Table Of ContentP088773-PR.qxd 8/20/05 2:25 PM Page xi
Foreword
For a field wildlife ecologist beginning a study, the fundamental question often boils down
to this: do I observe, count, and categorize my “critters” usually on a large spatial scale;
or capture, mark, and recapture them usually on a small spatial scale? To read much of
the current literature, especially in the more quantitative journals, one would think the
answer was to use mark and recapture almost exclusively — which is patently ridiculous.
Clearly the correct answer is the classic — it depends! This book has as its goal redress-
ing the balance by emphasizing the importance of approaches other than mark-based
wildlife population assessment methods. More power to them is my opinion!
The availability of accurate and precise estimates of the demographic parameters of
wildlife populations (recruitment rates, survival rates, movement rates, population sizes,
and population rate of change) is crucial to their successful conservation and manage-
ment. Some populations need management because of their importance as harvested
species, whereas other populations need conservation due to their rarity induced by
human causes such as human overpopulation, pollution, and habitat fragmentation. One
doesn’t need to be a “rocket scientist” to realize that the need for reliable estimates of
demographic parameters is growing more crucial by the day, whereas many wildlife and
conservation agencies have been and are suffering outrageous funding cuts.
In retrospect, it is very clear that a major milestone in the field was reached in 1973
when Seber published the first edition of his book on the estimation of animal abundance
and related parameters. For the first time a successful attempt had been made to synthe-
size the methods in a coherent pedagogy and show the strength and weaknesses of the
statistical models used. Seber’s book enabled statisticians and quantitative biologists to
make rapid and important advances in the 30 plus years since 1973. However, these
advances have been uneven. For example, for short-term studies on closed animal pop-
ulations, major research and synthesis has occurred for count methods where detection
is primarily related to distance (distance sampling). There has also been an explosion of
methods based on marked animals. Closed population capture-recapture and removal
methods are now on a sound footing. Open capture-recapture models and the robust
design have also seen major advances. Sophisticated software like DISTANCE and
MARK allow model selection and parameter estimation based on maximum likelihood
methods.
One area that has not received as much attention has been methods for analyzing
various types of counts (based on observation or removal), especially where age and sex
P088773-PR.qxd 8/20/05 2:25 PM Page xii
xii Foreword
categorizations are involved. This book has made an excellent attempt to fill that gap.
Many of the methods discussed in this book were historically derived by intuitive
approaches. However, for sound statistical inferences, the demographic methods must be
based on solid design principles and on properly specified sampling distributions and
likelihood functions. Thus, in some cases, new theory had to be developed before the
synthesis could take place and the book completed. In my opinion, this is one of the key
strengths of the book.
Are there other reasons why is this book important? To return to my initial theme, I
believe that statisticians and quantitative biologists have tended to focus on the develop-
ment of methods using marked animals. A fundamental reason for this is that marking
establishes known cohorts of animals and therefore makes modeling so much simpler for
the statistician. However, these methods are often expensive and suitable only for small
spatial scales, whereas many wildlife agencies have emphasized the importance of other
approaches that are less expensive in order to collect information on larger spatial scales.
As an example, let us focus for a moment on survival rate estimation of a fish popula-
tion in, say, a large lake. There are a plethora of methods used based on different types
of marking schemes. For example, an open capture-recapture model (Cormack-Jolly-
Seber) might be used or a tag-return model (Brownie) might be used if the population
of fish is exploited. Alternately, telemetry tagging models may be used. All these
approaches are very expensive and may be difficult to implement on a very large lake
(they also have very strong model assumptions). Therefore, an alternative “catch curve”
approach is often used by fisheries agencies because it is much less expensive. This
involves taking a random sample of the age distribution (or part of the age distribution)
of the population and using a catch-curve method. A critical concern, though, in the use
of catch-curve methods is the validity of the fundamental concept of a stable age distri-
bution that requires very strong assumptions of constant temporal recruitment and
survival. It may also be difficult to obtain a random sample, even of a subset of the
ages.
A foreword would not be complete without a few comments on where I think the
field is heading. So what will be some important research thrusts? One of them is the
integration of multiple approaches, which is a major focus of this volume. Integration
will often give estimates that have better precision and are more robust because they
allow weakening of assumptions. One of many examples in the book is the simultane-
ous estimation of survival rates from both age-based “catch-curve” and radiotelemetry
data.
The estimation of survival rates from catch curves illustrates another very important
principle, which is the integration of structural population dynamics models and
statistical models to get an estimate. This means that the training of quantitative scien-
tists working on wildlife population demography needs to include statistics, biomathe-
matics, ecology, and the mastery of sophisticated computer software and computer
programming. No longer can we afford the lack of integration and petty infighting
between university departments that reduces the effectiveness of true interdisciplinary
teaching and research.
Now that we have most of our models on a sound theoretical footing with well-defined
likelihood functions and access to enormous computing power, it is possible to build very
complex and intensive computer algorithms to compute estimates and their sampling dis-
P088773-PR.qxd 8/20/05 2:25 PM Page xiii
Foreword xiii
tributions. Several major themes are emerging: one is the use of bootstrap and other
resampling methods; a second is the now common usage of Monte Carlo simulation
methods to study the properties of estimators; and a third is the use of Bayesian methods
computed using Markov chain, Monte Carlo methods.
Dr. Kenneth H. Pollock
Professor of Zoology, Biomathematics and Statistics
Department of Zoology
North Carolina State University
Raleigh, North Carolina
P088773-PR.qxd 8/20/05 2:25 PM Page xv
Preface
In recent decades the quantitative field of wildlife demographics has increasingly focused
on animal marking studies to estimate population parameters (e.g., Seber 1973). There
is good reason for this trend; mark-recapture methods can provide precise and accurate
estimates of survival, abundance, density, and recruitment when sufficient numbers of
animals are marked, high capture probabilities can be expected, and the underlying sta-
tistical models are valid. The inherent costs and logistical difficulties of marking studies,
however, often restrict the scope of these investigations to intensive localized studies.
Theoretical considerations can also limit the flexibility and realism of marking models,
particularly in the area of abundance estimation of both closed and open populations.
Field biologists have therefore continued to embrace extensive cost-effective methods
that provide demographic information on a broader geographic scale. These methods
generally rely on visual counts, sex ratios, and age-structure data commonly collected by
wildlife agencies for many years. The underlying statistical and sampling models for
these demographic studies, however, have generally not received the same quantitative
scrutiny as statistical models used in mark-recapture theory. Moreover, there has been
little attention to coupling intensive marking models with extensive count, sex ratio, and
age-structure data. This union could be useful because of the statistical precision offered
from intensive marking studies and geographic advantages of extensive studies. The need
for cost-effective, wide-scale, and scientifically defensible demographic methods is moti-
vating this change.
Nationwide, the Endangered Species Act and Habitat Conservation Plans have placed
increasing demands on resource agencies to quantify status and trends of wildlife popu-
lations. At the same time, the human population in the United States has shifted from
a predominantly rural to an urban society. Associated with this shift, the general public
is viewing wildlife more and more as a nonconsumptive rather than as a consumptive
resource. Consequently, the general public is requiring more justification for wildlife
harvest regulations and has elevated wildlife management into the public arena. In
Washington State, for example, voters impatient with state biologists have substituted
legislative referenda for game management by scientific principles. Harvest apportion-
ment between sport and Native American hunters is also requiring more detailed assess-
ment of wildlife resources and the consequences of harvest management practices.
It is within this environment our book has been written. Our goal was to assemble the
many quantitative approaches wildlife biologists commonly use to analyze and interpret
P088773-PR.qxd 8/20/05 2:25 PM Page xvi
xvi Preface
count observations, and sex- and age-structure data. In assembling these methods, we
often needed to reformulate them in a modern statistical framework, permitting not only
parameter estimates, but also variance estimation and sample size calculations. To do so,
we needed to use a level of mathematical rigor that many biologists will find challeng-
ing. We felt that model development and specification was important for our goals and
to allow other investigators to extend these techniques into new situations and applica-
tions. The quantitative approach produced both a dilemma and a challenge.
The book is written foremost to be a practical guide to the analysis of sex, age, and
count data. To satisfy the need for both quantitative rigor and expository value, estima-
tion equations have been highlighted to distinguish them from model development. In
addition, the book includes numerous annotated examples of the statistical methods that
are clearly demarcated in the text. Biologists may wish to study a method by beginning
with the examples. The more quantitatively trained readers may wish to begin with the
model formulation. All readers should find the discussions of utility for each method
helpful.
The book concludes with a chapter on case studies. The intent is to bring together the
demographic tools presented in earlier chapters for the purposes of demographic assess-
ment and management. The examples were chosen to illustrate different applications and
joint use of multiple techniques for problem solving. The examples were not meant to
be exhaustive of the demographic scenarios or solution approaches available to biolo-
gists. Instead, we hope this Preface and the chapters that follow will kindle an interest in
exploring new and ever better approaches to wildlife demography for the benefit of
wildlife resources everywhere.
We wish to thank Gary Brundige, Andy Cooper, Todd Farrand, Sherry Gao, Bob
Gitzen, Mike Hubbard, Brian Kernohan, Mike Larson, Chad Rittenhouse, Gary Roloff,
Mark Rumble, Mark Ryan, John Schulz, Frank Thompson, Brian Washburn, and Pete
Zager for their timely reviews and constructive comments on the book. In addition, we
thank Clait Braun for reviewing and editing the entire manuscript. His comments greatly
improved the clarity, accuracy, and consistency of the book.
We would like to especially thank Rich Townsend and Jim Lady for their computer
and analytical support. Peter Dillingham wrote the Mathematica code for Appendix D.
Remington Moll carefully checked all examples contained within the book, and we
are very appreciative of his efforts. Manuscript preparation was provided by Cindy
Helfrich—without her help and devotion, this book could not have been produced.
Dr. Millspaugh would personally like to thank Rami for her support and patience while
writing the book. He would also like to thank the many people at the University of
Missouri including John Gardner, Gene Garrett, Jack Jones, Tom Payne, and Mark Ryan
who supported the project and provided him with time to write and visit Seattle. He would
like to thank his graduate and undergraduate students who continue to provide valuable
input on presenting quantitative methods to wildlife biologists. Rather than providing an
exhaustive list of influential collaborators and colleagues, he would like to acknowledge
personnel at Huntington Wildlife Forest, SUNY-ESF, SUNY Cobleskill, Custer State
Park, South Dakota Department of Game, Fish, and Parks, South Dakota State Univer-
sity, Boise Cascade Corporation, University of Washington, Raedeke and Associates,
Inc., University of Missouri, Missouri Department of Conservation, National Park
P088773-PR.qxd 8/20/05 2:25 PM Page xvii
Preface xvii
Service, and the U.S. Forest Service who sparked and encouraged his interest in quanti-
tative applications in wildlife management.
In addition, Dr. Ryding would personally like to thank the other two authors, John and
Josh. She greatly appreciates family members for their support; Dee and John Fournier,
Bill, Angela and Melissa Ryding, and Jan Beal. She would also like to thank friends who
have been there along the way, some of whom are mentioned above, Cindy H., Andy C.,
Rich T., Peter D., and also Kevin Brink, Anne Avery, Sarah Hinkley, Martin Liermann,
Owen Hamel, Vaughan Marable, Anna Bates, Erin Wolford, John Walker, Michelle
Adams, and Ken Wieman—and finally, the graduate students of the Interdisciplinary
Graduate Program for Quantitative Ecology and Resource Management at the University
of Washington and the staff of Columbia Basin Research.
Finally, Dr. Skalski would personally like to thank Lauri for her encouragement,
support, and patience while the book was being written. He would also like to thank the
students and faculty of the School of Aquatic and Fisheries Sciences, the Interdiscipli-
nary Graduate Program for Quantitative Ecology and Resource Management, and the
Wildlife Science Program at the University of Washington for their help and support.
Thanks are also extended to the Idaho Department of Fish and Wildlife and the
Washington Department of Fish and Wildlife for providing examples and inspiration for
this book. The School of Aquatic and Fishery Sciences provided funds to help defray
some of the developmental costs of this book. Program USER, illustrated in this book,
was developed with funds from the Bonneville Power Administration, Project 198910700,
of the Columbia River Fish and Wildlife Program.
John R. Skalski
Kristen E. Ryding
Joshua J. Millspaugh
P088773-Ch001.qxd 8/20/05 2:27 PM Page 1
1
Introduction
Chapter Outline
1.1 Historical Perspectives and Current Needs
1.2 Scope of Book
1.1 Historical Perspectives and Current Needs
Early efforts to assess demographics of wild animal populations often relied on sex-
and age-structure data collected from animal sightings or hunter bag checks. By use of
sex- and age-structure data, biologists estimated population sex ratios (Severinghaus
and Maguire 1955), productivity (Dale 1952, Hanson 1963), age-specific survival
(Hayne and Eberhardt 1952), harvest mortality (Allen 1942, Petrides 1954, Selleck and
Hart 1957), population abundance (Kelker 1943, DeLury 1945), and rates of population
change (Kelker 1947, Cole 1954). These techniques received substantial attention
early in wildlife management (Hanson 1963), perhaps because data needs were minimal,
data were relatively easy to collect, and the techniques were applicable over large
geographic areas. Moreover, the resulting analytical approaches used were a clever blend
of life-history knowledge and available survey data a biologist could readily use and
understand.
A drawback to the early heuristic procedures was lack of mathematical rigor in the
derivation of the estimators. Most of these estimators lacked explicit variance expres-
sions and statements of assumptions. Early efforts to catalogue and review these tech-
niques offered little guidance. In the Hanson (1963) monograph, variance estimation was
not addressed, presumably because of the complexity of such analyses and the space
required to present them (Hanson 1963:7). Although early researchers (e.g., Davis 1960)
recognized the need for variance estimates to assess the precision of demographic analy-
ses, these estimates were widely unavailable until later (e.g., Paulik and Robson 1969).
Even today, clear statements of assumptions and variance expressions are lacking for
many of these techniques. Without variance expressions and a clear statement of assump-
tions, there is no way to evaluate accuracy or precision of the demographic parameters.
Thus, biologists have no way to identify how much confidence to place in the demo-
graphic estimates. In a recent review, Skalski and Millspaugh (2002) provided variance
expressions and evaluated precision of the sex-age-kill model of population reconstruc-
tion (Creed et al. 1984). They found the required level of precision in field data collec-
tion necessary to provide useful estimates of population abundance was unattainable with
existing levels of effort. Numerous other techniques also need to be placed in a modern
statistical framework and evaluated to examine their usefulness.
P088773-Ch001.qxd 8/20/05 2:27 PM Page 2
2 Introduction
The repeated discovery, use, and modification of these sex- and age-structure proce-
dures has resulted in a duplication of efforts and inhibited further advancements. Hanson
(1963) attributed repeated rediscovery of sex- and age-structure-based demographic
assessments to several factors such as omission of important formulas or derivations of
those formulas in early publications, unfamiliar notation, and obscurity of the original
publications. His monograph (Hanson 1963) nicely summarized the available techniques
of the time to assess demographics from sex- and age-structure data and provided a few
important extensions. But his monograph fell short of providing suggestions for study
planning and sample size requirements, issues later addressed by Paulik and Robson
(1969) for change-in-ratio techniques. A need exists today for additional guidance when
planning field activities. Researchers should be aware that, for a given demographic
parameter and data type, there is often more than one estimator available. Choosing the
most appropriate estimator will depend on which assumptions are valid for a particular
data set and study objectives.
Sex- and age-structure techniques continued to be rediscovered, extended, and used
extensively throughout the late 1960s (e.g., Paulik and Robson 1969) and 1970s
(e.g., Lang and Wood 1976), and further attempts have been made to summarize the
available techniques (Udevitz and Pollock 1992). Roseberry and Woolf (1991) compared
several alternative approaches for estimating the abundance of white-tailed deer
(Odocoileus virginianus) by using harvest data and reconstruction techniques. Notable
among their contributions was a list of important assumptions and a discussion of
data requirements. Although discussed in terms of white-tailed deer, many of their sug-
gestions apply equally well to other species. However, no variance expressions were
offered, and their evaluation was strictly empirically based. Instead, they referred readers
to Seber (1973), who provided more thorough mathematical descriptions, along with vari-
ance estimators for some techniques. The work by Seber (1973) is still considered the
standard reference for many techniques that use sex- and age-structure data to estimate
abundance. Although the utility of Seber (1973) remains, many procedures for demo-
graphic assessment were omitted, and these techniques should be advanced with the same
rigor.
Despite the obvious weaknesses, demographic assessments based on sex, age, and
count data are still common today. For many wildlife agencies, sex and age data collected
during field surveys or through hunter check stations represent the only available demo-
graphic data to manage wildlife populations. For example, Skalski and Millspaugh (2002)
noted that at least 20 state agencies use the sex-age-kill model to estimate white-tailed
deer abundance. Although these techniques offer a convenient means of data collection
over extensive regions, they are not free from rigorous assumptions. Because sex- and
age-structure data are often opportunistically collected over large regions (e.g., at check
stations), it is tempting to overlook the assumptions and sampling requirements of these
data for demographic assessment. As a result, some researchers have been critical of
sex- and age-structure data for demographic assessment. Johnson (1994:438) writes,
“methods based on age-structure data have received much attention in the past, proba-
bly more than they merit considering their deficiencies.” Mounting pressure for effective
conservation strategies requires biologists to weigh the utility of different analytical and
sampling options in light of accuracy, precision, and economics. Because demographic
assessments based on sex- and age-structure data offer a convenient, geographically
extensive, and cost-effective means to acquire data, they will continue to be used by many
P088773-Ch001.qxd 8/20/05 2:27 PM Page 3
Scope of Book 3
agencies. Consequently, many of the unresolved issues in using these techniques must
be addressed.
1.2 Scope of Book
This book unifies, evaluates, updates, and illustrates methods of estimating wildlife
demographic parameters from sex ratios, age structures, and count data commonly col-
lected by wildlife biologists. The demographic parameters included are commonly used
in modeling population dynamics of wildlife species: productivity, survival, harvest rates,
abundance, and rates of population change. Our work focuses on estimation techniques
that use sex, age, and count data because (1) these data are relatively easy to collect for
game and nongame species compared with more expensive and labor-intensive tech-
niques that require animal marking or radio tagging; (2) these data are commonly col-
lected and used by wildlife management agencies; (3) these survey data have not received
the same statistical rigor that has been focused on other field data (e.g., mark-recapture
data); (4) these techniques are scattered throughout the literature with no cohesive syn-
thesis and evaluation; and (5) once formal statistical models for the analysis of sex and
age data have been developed, this information can be coupled with mark-recapture
models for more advanced demographic analyses.
This book provides a variety of statistical techniques that are useful in managing
wildlife resources. More efficient use of the data currently collected should aid in better
evaluation of population status and trends. Further, an understanding of the nature and
sources of variability should help direct data collection efforts. Greater understanding of
model assumptions and the magnitude of sampling error should also improve the inter-
pretation of information on population status and trends.
Most of the estimation techniques discussed in this book are widely scattered through-
out the literature. A source is needed for the derivation, likelihood functions, variance
expressions, and sample size calculations of these demographic methods. Although tech-
niques to estimate wildlife population demographics have been the focus of several
books, these books review methods that require animal marking (Seber 1982, Skalski
and Robson 1992, Thompson et al. 1998, Williams et al. 2001) or radio tagging (White
and Garrott 1990, Millspaugh and Marzluff 2001), or line-transect procedures (Buckland
et al. 1993). This book is different because it focuses on techniques that use sex ratios,
age structure, or count indices commonly collected by field biologists.
Part of the value in this work lies in presenting the estimators developed over many
years, and in various outlets (e.g., journal articles, books, dissertations, unpublished
agency reports), in one place, in a quantitative manner. By doing so, relationships among
techniques are made and gaps in knowledge are identified and filled. An area that should
be explored further is the use of auxiliary information to relax the assumptions of some
of these methods. For example, age-structure analysis is often based on the assumption
of a stable and stationary population, which may not be the case (e.g., Unsworth et al.
1999). Joint likelihoods using mark-recapture and age-structure data could be derived to
eliminate the assumptions of stable and stationary population for some estimators, and
to separately estimate natural and harvest survival probabilities.
The presentation of techniques in this book was structured so that the quantitative
goals of the estimator are understood and referenced with previous developments and
