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HANDBOOK OF CAPTURE–RECAPTURE ANALYSIS

Ear-tagged female polar bear with 2 cubs on the sea ice 60 miles northeast of Prudhoe
Bay, Alaska, 1985. (Photo by Steven C. Amstrup)

HANDBOOK OF
CAPTURE–RECAPTURE ANALYSIS
Edited by
Steven C. Amstrup, Trent L. McDonald,
and Bryan F. J. Manly
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD

Copyright © 2005 by Princeton University Press
Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock,
Oxfordshire OX20 1SY
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Handbook of capture–recapture analysis / edited by Steven C. Amstrup, Trent L.
McDonald, and Bryan F. J. Manly.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-691-08967-6 (cl : alk. paper)
ISBN-13: 978-0-691-08968-3 (pb : alk. paper)
ISBN-10: 0-691-08967-1 (cl : alk. paper)
ISBN-10: 0-691-08968-X (pb : alk. paper)
1. Animal populations—Mathematical models. I. Amstrup, Steven C.
II. McDonald, Trent L., 1965– III. Manly, Bryan F. J., 1944–
QL752.H36 2005
591.7'88'015118—dc22 2004065440
British Library Cataloging-in-Publication Data is available
Printed on acid-free paper. ∞
pup.princeton.edu
Printed in the United States of America
10987654321

Contents
List of Illustrations ix
List of Tables xi
Preface xvii
One 1
Introduction to the Handbook
Bryan F. J. Manly, Trent L. McDonald, and Steven C. Amstrup
1.1 Introduction 1
1.2 Overview of Chapters 2 to 8 3
1.3 Maximum Likelihood with Capture–Recapture Methods 9
1.4 Model Selection Procedures 17
1.5 Notation 19
Two 22
Classical Closed-population Capture–Recapture Models
Anne Chao and Richard M. Huggins
2.1 Introduction 22
2.2 Structure of Capture–Recapture Experiments and Data23
2.3 Early Models and Estimators 26
2.4 Limitations of Early Models and the Motivation for
More General Models 34
2.5 Chapter Summary 35
Three 36
Classical Open-population Capture–Recapture Models
Kenneth H. Pollock and Russell Alpizar-Jara
3.1 Introduction 36
3.2 The Original Jolly-Seber Model 38
3.3 The Jolly-Seber Likelihood Components 44
3.4 Restrictions and Generalizations of the Jolly-Seber Model45
3.5 Age-dependent Models 46
3.6 Goodness-of-Fit and Model Selection Issues 47
3.7 Examples 48
3.8 Conclusions 55
3.9 Chapter Summary 55

Four 58
Modern Closed-population Capture–Recapture Models
Anne Chao and Richard M. Huggins
4.1 Introduction 58
4.2 Discrete-time Models with Unequal Catchabilities 58
4.3 Continuous-time Models 78
4.4 Computing Considerations 85
4.5 Chapter Summary 86
Five 88
Modern Open-population Capture–Recapture Models
James D. Nichols
5.1 Introduction 88
5.2 Conditional Single-age Models 89
5.3 Conditional Multiple-age Models 102
5.4 Reverse-time Models 107
5.5 Unconditional Models 109
5.6 The Robust Design 116
5.7 Discussion 120
5.8 Chapter Summary 121
Six 124
Tag-recovery Models
John M. Hoenig, Kenneth H. Pollock, and William Hearn
6.1 Introduction 124
6.2 Assumptions of Brownie Models 128
6.3 Interpretation of the Tag-recovery Rate Parameter 128
6.4 Functional Linkage Between the Exploitation Rate and
the Survival Rate 131
6.5 Instantaneous Rate Models for Estimating Harvest and
Natural Mortality 131
6.6 Diagnostics and Tests of Assumptions 132
6.7 Preventing and Dealing with Failures of Assumptions134
6.8 Chapter Summary 140
Seven 142
Joint Modeling of Tag-recovery and Live-resighting Data
Richard J. Barker
7.1 Introduction 142
7.2 Data Structure 144
7.3 Simple Models 145
7.4 More General Models 156
7.5 Model Fitting and Assessment 157
vi CONTENTS

7.6 Tag Misreads and Tag Loss 161
7.7 Computing Considerations 161
7.8 Chapter Summary 163
Eight 165
Multistate Models
Carl J. Schwarz
8.1 Introduction 165
8.2 The Arnason-Schwarz Model 166
8.3 The Jolly-Seber Approach 177
8.4 Multisample Stratiﬁed Closed Populations 187
8.5 Multisample Stratiﬁed Open Populations 192
8.6 Chapter Summary 194
Nine 196
Examples
Trent L. McDonald, Steven C. Amstrup, Eric V. Regehr, and
Bryan F. J. Manly
9.1 Introduction 196
9.2 Open-population Analyses of Data on the
European Dipper 198
9.3 The Huggins Closed-population Model Applied to the
European Dipper Data 231
9.4 Assessing Goodness-of-Fit 236
9.5 Horvitz-Thompson Open-population Size Estimates 241
9.6 A Multistate (Multistrata) Model 245
9.7 Polar Bears in the Southern Beaufort Sea 247
9.8 Dead Recoveries of Mallard Ducks 254
9.9 Chapter Summary 263
Ten 266
Capture–Recapture Methods in Practice
Bryan F. J. Manly, Steven C. Amstrup, and Trent L. McDonald
10.1 Introduction 266
10.2 Closed-population Models 266
10.3 Open-population Models 267
10.4 Tag-recovery Models 269
10.5 Other Models 270
10.6 Model Selection 271
10.7 Known Ages 272
Appendix 275
A.1 Capability Matrix for Common Capture–Recapture
Software Packages 275
CONTENTS vii

A.2 General and Contact Information for Common
Capture–Recapture Software Packages Listed in Table A.1277
References 281
Contributor’s Notes 301
Index 303
viii CONTENTS

List of Illustrations
Frontispiece. Ear-tagged female polar bear with 2 cubs on the
sea ice 60 miles northeast of Prudhoe Bay, Alaska, 1985.
1.1. Jeff Mason ﬁres a shoulder-held cannon net used to
capture Bristle-thighed Curlews (Numenius tahitiensis)
on the Seward Peninsula, spring 1989. 2
1.2. Flowchart of the methods described in this book. 4
1.3. The full likelihood surface for the example with eight
sample times and information on the captures and
recaptures of 14 animals. 16
1.4. Black bear (Ursus americanus), near Council, Idaho,
1973, wearing numbered monel metal ear tags. 21
2.1. Endangered Néné goose (Nesochen sandvicensis)
wearing double leg bands. Island of Maui, Hawaii,
1998. 23
2.2. Fin-clipping Dolly Varden (Salvelinus malma malma) to
test retention of Floy Anchor Tag, Buskin River,
Kodiak Island, Alaska, 1992. 34
3.1. Flipper-tagged sea otter (Enhydra lutris), Monterey Bay,
California, 1995. 37
3.2. Jerry Hupp prepares to release a Canada goose (Branta
canadensis) after surgical implantation of a VHF
radio-transmitter, Anchorage, Alaska, 1999. 56
4.1. Mist-netting Bristle-thighed Curlews (Numenius
tahitiensis) on the Seward Peninsula, spring 1993. 59
4.2. Flipper-tagged female Californian sea lion (Zalophus
californianus) with her pup at Piedras Blancas,
California in 1995. 86
5.1. A leg-banded female Canada goose (Branta canadensis)
defends her nest near Anchorage, Alaska. 89
5.2. Estimated monthly survival probabilities and 95%
conﬁdence intervals from model (φ
s+t,p) for male and
female meadow voles at Patuxent Wildlife Research
Center. 103
5.3. Visible implant alpha-numeric tag in steelhead
(Oncorhynchus mykiss) smolt. 123
6.1. Half-length “Coded Wire Tag” implanted into 37-mm-
long pink salmon fry (Oncorhynchus gorbuscha.). 125

6.2. Bristle-thighed curlew (Numenius tahitiensis), marked
with Darvic leg bands and leg ﬂag, Seward Penninsula,
Alaska, 1990. 141
7.1. Tusk-banded Paciﬁc walrus (Odobenus rosmarus),
Round Island, Alaska, 1982. 143
7.2. Martha Tomeo creatively avoids being attacked by a
neck-collared Canada goose (Branta canadensis), as she
checks a nest near Anchorage, Alaska, 2000. 164
8.1. Close-up photo of a “Coded Wire Tag” for permanent
marking of many species of ﬁsh. 166
8.2. Radio-collared polar bear (Ursus maritimus) and new
cub on the sea ice north of Kaktovik, Alaska, April 1986. 194
9.1. Steven C. Amstrup gets acquainted with a polar bear cub
(Ursus maritimus) on the sea ice north of Prudhoe Bay,
Alaska, prior to application of ear tags and lip tattoos. 197
9.2. Pictorial representation of the three-dimensional array of
covariates used to parameterize capture–recapture
models. 225
9.3. Spreadsheet used to illustrate computation of the
Huggins model. 235
9.4. Annual population estimates for Southern Beaufort Sea
and Eastern Chuckchi Sea polar bears from the best
approximating capture–recapture model. 253
9.5. A poncho-marked and leg-banded sharp-tailed grouse
(Tympanuchus phasianellus) ready for release near
Decker, Montana, spring 1977. 265
10.1. Double ear-tagged black bear (Ursus americanus) cub
watches mom from an elevated perch, Boise National
Forest, Idaho, 1973. 274
x LIST OF ILLUSTRATIONS

List of Tables
1.1. Partial list of notation used throughout the book20
2.1. Individual capture history of 38 deer mice with six
capture occasions 24
2.2. Summary statistics for the deer mouse data 26
2.3. Fitted (expected) values for deer mouse data for
two models 30
3.1. Alligator between-year capture-history data collected by
Fuller (1981) for a population at Lake Ellis Simon,
North Carolina, from 1976 to 1979 48
3.2. Capture-history matrix for the Jolly-Seber model
(JOLLY) and the Cormack-Jolly-Seber model (MARK) 49
3.3. Estimates and approximate standard errors under the
Jolly-Seber model, the constant survival model, and the
constant survival and capture model for an alligator
population at Lake Ellis Simon, North Carolina, from
1976 to 1979 52
3.4. Tests for the Jolly-Seber model, the constant survival
model, and the constant survival and capture model for
an alligator population at Lake Ellis Simon, North
Carolina, from 1976 to 1979 53
3.5. Program MARK AIC model comparisons for an
alligator population at Lake Ellis Simon, North
Carolina, from 1976 to 1979 54
3.6. Comparison of Manly-Parr and Jolly-Seber parameter
estimates for the alligator data at Lake Ellis Simon,
North Carolina, from 1976 to 1979 55
4.1. Discrete-time models and associated estimation methods 73
4.2. Individual capture history of mouse with three
covariates: sex, age, and weight 75
4.3. Estimation results for various models with covariates 77
4.4. Hypothetical example of continuous-time data 79
4.5. Sighting frequencies of female grizzly bears 82
4.6. Estimates (with standard errors) for bear-sighting data 83
5.1. Adult capture history data for a six-period study of
meadow voles, Microtus pennsylvanicus, at
Patuxent Wildlife Research Center, Laurel,
Maryland, 1981 101

5.2. Parameter estimates under the general two-sex CJS
model (φ
s
*
t,p
s
*
t) for adult meadow voles studied at
Patuxent Wildlife Research Center, Laurel,
Maryland, 1981 102
5.3. Abundance and recruitment estimates under the JS
model for adult meadow voles studied at Patuxent
Wildlife Research Center, Laurel, Maryland, 1981 115
5.4. Estimated seniority parameters (γ
j
) and population
growth rates (λ
j) under the temporal symmetry models
(φ
t
,p
t
,γ
t
) and (φ
t
,p
t
,λ
t
) of Pradel (1996) for
capture–recapture data on adult male and female
meadow voles at Patuxent Wildlife Research Center 115
6.1. Lake trout tag-return data from Hoenig et al. (1998a)
showing the general structure of a tag-recovery matrix 126
6.2. Cell probabilities π
ijfor a general Brownie tagging model
withI=3 years of tagging and J=4 years of recaptures 127
6.3. Patterns in residuals from Brownie and instantaneous
rates models caused by failures of assumption 133
6.4. Table of residuals from the ﬁt of a model that incorrectly
assumes that newly tagged animals are fully mixed into
the population to the data in table 6.1 134
6.5. Cell probabilities π
ijfor an instantaneous rates tagging
model with I =3 years of tagging, J=4 years of
recaptures, and G=2 sexes 136
6.6. Expected recoveries for an age-structured Brownie model
withI=2 years of tagging and J=4 years of recaptures 137
6.7. Model ﬁts to the data in table 6.1 140
7.1. Encounter histories in program MARK format for the
joint analysis of live-recapture and dead-recovery data
from a study of paradise shelduck banded in the
Wanganui Region, New Zealand between 1986
and 1990 146
7.2. Extended m-array illustrating the combined recapture
and recovery data necessary for a joint analysis of
live-recapture and tag-recovery data 148
7.3. Extended m-array illustrating the joint live-recapture and
tag-recovery data from the paradise shelduck (Tadorna
variegata) banding study in the Wanganui Region,
New Zealand, 1986–1990 149
7.4. Summary statistics for the joint live-recapture and
tag-recovery data for paradise shelduck (Tadorna
variegata) banded in the Wanganui Region,
New Zealand, 1986–1990 153
xii LIST OF TABLES

7.5. Parameter estimates for the joint live-recapture and
tag-recovery data for paradise shelduck (Tadorna
variegata) banded in the Wanganui Region,
New Zealand, 1986–1990 under random emigration 153
7.6. Contingency table for the 1988 release cohort testing
whether the classiﬁcation of birds according to when
they were next encountered depends on their capture
history prior to release in 1988 155
7.7. Contingency table for the m
.3
(·)+z
3marked birds known
to be alive immediately after the 1988 sampling occasion
testing whether recapture or recovery after the 1988
sample depends on whether or not the bird was caught
in the 1988 sample 156
7.8. Model ﬁtting summary from ﬁtting the fully
time-dependent Markov, permanent, and random
emigration models to the paradise shelduck data 163
7.9. Parameter estimates for the paradise shelduck data
under random emigration from program MARK 163
8.1. Raw data (1986–1989) for the Canada goose study
(provided by J. Hines, Patuxent Wildlife Center) 173
8.2. Estimates from the goose data from the model
{φ
s*t,ψ
s*t,p
s*t} 174
8.3. Summary of model ﬁtting to the Canada goose data 175
8.4. Estimates from goose data from the ﬁnal model
{φ
s,ψ
s*(t
1=t
2,t
3),p
s*(t1=t2,t3)} 176
8.5. Summary statistics for female pink salmon tagged at
Glen Valley and recovered in the Fraser River Main
Stem arranged in a rectangular array 180
8.6. Detailed results from analyzing female Glen Valley
releases recovered in the Fraser Main Stem
only—ﬁnal pooling 186
8.7. Capture histories for the Barnacle goose experiment 190
8.8. Results from multistate multisample closed-model
ﬁtting to all areas for the Barnacle goose data 191
8.9. Estimates from model {p
s*t,ψ
s} (equal movement over
time, unequal resighting rates over time) for the
Barnacle goose example 193
9.1. Capture histories for 294 European dippers captured
between 1981 and 1987 in eastern France 199
9.2. Observed m-arrays for the European dipper data
in Table 9.1 200
9.3. Jolly-Seber estimates of survival and capture probabilities
and abundance for the European dipper example 202
LIST OF TABLES xiii

9.4. Manly-Parr estimates of number of animals known to be
alive, capture probability, and abundance from the
European dipper data 204
9.5. Parameter structure for European dipper model
(φ
s*t,p
s*t) 206
9.6. MARK parameter index matrices (PIMs) for the
European dipper model (φ
s*t,p
s*t) 207
9.7. Survival rate and capture probability estimates from
model (φ
s*t,p
s*t) for the European dipper data 209
9.8A. The MARK default design matrix for the European
dipper model (φ
s*t,p
s*t) 211
9.8B. An alternative parameterization of the design matrix for
the European dipper model (φ
s*t,p
s*t) 215
9.9. Estimates of beta coefﬁcients for the alternative
parameterization of the design matrix for the European
dipper model (φ
s*t,p
s*t), as shown in table 9.8B 216
9.10A. The design matrix for the European dipper model
(φ
s*t,p
s*t) using the treatment coding scheme and the
individual covariate sex
i 218
9.10B. An alternative parameterization of the design matrix
for the European dipper model (φ
s*t,p
s*t) using the
“treatment” coding scheme and the individual
covariatesex
i 219
9.11. Estimates of beta coefﬁcients for the alternative
parameterization of the design matrix for the European
dipper model (φ
s*t,p
s*t) using the “treatment” coding
scheme and the individual covariate sex
i, as shown in
table 9.10B 220
9.12. The MARK design matrix for the European dipper CJS
reduced-parameter model (φ
ﬂood,p
.) 223
9.13. The MARK design matrix for the simple example
model (φ
radio,p
radio), where radio is a time-dependent
individual covariate for a 5-occasion study 231
9.14. The MARK design matrix used to ﬁt the Huggins closed-
population model to the European dipper data 233
9.15. Chi-squared contingency table for Test 2 associated with
female European dippers and occasion #3 237
9.16. Chi-squared contingency table for Test 3 associated with
female European dippers and occasion #3 239
9.17. The MARK PIMs for the European dipper multistate
model (S
s
p
s
ψ
s
) 247
9.18. The variables considered in the polar bear study in the
Southern Beaufort Sea 250
xiv LIST OF TABLES

9.19. Brownie et al. (1985) format tag-recovery data for
29,000 mallards tagged over a 13-year period 256
9.20. Recovery matrix for mallard data, formatted for
input into program MARK 257
9.21. The MARK parameter information matrix (PIM) for
the survival parameter (S) of the Brownie model analysis
of the mallard band-recovery data 258
9.22. The MARK parameter information matrix (PIM) for the
recovery parameter (f) of the Brownie dead-recovery
model ﬁt to mallard band-recovery data 258
9.23. The MARK parameter information matrices (PIMs)
for the constant (homogenous) model (S,f) in the
Brownie model of for the mallard band-recovery data 260
9.24. The MARK design matrix for the reduced-parameter,
Brownie et al. model (S
cov,f
t) ﬁt to the mallard
band-recovery data 262
9.25. Covariate (ducks/pond) and estimates of survival
probabilities (S
i) and recovery probabilities (f
i) for
mallard tag-recovery data, using model (S
cov,f
i) 263
A.1. Capability matrix for common capture–recapture
software packages 275
A.2. General and contact information for common
capture–recapture software packages listed in table A.1 277
LIST OF TABLES xv

This page intentionally left blank

Preface
The ideato produce this book was conceived at the SEEM3 Conference
held in Dunedin, New Zealand, in 1999. This conference on capture–
recapture methods, as well as papers appearing in professional jour-
nalsand our personal experiences, convinced us that there is a wide gap
between statistician and biologist in the understanding of modern
capture–recapture analyses. In recent years, statisticians and mathemati-
cians have made great strides improving our ability to make use of data
collected when animals are repeatedly captured or observed. However,
whereas this ﬁeld of endeavor is as old as biology itself, we sensed that
the appreciation many practicing biologists have for modern methods
lags signiﬁcantly behind the recent mathematical and statistical develop-
ments. We have assembled the Handbook of Capture–Recapture Analysis
to guide biologists toward a greater appreciation of capture–recapture
methods in theory and practice.
This handbook is organized for ease of learning and understanding.
Critical introductory material and less complex methods are presented
early in the book. As the chapters increase in number (through to chap-
ter 8) so does the complexity of the material covered. Therefore, we sug-
gest that you carefully study chapter 1, before reading anything else. Af-
ter grasping the material therein, carefully read chapters 2, 3, and 4
before exploring the subsequent chapters. Once you have a solid grasp
of the concepts presented in those early chapters, it will be easier to ﬁnd
and understand descriptions of the more complex methods presented in
later chapters that may best suit your particular needs. Also, before
launching into methods described here, we encourage you to examine
the practical examples presented in chapter 9. These will help anchor
your understanding of the material that you read in the earlier chapters.
Finally, we encourage you to study the summaries in chapter 10. We feel
this approach will allow you to most efﬁciently learn and apply the ma-
terial in this volume to your particular research or management prob-
lems. As auxiliary information, a list of currently available software for
capture–recapture analysis is included in an appendix.
We would like to thank Nadine Wilson, Karyn Sernka, and Kim-
berly Bay for their valuable help in formatting the manuscript and for
compiling the references. We would also like to thank the authors
of the individual chapters who have persevered with us through this
process.

Western EcoSystems Technology, Inc. and the U. S. Geological Ser-
vices Alaska Science Center provided funding, in approximately equal
proportions, for the project.
Steven Amstrup, Trent McDonald, and Bryan Manly
June 2005
xviii PREFACE

HANDBOOK OF CAPTURE–RECAPTURE ANALYSIS

This page intentionally left blank

One
Introduction to the Handbook
BRYAN F. J. MANLY, TRENT L. M CDONALD,
AND STEVE C. AMSTRUP
1.1 Introduction
In September of 1802, Pierre Simon Laplace (1749–1827) used a capture–
recapture type of approach to estimate the size of the human popula-
tion of France (Cochran 1978; Stigler 1986). At that time, live births
were recorded for all of France on an annual basis. In the year prior to
September 1802, Laplace estimated the number of such births to be ap-
proximatelyX=1,000,000. These newly born individuals constituted
a marked population. Laplace then obtained census and live birth data
from several communities “with zealous and intelligent mayors” across
all of France. Recognizing some variation in annual birth rates, Laplace
summed the number of births reported in these sample communities for
the three years leading up to the time of his estimate, and divided by three
to determine that there were x=71,866 births per year (marked individ-
uals) in those communities. The ratio of these marked individuals to the
total number of individuals in the sampled communities, y=2,037,615
was then the estimate
of the proportion of the total population of France that was newly born.
On this basis, the one million marked individuals in the whole of France
is related to the total population Nas
Np≈1,000,000
so that
N≈=
1 000 000
0 0353
28 328 612
,,
.
,,
p==
71 866
2 037 615
0 0353
,
,,
.

This estimation procedure is equivalent to the Lincoln-Peterson capture–
recapture estimator described in chapter 2.
Although Laplace is commonly thought of as the ﬁrst to use the capture–
recapture idea, he was preceded by almost 200 years by John Graunt in his
attempts to use similar methods to estimate the effect of plague and the size
of populations in England in the early 1600s (Hald 1990). The theories
and applications of capture–recapture have moved far beyond the concepts
of John Graunt and Pierre Laplace in the ensuing centuries. Current meth-
ods do, however, share the basic concept, of ratios between known and
unknown values, that guided those pioneers.
Our purpose in this book is to provide a guide for analyzing capture–
recapture data that can lead the naive reader through basic methods, simi-
lar to those used by the earliest of workers, to an understanding of modern
state of the art methods. This handbook is intended primarily for biologists
who are using or could use capture–recapture to study wildlife populations.
To the extent practicable, therefore, we have kept mathematical details to
a minimum. We also have, beginning with this ﬁrst chapter, attempted to
explain some of the mathematical details that are necessary for a complete
conceptual understanding of the methodologies described. Also, authors
of each chapter have been encouraged to provide all the references that
are necessary to enable readers to obtain more details about the deri-
vations of the methods that are discussed. Therefore, this book also
will be a useful introduction to this subject for statistics students, and
2 MANLY, M CDONALD, AND AMSTRUP
Figure 1.1. Jeff Mason ﬁres a shoulder-held cannon net used to capture Bristle-
thighed Curlews (Numenius tahitiensis) on the Seward Peninsula, spring 1989.
(Photo by Robert Gill)

a comprehensive summary of methodologies for practicing biometri-
cians and statisticians.
The book is composed of three sections. Section 1 is this chapter,
which is intended to set the scene for the remainder of the book, to cover
some general methods that are used many times in later chapters, and
to establish a common notation for all chapters. Section 2 consists of
seven chapters covering the theory for the main areas of mark–recapture
methods. These chapters contain some examples to illustrate the analyti-
cal techniques presented. Section 3 consists of two chapters in which we
explicitly describe some examples of data sets analyzed by the methods
described in chapters 2 to 8. When useful throughout the book, we dis-
cuss computing considerations, and comment on the utility of the differ-
ent methods.
1.2 Overview of Chapters 2 to 8
Chapters 2 to 8 cover the main methods available for the analysis of
capture–recapture models. For those who are unfamiliar with these meth-
ods the following overviews of the chapters should be useful for clarify-
ing the relationships between them. Figure 1.2 contains a ﬂowchart of the
capture–recapture methods described in this section of the book. This
ﬂowchart may help to clarify the relationship between analyses, and will
indicate the chapter (or section) containing methods appropriate for a
particular data set.
Closed-population Models
A closed population is one in which the total number of individuals is
not changing through births, deaths, immigration, or emigration. The ﬁrst
applications of capture–recapture methods were with populations that
were assumed to be closed for the period of estimation. It is therefore
appropriate that the ﬁrst chapter in section 2 of this book should describe
closed-population models. In practice, most real populations are not
closed. Sometimes, however, the changes over the time period of interest
are small enough that the assumption of closure is a reasonable approxi-
mation, and the effects of violating that assumption are minimal. For this
reason, the analysis of capture–recapture data from closed populations
continues to be a topic of interest to biologists and managers.
In chapter 2, Anne Chao and Richard Huggins begin by discussing some
of the early applications of the capture–recapture method with one sample
to mark some of the individuals in a population, and a second sample to
INTRODUCTION TO THE HANDBOOK 3

see how many marked animals are recaptured. The data obtained from
the two samples can be used to estimate the population size.
A natural extension of the two-sample method, which can be traced
back to Schnabel (1938), involves taking three or more samples from a
population, with individuals being marked when they are ﬁrst caught.
The analysis of data resulting from such repeated samples, all within a
time period during which the population is considered closed, is also
considered in chapter 2. The goal still is estimation of the population
size, but there are many more models that can be applied in terms of
modeling the data. Chao and Huggins therefore conclude chapter 2 by
noting the need for more general models.
4 MANLY, M CDONALD, AND AMSTRUP
Huggins models
Section 4.2-
Models Incorporating
Covariates
Multi-state
models
Chapter 8
Otis models
Sections 2.3
and 4.2
Were
covariates
measured?
Were live
recaptures
obtained?
Jolly-Seber
models
Chapter 3
Tag recovery
models
Chapter 6
Modern open
population models
Chapter 5
Joint modeling of
live and dead
recovery
Chapter 7
Can measured
covariates explain
unequal
catchability?
Were individuals
captured in
different “states”?
Continuous
time models
Section 4.3
Were individuals
captured at
discrete times?
Were tags
recovered from
dead animals?
Is the
population open?
No Yes
No Yes No Yes
No YesNo Yes
No Yes
No Yes
Figure 1.2. Flowchart of the methods described in this book. Starting with Is
the population open?, unshaded boxes present Yes / No questions about the
characteristics of the capture–recapture study and data. The paths induced by
answers to these questions terminate at shaded boxes, which give the applicable
models and this volume’s chapter or section reference.

The discussion is continued by Chao and Huggins in chapter 4. There
they consider how the probability of capture can be allowed to vary with
time, the capture history of an animal, and different animals, through the
Otis et al. (1978) series of models. Other topics that are covered by Chao
and Huggins in chapter 4 are the incorporation of covariates that may
account for variation in capture probabilities related to different types of
individuals (e.g., different ages or different sexes) or different sample times
(e.g., the sampling effort or a measure of weather conditions), and a range
of new approaches that have been proposed for obtaining population size
estimates.
Basic Open-population Models
An open population is one that is (or could be) changing during the course
of a study, because of any combination of births, deaths, immigration, or
emigration. Because most natural wildlife populations are affected in this
way, the interest in using capture–recapture data with open popula-
tionsgoes back to the ﬁrst half of the 20th century when ecologists such
as Jackson (1939) were sampling populations that were open, and devel-
oping methods for estimating the changing population sizes, the survival
rates, and the number of individuals entering the populations between
sample times.
A major achievement was the introduction of maximum likelihood es-
timation for the analysis of open-population capture–recapture data by
Cormack (1964), Jolly (1965), and Seber (1965). This led to the devel-
opment of what are now called the Cormack-Jolly-Seber (CJS) and the
Jolly-Seber (JS) models. The CJS model is based solely on recaptures of
marked animals and provides estimates of survival and capture probabi-
lities only. The JS model incorporates ratios of marked to unmarked ani-
mals and thereby provides estimates of population sizes as well as survival
and capture probabilities. The fundamental difference between the two
is that the JS model incorporates the assumption that all animals are ran-
domly sampled from the population and that captures of marked and un-
marked animals are equally probable. The CJS model, on the other hand,
does not make those assumptions and examines only the recapture histo-
ries of animals previously marked.
The CJS and JS models are the main topics of chapter 3 by Kenneth H.
Pollock and Russell Alpizar-Jara. For the JS model, equations are provided
for estimates of population sizes at sample times, survival rates between
sample times, and numbers entering between sample times. In addition,
there is a discussion of versions of this model that are restricted in various
ways (e.g., assuming constant survival probabilities or constant capture
INTRODUCTION TO THE HANDBOOK 5

probabilities) or generalized (e.g., allowing parameters to depend on the
age of animals). The CJS model, which utilizes only information on the re-
captures of marked animals, is then discussed. As noted above, this model
has the advantage of not requiring unmarked animals to be randomly
sampled from the population, but the disadvantage that this allows only
survival and capture probabilities to be estimated. Population sizes, which
were the original interest with capture–recapture methods, cannot be di-
rectly estimated without the random sampling, which allows extrapolation
from the marked to the unmarked animals in the population.
Recent Developments with Open-population Models
Since the derivation of the original CJS and JS models there have been
many further developments for modeling open populations, which are
covered by James D. Nichols in chapter 5. These developments are pri-
marily due to the increasing availability of powerful computers, which
make more ﬂexible, but also much more complicated, modeling procedures
possible. Parameter values can be restricted in various ways or allowed
to depend on covariates related either to the individuals sampled or to
the sample time.
The ﬂexible modeling makes it possible to consider very large numbers
of possible models for a set of capture–recapture data, particularly if the
animals and sample times have values of covariates associated with them.
The larger number of possible models that can be considered with modern
computerized approaches elevates the importance of objective model se-
lection procedures that test how well each model ﬁts the data. It always
has been necessary to assess whether models were apt, how well they ﬁt
the data, and which of the models should be considered for ﬁnal selec-
tion. Our greater ability now to build a variety of models is accompanied
by a greater responsibility among researchers and managers to perform
the comparisons necessary so that the best and most appropriate models
are chosen.
The methodological developments in chapter 5 were motivated prima-
rily by biological questions and the need to make earlier models more bi-
ologically relevant. This underlying desire to generalize and extend the
CJS model resulted in several new models. These methods, covered in
chapter 5, include reverse-time modeling, which allows population growth
rates to be estimated; the estimation of population sizes on the assumption
that unmarked animals are randomly sampled; models that include both
survival and recruitment probabilities; and the robust design in which in-
tense sampling is done during several short windows of time (to meet the
assumption of closure) that are separated by longer intervals of time during
which processes of birth, death, immigration, and emigration may occur.
6 MANLY, M CDONALD, AND AMSTRUP

Population size estimates are derived from capture records during the short
time periods of the robust design, and survival is estimated over the longer
intervals between periods.
Tag-recovery Models
The tag-recovery models that are discussed by John M. Hoenig, Kenneth
H. Pollock, and William Hearn in chapter 6 were originally developed
separately from models for capture–recapture data. These models are pri-
marily for analyzing data obtained from bird-banding and ﬁsh-tagging
studies. In bird-banding studies, groups of birds are banded each year for
several years and some of the bands are recovered from dead birds, while
in ﬁsh-tagging studies, groups of ﬁsh are tagged and then some of them
are recovered later during ﬁshing operations. The early development of
tag-recovery models was started by Seber (1962), and an important mile-
stone was the publication of a handbook by Brownie et al. (1978) in
which the methods available at that time were summarized.
The basic idea behind tag-recovery models is that for a band to be re-
covered during the jth year of a study, the animal concerned must sur-
vive for j−1 years, die in the next year, and its band be recovered. This
differs from the situation with capture–recapture data where groups of
animals are tagged on a number of occasions and then some of them are
recaptured later while they are still alive.
Joint Modeling of Tag-recovery and Live-recapture
or Resighting Data
It is noted above that the difference between standard capture–recapture
studies and tag-return studies is that the recaptures are of live animals in
the ﬁrst case, while tags are recovered from dead animals in the second
case. In practice, however, the samples of animals collected for tagging
do sometimes contain previously tagged animals, in which case the study
provides both tag-return data and data of the type that comes from stan-
dard capture–recapture sampling.
If there are few recaptures of live animals, they will contribute little
information and can be ignored. If there are many live recaptures, how-
ever, it is unsatisfactory to ignore the information they could contribute to
analyses, leading to the need for the consideration of methods that can use
all of the data. This is the subject of chapter 7 by Richard J. Barker, who
considers studies in which animals can be recorded after their initial tag-
ging (1) by live recaptures during tagging operations, (2) by live resight-
ings at any time between tagging operations, and (3) from tags recovered
from animals killed or found dead between tagging occasions. In addition
INTRODUCTION TO THE HANDBOOK 7

to describing the early approaches to modeling these types of data, which
go back to papers by Anderson and Sterling (1974) and Mardekian and
McDonald (1981), Barker also considers the use of covariates, model
selection, testing for goodness of ﬁt, and the effects of tag loss.
Multistate Models
The original models of Cormack (1964), Jolly (1965), and Seber (1965)
for capture–recapture data assumed that the animals in the population be-
ing considered were homogeneous in the sense that every one has the same
probability of being captured when a sample was taken, and the same
probability of surviving between two sample times. Later, the homogene-
ity assumption was relaxed, with covariates being used to describe differ-
ent capture and survival probabilities among animals. However, this still
does not allow for spatial separation of animals into different groups, with
random movement between these groups. For example, consider an animal
population in which members move among different geographic locales
(e.g., feeding, breeding, or molting areas). Also consider that survival and
capture probabilities differ at each locale. Covariates associated with the
individual animals or sample times are insufﬁcient to model this situation,
and the movement between locations must be modeled directly.
In chapter 8, Carl J. Schwarz considers the analysis of studies of this
type, where the population is stratiﬁed and animals can move among strata
or states while sampling takes place. Analyses for these types of situations
were ﬁrst considered by Chapman and Junge (1956) for two samples from
a closed population, extended for three samples from an open population
by Arnason (1972, 1973), and to ksamples from an open population by
Schwarz et al. (1993b) and Brownie et al. (1993). These models can be
used to study dispersal, migration, metapopulations, etc. Although the
models were developed primarily to account for the physical movement
of animals among geographic strata, the models described in chapter 8
also work where states are behavioral (e.g., breeding or nonbreeding an-
imals each of which may be more or less available than the other) or habi-
tat related rather than just geographic. Chapter 8 also shows how live
and dead recoveries can be treated as different states, and describes how
covariates that change randomly with time can be used to describe indi-
viduals in different states.
The ﬁrst part of chapter 8 deals with the estimation of migration, cap-
ture, and survival probabilities for a stratiﬁed population, using a gen-
eralization of the Cormack-Jolly-Seber model. The last part considers
the estimation of population size using two or several samples from
a stratiﬁed closed population, and using several samples from an open
population.
8 MANLY, M CDONALD, AND AMSTRUP

1.3 Maximum Likelihood with Capture–Recapture Methods
Early methods for analyzing capture–recapture and tag-recovery data re-
lied upon ad hoc models for their justiﬁcation. However, by the late 1960s
the use of well-deﬁned probability models with maximum likelihood esti-
mation of the unknown parameters had become the standard approach.
The method of maximum likelihood, which is known to produce estimates
with good properties under a wide range of conditions, consists of two
steps. First, there is the construction of a model that states the probability
of observing the data as a function of the unknown parameters that are of
interest. This is called the likelihood function. Second, the estimates of the
unknown parameters are chosen to be those values that make the like-
lihood function as large as possible, i.e., the values that maximize the
likelihood.
For the data considered in this book, three related types of likelihood
functions need to be considered. The ﬁrst and simplest arises by modeling
the probability of observing the data from single independent animals, and
then constructing the full likelihood as the product of probabilities for
all animals. The second type of likelihood arises when data are grouped,
which leads to use of the multinomial distribution to describe the proba-
bility of observing all the capture data. The third type of likelihood arises
when data are collected from independent groups, which leads to likeli-
hoods that are the product of multinomial distributions.
To illustrate the ﬁrst type of likelihood, consider a four-sample exper-
iment where n
1animals are marked in the ﬁrst sample, no more mark-
ing is done, and recapture data are obtained during samples 2, 3, and 4.
Suppose that the probability of an animal surviving from the time of the
jth sample to the time of the next sample is φ
j(j=1, 2, or 3), and the
probability of a live animal being captured in the jth sample is p
j.
Assume further that a particular animal was captured on the ﬁrst cap-
ture occasion, and resighted on the third and fourth capture occasions.
The history of captures and resightings for this animal can be indicated
by the pattern of digits 1011, where a 1 in the jth position (counting
from the left) indicates capture or resight during the jth occasion, and 0
in the j th position indicates that the animal was not seen during the jth
occasion. Under these assumptions, the probability of observing this
particular pattern of resightings, conditional on the original capture, is
P=φ
1(1−p
2)φ
2p
3φ
3p
4 (1.1)
which is obtained by multiplying together the probabilities of surviving
until the second sample (φ
1), not being captured in the second sample
INTRODUCTION TO THE HANDBOOK 9

(1−p
2), surviving from the second to third sample times (φ
2), getting
captured in the third sample (p
3), surviving from the third to fourth sample
times (φ
3), and ﬁnally getting captured in the fourth sample (p
4).
Probabilities of capture and survival for each animal in a series of sam-
ples can be used to describe the probabilities of their capture histories as in
equation 1.1. The likelihood of observing all of the data is then the prod-
uct of the probabilities, i.e.,
(1.2)
whereP
jis the probability for the jth animal, assuming that the history
for each animal is independent of the history for all of the other animals.
Maximum likelihood estimation would involve ﬁnding the values of the
survival and capture probabilities that maximize L. Note that φ
3andp
4
cannot be estimated individually in this example because it is not possi-
ble to tell whether a large number of captured animals in the fourth and
last sample is due to a high survival rate from the previous sample time
or a high probability of capture. Therefore, only the product φ
3p
4can
estimated. Similarly, the capture probability cannot be estimated for the
ﬁrst occasion. In general, this sort of limitation applies at both ends of
capture–recapture histories.
The second type of likelihood is for grouped data. In this case, the
multinomial distribution is used to give the probability of the observed
data. With this distribution there are mpossible types of observation,
with the ith type having a probability θ
iof occurring, where
θ
1+θ
2+⋅⋅⋅+θ
m=1
If there is a total sample size of n, with n
iobservations of type ioccur-
ring so that n=n
1+n
2+⋅⋅⋅+n
m, then the multinomial distribution
gives the probability of the sample outcome (the likelihood) to be
(1.3)
a probability statement that is justiﬁed in many elementary statistics texts.
Typically, when a multinomial likelihood function like this occurs
in the following chapters then the θparameters will themselves be
functions of other parameters, which are the ones of real interest. For
example, consider a three-sample capture–recapture study on a closed
L
n
nn n
m
nn n
m=
!
!! !
12
12
⋅⋅⋅
⋅⋅⋅θθ θ
LP
j
j
n=
=
∏
1
1
10 MANLY, M CDONALD, AND AMSTRUP

population of size N, with a capture probability of p
ifor the ith sample.
The possible capture–recapture patterns with their probabilities are
then
P(000)=(1−p
1)(1−p
2)(1−p
3)=θ
1
P(100)=p
1(1−p
2)(1−p
3)=θ
2
P(010)=(1−p
1
)p
2
(1−p
3
)=θ
3
P(110)=p
1p
2(1−p
3)=θ
4
P(001)=(1−p
1)(1−p
2)p
3=θ
5
P(101)=p
1(1−p
2)p
3=θ
6
P(011)=(1−p
1)p
2p
3=θ
7
and
P(111)=p
1p
2p
3=θ
8
Ifn
iobservations are made of the ith capture–recapture pattern, then the
likelihood function would be given by equation 1.3, with the θvalues
being functions of the pvalues, as shown above. In addition, because
the number of uncaptured animals is unknown, this must be set equal
ton
1=N−n
2−n
3−⋅⋅⋅−n
8in equation 1.3. Maximum likelihood esti-
mates of N, p
1,p
2, and p
3would then be found by maximizing the like-
lihood with respect to these four parameters.
The third type of likelihood function occurs when the probability of
the observed data is given by two or more multinomial probabilities
like (1.3) multiplied together. This would be the case, for example, if the
three-sample experiment just described was carried out with the results
recorded separately for males and females. In that case there would be
one multinomial likelihood for the males and another for the females.
The likelihood for all the data would then be the product of these two
multinomials. The parameters to be estimated would then be the number
of males, the number of females, and capture probabilities that might or
might not vary for males and females.
Likelihood Example 1
In this and the next example we illustrate some of the calculations in-
volved in the maximum likelihood method. These examples are designed
to provide the reader with a better understanding of what is meant by
INTRODUCTION TO THE HANDBOOK 11

the phrase “estimates can be obtained by maximum likelihood” when it
is used in later chapters. They are by no means a full treatment of the
maximum likelihood method, but should be sufﬁcient to provide read-
ers with a clearer idea of the methodology behind many of the capture–
recapture estimates mentioned later.
Once a likelihood for the observed data is speciﬁed, the second step
in the maximum likelihood estimation process is to maximize the likeli-
hood to obtain parameter estimates. To illustrate this second step con-
sider again the four-sample capture–recapture experiment described above
for the ﬁrst type of likelihood. Suppose that n
1=2 animals are captured
and marked in the ﬁrst sample, and that one of these animals is recaptured
in samples three and four, while the other animal is only recaptured in
sample four. The capture histories for these two animals are then repre-
sented by 1011 and 1001.
Following similar logic to that used to derive equation 1.1, the proba-
bilities of the individual capture histories are
P
1=φ
1(1−p
2)φ
2p
3φ
3p
4
and
P
2=φ
1(1−p
2)φ
2(1−p
3)φ
3p
4
Assuming that the results for the two captured animals were indepen-
dently obtained, the full likelihood of obtaining both the capture histo-
ries is
Typically, the natural logarithm of Lis taken at this point because Land
ln(L) are maximized by the same parameter values, and the logarithmic
function ln(L) is generally easier to maximize on a computer. The log-
likelihood for this example is
ln(L)=ln(P
1)+ln(P
2)
=ln(φ
1)+ln(1−p
2)+ln(φ
2)+ln(p
3)+ln(φ
3)+ln(p
4)+ln(φ
1)
+ln(1−p
2)+ln(φ
2)+ln(1−p
3)+ln(φ
3)+ln(p
4)
=2[ln(φ
1)+ln(1−p
2)+ln(φ
2)+ln(φ
3)+ln(p
4)]+ln(p
3)
+ln(1−p
3
)
LP ppp p pp
j
j==− − −
=
∏
1
2
1 2 23 34 1 2 2 3 34
111[( ) ][( ) ( ) ]φφφφφφ
12 MANLY, M CDONALD, AND AMSTRUP

The process of “maximizing the likelihood” essentially entails repeat-
edly modifying the values of φ
iandp
iuntil ln(L ) cannot be increased
any more. To start the process, a set of initial parameters is deﬁned. In
this example, suppose that the maximization process is started with
φ
i=0.5 for all i , and p
i=0.5 for all i . Putting these initial values into
ln(L) gives
ln(L)=ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)
+ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)+ln(0.5)
=12 ln(0.5)
=−8.32
It is then possible to get progressively closer to the ﬁnal maximum by a
judicious choice of the changes to make to the parameters. In particular,
using the theory of calculus it is possible to determine the direction to
change each of the parameters so that ln(L) will increase. However, the
magnitude of the changes that will assure that the new values produce
the maximum is not known. Consequently, small changes in the param-
eters are made until further changes will not increase ln(L).
The technique relies on the calculation of the derivatives of ln(L) with
respect to the parameters, to specify which changes in the parameters
will increase ln(L ). These details are explained in texts on calculus, but are
unnecessary here. For illustrating the calculations, all one needs to know
is that the derivatives for the example being considered specify that chang-
ing the parameter estimates to φ
1=0.55,φ
2=0.55,φ
3=0.55,p
2=0.45,
p
3=0.50, and p
4=0.55 will increase ln(L). To check this, these values
can be used to calculate ln(L), which gives
ln(L)=ln(0.55)+ln(0.55)+ln(0.55)+ln(0.5)+ln(0.55)+ln(0.55)
+ln(0.55)+ln(0.55)+ln(0.55)+ln(0.5)+ln(0.55)+ln(0.55)
=10 ln(0.55)+2 ln(0.5)
=−7.36
Repeating the process of calculating the gradient and changing the pa-
rameter estimates will eventually maximize ln(L). For example, the new
derivatives calculated at the last parameter values specify that chang-
ing the parameter estimates to φ
1=0.59,φ
2=0.59,φ
3=0.59,p
2=0.41,
p
3=0.50 and p
4=0.59 will increase ln(L). The ln(L) value with these
new parameter estimates is−6.66.
INTRODUCTION TO THE HANDBOOK 13

In this particular example, the likelihood is overparameterized because
there are six parameters and only two capture histories. Overparame-
terization causes a number of problems, and, in particular, means that
some parameters must be assigned arbitrary values to ﬁx the other
parameters. This overparameterized likelihood was used here, however,
only to illustrate calculation of individual ln(L) values. In the next section,
more capture histories are used and a more complicated likelihood func-
tion is illustrated.
Likelihood Example 2
In the last example, two capture histories were used to illustrate calcula-
tion of individual ln(L) values. In this section, the more complicated like-
lihood function of the Cormack-Jolly-Seber (CJS) model that is described
in detail in chapter 3 and 5 is used to illustrate the process of maximizing
the likelihood.
Consider the situation where animals in an open population are cap-
tured, marked, and released back into the population at each of eight
capture occasions. To deﬁne the CJS likelihood, parameters p
jandφ
jfrom
the previous section are needed, plus an additional parameter for the
probability that an animal is never seen after a certain sample occasion.
Recall that p
jis the probability that an animal in the population is cap-
tured or observed at sampling occasion j, and that φ
jis the probability
that an animal in the population survives from sampling occasion jto
j+1. The new parameter needed for this situation will be called χ
j. It is
the probability that an animal is not caught or seen after sampling occa-
sionj.
Consider the capture history 01011000. Under the CJS model, the
probability of this capture history occurring, conditional on the ﬁrst cap-
ture, is
P=φ
2(1−p
3)φ
3p
4φ
4p
5χ
5
The ﬁrst part of this expression, φ
2
(1−p
3
)φ
3
p
4
φ
4
p
5
, is justiﬁed as in
earlier expressions of this type, so that a φ
joccurs for each interval be-
tween the ﬁrst and last sampling occasions when the animal was cap-
tured, a p
jparameter occurs for each occasion that the animal is captured
or seen, and a (1−p
j) term occurs for each occasion that the animal is
not captured or seen. The second part of P represents the probability
that the animal was not seen after occasion 5, and is represented by the
parameterχ
5.
Theχ
jparameters are, in fact, functions of the φ
jandp
jparameters. To
see this, consider the eight-sample capture–recapture study. By deﬁnition,
14 MANLY, M CDONALD, AND AMSTRUP

χ
8=1 because there is no possibility of capturing an animal after sample
eight. If an animal was last seen in the seventh sample, then the probabil-
ity of not seeing it in the eighth sample is the probability that the animal
died, plus the probability that it lived to the time of sample eight but
eluded capture, i.e.,
χ
7=(1−φ
7)+φ
7(1−p
8)
If an animal was last seen in the sixth sample, then the probability of
not seeing the animal in the seventh or eighth sample is the probability
that the animal died between the times of the sixth and seventh sam-
ples, plus the probability that it survived to the time of sample seven
but eluded capture and then subsequently either died between the times
of the seventh and eighth samples or eluded capture in the eighth sample,
so that
χ
6=(1−φ
6)+φ
6(1−p
7)[(1−φ
7)+φ
7(1−p
8)]
=(1−φ
6)+φ
6(1−p
7)χ
7
In fact, χ
jfor any jcan be calculated in the same way using the general
recursive formula
χ
j=1−φ
j+φ
i(1−p
j)χ
j+1
Now suppose that eight samples are taken and the capture histories
10100000 11000000
10001000 00010100
10100000 01000000
11000000 00101000
10000000 00000110
11000000 00001100
11100000 00010001
are obtained for 14 animals. Suppose further that it is assumed that
the probability of survival was constant during the study and that the
probability of capture was constant for all samples. If P
i
is the proba-
bility of capture history ioccurring under the CJS model, then the full
log likelihood for this set of capture histories is the sum of ln(P
i) for
i=1 to 14, i.e., ln(L)=Σln(P
i). If the constant probability of survival
parameter is 0.6 and the constant probability of capture parameter is
INTRODUCTION TO THE HANDBOOK 15

0.2, then the log likelihood for this set of data could be calculated by
settingφ
1=φ
2=⋅⋅⋅=φ
8=0.6 and p
2=p
3=⋅⋅⋅=p
8=0.2 in the CJS
expression for P
j
, taking the logarithms, and summing. If these calcu-
lations are carried out then it is found that ln(L )=−37.94. If the prob-
ability of survival were changed to 0.65 and probability of capture
changed to 0.25, then ln(L)=−35.18. According to the theory of max-
imum likelihood, the parameters φ=0.65 and p =0.25 have a higher
likelihood and are therefore better than the parameters φ=0.60 and
p=0.20.
A computer can be programmed to repeatedly improve estimates of
the parameters until ln(L) reaches a point where it cannot be increased
further. For example, the SOLVER routine in Microsoft Excel can be
used for this purpose providing that the likelihood function is not too
complicated. With the example set of data, ln(L) will eventually reach a
maximum of −32.60 when the survival parameter is φ=0.78 and the
capture probability parameter is p=0.35. Because this example involves
only two parameters, the entire likelihood surface is easy to plot and vi-
sualize, as shown in ﬁgure 1.3.
It is also possible to estimate the standard errors of parameter esti-
mates from the likelihood function. The mathematical details justify-
ing these estimates involve the second derivatives of ln(L), and will not
be covered here. It sufﬁces to say that the curvature of the likelihood
16 MANLY, M CDONALD, AND AMSTRUP
0.2 0.4 0.6 0.8 1.0
0.0
Probability of Survival (φ)
0.00.20.40.60.81.0
Probability of Capture (ρ)
Log Likehood
−160 −80
Maximum
Likelihood = -32.6
at (0.78, 0.35)
Figure 1.3. The full likelihood surface for the example with eight sample times
and information on the captures and recaptures of 14 animals.

provides some indication about the variance of the maximum likeli-
hood estimate. For example, ﬁgure 1.3 shows that the likelihood is rel-
atively ﬂat for φ between 0.4 and 0.9, and pbetween 0.15 and 0.6. It
can therefore be argued that any set of parameters in this ﬂat region of
the likelihood is reasonable. In general, if the likelihood has a ﬂat re-
gion that is large, then the maximum likelihood estimates have large
variances, but if the likelihood does not have a ﬂat region, or the ﬂat
region is small, then the maximum likelihood estimates have small
variances.
1.4 Model Selection Procedures
With the ﬂexible modeling procedures that have become possible in re-
cent years there has been a considerable increase in the number of mod-
els that can be considered for data sets with many sampling occasions.
For example, with an open population it is often the case that capture
and survival probabilities can be allowed to vary with time, the sex of
the animal, weather conditions, etc. The problem is then to choose a
model that gives an adequate representation of the data without having
more parameters than are really needed.
There are two results that may be particularly useful in this respect.
First, suppose that two alternative models are being considered for a set
of data. Model 1 has Iestimated parameters, and a log-likelihood func-
tion of ln(L
1) when it is evaluated with the maximum likelihood esti-
mates of the parameters. Model 2 is a generalization of model 1, with
theIestimated parameters of model 1 and another Jestimated parame-
ters as well, and it has a log-likelihood function of ln(L
2) when evaluated
with the maximum likelihood estimates of the parameters. Because model
2 is more general (e.g., more complex) than model 1, it will be the case
that ln(L
2) is less than or equal to ln(L
1). However, if in fact the extra J
parameters in model 2 are not needed and have true values of zero,
then the reduction in the log likelihood in moving from model 1 to
model 2,
D=2[ln(L
1)−ln(L
2)] (1.4)
will approximate a random value from a chi-squared distribution with
Jdegrees of freedom. Consequently, if D, the difference or deviance, is
signiﬁcantly large in comparison with values from the chi-squared
distribution, then this suggests that the more general model 2 is needed
INTRODUCTION TO THE HANDBOOK 17

to properly describe the data. If, on the other hand, Dis not signiﬁcantly
large, then this suggests that the simpler model 1 is appropriate.
A limitation with the test just described is that it applies only to nested
models, that is, where one model is a special case or subset of another
model. This has led to the adoption of alternative approaches to model
selection that are based on Akaike’s information criterion (AIC) (Akaike
1973; Burnham and Anderson 1998).
In its simplest form, AIC model selection involves deﬁning a set of
models that are candidates for being chosen as the most suitable for
the data. Each model is then ﬁtted to the data and its corresponding
value for
AIC=−2ln(L)+2P (1.5)
is obtained, where L is the maximized likelihood for the model, and Pis
the number of estimated parameters. The model with the smallest value
for AIC is then considered to be the “best” in terms of a compromise be-
tween the goodness of ﬁt of the model and the number of parameters that
need to be estimated. The balancing of model ﬁt and number of parame-
ters in the model is important in determining the precision of the estimates
derived.
A further comparison between models can be based on calculating
Akaike weights (Buckland et al. 1997). If there are Mcandidate models
then the weight for model iis
(1.6)
where∆
iis the difference between the AIC value for model iand the
smallest AIC value for all models. The Akaike weights calculated in this
way are used to measure the strength of the evidence in favor of each of
the models, with a large weight indicating high evidence.
There are some variations of AIC that may be useful under certain
conditions. In particular, for small samples (less than 40 observations
per parameter) a corrected AIC can be used, which is
(1.7)
wherenis the number of observations and Pis the number of estimated
parameters. Also, if there is evidence that the data display more variation
AIC AIC
()
()
c=+
+
−−
21
1
PP
nP
w
i
i
M=
−
+++
exp( / )
exp( / ) exp( / ) exp( / )
∆
∆∆ ∆
2
22 2
12 ⋅⋅⋅
18 MANLY, M CDONALD, AND AMSTRUP

than expected based on the probability model being used then this can
be allowed for using the quasi-AIC values
(1.8)
where cˆis an estimate of the ratio of the observed amount variation in
the data to the amount of variation expected from the probability model
being assumed, as explained more fully in chapter 9. The method for ob-
taining the estimate cˆdepends on the particular circumstances. When
more variation than expected under a certain model is displayed, the
data are said to be “overdispersed.” Overdispersion can arise in a number
of ways. The most common causes are model misspeciﬁcation (lack of
ﬁt) and a lack of true independence among observations. For example,
the statistical likelihood for a set of capture data may assume that cap-
ture histories follow a multinomial distribution with a particular set of
probabilities. If there is more variation in the capture histories than pre-
dicted by the multinomial distribution, the probabilities assumed in the
multinomial model are incorrect, implying that the covariate model is
misspeciﬁed, or there may be unaccounted for dependencies among the
histories. In some but not all cases, apparent overdispersion can be reme-
died by incorporating more or different covariates into the model. Of-
ten, however, it will not be possible to account for some amount of
overdispersion in the data.
1.5 Notation
A good deal of notation is necessary for describing the models used in
the remainder of this book. The variation in notation can be quite con-
fusing, particularly if sections of the book are read in isolation. To help
reduce this confusion, all authors have standardized their notations, to
the maximum extent practicable. In table 1.1 we have provided a sum-
mary of most of the notation used in the volume.
QAIC
ln( )
ˆ
=
−
+
2
2
L
c
P
INTRODUCTION TO THE HANDBOOK 19

20 MANLY, M CDONALD, AND AMSTRUP
TABLE 1.1
Partial list of notation used throughout the book
Symbol Deﬁnition
i An index for individual animals. Example: h
idenotes the capture
history for the ith animal.
j An index for capture occasions (sample times). Example: p
jis the
probability of capture for the jth sample.
k The number of capture occasions (samples)
N A population size
R A number of animals released
mornThe number of animals with a certain characteristic. Examples: m
h
is
the number of animals with capture history h, and n
jis the number of
animals captured in sample j.
h A capture history. example: h =001010.
φ An apparent survival probability
p A capture probability
γ A seniority probability
E A probability of emigration
χ The probability of not being seen after a trapping occasion
ξ The probability of not being seen before a trapping occasion
M The number of marked animals in the population
S A pure survival probability (not involving the probability of
emigration); also, the number of strata in a multistrata model
F A probability of not emigrating, equal to 1−E.
R A reporting probability
ρ A resighting probability
F A tag recovery probability, equal to r(1−S) when there is no
emigration
ψ A probability of moving between strata from one sampling occasion
to the next for a multistrata model
Note.In some cases, symbols not listed here may be deﬁned to represent different things
in different chapters. For example, in chapter 6 Srepresents a pure survival probability
that does not include probability of emigration, while in chapter 8 Srepresents the number
of strata in a multistrata model. These cases have been kept to a minimum and the mean-
ing of each symbol is clear from the context. Symbols listed here can be subscripted or su-
perscripted as needed. For example, N
i
might denote the sample size at the time of the ith
sample time. Also, a caret is often used to indicate an estimate, so that N
ˆ
indicates an esti-
mate of N.

INTRODUCTION TO THE HANDBOOK 21
Figure 1.4. Black bear (Ursus americanus), near Council, Idaho, 1973, wearing
numbered monel metal ear tags. (Photo by Steven C. Amstrup)

Two
Classical Closed-population Capture–Recapture Models
ANNE CHAO AND RICHARD M. HUGGINS
2.1 Introduction
This chapter reviews the classical models for closed populations (i.e., for
situations where the individuals in a population remain the same while it
is being studied) and the history of their development. The data structure
and necessary notation are introduced in section 2.2 via a small data set
on the captures of deer mice. Section 2.3 reviews classical two-occasion
and multiple-occasion models, i.e., models for situations where two or
more than two separate samples of animals are taken. Section 2.4 summa-
rizes the limitations of these classical models and provides motivations
for the more general models that are considered in chapter 4.
As noted in chapter 1, the idea of the two-occasion capture–recapture
method can be traced to Pierre Laplace, who used it to estimate the hu-
man population size of France in 1802 (Cochran 1978), and even ear-
lier to John Graunt who used the idea to estimate the effect of plague
and the size of the population of England in the 1600s (Hald 1990).
Le Cren (1965) noted that other early applications of this method to
ecology included Petersen’s and Dahl’s work on sampling ﬁsh popula-
tions in 1896 and 1917, respectively, because they recognized that the
proportion of previously marked ﬁsh captured by ﬁshermen constituted
a basis for estimating the population size of the ﬁsh. Lincoln was the
ﬁrst to apply the method to wildlife in 1930 when he used returned leg
bands from hunters to estimate duck numbers.
Important contributors to the theory of classical closed capture–
recapture methods include Schnabel, Darroch, Bailey, Moran, Chapman,
and Zippin, among others. The work by Schnabel (1938) and Darroch
(1958, 1959) provided the mathematical framework for the models. De-
tailed historical developments and applications are provided in Cormack
(1968), Otis et al. (1978), White et al. (1982), Pollock (1991), Seber
(1982, 1986, 1992, 2001), Schwarz and Seber (1999), and Williams et al.
(2002).

2.2 Structure of Capture–Recapture Experiments and Data
The raw data from closed capture–recapture experiments are the capture
records of all the individuals observed in a study. These are arranged in a
capture history matrix, as illustrated in table 2.1 with deer mice (Per-
omyscussp.) data collected by V. Reid. These data are displayed in the
format appropriate for CAPTURE, a widely used computer program for
the analysis of closed models (Otis et al. 1978; White et al. 1982; Rexs-
tad and Burnham 1991; section 4.4 of this book). The data arose from a
live-trapping experiment that was conducted for six consecutive nights
(columns) with a total of 38 mice (rows) captured over these six capture
occasions. The time period for the experiment was relatively short and it
was reasonable to assume that the population was closed.
In table 2.1, the capture history of each captured individual is expressed
as a series of 0’s (noncaptures) and 1’s (captures). Thus, in the example the
capture history matrix consists of 38 rows and 6 columns, with the rows
representing the capture histories of each captured individual and the
columns representing the captures on each occasion. The ﬁrst mouse, with
capture record 111111, was captured on all six nights. The second mouse,
CLASSICAL CLOSED-POPULATION MODELS 23
Figure 2.1. Endangered Néné goose (Nesochen sandvicensis) wearing double
leg bands. Island of Maui, Hawaii, 1998. (Photo by Steven C. Amstrup)

24 CHAO AND HUGGINS
TABLE 2.1
Individual capture history of 38 deer mice with six capture occasions
Occasion 1 Occasion 2 Occasion 3 Occasion 4 Occasion 5 Occasion 6
111111
100111
110011
110111
111111
110111
111110
111001
111111
110111
110111
111011
111111
101110
100100
010010
011001
010001
010101
011010
010101
010001
010011
001000
001111
001011
001111
001010
001000
000100
000111
000110
000010
000010
000010
000001
000001
000001

CLASSICAL CLOSED-POPULATION MODELS 25
with capture record 100111, was captured on nights 1, 4, 5, and 6, but not
on nights 2 and 3. Similar interpretations apply to other capture histories.
In larger studies with numerous capture occasions and many captured
individuals, the capture-history matrix becomes very large, and with the
classical models it is more convenient to represent the raw data by a tally
of the frequencies of each capture history, which retains most of the in-
formation in the original capture-history matrix.
For many classical estimation procedures, the following summary sta-
tistics are sufﬁcient for the statistical analysis:
k=the number of capture occasions;
n
j=the number of animals captured on the jth capture occasion,
j=1,..., k;
u
j=the number of unmarked animals captured on the jth capture
occasion,j=1, ..., k;
m
j=the number of marked animals captured on the jth capture
occasion,j=1,..., k, where m
1=0;
M
j=the number of distinct animals captured before the jth capture
occasion,j=1, . . . , k, where this is the same as the number of
marked animals in the population just before the jth capture
occasion, and of necessity M
1=0 and M
k+1is deﬁned as
the total number of distinct animals captured in the experi-
ment; and
f
j=the number of animals captured exactly jtimes,j=1,..., k.
These statistics are given in table 2.2 for the data in table 2.1. The sta-
tisticn
jdenotes the column sum for the jth column (occasion) in the cap-
ture history matrix, with (n
1,n
2, ..., n
6)=(15, 20, 16, 19, 25, 25). Out
of the n
janimals, there are u
jﬁrst captures and m
jrecaptures, so that
u
j+m
j=n
j, with (u
1,u
2,..., u
6)=(15, 8, 6, 3, 3, 3), and (m
1,m
2,...,
m
6)=(0, 12, 10, 16, 22, 22). The statistic M
jcan also be interpreted as
the cumulative number of ﬁrst-captures on the ﬁrst j−1 occasions, thus
M
j=u
1+u
2+⋅⋅⋅+u
j−1and (M
1,M
2,..., M
7)=(0, 15, 23, 29, 32, 35,
38). That is, the number of marked individuals in the population pro-
gressively increased from M
1=0 to M
7=38.
The row sum for each individual denotes the capture frequency of that
animal, and (f
1,f
2,..., f
k) represent the frequency counts of all cap-
tured animals. As shown in table 2.2, the frequency counts for the
mouse data are (f
1
,f
2
,..., f
6
)=(9, 6, 7, 6, 6, 4). That is, 9 animals were
captured once, 6 animals captured twice, . . . and 4 animals captured on
all 6 occasions. The term f
0is the number of animals never captured,
so that f
1+f
2+⋅⋅⋅+f
k=M
k+1andf
0+f
1+⋅⋅⋅+f
k=N. Therefore,
estimating the population size Nis equivalent to estimating the number
of missing animals, f
0.

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powerful Gavāksha—surrounded by a koti, remained by the side of
Rāma. And that destroyer of foes—the exceedingly mighty Dhumra
of the bears of terrific wrath, remained by the side of Rāma—where,
surrounded by vigilant counsellors, and bearing a mace in his hand,
stood the exceedingly strong Bibhishana, endowed with wonderful
powers, in complete panoply. And Gaya, and Gavāksha, and Gavaya,
and Sarabha, and Gandhamadana, protected the monkey-army,
coursing all around. And then, his soul wrought up with wrath,
Rāvana—lord of Rākshasas—speedily ordered the whole host to sally
out. Hearing those words, which came out from Rāvana’s mouth, all
of a sudden the night-rangers sent up a dreadful yell. Then awoke
the kettle-drums, having moon-like pale faces,—sounded by means
of golden sticks. And conchs by hundreds and by thousands, capable
of producing loud blares, filled with air proceeding from the mouths
of dreadful Rākshasas,—were winded. And with conchs placed in
their mouths, those night-rangers, having bodies blue like those of
Cukas, resembled masses of clouds, with lightning and cranes. And,
commanded by Rāvana, the troops cheerfully issued forth like the
onrushing of the mighty main filling all at the time of the universal
dissolution. And then the monkey-army gave a roar, spreading all
around; and it seemed as if the sound filled all Malaya with its sides
and caves. And sounds of conchs, and drums, as well as the leonine
shouts of the impetuous (warriors); made the earth, air, and ocean,
resound; and these mixed with the roars of elephants, the neighing
of steeds, the rattle of the car-wheels, and the tread of the
Rākshasas’ feet. And in the meantime there commenced a mighty
encounter between the Rākshasas and the monkeys, like that which
took place of yore between the gods and the Asuras. And displaying
their prowess, they¹²⁸ began to slaughter monkeys with maces, and
darts, and adzes. And the vehement monkeys (on their side)

slaughtered Rākshasas with trees and tops of crags as well as with
their nails and teeth. And a mighty sound arose of ’Victory unto king
Sugriva!’ and ’Victory unto thee, O king,’—each army taking the
name of its king. And then other dreadful Rākshasas that were
stationed upon the wall, dropping down, pierced the monkeys with
darts and bhindipālas. And (thereat) the monkeys, flying into fury,
descending to the earth and bounding, brought down the Rākshasas
with their arms. And that encounter of the Rākshasas and the
monkeys was mighty and wonderful, and the ground became wet
with flesh and gore.
¹²⁸ Rākshasas.
SECTION XLIII.
And as the high-souled monkeys and Rākshasas fought on, their
wrath vastly increased at sight of each other’s forces. And furnished
with steeds in golden trappings; and elephants resembling flames of
fire; and cars appearing like (so many) suns; and shining armour,—
the valiant Rākshasas issued, making the ten cardinal points
resound. The Rākshasas of terrific exploits were burning for victory
on behalf of Rāvana.—And the mighty monkey-army also, eager for
victory, darted against the host of the Rakshas of dreadful deeds.
And in the meanwhile, as either party assailed the other, there took
place single combats between the Rākshasas and the monkeys. And
as Andhaka had combated with the Three-eyed (deity)¹²⁹ that
Rākshasa, the exceedingly energetic Indrajit, fought with Angada,
son unto Vāli. Sampati, hard to bear, engaged with Prajangha; and

the monkey, Hanumān, entered into conflict with Jambumāli. And
Rāvana’s younger brother, Bibhishana, fired with wrath, encountered
Satrughna, endowed with exceeding impetuosity. And the highly
powerful Nila engaged with Nikumbha. And Sugriva—lord of
monkeys—undertook Praghasa, and the graceful Lakshmana was
engaged with Virupāksha. And the exceedingly irrepressible Agniketu
and the Rākshasa—Raçmiketu—and Mitraghna and Yajnakopa, were
engaged with Rāma. And Vajramubhthi encountered Mainda, and
Açaniprabha, Dwivida. And those foremost of monkeys fought with
those dreadful Rākshasas,—the heroic and terrible Pratapana,
incapable of being overcome in battle, was combating with Nala of
terrific force; and that lusty son of Righteousness, well-known as
Sushena,—a mighty monkey—battled with Vidyunmāli. And other
fearful monkeys encountered other Rākshasas; and many were the
encounters that took place. And great and fierce was the
engagement that took place between the heroic Rākshasas and
monkeys burning for victory, capable of making people’s hair stand
on end. And from the persons of the Rākshasas and the monkeys
there flowed a river of gore, having hair for grass (growing on its
banks), and the bodies of the warriors for pieces of planks floating
(adown the current). Indrajit, growing enraged, with his mace dealt
a blow at that tearer of hostile ranks, Angada,—like him of an
hundred sacrifices striking with his thunderbolt. Thereat, that
graceful monkey, Angada, gifted with vehemence, with his mace
crushed his car decked in gold, together with the steeds and the
charioteer. Sampāti was pierced with three arrows by Prajangha; and
the former (in his turn) slew Prajangha on the edge of battle with an
Açwakarna.¹³⁰ And Jambumāli, mounted on a car, possessed of
prodigious strength, fired with wrath, with all the access of force
derived from his car, wounded Hanumān between his paps. Thereat,

getting at his car, Hanumān—son unto the Wind-god—with a slap
speedily crushed his adversary’s vehicle along with the Raksha. Then
the terrific Pratapana, roaring, rushed at Nala; and thereat Nala,
with his body pierced with sharp shafts by that swift-handed Raksha,
plucked out Pratapana’s eyes, and cast them to the earth. And that
lord of monkeys, Sugriva, with a _Saptaparna_¹³¹ swiftly slew
Praghasa, who appeared to be devouring up the troops. And,
tormenting the Rākshasa of dreadful form with a shower of shafts,
Lakshmana slew Virupāksha with a single arrow. And the
irrepressible Agniketu, the Rākshasa Ragmiketu, Mitraghna and
Yajnakopa, with their arrows rendered Rāma aflame. Thereat, Rāma,
growing wroth, in battle severed the heads of those four by means
of four shafts, dreadful, and resembling the tongues of a flame. And
Vajramushti was slain in conflict by Mainda with a clenched fist; and
down came he to the ground along with his car and horses, like a
turret toppling (headlong). And Nikumbha in fight wounded Nila
resembling a mass of blue collyrium, with sharpened shafts,—as the
Sun pierceth clouds with his rays. Again with an hundred arrows,
that light-handed night-ranger pierced Nila in the field; and
Nikumbha laughed thereat. At this, even as Vishnu did in battle, Nila
with a wheel of his¹³² car, cut off in conflict Nikumbha’s head
together with that of his charioteer. And Dwivida, possessed of the
touch of the Vajra and thunder-bolt, in the presence of the entire
Rākshasa host hurled a mountain-peak at him that was endowed
with the splendour of the thunder-bolt. And Açaniprabha in
encounter pierced that foremost of monkeys, Dwivida, with shafts
resembling thunder-bolts. Thereat, beside himself with wrath, with
his entire body wounded with arrows, Dwivida with a sāla destroyed
Açaniprabha along with his car and horses. And Vidyunmali,
mounted on a car, assailed Sushena with shafts decked with gold,

and began to shout momentarily. Seeing him mounted on his car,
Sushena—best of monkeys—taking up a huge crag, swiftly brought
his car down to the ground. Thereat, endowed with lightness, that
night-ranger, Vidyunmāli, at once extricating himself from his car,
stood on the ground with a mace in his hand. Thereupon, that
foremost of monkeys, Sushena, growing furious, taking up a gigantic
crag, rushed at the night-ranger. And as he was descending, the
night-ranger, Vidyunmāli, with his mace swiftly hit at the breast of
Sushena—greatest of monkeys. Thereat, without thinking at all of
the terrific hit of the mace, that best of monkeys in mighty conflict
brought down that¹³³ upon his¹³⁴ head. And, assailed with the
crag, the night-ranger, Vidyunmāli, having his chest crushed, fell
down to the earth, deprived of life. And, like the celestials warring
against the Daityas, the heroic monkeys warred on and confounded
the valiant rangers of the night. And frightful was the field of battle,
with darts, and other arms; and clubs, and javelins, and lances, and
other weapons; and with broken cars, and war-horses, and mad
horses slain, and monkeys and Rākshasas; and wheels and
akshas,¹³⁵ and yokes and standards,—broken and scattered over
the ground; and swarms of jackals began to range on all sides of the
monkeys and the Rākshasas; and _Kavandhas_¹³⁶ began to rise in
that terrific encounter, resembling the encounter of the gods and the
Asuras. Thus destroyed by the foremost of monkeys, the rangers of
night, beyond themselves with the smell of blood,—eagerly wishing
for the setting of the Sun,¹³⁷ again made active preparations for a
renewal of the fight.
¹²⁹ Siva, fabled to have three eyes.—T.
¹³⁰ A kind of tree.

¹³¹ A tree.
¹³² Nikumbha’s.
¹³³ The crag, which he had at first hit.—T.
¹³⁴ Vidyunmāli’s.
¹³⁵ A part of a wheel.
¹³⁶ Spectres having bodies without heads.
¹³⁷ This was because, as intelligently remarks Rāmānuja, night-
rangers grow powerful at night.—T.
SECTION XLIV.
As the monkeys and the Rākshasas thus fought on, the sun set, and
the fatal Night came. And then commenced a night-engagement
between the dreadful Rākshasas and the monkeys of fixed hostility,
each party burning for victory. And in that profound darknesss, the
monkeys and the Rākshasas began to slay each other, exclaiming,
—’Thou art a Rākshasa,’ and ’Thou art a monkey.’ And in that army
there was heard a mighty uproar of ’slain,’ ’rive!’ ’come!’ ’why fliest?’
And, dark-hued, the Rākshasas, equipped in golden mail, in that
deep darkness appeared like elevated hills clad with woods of
flaming medicinal herbs. And in that limitless gloom, the Rākshasas,
transported with wrath, advanced with impetuous speed, devouring
monkeys. And, fired with terrible wrath, they,¹³⁸ bounding up, with
their sharp teeth tore up steeds caparisoned in gold, and standards

resembling venomous serpents. And the lusty monkeys in battle
agitated the Rākshasa host,—and, waxing furious, with their teeth
pulled and bit elephants and the riders thereof, and cars furnished
with flags and standards. And Rāma and Lakshmana with shafts
resembling venomous serpents, slaughtered the foremost among the
Rākshasas—both those that were seen and those that were not.—
And the dust of the earth arising from warring combatants, and from
the hoofs of horses and the wheels of cars, choked up eye and ear.
And as the mighty encounter, capable of making people’s hair stand
on end, went on, there flowed a fearful river of gore. And the
sounds of kettle-drums and Mridangas and Panavas, mingled with
those of conchs and car-wheels,—were wonderful (to hear). And the
sounds of steeds neighing, and Rākshasas (roaring), and monkeys,
rejoicing,—were something tremendous. And, with able monkeys
slain; and darts and javelins and axes; and slaughtered Rākshasas
wearing forms at pleasure, lying mountain-like,—the field of battle,
seeming to have offerings of arms representing flowers,—became
difficult to recognise, and inaccessible; and the earth was drenched
with streams of blood. And that Night, destructive to monkeys and
Rākshasas,—was dreadful, and difficult of being out-sped by all,—
like unto the Fatal Night of beings. And in that profound darkness,
the Rākshasas with great vivacity attacked Rāma with a shower of
shafts. And the roars of those beings as they advanced, sending up
shouts in anger, resembled the dashing of the Ocean at the time of
the universal dissolution. And in the twinkling of an eye, Rāma by
means of six shafts resembling tongues of flames, struck six of the
night-rangers; viz., Yajnaçatru, irrepressible (in fight),—and
Mahāpārcwa, and Mahodara, and the huge-bodied Vajradanashtra,—
and those two—Suka and Sārana. And, pierced in their vitals with
Rāma’s shafts, they, having only their lives left to them, disappeared

from the field. Then in the twinkling of an eye, that Mahāratha
rendered all sides clear (of all gloom) by means of arrows
resembling tongues of fire; and those other heroic Rākshasas that
were in front of Rāma, were destroyed on approaching the place,
like insects approaching a fire. And with shafts plated with gold lying
in all directions, the night resembled one in autumn decked with
fireflies. And in consequence of the uproar occasioned by the
Rākshasas, and the sounds of drums, that night, already dreadful (in
itself), became all the more so. And on that sound attaining
dimensions on all sides, it seemed as if the mount Trikuta,
containing numerous caverns, had been speaking. And huge-bodied
Goāngulas of equal lustre with darkness itself,¹³⁹ binding fast the
night-rangers with their arms, began to swallow them up. And
Angada was present in the encounter, for slaying foes, And Indrajit,
fairing sadly at the hands of Angada, abandoning his vehicle, and
having his horses as well as his charioteer slain, vanished then and
there. And that feat of Vāli’s son, worthy of being honored, all the
celestials with the saints and both Rāma and Lakshmana lauded to
the eight. All beings were acquainted with the might of Indrajit in
battle; and, therefore, witnessing his discomfiture, and seeing that
high-souled one, they rejoiced exceedingly, and, seeing the enemy
vanquished, all the monkeys with Sugriva and Bibhishana,
experiencing high delight, exclaimed,—"Excellent!" "Excellent!" And,
beaten by Vāli’s son of dreadful deeds, Indrajit was fired with a
mighty wrath. And, being handled hard in battle, and having
vanished from the field, the heroic and wicked son of Rāvana, who
had received a boon from Brahmā, transported with passion,—
remaining invisible, began to discharge sharpened shafts of the
splendour of the thunder-bolt. And worked up into rage, he in the
conflict pierced Raghu’s sons, Rāma and Lakshmana all over their

bodies, with terrific arrows consisting of serpents. And himself engirt
with illusion, that night-ranger, given to fighting in crooked ways,—
remaining invisible to all creatures,—stupified the descendants of
Raghu in battle; and by means of his shafts bound the brothers,
Rāma and Lakshmana. And then in the sight of the monkeys, those
heroes and foremost of men were suddenly overpowered with shafts
by the enraged (Indrajit). And when the son of the Rākshasa
monarch felt himself incompetent to cope with them¹⁴⁰ openly, then
that impious one, resorting to illusion, bound those princes (by that
means).
¹³⁸ i.e. the monkeys, as appears from the context.—T.
¹³⁹ Irony.
¹⁴⁰ Rāma and Lakshmana.
SECTION XLV.
Then, anxious to ascertain his¹⁴¹ course, the kings son possessed of
prowess, and endowed with exceeding strength, Rāma, ordered ten
of the monkey-leaders. And that repressor of foes ordered Vāli’s son
—Angada, the vigorous Sarabha, Dwivida, Hanumān, the mighty
Sānuprastha, Rishabha and Rishabhaskandha. Thereat with alacrity
those monkeys, weilding mighty trees, shot up into the sky, and
began to scour the ten cardinal points. And Rāvana’s son, skilled in
arms, resisted the impetuous march of those vehement ones by
means of a powerful weapon as well as arms more forceful (than the
force of their rush). And the exceedingly vehement monkeys, cut

and mangled with nārāchas, saw him in the dark like the sun
enveloped in clouds. And that conquerer in battle, Rāvana’s son,
with shafts sorely pierced the persons of Rāma and Lakshmana. And
both Rāma and Lakshmana had their bodies entirely covered by the
angry Indrajit with shafts turned into serpents. And from their
wounds blood began to gush out in streams; and they looked like
flower-crowned Kinçukas. Then that one having red corners unto his
eyes and resembling a mass of crushed collyrium, Rāvana’s son, said
unto the brothers, as he vanished,—"When I fight remaining
invisible, even Sakra—the lord of the celestials—cannot see or
approach me,—and who are ye? And I, with my soul surcharged
with wrath, shall, assailing them with showers of weapons furnished
with Kanka feathers, send Raghu’s sons to the abode of Yama".
Having spoken thus unto the brothers—Rāma and Lakshmana,
cognizant of righteousness—(Indrajit)—pierced them with sharpened
shafts, and shouted in joy. And stretching his large bow, that one
sable like unto a mass of crushed collyrium again discharged terrific
shafts in battle. And that one versed in the inner sense of things,
with whetted arrows pierced the vitals of Rāma and Lakshmana and
shouted momentarily. And fast bound by the shackles of shafts on
the edge of battle, they¹⁴² could not attain respite for a moment.
Then with their persons pierced with shafts and darts, and
resembling the flags of the Great Indra let loose from the cords and
trembling (in the air),—and with their bodies bristling with arrows,—
those heroes and mighty bowmen—lords of the earth—tormented in
consequence of their vitals having been pierced, dropped down to
the earth. And those heroes, bathed in blood, and their persons
covered with arrows,—pained and suffering terribly, lay down as
became heroes. And there was not so much room unpierced in their
persons as could be measured by a finger; and they were wounded

with arrows up to the fore-parts of their hands.¹⁴³ And they being
wounded by that fell one capable of assuming shapes at will, blood
violently gushed out of their bodies like water from a spring. And
Rāma fell first, pierced in the vitals with the shafts. And the same
Indrajit who had formerly wrathfully routed Sakra.(now) pierced
(Rāma) with nārāchas knotted with gold, and having polished heads;
swift-speeding; and resembling dust carried about by the wind; and
half-nārāchas; and darts resembling anjalis;¹⁴⁴ and vatsadantas;¹⁴⁵
and sinhadanshtras;¹⁴⁶ and razors; and, resigning his stringless bow
decked in gold and curved in three places,—with its part for grasping
shattered—he¹⁴⁷ lay down like a hero. And seeing Rāma—foremost
of men—down within arrow-range, Lakshmana despaired of his life.
And seeing his brother, Rāma, having eyes resembling lotus-petals
and ever delighting in battle, himself the refuge of others,—lying
down in the field; (Lakshmana) began to weep. And the monkeys
also, seeing him, were plunged in sorrow; and they, their eyes
flooded with tears, began to cry in grief of heart. And when they had
been bound and had laid themselves down as become heroes, the
monkeys stood around them,—and, conversing with one another,
they, headed by the son of the Wind, were seized with extreme
sorrow.
¹⁴¹ Indrajit’s.
¹⁴² i.e. Rāma and Lakshmana.
¹⁴³ This sloka is rather obscure, and the Bengali translators
have conveniently passed it by!—T.
¹⁴⁴ The hands joined at the lower sides, with the palms hollowed.
—T.

¹⁴⁵ Weapons resembling the teeth of a calf.
¹⁴⁶ Weapons resembling the lion’s teeth
¹⁴⁷ Rāma.
SECTION XLVI.
And the rangers of woods, gazing at the earth and the sky, at length
cast their eyes on the brothers—Rāma and Lakshmana, covered all
over with arrows. And after that Rākshasa had gone away having
performed his work, like the God¹⁴⁸ going away, after having
showered,—there came to that place Bibhishana with Sugriva. And,
mourning Raghu’s sons, there also came in all haste Nila and
Dwivida and Mainda and Sushena and Kumuda and Angada in
company with Hanumān. And moveless; breathing low,—covered
with blood,—pierced all over with net-works of shafts; dumb;
they¹⁴⁹ were lying on the field. And they were sighing like serpents;
and were inert; and deprived of prowess; and washed in blood; and
looking like unto golden standards. And as they lay moveless, as
become heroes, the leaders of monkeys environed them with tear-
charged eyes. And seeing the sons of Raghu lying, covered with
showers of shafts, the monkeys, with Bibhishana, were pained
(exceedingly). And the monkeys, surveying the sky as well as all
directions, could not see Rāvana’s son in battle enveloped with
illusion. And then Bibhishana by means of illusion saw his brother’s
son staying before, hidden by illusion. And Bibhishana saw that hero
of incomparable deeds, who had no compeer in the field and who
had energy, fame and prowess,—as he remained invisible in

consequence of the Boon received from Brahma. And Indrajit, seeing
his own feat and them lying at length, spake in excess of joy,
gladdening all the Rākshasas,—"The brothers—Rāma and
Lakshmana, possessed of great strength, who had slain Khara and
Dushana, are themselves slain with my shafts. And all the celestials
and Asuras assembled together with the saints, are incompetent to
emancipate these from the fetters of my shafts. He for whom my
father was exercised with anxiety and tormented by grief, for whom
my sire used to spend nights without pressing his bed,—for whom
this entire Lankā had resembled a river turbulent in the rainy reason,
—that same evil sticking by the root of all, hath been dispensed his
quietus by me. And like clouds of autumn, the prowess of Rāma and
Lakshmana as well as that of all the rangers of the woods, hath
been rendered useless". Saying this in the presence of all the
Rākshasas, Rāvana’s son—destroyer of foes—menacing the monkey-
leaders, hit Nila with nine arrows, and hurt Mainda and Dwivida each
with three powerful shafts. And piercing Jambavān with an arrow in
the chest, that mighty bowman discharged ten at Hanumān. And
Rāvana’s son possessed of exceeding impetuosity, pierced in the
conflict with two shafts each Gavāksha and Sarabha of
immeasurable vigor. And Rāvana’s son, summoning celerity, pierced
the king of Golangulas and Vāli’s son, Angada, with innumerable
arrows. And the powerful son of Rāvana, endowed with might,
piercing the foremost monkeys with shafts resembling tongues of
flames, set up shouts in the field of battle. And tormenting the
monkeys with volleys of shafts and striking terror into them, that
mighty-armed one, bursting out into a laugh, said,—"Let the
Rākshasas behold these brothers, lying fast bound with dreadful
arrows, in front of the forces". Thus addressed, those Rākshasas—
wily warriors all—resembling masses of clouds, witnessing that deed

(of Indrajit), struck with wonder and rejoicing (greatly), set up
tremendous roars. And thinking that Rāma was slain, they honored
Rāvana’s son. And seeing the brothers—Rāma and Lakshmana—
motionless, and lying inert on the ground,—they took them for slain.
And, experiencing excess of joy, Indrajit—conquerer in conflict—
entered the city of Lankā, rejoicing all the Nairitas. Seeing the bodies
as well as the limbs of Rāma and Lakshmana, covered entirely with
arrows, fear took possession of Sugriva. Thereat Bibhishana said
unto that lord of monkeys, staying in woe begone guise, with a
tearful countenance, and his eyes wild with wrath,—"Do not give
way to fear, O Sugriva. Restrain thy rising tears! This is the way of
warfare: victory is not (always) sure. But, O hero, if Fortune
ultimately smile upon us, this stupor shall go off from these high-
souled and exceedingly powerful ones. Therefore, O monkey, do
thou cheer me, who am forlorn". Saying this, with his hand
Bibhishana washed Sugriva’s graceful eyes with water. And taking
water, the righteous Bibhishana by means of his knowledge, washed
Sugriva’s eyes therewith. And washing the face of the intelligent
monkey-monarch, Bibhishana spoke these words, seasonable and
sedate,—"O foremost of monkey-kings, this is no time for being
overcome with stupor. At this hour, even immoderate affection may
lead to destruction. Therefore, casting off stupor, which tends to mar
all work, do thou bethink thee how thou mayst serve this army
headed by Rāma. Or do thou protect Rāma so long as he doth not
regain consciousness; and when the Kākutsthas shall have regained
consciousness, all our apprehension shall vanish. This is nothing to
Rāma, and Rāma is not dying. And Lakshmi,¹⁵⁰ who is incapable of
being attained by those that are doomed, shall not forsake this one.
Therefore do thou comfort thyself, do thou also cheer up thy own
forces,—while I am engaged in composing all the troops. O best of

monkeys, these with distended eyes, come under the governance of
terror, are, stricken with panic, whispering into each other’s ears. But
seeing me, let the forces rushing about, cheered up,—as well as the
monkeys,—cast off all fear, like a wreath that hath been used
before". Thus comforting Sugriva, Bibhishana—lord of Rākshasas—
again instilled spirits into the flying forces of monkeys. And Indrajit—
worker of mighty illusions—accompanied by his troops, entered the
city of Lankā and presented himself before his father. And
approaching Rāvana and saluting him with joined hands, he
informed his sire of the welcome tidings that Rāma and Lakshmana
had been slain. And hearing that his foe had fallen, Rāvana springing
up in the midst of the Rākshasas, with great joy embraced his son.
And scenting the crown of his head, (Rāvana) with a delighted heart,
asked (Indrajit as to all that had taken place). And on being asked,
he (Indrajit) truly related unto his sire how (Rāma and Lakshmana)
had been rendered senseless and lack-lustre by being fastened with
shafts. Thereat, with rapture surcharging his inmost soul, Rāvana,
hearing the speech of the mighty car-warrior, banished his fear of
Daçaratha’s son,—and rising up, honored his son with glad words.
¹⁴⁸ Indra.
¹⁴⁹ Rāma and Lakshmana.
¹⁵⁰ The goddess of prosperity.
SECTION XLVII.

When Rāvana’s son entered Lankā, after having accomplished his
purpose, the foremost monkeys protected Rāghava, surrounding him
on all sides. And Hanumān, and Angada, and Nila, and Sushena, and
Kumuda, and Nala, and Gaya, and Gavāksha, and Panasa, and
Samprastha—a mighty monkey—and Jāmbavān, and Rishava, and
Sunda, and Rambha, and Satavali, and Prithu,—all forming
themselves into array, and equipped with trees on all sides, and
remaining vigilant,—the monkeys kept gazing at all sides, awry and
upwards; and even when a straw stirred, they thought it to be a
Rākshasa. And Rāvana, on his part, experiencing the height of
exaltation, summoned the Rakshasis engaged in guarding Sitā.—And
thereat the Rakshasis—Trijata and others—presented themselves at
his command. And then the lord of Rākshasas, delighted, addressed
then the Rakshasis, saying,—"Tell Vaidehi that Rāma and Lakshmana
have been slain in battle by Indrajit. And taking her on Pushaka,
show her (Rāma and Lakshmana) lying slain on the field of battle.
That one depending on whom she had proudly set her face against
me,—that husband of hers, along with his brother, hath been slain in
conflict. And then Mithila’s daughter, her fear gone off with her
anxiety, and herself losing all support,—Sitā—daughter unto Mithila
—decked out in all ornaments, shall seek me. And today beholding
Rāma with Lakshmana, come under the sway of Time, she, finding
no other way, shall desist from her present course. And seeing no
other resourse, that one of expansive eyes shall of herself seek me".
Hearing those words of the wicked-minded Rāvana, the Rakshasis,
saying,—"So be it,"—went to where Pushpaka was. Then taking
Pushpaka, the Rakshasis at Rāvana’s command went to Maithili
staying in the açoka wood. Then, taking Sitā, who was overcome
with grief for her lord, the Rakshasis, placed her on the car,
Pushpaka. And placing Sitā on Pushpaka along with Trijata, Rāvana

took her all around (Lankā) crowded with ensigns and standards.
And the lord of Rākshasas jubilantly proclaimed in Lankā,—"Rāghava
as well as Lakshmana have been slain by Indrajit in battle". And
going about with Trijata, Sitā saw all the monkey-troops slain. And
she found the flesh-eaters elated in spirits, and the monkeys
afflicted with extreme grief at the side of Rāma and Lakshmana.
Then Sitā beheld both Lakshmana and Rāma lying in the field,
senseless and bound with arrows. And those heroes were lying on
the earth, their mail torn, their bows cast off, their bodies mangled
all over and thickly pierced with shafts. And seeing those brothers,—
foremost of heroes and best of men—having eyes resembling white
lotuses, and themselves like unto Kumaras,—lying in the field,¹⁵¹—
the fire-sprung one, Sitā, striken with grief, began to weep piteously.
And that black-eyed one of an excellent person, Janaka’s daughter—
seeing them roll in the dust, broke out into lamentation. And with
her eyes shedding plentiful tears, she seeing those brothers,
endowed with god-like prowess, concluded them to be dead $ and
overwhelmed with grief, spoke as follows.
¹⁵¹ Virān nararshabkān—heroes and best of men—occurs
again,—left out on the score of redundancy.—T.
SECTION XLVIII.
And seeing her husband, as well as the exceedingly powerful
Lakshmana,—slain, Sitā, afflicted with grief, burst into bitter
lamentation. "The soothsayers had said that I should have sons, and
should never be a widow. But on Rāma being slain, it seems now

that those ones, possessed of knowledge, had spoken untruthfully.
And those also, who having celebrated sacrifices and rites, had said
that I should become the queen (of Rāma),—on Rāma being slain,
seems to-day to have spoken a falsehood, although they are
possessed of knowledge. And they also asserted that I should be
honored of the wives of heroic kings as well as of my lord,—but on
Rāma being slain, they seem to have uttered a falsehood, although
possessed of knowledge. And those twice-born ones that in my
hearing had said auspicious words, on Rāma being slain, seem to-
day to have spoken a falsehood, although they were possessed of
knowledge. These lotus-marks on the feet, betokening unto
gentlewomen possessing them, that they are to be installed in the
kingdom in company with their husbands—who are kings,—are on
me. And those marks find I none on me by which women of rare
fortune come by widowhood,—but I find that in me these good
tokens are nullified. Those marks that are pronounced infallible by
those versed in such knowledge, on Rāma being slain, are nullified in
me. My hairs are fine, equal, and blue; my eye-brows touch each
other; my hips are devoid of down and round; and my teeth are
close. My temples, and eyes, hands, feet, ankles, and thighs are
equal. And my fingers are furnished with round nails, and are plump
and even in the middle. And my breasts are close and firm and
developed, and have their nipples sunk. And my navel is depressed,
with high sides. And my chest is swelling. And my complexion is like
the hue of gems,—and my down soft. And they said that I was
furnished with twelve auspicious signs. And my hands in the middle
parts of my fingers contain wheat-marks; and in the spaces between
the fingers, have no uneven corners. And my feet also partake of the
general complexion. And my laugh is a gentle smile. And those
versed in marks of women knew that I was possessed of such

marks. And those Brāhmanas skilled in telling fortune said that I
should be installed in the kingdom along with my husband; but all
that hath been falsified. Having purified Janasthāna (of Rākshasas),
obtained tidings of me, and crossed the Ocean¹⁵² incapable of being
Agitated, those brothers have been slain in the footprint of a cow!
The descendants of Raghu had obtained Vāruua and Agneya and
Aindra and Vāyava and Brahmaçiras weapons.¹⁵³ Through illusion
have those lords of me, who am forlorn—Rāma and Lakshmana,
resembling Vāsava himself in battle,—been slain. Coming in battle
within ken of Rāghava, a foe, even if he be endowed with the
fleetness of thought,—doth not go back, living. There is nothing
which is too hard for Time; and the Destroyer is incapable of being
overcome; inasmuch as Rāma along with his brother Lakshmana
hath fallen in fight. And I do not so much mourn Rāma or the mighty
car-warrior—Lakshmana—or, for that matter, self,—as I do the
wretched Mother-in-law of mine. She ever thinketh of the period of
the promise. ’When shall I behold Sitā and Lakshmana with
Rāghava?’" As she was thus lamenting, the Rakshasi, Trijata, said,
—"O exalted lady, do not weep thus. Thy lord liveth. And, O dignified
one, I shall unfold unto thee potent and probable reasons why the
brothers Rāma and Lakshmana live. When their leader falleth, the
countenances of the warriors in battle are not overspread with
passion, or display cheerfulness and vivacity. And, O Vaidehi, if those
had lost their lives, this celestial chariot, named Pushpaka, would not
have held thee. An army that hath its heroes and chiefs slain—
becoming dispirited and drooping, rangeth the field, like a vessel on
water that hath lost its helmsman. But, O lorn one, these troops,
betraying neither agitation nor anxiety, are guarding the Kākutsthas.
This I tell thee of them out of affection. Do thou, at this conclusion
bringing in joy, take comfort; and behold the Kākutsthas unslain.

This I tell thee from affection. I never told thee untruths heretofore;
nor, O Mithilā’s daughter, will I tell them unto thee now. Thou by
virtue of thy character conducive to delight, hast found an access
into my heart. These even the celestials and Asuras with Indra (at
their head) are incompetent to quell. Seeing such sight, I speak to
thee as to their being alive. And behold, O Maithili, this mighty
wonder! These are lying insensible with arrows; but of those Grace
hath not taken leave. It generally happens that the faces of persons
dead and gone, are unsightly to a degree. Therefore, O Janaka’s
daughter, leave off grief and sorrow and stupor. For the sake of
Rāma and Lakshmana thou canst not today put a period to thy
existence". Hearing her words, Mithila’s daughter—Sitā—resembling
the daughter of a celestial, with hands joined, said,—"May this be
so!" Then turning away the car Pushpaka fleet as the mind, the
distressed Sitā entered Lankā along with Trijata. Then in company
with Trijata, alighting from Pushpaka, she along with the Rakshasis
entered the açoka wood. And entering that sporting-ground of the
Rākshasa lord abounding in woody tracts, Sitā, having beheld those
princes and reflected on them, became subject to a mighty grief.
¹⁵² The commentator assigns a metaphorical sense to ocean,—
but this is hardly necessary.
¹⁵³ ’And did they not remember this now?’ completes the sense.—
T.
SECTION XLIX.

Bound up terribly with shafts, Daçaratha’s sons, lying down bathed
in blood, sighed hard like unto serpents. And all those foremost
monkeys, along with Sugriva, possessed of exceeding strength,—
overwhelmed with sorrow, remained surrounding those high-souled
ones. In the meanwhile, the powerful Rāma, albeit fast bound by the
shafts, awoke by virtue of the exceeding toughness of his person, as
well as his might. Then, seeing his brother, having a distressful
countenance, covered with blood, feeble, and fast bound by the
shafts,—Rāma, greatly aggrieved, began to mourn. "Of what use
unto me is the recovery of Sitā, or life either, when to-day I see my
brother vanquished in fight and lying down in the field? Seeking in
the world (of men), I may light upon a woman like Sitā; but never
on a brother, or a helper, or a warrior like unto Lakshmana. If that
enhancer of Sumitrā’s joy have met with his end, my life I must
renounce in the sight of the monkeys. What shall I say unto
Kauçalyā: and what shall I say unto Kaikeyi? And what shall I say
unto mother Sumitrā, eager for a sight of her son? And if I go (back)
without him, how shall I soothe her, like unto a cow reft of her calf;
and trembling; and resembling a mourning Kurari? And how shall I
say unto Satrughana and the illustrious Bharata,—’He went with me
to the forest; but I come (back) here without him?’ I shall not be
able to bear the rebuke of mother Sumitrā. Therefore even here
shall I renounce my person; for certainly I dare not live. Fie on me,
who am wicked and base; for me this Lakshmana, brought down,
lieth in the field of battle, like one that is without life. O Lakshmana,
thou ever comfortest me when I am dispirited. But to day, having
lost thy life, thou canst not speak to me, who am afflicted. Thou, O
hero, who hadst in battle slain innumerable Rākshasas lying around,
hast (at length) thyself been slain in the field with shafts. And lying
down in the battle-field, bleeding, and covered with arrows, thou

appearest like the Sun when he hath gone up the Setting-hill. And in
consequence of shafts piercing thy vitals, thou canst not speak; but
thy visible expression, albeit thou art dumb, betokens pain. O thou
endowed with exceeding splendour, even as thou didst follow me
into the forest, will I follow thee unto the mansion of Yama. Thou,
having dear friends, and ever following me, hast come by this plight
in consequence of my reprehensible conduct. I do not remember
having heard any harsh speech from the heroic Lakshmana, even
when he had happened to be exceedingly wroth. He that could
discharge at one shot five hundred shafts,—that Lakshmana is
superior to Kārttaviryya himself in that weapon—the bow. He that
with his arms could resist the arms of Sakra himself,—that one
worthy of a costly couch—lieth down on the ground, slain. And that
false babble shall now, without doubt, consume me; for by me hath
not Bibhishana been made monarch of the Rākshasas. Do thou, O
Sugriva, this very moment retrace thy steps. Bereft of thy strength
through me, thou wilt be worsted by Rāvana. And, O Sugriva,
placing Angada to the fore, do thou, taking thy host as well as the
equipage, in company with Nila and Nala, cross over the Ocean. By
thee hath been achieved a mighty feat incapable of being done by
another in battle. And pleased am I with the king of bears, and the
lord of Golāngulas; and Angada hath quit himself nobly, as also
Mainda and Dwivida. And Keçarin and Sampāti have both fought
terribly. And Gavaya, and Gavāksha, and Sarabha, and Gaja,—and
other monkeys have fought as others are incapable of fighting,—
determined to lay down their lives (for me). But, O Sugriva, man
cannot overrule Destiny. Thou, my friend, fearing righteousness,¹⁵⁴
hast done what lay in thy power. And, Ye foremost of monkeys, ye
also have acted as becometh friends. Now, with my permission, go
ye whithersoever ye are minded". Hearing Rāma’s lament, the

monkeys—those dark-eyed and others—began to shed tears from
their eyes. Then Bibhishana, quieting the army, taking a mace in his
hand, swiftly went to where Rāghava was. And seeing him fast
making his way, resembling a mass of dark collyrium, the monkeys
taking him to be Rāvana’s son,¹⁵⁵ began to run away.
¹⁵⁴ Dharma-bhiru—fearing righteousness—is the epithet
generally applied to persons fearing not in fact righteousness, but
unrighteousness. This may be taken as an idiotism in Sanskrit.—T.
¹⁵⁵ Indrajit. Such was the fear he had spread by his
redoubtable deeds!—T.
SECTION L.
Then out spake the highly energetic and exceedingly mighty king of
monkeys,—"Why is this host agitated like a bark driven hither and
thither by the wind?" Hearing Sugriva’s speech, Vāli’s son said,
—"Dost thou not see both those heroes—sons of Daçaratha:—Rāma
and that mighty car-warrior—Lakshmana—covered with arrows? And
(dost thou not see) those high-souled ones lying in the field of
battle, covered with blood?" Thereat, the lord of monkeys, Sugriva,
spake unto his son,¹⁵⁶ Angada—"I do not deem it without cause.
This may have come to pass through sheer fear. These monkeys
with sad faces, leaving their arms behind them, are flying in all
directions, their eyes distended in affright. And they are not
ashamed of each other, and they do not cast their looks back. And
they hug each other, and go leaping over the fallen". In the
meanwhile, that hero, Bibhishana, bearing a mace in his hand,

(approaching), greeted Sugriva as well as Rāghava with blessings of
victory. And Sugriva, seeing Bibhishana, capable of inspiring fear in
the monkeys, spoke unto the high-souled sovereign of bears, who
stood by,—"This is Bibhishana that hath come hither, seeing whom
the foremost among the monkeys, from fear of Rāvana’s son who,
they apprehend, he is,—are fleeing away, seized with a panic. Do
thou at once stay these agitated with fear and scampering all
around; and proclaim,—’This is Bibhishana, who hath come here.’"
Thus directed, Jāmbavān—king of bears—restraining those that were
flying, composed the monkeys. Hearing the bear-king’s words, and
seeing Bibhishana, the monkeys, renouncing fear, desisted (from
their flight). Then the righteous Bibhishana, viewing Rāma’s as well
as Lakshmana’s body pierced with arrows, was exceedingly
aggrieved. And washing their eyes with water, he, with his mind
overpowered with grief, began to weep and broke out into
lamentation,—"The Rākshasas, fighting in wily ways, have brought
to this pass these ones endowed with prowess and possessed of
every perfection and gifted with might (of arm). And with his guileful
mind, that brother’s son of mine, wicked-souled and an evil son
(unto me),—hath deceived these ones of straight prowess. Pierced
with innumerable shafts, and covered with blood, these are lying on
the ground like Salyakas¹⁵⁷. Those depending on whose prowess, I
had sought eminence, those foremost of men, sleep here soundly for
renouncing their bodies. Living, today I am in distress: and my
desire of dominion is annihilated; and my foe, Rāvana, hath his
promise fulfilled and his aim crowned with success". As Bibhishana
was thus lamenting, the lord of monkeys—Sugriva—endowed with
strength, embracing him, spoke unto him,—"O thou cognisant of
righteousness, thou wilt herein Lankā obtain empire: no doubt of
this; and Rāvana along with his sons will be disappointed in their

expectations. Both these—Rāma and Lakshmana—are under the
aegis of Gāruda; and, casting off their stupor: they will in battle slay
Rāvana along with his adherents". Having thus soothed and
comforted the Rākshasa, Sugriva addressed his father-in-law, who
was at his side, saying,—"Do thou along with numbers of heroic
monkeys, taking those repressors of foes, the brothers—Rāma and
Lakshmana—when they shall have regained their consciousness,
repair to Kishkindhā. And I, slaying Rāvana along with his sons and
friends, shall bring back Mithila’s daughter, even as Sakra recovered
the lost Srī". Hearing the words of the monkey-king, Sushena said,
—"I had witnessed the war of yore between the gods and the
Asuras. Then the Dānavas, enveloping themselves, momentarily
destroyed the deities, albeit versed in arms and accomplished in
weapons. And they, their senses lost, and their lives departed,
Vrihashpati treated by means of his knowledge of mantras, as well
with medicines. Let Sampati, Panaca, and other monkeys speedily
hie to the Milky Ocean for the purpose of bringing those medicines.
And the monkeys well know that mighty mountainous medicine—
divine and capable of reviving the dead,—and made by the deities
themselves—viçalyā. There are (the mountains) named Chandra and
Drona: where the ambrosia was churned, there is that supreme
drug. And those mountains have been placed by the deities in the
mighty deep. And, O king, let the son of the Wind-god go thither".
In the meanwhile, the wind arose, and masses of clouds appeared
along with lightning. And the wind blew, agitating the waters of the
deep, and shaking the mountains. And mighty trees of the ocean-
islands, broken down by the terrible wing-raised wind, began to
topple headlong into the salt waters. And the serpents dwelling
there were seized with affright; and speedily all the aquatic animals
dived deep into the salt sea. And then in a moment the monkeys

saw Vinatā’s son, possessed of terrific strength,—like unto a flaming
fire. And seeing him come, the serpents began to dart away,—those
exceedingly powerful ones that, turning into shafts, had bound those
persons.¹⁵⁸ Then, touching the Kākutsthas and saluting them,
Suparna rubbed with his hands their countenances furnished with
the splendour of the Moon. And their wounds, on being touched by
Vinatā’s son, were (immediately) healed; and the bodies of both
speedily became cool and shone with an excellent complexion. And
they attained immense energy and prowess; and a double share of
strength, and of rational and perceptive powers, and of memory.
And then raising them up, the exceedingly energetic Gāruda,
resembling Vāsava himself, embraced both joyfully. And then Rāma
addressed (Gāruda), saying,—"By thy grace we have through means
survived the mighty calamity that had sprung from Rāvana’s son;
and we have also speedily been rendered strong. And my heart is
delighted on having thee, like unto my father, Daçaratha, or my
grand sire, Aja. Who art thou, furnished with beauty, and bearing
wreaths and unguents (on thy person); clad in stainless attire; and
adorned in noble ornaments?" Unto him spake the exceedingly
energetic son of Vinatā endowed with great strength,—the lord of
birds, with a pleased heart, and his eyes wild with glee,—"O
Kākutstha, I am thy friend—thy life ranging externally—Garutman. I
am come hither for aiding you. Neither the highly powerful Asuras,
nor the exceedingly strong monkeys, nor the celestials along with
the Gandharbas, having him of an hundred sacrifices at their head
are,—capable of delivering (any one) from these dreadful arrowy
bonds, which had been forged by Indrajit of tortuous deeds by help
of illusion. These serpents—offspring of Kadru—are sharp-fanged
and venomous; and had bound thee as arrows through the potency
of illusion. O Rāma having truth for prowess, thou art fortunate,—

along with that destroyer of foe in fight, Lakshmana. Hearing this, I,
summoning energy, have come hither swiftly. And I, doing by thee
as a friend, have from affection at once set you free from these
dreadful arrowy bonds. But thou shouldst always be on thy guard.
By nature the Rākshasas have cunning shifts in fight and thou, who
art heroic and of a pure spirit, canst but rely on thy simplicity alone
for strength. Therefore thou must not trust the Rākshasas in the
field of battle. By this one instance (thou must know; that Rākshasas
are ever deceitful in fight". Having said this, the wondrous mighty
Suparna, embracing Rāma) tenderly (again), said,—"My friend
Rāghava, O thou who even cherishest affection for thy foes, permit
me thou. I shall go at pleasure. And, O Rāghava, entertain no
curiosity as to our friendship.¹⁵⁹ When, O hero, thou shalt have
achieved success in battle, thou shalt know all about this friendship
of ours. And with the surges of thy shafts, making Lankā contain
only children and aged, and slaying thy foe, Rāvana, thou shalt
recover Sitā". Having spoken thus, Suparna, endowed with fleet
vigor, having rendered Rāma hale in the midst of the monkeys,—
having gone round them and embraced them also,—that one
possessed of prowess,—set out, covering up the sky, like unto the
wind. And seeing Raghu’s sons rendered hale, the monkey-leaders
set up leonine roars, and began to flourish their tails. And then beat
the kettle-drums and the drums struck up. And conchs were
cheerfully blown; and shouts were sent. And others struck at their
arms with their hands. And the monkeys, accustomed to battle with
trees, uprooting them, stood by hundreds and thousands. And
emitting tremendous roars and thereby frightening the night-
rangers, the monkeys, eager for encounter, approached the gate of
Lankā. And that mighty and dreadful din raised by the monkeys,

resembled the terrible rumbling of the clouds at midnight about the
end of Summer.
¹⁵⁶ His step-son, for Sugriva had married Angada’s father’s
wife, after Rāma had slain Vāli in Kishkindha.—T.
¹⁵⁷ A tree.
¹⁵⁸ Rāma and Lakshmana.
¹⁵⁹ i.e. how it happened.
SECTION LI.
Then Rāvana heard the tumult raised by the highly energetic
monkeys roaring in company with the Rākshasas. And hearing that
low and solemn noise—that prodigious uproar—Rāvana said in the
midst of his counsellors,—"From mighty roars that are heard of in
innumerous delighted monkeys,—resembling the roar of clouds,—it
is evident, beyond a doubt, that there is great rejoicing there. And
the salt Ocean is vexed with these thundering noises. The brothers—
Rāma and Lakshmana—have been fast bound with sharp shafts; and
here this uproar is exciting my alarm". Having spoken thus unto his
ministers, the lord of the Rākshasas addressed the Nairitas present
there, saying,—"Do you speedily acquaint yourselves with the cause
of rejoicing that hath arisen of these monkeys on this mournful
occasion". Thus accosted, they hurriedly mounting up on the wall,
surveyed the forces maintained by the high-souled Sugriva as well as
those exalted ones—Raghu’s sons— emancipated from their terrific

arrowy fetters and arisen (now)". Thereat, with their hearts wrought
up, grim-visaged Rākshasas descending from the wall, appeared
before the Rākshasa-lord with pale faces. And then with woe-begone
faces, those Rākshasas, skilled in speech, faithfully informed Rāvana
in full of that unfortunate circumstance. "Those brothers—Rāma and
Lakshmana—who had in battle been bound up in arrowy fetters by
Indrajit,—and whose arms lay moveless,—having been emancipated
from the arrowy bonds, are seen in the field of battle; and those
ones like unto the foremost of elephants in strength, seem like
elephants that have snapped their fetters". Hearing those words of
theirs, the exeedingly powerful lord of the Rākshasas was wrought
up with anxiety and anger, and his countenance lost its complexion.
"Indrajit, having routed them in conflict, had bound them by means
of irrisistible and terrible arrows, resembling venomous serpents,
and like unto the Sun himself,—which had been conferred on
(Indrajit) as boons. But if my enemy, having actually been bound by
the weapons, can have been liberated, all this strength of mine I see
placed in peril. And those shafts resembling Fire in fierceness, which
had in battle deprived my foes of their lives,—have forsooth been
rendered fruitless". Having said this in high rage, Rāvana, sighing
like a serpent, addressed a Rākshasa, named Dhumrāksha, seated in
the midst of the Rākshasas,—"O thou of dreadful prowess,
surrounded by a mighty force, do thou march forth to compass the
destruction of Rāma along with the monkeys". Thus accosted by the
intelligent lord of the Rākshasas, Dhumrāksha, turning about, issued
out of the abode of the king. And speedily sallying forth from the
gate of (Rāvana’s) residence, he said unto the general of the forces,
—"Do thou speedily move off thy forces. Why should a warrior
linger?" Hearing Dhumrāksha’s words, the general of the forces,
following them, at the command of Rāvana forthwith made the army

ready. And those powerful and dreadful night-rangers, bursting with
high spirits,—with bells tied to their arms,—set up shouts, and
surrounded Dhumrāksha. And bearing various weapons in their
hands, and wielding darts and clubs, and equipped with maces and
bearded darts and rods and iron bludgeons and parighas and
bhindipālas and lances and nooses and axes,—those terrific
Rākshasas sallied out, roaring like unto clouds. And others,
accoutred in armour, with cars; adorned with banners; furnished
with golden networks, and mules having various faces, and
extremely swift steeds, and lusty elephants in rut,—tiger-like Nairitas
incapable of being subdued, even as tigers—sallied out (thereafter).
And then Dhumrāksha himself ascended a superb car, bearing faces
of deer and lions decked with gold,—and sending forth a loud clatter.
And the highly powerful Dhumrāksha, surrounded by Rākshasas,
cheerfully issued out of the Western Entrance, where Hanumān was
posted. And thereat, fell fowls of the air forbade that exceedingly
dreadful Rākshasa of a fearful form, as he went out ascending an
excellent car, yoked with mules, and sending sharp sounds. And an
exceedingly terrific vulture alighted at the crest of the car; and
forming themselves into lines, vultures began to drop down about
the top of the banner. And emitting a frightful cry, (a headless trunk)
dropped down before Dhumrāksha. And that god¹⁶⁰ showered down
blood; and the earth shook. And the wind blew awry with a sound
resembling thunder. And every side, covered with darkness,
appeared dim. And witnessing those dreadful inauspicious omens at
the outset, fraught with fear unto the Rākshasas, Dhumrāksha was
greatly aggrieved; and the Rākshasas marching before him, were
stupified. And then as that strong and fearful one, eager for
encounter, surrounded, by innumerable night rangers, issued out (of
the city), he beheld that monkey-host, protected by the arm of

Rāghava,—resembling the deep at the time of the universal
dissolution.
¹⁶⁰ Indra—cloud-compeller.
SECTION LII.
Seeing the Rākshasa—Dhumrāksha of dreadful prowess—issue out,
the monkeys, rejoicing greatly, eager for encounter, set up roars.
And then there took place a terrific conflict between the monkeys
and the Rākshasas, charging each other with fearful trees, and
darts, and maces. And the Rākshasas began to scatter the dreadful
monkeys on all sides; and the monkeys (on their part) felled the
Rākshasas with trees. And the Rākshasas, growing enraged, began
to pierce the monkeys with straight speeding sharp shafts winged
with Kanka plumes. And riven by the Rakshas with dreadful clubs
and bearded darts, daggers and maces and terrible and curious
bludgeons and grasped javelins,—the exceedingly powerful
(monkeys), their anger aroused, began with alacrity to perform
deeds of intrepid valour. And those monkey-leaders, their bodies
pierced with shafts and their persons riven with darts, took up trees
and crags. And those monkeys, endowed with terrific vehemence,
sending up shouts, and proclaiming their respective names, set
about tossing the brave Rākshasa ranks. And that conflict between
the Rākshasas and the monkeys, waged with diverse rocks and
innumerable trees, waxed exceedingly furious. And some among the
Rākshasas feeding on gore—on being agitated by the monkeys
burning for victory,—began to vomit blood. And some were severed

along their flanks; and, some, slain with trees, were heaped up; and
some were crushed with crags; and some were torn with teeth. And
some being broken down by means of broken standards, and some
by means of fallen swords, and some crushed down by cars,—the
rangers of the night suffered sorely. And (anon) the earth was
covered with huge elephants measuring mountains, and mountain-
tops, and steeds crushed, and the riders thereof,—all borne down by
the monkeys. And bounding again and again, the vehement
monkeys endowed with terrific prowess, with their finger-nails tore
up the Rākshasas by the mouths. And with woe-begone faces, and
with hair dishevelled, (the Rākshasas), stupified with the smell of
blood, saught the earth. And other Rākshasas endowed with
dreadful vigor, waxing wondrous wroth, dealt the monkeys slaps
with hands having the touch of the thunder-bolt. And, gifted with
greater impetuosity, the monkeys felled the impetuous (Rākshasas)
with blows, and feet and teeth; and some were slain with trees. And
seeing the forces fleeing away, that foremost of Rākshasas—
Dhumrāksha—flying into fury, began a terrific conflict with the
monkeys desirous of encounter. And some of the monkeys, sore
assailed with prāças, began to bleed; and some, wounded with
maces, dropped down to the ground. And some were beaten hard
with bludgeons; and some were cleft with bhindipālas. And some, on
being assailed with bearded darts, became insensible and lost their
lives. And some among the monkeys lay slain on the ground,
drenched in blood. And some, fleeing away from the field, were
slaughtered by the infuriated Rākshasas. And some, having their
breasts pierced, lay on their sides. And some were riven with
tridents; and the entrails of some had come out. And that mighty
and dreadful encounter of the Rākshasas and the monkeys, was
waged with countless weapons and rocks and trees. And that battle

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Handbook of Capture Recapture Analysis Steven C. Amstrup (Editor)

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