response. In both cases, h ow ever, a response is reinforced only w hen a specific interval o f tim e has elapsed. C hoice pro ced u res often involve different d urations to be ju d g e d , but in these situations there is one c u to ff o r criterion interval such that shorter durations occasion one set o f conseq u en ces and longer d urations another. In contrast to the previous e x p erim e n ts, the present e xperim ents used a d is­ crim ination task that differed from the e arlie r w ork in tw o basic w ays: (a) T he task involved the presentation o f tw o stim ulus durations rath er than o n e , and (b) the consequences for responding depended on the d ifference betw een the tw o durations rather than on the difference betw een a duration and a single fixedcriterion interval. S p ecifically , pig eo n s w ere p resented w ith tw o k ey-light d u ra ­ tions in succession, and then tw o choice keys w ere lit. O ne response w as re in ­ forced if the first duration w as sh o rter than the seco n d , and the alternate response w as reinforced if the first d u ration w as lo n g er than the second. T he experim ents b e ar on issues related to tim e p erception. T he paired-com parison task parallels one that is com m only used to study tim e perception w ith hum ans (e .g ., D o o b , 1971), and thus it p erm its com parisons betw een hum an and anim al data. In a ddition, the ex p erim en ts have im plications for theories o f a n i­ mal tim e percep tio n , such as the internal clock m odel o f C hurch and his a sso ci­ ates (e .g ., C h u rch , 1978; M eek & C h u rch , 1983; R oberts & H older, 1982). T he experim ents w ere not designed as a test o f any m odel, but they do bear on m odels o f tim ing.

1.

PERCEPTION OF TIME

5

The experim ents also have im plications for m em ory and d iscrim ination learn­ ing in anim als. M em ory co u ld be a factor because the stim ulus in any duration task lasts o v er tim e. T he p aired-com parison task is o f p articu lar interest in this regard because choice depends on tw o successively p resented duratio n s, w ith the first alw ays delay ed from choice. F inally, the e xperim ents have im plications for d iscrim ination learning because the paired-com parison task requires a relational judgm ent. W e return to these issues a fte r the data have been presented.

GENERAL METHOD Figure 1.1 d iagram s the general p rocedure used in both experim ents. A trials procedure w as used. At the b eginning o f each trial the c en ter key o f a three-key

DURATION 1 > DURATION 2

DURATION 1 < DURATION 2

FIG. 1.1. A schematic of the procedure. Each circle represents a response key. The labels W , R, G , and Y stand for key colors white, red, green, and yellow. (From Fetterman & Dreyfus, 1986 by permission o f Elsevier Biomedical Press B .V .)

6

FETTERMAN AND DREYFUS

pigeon ch am b er w as lit by w hite light. A peck to this key c hanged the color to red and initiated the first duratio n . T he light rem ained on for a given duratio n , w hich changed from trial to trial, and then w ent o ff independently o f behavior. U nder m ost conditions the offset o f red w as follow ed im m ediately by the onset o f green, w hich d em arcated the second duration. U nder som e co n d itio n s, an in­ terstim ulus interval, d u rin g w hich the key lights w ere o ff, separated the tw o durations. In eith er case the green stim ulus rem ained on for a sp ecified duration, changing from trial to trial, and then w ent o f f independently o f behavior. O ffset o f green w as follow ed by the onset o f tw o side key lights. A response to one side key w as reinforced if the first duration w as shorter than the seco n d , w hereas the alternate response w as reinforced if the first duration w as longer than the second. C orrect choices w ere reinforced a ccording to a random -ratio tw o schedule. Every other response, on the av erag e, p roduced 3-seconds access to food, follow ed by a 12-second intertrial interval. C orrect responses that did not result in access to food sim ply p roduced a 15-second intertrial interval, as did all incorrect choices. T he key lights and a h ouselight that w as norm ally on d uring trials w ere all o ff during food delivery and intertrial intervals. S essio n s w ere conducted 6 days a w eek w ith each session lasting until 80 reinforcers had been delivered.

EXPERIMENT 1 For the first e x p e rim e n t,1 tw o groups o f four durations w ere used to construct the duration pairs. T h e first group o f d urations included d urations o f 0 .5 , 1, 2, and 4 seconds. E ach o f these tim es served as the first (red) and second (green) duration o f a pair in such a w ay that each duration w as com bined w ith the other three in all possible w ays: 0 .5 sec o f red w as follow ed by 1, 2 , or 4 seconds o f green; 1 second w as follow ed by 0 .5 , 2, o r 4 seconds, etc. T he different pairs w ere arranged in an irregular o rd e r, w ith each pair o ccurring equally often. O nce perform ance becam e stable under these conditions (approxim ately 50 sessions exposure), a new gro u p o f d urations w as used for the duration pairs: 2, 4 , 8, and 16 seconds. T hese d urations w ere p resented in the 12 d ifferent com binations o f each duration fo llow ed by the o th er 3, as w as the case under the first condition. G en eralization tests w ere given at the end o f training under each range o f durations. N ove! d uration pairs w ere introduced as probes that w ere interm ixed with the standard training d urations. R esponses to these novel pairs w ere never reinforced with food. Instead choices sim ply initiated the intertrial interval. T he novel pairs consisted o f cases w here the tw o durations w ere the sam e ( e .g ., 2 seconds follow ed by 2 seco n d s), consisted o f d urations that lay w ithin the range o f training d urations ( e .g ., 3 seconds follow ed by 2 seco n d s), and consisted o f d urations that lay outside the range ( e .g ., 20 seconds follow ed by 16 seconds). 'Portions of Experiment 1 were reported at the Eastern Psychological Association, Baltimore, 1982.

1.

PERCEPTION OF TIME

7

N o rm a lly the red stim u lu s w a s fo llo w ed im m e d ia tely by g re e n , so a final set o f c o n d itio n s im p o sed an in te rstim u lu s in te rv al b e tw ee n red and g reen in o rd e r to separate the first d u ra tio n from the se c o n d . T h e in te rstim u lu s in te rv als w ere 0 , 2, and 5 se c o n d s u n d e r o n e c o n d itio n and 0 , 10, and 30 se c o n d s u n d e r a se c o n d co n d itio n . In terstim u lu s in te rv als w ere im p o sed o n ly u n d e r the se c o n d ran g e o f duratio n s. F igure 1.2 p ro v id e s the basic in fo rm a tio n on d isc rim in a tio n p e rfo rm a n c e w ith both sets o f d u ra tio n pairs. T h e left side sh o w s p e rfo rm a n c e w hen the d u ra tio n s w ere 0 .5 , 1 , 2 , and 4 se c o n d s. T h e rig h t sid e sh o w s p e rfo rm a n ce for d u ra tio n s o f

SECOND • 0 .5 o j

L±J CO 2 O Q_ CO L±J cn

a 2 * 4

DURATION

5 EQUAL PROBES

(sec) 0• 42

55

I— u_ Ll ) _J

91

>_J CO < CD

85

o

cr IN­

FIRST

DURATION

(sec)

FIG. 1 .2 . Probability o f a left-key response (reporting the first duration to be longer than the second) as a function o f the first duration o f a pair. Data are presented when two different ranges o f durations were used. Data for unequal pairs were com puted from totals o f the last three sessions of training. Data for equal probe pairs w ere taken from the first day on which these test pairs were introduced. (From Feiterm an & Dreyfus, 1986 by perm ission o f Elsevier B io­ medical Press B .V .)

8

FETTERMAN AND DREYFUS

2 , 4 , 8, and !6 seconds. D ata are included for the probe trials in w hich the first and second d urations w ere equal. F igure 1.2 gives the p robability o f a left response (duration 1 longer than duration 2) as a function o f the value o f the first duration o f a pair at each second duration. D ifferent values o f first durations are ordered along the horizontal axis w hereas different values o f second duration are represented by differen t sym bols. T he filled circ le s, for e x am p le, show p erfo r­ m ance w hen 0 .5 , 1, 2, and 4 second durations w ere follow ed by 0 .5 seconds. T h e figure show s that the anim als g enerally w ere correct in reporting that the first duration w as longer. T he data in this figure indicate that perform ance w as g e n er­ ally accurate, w ith the functions show ing an abrupt transition from a low to high probability as the first d u ration c hanged from shorter to longer than the second. A ccuracy increased as the difference betw een the tw o durations increased; as the duration difference increased the p robabilities approached 0, w hen the first d u ra ­ tion w as shorter than the seco n d , or 1.0 w hen the first w as longer. Perform ance w as sim ilar across both ranges o f durations and accuracy w as high under both conditions (ap p ro x im ately 85% for all pairs o f durations). W hen equal d urations w ere arranged on probe trials (sym bols surrounded by squares), probability m easures w ere v ariab le, ranging around 0 .5 0 . T his result is not unexpected because neither duration w as longer. A lthough perform ance w as variable, roughly tw o thirds o f the points (21 o f 32 cases) fall below 0 .5 0 , m eaning that the pig eo n s m ore often than not reported the first o f tw o equal durations as being shorter. T he finding, w hich could be view ed as a negative tim e-order e rro r, is so m etim es obtain ed w ith hum an tim e ju d g m e n ts (e .g ., A llan, 1977). N ovel duration pairs w ere introduced under both duration ranges. Figure 1.3 show s accuracy m easures for these transfer tests follow ing training on the first grou p o f d urations (top) and on the second group (bottom ). T he figure show s perform ance averaged for the four pigeons; the vertical bars indicate plus and m inus one standard erro r o f the m ean. F igure 1.3 show s that transfer to novel duration pairs w as g enerally quite good; accuracy m easures above 70% were obtained for individual pigeons in nearly three-quarters o f the cases. In som e instances, accuracy w as related to the relative difference betw een p air m em bers. A ccuracy w as high w ith relatively large differences (for instance, 6 vs. 2 seconds and 12 vs. 6 seconds) but w as g enerally low er w hen the d ifference w as sm all (for exam ple, 4 vs. 3 seconds and 8 vs. 6 seconds). A ccuracy w as at o r below chance level on som e probe pairs ( e .g ., 4 vs. 3 seconds and 20 vs. 16 seco n d s), and these results im plicate factors apart from the relative tem poral difference o f the tw o d urations. T w o factors m ay account for the relatively p o o r tran sfer to som e o f the novel duration pairs. First, accuracy was low only on problem s w here the first duration w as longer than the seco n d , an outcom e consistent w'ith the negative tim e-order errors observed w ith equal duration pairs. T he po o r perform ances m ay have resulted from a differential w eighting o f the values o f the tw o duratio n s, with the nom inal value o f the first

1. FIRST

O

o O'

9

RANGE

3 6 2 4 3 6 2 4

SECOND Ll I

PERCEPTION OF TIME

2nd

RANGE

I00

LU

a 50

2 2 3 4 6 6 6 8 8 12 12 12 16 16 2 0 1st I 3 2 6 4 12 8 12 6 6 8 16 12 2 0 16 2nd

DURATION

PAIR (sec)

FIG. 1.3. A ccuracy on novel duration pairs in the generalization tests that fol­ lowed training. The top panel shows perform ance on tests that followed training with durations 0 .5 , 1, 2, and 4 seconds; the bottom panel show s perform ance following training with durations o f 2, 4 . 8 . and 16 seconds. Data were pooled over three sessions for each pigeon. The histogram s show average perform ance for the four birds and the lines represent standard errors o f the mean. (From Fetterman & D reyfus, 1986 by perm ission o f Elsevier Biomedical Press B .V .)

du ratio n red u ced by som e a m o u n t (a n e g ativ e tim e -o rd e r e rro r). T h is in te rp re ta ­ tion w ould e x p la in th e re d u ctio n s in a cc u rac y fo r so m e p ro b lem s ( e .g ., 3 vs. 2 se c o n d s), and th e re v ersa ls (c ase s w here a cc u rac y w as su b sta n tia lly b elow chance) in o th e r in stan c es ( e .g ., 6 vs. 4 se c o n d s a n d 12 vs. 8 se c o n d s). S e c o n d , in so m e in sta n c e s, it a p p e a rs th at re sp o n d in g w as c o n tro lle d e x c lu siv e ly by the value o f the se c o n d d u ra tio n . A c cu ra c y w as c o n siste n tly low on probe tria ls in w hich the lo n g est train in g v a lu e w as p re sen te d last, fo llo w in g a novel d u ra tio n that w as e v e n lo n g e r ( e .g ., 6 v s. 4 se c o n d s a n d 20 v s. 16 se c o n d s). T h ese resu lts suggest that p e rfo rm a n ce m ay have b e en c o n tro lle d sim p ly by the v alue o f the second d u ra tio n . D u rin g tra in in g , th ese v a lu e s w ere lo n g e r th an any o f the o th e r d u ra tio n s. T h u s, the a n im a ls m ig h t have lea rn ed to resp o n d on the b a sis o f the single d u ra tio n o n ly . U n d e r train in g c o n d itio n s th is stra te g y p ro d u c ed n early p erfect d isc rim in a tio n but led to a b y sm al p e rfo rm a n c e on c ertain p ro b e trials.

10

FETTERMAN AND DREYFUS

T h e p attern o f re su lts th u s in d ic a te s that th ere w as a tem p o ral tra n s p o sitio n , but that the tran sp o sitio n w as lim ite d by tim e -o rd e r e rro rs and end e ffe c ts from the longest d u ra tio n s. In the final set o f c o n d itio n s, in te rstim u lu s in terv als w e re in serted b etw een the m em bers o f a d u ra tio n p a ir. A c cu ra c y d e clin ed as the in te rstim u lu s in terv al w as in creased from 0 to 30 se c o n d s, but acc u rac y levels re m a in e d a b o v e ch an c e ev en w ith the 3 0 -se co n d in te rstim u lu s interv al. A c cu ra c y m ea su re s, a v era g ed o v e r the fo u r p ig eo n s w ere 9 1 , 8 8 , 8 3 , 7 2 , and 12% w hen the in te rstim u lu s interv al w as 0 , 2 , 5, 10, and 30 se c o n d s, re sp ec tiv e ly . F igure 1.4 sh o w s the e ffe c ts o f the in te rstim u lu s in terv al fo r the v ario u s d u ration p a irs, and it sh o w s a cc u rac y at e ac h v alue o f the first d u ra tio n (left c o lu m n ) o r sec o n d d u ra tio n (rig h t c o lu m n ) c o lla p sed a cro ss all v alu es o f the o p p o sin g p a ir m em b e r. F o r e x a m p le , the filled circ le s o n th e left are a ccu racy scores w'hen th e 2 -se co n d first d u ra tio n w as p a ire d w ith th e 4 -, 8 -, o r 16-second • 2 sec FIRST

o 4 sec

* 8 sec

DURATION

» 16 sec

SECOND DURATION

LYA0

2

5

10

30

0

2

5

10

30

INTERSTiMULUS INTERVAL (sec) FIG. 1.4. A ccuracy as a function o f (he interstimulus interval betw een the first and second durations. A ccuracy is presented for each value o f the first and second duration (e .g ., 2 vs. 4 , 8 , and 16 seconds). Each point, except those for the 0second interstim ulus interval, represents perform ance over the final three sessions o f a condition. Data for 0-second intervals are averages of tw o 3-day exposures. (From Fetterm an & D reyfus, 1986 by perm ission o f Elsevier Biomedical Press B. V.)

1.

PERCEPTION OF TIME

11

duration. N ote that the filled sym bols represent extrem e values (2 and 16 se c ­ onds), w hereas the unfilled sym bols represent interm ediate values (4 and 8 seconds). T he left colum n show s that the in terstim ulus interval affected p erfo r­ m ance for the various duration pairs. T here w as a tendency for accuracy to decline m ore w hen the first d uration w as extrem e ( i.e ., 2 o r 16 seconds) than when it w as interm ediate ( i.e ., 4 o r 8 seconds). T he m ore striking and infor­ m ative results are found in the right colum n. A ccuracy declined for problem s in which the second m em ber o f a p a ir w as one o f the interm ediate duratio n s, a pproaching the chance level w hen the 30-second interstim ulus interval w as used. In c o n trast, the changes in accuracy w ere less system atic and w ere m uch less pronounced w hen the second duration w as either 2 o r 16 seconds. In fact, w ith a second duration o f 2 o r 16 seco n d s, there w as very little change in accuracy for Pigeons 63 and 85 across the entire range o f delays. T he pattern o f results is not surprising but is instructive. C onsider first the findings that accuracy w as largely u naffected w hen the second duration w as 2 seconds o r 16 seconds. B ecause these w ere ex trem e values th eir occurrence alone w ould provide sufficient inform ation for the co rrect resp o n se, regardless o f the first d uration. T hese values rem ained p redictive even w hen the first duration was no longer rem em bered because o f a long delay. W hen, h o w ev er, the second duration w as one o f the in term ediate values, eith er 4 o r 8 seconds, the inform a­ tion provided by eith er o f these tw o d urations w as not su fficient by itself; these durations w ere p receded som etim es by shorter and so m etim es by longer d u ra­ tions. T he findings are consistent w ith the transfer data in suggesting that the pigeons responded on the basis o f the second duration alone w henever an e x ­ trem e value w as p resented last. T he results from the right colum n bear on those in the left colum n w here accuracy tended to decrease m ore w hen the first d u ra­ tion w as 2 o r 16 seconds as opposed to 4 or 8 seconds. T he extrem e values o f the first d uration, 2 and 16 seco n d s, w ere paired m ore often w ith 4- and 8-second durations as the seco n d -p air m em ber. T his m ore frequent pairing o f first d u ra ­ tions w ith the “ c o n fu sin g ” second durations u n doubtedly resulted in low er accuracy. T h u s, changes for the first- and seco n d -p air m em bers appear to result from the d ependencies betw een the values o f the pair m em bers.

Summary E xperim ent 1 show ed that pigeons w ere capable o f p erform ing a p aired -co m ­ parison task involving d urations. A ccuracy w as sim ilar across tw o ranges o f durations. T here w as som e tran sfer to novel duration pairs on generalization tests, but tran sfer w as lim ited to a certain degree by tim e-o rd er errors, and by end effects that are probably inevitable w hen a lim ited num ber o f values are used to construct stim ulus pairs. A ccuracy w as also affected w hen delays w ere placed betw een the tw o duratio n s, but the results show ed that the pigeons could still respond appropriately even w hen the tw o durations w ere separated in tim e. The

12

FETTERMAN AND DREYFUS

pattern o f results suggests that the task w as relational only insofar as the anim als w ere forced to m ake relational ju d g m e n ts ( i.e ., w ith the interm ediate durations). W hen, h ow ever, the anim als could use the inform ation provided by one duration only, they appeared to d o so.

EXPERIMENT 2 A lthough the results o f E xperim ent 1 c ould be interpreted as p ro viding evidence for relational ju d g m e n ts in a duration com parison task, the inherent lim itations that com e from using few d urations suggested a better procedure. A cco rd in g ly , a second ex p erim ent w as designed that w as identical to the first except that m any duration pairs w ere used. F or the experim ent, durations w ere determ ined ran­ dom ly as o pposed to the fixed p airs o f E xperim ent 1. W hen the first (red) duration began, a 1-second tim e r p u lsed a pro b ab ility gate set at a probability o f 0 .1 0 , w ith the output o f the p robability gate ending the first d uration. T he sam e conditions held for the second (green) d uration. In effect, the o peration o f this circuit produced d urations that averaged 10 seconds, but w ith an actual range from 1 to 6 0 - 7 0 seconds. T his random way o f p roducing d urations resulted in a very large num ber o f d uration pairs th at, in p ractice, turned out to be betw een 600 and 7 00 pairs. T he p u rp o se o f the experim ent w as to assess perform ance u nder this com plex task w here the o p portunity to respond on the basis o f a singlep a ir m em b er w as g reatly reduced. O th er than the change in the w ay the durations w ere arranged, the pro ced u re w as like that show n in F ig. 1.1 and d escribed in the general m ethod. T he sam e four pigeons w ere the subjects. Figure 1.5, 1.6, 1.7, and 1.8 show p erfo rm an ce for the individual pigeons. T hese are m atrix-type figures show ing correct and incorrect responses for the different pairs o f durations. B ecause there w ere so m any com binations o f p airs, data w ere pooled across fo u r sessions for each figure. T he figures only include data from durations o f 20 seconds o r less. L o n g er durations did o c cu r, but only relatively infrequently. B ecause there w ould be few instances o f these longer d uratio n s, the data w ere not included. E ach sym bol represents the outcom e on an individual trial. F illed circles represent a co rrect response and X s represent an incorrect response. T he sym bols are placed in im aginary squares that correspond to each duration pair. In Fig. 1.5, for e x am p le, there are three circles in the u p p er left w hen the first duration o f 19 seconds w as follow ed by a second duration o f 1 second. T he figure show s that this p a ir occurred three tim es and the anim al responded correctly all three tim es. Sim ilarly there w as one instance o f 18 seconds follow ed by 1 second (co rrect), three instances o f 17 seconds follow ed by 1 second (all co rre c t), and so on. T he lines draw n through the m atrices represent the relative differences betw een the d urations. T he 4:1 line is draw n through pairs in w hich the first duration w as four tim es g reater than the second

1.

41

2 1

PERCEPTION OF TIME

i.5'l

13

II C o rre ct

•

In c o rre c t *

L e ft o I Equal Right &\ FVobes

II.5

12

|:4

I

2

3

4

5

6

7

8

9

SECOND

IO

II 12

13 14

15

’6

17

18

19 2 0

DURATION

FIG. 1.5. Performance on different duration pairs for Pigeon 63. A ccuracy on a particular problem is indicated by the sym bols plotted at the intersection of the first and second duration. Each filled circle represents a correct choice, w hereas each X represents an incorrect choice. On problem s with equal first and second durations, unfilled circles and triangles represent left and right responses, respectively. Data were pooled across four sessions. Data are not included when the durations were longer than 20 seconds.

( e .g ., 20 vs. 5 se c o n d s, 16 vs. 4 se c o n d s, 4 vs. 1 se c o n d ). T h e 1:1 line in d ic a te s cases in w hich the tw o d u ra tio n s w ere e q u a l. In th ese c ases th ere w as no c o rre c t resp onse (and no fo o d , o n ly the in te rtria l in terv al). U n filled circ le s in d ic a te a left-key re sp o n se , w h ereas u n fille d tria n g les in d icate a rig h t-k e y re sp o n se. P erfo rm an c e w as sim ila r fo r the fo u r p ig eo n s. In all c ases a ccu racy w as h ig h , w hich is in d ic a te d by the large n u m b ers o f fille d c irc le s (c o rre c ts) in each fig u re. Incorrect re sp o n se s o c cu rre d m u ch less o ften . P e rfo rm an c e g e n era lly w as sim ila r fo r re la tiv e ly sh o rt and re la tiv e ly long d u ra tio n s. T h e m a jo r d e te rm in a n t o f accu racy w as the re la tiv e d iffere n ce b e tw ee n the tw o d u ra tio n s. M o st in co rrect responses o c cu rre d w hen the ra tio s o f the tw o d u ra tio n s fell b e tw ee n 1.5:1 and

14

FETTERMAN AND DREYFUS

4:1

2\

I.5I

SECOND DURATION FIG. 1.6. Performance on different duration pairs for Pigeon 55. See Fig. 1.5 for description o f the figure and symbols.

1:1.5. Incorrect resp o n ses o ccurred only rarely (and for Pigeon 55 never) w hen the ratios o f the tw o durations w ere greater than 4:1 and 1:4. E rrors becam e m ore frequent as the ratio o f the tw o du ratio n s approached 1:1. Figure 1.9 sum m arizes the individual p oints in Fig. 1 .5 -1 .8 . Figure 1.9 show s the p robability o f a right-key response (duration 1 less than duration 2) as a function o f the ratio o f the d u ratio n pair. T he points are plotted at the m idpoint o f the categories o f stim uli and represent the average duration p a ir ratio. T he left colum n provides data for all problem s. T he d a ta are characterized by ogival functions relating choice p robability to duration p air ratio. T he probability o f a right-key response w as ap propriately n e ar 0 w hen the first d uration w as relatively longer than the second (4:1 ratio). T he p robability increased as the durations becam e relatively m ore sim ilar and it approached 1.0 as the second duration becam e progressively lo n g er than the first (1:4 ratio). T he point o f subjective equality (P S E ) w as calculated from the data in the left colum n o f Fig. 1.9. T he PS E represents the value o f the du ratio n -p air ratio at

1.

PERCEPTION OF TIME

C o rre ct • In c o r re c t x

18 17

Lef t o Right *

16

O

15

Equol P ro b e s

15

M < 13 c r 12 ID O ii

I— 10 CO

9

£

8

^

7 6 5 4 3 2

I

2

3

4

5

6

7

8

9

10 II

12 13 14 15 16 17 8

19 20

SECOND DURATION FIG. 1.7. Performance on different duration pairs for Pigeon 91. See Fig. 1.5 for description o f the figure and symbols.

w hich the probability o f a right-key response w as equal to 0 .5 0 . T he m easure indicates w hether the pig eo n s w eighted equally the values o f the first and second durations. T he PS E s for the four birds averaged 1.2:1 (range 1.1:1 to 1.3:1), indicating that the tw o durations w ere ju d g ed as equal w hen the first duration w as approxim ately 20% longer than the second. T his finding is consistent w ith the negative tim e-o rd er errors o bserved in E xperim ent 1. T he right colum n provides separate functions for c ases w here both durations w ere less than o r equal to 10 seconds (filled triangles) and w hen one o r both durations w as longer than 10 seconds (unfilled circles). T h e purpose is to provide a com parison o f p erform ance w hen durations w ere relativ ely short and relatively long. T he com parison is sim ilar to that o f E xperim ent 1 w hen tw o duration ranges w here used. H ere the w ider range o f durations allow ed for a com parison w ithin the sam e situation. T he tw o sets o f data for each bird w ere generally sim ilar in appearance, w ith ap proxim ately equal slopes. T he slope o f an ogive gives an index o f discrim ination sensitivity. Steeper slopes reflect greater sen-

16

FETTERMAN AND DREYFUS

19

Correct • In c o r re c t x

18 17

L e ft © Right a

Equol Prob es

SECOND DURATION FIG. 1.8. Performance on different duration pairs for Pigeon 85. See Fig. 1.5 for description of the figure and symbols.

sitivity by show ing a g re ater change in perform ance as a function o f changes in the stim ulus dim en sio n . C om p arab le slopes indicate sim ilar sensitivity. In the present case the finding m eans that discrim in atio n perform ance w as sim ilar in term s o f sensitivity regardless o f the length o f the d urations. T here w as one differen ce betw een the functions for three o f the four pigeons. T he functions for long-duration pairs w ere displaced to the left o f the functions for sh ort-duration pairs. C hanges in the entire ogive to the left o r right serve as an index o f response bias ( e .g ., S tubbs, 1976). T he bias w as an increased tendency to em it a right-key response and m eans that there w as an increased tendency to respond that the first duration w as shorter than the second (or that the second w as longer than the first) w hen one o r both d urations becam e long. T here are tw o possible reasons for this bias. F irst, w hen the second duration w as long, the first d uration w as n ecessarily separated from a choice by a longer tim e than w ould be the case w hen the d urations w ere short. T h is longer delay could contribute to reduced m em ory o f the first duratio n . T his reduced rem em -

1.

PERCEPTION OF TIME

17

berance o f the first duratio n , coupled w ith the long length o f the second d uration, m ight naturally produce a “ b ia se d ” m em ory for the first duratio n , and thus a tendency to perceive the second duration as longer than the first. T his in terp reta­ tion is c o n sisten t w ith the o ccurrence o f negative tim e-o rd er errors described earlier. A n d , it is consisten t w ith o th er research that has show n a bias in m em ory for durations w hen delays are im posed betw een the duration and choice (Spetch & W ilkie, 1983). A second source o f b ias is related to the p robability o f o ccurrence o f different groups o f problem s. B ecause the d urations w ere arranged random ly, the d ifferent c om binations o f pairs did not o c cu r equ ally , as Fig. 1.5, 1.6, 1.7, and 1.8 dem onstrate. T he d ifferent p robabilities o f o ccurrence o f the duration pairs (e .g ., long vs. short; short vs. long, e tc .) could account for biased responding in a w ay sim ilar to that ob serv ed for the probe trials in the first experim ent. C areful e xam ination o f F ig. 1 .5 -1 .8 reveals that w hen one m em ber o f a duration p a ir was longer than 10 seconds (all problem s excluding those in the lo w er left quadrant) it w as m ore probable that the o th er m em ber o f the p air w as sh o rter than

ALL

PROBLEMS

* D, ond 02 £ ( 0 sec

0 Di or 02 > 10sec

FIG. 1.9. Probability of a right-key response (reporting the second dura­ tion as longer than the first) as a func­ tion o f the ratio o f the duration pairs. The left column shows performance for all duration pairs. The right col­ umn shows performance when both durations were 10 seconds or less (filled triangles) and when one or both durations were longer than 10 seconds (unfilled circles). The points are plotted at the midpoint of the cat­ egories o f stimuli and represent the average duration pair ratio for each category. The data were pooled over four sessions for each pigeon.

DURATION PAIR

RATIO ( D ,/0 2)

18

FETTERMAN AND DREYFUS

10 seconds (cf. the p roblem s in the upper left and lo w er right quadrants with those in the upper right). F ocusing upon those p roblem s in the upper right quadrant o f the figures show s that, fo r each anim al, perform ance w as m ore accurate for those pro blem s below the 1:1 d iagonal than for those above. T h u s, when both durations w ere longer than 10 seconds, all birds show ed a bias to respond that the second (and m ost recent) duration w as longer. H ow ever, this sam e bias is not o bserved fo r p roblem s in the low er left quadrant o f Fig. 1 .5 1.8, w hen both d urations w ere less than 10 seconds. P erhaps bias w as influenced by the probability o f the differen t types o f duration pairs. W h atev e r the source o f bias, it should be noted that the degree o f bias w as not great and w as not observed in all pigeons. A n d , in spite o f a bias, sensitivity w as sim ilar o v e r the range o f d urations that com prised the duration pairs. In su m m ary , the results o f the second experim ent support and ex ten d those o f the first. T he pig eo n s w ere able to respond appropriately even w hen m any different duration pairs w ere used. Use o f m any duration pairs afforded a p ro ­ cedural im provem ent that reduced end e ffects and forced relational ju d g m e n ts.

Discussion T he m ain findings o f the e xperim ents w ere the follow ing: (a) T he anim als w ere able to d iscrim inate the d ifference betw een tw o durations p resented in su c c es­ sion; (b) discrim ination accuracy depended on the relative rath er than the ab so ­ lute d ifference betw een the tw o d urations; (c) p erfo rm an ce w as sim ilar w hether the durations w ere short o r long; d iscrim ination sensitivity w as sim ilar across the tw o ranges o f E xperim ent 1 and w as sim ilar for short and long duration pairs in E xperim ent 2; (d) a ccuracy declined w hen a delay w as interposed betw een the tw o d urations, but rem ained relatively high until the delay s approached 30 sec­ onds; (e) negative tim e-o rd er errors ap parently occurred in som e cases; ( 0 the pigeons seem ed able to respond to the relational features o f the task, but the occurrence o f end effects suggests restrictions on discrim ination based solely on stim ulus relations. The findings are consisten t w ith prev io u s findings on duration discrim ination, and they dem onstrate that the paired-com parison pro ced u re, although d ifferent from previous p rocedures in a basic w ay, produced findings sim ilar to o th er discrim ination procedures that also assess tim e perception. T here are several w ays in w hich the differen t sets o f data are com parable. F irst, the ogival func­ tions are sim ilar to those o btained in previous psychophysical e xperim ents with pigeons (S tubbs, 1968) and rats (C h u rch , 1980). W eb er fractions can be c o m ­ puted from ogives and provide a sum m ary m easure o f sensitivity ( e .g ., S tu b b s, 1979). W eb er fractions in previous psychophysical trials procedures have g e n er­ ally ranged around 0 .2 0 - 0 .3 0 . W eb e r fractions for the p aired-com parison task averaged .41 (range .36 to .46) for the fo u r pigeons. T h e W eb er fractions w ere obtained by d ividing the difference lim en (75th percentile m inus the 25th p e rce n ­

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PERCEPTION OF TIME

19

tile divided by tw o) by the PSE. C o n sid erin g that W eber fractions vary so m e ­ w hat due to procedural d ifferen ces, and that the p aired-com parison task is p ro b a ­ bly m ore com plex for the an im als, the data indicate that perform ance w as com parable not ju st in a general w ay but also in the d egree o f sensitivity. A second point o f ag reem ent w ith prev io u s research w as the finding that d iscrim ination accuracy w as a function o f the relative difference betw een the tw o durations. A ccuracy on sim pler duration tasks also depends on the relativ e, not the absolute, d ifference betw een durations ( e .g ., C hurch & D eluty, 1977; S tu b ­ bs, 1968). T he p resent e xperim ents confirm the previous results and extend them to a m ore com p lex d iscrim ination task w here choices w ere based on the dif­ ference betw een tw o successively p resented d urations. A third point o f co m ­ parison betw een the p re sen t and past research is that p erfo rm an ce w as c o m p ara­ ble across differen t ranges o f durations. P revious w ork w ith sch ed u les, with psychophysical trials p ro c ed u re s, and w ith free-operant psychophysical p ro ­ cedures have d em onstrated that perform ance rem ains sim ilar w hen tim es vary over a w ide range ( e .g ., G ib b o n , 1977; S tubbs, 1980). T he range o f durations w as not as great in the presen t study as in previous stu d ies, and thus the p o s­ sibility exists that accuracy m ight declin e w hen lo n g er durations are used. H ow ­ ever, ongoing research w ith lo n g er d urations indicates that perform ance rem ains substantially unchanged o v e r a w ide range o f d urations. A fourth com parison concerns the effects o f delay. C hurch (1980) trained rats to m ake one choice response given a prio r short d u ratio n , and a second response given a long. D ifferent delays w ere then interposed betw een durations and choice, w ith the result that accuracy declined as a function o f delay (see also Spetch & W ilkie, 1982, 1983). T h e results are c o n sisten t w ith those o f E xperi­ m ent 1 w here accuracy declined w hen delays w ere interposed betw een the tw o durations. A n d , in both this experim ent and C h u rc h s’, accuracy w as well above chance w ith delays o f up to 10 seconds. S im ilar effects o f in terstim ulus delays have been found w ith paired -co m p ariso n tasks involving visual stim uli (Shim p & M offitt, 1977; W h ite, 1974). N egative tim e-o rd er errors w ere observed in both e x p erim e n ts, and these results seem to be like those o btained w ith hum an tim e ju d g m e n ts. O u r data suggest that pig eo n s, like h u m an s, do not give equal w eight to each m em b er o f a duration pair; instead , perform ance suggests that the nom inal value o f the first pair m em ber is reduced by som e am ount. T h e in terpretation o f tim e -o rd er errors in hum an tim e ju d g m e n ts is cu rrently a m atter o f som e dispute. Som e investiga­ tors (e .g ., A llan, 1977, 1979) suggest that tim e-o rd er errors result from a re ­ sponse bias that is based on a criterion established by the range o f durations to be ju d g ed . T hus errors are p resum ed to arise from the decision process. O thers (e .g ., Jam ieson & P etru sic, 1975) attribute these errors to distortions in p erce p ­ tual m em ory for the durations. In the case o f the p re sen t experim ents, it seem s unlikely that tim e -o rd er errors w ere the o utcom e o f a single factor, a n d , in at least som e instances, it is questionable w hether the o bserved pattern o f resp o n d ­

20

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ing reflected a true tim e-o rd er e rro r as the term is usually defined. W hen, for exam ple, pairs o f equal d urations w ere p resented on probe trials in E xperim ent 1, the anim als tended to respond on the right indicating that the first duration w as shorter than the second. In som e cases, these “ e rro rs” m ay have b een co m p ara­ ble to those obtained w ith hum ans. In o th er instances, h ow ever, there is probably a sim pler ex planation. W henever the longest value o f a group o f durations w as presented on equal probe trials (4 vs. 4 seconds and 16 vs. 16 seconds), the anim als tended to respond alm ost e x clu siv ely on the right (see F ig. 1.2). In these cases, it seem s likely that the pigeons w ere responding on the basis o f the second duration only becau se, d uring train in g , these values w ere longer than any o f the other d urations. T h ere fo re, som e o f the “ tim e-o rd er e rro rs” occurred because the anim als responded on the basis o f a single d uration only. A sim ilar pattern o f responding was o bserved on o th er novel duration pairs introduced on probe trials (see Fig. 1.3). N egative tim e-o rd er errors w ere also o bserved in E xperim ent 2, w hen m any duration pairs w ere used. C alculations show ed that the P S E s for the duration p air ratio averaged 1.2:1, indicating a negative tim e-order erro r. Use o f a large num ber o f duration pairs m ade it m ore d ifficult for the pigeons to respond appropriately on the basis o f a single d u ration; it is likely, therefore, that the errors in E xperim ent 2 resulted from factors o ther than th ose ju st d escrib ed . O ne possibility (discussed earlier) is that tim e -o rd er errors resulted from factors relat­ ed to m em ory. T h e errors w ere m ost p ronounced w hen d urations w ere long; longer durations m eant longer delay s b etw een the first d uration and choice and, perhaps, reduced m em ory for the first duratio n . Stated d ifferen tly , choice seem ­ ingly w as influenced to a g reater d egree by the seco n d , m ore recent (and perhaps better rem em bered), p air m em b er than by the first. A second possibility concerns the different p robabilities o f o ccurrence o f the d uration pairs ( e .g ., long vs. short; long vs. long, e tc .); in som e in stan ces, responding m ay h ave been influ­ enced by the heterogenous d istribution o f the d ifferent problem types. T he o u t­ com e m ight have been a biased pattern o f responding that resem bled a tim eorder-like effect but arose from factors unrelated to tim e-o rd er effects. In sum , although o u r d a ta suggest the p ossibility o f tim e-o rd er e ffects, the evidence is far from c onclusive. T h e e xperim ents necessary to d em onstrate these effects w ould require the use o f longer d urations a n d /o r differen t distrib u tio n s o f problem types. T he experim ents have im plications for m em ory, and for m odels o f tim e perception that rely on a m em ory concept. T im e p erception m ay be tied to m em ory for events d uring a tem poral interval ( e .g ., the pulses o f an internal pacem aker); the m ore e v en ts, the longer the perceived duratio n . T y p ically , sh o rt­ term (or w orking) m em ory is assessed w ith p rocedures like d elayed-m atching-tosam ple (D M T S ) in w hich c h o ice responses are reinforced d epending on the prio r presentation o f on e o f tw o stim uli ( e .g ., a red o r green key light). T he general outcom e o f exp erim en ts w ith D M T S procedures is that accuracy declin es to

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PERCEPTION OF TIME

21

chance levels w hen delays on the ord er o f seconds are im posed betw een the sam ple stim ulus and choice ( e .g ., R oberts & G rant, 1976). T he paired c o m ­ parison task w ould seem to have aspects o f a m em ory task , because there w as a delay betw een the first duration and choice produced by the second duration. H ow ever, o u r results are som ew hat paradoxical in light o f traditional view s o f m em ory, because perform ance (sensitivity) w as sim ilar w h eth er the durations were short o r long, and, h en ce, w hether a sh o rter o r lo n g er delay w as interposed betw een the first duration and choice. Predictions based on traditional notions o f m em o ry , and on m em ory research, suggest that accuracy should be low er w hen longer durations w ere used. N ot only w as accuracy sim ilar for both sh o rt and long duratio n s, but it also rem ained relatively high in spite o f delays im posed betw een the first and second d urations. The perform ance w ith these delays suggests one w ay in w hich the p aired-com parison results m ay be con sisten t w ith findings on m em ory. C hoice accuracy declines in conditional discrim in atio n tasks w hen delays are used, and accuracy m ay decline to chance levels w ith delays o f only a few seco n d s. H ow ever, the degree o f the decrem ent depends on the specific task. A ccuracy m ay decline to chance levels w ith short delays (e .g ., 5 seconds) w hen the stim uli to be d iscrim i­ nated are sim ply red and green lights. B ut accuracy m ay rem ain h ig h er and for longer delays (e .g ., 30 seconds) w hen differential response requirem ents are added ( e .g ., C o h e n , B rady, & L o w ry , 1981). T asks that actively involve the anim al and produce differen t b ehavior to different stim uli ap p ear to produce perform ance that is m ore resistant to the effects o f delay. D uration tasks m ight belong in this c ategory. E xplicit responses are not req u ired , but d uration tasks actively involve the anim al because the stim ulus m ust som ehow be e ngaged o v er the duration it lasts. If the logic o f this argum ent is co rrect, the duration task m ight be a very “ m em o rab le ” task, as the delay condition suggests. T h is in terpretation retains the traditional notion o f m em ory and suggests that the durations m ight not have been long enough for tem poral lim its on m em ory to influence perform ance. T he change in bias w ith long durations in E xperim ent 2 co u ld be interpreted as due to the lim itations o f m em ory. O ther aspects o f the d ata, h o w ev er, are inconsistent w ith the m em ory view . T he interm ittent “ v e ry -lo n g ” problem s not c overed in Fig. 1 .5 -1 .8 g e n ­ erally w ere responded to c o rrectly , and ongoing research w ith longer durations so far show s that anim als can respond appropriately (see also S tubbs, D reyfus, & F etterm an, 1984). In a ddition, inspection o f Fig. 1 .5 - 1 .8 reveals that, w hen the second duration w as long (right-hand colum n o f the m atrice s), accuracy varied as a function o f the ratio o f the tw o d urations and did not depend on the length o f the second duratio n , as m em ory accounts w ould predict. T hese results suggest that traditional notions about m em ory m ay have to be reevaluated. E xplanations o f perform ance in m em ory tasks such as D M TS rely heavily on the concept o f a m em ory representation ( e .g ., see R oitblat, 1982, 1984). In D M T S , for e x am p le, it is assum ed that a m em ory rep resentation o f the sam ple

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(or response rule) m ediates the delay betw een the offset o f the sam ple and choice and enables the anim al to respond appropriately. A ccuracy d eclines as the delay betw een the sam ple and choice is lengthened because the inform ation in w orking m em ory is transient. A gro w in g body o f m em ory research has focused on elu ­ cidating the properties o f these internal codes o r re p re se n tatio n s, and on factors that influence the nature and persistence o f m em ory representations (see R oitblat, 1982, 1984). A nu m b er o f w orkers in the tim e percep tio n area have adopted a m em ory fram ew ork and the concept o f a m em ory representation fo r tim e. F o r e x am p le, in the inform ation-processing m odel o f G ib b o n , C h u rch , and th eir collaborators (e .g .. G ibbon & C h u rch , 1984), recently p resented d urations are represented in a w orking m em ory com p o n en t. T he “ stim u lu s” fo r the d uration consists o f pulses from an internal p ace m a k e r that are sto re d , tem porarily, in w orking m em ory. T im e is represented as an accum ulation o f events in a m em ory reg ister, and presum ably the representation functions in m uch the sam e w ay as representations in D M TS tasks; it serves as one o f the m ediative links betw een the “ stim u lu s” and a response (see S h im p , 1978; S petch & W ilkie, 1982, 1983 for o th er exam ­ ples o f a m em orial-representational approach to tim e p erception in anim als). As suggested in the preced in g d iscu ssio n , this m em orial-representational view o f tim e perception is inconsistent w ith the results o f o u r experim ents. S tubbs, D reyfus, and F etterm an (1984) have proposed an alternate fram ew ork for considering a n im a ls’ tim e perception. T his approach places tim e perception w ithin the context o f o th er com plex p erceptual p h e n o m e n a such as space and m otion p erception (cf. G ib so n , 1975, 1979). T he p erceptual approach replaces the traditional d istinction betw een perception and m em ory w ith the view that the “ stim u lu s” for perceptual ju d g m e n ts m ay last only a m om ent o r m ay extend o v er a period o f tim e ( e .g ., G ib so n , 1960, 1979). In this view , organism s perceive structure in th eir e n vironm ent. T his structure can result from events ordered in space o r o v e r tim e. In the fo rm er case w e re fe r to sim ultaneous structure and in the latter sequential structure (see G ib so n , 1966 for a fuller discussion). V iew s that subscribe to the traditional division betw een perception and m em ory m ust co n fro n t the issue o f w here the presen t ends and the past begins, an issue that had defied resolution (see W ilcox & K atz, 1981 fo r a fu ller discussion o f this issue). T h e perceptual approach resolves the “ p ro b lem ” o f m em ory for events o v e r tim e by d isolving the b oundary betw een p erception o f the present and m em ory fo r the past. In the case o f tim ing, the “ stim u lu s” does not consist o f a m em orial rep resentation o f the accum ulated beats o f an internal clock; instead the stim ulus for tim ing consists o f the pattern o f events that occur d uring the interval (G ib so n , 1975). T h u s, fo r the paired-com parison task , the stim ulus for co m parative ju d g m e n ts o f tim e extends over the length o f the tw o durations. In addition to the m em ory issue, the results o f these e xperim ents pose other problem s for current m odels o f anim al tim ing b e h av io r (e .g ., C h u rch , 1978;

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PERCEPTION OF TIME

23

G ibbon, 1977). T he various discussions and d iagram s o f these m odels take the form o f a m ultistage process that intervenes betw een the stim ulus and the re­ sponse. T he m odels w ere designed to account for behavior in both tem porally defined schedules and in psychophysical tasks. It w ould ap p ear that the m odels will have to be m odified to account fo r perform ance in the p aired-com parison task. C urrent versions treat situations like the fixed-interval schedule and p sy ­ chophysical discrim inations by positing a com parison o f the clo ck setting held in w orking m em ory w ith a reference m em ory o f the tim e at w hich food w as pre­ sented. T he paired -co m p ariso n results indicate that the m odel w ould have to be m odified to include com parisons o f the clock setting w ith the ev er-changing m em ory o f a p rio r clock setting, or perhaps by positing the com parison o f tw o c locks, or a c o u n tu p -c o u n td o w n co m p arato r circu it, or the lik e .2 T he study o f hum an tim e perception has involved the use o f a w ide variety o f p rocedures that include com parison task s such as the p aired-com parison task and the m ethod o f reproduction. A s a result o f this v ariety, hum an m odels o f an internal clo ck ( e .g ., T reism an, 1963) are m ore com plicated than the anim al versions. T hey d o , how ­ ev er, include the necessary com parison processes to a cco u n t for the pairedcom parison data. A nim al clo ck m odels w ill have to be m odified and m ade m ore com plex and w ill p robably have to take on the form o f the previous hum an m odels to account for the grow ing variety o f results w ith anim al experim ents. T he e xperim ents d iscussed here have also d em onstrated that anim als can discrim inate the difference betw een tw o successively presen ted durations that are alw ays changing. T hese results indicate that the pigeons w ere able to m ake accurate relational ju d g m e n ts. E vidence for relational ju d g m e n ts com es from the findings that the anim als could d iscrim inate the difference betw een different duration pairs in E xperim ent 1, and that there w as generalization w hen novel pairs w ere introduced. T he stro n g er evidence com es from E xperim ent 2, w here the pigeons accurately d iscrim inated hundreds o f duration pairs. W e did not, how ever, test the lim its o f relational responding follow ing training in E xperim ent 2. The required tests w ould involve transfer tests w ith novel durations outsid e the range o f the training d u ratio n s, o r cross-m odal generalization tests. T he evidence indicates that relational ju d g m e n ts w ere involved, but som e evidence suggests lim its on this type o f ju d g m e n t. T he data on novel d u ratio n s that w ere longer than training durations in E xperim ent 1 and the pattern o f erro rs w hen delays w ere interposed suggest instances w here choices did not appear to depend on the relational features o f the task. T h u s, the pigeons appeared to respond on the basis 2Meck and Church (1984) have recently modified this model to account for animals’ ability to time two durations simultaneously. The modification incorporates additional accumulators that pre­ sumably enable the animal to “ attend” to two or more durations at the same time. Each accumulator registers counts from the same pacemaker, but the accumulated counts represent separately the concurrently presented durations. This modification, however, is not sufficient to account for perfor­ mance on the paired-comparison (ask, where two durations are presented in succession, not simul­ taneously, and where the animals must compare somehow the recently presented durations.

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FETTERMAN AND DREYFUS

o f stim ulus relations w hen relational ju d g m en ts w ere forced by the p rocedure, w hereas in o th er cases responding w as c ontrolled by factors o th er than stim ulus relations. T he findings regarding relational ju d g m e n ts have im plications for the conduct o f discrim ination exp erim en ts in general. R esearch on relational concepts in anim als has often used tran sfer tests as a m easure o f relational responding. In the usual procedure, anim als are train ed on a m atching-to-sam ple task, follow ed by a transfer test w ith new stim uli. T he general findings are that pigeons show little transfer w hen new problem s are introduced (C arter & W erner, 1978). Part o f the reason for this lack o f tran sfer m ay be that the p rocedures are not optim al for transfer to result. T he p aired-com parison task offers possib ilities as such a task b ecause it has m any d ifferent com binations and it forces relational ju d g m en ts. M atching tasks m ight be the equiv alen t o f using a sm all nu m b er o f durations (cf. results o f E xperim ent 1). Use o f large num bers o f stim uli forces relational ju d g m en ts and m inim izes the use o f specific responses to specific stim uli. A n i­ m als m ay learn sim ple responses w hen cond itio n s perm it but m ay also learn a m ore general response pattern w hen cond itio n s require them . R esults o f transfer tests w ould probably d iffer in these tw o cases ( e .g ., see W right, Santiago, U rcuioli, & S ands, 1983). It w ould seem then that the c om parison-type task need not be restricted to duration tasks but can prove useful for o th er stim ulus d im e n ­ sions as w ell.

SUMMARY T he experim ents d em onstrated that pigeons can perform a paired-com parison task involving d urations. T he findings w ere, in som e resp ects, sim ilar to those obtained w hen sim pler pro ced u res are used to study tim e perception in anim als. A nd, the results w ere co m p arab le to som e o f the findings obtained w ith hum ans. H ow ever, o u r data ap p ear to be inconsistent w ith current theoretical treatm ents o f tim e p erception in anim als. T he results are d ifficult to reconcile w ith a m em oiy-based view o f tim e percep tio n , and w ith inform ation-processing m odels that lack the features n ecessary to handle the com p lex ities o f the paired-com parison task. T he findings also suggest that pigeons are cap ab le o f responding on the basis o f stim ulus relations w hen relational ju d g m e n ts are forced by the task requirem ents. T he research raises a nu m b er o f issues reg ard in g tim e perception and m em ory in anim als, and the p aired-com parison task offers prom ise as a new m ethod for studying these issues. F or e x am p le, how m ight ch an g es in the range o f durations affect p erform ance? O r, can pigeons m ake sa m e/d iffe re n t (rather than sh o rt­ e r/lo n g er) ju d g m e n ts w hen d urations are used? T he present e xperim ents re p re ­ sent only an initial step tow ard the use o f m ore varied and com p lex pro ced u res in the study o f tim e perception in anim als.

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PERCEPTION OF TIME

25

AC K N O W LE D G M E N TS T he a u th o rs are g ra te fu l to A lan S tu b b s w h o has c o n trib u te d a g re at d eal to this w o rk and has given freely o f his tim e a n d im a g in atio n . J. G . F etterm an is no w at th e D ept, o f P s y ch o lo g y , N o rw ic h U n iv e rsity , N o rth field , VT. L. R . D re y fu s is a t th e D e p t, o f P s y c h o lo g y , L o y o la U n iv e rsity , N ew O rle a n s, L A . T he a uthors w ish to a c k n o w le d g e the su p p o rt o f N o rw ic h U n iv e rsity d u rin g the p re p ara ­ tion o f this m an u scrip t.

REFERENCES Allan, L. (1977). The time-order error in judgments of duration. Canadian Journal o f Psychology, 29, 2 4-31. Allan, L. (1979). The perception of time. Perception and Psychophysics, 26, 340-354. Anderson, A. C. (1932). Time discrimination in the white rat. Journal o f Comparative Psychology, 13, 2 7-55. Boring, E. G. (1942). Sensation and perception in the history o f experimental psychology. New York: Appleton. Carter, D. E ., & Werner, T. J. (1978). Complex learning and information processing by pigeons: A critical analysis. Journal o f the Experimental Analysis o f Behavior, 29, 565-601 Catania, A. C. (1970). Reinforcement schedules and psychophysical judgments: A study of some temporal properties of behavior. In W. N. Schoenfeld (Ed.), The theorytof reinforcement sched­ ules (pp. 1-42). New York: A ppleton-Century-Crofts. Church, R. M. (1978). The internal clock. In S. H. Hulse, H. Fowler, & W. K. Honig (Eds.), Cognitive processes in animal behavior (pp. 277-310). Hillsdale, NJ: Lawrence Erlbaum Associates. Church, R. M. (1980). Short-term memory for time intervals. Learning and Motivation, 11, 2 0 8 219. Church, R. M ., & Deluty, M. Z. (1977). Bisection of temporal intervals. Journal o f Experimental Psychology: Animal Behavior Processes, 3, 216-228. Cohen, L. R ., Brady, J., & Lowry, M. (1981). The role of differential responding in matching-tosample and delayed matching performance. In M. L. Commons & J. A. Nevin (Eds.), Quan­ titative analyses o f behavior: Vol. 1 Discriminative properties o f reinforcement schedules (pp. 345-364). Cambridge, MA: Ballinger. Cowles, J. T ., & Finan, J. L. (1941). An improved method for establishing temporal discrimination in white rats. Journal o f Psychology, 11, 335-342. Doob, L. W. (1971). Patterning o f time. New Haven: Yale University Press. Eisler, H ., Linde, L ., Throeng, G ., Lazar, R ., Eisler, B ., & Hellstrom, A. (1980). A complemen­ tary bibliography of the psychology of time. Journal Supplement Abstract Service (American Psychological Association), 10, (MS 2101). Fraisse, P. (1963). The psychology o f time. New York: Harper. Fraisse, P. (1978). Time and rhythm perception. In E. C. Carterette & M. P. Friedman (Eds.), Handbook o f perception: Vol. 8 Perceptual coding (pp. 203-247). New York: Academic Press. Fraisse, P. (1984). Perception and estimation of time. Annual review o f psychology, 35, 1-36. Frankenhauser, M. (1959). Estimation o f time: An experimental study. Stockholm: Almqvist & Wiskell. Gibbon, J. (1977). Scalar expectancy theory and W eber’s law in animal timing. Psychological Review, 84, 279-285. Gibbon, J., & Church, R. M. (1984). Sources of variance in information processing models of

26

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timing. In H. L. Roitblat, T. G. Bever, & H. S. Terrace (E ds.), A nim al cognition (pp. 465 -4 8 8 ). Hillsdale, NJ: Lawrence Erlbaum Associates. G ibson, J. J. (1960). T he concept of the stimulus in psychology. Am erican Psychologist, 16, 6 9 4 703. G ibson, J. J. (1966). The problem of temporal order in stimulation and perception. Journal o f Psychology, 62, 142-149. Gibson, J. J. (1975). Events are perceivable but time is not. In J. T. Fraser & N. Lawrence (Eds.), The study o f tim e: II (pp. 2 9 5 -3 1 0 ). New York: S pringer-V erlag. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: H oughton-M ifflin. Jam ieson, D. G ., & Petrusic, W. M. (1975). The dependence o f tim e-order error direction on stimulus range. Canadian Journal o f P sychology, 29, 175-182. M eek, W ., & Church, R. M. (1983). A mode control model o f counting and timing processes. Journal o f Experim ental Psychology: A nim al B ehavior Processes, 9, 3 2 0-334. M eek, W ., & Church, R. M . (1984). Sim ultaneous tem poral processing. Journal o f Experim ental Psychology: A nim al B ehavior Processes, 10, 1-29. Om stein, R. E. (1969). On the experience o f time. Baltimore: Penguin. Pavlov, I. P. (1927). Conditioned reflexes. (Translated by G. V. A nrep.) London: Oxford Univer­ sity Press. Platt, J. R. (1979). Tem poral differentiation and the psychophysics o f time. In M. D. Zeiler & P. Harzem (Eds.), A dvances in the analysis o f behavior: Vol. 1 Reinforcem ent and the organization o f behavior (pp. 1 -29). C hichester, England: W iley. Richelle, M ., & Lejeune, H. (1980). Tim e in anim al behavior. New York: Pergamon. Roberts, S ., & Holder, M. (1982, June). Are time-discrimination procedures realistic? Paper pre­ sented at the Fifth Sym posium on Quantitative Analyses of Behavior held at Harvard University: Cam bridge, MA. Roberts, W. A ., & G rant, D. S. (1976). Studies o f short-term m emory in the pigeon using the delayed-m atching-to-sam ple procedure. In D. L. M edin, W . A. Roberts, & R. T. Davis (Eds.), Processes o f anim al memory (pp. x -y ). Hillsdale, NJ: Lawrence Erlbaum Associates. Roitblat, H. L. (1982). The m eaning of representation in animal memory. The Behavioral and Brain Sciences, 5, 3 5 3-406. Roitblat, H. L. (1984). Representations in pigeon working m em ory. In H. L. Roitblat, T. G. Bever, & H. S. Terrace (E ds.), A nim al cognition (pp. 7 9 -9 7 ). Hillsdale, NJ: Lawrence Erlbaum Associates. Sams, C. F ., & T olm an, E. C. (1935). Tim e discrim ination in white rats. Journal o f Comparative Psychology, 5, 2 5 5 -2 6 3 . Shimp, C. P. (1978). M em ory, temporal discrim ination, and learned structure in behavior. I n G . H. Bower (E d.), The psychology o f learning and motivation (Vol. 12, pp. 3 9 -7 6 ). New York: Academic Press. Shimp, C. P ., & M offitt, M. (1977). Short-term m em ory in the pigeon: Delayed-pair-com parison procedures and som e results. Journal o f the Experim ental A nalysis o f Behavior, 28, 13-25. Skinner, B. F. (1938). The behavior o f organisms. New York: A ppleton-C entury-C rofts. Spetch, M. L ., & W ilkie, D. M. (1982). A system atic bias in pigeons' m em ory for food and light durations. B ehaviour A nalysis Letters, 2, 2 6 7-274. Spetch, M. L ., & W'ilkie, D. M. (1983). Subjective shortening: A model of pigeons’ m em ory for event duration. Journal o f E xperim ental Psychology: A nim al B ehavior Processes, 9, 14-30. Staddon, J. E. R. (1974). Temporal control, attention, and memory. Psychological Review, 81, 375-391. Stubbs, D. A. (1968). The discrim ination o f stimulus duration by pigeons. Journal o f the E xperi­ mental A nalysis o f Behavior, 11, 2 2 3 -2 5 8 . Stubbs, D. A. (1976). Response bias and the discrim ination o f stim ulus duration. Journal o f the Experimental A nalysis o f Behavior, 25, 2 4 3-250.

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27

Stubbs, D. A. (1979). Tem poral discrim ination and psychophysics. In M. D. Zeiler & P. Harzem (E ds.), Advances in the analysis o f behavior: Vol. 1 Reinforcem ent an d the organization o f behavior (pp. 341 -3 6 9 ). C hichester, England: W iley. Stubbs, D. A. (1980). Discrimination o f stim ulus duration and a free-operant psychophysical pro­ cedure. Journal o f the E xperim ental Analysis o f Behavior, 33, 167-185. Stubbs, D. A ., Dreyfus, L. R ., & Fetterm an, J. G. (1984). The perception o f temporal events. In J. Gibbon & L. Allan (E ds.), A nnals o f the N ew York Academ y o f Sciences: (Vol. 423) Timing and time perception (pp. 3 0 -4 2 ). New York. Triesm an, M. (1963). Tem poral discrim ination and the indifference interval: Im plications for a model o f the “ internal clo c k .” P sychological M onographs, 77, (W hole No. 576). W hite, K. G . (1974). Tem poral integration in the pigeon. British Journal o f Psychology, 65, 4 3 7 444. W ilcox, S ., & Katz, S. (1981). A direct realistic alternative to the traditional conception o f m em o­ ry. B ehaviorism, 9, 2 2 7 -2 3 9 . W oodrow, H. (1951). Tim e perception. In S. S. Stevens (E d.), H andbook o f experim ental psycholOgy (pp. 1224-1236). New York: W iley. W right, A. A ., Santiago, H. C ., Urcuioli, P. J ., & Sands, S. F. (1983). M onkey and pigeon acquisition o f the sam e/different concept using pictorial stimuli. In M. L. Com m ons, R. J. Herm stein, & A. R. W agner (E ds.), Q uantitative analyses o f behavior: Vol. IV, Discrimination Processes (pp. 2 9 5 -317). Cam bridge, MA: Ballinger.

T h i s p a g e i n t e n ti o n a ll y left b l a n k

2

Behavioral Models of Delayed Detection and Their Application To the Study of Memory

Dianne M cC arthy K. G eoffrey W h ite University o f Auckland and University of Otago, N ew Zealand.

In its sim plest form , the d etection task involves presen tin g one o f tw o d iscrim i­ native stim uli to a subject train ed to rep o rt w hich stim ulus had been presented. Signal-detection p erfo rm an ce is typically exam ined w hen the stim uli are presen t­ ed in w ell-defined observation intervals and d etection responses are em itted in the presence of, o r im m ediately a fte r presentation of, the discrim in ativ e stim uli. A behavioral m odel o f detection perform ance (D avison & T u stin , 1978) has been show n to pro v id e an excellent fit to data obtained from sim ple detection tasks using anim als as sub jects. M cC arthy and D avison (1 981a, b) have published review s show ing that both rein fo rcem en t and stim ulus v ariables can be su ccess­ fully captured w ithin this th eoretical fram ew ork. H um an detection ex p erim en ts report decreases in discrim inability w hen the availability o f the detection response is delay ed for som e period o f tim e fo llo w ­ ing stim ulus presentation (for e x am p le, E gan, G reen b erg , & S chulm an, 1961). C onsistent w ith the findings o f hum an d elayed-detection ex p erim en ts, M cC ar­ thy, D avison, and Je n k in s (1982) found that w ith pigeons even a very sm all delay betw een stim ulus presen tatio n and response availability w as su fficient to decrease stim ulus discrim in ab ility from its value obtained w hen the d etection response w as e m itted in the p resence o f the stim ulus. D elayed-detection tasks are m em bers o f a m ore general class o f experim ental p a rad ig m s— d e la y ed conditional-discrim ination tasks. O th er m em bers o f this c la ss include paradigm s co m ­ m only used to study anim al and hum an m em ory. F o r e x am p le, the delayedm atching-to-sam ple task , the delayed -sy m b o lic-m atch in g -to -sam p le task, and the d elayed-com parison task are all characterized by the inclusion o f a tem poral interval betw een the presen tatio n o f a stim ulus and the occurrence o f a response occasioned by that stim ulus. 29

30

M cCa r t h y

a n d w h it e

T he purpose o f this c h ap ter is tw ofold: F irst, it ex tends the D avison and T ustin (1978) behavioral m odel o f p erfo rm an ce on sim ple detection tasks to account for data from d elayed d etection tasks. S econd, it d em onstrates the a p ­ plication o f this m odel to the study o f m em ory a n d , in particu lar, it exam ines, via this behavioral fram ew o rk , the role o f differential reinforcem ent in m em ory experim ents.

SIMPLE DETECTION Figure 2.1 show s the stim u lu s-re sp o n s e m atrix for ev en ts in an o perant analog o f the discrete-trial “ y e s - n o ” detection task, typically arranged for anim al su b ­ jec ts. L eft- and right-key responses are the choices available for the anim al to report the presence o f the tw o d iscrim inative stim uli, S , and S 2• In the m atrix draw n in Fig. 2 .1 , P w d enotes correct left-key responses in the presence of, or im m ediately after, 5 , presen tatio n s, and P z d enotes correct right-key responses in the presence o f, o r im m ediately after, S 2 presentations. P v denotes incorrect left-key responses during o r a fter S 2 presentations, and P x denotes incorrect right-key responses d uring o r a fter 5 , p resentations. T y p ic ally , correct left- and right-key responses are reinforced (represented by R w & R z, respectively) and errors have no consequence. D avison and T u stin (1 978), like N evin (1 970), noted that the sim ple detection paradigm arranges tw o con cu rren t c h o ic es, one each in the presence o f, o r im m ediately after presentation o f, the stim uli to be d iscrim inated. D avison and T ustin drew on the success w ith w hich the g e neralized-m atching law (B aum , 1974) described b e h av io r on concurrent schedules o f reinforcem ent. T hey p ro ­ posed a m odel that assu m ed that ratios o f choice responses in the tw o stim uli w ere

RESPONSE

tn

FIG. 2.1. The stim ulus-response matrix for a y e s-no detection task typically arranged for animals. RFT denotes reinforcement, EXT denotes extinction, and W , X, Y, and Z tally the number o f events in each cell.

2.

BEHAVIORAL MODELS

31

a pow er function o f the ratio o f reinforcers o btained for those choices. In a ddition, D avison and T ustin proposed that perform ance in the detection situation w ould also be a function o f the extent to w hich the stim uli w ere discrim inable. T hey w rote tw o generalized -m atch in g -law equations w ith an added d iscrim inability term to d escribe b ehavior in the detection paradigm . D uring, o r im m ediately after, 5 , presentations: log

= a n log * X

+ log c + log d.

(1)

Z

D uring, o r im m ediately after, S 2 presentations: log ( ^ )

= an log

+ log c -

log d.

(2)

H ere, P and R d enote nu m b er o f responses em itted and nu m b er o f reinforcers obtained, respectively, and the subscripts re fe r to the cells o f the m atrix show n in Fig. 2 .1 . The re inforcem ent ratio, R J R Z, quantifies a left-right rein fo rcem en t bias caused by different num bers o f reinforcers being obtained on the left and on the right keys. T he p aram eters a n and ar2 m easure the sensitivity o f le ft-rig h t b ehavior allocation to changes in the le ft-rig h t reinforcem ent ratio in the p re s­ ence o f each o f the tw o stim uli. L og c represents inherent bias, a constant bias in 5, and S 2 that rem ains invariant across reinforcem ent and stim ulus changes. L og d m easures the discrim in ab ility o f the tw o stim uli. T he b etter the subject can discrim inate 5 , from S 2, the larger will be log d and so the larger the ratio P J P X and the sm aller the ratio P J P Z. B ecause the num erators in E quations 1 and 2 are both left-key resp o n ses, log d is positive in E quation 1 and negative in E quation

2. The D avison and T ustin (1978) m odel em bodies the traditional detectiontheory separation betw een the effects on behavior o f sensory and nonsensory variables. D iscrim inability and reinforcem ent bias have been show n to have independent b ehavioral effects in that sensitivity to reinforcem ent (a r) does not vary as a function o f discrim inability (M cC arthy & D avison, 1980b). E quations 1 and 2 can therefore be co m bined to specify how in dependent m easures o f stim ulus d iscrim inability and response bias can be obtained. S ubtracting E qua­ tion 2 from E quation 1 and rearranging gives a bias-free m easure o f stim ulus discrim inability:

log d = . 5 log ( £ » £ * ) . \

r xr y/

(3)

A dding E quation 2 to E quation 1 and rearranging gives a d iscrim inability-free m easure o f response bias:

32

M cCa r t h y

a n d w h it e

(P P \ log response bias = .5 log I p I•

(4)

A n ex tensive p rogram o f research conducted o ver the last few years has d em onstrated the efficacy o f this behavioral m odel in accounting for data o b ­ tained in both the discrete-trial psychophysical experim ent and the free-operant m ultiple-concurrent schedule discrim ination task. On the one h an d , sim ple d e ­ tection perform ance has been describ ed w hen eith er reinforcem ent param eters (for exam p le, relative rein fo rcer frequency, M cC arthy & D avison, 1979; ab so ­ lute rate o f rein fo rcem en t, M cC arthy & D avison, 1982), o r stim ulus param eters (for e x am p le, M cC arthy & D av iso n , 1980a) have been m anipulated. In a ddition, the role o f differential rein fo rcem en t in d etection experim ents has been clarified (M cC arthy & D avison, 1981a, 1984). T he im portance o f a tru ly bias-free m ea­ sure o f discrim in ab ility in th reshold studies has a lso been d em onstrated (M cC ar­ thy, 1983). On the o th er hand, the m odel has p ro v id ed , for the first tim e, a quantification o f stim ulus effects in free-operant m ultiple-concurrent schedule paradigm s (M cC arthy, D avison, & Je n k in s, 1982). Such a unified account o f the effects o f stim ulus and response-bias variables provides the basis for a qu an ­ titative m odel describ in g b ehavior in a diversity o f paradigm s. T his chapter exam ines extensions o f the D avison and T u stin (1978) m odel that have been p roposed to account fo r b eh av io r in the situation w here the tim e betw een stim ­ ulus and response events in the detection task is p aram etrically m anipulated.

DELAYED DETECTION Models T w o extensions to the D avison and T ustin (1978) m ode! have been proposed to account for the situation in w hich tem poral delays are interpolated betw een presentation o f th e stim uli in the detection task and the availability o f the choice responses. W hite and M cK en zie (1982) investigated the m anner in w hich the accuracy o f discrim in atin g relational versus single or elem ent stim uli decreases w ith increasing tim e since their presen tatio n . U sing pigeons as subjects and w avelength as the discrim in ativ e-stim u lu s d im en sio n , they suggested that the effect o f the delay w as to d egrade discrim in ab ility according to a negative e x p o ­ nential function o f tim e; that is, the delay d ecrem en ted d iscrim inability (log d) as follow s: log d, = log d c e ~ b‘.

(5)

H ere log d, m easures the discrim inability o f the stim uli at tim e t, log d n re p re ­ sents the discrim in ab ility at tim e t = 0 , / is the d elay , and b is a tim e constant describing the rate o f decrem en t o f log d, o v e r tim e. W hen t is m easured in

2.

BEHAVIORAL MODELS

33

seconds, b is in (second) - '. S ubstituting this expression for log d in E quation 3 o f the D avison and T ustin m odel gives:

(6)

M cC arthy (1981) p roposed an alternative m odel in w hich rate o f decay w as not constant, but rath er, d ecreased w ith increasing delay. T his is consistent with m uch research on hum an long-term m em ory (for exam ple, W ick elg ren , 1975a). M cC arthy suggested that the function relating stim ulus discrim inability and tim e is a rectangular hyperbola; that is:

(7) H ere h represents the h a lf life, o r tim e i at w hich d iscrim inability (log dn) falls to one half its initial value, t and log da represent, resp ectiv ely , delay and d iscrim i­ nability at tim e / = 0 , as in the exponential m odel (E quation 5). W ith d iscrim i­ nability represented as a rectangular-hyperbolic function o f tim e, E quation 3 o f the D avison and T ustin (1978) m odel becom es:

(8 )

A ccording to this m odel, the rate o f decay o f log d, o v er tim e t is not constant. R ather, rate o f decay decreases as t increases; that is: d i\o g d ,) _ dt

h \o g d a (h + t) 2 '

In ord er to com pare these tw o m odels w ith resp ect to th eir ability to describe the data, an experim ent w as conducted in w hich the delay betw een stim ulus presentation and response availability w as p aram etrically varied in an otherw ise standard signal-detection p arad ig m . T he data w ere analyzed according to both the negative-exponential m odel (E quation 6) and the rectangular-hyperbolic m odel (E quation 8).

Experiment 1 in the first experim ent reported here (H arn ett, M cC arthy, & D avison, 1984), six hom ing pigeons, m aintained at 85% body w eight, w ere train ed on a d iscrete-trial light-intensity d iscrim ination task. T rials began w ith the illum ination by w hite light o f the c en ter key o f a three-key array. T he tw o side keys w ere initially darkened, and responses on these tw o key s had no scheduled consequences. T he

34

M cCa r t h y

a n d w h it e

lum inance o f the w hite c en ter key w as eith er 2 .6 9 c a n d e la s/m e te r2 (5 ,) o r 1.26 c a n d e la s/m ete r2 (S 2)■ B oth these intensities o ccurred eq u ally often on the c en ter key. O ne peck on the illum inated c en ter key ex tinguished the cen ter-k ey light and initiated a delay interval o f t seco n d s, w here t w as varied in an irregular sequence across ex perim ental cond itio n s (t — 0 , .7 5 , 1.5, 3 .0 , 5 .0 , 7 .5 , 10, and 15 seconds). O n com p letio n o f the d e la y , the tw o side keys w ere lit eith er red (left) and green (right) o r green (left) and red (right). T he o ccurrence o f red and green on the left and right keys w as random ized (p = .5) across trials. C orrect choice responses w ere pecks on the red side key a fter presentation o f the brighter stim ulus (S p 2 .6 9 c d /m 2) on the c en ter k ey , and pecks on the green side key after presentation o f the d u lle r stim ulus (S 2, 1.26 c d /m 2) on the c en ter key. C orrect red and g reen choice responses w ere interm ittently reinforced w ith 3second access to w h eat acco rd in g to tw o c oncurrent v a riable-interval (V I) 30second schedules. (In this w ay, delay and total rein fo rcer rate w ere not co rre ­ lated.) T he schedules w ere a rran g ed depen d en tly (S tubbs & P liskoff, 1969) on the red and green side keys. F o r exam p le, if a rein fo rcer w as set up on the red schedule, both V I tim ers stopped and a re in fo rc er w as u navailable for correct green choices until the red rein fo rcer w as taken. T his is a controlled-reinforcem ent-ratio p rocedure that m inim izes the d evelopm ent o f response bias (M cC ar­ thy & D avison, 1981a, 1984). W hen a correct red o r green choice response had been em itted, but a food re in fo rc er w as not set up by eith er VI tim er, a m agazine light alone w as p resented fo r 3 seconds. Incorrect choice responses (red pecks after presentation o f the d u lle r stim u lu s, and green pecks after presentation o f the b righter stim ulus) produced a 3-second blackout d u rin g w hich tim e all c h am b er lights w ere ex tinguished and key pecks had no scheduled consequences. A new trial (that is, presentation o f the w hite cen ter-k ey light) began after food, m ag a­ zine light, o r b lackout had been p roduced. In ad d itio n , a noncorrection procedure w as in effect th roughout the experim ent. P resentations o f S , and S 2 on the center key d uring any trial w ere in dependent o f the accuracy o r the stim ulus on the preceding trial. Figures 2 .2 and 2 .3 show p oint estim ates o f discrim inability at tim e t, log d t (obtained using E quation 3), as a function o f delay (, fo r all six birds. F igure 2.2 show s these data fit by the n egative-exponential m odel. N o n lin ear least-squares fits o f E quation 6 are show n in Fig. 2 .2 as solid lines. A lso given in Fig. 2 .2 are the values o f the decay rate b, the p redicted values o f log d a, and the m eansquare e rro r o f the estim ates. V alues o f b, o r the rate o f decay o f discrim inability over tim e, ranged from .13 se c o n d - 1 (B ird 54) to 4 .7 5 s e c o n d - 1 (B ird 55). L og d(, values, that is, discrim in ab ility at tim e t = 0 seconds, predicted by these exponential fits ranged from .65 (B ird 55) to 1.19 (B irds 53 to 56). G en erally , the fits w ere g o o d , as is show n by the sm all m ean-square erro rs, the e xception being B ird 53. Figure 2 .3 show s the sam e estim ates o f log d, as show n in Fig. 2 .2 , but here the data w ere fitted by rectan g u lar hyperbolic functions. N o n lin ear least-squares

2.

BEHAVIORAL MODELS

0 • -I9e

0-6

-nse

55

52

b . 212

0 * 4749

>OQSo ■ -649

log do • -827 m se « -009

FIG. 2 .2 .

127

I00 Co

log d0 • 995 m s e • 007

rose « -0 0 0 6

E x p e r im e n t 1. P oint e s ­

tim ates o f stim u lu s d isc rim in ab ility at tim e t (lo g d,) as a fu nction o f d e ­ lay t for all six bird s. N o n lin ea r leastsquares fits to the n e g a tiv e -e x p o n e n ­ tial m odel (E q u atio n 6) are sh o w n as solid lines. A iso sh o w n for each bird are the va lu e s o f the d eca y rate ( b) y the p redicted v alues o f initial d is­ c rim in ab ility (lo g da), and the m eansquare e rro r (M S E ) o f the estim a te s.

FIG. 2 .3 .

DELAY

(sec)

E x p e r im e n t 1. Point e s ­

tim ates o f stim u lu s d isc rim in ab ility at tim e t (lo g d,) as a fu nction o f d e ­

56

lay t for all six b ird s. N o n lin ea r least-

h . 776 log G0 • 1-263

sq u ares fits to the re ctan g u lar-h y p er-

m s e ■ -0 C 0 8

bolic m odel (E quation 8) are show n as solid lin es. A lso sh o w n fo r each bird are the v alu es o f the h a lf-life (h ), the p redicted v alu es o f initial d is ­ crim in ab ility (lo g d 0) y and the m eansquare e rro r (M S E ) o f the estim ates.

DELAY

35

36

M cCa r t h y

a n d w h it e

fits o f E quation 8 are show n in Fig. 2 .3 as solid lines. A lso giv en in Fig. 2 .3 , for each bird, are the p redicted values o f h (the tim e at w hich discrim inability falls to one h a lf o f its initial v alue), log d u (the value o f discrim inability at tim e t = 0), and the m ean square e rro r o f the estim ates. P redicted values o f h ranged from 0.00001 second (B ird 55) to 1.35 (B ird 53). A g ain , the fits w ere very g o o d , as is show n by the sm all m ean-square errors. A com parison o f Fig. 2.2 and 2.3 suggests that both the negative-exponential (E quation 6) and the re ctangular-hyperbolic (E quation 8) m odels are able to account for the data from a delayed -d etectio n task equally w ell. B oth m odels account for a high percen tag e o f the data variance and are not d iscrim inable in term s o f goodness o f fit. A com parison o f o btained and predicted log da values show ed that the negative-ex p o n en tial m odel underpredicted log da for five o f the six birds. T he rectan g u lar-h y p erb o lic m odel underpredicted log d a for four o f the six birds. In n eith er case w ere these u nderpredictions statistically significant. H ow ever, the m ean-square erro r o f the log d a estim ates for the exponential m odel w as .1 0 , w hereas that for the re ctangular-hyperbolic w as .04. A c o n sid ­ eration is now g iven to how data o btained from o th er delayed conditionald iscrim ination tasks m ay be accom m odated b y these tw o m odels.

ANIMAL MEMORY STUDIES Procedures for stud y in g anim al m em ory are characterized by the inclusion o f a tem poral interval betw een the p resentation o f a stim ulus and the o ccurrence o f a response o ccasioned by that stim ulus. P rocedurally, th ere fo re, they are an alo ­ gous to the d elayed-detection paradigm and, as su ch , m ay be q u antifiable in the sam e m anner. T h is section investigates the ap plicability o f the present extensions o f the D avison and T u stin (1978) signal-detection m odel to data o btained in anim al m em ory experim ents. R em em bering in p ig eo n s, for e x am p le, is typically studied using the delayedm atching-to-sam ple (D M T S ) p rocedure (B lough, 1959) in w hich a sam ple stim ­ ulus is follow ed by tw o com parison stim uli a fte r a d elay, o r “ re te n tio n ,” inter­ val. W hen one o f the com parison stim uli m atches the sam p le, the choice re ­ sponse is “ re co g n itio n ” in that it occurs in the presence o f the p reviously presented sam ple. S uccessive m atching-to-sam ple is an alternative recognition procedure in w hich eith er a choice response (M acP hail, 1980; S him p & M offitt, 1977) o r responding on a single key (N elson & W asserm an, 1978; W asserm an, N elson, & L arew , 1980) occurs in the presence o f a single com parison stim ulus. By c o n trast, the delayed -sy m b o lic-m atch in g -to -sam p le (D S M T S) p rocedure presents com parison stim uli that d iffer from the sam ple. T he choice response (Jans & C atania, 1980; M a k i, M o e, & B ierley, 1977; W ilkie, S u m m ers, & S petch, 1981) o r resp o n d in g on a single key (W ilkie & W ilson, 1977) thereby occurs in the absence o f the p rio r sam ple stim ulus and is “ re ca ll” b ehavior.

2.

BEHAVIORAL MODELS

37

A vast literature attests to the fact that accuracy o f m atching on the D M TS and D SM TS tasks decreases as the tem poral delay betw een sam ple and com parison stim uli increases (for exam p le, B errym an, C u m m in g , & N e v in , 1963; D ’A m ato, 1973; G rant & R oberts, 1973; Jans & C atan ia, 1980; N elson & W asserm an, 1978; S him p & M offitt, 1977; W asserm an, N elso n , & L arew , 1980). Y et, an experim ental analysis o f rem em bering has not progressed (S him p, 1976), and quantification has not been fo rthcom ing in this area o f research. H ere, an attem pt is m ade to quantify the decrease in m atching accuracy over tim e w ithout regard to the structure o f m em ory. R ather, the D M T S and the D S M T S tasks are view ed in this chapter sim ply as delayed d etection tasks and the decrease in discrim i­ nability (accuracy) o v er tim e is quantified w ithin the fram ew ork provided by the D avison and T u stin (1978) d etection m odel. T he functions specified by E quation 6 (the n eg ative-exponential m odel) and E quation 8 (the rectangular-hyperbolic m odel) for the d elayed-detection task m ay also be interpretable in m em ory re ­ search. M easu rem en t o f reco g n itio n or recall in term s o f the discrim inability o f the stim uli at tim e t after th eir p resentation (log d,) is con sisten t w ith the notion that rem em bering is b ehavior under the control o f p rio r discrim inative stim uli (C atania, 1979). T he rate o f d ecrem en t in “ m e m o rab ility ” is giv en by b, and h is the tim e at w hich “ m em o rab ility ” is one h a lf the value o f the initial d iscrim i­ nability o f the stim uli at tim e t = 0 seco n d s, log d a. M any v ariables are know n to influence rem em bering (fo r exam p le, training, sam ple response re q u ire m e n ts, prior trials, and novel stim ulation during the retention interval). T he specific e ffe c ts o f m any o f these variables m ay not be entirely clear in the absence o f a theoretical c ontext to d irect their interpretation. It is therefore o f interest to see w hich p aram eters (b , h, or log da) appear to be changed by m an ipulation o f these variables. T h e effects o f som e are im m ediately clear. F or exam p le, the physical p roperties o f the stim uli ought only to affect initial d iscrim inability (log da). O ther variables that m igh t affect initial d iscrim i­ nability include train in g , the ratio requirem ent for sam ple-stim ulus responding, sam ple-stim ulus duratio n , size o f sam p le-stim u lu s set, and p rio r, interfering trials. V ariables affecting b or h could be those com m only believed to induce retroactive interference (that is, events occurring d uring the delay interval), and rehearsal. T he effects o f som e o f these variables on b, h, and log da w ere exam ined by reanalyzing data from three experim ents in w hich these variables had been m a­ nipulated. U n fortunately, in no case w ere the raw data av ailable from w hich bias-free values o f log d, could be directly calculated. R ather, w e had to content ourselves w ith an alternative discrim inability index, the logarithm o f the ratio o f the num ber o f correct responses to the num ber o f erro rs, log (C /E ). T h is m easure is only totally free o f the e ffe c ts o f response bias if the effects o f the biaser are sym m etric in the tw o stim u li. A s a check o n the utility o f this m easure, the data from E xperim ent 1 (the in te nsity-discrim ination experim ent) w ere reanalyzed using log (C /E ), and not log d r as the dependent variable in E quations 6 and 8.

38

M cCa r t h y

a n d w h it e

E stim ates o f the p aram eters o f both the negative-exponential and the rectangularhyperbolic m odels that w ere obtained using the lo g -co rrect-to -erro r ratio w ere in no case differen t from those values o btained using the log d, m easure. S eco n d , in o rd er to m inim ize the influence o f response bias on the lo g -co rrect-to -erro r ratio, data w ere chosen for reanalysis only if no obvious sources o f response bias w ere p resent in the experim ental pro ced u re (for e x am p le, different rein fo rcer m ag n i­ tudes, d elay s, e tc .). In a d d itio n , w here possible, group data w ere used to o btain relatively bias-free log (C /E ) ratios. A veraging data across subjects tends to cancel out any idiosyncratic biases that individual subjects m ay show . T his is not, o f co u rse, the case if there is som e procedural biaser present. T he first set o f data is from an ex p erim ent reported by R oberts (1972) investi­ gating the effects o f rehearsal on short-term m em ory in the pigeon. U sing a standard D M T S p rocedure w ith d ifferent hues as the stim u li, R oberts m an ip u ­ lated “ re h ea rsa l” o f the sam ple hue by c hanging the fixed-ratio (FR ) req u ire­ m ent on the sam ple (center) key from F R 1 (one peck o n sam ple stim ulus initiated delay) through FR 5 to FR 15 (15 pecks on the sam ple stim ulus are necessary' before the introduction o f the delay). T he delay intervals betw een sam ple and com parison p resentation w ere 0, 1, 3, o r 6 seconds. Percentage o f correct responses grouped o v er 10 pigeons w as m easured from R o b e rts’ (1972) Figure 1 (p. 76) and converted to a lo g -co rrect-to -erro r ratio. T hese ratios are plotted in Fig. 2 .4 as a function o f delay for each sam plestim ulus FR requirem ent. F igure 2 .4 A show s the data fitted by the negativeexponential m odel (E quation 6 ), and Fig. 2 .4 B by the rectangular-hyperbolic m odel (E quation 8). B oth m odels provided very good fits to the data but the rectangular-hyperbolic m odel accounted for a hig h er percentage o f the data vari­ ance than did the n eg ative-exponential m odel. A lso , as is clearly seen in Fig. 2 .4 , it also proved to be a b etter pred icto r o f log d0 than w as the negativeexponential m odel. B oth m odels show ed increases in log d() as the FR requirem ent w as increased from FR 1 to FR 15. T h is result is consistent w ith W ic k elg re n ’s (1966) finding that d ' increased w hen the d uration o f the standard tone w as increased in a d elayed-com parison task w ith hum ans. In addition, as log d a increased, its halflife, h, increased and its rate o f d e ca y , b, d ecreased. R ehearsal in short-term m em ory ex p erim en ts, then, appears to affect both initial log d v and the decay param eters b and h. T his fin d in g is c o n sisten t w ith results from hum an short-term m em ory studies. F or e x am p le, H elly er (1962) found that rehearsal o f consonant trigram s raised the level o f the short-term retention curve (that is, increased log da) and decreased the rate at w hich the curve fell. A second set o f data w as afforded by an experim ent reported by G rant (1975). T his experim ent investigated proactive interference in pigeon short-term memory' by p receding a D M T S task (T rial 2) by a p rio r, co n flictin g , D M T S task (T rial 1). T he question G rant asked w as w hether T rial 1 w ould increase the rate o f fo rg et­ ting on T rial 2. If so , w hat w as the effect o f m ore than one T rial 1 presentation on

2. A

BEHAVIORAL MODELS

39

E XP O N E N T IA L

FIG. 2.4. D ata fro m R oberts (1972). Point estimates o f stimulus discriminability (log C /E ) as a func­ tion o f delay for three center-key FR requirements. Figure 2.4A shows the data fit by the negative-exponential model (Equation 6). Figure 2.4B shows the data fit by the rectangularhyperbolic model (Equation 8 ). (See text for further explanation.)

T rial 2 p erform ance? L og (C /E ) values fo r T rial 2 p erfo rm an ce w ere calculated from the p ercent-correct m atches reported in G ra n t’s Figure 1 (p. 210) and were plotted as a function o f the delay interval on the second D M T S task (that is, T rial 2). U sing grouped data for 10 pig eo n s, and four delay intervals (0, 2, 6, & 10 seconds), T able 2.1 show s the results o f the reanalysis for the fo u r groups (0, 1, 4 , & 6 T rial 1 p resen tatio n s, respectively). E xcellent data fits w ere obtained but, a g ain , the hyperbolic m odel provided an overall better description o f the data than did the ex ponential. A s T able 2.1 show s, both m odels show ed a decrease in initial discrim inability (log d j as the num ber o f preceding T1 trials w as increased from zero to six. In ad d itio n , b (rate o f decay) increased and h (the h a lf life) d ecreased , as log d o d ecreased for the 0, 1, and 4T1 p resentations. W hen 6T1 p resentations p receded T rial 2, h ow ever, the trends in both b and h reversed. It w ould appear, th en , that p roactive inter­ ference affects the initial discrim inability param eter, w hich supports G ra n t’s (1975) conclusion that prio r learning g enerates a “ re te n tio n ” deficit in pigeon short-term m em ory. Several studies o f p roactive interference in hum an sh o rt­ term recall m em ory also support these results (for e x am p le, K eppel & U n d er­ w ood, 1962). H o w ev er, the effects o f p roactive interference on the decay param ­ eters b and h still rem ain unclear, although the preceding reanalysis does tend to suggest an effect. D ata reported by B errym an, C um m ing, and N evin (1963) on the acquisition o f D M TS perform ance in pigeons allow the effects o f a third v a ria b le — train ­ ing— to be assessed w ithin the presen t quantitative fram ew ork. In this e x p eri­ m ent, the sam ple stim ulus w as eith er a red , g reen , or blue c en ter key. O ne peck on the c enter key ex tinguished the center-key light and, after a delay o f 0 , 1, 2, 4 , 10, or 24 seco n d s, turned on the tw o side-key co m p ariso n stim uli. A p eck on

40

M cCa r t h y

a n d w h it e

TABLE 2.1 Data from Grant (1975) Reanalyzed According to the Negative-Exponential Model (Equation 6) and the Rectangular-Hyperbolic Model (Equation 8) Hyperbolic Group

l»8

0 1 4 6

h

VAC

M SE

1.210 .986 .637 .614

2.338 .868 .293 .671

98% 92% 96% 82%

.002 O il .003 .014

Exponential Group

log d„

b

VAC

MSe

0 Tl 1 Tl 4 Tl 6 Tl

1.134 .985 .637 .620

.198 .584 .969 .582

90% 89% 96% 87%

.014 .015 .003 .010

Tl Tl Tl T!

the side key w ith a hue that m atched the cen ter-k ey hue produced rein fo rcem en t, a nonm atching side-key peck w as follow ed by blackout. M atching perform ance w as m easured across consecutive blocks o f 12 training sessions. Percent-correct m atches w ere calculated from B errym an et a l.’s (1963) Figure 4 (p. 106) and w ere converted to a log c o rrect-to -erro r ratio. T he resultant d iscrim inability estim ates w ere then plotted as a function o f delay. Figure 2.5 show s, as an e x am p le, log (C /E ) as a function o f delay for one subject (B ird 171). F or the sake o f brevity, only n o nlinear least-squares fit to the rectangularhyperbolic m odel (E quation 8) are show n, together w ith the values o f h and log d r> for four consecutive blocks o f training sessions (S essions 1 -4 8 ). (F unctions

Sessions 1-12 h=-54 logd0= 74

',

Sessions 13-24 1 71

110 • ‘•

FIG. 2.5. Data from Berryman, Gumming, a n d Nevin (1963). Point

'

Sessions 37-48 91 2 23

• 16

24 0 DELAY (sec)

16

24

estimates o f stimulus discriminability (log C /E ) as a function of delay for bird 171 across consecutive blocks of 12 training sessions. Nonlinear leastsquares fits to the rectangular-hyper­ bolic model (Equation 8) are shown as solid lines, together with the pre­ dicted half-life (h) and initial dis­ criminability (log d„).

2.

BEHAVIORAL MODELS

41

for S essions 4 9 - 6 0 w ere not n oticeably different from those for S essions 3 7 - 4 8 and so are not p resented here.) A s Fig. 2.5 clearly show s, log d 0 increased as a function o f the num ber o f training sessions, but no trend w as observable in the decay param eter, h. N on lin ear least-squares fits to the n eg ative-exponential m odel (not show n here) also produced increases in log d0, but no changes in b, across training sessions.

Conclusions from Animal Studies T he preceding reanalyses o f data from studies o f pigeon sh o rt-term m em ory have proved p articularly inform ative with regard to the effects o f certain variables on short-term m em ory. T h e reanalyses presen ted here used the D avison and T ustin (1978) m odel w ith tw o altern ativ e extensions to account for D M TS data. T hey suggest that variables having a strong influence on log dQ are training (B errym an et a l., 1963), rehearsal o f the sam ple stim ulus (R o b erts, 1972), and p rio r, inter­ fering trials (G ran t, 1975). T heir influence on the rate o f decay (b ) and the halflife (h) are, h o w e v er, m uch less clear. R ehearsal appears to have a significant influence on decay rate, as d o , p o ssib ly , prio r trials. It is to o soon to m ake any decisive c o n clu sio n s, and m ore research is needed to clarify the influence o f these variables on decay param eters. Insights w ill not be fo rth co m in g , h ow ever, if researchers continue to em ploy percent correct as a m easure o f m atching accuracy. O ne o f the m ajor strengths o f the D avison and T ustin (1978) m odel, like signal-detection theory, lies in its provision o f a true bias-free m easure o f discrim inative perform ance (log d). B ut, unlike signal-detection theory, the d erivation o f log d is not based on h y p o ­ thetical distributions o f the evidence variable. A lthough it is w ell know n in psychophysical research that percent co rrect is a biased m easure o f perform ance (for exam p le, W rig h t, 1974), researchers in the field o f anim al m em ory have continued, alm ost w ithout e x cep tio n , to use the p ercent-correct m easure as an index o f m atching accuracy. O ne m ust ask, th ere fo re, ju st w hat is decreasing over tim e in the various anim al m em ory p arad ig m s— accu racy itself, o r accuracy c ontam inated by response bias? T his question is p articularly im portant in relation to experim ents that em ploy an uncontrolled rein forcem ent-ratio procedure. In such a pro ced u re, the obtain ed-reinforcem ent ratio for correct m atches is free to covary w ith the a n im a l’s preference, and extrem e response biases m ay develop (M cC arthy, 1983; M cC ar­ thy & D avison, 1981a). In m atching-to-sam ple pro ced u res, for exam p le, anim als tend to develop strong position biases (see C um m ing & B errym an, 1965). Figure 2 .6 show s p oint estim ates o f response bias, obtain ed using E quation 4 w ith the proportions o f hits and false alarm s reported by Jans and C atan ia (1980) on a DM TS task , as a function o f delay. H ere, pigeons w ere required to peck the left o r right o f tw o w hite keys d ep en d in g on w hether a red or green stim ulus had appeared on the c en ter key. T he o p portunity to peck the w hite key w as delayed

42

M cCa r t h y

a n d w h it e

DELAY

FIG. 2.6. D a ta fro m J a n s a n d C a ta n ia (1980). Point estim ates o f response bias as a function of delay for both standard (STD ) trials and ac­ tivity (ACT) trials. ,jr- denotes infinity and data points with an arrow above them signify a bias value beyond the range of the Y -axis. (See text for fur­ ther explanation.)

(sec J

for 0 to 6 se c o n d s a fte r p re se n ta tio n s o f the red o r g reen c e n te r key. A ll c o rre c t left- and rig h t-k e y re sp o n se s p ro d u c e d a 3 -se co n d re in fo rc er. T h is is an u n c o n ­ trolled re in fo rc e m e n t-ra tio p ro c ed u re in w hich the bird m ay o b tain ali its re in fo r­ cers by re sp o n d in g e x c lu siv e ly on the one k ey . A s F ig. 2 .6 sh o w s, all birds d e v elo p ed ex tre m e re sp o n se b iases on both the stan d ard (S T D ) trials (th at is, no ev en ts o c cu rre d in the d e la y in te rv a l), and the a ctiv ity (A C T ) tria ls (th at is, fe ed e r o p e ratio n s o c cu rre d d u rin g the d e la y in te rv al). In fa ct, B ird 41 resp o n d ed e x clu siv ely on the right key w hen the d e la y interval w as in cre ased a b o v e 1 seco n d on A C T tria ls. T h e p e rc e n t-c o rre c t m easu re c a n n o t p ro v id e an in d ex o f acc u rac y (d isc rim in ab ility ) u n c o n ta m in a te d by th ese e x tre m e re sp o n se b iases. F o r c o m p a ris o n , F ig . 2 .7 sh o w s p o in t e stim a te s o f re sp o n se b ias fo r all six birds at e ac h d e la y in o u r lig h t-in te n sity d e la y e d -d e te c tio n e x p e rim e n t (E x p e ri­ m ent 1) re p o rte d e a rlie r. A s seen in F ig . 2 .7 , re sp o n se b ias did not d e v ia te sig n ific a n tly from the solid line re p re se n tin g zero b ias a s d e la y w as in cre ased .

=fcr- SI 52

53

2

4

6

8

10 12

DELAY (sec)

14

FIG. 2 .7 . E x p e rim en t 1. Point es­ tim ates o f response bias as a function o f delay for all six birds. The solid, horizontal line shows 0 bias, points above, a left-key bias, and points be­ low, a right-key bias.

2.

BEHAVIORAL MODELS

43

T his result w as to be ex p ected because dependent concurrent V I schedules w ere used in E xperim ent 1 to control the obtain ed -rein fo rcem en t ratio so that extrem e response biases could not develop as the delay interval w as increased (i.e ., discrim inability decreased). Until research ers com m ence using both a controlledreinforcem ent-ratio p ro ced u re (like E x p erim en t 1 reported here) and a m odel in which discrim inability and response bias can be independently m easured, q u a n ­ tification in anim al m em ory w ill not progress.

HUMAN MEMORY STUDIES By contrast, q uantification in hum an m em ory has been rife, and the literature abounds with m athem atical descriptions o f m em ory p ro cesses. N o attem pt is m ade here to cover this ex tensive literature. R ather, attention is focused ex­ clusively on those m odels that propose exponential decay functions (for ex am ­ ple, W ickelgren, 1969, 1970a, 1975b; W ickelgren & N o rm an , 1966). T he clo s­ est paradigm on the hum an level to D M TS o r D SM T S w ith the pigeon appears to be the d elayed-com parison p rocedure used to study hum an re cognition m em ory for nonverbal (for e x am p le, W ick elg ren , 1966, 1969; M assaro, 1970a, b) or verbal (for e x am p le, W ickelgren, 1967, 1970b, 1972) stim uli. In studies investigating hum an recognition m em ory for p itch , for exam p le, subjects are required to m ake “ sa m e -d iffe re n t” ju d g m e n ts o f the frequency o f tw o pure tones (the stan d ard , S , and the com p ariso n , C , tones) p resented su c ­ cessively and separated by a tim e interval (usually filled w ith an interference tone to prevent rehearsal o f the S tone d uring the delay interval). In verbal stu d ies, the discrim ination is com m only betw een w hich item s in a recognition test w ere on the original learning list (old item s) and w hich w ere not (new item s). T he subject, in effect, responds “ y e s” o r “ n o ” d epending on w hether he thinks the stim ulus is an old one. T hese m em ory tasks are very sim ilar to a (delayed) “ y e s n o ” detection task in p sychophysics. U n derstandably, m odels o f the m em ory process have developed in parallel w ith m odels o f the d etection process (G reen & Sw ets, 1974). W ith these p arad ig m s, accuracy has been found to d ecrease w ith increasing delay. T he e xponential-decay law is the m ost pervasive function in the analysis o f data from these p rocedures. It appears as a fundam ental equation in term s o f w hich m any o th er findings are expressed (B anks, 1970). For exam p le, using the d ecision-m aking assum ptions o f signal-detection theory and the d etection-theory discrim inability index d ' as a m easure o f m em ory stren g th , W ickelgren and N orm an (1966) developed a form al m odel for short-term recognition m em ory that proposed an exponential decay o f the strength o f the short-term m em ory trace. T he m odel has subsequently been developed and tested in a num ber o f experim ental studies. In these ex p erim en ts, em pirical strength-retention fu n c­ tions w ere derived by p lotting strength values (d 1) as a function o f the delay o f

44

M cCa r t h y

a n d w h it e

testing (for e x am p le, W ick elg ren , 1969, 1970b, 1972) o r as a function o f the n um ber o f intervening item s (for e x am p le, N o rm an , 1966; W ickelgren, 1970b; W ickelgren & N o rm an , 1966). T hese plots w ere fitted by eith er sim ple ex p o n en ­ tials (like E quation 6 here) or by the sum o f tw o exponentials. F or exam p le, W ickelgren (1969) suggested that th e m em ory trace fo r pitch w as com posed o f a short-term trace that d ecayed e xponentially at a rate o f app ro x im ately . 12 to .29 second " ’, and an in term ediate-term trace that decayed e xponentially at a rate o f a pproxim ately .02 second - '. S im ilarly, verbal m em ory has som e kind o f sh o rt­ term trace w ith a decay rate o f about .0 6 to .12 second - ', and a longer term m em ory trace w ith a decay rate o f .0 0 3 2 to .0067 se c o n d - 1 (W ickelgren, 1975a; W ickelgren & B erian, 1971). T he procedural ch aracteristics o f these hum an m em ory studies, like those o f the anim al m em ory studies discussed e arlie r, m ake them am enable to analysis w ithin the present delayed -d etectio n fram ew ork, that is, subjects are being asked to m ake a discrim ination betw een stim uli that are separated in tim e. It should be noted at the o u tse t, h o w e v er, that there is no desire here to address the question o f w hether d istinctions can be m ade betw een sho rt-term , interm ediate-term , o r long-term m em ory traces. N o r w ill the debate be entered as to w h eth er the forgetting o v er tim e o bserved in these studies is due to retroactive interference (num ber o f in tervening stim uli) or to the passage o f tim e, or both (see M assaro, 1970a, b, c; W ickelgren, 1970b). R ather, the prim ary interest in this c h ap ter is to d isco v er w h eth er the p re sen t re ctangular-hyperbolic m odel (E quation 8 ) could d escribe those data that have h itherto com m only been fitted by an exponential function. W ickelgren (1 9 6 6 ), for e x am p le, studied delayed com parison o f pitch w ith five hum an subjects. T rials began w ith a “ re a d y ” signal follow ed by the p re sen ­ tation o f a standard (S) tone lasting 2 seco n d s, follow ed im m ediately by an interference (I) tone o f 9 30 cycles p e r second (cps) and lasting 2 , 4 , o r 8 seconds. A t the term ination o f the I tone, a c om parison (C ) tone o f 2 seconds duration w as presented. T his w as follow ed by a 4 -second period in w hich the subjects w ere required to decide w hether the S and C tones w ere the “ sa m e ” o r “ d iffe re n t.” T here w ere three I tone d urations (that is, three delay intervals, f, = 2, 4 , & 8 seconds), three S tones (800, 820, & 840 cp s), and three C -S tone d ifferences (0, + 10, & + 1 5 cps). T h e zero-difference c onditions occurred as often as both positive-difference conditions co m b in ed . T hus, the procedure is d irectly a n alo ­ gous to the successive D M T S task ro utinely used to study anim al m em ory; that is, subjects w ere required to discrim in ate C tones separated tem porally from , and eith er identical to o r hig h er th an , the S tone. V alues o f d ' (w hich are linearly related to the present log d m easure o v e r the usual range, D avison & T u stin , 1978) for the com parison o f C = S and C = S + 10 for the first three subjects (taken from T able 1, p. 255; W ickelgren, 1966) w ere plotted here as a function o f the delay interval for each o f the three S-tone intensities (8 0 0 , 820, & 840 cp s). T ab le 2 .2 show s the results w hen the data w ere

2.

BEHAVIORAL MODELS

45

TABLE 2.2 Data from Wickelgren (1966) Reanalyzed According to the Negative-Exponential Model (Equation 6) and the Rectangular-Hyperbolic Model (Equation 8) Hyperbolic Subject JF

RR

JK

Exponential Subject JF

RR

JK

S tone (cps)

d'a

h

VAC

MSE

800 820 840 800 820 840 800 820 840

5.17 8.49 3.93 5.21 2.72 3.95 5.26 2.45 2.70

12.57 1.23 9.13 2.44 6.65 7.59 0.95 3.23 2.85

98% 99% 97% 96% 100% 100% 99% 96% 97%

.006 .009 .007 .022 .0003 .0004 .001 .004 .003

S tone (cps)

d'„

b

VAC

MSE

800 820 840 800 820 840 800 820 840

5.00 4.50 3.67 3.89 2.48 3.64 2.52 1.89 2.01

.058 .182 .070 .158 .089 .081 .208 .125 .133

99% 93% 94% 99% 100% 99% 99% 91% 92%

.003 .048 .012 .004 .0001 .003 .001 .010 .009

fitted by the rectangular-hyperbolic m odel (E quation 8). For com parison, the sim ple-exponential m odel (E quation 6) was also fitted to these data (but see later), and the results o f this analysis are also show n in T able 2.2. Both m odels provided very good fits to the data. The m ost significant outcom e o f this reanalysis, how ever, is that the present hyperbolic m odel accounted for the data in six o f the nine com parisons better than the sim ple-exponential m odel routinely used by W ickelgren and others in short-delay studies such as this. For both m odels, d ’0 (that is, estim ates o f the initial discrim inability o f the S and C tones) did not vary system atically with the intensity o f the S tone. H ow ever, the tw o m odels did predict very different d ' a values (as we saw earlier in the delayeddetection and anim al m em ory studies). For exam ple, for Subject JF , at S = 820 cps, the d ' a value predicted by the hyperbolic m odel w as 8 .4 9 , w hereas that predicted by the exponential was 4.5 0 . Sim ilarly, for Subject JK at S = 800 cps, the difference in predicted d ' 0 values was again tw ofold. In fact, in all nine cases, the hypobolic m odel predicted higher d ' 0 values than did the exponential. As no zero-delay condition w as run, these predictions cannot be com pared with

46

M cCa r t h y

a n d w h it e

obtained d '0 values. F o r tw o o f the subjects (JF and JK ), n eith er b n o r h varied system atically w ith the intensity o f the S tone. H ow ever, fo r Subject R R , as the S-tone intensity increased from 800 to 840 cp s, b (rate o f decay) d ecreased and h (the h a lf life) increased. T o su m m arize, th e n , the preced in g reanalysis dem o n strates th at, fo r shortdelay studies at least, although a sim ple exponential decay function fits the data well (as has com m only been reported in the literatu re), the rectangular-hyperbolic m odel p resented here is an equally adequate d e sc rip to r o f the data. H o w ev ­ er, w hen long-term retention is the variable under stu d y , it has b een w ell e stab ­ lished that forgetting rate d ecreases w ith increasing delay regardless o f w hich dependent m easure o f m em ory is used (W ick elg ren , 1975a). For e x am p le, W ick ­ elgren (1972) found that fo rgetting rate c o ntinuously decreased w ith increasing retention intervals from delays o f tens o f seconds up to delays o f o v e r 2 years. W ickelgren and B erian (1971) reported that decay w as m ore rapid at sh o rt delays a n d /o r slo w er at lo n g er delays than w as p redicted by a sim ple-exponential decay theory. T hese findings certainly elim inate a sim ple (constant-decay) exponential function for long-delay studies (but not, as W ickelgren, 1969, 1970b pointed out, nonexponential decay functions that are well Fitted by the sum o f tw o exponentials w ith very differen t decay rates; W augh & N orm an, 1965; W ick­ elgren, 1969). T he hyp erb o lic m odel (w ith its d e creasing decay rate o v e r tim e), how ever, rem ains a viable p roposition. T o test the efficacy o f the present h y p e r­ bolic m odel in describ in g data from longer delay stu d ies, w e reanalyzed data from an ex p erim ent reported by W ickelgren and B erian (1971). In this study, retention functions w ere determ ined fo r four hu m an subjects fo r recognition m em ory for one o r six letters at 14 different delays from 3 seconds to 5 m inutes. L og d, values w ere calculated (u sin g E quation 8 w ith the proportions o f correct and false recognition p robabilities reported by W ickelgren & B erian) and plotted as a function o f delay. F igure 2.8 show s the results o btained w hen these data w ere fitted by the rectan g u lar-h y p erb o lic m odel. A s Fig. 2.8 show s, the h y p e r­ bolic m odel provided a reasonable fit to the d ata, show n by the ra th e r sm all m ean-square errors o f the estim ates. In tw o cases. S ubjects M M and P S , p re­ dicted log d a values w ere low er for g re ater storage load. In the cases o f the o th er tw o subjects, h o w ev er, log d 0 values w ere m uch the sam e regardless o f storage load. In all fo u r cases, h (the tim e t at w hich log d n falls to one h a lf its initial value) w as sm aller for g re a te r storage load. T h u s, the hyperbolic m odel can handle data from long-term m em ory stu d ies, b u t no a ttem pt is m ade here to assess its m erits relative to o th er m odels (fo r exam p le, the exp o n en tial-p o w er m odel used by W ickelgren & B e ria n , 1971). Before leaving this section on hu m an m em o ry , it is d esirable to m ake a connection b etw een the present delay ed -d etectio n m odels (E quations 6 & 8) and a m ore recent m em ory m odel proposed by W ickelgren (1975b). In all his e x p eri­ m ental studies p rio r to 1975, W ickelgren m aintained a m ethodological d istin c ­ tion betw een m em ory tested at short d e la y s (usually less than about 10 seconds)

2.

*

_______

0 ----------1----------1 ----------*--------i---------- k ---------J ___.__________ J 0

50

100

150

BEHAVIORAL MODELS

47

* ----------i—

200 250 300 50 DELAY (se c )

100

150

200

250

300

FIG. 2 .8 . D ata fro m W ick elg ren a n d B eria n (1971). Point estim ates o f stim ­ ulus discrim inability at time t (log d,) as a function o f delay for four human subjects on a recognition mem ory task for one (open circles) or six (closed circles) letters. N onlinear least-squares fits to the rectangular-hyperbolic model (Equation 8) are shown as solid lines or dashed lines, respectively, for storage loads o f one or six letters. A lso shown for each subject and for each storage load are the predicted values o f the half-life (A), initial discrim inability (log d j , and the mean-square error (MSB) o f the estim ates.

and m em o ry tested at lo n g d e la y s (te n s o f se c o n d s to y e a rs). W ick elg ren g e n e r­ ally su p p o rte d the n o tio n o f som e k in d o f sh o rt-term m em o ry w ith a tim e c o n ­ stant in the o rd e r o f se c o n d s (th e “ sh o rt tra c e ” ) d istin c t from so m e ty p e o f lo n g er term m em o ry th at m ig h t last fro m ten s o f se c o n d s to y e ars (th e “ long tra c e ” ). H o w ev e r, W ic k elg re n (1 9 7 5 b ) su g g e ste d that no d istin c tio n need be m ade b etw een sh o rt-te rm and lo n g -te rm m e m o ry . R a th e r, he p ro p o se d a sin g le -tra c e , tw o -p ro ce ss th eo ry to d e sc rib e th e form o f re te n tio n fu n c tio n s. A g a in , w ith o u t en try in to th e sin g le -v e rsu s m u ltitra c e d e b a te , o r into d isc u ssio n o f e v id e n ce for o r a g ain st the e x iste n ce o f m em o ry tra c e s, p re se n ta tio n o f W ic k e lg re n ’s sin g le ­ trace th eo ry th at is p a rtic u la rly re le v a n t in th e p re se n t c o n te x t is n ow m ad e. A c co rd in g to h is th e o ry , th e re te n tio n fu n c tio n tak e s the fo llo w in g form : dm = \ ( 1 + p r ) - ^ (< ?-"')

(9)

w here \ , (3, tji, and -tt > 0 . In this e q u a tio n , d m re p re se n ts the d ' m ea su re o f m em o ry stren g th at tim e t, \ re p re se n ts the d e g re e o f le a rn in g , (3 and i{/ re p re se n t ra te p a ram ete rs c h a ra c te riz ­

48

M cCa r t h y

a n d w h it e

ing the tim e-decay p ro cess, and it represents the rate p aram eter (depending on the sim ilarity o f interpolated and learned m aterial) o f the interference process. In E quation 9 preced in g , -n w ill approxim ate 0 for m ost o f the e xperim ents that have been reanalyzed here because no retroactive stim uli occurred in the delay interval. (T he exception w as W ick elg ren ’s 1966 study in w hich an interference tone occurred d u rin g the delay interval. H ow ever, W ickelgren (1969) reported no effect on the form o f the retention functions w hen the intensity o f the in ter­ ference tone w as v a rie d .) E quation 9 thus becom es: d m = X(1 + p o - ’41

(10)

If t|/ equals un ity , E quation 10 becom es a re ctangular-hyperbolic function w ith X = d ' at t = 0, and p = 1/7?. A s has already been dem o n strated , a rectangularhyperbolic m odel, w ithout bein g raised to a pow er o th er than un ity , is an ad e­ quate d escrip to r o f all the data analyzed in this chapter. W ith high proportions o f the data variance accounted for by the hyperbolic m odel, it is doubtful w h eth er a pow er-function transform ation w ould m ake any significant gain in the fit b e ­ tw een the data and the m odel. T he only reason that a p o w er-function tran sfo rm a­ tion w ould be necessary w ould be in the event that the data system atically deviated from an h y perbolic-decay function. T he data that are av ailable from the published e xperim ents that are reanalyzed here are not detailed enough to allow this possibility to be assessed. E ssentially, th en , W ic k elg re n ’s (1975b) single-trace, tw o-process theory su p ­ ports an hyperbolic ex ten sio n , rath er than a sim ple-exponential ex ten sio n , o f the D avison and T ustin (1978) m odel to describe the d egradation in stim ulus d is­ crim inability o v e r tim e. W ith the relation betw een d iscrim inability and tim e thus specified, and the procedural sim ilarities betw een d elayed-detection and m em ory paradigm s noted, the effects o f differential reinforcem ent on m em ory-retention functions are now open to investigation. T he m ajor interest here is w hether discrim inability degraded by tim e (log d ,) is affected by differential rein fo rce­ m ent, o r w hether, as the present extension to the D avison and T ustin m odel sugg ests, log d , and reinforcem ent are independent o f one another.

ROLE OF DIFFERENTIAL REINFORCEMENT IN MEMORY RESEARCH D avison and T u stin ’s (1978) behavioral m odel o f d etection perform ance has allow ed the role o f differential reinforcem ent to be clearly d elineated fo r the first tim e in psychophysics (see M cC arthy & D avison, 1981a, for a rev iew ), and in classical-threshold studies (M cC arthy, 1983). H ere, the D a v iso n -T u stin m odel is used to investigate the role o f reinforcem ent in m em ory ex p erim en ts, a ne­ glected area o f investigation. In fa ct, to o u r know ledge, no current m odel o f

2.

BEHAVIORAL MODELS

49

anim al o r hum an m em ory can handle differential reinforcem ent o f the recall or recognition response. W hereas it is w ell know n that stim ulus discrim in ab ility is unaffected by reinforcem ent variation in the standard (no-delay) task (for ex am ­ ple, M cC arthy & D avison, 1980b), the question posed here is w h eth er d iscrim i­ nability w ould rem ain in dependent o f re inforcem ent variation w hen d ifferent tem poral delays occurred betw een presen tatio n o f the stim uli and the availability o f the choice response.

Experiment 2 T o answ er this q u e stio n , a second experim ent w as conducted (H arnett, M cC ar­ thy, & D av iso n , 1984) using the sam e subjects, ap p aratu s, and procedure as those reported earlier for E xperim ent 1 (the delayed -in ten sity -d iscrim in atio n task). T h e exceptions w ere that only tw o delay cond itio n s w ere carried out (3 seconds and 10 seconds). A t both o f these d elay s, the relativ e-rein fo rcer frequen­ cy for correct red- an d g reen-key responses w as varied by c h an g in g the d e p en ­ dent concurrent sch ed u les across four conditions: V I 17 seconds (red) VI 135 seconds (green); VI 75 seconds (red) VI 19 seconds (green); VI 19 seconds (red) VI 75 seconds (green); V I 135 seconds (red) V I 17 secon ds (green). A fifth data point for each delay (equal rein fo rcer frequency for co rrect red and green re ­ sponses, that is, VI 30 seconds VI 30 seconds) w as contrib u ted by tw o conditions o f E xperim ent 1. T his arrangem ent kept the overall rate o f reinforcem ent c o n ­ stant at four reinforcers per m inute throughout the experim ent. Sensitivity to relativ e-rein fo rcer frequency (ar ) w as estim ated for each o f the six birds by perform ing least-squares linear regression analyses on E quation 1 (S’, p erform ance) an d E quation 2 (S2 p erform ance). T his analysis w as carried out for each o f the tw o delay c onditions (3 seconds & 10 seconds) using each o f the last five se ssio n s’ data for each reinforcem ent condition ( i.e ., 25 data p oints p er analysis). T he slo p es and intercepts w ere estim ated w ith very sm all standard d eviations, and the m ean-square erro r o f the estim ates ranged from .01 to . 10. C om posite ar estim ates (one h a lf the sum o f the slopes o f E quations 1 & 2 ), and log d , estim ates (one h a lf the difference betw een the intercepts o f E quations 1 & 2) are show n in T ab le 2 .3 for each bird at both 3-seconds and 10-seconds delays. A s T able 2.3 sh o w s, for each bird, discrim inability (log d t) w as lo w er at the 10-seconds delay than at the 3-seconds delay. T he m ean log ^ 3 _ seconds» a v er­ aged across all six birds, w as .4 5 , w hereas that for log d l0 ^ seconds w as .18. H ow ever, there w as no significant d ifference in rein fo rcem en t sensitivity be­ tw een the tw o delays. (M ean ar = .44 at both the 3-seconds and 10 seconds delays.) T his con stan cy in the sensitivity o f b ehavior to changes in the relativereinforcer rate w ith co n co m itan t decreases in stim ulus discrim inability d em o n ­ strates the in d ependence from one an o th er o f discrim in ab ility (log d ,) and relative-reinforcer frequency variation in a c om m on anim al m em ory paradigm .

50

M cCa r t h y

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TABLE 2.3

Experim ent 2: Estimates of Reinforcement Sensitivity (ar) and Stim ulus D iscrim inability (log d,) at Each of Two Delays (f) (See Text for Further Inform ation) I: — 3 sec

t - 10 sec

Subject

ar

log d,

ar

log d,

51 52 53 54 55 56 MEAN

.47 .68 .19 .33 .63 .35 .44

.79 .72 .54 .38 .03 .26 .45

.62 .53 .42 .39 .36 .32 .44

.27 .24 .26 .15 -.0 2 .17 .18

GENERAL CONCLUSIONS T his chapter has ex tended the D avison and T ustin (1978) d etection m odel to account for data from tw o d elayed-detection studies in w hich the d iscrim inative stim uli and the av ailability o f the choice responses w ere tem porally separated. In addition, by q uantifying a d ecrease in m atching accuracy as a decrease in d is­ crim inability (log d r) over tim e, the m o d el’s ability to account for data from delayed m atching-to-sam ple and delayed -sy m b o lic-m atch in g -to -sam p le p ro ­ cedures com m only used to study anim al m em ory has been dem onstrated. A nim al m em ory e x p erim e n ters, lacking any conceptual fram ew ork for the separation o f response bias from sensory o r m em ory factors, have routinely used “ percent c o rre c t’’ to m easure the decrease in m atching-to-sam ple procedures. H ow ever, as has been show n here, the D avison and T ustin (1978) m odel, w ith its bias-free d iscrim inability m easure, p rovides an excellent d escription o f d elayedm atching p erform ance. W ithin this m odel, (1) initial learning can be c aptured by the discrim inability index (log d j , (2 ) d e creasing m atching accuracy o v er tim e can be m easured as a decrease in discrim in ab ility (log d,) o v er tim e, and (3) the various biasers ( e .g ., instructions, rein fo rcers, e tc .) can be captured by the d iscrim inability-free response-bias m easure (E quation 4 ). T his separation is not possible if “ percent c o rre c t’’ is used as the dependent variable. W ithin the D a v iso n -T u stin fram ew ork, the m easurem ent o f the m any variables know n to influence m em ory (for e x am p le, learning, rehearsal, interference, e tc .), and the effects o f differential reinforcem ent on these variables, m ay now be em pirically investigated.

2.

BEHAVIORAL MODELS

51

T he results o f the presen t reanalyses from hum an m em ory paradigm s suggest that a rectan g u lar-h y p erb o lic extension to the D avison and T ustin (1978) m odel (E quation 8) is a p articularly app ro p riate descrip to r o f the d ecrease in d iscrim i­ nability o bserved o ver tim e in these studies. W hereas a sim p le exponential function w ith its constant decay rate (E quation 6 ) m ay be adequate for shortdelay studies (that is, delays up to about 10 seconds), the rectangular-hyperbolic function w ith its decreasing decay rate is n ecessary to account for data from longer delay studies (that is, t > 10 seconds). T h u s, a re ctangular-hyperbolic e xtension o f the D a v iso n -T u stin m odel holds the p rom ise o f providing an e le ­ gant and c o m prehensive description o f b ehavior in a w ide v ariety o f delayeddetection and m em ory paradigm s. In all the m em ory p arad ig m s d iscussed h ere, the central concern has been w ith a tem poral separation betw een the to-be-rem em bered stim ulus and the su b ­ sequent choice response. T h u s, w e have interpreted the decrease in stim ulus discrim inability as a function o f increasing tim e betw een stim ulus presentation and the availability o f the choice response. H ow ever, because the response o ccasioned by a p articu lar stim ulus is d ela y ed , the rein fo rcer a sso ciated w ith that stim ulus is also delayed. Q uite clearly , tw o p ro cesses are occurring in m em ory experim ents: (a) a stim u lu s-re sp o n s e delay and (b) a stim u lu s-rein fo rcer delay. In other w ords, delay o f choice and delay o f rein fo rcem en t are confo u n d ed in this design. In a stan dard-detection situation, w hen the choice response is im m ediate­ ly available a fter stim ulus presen tatio n but the re in fo rc er for that response is delayed, stim ulus discrim inability decreases (Jenkins, personal com m unication). T he critical q uestion that m ust now be asked is: W hat causes d iscrim inability to fall? In o th er w ord s, w hat are the separate c ontributions o f a stim ulus-reinforcer d elay and a re sp o n se -rein fo rce r delay on stim ulus d iscrim inability at tim e t since stim ulus o ccu rren ce? C learly , this question can only be addressed w ithin a fram ew ork that provides an independent assessm ent o f the effects on b ehavior o f differential rein fo rcem en t and d iscrim inative stim uli. T he D a v iso n -T u stin (1978) m odel, ex tended by a rectangular-hyperbolic relation betw een d iscrim i­ nability and tim e, offers a m ost appropriate m eans o f addressing this critical issue.

ACKNOWLEDGMENTS W e are g ra te fu l to M ic h a e l D a v iso n , P e te r E. J e n k in s , T o n y N e v in , and H o w ard R ac h lin fo r c o n stru ctiv e c o m m e n ts o n an e a rlie r d ra ft o f this c h a p te r, to M ich a e l C o m m o n s fo r his h e lp in th e p re p a ra tio n o f th e m a n u sc rip t, a n d to the N ew Z e a la n d U n iv e rsity G rants C o m m itte e fo r its su p p o rt o f th e re se a rc h re p o rte d h ere. In a d d itio n , D ianne M cC a rth y w ould like to th a n k th e R o y al S o c ie ty o f N ew Z e a la n d fo r its g e n e ro u s g ra n t to w a rd the co st o f a tte n d in g th e S y m p o siu m .

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M cCa r t h y a n d w h it e

REFERENCES

Banks, W . P. (1970). Signal detection theory and human memory. Psychological Bulletin, 74, 8 1 99. Baum, W. M. (1974). On two types o f deviation from the m atching law: Bias and undermatching. Journal o f the E xperim ental A nalysis o f Behavior, 22, 23 1 -4 2 . Berryman, R ., Cum m ing, W . W ., & Nevin, J. A. (1963). Acquisition o f delayed m atching in the pigeon. Journal o f the E xperim ental Analysis o f Behavior, 6, 101-07. Blough, D. S. (1959). Delayed m atching in the pigeon. Journal o f the E xperim ental Analysis o f Behavior, 2, 151-60. Catania, A. C. (1979). Learning. Englewood Cliffs, NJ: P rentice-H all. Cum ming, W . W ., & Berrym an, R. (1965). The complex discrim inated operant: Studies o f matching-to-sample and related problems. In D. I. M ostofsky (E d.), Stim ulus generalization (pp. 2 8 4 330). Stanford: Stanford University Press. D ’Amato, M. R. (1973). Delayed m atching and short-term mem ory in m onkeys. In G. H. Bower (E d.), The psychology o f learning and motivation: A dvances in research and theory (Vol. 7, pp. 2 2 7 -6 9 ). New York: Academ ic Press. Davison, M. C ., & T ustin. R. D. (1978). The relation between the generalized m atching law and signal detection. Journal o f the E xperim ental A nalysis o f Behavior, 29, 331-36. Egan, J. P., Greenberg, G. Z ., & Schulm an, A. I. (1961). Operating characteristics, signal detec­ tability, and the method of free response. The Journal o f the Acoustical Society o f Am erica, 33, 993-1007. G rant, D. S. (1975). Proactive interference in pigeon short-term m em ory. Journal o f Experimental Psychology: A nim al B ehavior Processes, 104, 20 7 -2 0 . G rant, D. S ., & Roberts, W . A. (1973). Trace interaction in pigeon short-term m em ory. Journal o f Experim ental Psychology, 101, 2 1 -2 9 . Green, D. M ., & Swets, J. A. (1974). Signal detection theory and psychophysics. New York: Robert E. Krieger. Harnett, P., M cCarthy, D ., & Davison, M. (1984). Delayed signal detection, differential reinforce­ m ent, and short-term m emory in the pigeon. Journal o f the E xperim ental Analysis o f Behavior, 42, 87 -1 1 1 . Hellyer, S. (1962). Frequency of stim ulus presentation and short-term decrement in recall. Journal o f Experimental Psychology, 64, 650. Jans, J. E ., & Catania, A. C. (1980). Short-term rem em bering o f discrim inative stimuli in pigeons. Journal o f the Experim ental A nalysis o f Behavior, 34, 177-83. Keppel, G ., & Underwood, B. J. (1962). Proactive inhibition in short-term retention o f single items. Journal o f Verbal Learning and Verbal Behavior, 1, 153-161. M acPhail, E. M. (1980). Short-term visual recognition memory in pigeons. Quartery Journal o f Experimental Psychology, 32, 52 1 -3 8 . M aki, W. S ., M oe, J. C ., & Bierley, C. M. (1977). Short-term m emory for stimuli, responses, and reinforcers. Journal o f E xperim ental Psychology: Anim al Behavior Processes, 3, 156-77. M assaro, D. W. (1970a). Retroactive interference in short-term recognition memory for pitch. Journal o f Experim ental Psychology, 83, 3 2 -3 9 . M assaro, D. W. (1970b). Forgetting: Interference or decay. Journal o f Experim ental Psychology, 83. 2 3 8 -4 3 . M assaro, D. W . (1970c). Perceptual processes and forgetting in m em ory tasks. Psychological R eview , 77, 55 7 -6 7 . M cCarthy, D. (1981). Tow ard a unification of psychophysical and behavioural research. N ew Z ea ­ land Psychologist, 10, 2 -1 4 .

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McCarthy, D. C1983). M easures o f response bias at m inim um-detectable luminance levels in the pigeon. Journal o f the E xperim ental Analysis o f Behavior, 39, 87 -1 0 6 . McCarthy, D ., & Davison, M. (1979). Signal probability, reinforcem ent and signal detection. Journal o f the E xperim ental Analysis o f Behavior, 32, 37 3 -8 6 . McCarthy, D ., & D avison, M. (1980a). On the discrim inability of stim ulus duration. Journal o f the Experimental Analysis o f Behavior, 33, 187-211. M cCarthy, D ., & D avison, M. (1980b). Independence o f sensitivity to relative reinforcem ent rate and discrim inability in signal detection. Journal o f the Experim ental A nalysis o f Behavior, 34, 2 7 3 -8 4 . M cCarthy, D ., & D avison, M. (1981a). Towards a behavioral theory of bias in signal detection. Perception and Psychophysics, 29, 3 7 1 -8 2 . McCarthy, D ., & Davison, M. (1981b). M atching and signal detection. In M. L. Com mons & J. A. Nevin (E ds.), Quantitative analyses o f behavior: Vol. I , Discrim inative properties o f reinforcement schedules (pp. 393 -4 1 7 ). Cam bridge, MA: Ballinger. McCarthy, D ., & D avison, M. (1982). Independence o f stim ulus discrim inability from absolute rate of reinforcem ent in a signal-detection procedure. Journal o f the Experim ental Analysis o f Behavior, 37, 37 1 -8 2 . McCarthy, D ., & Davison, M. (1984). Isobias and alloiobias functions in animal psychophysics. Journal o f E xperim ental Psychology: A nim al B ehavior Processes, 10, 390-409. M cCarthy, D ., D avison, M ., & Jenkins, P. (1982). Stim ulus discrim inability in free-operant and discrete-trial detection procedures. Journal o f E xperim ental Analysis o f Behavior, 37, 199-215. Nelson, K. R ., & W asserm an, E. A. (1978). Tem poral factors influencing the pigeon’s successive m atching-to-sample perform ance: Sam ple duration, intertrial interval, and retention interval. Journal o f the E xperim ental A nalysis o f Behavior, 30, 153-62. Nevin, J. A. (1970). On differential stim ulation and differential reinforcem ent. In W. C. Stebbins (E d.), A nim al psychophysics (pp. 4 0 1 '4 2 3 ). New York: A ppleton-C entury-C rofts. Norman, D. A. (1966). Acquisition and retention in short-term m em ory. Journal o f Experimental Psychology, 72, 36 9 -8 1 . Roberts, W. A. (1972). Short-term retention in the pigeon: Effects of repetition and spacing. Journal o f Experim ental Psychology, 94, 7 4 -8 3 . Shimp, C. P. (1976). Organization in memory and behavior. Journal o f the Experim ental Analysis o f Behavior, 26, 113-30. Shimp, C. P., & M offitt, M. (1977). Short-term m emory in the pigeon: Delayed-pair-com parison procedures and som e results. Journal o f the Experimental A nalysis o f Behavior, 28, 13-25. Stubbs, D. A ., & Pliskoff, S. S. (1969). Concurrent responding with fixed relative rate o f reinforce­ ment. Journal o f the E xperim ental A nalysis o f Behavior, 12, 88 7 -9 5 . W asserman, E. A ., Nelson, K. R ., & Larew, M. B. (1980). Memory for sequences o f stimuli and responses. Journal o f the Experim ental A nalysis o f Behavior, 34, 4 9 -5 9 . Waugh, N ., & Norm an, D. (1965). Primary memory. P sychological Review, 72, 89 -1 0 4 . W hite, K. G ., & M cKenzie, J. (1982). Delayed stim ulus control: Recall for single and relational stimuli. Journal o f the E xperim ental A nalysis o f Behavior, 38, 3 0 5-312. W ickelgren, W. A. (1966). Consolidation and retroactive interference in short-term recognition memory for pitch. Journal o f Experim ental Psychology, 72 , 2 5 0 - 59. W ickelgren, W. A. (1967). Exponential decay and independence from irrelevant associations in short-term recognition m emory for serial order. Journal o f Experim ental Psychology, 73, 165— 71. W ickelgren, W. A. (1969). Associative strength theory o f recognition mem ory for pitch. Journal o f M athem atical Psychology, 6, 13-61. W ickelgren, W . A. (1970a). M ultitrace strength theory. In D. A. Norman (E d.), M odels o f Human M emory (pp. 6 5 -1 0 2 ). New York: Academ ic Press.

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W ickelgren, W . A. (1970b). Tim e, interference, and rate of presentation in short-term recognition memory for items. Journal o f M athem atical Psychology, 7, 2 1 9 -3 5 . W ickelgren, W. A. (1972). Trace resistance and the decay o f long-term m em ory. Journal o f M athe­ matical Psychology, 9, 4 1 8 -5 5 . W ickelgren, W . A. (1975a). The long and the short o f m em ory. In D. Deutsch & J. A. Deutsch (E ds.), Short-term m em ory (pp. 4 1 -6 3 ). New York: Academic Press. W ickelgren, W. A. (1975b). M ore on the long and short of memory. In D. Deutsch & J. A. Deutsch (Eds.) Short-term m em ory (pp. 6 5 -7 2 ). New York: Academ ic Press. W ickelgren, W. A .. & Berian, K. M. (1971). Dual trace theory and the consolidation o f long-term memory. Journal o f M athem atical Psychology, 8, 4 0 4 -1 7 . W ickelgren, W. A ., & Norm an, D. A. (1966). Strength m odels and serial position in short-term recognition memory. Journal o f M athem atical Psychology, 2, 31 6 -4 7 . W ilkie, D. M ., Sum m ers, R. J ., & Spetch, M. L. (1981). Effect o f delay-interval stimuli on delayed sym bolic m atching to sam ple in the pigeon. Journal o f the E xperim ental Analysis o f Behavior, 35, 153-60. W ilkie, D. M ., & W’ilson, C. S. (1977). Control of pigeon’s pecking by trace stimuli. Journal o f the Experimental A nalysis o f Behavior, 27, 2 9 3 -9 9 . W right, A. A. (1974). Psychom etric and psychophysical theory within a fram ework o f response bias. Psychological Review, 81, 3 2 2 -3 4 7 .

3

An Adjusting Procedure for Studying Delayed Reinforcement

Jam es E. M azur Harvard University

As m any o f the chapters in this volum e illustrate, a ho st o f pro ced u res have been used to study choice b etw een d elayed reinforcers. O ne d im ension that helps to distinguish am ong the differen t procedures is the duration o f the choice period. T he concu rren t-ch ain p rocedure (see D av iso n , this volum e; F antino, A barca, & D unn, this volum e) typically involves an extended choice period in w hich m any responses m ay be em itted . A t the o th er extrem e are p rocedures w ith very b rie f choice perio d s, in w hich each trial includes only a single-choice response (E isenberger & M asterson, this volum e). B oth types o f procedure have th eir strengths and w eaknesses. A m ajor advantage o f m ultiple-response procedures is that they usually produce g radations o f choice proportions that provide inform ation about the degree o f p reference for one alternative o v er another. In co n trast, choice proportions are less inform ative in single-response p ro ced u res, because subjects often show near-ex clu siv e p reference for one altern ativ e o r the other. T o the extent that n ear-exclusive p reference is o bserved in a single-response p rocedure, this procedure can indicate w hich alternative is preferred but not how strongly it is preferred. A disadvantage o f m ultiple-response pro ced u res, h o w ev er, is that w hen d e ­ layed reinforcers are under investigation the tim e spent in the choice period serves as an ad ditional delay that com bines in som e ill-defined w ay w ith the nom inal delay to determ in e ch o ice. T hus Fantino (1969) show ed that choice p roportions in a c o n cu rren t-ch ain schedule depend not only on the delays before reinforcem ent (in the second link o f the chain) but also on the d u ration o f the choice period (the average length o f the initial link). In a single-response pro­ cedure, on the o th er h an d , the choice period is as b rie f as possible, so that the actual delay betw een response and reinforcem ent is essentially the sam e as the 55

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nom inal delay. If o n e ’s goal is to understand the relationship betw een delay and choice behavior, the sim plicity o f the single-response p rocedure m akes it appealing. A lthough the single-response p rocedure does not provide inform ation about the degree o f p referen ce, it can be used to estim ate the “ indifference p o in t” betw een tw o alternative reinforcers. F o r e x am p le, suppose a subject show s a preference for an im m ediate 2 -second re in fo rc er o v e r a 6 -second rein fo rcer d e ­ layed 6 seconds. F u rth erm o re, suppose this subject prefers the 6 -second rein­ forcer if its delay is only 4 seconds. By interpolation, w e can estim ate that the subject w ould be in different betw een an im m ediate 2 -second rein fo rcer and 6 second reinforcer delay ed ap proxim ately 5 seconds. (O f co u rse, o th er delays could be tested to m ake this interpolation m ore ex ac t.) T he e xperim ents reported in this c h ap ter w ere designed to obtain such in d if­ ference points betw een tw o alternatives as efficiently as possible. T o do so, an adjusting p ro c e d u re , o r w hat is som etim es called a titration schedule, w as e m ­ ployed. In an adjusting pro ced u re, som e aspect o f the experim ental situation (e .g ., the intensity o f a light o r a shock, the size o f a fixed-ratio requirem ent) is varied sy stem atically in response to the su b je ct’s behavior. A lthough adjusting procedures have been used in m any behavioral studies (e .g ., Field & B oren, 1963; R achlin, 1972; V erhave, 1963), no previous studies have used these p ro ­ cedures to estim ate an indifference point betw een tw o alternative reinforcers. B esides providing in form ation about delayed rein fo rcem en t, the present studies dem onstrate that an adjusting p rocedure can be profitably used to study choice betw een tw o reinforcers. T he general pro ced u re o f E xperim ent 1 can be sum m arized w ith the aid o f Fig. 3 .1 . Pigeons chose betw een 2 seconds o f grain a fter a fixed d elay and 6 seconds o f g rain a fte r a d elay that increased o r decreased d epending on the su b ject’s prio r choices. M ore sp ecifically , if a subject show ed a p reference for the 6 -second rein fo rcer, its delay w as increased on subsequent trials. If the subject show ed a p reference for the 2 -second rein fo rcer, the delay for the 6 second rein fo rcer w as d ecreased so as to increase its attractiveness. F igure 3.1 show s that w ithin a given condition ( e .g ., co ndition i) the delay for the 2-second reinforcer w as constant (as defined by a single point on the Jt-axis), w hereas the delay fo r the 6 -second re in fo rc er assum ed a range o f values (as depicted by the length o f the tw o -p o in ted arrow ). O nce subjects becam e acquainted w ith the adjusting p rocedure, the delays fo r the 6 -second rein fo rcer tended to fluctuate w ithin a relatively narrow ran g e, and the m iddle o f this range w as treated as a m easure o f the indifference p oint b etw een the tw o reinforcers. W hereas the delay for the 2 -second re in fo rc er w as constant w ithin a co n d itio n , it w as varied from condition to condition (as illustrated in Fig. 3 .1 , w here the delay fo r the 2-sec reinforcer is larg er in co ndition / than in co ndition i). In this w ay, a nu m b er o f indifference p oints could be obtained betw een these tw o re in fo rc er am o u n ts, and an “ indifference c u rv e ” c ould be plotted w ithin the c o ordinates o f Fig. 3 .1 . The

3.

STUDYING DELAYED REINFORCEMENT

57

cr UJ o oc 0 Uz

EXPERIM ENT

I

A

UJ

c o

cc o UJ

CO 1 CO

cr o Ll

A

S\/

c o '-r5 c o

_j UJ

Q

DELAY

FOR 2 - SEC REINFORCER

FIG. 3.1. The general procedure o f Experiment 1. The arrows show that the delay for the 6-second reinforcer was adjusted within a condition.

next section explains how such an indifference curve can provide insight into the nature o f rein fo rcer delay.

THE DELAY-OF-REINFORCEMENT FUNCTION AND AN INDIFFERENCE CURVE ANALYSIS A lthough it has long been recognized that the “ v a lu e ” o r effectiveness o f a reinforcer decreases w ith increasing d elay, there has been no consensus about w hich m athem atical e xpression best characterizes this re lationship. T he present studies w ere conducted to d istinguish betw een several sim ple decay functions and determ ine w hich function is m ost adequate. E ach o f the four equations selected for exam ination describes a function that is concave dow nw ard and that approaches a value o f 0 as delay approaches infinity. B ecause am ount o f re in ­ forcem ent also played a role in E xperim ent 1, each equation includes a param ­ eter, A , w hich is assum ed to be m onotonically related to the am ount o f rein fo rce­ m ent; that is, in each equation it is assum ed that A is larger for a 6 -second reinforcer than for a 2 -second rein fo rcer, but no assum ptions are m ade about how m uch larger. B ecause rein fo rcer value, V, is p roportional to A in each e quation, these equations assum e only that value is m onotonically related to am ount. In all four e quations, D represents re in fo rc er d elay , and A' is a free param eter that can

58

MAZUR

vary to account for individual differences am ong subjects o r procedural dif­ ferences am ong experim ents. Equation 1 is a sim ple exponential equation sim ilar to H ull’s (1943) delay function: Vl = A te ~ KD
],

Jo

R (s) =

+

Jo Both integrals w ere evalu ated at s = 1 for convenience. D etails o f th eir e v alu a ­ tion can be found in M cD ow ell and K essel (1979). S ubstituting these equations into E quation 7 gives As( \ - e

~ w*)e~