EPA/600/R-06/038
ERASC-006
April 2006
ASSESSING RISKS TO POPULATIONS AT SUPERFUND AND RCRA SITES
CHARACTERIZING EFFECTS ON POPULATIONS
by
Wayne R. Munns, Jr. and Matthew G. Mitro
U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research laboratory
Atlantic Ecology Division
Narragansett, RI 02882
Ecological Risk Assessment Support Center
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH
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AUTHORS, CONTRIBUTORS AND REVIEWERS
AUTHORS
Wayne R. Munns, Jr.
U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research Laboratory
Atlantic Ecology Division
Narragansett, RI 02882
Matthew G. Mitro
U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research Laboratory
Atlantic Ecology Division
Narragansett, RI 02882
(currently employed at Wisconsin Department of Natural Resources, Monona, Wisconsin)
REVIEWERS
Wayne G. Landis
Western Washington University
Institute of Environmental Toxicology and Chemistry
516 High Street
Bellingham, WA 98225-9180
Mary T. Sorensen
ENVIRON International Corporation
1600 Parkwood Circle, Suite 310
Atlanta, GA 30339
ACKNOWLEDGMENTS
Programmatic review of the document was conducted by Susan Roddy, EPA Region 6;
Gina Ferreira, EPA Region 2; Dale Haroski (currently, Office of the Administrator); and Dale
Hoff, EPA Region 8. Glenn Suter of EPA's National Center for Environmental Assessment,
ORD, kindly provided text describing development of the assessment population concept.
Technical review of the previous draft of this document was conducted by Rick Bennett, Gina
Ferreira, Tim Gleason, Anne Kuhn, Joe LiVolsi, William "Skip" Nelson, Nathan Schumaker,
Charlie Strobel, Glenn Suter, Sharon Thorns, and Steve Wharton.
n
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TABLE OF CONTENTS
Page
AUTHORS, CONTRIBUTORS AND REVIEWERS ii
ACKNOWLEDGMENTS ii
GLOSSARY OF KEY TERMS v
1. Statement of Problem and Scope of Response 1
2. Definition of Population 3
2.1 Ecological Definitions 3
2.2 Operational Definitions - the Assessment Population Concept 4
3. Survey of Population-Level Attributes 10
3.1 Population Abundance 10
3.2 Population Growth 13
3.3 Population Structure 14
3.4 Population Persistence 16
3.5 Considering Attribute Selection 17
3.6 Ecological Significance of Responses 18
4. Linking Effects on Individuals to Population Response 21
4.1 About Models 21
4.2 Extrapolation Models 24
4.3 Extrapolating From Toxicity Test Data 34
4.4 Considering Spatial Scale 38
4.5 Considering Model Selection 40
4.6 Considering Uncertainty in Extrapolation 42
5. Measuring Population Attributes and Parameters in the Field 47
5.1 Measuring Population Abundance and Density 47
5.2 Measuring Population Growth 51
5.3 Measuring Population Structure 57
5.4 Measuring Population Persistence 57
5.5 Considering Scalar Issues 59
5.6 Considering Uncertainty in Field Measurements 60
111
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TABLE OF CONTENTS (cont.)
Page
6. Outstanding Research Issues for Superfund and RCRA 62
7. References 65
APPENDIX: ERASC Request 81
IV
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GLOSSARY OF KEY TERMS
assessment population
bottleneck effect
carrying capacity
cohort
compensation
compensatory mechanism
critical abundance
demographic rates
density dependence
emergent property
equilibrium abundance
error
a group of conspecific organisms occupying a defined area
which has been selected to serve as an assessment endpoint
entity for an ecological risk assessment
a reduction in genetic heterogeneity within a population as
a result of stressor-induced mortality
the maximum abundance of a biological population that is
sustainable by a habitat or environment
a group of similarly-aged members of a population
a feedback between the density of a population and some
biological property of that population (typically
demographic rates) (synonymous with density dependence)
a biological mechanism, such as homeostatic acclimation of
individuals, genetic adaptation, and density dependence in
vital rates and migration, that can ameliorate adverse
effects over the short or long term
the specific population density or abundance below which
adverse population-level effects are known or suspected to
occur
age- or stage-specific birth and death rates of individuals
within the population (synonymous with vital rates)
a feedback between the density of a population and some
biological property of that population (typically
demographic rates) (synonymous with compensation)
a property of a system that cannot be predicted simply by
understanding processes occurring at lower levels of
organization in that system
the abundance of a population at steady state
uncertainty resulting from the use of the wrong methods,
models, and data in assessment activities
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ignorance
inbreeding depression
life-table
meta-analysis
metapopulation
parameterization
population
population attribute
population measure
prediction
projection
sensitivity analysis
state variable
subpopulation
uncertainty resulting from a lack of knowledge about the
true value of a parameter that can result from inadequate or
imperfect measurement
detrimental changes in birth and death rates resulting from
reduced genetic diversity (usually a problem of small
effective population sizes)
age- or stage-specific schedules of fecundity and
survivorship
an analysis that compares the outputs of two or more
models constructed using different assumptions
a biological population consisting of two or more
subpopulations separated in space
quantification of the variables in a model
variously: a collection of individuals of a single species that
occupy some defined geographical space; a subset of all
individuals of a given species that share a common area and
that interbreed
a characteristic of the assessment population
a metric used to quantify a population attribute
a quantitative description of the future abundances or
behavior of a population
a qualitative description of the future abundance or
behavior of a population assuming constant environmental
conditions
an evaluation of the influences of model variables on model
outputs
a component or property of the system being modeled that,
when aggregated with other state variables, determines
what the system looks like
an internally coherent subdivision of the larger population
VI
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transition probability a demographic model parameter describing the likelihood
that individuals will move from one age or stage to another
transmutation qualitative changes in the causes and mechanisms of
response at different levels of biological organization
variability uncertainty resulting from actual differences in the value of
a parameter or attribute among units in a statistical
population
vital rates age- or stage-specific birth and death rates of individuals
within the population (synonymous with demographic
rates)
vn
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1. Statement of Problem and Scope of Response
In July 2000, ORD's Ecological Risk Assessment Support Center received a request from
the Ecological Risk Assessment Forum (ERAF) to provide insight to issues associated
with site-specific ecological risk assessments involving populations (Appendix). This
request contained questions that have frequently been asked in the context of several
regulatory programs, including Superfund, Resource Conservation and Recovery Act
(RCRA), pesticide registration, water quality criteria and standards development, and
National Pollutant Discharge Elimination System (NPDES) permitting, as well as in
efforts undertaken by natural resource trustees. These questions include:
How should populations be defined?
What should we measure to characterize populations?
How do we make the connection between measurements made on individual
organisms and population effects?
How can we measure and interpret effects on natural populations?
What spatial and temporal scales are appropriate when assessing risks to populations?
Although relevant to almost all risk assessments involving populations, the problem
reflected in these questions is particularly acute in the Superfund Remedial
Investigation/Feasibility Study (RI/FS) and RCRA Facility Investigation/Corrective
Measures Study (RFI/CMS) processes. While objectives like "population effects will be
addressed" are something to be desired and are often required, Remedial Project
Managers (RPMs) and site managers may lack practical knowledge of the concepts,
approaches, and methods for assessing the effects of environmental stressors on
populations. This problem creates difficulties during the problem formulation stage of
the assessment and often leads to uncertainty in the interpretation and use of assessment
results in support of management decisions.
This white paper attempts to support performance and interpretation of population-level
risk assessments conducted during Superfund RI/FS and RCRA RFI/CMS processes by
providing information relevant to the above questions. Its structure and content are
determined by the ERASC request and subsequent discussions with ERASC and
Regional Office staff. It does not attempt to provide specific, "how to" guidance for
performing site-specific population-level risk assessments, and it specifically avoids
explicit consideration of salient exposure analysis methods and approaches for risk
characterization (i.e., for comparing and interpreting site-related population-level effects).
Although much needed, development of such guidance is well beyond the scope of the
ERASC support function. Rather, the focus of this white paper is strictly on issues
relevant to characterizing effects on populations. And although structured in a way to
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support site-specific risk assessment for Superfund and RCRA, it is written primarily
from the viewpoint of population ecology. (As this white paper was being reviewed, the
Society of Environmental Toxicology and Chemistry (SETAC) organized an international
workshop on population-level ecological risk assessment. This workshop addressed
many of the issues salient to the ERASC request, and considered other issues that may be
germane to assessing risk to populations at Superfund and RCRA sites. The proceedings
of that workshop (Barnthouse et al, in review) were undergoing external peer review as
the current document was being finalized. Agency staff are encouraged to refer to
Barnthouse et al. (in review) for discussions of several scientific issues, management and
population protection issues, empirical and modeling tools, and application of the
Agency's Ecological Risk Assessment Guidelines to population-level ecological risk
assessment.)
In addition to this context-setting material, the white paper consists of seven major
sections: Section 2 describes ways in which populations can be defined relative to site-
specific risk assessments, settling upon the concept of "assessment population" as
described by the Risk Assessment Forum's recently completed Generic Endpoints for
Ecological Risk Assessments project; Section 3 enumerates the attributes that describe
populations, and offers some opinion about which might be relevant to Superfund and
RCRA risk assessments; Section 4 surveys mathematical and other models that can be
used to extrapolate effects on individuals to population response, and includes
information about using toxicity test data in such extrapolations; Section 5 describes
techniques and issues associated with estimating population attributes, and the
demographic parameters used to calculate them, in populations at field sites; Section 6
identifies some of the major outstanding research needs relative to population-level risk
assessments, and describes some of the work ORD is conducting to meet those needs; and
Section 7 lists the extensive literature cited throughout the paper, identifying key
references for additional description of relevant topics.
Although reasonably complete, no attempt was made in this white paper to provide an
exhaustive review of available concepts and methods in population ecology. The
information contained herein should be used as an entree and primer to the state-of-the-
science that supports evaluation of population-level effects. With time and significant
additional effort, this work might form the basis of guidance for assessing risks to
populations. Plans for accomplishing this have yet to be identified.
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2. Definition of Population
What is a population?
This question is of central importance when establishing assessment endpoints and
identifying analysis activities as part of a site-specific risk assessment. Several
definitions have been used for the term population, including general definitions used in
classical ecology and modern biology, and operational definitions developed for specific
purposes. The usefulness of any of the definitions in a Superfund or RCRA risk
assessment depends upon the context of the assessment and the risk it is attempting to
characterize.
2.1 Ecological Definitions
In the most general sense, a population is simply a collection of individuals of a single
species that occupy some defined geographical space. This definition works well for
many ecological studies, as long as the rates of migration into and out of that collection of
individuals are small relative to rates of internal replacement (i.e., reproduction). More
specific definitions add requirements for interbreeding and the exchange of genetic
material. Thus, a population can be defined on the basis of a shared gene pool. Such a
collection of individuals can be called a Mendelian population (Pianka, 1974), reflecting
classical concepts of Mendelian segregation and heredity. Mendelian populations might
be defined on the basis of genotypes and allele frequencies, using modern techniques of
population genetics and molecular biology. This definition, of course, applies to
organisms that reproduce sexually, as true asexual organisms have no opportunity for
genetic exchange.
Thus, the term population as used in ecological studies denotes a subset of all individuals
of a given species that share a common area and that interbreed. In reality, it is unlikely
that all individuals in a given geographical space truly interbreed. Population studies
therefore generally rely on demarcations imposed by boundaries that constrain organism
movement (or more specifically, genetic exchange) such that the dynamics of population
size and structure are controlled by processes operating internally as opposed to by
external processes such as migration. Such boundaries can be natural (as functions of
geography and geology) or artificial and imposed. However, when boundaries are not
obvious, or when they don't appear to coincide with those of the hazardous waste site or
operable unit/waste management unit, the question of how to define the population for the
purposes of the assessment likely remains.
There is a substantial literature describing the concepts and theory of population ecology
that build from these general definitions. Because most of this is beyond the scope of this
white paper, we refer those interested to any modern, general ecology text.
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2.2 Operational Definitions - the Assessment Population Concept
Academic definitions notwithstanding, a population needs to be defined in a manner
meaningful to site-specific risk assessments to be useful to the Superfund and RCRA
processes. The U.S. EPA's Risk Assessment Forum (RAF) has undertaken a project to
develop generic endpoints for ecological risk assessment. Recently finalized, this effort
has drafted two operational definitions relevant to site-specific population-level risk
assessments (U.S. EPA, 2003):
Assessment Population - A group of conspecific organisms occupying a defined area
which has been selected to serve as an assessment endpoint entity for an ecological risk
assessment.
Assessment Community or Assemblage - A group of organisms occupying a defined area
which has been selected to serve as an assessment endpoint entity for an ecological risk
assessment. The group may include all organisms in the area, in a taxon (a plant
community or bird community), or in certain samples (macroinvertebrates in Hester-
Bendy samples).
Reflecting the intent of the Generic Ecological Assessment Endpoints project, the
remainder of this document relies on the assessment population concept (see Text Box 1
for further discussion on assessment populations and communities).
Factors to consider in problem formulation when defining the assessment population
include various ecosystem and receptor characteristics, such as the biology and life
history of the species, it's range relative to the hazardous waste site or operable unit, and
the potential for movement between subpopulations. In addition, conservation
management and policy goals and other factors that define the decision context of the risk
management question are important considerations. Probably the most important
consideration is driven by site management goals that the risk assessment is intended to
support (see Munns et al, 2002). These goals establish the specific risk questions to be
asked in the assessment, the analysis approaches to answer the questions, and ultimately,
the definition of assessment population.
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Text Box 1. Assessment Populations and Communities
(Prepared by Glenn Suter, ORD National Center for Environmental Assessment (NCEA),
for the RAF generic endpoints project; U.S. EPA, 2003)
Because the conventional ecological meaning of populations and communities presents
problems in practice, this document introduces the terms "assessment population" and
"assessment community" (defined in text). Although ecological assessment endpoints
inevitably include population properties such as abundance and production, and community
properties such as species richness, it is difficult to delineate populations and communities in
the field. Classically defined populations are discrete and interbreeding. Classically defined
communities are discrete and their constituent species are relatively consistent and interact in
predictable ways. Although these classical definitions have been important to the
development of genetics, evolution, and ecology (e.g., Hardy-Weinberg equilibrium and the
competitive exclusion principle), they have always had manifest limitations in practice. More
recently, ecology has become more focused on temporal dynamics, spatial patterns and
processes, and stochasticity that belie the notion of static, independent populations. One
example of this is metapopulation analysis which reveals that population dynamics are
significantly determined by exchange of individuals among habitat patches or differential
movement across a landscape that continuously varies in suitability (Hanski, 1999).
Communities are subject to the same dynamics. For example, the species diversity of Pacific
coral reefs is apparently determined by the availability of recruits from other reefs within 600
km (Bellwood and Hughes, 2001). If the composition of coral reefs, which would appear to
be classic discrete communities, is in fact determined by regional dynamics, there is little
chance of delimiting discrete communities in general.
Populations may be readily delimited if they are physically isolated within a broader species
range (e.g., a sunfish population in a farm pond) or if the species consists of only one
spatially discrete population (e.g., the endangered Florida panther, whose current range is
restricted almost exclusively to southwest Florida). Otherwise, population boundaries are
difficult to define because they are typically structured on multiple scales. Genetic analyses,
which are needed to define discontinuities in interbreeding frequencies, are not a practical
option for most ecological risk assessments.
The practical problems are even greater for communities. Although the members of a
population consist of a single species, it is not always clear whether a particular group of
organisms constitutes an instance of a particular community type. This is because the species
composition of communities varies over space and time.
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Text Box 1 (cont.)
To protect properties such as population production or community species richness, it is
necessary to develop a pragmatic solution to these problems. An example of such a solution is
the approach taken by the Nature Conservancy and NatureServe (formerly the Association for
Biodiversity Information) to inventory and map biodiversity (Stein et al., 2000). Because it is
not feasible to define discrete populations or communities, these organizations inventory and
map occurrences of conservation elements, which may be defined at various scales, depending
on the elements and circumstances. For example, a plant community occurrence may be "a
stand or patch, or a cluster of stands or patches." However, an occurrence of a bird species
would be defined quite differently.
We propose a similar solution for GEAEs [generic ecological assessment endpoints]. For
individual assessments, the population or community entities to be protected must be defined
during the problem formulation stage of risk assessment. These assessment populations and
assessment communities should be defined in a way that is biologically reasonable, supportive
of the decision, and pragmatic with respect to policy and legal considerations. For example, it
would not be reasonable to define the belted kingfishers occurring in a 20 m stream reach as
an assessment population if that reach cannot fully support one belted kingfisher pair. On the
other hand, even though the kingfisher's range is effectively continuous, it would not be
reasonable to define the entire species as the assessment population, given that it ranges across
nearly all of North America. Rather, it may be reasonable to define the kingfishers on a
watershed or a lake as an assessment population.
Assessment populations may be defined by nonbiological considerations as well. For
example, for Superfund ecological risk assessments on the Department of Energy's Oak Ridge
Reservation, populations of large terrestrial vertebrates were delimited by the borders of the
reservation (Suter et al., 1994). This definition was reasonable not only because the
Superfund site was defined as the entire reservation, but also because the reservation was large
enough to sustain viable populations of deer, wild turkey, and bobcat, among others.
Although the reservation is more forested than are the surrounding agricultural and residential
lands, its borders are not impenetrable and are not ecologically distinct at all points. However,
the pragmatic definition proved useful and acceptable to the parties. For similarly practical
reasons, one might define an assessment community of benthic invertebrates in the first fully
mixed reach of a stream receiving an effluent.
The selection of a scale to define an assessment population or community involves a tradeoff.
If the area is large relative to the extent of the stressor, the effects of that stressor will be
diluted. However, if the area is small, the assessment population or community may be
significantly affected but may seem too insignificant to prompt stakeholder concern or action
by the decisionmaker. Hence, appropriate spatial scales should be determined during the
problem formulation stage for individual risk assessments, taking into consideration both the
ecological and policy aspects of the problem; it should not be manipulated during the analysis
to achieve a desired result.
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Imprecisely framed or communicated management goals can lead to confusion about how
to conduct the assessment and interpret its results. It probably is too vague to state the
goal simply as "to control risks of the site to a naturally occurring population." Such a
goal can open the door to a range of analysis approaches, and can result in answers that
may not address the intent of site managers directly. Often, this problem boils down to
one of incomplete specification of the goal relative to spatial and scalar relationships
between the site and the natural range of the population. It may be useful to consider
three general scalar situations or cases (Figure 1) as they relate to management goals, lead
to different assessment questions, and therefore different analysis approaches:
Case 1 - The site boundaries encompass the majority of the natural range of the
population.
Case 2 - The site is located within, and is substantially smaller than, the natural
range of the population.
Case 3 - The site is located outside the seasonal range of the population, but some
portion of individuals utilize the site during migration.
The simple management goal articulated above is applicable in each of these cases, and
while it is possible (and reasonable) to assess the risks of the site to the entire population
in each case, the relevant assessment questions and analysis approaches likely would
differ. Certainly, the level of adverse effect on overall population dynamics expected
from a given site would differ across cases, with Case 1 representing the greatest risk and
Case 3 the smallest (simply as a function of the proportion of the population exposed).
Therefore, differences in the analysis approaches to address the simply-stated goal, and
their outcomes, can contribute to problems in interpretation of assessment results.
Clarification of the management goal by defining the assessment population should help
to minimize such problems. In situations like Cases 2 and 3, if the goal is to manage site
risks as if the population's range was limited to the site itself (making the analysis most
conservative and analogous to that for Case 1), the assessment population should be
defined as those organisms using the site. This might be the appropriate goal when the
health and sustainability of local subpopulations are a concern for aesthetic or other
societal reasons. In this situation, special consideration may need to be given in the
analysis to migration of individuals from and to the surrounding area. Conversely, when
the goal is to manage risks of the local site in its broadest context, the assessment
population might be defined as the entire natural population. This situation might arise
when particular advocacy groups, operating as stakeholders in the risk assessment/risk
management process, are concerned more about overall cumulative risks to a resource
species (for example, northern pintail ducks) than they are about local site effects. The
analysis in this situation should include evaluation of how localized adverse effects on
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Casel
Case 2
CaseS
Range of
Population
ate
Boundaries
rrigratory
route
Figure 1. Spatial and scalar relationships between site and
range of population. See text for explanation of cases.
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individuals at the site impact the dynamics of the broader population as a whole; if severe
effects occur within the site, the site might act as a "sink" that continually removes
individuals from the assessment population in a manner that significantly reduces overall
population abundance.
In final analysis, the definition of population used within a site-specific risk assessment is
situationally-dependent and specific to the management goal and risk problem being
addressed. Clear communication of how the population is defined and the assumptions
made to support that definition will guide analysis approaches and facilitate
understanding of assessment results and limitations by site managers and stakeholders.
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3. Survey of Population-Level Attributes
Populations and their vitality can be characterized using a number of different attributes.
However, not all population-level attributes are useful in site-specific risk assessments;
use of some of the more esoteric attributes is perhaps best reserved for theoretical
exercises of population biology. Some 16 attributes potentially useful in Superfund and
RCRA assessments are described below, and are summarized in Table 1. These are
organized into four broad, and potentially overlapping, categories: abundance, population
growth, structure, and persistence. Much of the following has been abstracted from
Maltby et al. (2001); additional considerations about specific attributes can be found there
and in modern ecological texts.
3.1 Population Abundance
Population size - Population size, expressed as total number of individual organisms,
total biomass, or any other summed quantity of mass or energy, is one of the most basic
attributes of a population. It usually is denoted by N or Nt, where t equals time, although
when expressed as biomass or some other quantity, other symbols may be used.
Population density - Density is simply the size of a population expressed on a per area or
per volume basis. It is a convenient way to describe abundance in that it facilitates
comparisons of abundance among populations or areas. Probably more importantly,
however, the density of a population has implications to regulation of the population, in
that density dependence (or compensation) can influence the demographic rates that
determine population abundance. Although simple in concept, the idea that density can
affect birth and death rates (say, through intraspecific competition for limiting resources)
can be difficult to quantify and model.
Equilibrium abundance - The equilibrium abundance, or steady state abundance of a
population is that population size at which inputs to the population (births, immigration)
are exactly balanced by losses (deaths, emigration). It is related to the concept of carrying
capacity, the number of individuals that the resources of the environment can support
without increasing or decreasing. Maltby et al. (2001) suggest that changes in
equilibrium abundance have greater significance than do changes in population size, since
the former implies some long-term effect whereas the latter implies a temporary effect.
Equilibrium abundance is probably best thought of as a theoretical concept in that most
populations actually fluctuate around some average abundance as a result of
environmental variability, demographic stochasticity, and so on.
Production and yield - These two attributes generally relate to the amount of a
population (in terms of biomass or numbers) that can be harvested from a population.
Generally applied in fishery management, they are appropriate for any situation in which
the population is managed for take.
10
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TABLE 1
Population-level Attributes for use in Ecological Risk Assessment
(see Maltby et al., 2001 for other descriptive information)
Attribute
Measure
Example Units of
Measurement
Applicability to Site-Specific
Risk Assessment*
Abundance
population size
population density
equilibrium abundance
production/yield
spatial distribution
numbers, biomass, energy
content, etc.
population size per unit area
or volume
steady-state numbers,
biomass, energy content,
etc.
harvestable quantity
extent of spatial occupation,
number of habitat patches
used
#, kg
#/km2, g/m3
#, kg
kg, #
hectares, # of
patches
general
general
specific
specific
specific
Growth Rate
population growth rate
change in population size
per unit time
A#/At, d#/dt
general
Structure
age/size/stage structure
genetic diversity
tolerance distribution
sex ratio
spatial distribution
distribution of population
among classes of
age/size/developmental
stage
heterogeneity in gene
frequency
variability in resistence to
stressor effects
proportion of one sex
relative to the other
extent of spatial occupation,
number of habitat patches
used
#/class, kg/class
various indices
# affected in each
treatment
o":?
hectares, # of
patches
general
specific
specific
specific
specific
11
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TABLE 1 (cont.)
Attribute
Measure
Example Units of
Measurement
Applicability to Site-Specific
Risk Assessment*
Persistence
probability of extinction
time to extinction
quasi-extinction
minimum viable
population
stability
recovery time
spatial distribution
likelihood that population
abundance will go to zero
time between introduction
of stressor and population
extinction
likelihood that population
size will fall below some
defined abundance
smallest population
abundance that will persist
for a fixed period of time
resistence or resilience to
change
time between removal of
stressor and return of
population to equilibrium
abundance
extent of spatial occupation,
number of habitat patches
abused
probability curves
years
probability curves
#, kg
years
hectares, # of
patches
specific
specific
specific
specific
specific
specific
specific
Information in this column reflects value judgments by the authors
12
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Spatial distribution - The spatial distribution of a population might be thought of as an
attribute related to abundance, structure, and/or persistence. As an abundance attribute, it
is related to population size - as the range of the population increases, its abundance also
increases (assuming density to be constant). As a structure attribute, it describes the
locations of the population and its uses of various habitats in the landscape. And as a
persistence attribute, it can be related to the probability that a population will become
extinct due to the local effects of anthropogenic stressors and environmental variability.
However, few examples exist of the direct use of this attribute as an indicator of
population level effect (but see Goldingay and Possingham, 1995).
3.2 Population Growth
Population growth rate - Changes in population abundance can be characterized by
population growth rates that express those changes as a function of time. Population
growth rate is generally denoted as r, the intrinsic rate of natural increase (also referred to
as the Malthusian parameter), or as A, the finite rate of population increase (also called
the population multiplication rate). These two rates are related mathematically (r =
ln(A)), and their use to express population growth rate generally is a matter of preference,
although the nuances of how they are calculated and how they are used in population
models (see below) can dictate which expression to use. Generally, r ranges from -<» to
+°°, and is symmetric around the value 0, which represents zero population growth. Thus,
values less than 0 indicate a declining population abundance, whereas positive values of r
indicate a growing population. A, on the other hand, ranges from 0 to +°°, with a value of
unity representing zero population growth, values less than unity a declining population,
and values greater than unity a growing population. Thus, at r = 0 and A = 1, births and
immigration into the population are exactly balanced by deaths and emigration out of the
population.
In addition to characterizing changes in abundance through time, population growth rate
can be thought of as an attribute related to population fitness (Leslie, 1945; Demetrius,
1975; reviewed in Caswell, 2001). That is, in a theoretical sense, populations with
genotypes more suited to a particular environment should have greater rates of population
growth than do those less well suited, and as a result, the better suited (i.e., more "fit")
population will out compete all others (all else being equal). Conversely, the degree to
which population growth rate is adversely affected by environmental conditions (e.g.,
contaminant loadings) is a measure of risk to the population. In extreme cases,
population growth rate may be reduced to such an extent that the population is projected
to go (at least locally) extinct. Less radical reductions might increase the risk of
extinction when such impacts occur in conjunction with other environmental insults or
with stochastic fluctuations in controlling processes.
Population growth rate, and the extent to which it is impacted by stressors, is therefore of
central importance in ecological and evolutionary theory. It is generally acknowledged to
be the key variable linking individual effects to populations (Sibly, 1999; Calow et al.,
13
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1997), is a fundamental underpinning to population regulation (Sinclair, 1996), and
underlies most fisheries and wildlife management concepts and approaches (Sutherland
and Reynolds, 1998). However, the use of population growth rate in ecotoxicology has
been limited (Sibly, 1996), despite its usefulness as a measure of stress having been
demonstrated some 40 years ago (Marshall, 1962). As with changes in all population-
level attributes, care should be taken in the interpretation of differences in population
growth rate potentially attributable to a hazardous waste site, since factors other than
toxic chemicals can and do influence this attribute.
3.3 Population Structure
Age/size/stage structure - Population structure can be characterized by the relative
distributions of individuals (orbiomass) among classes of age, individual size, and
developmental stage. These classes can be delimited on a fairly arbitrary basis (such as
years in calendar time), or can be tightly linked to the biology of the species (e.g., eggs,
larvae, pupae, adults). In general, the distribution of individuals among classes is an
indication of the status of the population. In populations that are growing rapidly, the
distribution of individuals typically is skewed towards the younger classes. The opposite
may be true for populations experiencing reductions in overall size. To illustrate this
idea, human populations in developing countries that are experiencing relatively rapid
population growth generally have lots of young and few old adults, whereas the
distribution among ages in industrialized countries with more stable population sizes
tends to be more even (Thomlinson, 1965).
Anthropogenic stressors can affect the age or size structure of a population by modifying
the processes of births and deaths. Depending upon how these effects manifest, the
age/size/stage structure can shift from pre-exposed conditions in ways that do not map
neatly onto the generalization above. If, for example, the susceptibility of individuals to a
particular chemical increases with age, the resulting distribution might still be skewed
towards younger age classes, even though a population-level effect is occurring. Thus,
caution is needed when interpreting age/size/stage distributions. However, a comparison
of assessment population structure with that of a pre-exposed or reference population
would still indicate an effect.
Genetic diversity - The genetic diversity of a population may be related to its fitness (i.e.,
its ability to persist through time). Population biology theory suggests that populations
with greater genetic heterogeneity in fitness-related genes should be able to withstand a
wider range of environmental conditions (including the presence of anthropogenic
stressors) than can those with less diversity. Thus, genetic diversity can be an indicator of
susceptibility to future environmental impact. It also can be an indicator of current and
past stress, because such stress can reduce genetic heterogeneity when population size
decreases rapidly in response to disturbance (the so-called bottleneck effect; Weins,
1977). Chronic or multiple episodic stressors may cause multiple bottlenecks,
magnifying the reduction in genetic diversity, and there is mounting evidence that non-
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migratory populations at sites that have experienced pollution or other forms of
disturbance have reduced genetic diversity (Lavie andNevo, 1982; Lavie et al., 1984;
Nevo et al., 1986; Benton and Guttman, 1990). Reduced genetic diversity can expose the
population to greater risks of adverse impact from other anthropogenic stressors, disease,
and environmental stochasticity, and can cause detrimental changes in birth and death
rates (inbreeding depression). The importance of genetic diversity in fitness-related genes
to the persistence of wild and captive populations has been recognized by conservation
biologists and is incorporated into management strategies for the preservation of
threatened and endangered species. It should be noted that pollution stress can also
increase genetic diversity through selection for tolerant genotypes in populations that still
contain pollution-sensitive genotypes, but interesting, that mechanism would produce a
pattern consistent with the general heterogeneity/persistence argument (i.e., increased
heterogeneity and increased likelihood of persistence).
Tolerance distribution - Basically a concept of ecotoxicology, the distributions of
tolerances (or conversely, susceptibilities) to chemical stressors is directly related to the
previous attribute in that tolerance is aphenotypic measure of the underlying genetics. As
with shifts in genetic diversity, temporal or spatial changes in tolerance distribution of the
assessment population relative to pre-exposed or reference populations can provide an
indication of population-level effects.
Sex ratio - The sex ratio of a population describes the relative abundances of the two
sexes in sexually reproducing dioecious populations (and sometimes seasonally
parthenogenetic species, such as daphnids, rotifers, and aphids). Substantial theory exists
concerning the evolutionary consequences of skewed sex ratios in populations (Maynard
Smith, 1978), although the use of this attribute as an indicator of population-level effects
is limited primarily to quantifying differential effects among the sexes. However, it also
can provide information regarding the mechanisms of such effect. For example, certain
chemicals have been demonstrated to interfere with hormonal systems controlling sexual
differentiation in certain birds (Fry and Toone, 1981), mammals (Jones and Hajek, 1995;
Gray and Kelce, 1996), reptiles and amphibians (Bergeron et al., 1994; Guillette et al.,
1994, 1995), and fish (Gimeno et al., 1996; Jobling et al., 1996; Gray and Metcalfe,
1997). In such cases, ecological theory (if not empirical evidence) suggests that a change
in sex ratio affects population dynamics by influencing total reproductive output of the
population and by altering frequencies of encounter between the sexes during the
reproductive season (Kalmus and Smith, 1960; Hamilton, 1967). Stressor-induced
imposex, such as that reported for certain invertebrates (Gibbs and Bryan, 1986; Moore
and Stevenson, 1991), should have population-level ramifications similar to changes in
sex ratio. Thus, sex ratio is a potentially useful attribute in descriptions of the effects of
stressors, particularly in situations where such effects might be diagnostic.
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3.4 Population Persistence
Probability of extinction and time to extinction - Probability of extinction and time to
extinction are related measures of population persistence. Probability of extinction as an
attribute describes the likelihood that population abundance will go to zero under defined
demographic, genetic, and environmental conditions. Time to extinction can be derived
directly from the probability of extinction (Foley, 1994; Gillman and Hails, 1997).
Examples of the use of these attributes are described by Harrsion et al. (1991) and Foley
(1994) for butterflies, and Gillman and Silvertown (1997) for plants. Snell and Serra
(2000) recently suggested that probabilities of extinction can be used to interpret the
ecological significance of toxicity test results. Because they are difficult to quantify in
natural populations, and are only slightly less so in laboratory experiments (due to the
replication required), estimates of these attributes are best made using modeling and
simulation techniques.
Quasi-extinction - Related to probability of extinction is quasi-extinction, defined as the
probability that the population will fall below some critical abundance (Ginzburg et al.,
1982). Critical abundance can be thought of in terms of specific population densities
below which adverse effects are known, or suspected to occur. For example, critical
densities of puma may exist below which individuals are no longer able to find mates for
reproduction. Similarly, critical population sizes of commercially-harvested shellfish
might be identified (through, say, a cost-benefit analysis) below which harvest is no
longer economically feasible. As with probability of extinction, quasi-extinction is best
analyzed using modeling and simulation techniques. Maltby et al. (2001) describe a
method by which the quasi-extinction probability curves that result from such analyses
could be used to evaluate the ecological significance of estimated risks.
Minimum viable population - Also related to probability of extinction is the concept of
minimum viable population (MVP), defined as the smallest population abundance that
will persist for some specified length of time with a given probability. Based on the
expectation of a negative relationship between absolute population abundance and the
likelihood of extinction (due to the effects of stressors or environmental variability), it,
like the previous two attributes of persistence, is best quantified using modeling and
simulation techniques. Examples of MVP as an attribute are given by Samson et al.
(1985), Shaffer and Samson (1985), and Goldingay and Possingham (1995).
Stability - Broadly defined, population stability is the tendency of a population to remain
at or near its equilibrium abundance when disturbed (Haberman, 1977; see Lewontin
(1969) and May (1973) for discussions of the various meanings of stability in an
ecological context). A stable population is one that "resists" adverse impacts due to
disturbance, or one that recovers to its equilibrium abundance once disturbed.
Destabilization of population dynamics can lead to large changes in abundance, thereby
increasing the probability of extirpation (as well as disruption of community and
ecosystem structure and function). Stability (in addition to population abundance itself)
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also is inversely related to the probability that the population will be driven to local
extinction as a result of stressor exposure. Because it reflects the resilience of a
population following disturbance, stability may be more important to population
sustainability than is population growth rate. Unfortunately, stability is very difficult to
measure directly (Connell and Sousa, 1983), although it can be evaluated using models.
Because of this, stability as an attribute for population-level ecological risk assessment
likely is limited.
Recovery time - When a population is disturbed from its equilibrium or pre-exposed
abundance, the time it takes to return to that abundance is called its recovery time.
Recovery time is a highly attractive population-level attribute in that it is readily
understood and appreciated by regulators, managers, and the public. In part because of
this, recovery has been advocated in the consideration of adversity of effect by the
Agency (U.S. EPA, 1998). However, several conceptual and methodology issues can
confound its use in site-specific risk assessments. Because it may be unrealistic to expect
a population to return exactly to its predisturbed abundance, criteria must be established
to define when recovery has occurred (or is sufficient). These might include aspects of
absolute population abundance (e.g., 90% of original population size; Sherratt et al,
1999), natural variability in that abundance (e.g., within two standard deviations of long-
term mean abundance; Weins, 1996), its abundance relative to a reference or control
population (e.g., 90% of reference population density; Thacker and Jepson, 1993), or
perhaps its population growth rate relative to that of a reference or control population
(e.g., 90% of the growth rate of an unaffected population; Kareiva et al., 1996).
3.5 Considering Attribute Selection
Which attributes should be evaluated to characterize population-level effects at Superfund
and RCRA sites? Unfortunately, there likely is no one single best answer to this
question, and, as is the case with defining the assessment population (the "ecological
entity" element of the operational definition of the assessment endpoint; sensu U.S. EPA,
1998), selection of the population attribute (the "characteristic of the entity" in definition
of the assessment endpoint) should depend on the goals of the assessment. However,
consideration of several criteria should help guide attribute selection in any given risk
assessment. Four of these would be: the relevance of the attribute to the assessment
population, the susceptibility of the attribute to contaminants at the site, its relevance to
stakeholders and the risk management and communication processes, and the tractability
(ease) of its measurement. In most regards, these criteria mirror the general guidance
provided by U.S. EPA, (1998) and program-specific documentation.
There are few, if any, broad ecological considerations to help evaluate the importance of
population attributes to the assessment population generically. However, some attributes
may have more meaning than others. For example, sex ratio has no meaning for species
displaying obligatory parthenogenesis, whereas other attributes reflecting population
structure (e.g., genetic diversity) may be critically important. From an evolutionary point
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of view (admittedly not a typical view of site-specific risk assessments), attributes
reflecting population persistence likely have more meaning than those reflecting
abundance, growth rate, or structure, but have less meaning in the context of shorter-term
ecological phenomena (e.g., role in community dynamics, nutrient cycling). Part of the
difficulty when evaluating this criterion is a lack of understanding and consensus as to the
definition of a "healthy" population.
There also are no a priori reasons to suspect certain attributes to be more susceptible to
chemical stressors than others. Plausible biological mechanisms exist to link effects on
any particular attribute to chemical exposure, oft times in interrelated fashion. For
example, a chemical linked to differential mortality or reproduction may affect population
structure as measured by age structure or genetic diversity, which in turn may be reflected
directly in abundance, directly in growth rate, or indirectly in persistence as a function of
changing resistence to additional stressors. Despite this, understanding biological
mechanisms may help to identify which attributes would respond more quickly or signal
the effect more strongly.
From a stakeholder and risk communication perspective, changes in abundance and
persistence arguably are more understandable and obvious effects than are attributes of
growth rate or structure. And certain attributes are more easily measured (e.g., those
reflecting abundance) than others (e.g., stability). But in the end, there is no one "best"
attribute for evaluation in a population-level risk assessment. As with definition of the
assessment population (Section 2), selection of the population attribute is situationally-
dependent and specific to the management goal and risk problem being addressed. Clear
communication of why any particular attribute is selected will facilitate understanding of
assessment results and limitations by site managers and stakeholders.
3.6 Ecological Significance of Responses
The ability to measure or quantify population-level effects is only part of the problem in
site-specific risk assessment - changes in population attributes due to exposure to
stressors must be interpreted to understand the significance of estimated risks.
Appreciation of this significance is crucial to developing, executing, and interpreting
ecological risk assessments. A question central to this issue is: "What do the magnitude
and direction of observed attribute response mean from an ecological standpoint?". This
question can be restated simply as: "So what?". Answering this question is not
straightforward, and presents complex challenges that have yet to be overcome by
science. The following material is intended only to be an introduction to this issue;
considerable work remains to advance the theory and practice of population ecology to
the point where the ecological significance question can be answered satisfactorily.
Except in extreme situations (e.g., extinction), ecological significance is difficult to
establish for at least four reasons. First, all ecological systems, including populations,
display natural variability: population abundances fluctuate (perhaps around some steady-
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state abundance) due to environmental and demographic stochasticity, age structures
change as reflections of year-class strengths, sex ratios vary randomly (or otherwise)
around values of 1:1, and so on. Such variation has been called process variation. The
challenge is to distinguish changes caused by anthropogenic stressors against this
background of natural variability. Historically, inferential statistics has been used to
make such distinctions. This has lead to application in a number of programs of
seemingly arbitrary "bright lines" that form the basis of regulatory decisions (Chapman et
al., 2002). Yet, statistical differences (the detection of which are functions of the test and
sampling designs, natural variation, and the magnitude of "treatment" differences) do not
necessarily equate with changes that are important ecologically. Establishing ecological
significance is also hindered for a second reason: ecological systems typically vary in
near-continuous fashion, such that in the absence of thresholds or obvious breakpoints,
the importance of subtle changes is difficult to establish relative to less subtle changes. A
third reason confounding interpretation of ecological significance is the existence of
compensatory mechanisms, such as homeostatic acclimation of individuals, genetic
adaptation, and density dependence in vital rates and migration, that can ameliorate
adverse effects over the short or long term. Finally, there are few (if any) "values" that
ecological systems place on themselves. In the absence of such values, ecological change
is interpreted in the context of societal desires, preferences, needs, and policies.
In 1994, the U.S. EPA's RAF published an issue paper on the general topic of ecological
significance as it pertains to risk assessment (Harwell et al., 1994). That paper offers a
definition of ecological significance consisting of components that reflect both ecological
structure and function, and societal values. Paraphrased from Harwell et al. (1994), an
ecologically significant change is one that is important to the structure, function, or health
of the system, exceeds natural variation, and is of sufficient type, intensity, extent, or
duration to be important to society. Although their definition was offered in the context
of the significance of estimated risk, it also can be applied to the significance of changes
measured in population attributes themselves. Harwell et al. (1994) offer a tiered
ecological significance framework or road map and general criteria for establishing
ecological significance that include consideration of the nature and variability of the
attribute, the temporal and spatial scales of effect, the magnitude and reversibility of the
effect, and other considerations. They also suggest how issues of ecological significance
can be used to support decision-making. Given our current state of understanding of
population ecology, and in the absence of objective, quantifiable criteria against which
the importance of observed or predicted change in population-level attributes can be
judged, establishing ecological significance will continue to rely on sound professional
judgement reflecting the considerations offered by Harwell et al. (1994) and the work
cited therein. General guidance for evaluating ecological significance is given in U.S.
EPA (1998).
Although discussed in terms of changes measured or predicted in population-level
attributes themselves, questions of ecological significance are also cogent from the
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standpoint of predicting population-level effects from those measured in individuals.
Methods for linking effects on individuals to population response are described in the
next section.
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4. Linking Effects on Individuals to Population Response
Most population-level attributes, including abundance attributes, are determined by the
vital rates (births, deaths) of individuals within the population, as well as the rates of
migration into and out of the population. These four rates - births, deaths, immigration,
and emigration - are necessary and sufficient to describe changes in population numbers
through time, although additional information (e.g., individual growth rates, weight-age
relationships) may be needed for some expressions of abundance (e.g., biomass). Any
factors that influence these processes, either directly or indirectly, can have population-
level consequences. Linkages between effects on vital rates and those on population
dynamics, or between effects on the biochemical and physiological processes that
determine vital rates and effects on populations, can either be established empirically by
correlating responses at different levels of biological organization, or by determining
causal relationships and constructing mechanistic models (see Maltby et al., 2001 for a
conceptualization and discussion of these linkages). Thus, with some degree of
understanding of how changes in vital rates manifest into population consequences (i.e.,
mechanistic understanding), effects measured at the level of individuals can be
extrapolated to expected population-level responses. Extrapolation of this latter type is
usually accomplished using models that integrate the effects of stressors on survivorship
and fecundity.
This section focuses primarily on modeling approaches that can be used to assess risks to
populations. Its content is derived primarily from Munns (1988) and Maltby et al. (2001).
Although their description is beyond the intended scope of this white paper, empirical
approaches (including extrapolation among species as well as among attributes) have
been developed that can be useful for site-specific risk assessments [see Munns (2002)
for a general discussion of extrapolation issues in risk assessment].
4.1 About Models
In his broad discussion of ecological theory and models, Levins (1968) describes a
triangular scheme for ordinating ecological models that has the attributes of generality,
realism, and accuracy (originallyprecision1) as its apices (Figure 2). In this context,
general models are those that tend to be simple and apply to a broad range of situations,
and therefore are appropriate for exploring relationships among model parameters and
outputs. Realistic models attempt to account for known relationships and processes in
ecological systems, and as a result can be relatively complex. Accurate models are
constructed with an objective to minimize numerical differences between model outputs
and actual ecological dynamics. Their case-specific nature limits their use in broader
applications.
Use of the terms accuracy and precision in this white paper follows their connotations in the field of
inferential statistics. Accuracy refers to how well an estimate matches the true value of a particular parameter or
value being estimated (in this case, population abundance), and typically is quantified using some measure of bias.
Precision refers to the amount of variation among multiple estimates made of the parameter, and usually is expressed
using some measure of scatter.
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GENERALITY
Theoretical
Models
A ppli cabl e in most situati ore
Donl predct specific outcomes well
Topically "simple"
Goodfor exploring relationsN ps
Applied Models
Accourt for known relationsH ps
May be complex
"Physics"
Models
ACCURACY
Accurately describe specific
situ* ore
Mary have limited use in other
situations
Typically detail ed
Figure 2. Ordination scheme for ecological
models (modified from Levins, 1968).
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Levins (1968) pointed out that any two of these attributes can be maximized at one time,
but that it is not possible to maximize all three with a single model. Typically, models
developed for use in applied situations (e.g., conservation biology) are intended to give
realistic, accurate answers; model parameterization depends upon the actual conditions of
the situation being modeled (e.g., the specific life history and demographic characteristics
of the species of interest). Increased generality can be achieved, for example, by
expanding the range of values assumed for particular model coefficients, or by assuming
broad functional relationships among parameters, but such actions necessarily reduce the
accuracy achievable in any particular application. Model accuracy can be enhanced by
increasing the specificity of model parameterization relative to a particular species or
environmental situation.
With this ordination scheme in mind, ecological models, and specifically population
models, can be used in site-specific risk assessments for at least three, arguably different
purposes. The first is to detect (and perhaps diagnose the causes of) previous or ongoing
adverse effects on population dynamics. Such uses typically require sufficient high
quality data to be able to detect changes in population abundance (methods for which are
described in the next section), and to relate those changes to variation in chemical
exposure, habitat quality, or other forms of disturbance. The second purpose is to project
the consequences of a given set of environmental conditions (or changes in conditions) to
the dynamics of a population. Here the intent may be to evaluate the ramifications of
particular environmental management decisions as determined by trends in population
numbers or changes in extinction probabilities. The final purpose is to forecast or predict
the future behavior of the population based on a understanding of environmental
variability and the dynamic interactions of density and biological processes (e.g., births
and deaths). [The distinction between projection and forecasting used here follows that
given by Caswell (1986, 2001).] This last use of population models may produce the
most accurate results, although the generality of the analysis will suffer. It requires
knowledge of how the major environmental and biological determinants of population
dynamics (including such things as climate, prey availability, etc.) will themselves change
through time (or, in a probabilistic sense, their future distributions), and sufficiently
detailed understanding of the mechanisms through which these changes affect the
population. Also required is understanding of how population density itself influences
births, deaths, and migration through density dependence of these rates. Except in rare
situations, such knowledge and understanding is difficult to obtain.
Prior to description of specific model formulations, it may be instructive to consider the
assumptions and potential limitations of different modeling approaches. As a first cut,
population models (indeed, almost all mathematical models) can be either deterministic
or stochastic. Deterministic models treat all internal relationships (processes,
mechanisms, transfer functions, etc.) as nonrandom; that is, they assume no random
variation in how one state variable (in its simplest definition, a component or property of
the system being modeled that, when aggregated with other state variables, determines
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what the system looks like) relates to another. This is not to say that one state variable
cannot be a function of another; rather that even those functions contain no randomness.
Because of this, the outputs of deterministic models are determined completely by their
initial starting conditions - no matter how many times the model is run, the output will be
the same as long as the values of model parameters are not changed by the user.
Deterministic models sometimes can be solved analytically. Stochastic models, on the
other hand, assume that at least some of the internal relationships have a random
component. Their outputs are only partially dependent on initial starting conditions, and
the exact values of output generally cannot be predicted in advance (although they might
be bounded). Stochastic modeling approaches reflect the randomness inherent in
biological and environmental processes, and usually assume specific probability
distributions for the values that state variables can take. Stochastic models cannot be
solved analytically except under certain conditions (such as when parameters are
distributed normally), and Monte Carlo and other simulation techniques have been
developed to support analysis of these models (see, for example, U.S. EPA, 1996).
Models (and their variables) can also differ in how they treat time. Discrete time models
assume time to be "jumpy", that is, time is handled as a series of blocks (seconds, days,
years, etc.), with the values of model variables being updated only once during each block
or time step. Discrete time models often are represented by difference equations. In
contrast, continuous models assume time to flow continuously, such that model variables
take on the value appropriate to any instant in time. Continuous time models can take the
form of differential equations with respect to time.
Similar to how they treat time, models can also assume that their variables (and therefore
the state of the model system itself) are either discrete or continuous. Discrete state
models (and their variables) can take on values selected from a finite set of possible
alternatives only. That is, parameter and model outputs are characterized by
discontinuous changes in value; they can be X1? X2, or X3, but not something between Xj
and X2. Continuous state models include variables that can take on any value (perhaps
within some bounded range), and outputs are characterized by smooth changes in value.
Any particular model can, of course, assume a combination of the three approaches
above. For example, a modeling approach might assume stochasticity in the values that
its discrete state variables take on through continuous time. The approach taken in model
formulation in part determines it strengths and limitations for use in site-specific risk
assessments. Together with other considerations, these issues are explored to support of
model selection in this section.
4.2 Extrapolation Models
A plethora of models useful in describing population dynamics has evolved since the
early demographic investigations of Malthus (1798) and his contemporaries. The
following presentation is intended to provide a cursory overview of the types and classes
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of population models potentially useful in site-specific risk assessments. Both general
constructs, and those developed specifically for analysis of fishery production, are given.
More detailed reviews of the fishery models are given in Ricker (1975) and Sissenwine et
al. (1979). Vaughan et al. (1984) discuss the utility of fishery models to assessing the
effects of stress on fish populations. The discussion of fishery approaches given here is
based in part upon the Vaughan et al.'s treatment of such models. Barnthouse et al.
(1986) review population models for use in risk assessment, and Barnthouse (1992)
provides additional information about individual-based models. Emlen (1989) provides a
then-state-of-the-art review of use of population models in ecological risk assessment
focusing on terrestrial species, and Emlen and Pikitch (1989) offer views on how to
approach structuring population modeling exercises to support risk assessment.
Barnthouse (1993) describes modeling approaches for evaluating population-level effects
in the context of ecological risk assessment generally, and Barnthouse (1996) reviews
population modeling approaches with particular reference to pesticide risk assessments.
Pastorok et al. (2002) discuss the use of ecological models, including some population
models, to assess risks of chemicals. Most recently, Munns et al. (in review) describe
modeling approaches to population-level risk assessment, offering sidebar examples of
model applications in a variety of regulatory contexts.
The general forms taken by models in each class, their equilibrium solutions (where
appropriate), important assumptions, and data requirements necessary for
parameterization, are briefly discussed. Most of the approaches described here do not
include explicit terms for contaminant effects in the general form of the model. In these
cases, impacts important to the dynamics of the population may be modeled through
variation in rates and coefficients associated with fecundity, mortality, and in the case of
yield-type models, with individual growth rate. When treated in this manner,
contaminants are viewed no differently than other sources of variation in these vital rates.
General, heuristic models Several models have been developed which are of heuristic
value in the general description of population growth. Two such models are those
describing simple exponential growth:
dN/dt = rN Eq. 1
and logistic growth (Verhulst, 1838):
dN/dt = rN(l-N/K) Eq. 2
where N is population size at time t, r is the intrinsic population growth rate [= birth rate
(b) - death rate (d)], and K is the so-called carrying capacity of the environment.
Heuristic models typically are of limited value in field settings (except for short periods
of time following new species introductions), and therefore will not be discussed further.
However, several classes of models which may be useful in site-specific risk assessments
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have terms which take on the forms of Eqs. lor 2. An investigation of the behavior of
these models may be found in May (1976).
Demographic models - Many models used in the analysis of population dynamics
incorporate age-specific demographic information. A relatively simple formulation
which has been popular in the investigation of contaminant effects on population growth
rate (e.g., Daniels and Allan, 1981; Allan and Daniels, 1982; Gentile et al, 1982, 1983) is
the stable age equation (Lotka, 1925), or so-called life table approach. Age-specific
schedules of fecundity and survivorship are the sole data requirements for this model,
information that is easily obtained in laboratory experiments or field studies. The discrete
version of this model (Leslie, 1948; Michod and Anderson, 1980; Caswell, 2001, p. 197)
takes the form:
1=SA-(X + 1)4«*X Eq. 3
where A is the geometric rate of population increase, 4 is the probability of an individual
surviving to age x, and
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by a series of difference equations as:
Eq. 6
where fx is the fecundity of age class x and Px is the probability of survival of females
from age class x-1 to class x. In matrix notation:
n, = M nM Eq. 7
where nt and nt.j are vectors of age class sizes, and M is the Leslie projection matrix
consisting of fecundities across the top row, survivorship probabilities down the first
subdiagonal, and zeros elsewhere. In addition to describing total population size and the
distribution of individual ages through time, Eq. 7 can be solved directly for its
characteristic root, A, the geometric rate of population increase:
M-AI|=0 Eq. 8
where I is the identity matrix of M. Some important assumptions associated with the
basic model are that: 1) schedules of fecundity and survivorship are independent of
density and time; 2) fecundity and survivorship are constant within each age class; and 3)
no net migration occurs. With these assumptions, population projection matrix models
behave similarly to Eq. 1: that is, growth is exponential (once a stability in age distribution
has been reached). The impacts of environmental stressors can be projected in a manner
similar to that used in the stable age equation: modifications can occur to fecundity and
survivorship rates in the projection matrix. Projection matrix models have been
generalized to stage-specific models, where stages can be defined as developmental
stages, length classes, weight classes, or any other stage appropriate to a particular species
(Lefkovitch, 1965). Changes from one stage to another are accomplished by non-zero
transition or growth probabilities in M such that individuals can remain in the current
class through time (i.e., no individual growth), or can move to other classes as dictated by
individual growth and development rates instead of time alone [see Werner and Caswell
(1977) and Caswell (1982, 2001) for further discussion of stage-classified matrix
models]. With this modification, contaminant effects may also be modeled as changes in
these transition probabilities.
The use of projection matrix models to characterize the adverse effects of chemical
stressors on population dynamics has increased over the last decade or so, examples of
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which can be used to illustrate this approach. For instance, Pesch et al. (1991) evaluated
the effects of contaminated dredged material on population growth rates of the marine
infaunal polychaete, Neanthes arenaceodentata. They used an experimental design
consisting of replicate exposures to four sediment treatments to obtain estimates of vital
rates for each of nine 18-day ages classes. The resulting schedules of survivorship and
fecundity were used as input to an age-classified deterministic matrix model to calculate
treatment-specific estimates of A, the finite rate of population increase. Population
growth rates were found to decrease with increasing concentrations of the contaminated
sediment, a relationship that compared favorably (albeit qualitatively) with observations
made at an experimental disposal site (Pesch et al., 1991).
In an evaluation of potential adverse impacts associated with offshore disposal of
municipal sewage sludge, Munns et al. (1996) conducted a prospective assessment of risk
to populations of marine copepod that used an age-classified projection matrix model, the
results of standard toxicity tests of the sewage sludge, and exposure models developed to
describe sludge concentrations in the water column around and downstream of the
disposal site. They simulated passive advection of the population with prevailing
currents through the sludge exposure field, adjusting vital rates on a daily time step in
accordance to the concentration of sludge encountered by the population on each day.
Environmental stochasticity was simulated by allowing concentrations in the exposure
field to vary lognormally. Munns et al. (1996) expressed risk estimates as a 3-
dimensional response surface defined by axes of sludge loading rate, environmental
stochasticity, and population growth rate with the intent of providing regulators with the
information needed to select acceptable levels of disposal activity. Similar population-
level assessments were conducted for relatively sedentary tilefish, Lopholatilus
chamaeleonticeps, and the migratory Atlantic bluefin tuna, Thunnus thynnus (Munns,
1988).
Two examples of the use of projection matrix models relate to Superfund sites. First,
Munns et al. (1997) developed a stage-classified model to describe the population-level
effects of exposure to polychlorinated biphenyl (PCB)-contaminated sediment on the
estuarine fish, Fundulus heteroclitus, residing at the New Bedford Harbor (MA)
Superfund site. Using data obtained from field-collected fish, they developed exposure-
response curves relating population growth rate to PCB liver burdens. In that same paper,
Munns et al. developed a similar relationship for total dioxin body burden for fish fed
contaminated diets. In support of an RI/FS at the Portsmouth Naval Shipyard (ME),
Gleason et al., (2000) modeled the population responses of the purple sea urchin, Arbacia
punctulata, resulting from exposure to lead, a primary contaminant of concern in the
estuarine waters surrounding the Shipyard. They used standard bioassay data collected
during site investigations to parameterize a stage-classified model designed explicitly to
reflect the life history stages and vital rates represented by the bioassays. The population
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growth rate exposure-response relationship resulting from this effort was used
subsequently in a weight-of-evidence characterization of ecological risks at the site (U.S.
Navy, 2000; Johnston et al, 2002).
Three recent examples illustrate the development of projection matrix models for the
expressed use of interpreting the ecological significance of toxicity test results as
indicators of population-level effects. Reflecting the empirical approach mentioned
earlier for extrapolating individual-level attributes to population response, Kuhn et al.
(2000) used data from life cycle chronic tests to project the effects of some 20 chemicals
on the mysid shrimp, Americamysis (formerly Mysidopsis) bahia, population dynamics.
They then compared the concentration-based toxicity test statistics derived from standard
96-hr acute tests, 7-day rapid chronic tests, and the full life cycle tests for each of these
chemicals to the chemical concentration projected by the model to represent the threshold
of adverse population effects (denoted C*) using correlation analyses. Several strong
correlations were observed, including (surprisingly) between C* and the acute LC50.
Kuhn et al. (2001) subsequently demonstrated that the age-classified model,
parameterized for the chemical nonylphenol using standard toxicity test data, projected
the dynamics of A. bahia reasonably well in a multigenerational experiment conducted in
the laboratory. [As an aside, these data have been used by Maltby et al. (2001) to
evaluate model formulations other than the original projection matrix model.] Most
recently, Kuhn et al. (2002) have developed a projection matrix model to assist in
understanding the ecological significance of standard toxicity test results for the estuarine
amphipod, Ampelisca abdita.
Many other examples of the use of projection matrix models in the fields of
ecotoxicology, fishery and game management, and conservation management can be
found in the scientific literature. Given the ease with which the responses of individuals,
measured in toxicological studies, can be linked to population-level attributes, and their
relative flexibility to accommodate a wide variety of populations and environmental
situations, projection matrix models appear to hold much promise for site-specific risk
assessment. Further, analytical methods have been developed to evaluate systematically
the relative sensitivity of A, to proportional changes in the transition probabilities
(demographic rates) of the projection matrix. Called elasticity analysis (Caswell et al.,
1984; de Kroon et al., 1986), this technique can be used to identify which demographic
parameters influence population growth rate the most when changed, thereby focusing
attention on those parameters (say, through targeted toxicity tests) in population-level risk
assessments. Caswell (2001) describes matrix models in great detail, and discusses other
forms of structured population models (discrete-state delay-differential equations in
continuous time, continuous-state integrodifference equations in discrete time, and
continuous-state partial difference equations in continuous time), the use of which in
Superfund and RCRA site-specific risk assessments likely is limited at present.
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Fishery models - This broad class of models, developed primarily for use in fisheries
management, typically are framed in terms of biomass or numbers yield to the fishery.
For example, surplus production models incorporate terms of biomass production and
fishing effort to describe changes in population biomass. As opposed to the approaches
described earlier, knowledge of the demographic characteristics of the population is not
required to make this assessment; time series of catch biomass and fishing effort are the
sole data requirements. The general form of such models is:
dB/dt = B R[B] - qfB Eq. 9
where B is population biomass, q is a coefficient of catchability, f is fishing effort (thus qf
represents fishing mortality) and R is some regulatory function which is itself a function
of B. The term B R[B] describes changes in biomass in the absence of fishing mortality.
R[B] can take any appropriate form, such as that proposed by Graham (1935) and used by
Schaefer (1954, 1957):
R[B] = r (1 - B/K) Eq. 10
where r and K are as described previously, but in units of biomass instead of numbers. In
the absence of fishing, the population is self-regulating, and Eq. 9 describes a parabola
symmetric about %K. Integration of Schaefer's surplus production model yields a
logistic trajectory of biomass through time. Pella and Tomlinson (1969) generalized
R[B] to include nonsymmetric biomass yields. Some important assumptions associated
with surplus production models are that: 1) catch per unit effort is proportional to total
population biomass; 2) fishing effort is proportional to fishing mortality, but independent
of total population biomass; 3) population size is always at equilibrium given constant
fishing effort; 4) the age structure of the population is stable given constant fishing effort;
and 5) no net migration occurs. The effects of environmental stressors could be
incorporated into surplus production models by modifying the form or values assumed in
the regulatory function (changes in r or K), in the coefficient of catchability (due to
modification of individual growth rates or behavioral changes), or as a loss to production
in addition to fishing mortality.
Another class of models developed for fishery applications are the yield models. These
models incorporate age-specific schedules of weight and cohort (groups of similarly-aged
members of the population) numbers, and are used to estimate the yield of individual
cohorts following recruitment to the fishery. They take the general form:
dY/dx = F N(x) W(x) Eq. 11
where Y is the biomass yield to the fishery, F is the instantaneous fishing mortality rate,
N(x) is an expression of population numbers of age x, and W(x) is an expression of the
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weight of an individual of age x. N(x) can be described by some appropriate function
such as that used by Beverton and Holt (1957):
N(x) = N(xc) exp {-(M + F) (x - xc)} Eq. 12
where x is the age of recruitment into the fishery (x>xc), N(xc) is the number of recruits
into the fishery, and M is the instantaneous natural mortality rate. Thus, the size of the
cohort decreases exponentially with time. Weight at age x can be described by an
appropriate function, such as the von Bertalanffy (1938) growth equation:
W(x) = W. (1- exp[-k (x-x0)]}3 Eq. 13
where WM is the assumed asymptotic weight of an individual, k is some individual growth
rate, and x0 is the hypothetical age of an individual of weight zero. With the substitution
of Eqs. 12 and 13 into Eq. 11, integration of Eq. 11 yields:
Y = F N(xc) W. S {(Un exp[-nk(tc-t0)]) / (F + M + nk)} Eq. 14
where Un are integration constants taking on values of 1, -3, 3, and 1 for n = 0, 1,2, and 3,
respectively. Some important assumptions associated with yield models are that: 1)
mortality is independent of density with rates remaining constant following recruitment
into the fishery; 2) the growth function adequately describes individual growth following
recruitment; 3) all individuals of a cohort recruit at the same instant; and 4) no net
migration occurs. The effects of environmental stressors can be incorporated into such
models through variation in growth rate (k) in Eq. 13, or through changes in mortality
occurring beyond age xc as characterized by N(x). Additionally, reproductive effects can
be incorporated implicitly through reduction in the number of recruits entering the fishery
at age xc.
Stock recruitment models describe recruitment of numbers into the fishery, rather than
biomass yield to the fishery subsequent to recruitment. The data requirements of such
approaches include estimates of stock size and the subsequent number of recruits over
time. The general form of such models is similar to the simple exponential growth model
(Eq. 1):
dN/dt = -MN Eq. 15
where M is a parameter involving mortality that may incorporate both density-dependent
(md) and density-independent (m0) terms (Ricker, 1954):
M = m0 + mdN(ts) Eq. 16
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where N(ts) is the stock size at time of spawning, ts. Integration of Eq. 15 with Eq. 16
substituted for M yields the number of recruits, R, At units of time after spawning:
R(ts+ At) = f exp(-m0 At) N(ts) exp[md AtN(ts)] Eq. 17
where f is the fecundity of a recruited fish. Some assumptions of this model include that:
1) effects of density occur prior to recruitment, with N(ts) being the important density; 2)
fecundity is unaffected by population density or fish size; and 3) no net migration occurs.
Contaminant effects could be incorporated into the mortality terms, or in the average
fecundity of recruited individuals.
Other models - Classes of models other than the demographic and fisheries approaches
already discussed may have potential utility in assessing site-specific risks; four are worth
mentioning briefly here. The first of these is based upon statistical description of time
series of population abundance or biomass parameters. These empirical models attempt
to describe temporal fluctuations in population size based largely upon the past behavior
of the population and associated environmental data. No explicit parameterization of
demographic processes need be involved. Instead, regression analysis is used to estimate
coefficients associated with terms for environmental processes deemed important to the
temporal fluctuations, as well as with autocorrelative terms. Thus, population size, N, is
described as some function,/ of environmental parameters, T;, and past population size
with time as:
N =/(₯,, N,t) Eq. 18
Typically, these models are built by the parsimonious inclusion of variables in an iterative
fashion, until the fitted model meets certain criteria (for example, the model reasonably
describes the behavior of N, and no autocorrelation of regression residuals exists).
Impacts ascribable to changes in anthropogenic stressors could be detected through use of
intervention terms (if relatively discrete changes in stressor exposure are known to occur
at specific times), or through development of transfer functions relating time series of
stressor loading or concentration to the time series of population size. Population size
may also be forecast into the future once a reasonable model is developed (although not
without a great deal of uncertainty). One potential drawback inherent in this approach is
the requirement of long series of uniformly spaced data points; such data sets may not
exist for the assessment population. Discussion of this and other problems, and of the
techniques associated with time series analysis, is given in Box and Jenkins (1976).
Examples of the application of this approach to investigation of near-shore pollution
loadings and fishery stocks is given in Polgar et al. (1985) and Summers et al. (1985).
As a class, individually based models (IBMs) cover an enormous range of specific model
formulations (de Roos et al., 1991). The theme common to this class of models is that the
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basic unit of model formulation is the individual organism, with descriptions of
population dynamics simply being the summation of simulated stochastic outcomes for
each individual. As a result, IBMs can accommodate a great deal of variation and
complexity in the behavior of individuals and their interactions with biotic and abiotic
components of the modeled environment, and therefore can reflect a great deal of realism.
IBM simulations are computationally intensive, and their formulation can be non-trivial.
Choices must be made between simulating in discrete time (in which case the order of
biological and environmental "events" within each time step become important), or using
event-driven accounting methods with time handled as a continuous variable and
population state being updated with each event. Effects of environmental stressors can be
incorporated in IBMs directly, using information derived from toxicity tests, time-to-
death studies, and any number of other information sources that relate stressor exposure
to physiological and individual-level attributes. As an example of this approach, Nisbet
et al. (1989) describes an IBM developed for Daphnia. Grimm (1999) reviews some 50
IBMs developed for animals.
Vaughan et al. (1984) discuss one form of IBMs, introduced to fishery management by
Ursin (1967), which is based upon the bioenergetics of individual organisms within the
population. Weight-specific rates of important physiological processes are summed to
describe changes in biomass (B) of individuals within a cohort as:
(l/B)dB/dt = C-(R + F + U + P) Eq. 19
where C is consumption rate, R is respiration rate, F is egestion rate, U is excretion rate,
and P is reproductive loss. Typically, each of the terms in Eq. 19 is expanded to include
appropriate influencing processes such as temperature, dissolved oxygen concentration,
or activity level. Changes in biomass are summed over individuals within a cohort, and
some mortality process is introduced. Although fairly data-intensive in that the
environmental factors influencing each physiological rate must be quantified, Vaughan et
al. (1984) indicate a major advantage of this approach over some others: contaminant
stresses may be modeled at a basic, mechanistic level. However, because of the
difficulties associated with quantifying the physiological processes of assessment
populations, the utility of bioenergetics models, like other data-intensive modeling
approaches, may be limited in site-specific assessments to "high priority" assessment
endpoints (e.g., for endangered species).
All of the above models are, to a large degree, quantitative in nature. Qualitative
population models have also been formulated which may be appropriately applied in this
context. Among the more promising is loop analysis (Levins, 1975). This approach can
be used to examine the behavior of a partially specified system based solely upon the
signs of the interactions between various components of that system. In the context of
population modeling, the components of the system would be identified as different ages
or developmental stages in a fashion similar to that used in population projection matrix
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models. The methods employed in loop analysis depend upon the equivalence of
differential equations near equilibrium, and matrices and life history diagrams (Levins,
1975). Although loop analysis appears to have limited value in exploring the dynamics of
populations in isolation, it may be valuable in examining age/stage structure effects
resulting from contaminant insult. An advantage of this approach in site-specific risk
assessments lies in its minimal data requirements.
4.3 Extrapolating from Toxicity Test Data
Use in risk assessment of any of the extrapolation models described above typically
requires quantitative information about the values that model parameters take under
different exposure scenarios. Section 5 of this white paper describes some of the
techniques that can be used to obtain this information for field populations occupying the
site (and associated reference areas). Data to parameterize models can also be obtained
from laboratory-based toxicity tests and experiments. In both approaches, the question is
one of how to link responses measured in individuals to their population-level
consequences. Although the material provided here is most relevant to the demographic
modeling approaches described earlier, it applies to a majority of the other model
formulations as well.
Assuming no net migration into or out of the population, the necessary and sufficient
rates to describe population dynamics are births and deaths within the population (see
above). Although the number of offspring produced by an individual female and the
probability that an individual will die (or survive) at any particular instant are determined
by any number of environmental, physiological, and historical factors, the effects of
chemical stressors on these two vital rates can be estimated using toxicity tests and
laboratory experiments. Such tests usually are performed in a manner that isolates the
effects of the chemical stressor(s) from all other environmental influences through
standardization - all non-chemical variables are held constant (within and across like-
tests) such that the differences in responses observed across exposure conditions are
attributable almost solely to the chemical(s). Such standardization supports
understanding of differences among species in their sensitivities to single chemicals (or
environmental media in the case of complex mixtures like sediments), and the "potency"
of different chemicals to a single species, but results in effects information that likely
underestimates effects expected to occur at the site. This is because only direct toxic
effects are measured in standard toxicity tests; effects on vital rates that result from
changes in species interactions (competition, predation, disease) and the interactions
among biological and environmental factors (temperature, water availability, etc.) are
purposely minimized. Thus, standard toxicity tests isolate the effects of the chemical (or
environmental medium) from all others.
Of course, standard toxicity tests have been developed for a number of different species
and exposure conditions (principally duration). Excluding for the moment bioassays
designed primarily to measure physiological attributes (biomarkers and bioindicators; but
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see Maltby et al., 2001 for a description of extrapolation across multiple levels of
biological organization), the measurements made in such tests usually include mortality
(in short-duration or "acute" tests), but also can include reproduction (in longer-duration
or "chronic" tests), and in some cases, changes in individual growth (as measured by size
or weight). These first two attributes can be used to estimate the vital rates required by
extrapolation models with appropriate consideration of the conditions of toxicity testing
and the requirements of the model.
Standard toxicity tests provide information most relevant to the purpose and conditions of
the test. Thus, if the test measures acute mortality of neonatal Daphnia over a 96-hr
exposure period (and assuming all quality assurance requirements have been met), the
resulting data adequately describe the rate at which newborn Daphnia will survive a 96-hr
period of exposure to each concentration tested. It does not, however, directly provide
survivorship data for older individuals, nor information about what reproductive effects
might be elicited. Standard tests rarely measure both survival and reproductive effects
over the full life span of the test species; this creates some practical difficulties with
respect to extrapolating test results to population level effects. Yet, with appropriate
acknowledgment of their concomitant uncertainties, a number of approaches can be
employed that can utilize even minimal toxicity data sets to estimate population
responses. The value of any of these approaches depends upon the goals of the risk
assessment with respect to desired level of conservatism (safety) in the risk estimated,
and the cost and likelihood of obtaining additional data for model parameterization.
Using data only as measured - Probably the least conservative use of standard
toxicity data is to model population response as if the chemical (or environmental
medium) only affected the life stage tested. For example, the Daphnia test data
described above might be used to estimate population-level risk if the assumption
was that the chemical only affected neonates. Clearly, this analysis approach
would underestimate risk if the survivorship of other age classes were also
affected, or reproductive effects could occur.
Extrapolating effects to other ages or life stages - Although differences in the
sensitivities of age- and stage-classes may exist, the responses of a tested class can
be extrapolated to those of untested classes by assuming functional relationships.
The simplest relationship to assume is equality, that is, the response of class X is
equal to that of class Y. With additional information, more complex relationships
could be assumed. By extrapolating test data to the responses of all classes,
(presumably) more realistic estimates of population risk can be made. However,
two cautions are appropriate here. First, without appropriate knowledge of the
relationships among the responses of different classes, errors can be introduced
into the analysis which may be difficult to identify and interpret (class X may be
more, equal, or less sensitive than class Y, and the resulting influence of risk
estimates would be unrecognized). The second is related to the axiom that "an
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individual can't be killed twice", meaning that younger individuals that die may
shift the distribution of individual sensitivities in older age classes to the right
(less sensitive) in long-term exposures (typical of site-specific risk problems).
Without recognition of this shift, estimates of risk would be relatively
conservative.
Extrapolating effects to other vital rates - Similarly, reproductive effects could be
extrapolated assuming some relationship between survivorship and fecundity.
The cautions offered above are relevant here as well. [As an aside, individual
growth effects can also be extrapolated to changes in reproduction and
survivorship when their functional relationships (e.g., smaller individuals produce
fewer offspring) are known.]
Extrapolating effects across test exposure durations - As indicated earlier, how
toxicity test data are used in extrapolation models depends on the requirements of
the model itself. A model that describes the population as a sequence of year-long
age-classes requires data couched in terms of annual rates. The potential
mismatch between model requirements and toxicity test durations and data is
obvious, but it can be overcome mathematically (see details in Caswell, 2001, and
an example in Munns et al., 1997). Uncertainties associated with using data
obtained on time scales different from those required by the model include not
only the propagation error inherent in mathematical manipulations, but also those
due to differences in the mechanisms of toxicity that may be in operation under
different combinations of concentration and exposure duration (i.e., acute versus
chronic).
A laboratory-based approach for obtaining the data needed to parameterize extrapolation
models that avoids some of the issues above involves performance of a life table response
experiment (LTRE). In ecology, life tables are age- or stage-specific schedules of
survivorship and reproduction that can be used in demographic extrapolation models to
estimate population-level effects associated with some environmental situation or
experimental treatment. LTREs can be used to generate these schedules for different
chemical exposure conditions. Typically, the duration of LTREs correspond with the life
span (or at least life cycle) of the species involved in the experiment, although partial life-
cycle tests can, in some situations, provide sufficient information (e.g., Daniels and Allan,
1981). Use of LTREs to help parameterize population models is described in detail in
Caswell (2001). Because LTREs evaluate effects on all vital rates for all classes, the need
to extrapolate limited data is reduced or eliminated. Unfortunately, "standardized" (in the
sense of toxicity tests) LTREs typically do not exist, and LTREs generally are more
expensive to perform than are standard toxicity tests.
Expanded descriptions of two examples of extrapolation modeling introduced earlier
illustrate the use of toxicity test data to parameterize population models for use in risk
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assessment. The first involves Kuhn et al.'s (2002) development of a projection matrix
model to assist in extrapolating standard toxicity test results for the estuarine amphipod,
Ampelisca abdita. Used commonly in a number of regulatory and monitoring programs,
the standard solid-phase Ampelisca test involves exposing approximately 20-day old
animals (based on size) for 10 days under static conditions (ASTM, 1993). Kuhn et al.
(2002) constructed a model that divided Ampelisca'?, life cycle into seven 10-day age
classes, such that data from the standard test corresponded to survivorship between the
second and third (juvenile) age classes. Mean survivorship over the course of a standard
test (equivalent to the transition probability between classes 2 and 3 in the model) of Cd-
spiked sediment was calculated as the number of individuals in a treatment replicate alive
at the end of the test divided by the number at the start of the test, averaged across
replicates. [As an aside, the variance observed among replicates can be used to quantify
uncertainty in population effect estimates, or to describe probability distributions in
probabilistic assessments.] Kuhn et al. (2002) also had conducted a full 70-day
experiment to provide demographic information to parameterize a "base" model that
reflected Ampelisca vital rates in the absence of Cd exposure (i.e., using reference
sediment). Under various assumptions of how standard 10-day mortality related to
Ampelisca vital rates, Kuhn et al. (2002) developed empirical extrapolation relationships
between test results and population effects. These relationships can be used to interpret
sediment toxicity test data in the context of population-level risks to amphipods at
contaminated sediment sites.
The second example is Kuhn et al.'s (2000) use of data obtained from standard life cycle
chronic tests to project the effects of some 20 chemicals on mysid shrimp, Americamysis
(formerly Mysidopsis) bahia, population dynamics. The life cycle test for A bahia is in
most regards comparable to an LTRE, in that mortality and reproduction of test
populations are followed on a regular (in this case, daily) basis over the course of a long-
term exposure. Survivorship was calculated daily, using the same method as in the
Ampelisca example, to parameterize a projection matrix model constructed with 24-hr age
classes. The fecundity of each age class was calculated as the number of female offspring
produced each 24-hr period, divided by the number of females alive during that period.
Population models were uniquely parameterized for each treatment level of each
chemical, and were used to develop chemical-specific exposure-(population growth rate)
response relationships. These relationships could then be used to estimate the population-
level effects of any given exposure concentration of each chemical. As mentioned earlier,
Kuhn et al. (2001) subsequently demonstrated that the age-classified model,
parameterized for the chemical nonylphenol using standard toxicity test data, projected
the dynamics of A. bahia reasonably well in a multigenerational experiment conducted in
the laboratory, adding confidence to the use of the models for predicting population-level
risk. [As an aside, Maltby et al. (2001) describe how alternate formulations influence the
accuracy of population models in predicting the results of the multigenerational
experiment.]
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It should be noted that descriptions of the use of toxicity test data in population
extrapolations models to this point have been restricted to situations in which exposure is
assumed to be constant. Except under certain conditions (e.g., benthic organisms in
contaminated sediment), it is unlikely that the risk scenarios evaluated at Superfund and
RCRA sites would involve static exposure. More often, organisms are thought to
experience variable exposure as they move through the environment, or the environment
(e.g., water) moves past them. With appropriate caveats and acknowledgment of
uncertainties, toxicity test data can also be used in these situations. One approach for this
is to use test data to construct treatment-wise exposure-response curves relating either
vital rates or population-level attributes to exposure concentration. These relationships
can be used with dynamic simulations of exposure through time or across space to
provide more realistic assessments of population risk by dividing time into discrete units,
each with a potentially unique exposure concentration which is translated into an effect
through the response curve(s). This approach is illustrated in Munns et al. (1996) in an
assessment of population risks associated with aquatic sewage sludge disposal. As with
all of the uses described here, this approach comes with limiting assumptions that
influence interpretation of the analysis.
The information presented above applies to situations in which the assessment population
is of the same species as that used in the toxicity test or LTRE. Although their
description is beyond the scope of this white paper, approaches exist for extrapolating
effects across species when needed. Such extrapolations can be made either at the level
of the test data themselves (e.g., mortality of species X extrapolated to mortality of
species Y, followed by use of the extrapolated data to model a population of species Y),
or at the population level (e.g., mortality of species X used to model a population of
species X, followed by extrapolation to a population of species Y). A general description
of cross-species extrapolation issues can be found in Munns (2002); more detailed
accounts are given in Mayer et al. (1987), Suter (1993) and references cited therein.
4.4 Considering Spatial Scale
The extrapolation modeling approaches considered above typically assume the
environment, and how individuals react to it, to be spatially homogeneous. Moreover,
considerations of the geographical boundaries chosen when defining the assessment
population are conceptually irrelevant to application of the models. However, natural
populations exist in landscapes (or waterscapes) that consist of mosaics of habitat type
and stressor concentration. The vital rates of individuals residing primarily in one patch
(defined in terms of habitat quality and stressor concentration) likely differ from those
living in other patches. The dynamics of these local groups, in aggregate, determine the
dynamics of the overall population. Furthermore, refugia in the landscape (patches with
low concentrations of anthropogenic stressors) can act as population sources for
movement of individuals into areas impacted by stressors, potentially ameliorating the
effects of those stressors on the local scale. Conversely, impacted areas can act as sinks
into which individuals from unimpacted areas move, depressing overall population
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abundance (see Landis, 2002 for a demonstration of these effects, and Landis, in review
for a discussion of the implications of patch dynamics to understanding population-level
effects).
Historically, population models incorporating a spatial context have been applied to
questions of conservation biology, pest dispersal and invasion, and other population
management issues. Their use to address population-level effects of chemical stressors is
relatively new, although examples exist in the literature (e.g., Thomas et al., 1990;
Sherratt and Jepson, 1993; Pulliam, 1994; Jepson and Sherratt, 1996; see chapters in
Barnthouse et al., in review for convenient summaries). Valuable discussions of
modeling population dynamics in a spatial context are given by Okubo (1980), Hanski
(1991, 1996, 1997, 1999), Hanski and Gilpin (1991), Dunning et al. (1995), and Tilman
and Kareiva (1997). Specific model formulations accounting for spatial heterogeneity fall
into two broad classes, as described below. Table 2 identifies particular models and their
assumptions.
Metapopulation models divide the overall population into subpopulations that
communicate with one another through immigration and emigration. Conceptually,
subpopulations are treated almost as individuals, with extinction and recolonization
driving local dynamics. Such models do not necessarily incorporate habitat quality and
stressors explicitly; rather, the environment can be described mathematically as a series of
more-or-less identical patches. Metapopulation models can be used to explore the
influence of: 1) the size, spacing, and density of patches, 2) rates and forms of movement
among patches, and 3) rates of extinction within patches on population persistence and
spatial distribution. See Levins (1969) for early considerations of the metapopulation
modeling approach.
Spatially-explicit models increase ecological realism by incorporating landscape structure
and habitat quality explicitly. These models differ primarily from metapopulation models
in that the spatial context of patches is important not only to migration among patches,
but also to the internal dynamics of subpopulations within patches. Internal
subpopulation dynamics can be modeled by relating aspects of habitat quality to average
vital rates, or even by allowing environmental parameters to affect individual
physiological and behavioural responses using an individual based modeling approach.
Variation in habitat quality can be incorporated using spatially-referenced data sets of
land use patterns, landscape characteristics, and stressor distributions. For example,
Akfakaya and Atwood (1997) developed a spatially-explicit model of threatened
California gnatcatcher (Polioptila californica californica) dynamics to support protection
of this subspecies and its habitat from land development in southern California, USA.
The habitat requirements of P. c. californica were determined by relating habitat
characteristics to patterns of habitat use. These relationships were used to develop habitat
suitability functions, which in turn were used to score the quality of grid cells modeled in
the landscape based on geographic information system (GIS) data on land cover and
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topography. A two-stage stochastic projection matrix model with density dependence
was used to model gnatcatcher dynamics within patches. Population-wide vital rates in
this model were estimated from existing data sets, independent of habitat suitability, and
were allowed to vary randomly to reflect environmental and demographic stochasticity.
Akfakaya and Atwood (1997) used their model to relate probabilities of population
decline (quasi-extinction) to a variety of environmental and demographic parameters,
with an intent of supporting evaluation of various resource management options. More
recently, Schumaker (1998) developed a spatially-explicit modeling platform that permits
incorporation of GIS-referenced habitat data, specification of functional relationships
between habitat quality and demographic response, and specification of rules to describe
movement of individuals among patches. Schumaker's model, PATCH, is being updated
to include the effects of chemical stressors on vital rates (N. Schumaker, ORD NHEERL,
personal communication).
The ability to model populations in a spatially-explicit manner offers the opportunity to
address some aspects of the question raised earlier about the scales appropriate for
defining the assessment population. When clear boundaries that delimit the population
cannot be established, if issues remain relative to the adverse effects of local hazardous
waste sites on populations inhabiting large geographic ranges, or uncertainty exists about
the extent to which local effects might be ameliorated by immigration from surrounding
areas, a modeling analysis that varies the spatial boundaries in the definition of the
population may provide some answers. One objective of this type of analysis might be to
define the relationship between expected population-level effect and the spatial scale used
to delimit the population. This relationship might take the form of a "scale-response"
curve (conceptually analogous to a stressor-response curve) that could be used to help
understand the ecological significance of site risks. The analysis could provide insights
to the severity and extent of adverse effects, as well as the potential for population
recovery as local effects are "diluted" by migration into the site from surrounding areas.
When weighed against the regulatory requirements, policy considerations, and
stakeholder interests driving problem formulation of the assessment, the results of this
type of analysis could provide significant support to the decision-making process.
4.5 Considering Model Selection
Given the range of options for linking individual-effects to population response, which
model should be used? That choice is situationally-dependent, and should reflect a
number of considerations, including the assessment endpoint and how risk estimates will
be used in the decision process, the model's intended use, the biology of the assessment
population, the availability of information and data describing that biology, the resources
available for performing the assessment, and so on. Additionally, the informational
requirements of the selected model must be satisfied.
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TABLE 2
Population Modeling Approaches Incorporating Spatial Context
(modified from Maltby et al., 2001)
Model
Levins' model
(and variants)
incidence function
model
reaction-diffusion
models
cellular-
automaton-like
models
Assumptions
continuous time,
discrete space
continuous time,
discrete space
continuous time,
continuous space
discrete time,
discrete space
Comments
breaks habitat into an infinite
number of distinct sites; assumes
global random dispersal of
recruits
breaks habitat into a finite
number of distinct sites of
differing size; assumes localized
dispersal of recruits
local populations grow
("reaction") and spread through
space ("diffusion")
divides habitat into contiguous
sites ("cells"); assumes dispersal
among adjacent sites
References/
Applications
Levins (1969)
Hanksi(1991, 1996, 1997)
Lamberson et al. (1992)
Hanski(1994)
reviewed in Okubo (1980)
Ak9akaya and Atwood (1997)
Schumaker (1998)
The data requirements of models deserve special consideration in selecting the
appropriate model for assessment purposes. The degree to which these requirements can
be satisfied determines, at least in part, which models may be successfully employed. In
this regard, some of the modeling techniques discussed earlier (e.g. time series analysis)
require only that the total abundances of the population or specific life stages be known.
However, such approaches do not easily permit incorporation of mechanistic information
regarding toxicity or population control, and therefore are of limited use in examining
scenarios involving short-term temporal variation in exposure, incremental effects of
multiple stressors, or the ramifications of various remediation options. At the other end
of the spectrum are formulations such as IBMs which require detailed knowledge of
physiological and metabolic processes and how these influence the vital rates of fecundity
and survivorship. The realism of these approaches is further enhanced through
incorporation of density influences on or stochastic variation in these processes. Such
data are difficult to obtain, yet their inclusion into appropriate models permits the most
detailed assessments. Recent useful discussions of density dependence relevant to
ecological risk assessment can be found in Sabo et al. (2004) and Moe (in review).
Consideration of the ease with which assessment population-specific information can be
obtained is important. Does valuable information exist regarding temporal and spatial
patterns of abundance? Perhaps the most cost-effective source of such data is historic
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data bases obtained for other purposes. Can the life history characteristics of critical life
stages be determined from field collections or from the literature? Can sensitivity and the
modes of toxicity be examined in the laboratory? Such determinations, if they can be
made, are usually performed at increased cost. Thus, the availability of information
regarding the life history of the species and the dynamics of individual growth and
development is crucial to determining model selection. Further, difficulties in obtaining
information about populations at hazardous waste sites may affect the ability to evaluate
the veracity of estimates of risk.
The model formulation used to examine effects must also permit isolation of the
population attribute of interest (as defined by the assessment endpoint) for detailed
analysis. Models which do not incorporate parameterization of specific vital rates offer
little in the way of examining subtle effects on those rates. It also may be desirable to be
able to parameterize aspects of the measured or expected exposure regime experienced as
a result of disposal and site conditions, and further, to incorporate the functional form
(e.g. linear, threshold) of the response displayed by target attributes. Dynamic computer
simulations incorporating both exposure conditions and the resulting population-level
effects can go a long way towards satisfying these requisites. Finally, the model selected
for application should permit incorporation of the detail of species-specific information
available, because such models arguably yield the most realistic assessments of risk.
Additional discussion of model selection and the factors to be considered is given in
Munns et al. (in review).
4.6 Considering Uncertainty In Extrapolation
Extrapolation and the use of models introduces uncertainty and potential error into risk
assessment. Knowledge about the nature and sources of uncertainty associated with
extrapolation can improve assessment planning and inform risk managers about how
assessment results can be used in decision making. As summarized by Munns (2002), a
useful way to think about uncertainty is to partition its sources among three distinct
components (Suter, 1993; see Seiler and Alvarez, 1995 for other terminology and
definitions): variability, also called heterogeneity or stochasticity, ignorance or lack of
knowledge, and error. Variability is a component of all ecological systems, and
represents actual differences in the value of a parameter or attribute among units in a
(statistical) population. For example, organisms display variability in their susceptibility
to chemical stressors, such that some individuals die at lower exposure concentrations
than do others, a fact described by the classic exposure (dose)-response relationship.
Variability cannot be reduced by taking additional measurements of a parameter, although
it can be quantified more accurately using larger sample sizes. Ignorance represents a
lack of knowledge about the true value of a parameter that can result from inadequate or
imperfect measurement. It can, however, be reduced with the collection of additional
data and information. Continuing the toxicity example, there is a true value at any point
in time for the mean susceptibility of individuals in the population, and our estimate of
that value improves as a function of the number of toxicity tests we run to estimate it.
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The final source of uncertainty in risk assessment, error, results from the use of the wrong
methods, models, and data in assessment activities. Error can be corrected or minimized
by understanding the uses and limitations of various methods and models to answer
specific risk questions, and by rigorous attention to assessment quality.
Extrapolation of population response from effects measured in individuals introduces
uncertainty primarily through ignorance. This uncertainty arises from a lack of
understanding of the processes and mechanisms that determine how populations operate,
how they respond to environmental stressors, and how best to model them. For example,
substantial evidence exists, and it is general knowledge that, population abundance is
influenced by processes that are affected by density. However, the exact mechanisms by
which density dependence operates, how best to model those mechanisms, and the values
that should be assigned to model parameters involved in the density effect(s) generally are
unknown (except in isolated instances). Incorporation of density-dependence into models
without this knowledge introduces uncertainty that may not be compensated by supposed
increase in realism achieved by that incorporation (see below). Additionally, inferences
of population response based on observations made at lower levels of biological
organization can err if emergent properties (Harre, 1972; Salt, 1979) control population
dynamics. Qualitative changes in the causes and mechanisms of response at different
levels of biological organization, also called transmutation (O'Neill, 1979), produce
nonlinearities that can confound our ability to predict the nature and magnitude of risks.
The existence of nonlinearities and emergent properties potentially limits the usefulness
of extrapolation models to assess risk (see, for example, Bella, 2002).
Uncertainty arising from ignorance can be addressed in at least four ways. One is to
perform a meta-analysis (Arnqvist and Wooster, 1995) of the type that compares the
outputs of two or more models constructed using different assumptions about how
population-controlling processes operate. For example, two or more fishery models
might be used to make projections, and their resulting outputs used to bound the range of
possible effects. Differences in output could also suggest closer examination of model
assumptions and approaches, leading to the selection or rejection of specific formulations.
Such meta-analyses clearly increase the costs of the assessment, but that added burden
might be warranted if the costs associated with making a wrong management decision are
high.
An arguably less costly approach to addressing ignorance is to perform sensitivity
analyses of model performance and output in which parameter values are varied
systematically. In this manner, the influences of particular assumptions and modeled
relationships on model output can be evaluated. Attention to those parameters and
relationships that most influence model output, say by improving data quality or by
conducting additional research to enhance understanding of how biological processes
operate, should reduce uncertainties with the model and thereby improve the estimates of
risk.
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A third approach for reducing ignorance is to strive for enhanced realism in the modeling
effort. This can be accomplished in a number of ways. For example, the demographic
and fishery approaches described above are deterministic in their general formulation.
Introduction of stochastic variation in mechanistic processes or vital rates permits, for
example, description of the distribution of population numbers under steady state
(Costantino and Desharnais, 1981; Dennis and Costantino, 1988) or impacted conditions,
as opposed to single point estimation. With such, different realizations of model outputs
are assigned probabilities, offering a means to bound the range of possible outcomes and
to identify those that are more likely. [As an aside, characterization of steady state
distributions for unimpacted populations would permit estimation of the magnitude of
population change needed to detect contaminant impact using inferential statistics.] Of
course, introduction of stochasticity in model parameters also addresses the first source of
uncertainty mentioned above, that is, variability.
Realism can also be enhanced by incorporating homeostatic and genetic compensatory
mechanisms explicitly into the model formulation. An implicit assumption of the
population models described above is that individuals are genetically identical to one
another. That is, the dynamics of the population are treated as being independent of
genetic variation and allele frequency. However, the impact that a given concentration of
contaminants will have on a population is related to the fitness of individuals relative to
such exposure. Populations displaying allele frequencies near those which accrue
maximum fitness under conditions of contaminant insult will show minimum impact
relative to native populations. Although long a goal in population biology, marriage of
population dynamics theory with population genetics into single models has taken place
only relatively recently (e.g., Desharnais and Costantino, 1983). Despite their increased
realism, and except for selected applications developed in conservation biology that
include effects of inbreeding as population size decreases (e.g., Lacy, 1993), such models
are not sufficiently developed to be of much use in the context of site-specific risk
assessments. However, genetic adaptation to contaminant insult is an important
consideration in Superfund and RCRA assessments that should be explored more fully
(Nacci et al, 2002).
With the exception of metapopulation and spatially-explicit formulations, all of the
mechanistic models discussed here assume no net migration. Clearly, realistic and
precise characterization of population dynamics requires quantification of the rates of
both immigration and emigration. In closed populations, such as those bounded by
geographical or environmental constraints, these rates are sufficiently low to be treated as
zero. However, migration into and out of many populations associated with hazardous
waste sites may not be so constrained. In these situations it may be appropriate to
parameterize migration as a time or population density-dependent process.
As suggested earlier, model realism can be enhanced by incorporation of density-
dependence in fecundity, survivorship, individual growth, and migration rates into those
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formulations where no such dependency exists. Instances in nature where demographic
processes are unaffected by such influences probably are rare (Slobodkin, 1987). Further,
introduction of time lags in the realization of density (Marchesseault et al., 1976) as well
as other effects arguably result in more realistic models (May, 1973). Levin and
Goodyear (1980) explore the behavior of a population projection matrix model with
density dependence added. Parameterization of density-dependence (termed
compensation in fishery science) is problematic in the formulation of population
dynamics models. An overview of the difficulties associated with measurement and
parameterization of such affects in fisheries management are given by Goodyear (1980).
One last modification affecting model realism is incorporation of species interactions
(e.g., competition, predation). Populations don't exist in isolation; they interact with
other populations in the community in ways that can have as profound impacts on their
dynamics as do anthropogenic stressors. Yet, many of the formulations described above
treat populations as if they were isolated from such interactions. Exceptions to this
include those that include fishing or harvesting pressure (where humans are a predator),
and IBM formulations that include interspecific competition and predation. Numerous
approaches for modeling species interactions and community dynamics exist, description
of which is beyond the scope of this white paper. However, the extent to which such
approaches improve risk assessment of populations remains to be determined.
The most obvious way to reduce uncertainty arising from both ignorance and error, is to
test model outputs against known results. Generally, questions of uncertainty relative to
the use of models in risk assessment often devolve to ones of model verification and
validation. These terms have been used inconsistently (and sometimes interchangeably)
in the ecological literature, leading to considerable confusion and, we suggest,
obfuscation of the important underlying question: "Does the model work as intended?"
(Mitro, 2001). Rather than adding to assessment uncertainties by questioning model
verification/validation, we recommend that RPMs and site managers seek to understand
how models were tested and evaluated in a manner that facilitates understanding of their
uses and potential limitations in site-specific risk assessments. The goal of model
evaluation is to characterize the relationships between predictions or projections
generated from available data and modeling constructs, and the actual population-level
responses observed at the site. Field evaluation of the modeling and assessment
procedures, and monitoring in general, are complex subjects which cannot be addressed
adequately here. However, three points mentioned below are worth considering, as they
potentially affect the feasibility of population-level assessments. More detailed
discussions of problems associated with monitoring and model evaluation are provided in
Cairns et al. (1984) and others. [One of us (MM) currently is conducting an evaluation of
the degree to which population models have been tested, and how they performed against
their intended use, based on a review of existing literature.]
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Biological systems are often characterized by considerable temporal and spatial variation,
the degree of which changes across scales of measurement. For instance, local densities
of zooplankton vary in response to variation in water circulation processes, such as
Langmuir cell formation, but also change in absolute abundance as a result of intrinsic
and external regulatory processes. This variation should be adequately addressed through
timely application of appropriately designed sampling programs so that changes in
population attributes can be ascribed to either contaminant impact or other causes.
Inadequate replication in sampling designs may hinder detection of change, let alone
proper quantification of that change.
Successful evaluation methods should also incorporate examination of exposure
conditions to avoid drawing incorrect conclusions concerning the correspondence
between model projections or predictions and responses observed in the field. Potentially
confounding effects of multiple stressors should be identified and factored into a
reevaluation of expected population-level change. Problems of scale are also cogent here.
Evaluation of models used to predict or describe exposure regimes is therefore extremely
important to successful evaluation of population modeling assessments.
As a final consideration relative to model testing, such evaluations may only be relevant
for those cases in which actual forecasts (as defined earlier) of population responses are
made. Risk assessments based upon projections of response, at least at some level,
require constancy in environmental conditions. Constancy in natural biological systems
is rare indeed. This is not to say that models that project population change cannot be
used in dynamic simulation. However, only qualitative correspondence between
simulation results and the actual behavior of the population in the field might be expected
in those cases.
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5. Measuring Population Attributes and Parameters in the Field
Data collected through field measurements can be used to parameterize population
models described in the previous section, to evaluate the outputs of those models, or,
independent of models, to assess the effects of toxic chemicals at a site directly. In all
these cases, there are inherent difficulties in measuring characteristics of natural
populations in the field as compared to laboratory settings. The opportunity exists in
laboratory studies to have almost complete knowledge of the population: exactly how
many individuals are in the population, its age structure, the rate at which individuals are
added to or removed from the population (through the processes of birth, death, and
migration), and the rate at which population abundance changes. Such complete
knowledge is nearly impossible of natural populations, especially animal populations.
Statistical sampling is almost always necessary to estimate model parameters, evaluate
model outputs, or characterize the status and dynamics of populations in response to
chemical exposure. This section describes some techniques for field sampling and data
analysis to support estimation of population-level attributes and the parameters used to
calculate them, and is organized around the major categories of attributes described in
Section 3 (additional information can be found in Suter et al., 2000). It does not,
however, provide a step-by-step procedure for conducting field-based assessments of
population risk from chemicals at Superfund and RCRA sites.
5.1 Measuring Population Abundance and Density
Estimation of population abundance and population density are two separate yet
interrelated problems. If population abundance and the total area or range of distribution
are known, then density can be estimated simply by their ratio. However, techniques
exist to estimate population abundance without precise knowledge of the area over which
the population is distributed. Alternatively, area can be fixed and the density of the
animal population in that area can be estimated.
If every individual in a population (or in a defined area) can be detected or captured (i.e.,
the probability of detection or capture,/?, equals 1.0), then a census of the population can
be taken to determine its abundance or density. For many plants, larger birds (common
loon, trumpeter swan), and mammals (elk, bison) that are highly visible, p often can be
assumed to be 1, and a census performed. However, if p is actually less than 1, the
census will be biased negatively (i.e., abundance or density will be underestimated).
Aquatic animals such as fish, and many birds and mammals are not readily detectable or
amenable to capture. For these populations, information from individuals that are seen
can be used to make inferences about population size. Two techniques that can be used
in this regard are capture-recapture and distance sampling', capture-recapture studies
focus on the estimation of abundance (among other parameters), while distance sampling
studies focus on the estimation of density. Because a large and well-developed literature
exists on capture-recapture and distance sampling techniques for animals (Otis et
al., 1978; White et al., 1982; Seber, 1982, 1986, 1992; Buckland et al., 1993; Schwartz
and Seber, 1999), these methods are described here only generally.
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Capture-recapture - Capture-recapture techniques are used to estimate abundance. In
capture-recapture sampling, individuals are captured and are in some way marked,
tagged, or banded (Neilsen, 1992; Murray and Fuller, 2000), such that these individuals
can be identified on subsequent recapture occasions. Marks may be unique to the animal
or unique to the capture occasion such that capture histories can be identified. This
information is used to construct a capture history matrix that comprises a coded list of
unique capture histories for two or more sampling occasions and identifies how many
individuals have each capture history. For example, if a population of fish were captured
and marked on five days and 57 fish were captured on days 2 and 5 (but not on days 1,3,
and 4), then 57 fish would have the unique capture history "01001". A set of capture
histories can be analyzed using a suite of models to estimate abundance.
The assumption of population closure is important to consider when using capture-
recapture to estimate abundance. A population is considered closed if no births, deaths,
or migration occur during the sampling period. Different estimators of abundance are
used for closed versus open populations. Other important assumptions for capture-
recapture studies include: 1) every animal in the population on the/11 sampling occasion
has the same probability,^, of capture (i.e., equal catchability); 2) marks, tags, or bands
are neither lost nor overlooked over the course of the study; and 3) all samples are
effectively instantaneous relative to the period between samples, and captured individuals
are released immediately after sampling. Violations of these assumptions can result in
biased or imprecise estimates of abundance.
Violations of the closure assumption can be minimized by sampling over a restricted time
period during which births, deaths, and migration do not occur or are minimal. Closure
with regards to migration can be ensured for some populations by physically isolating
them. For example, blocking nets can be used in small streams to prevent fish from
moving into or out of a sample reach. Physically isolating a population is often not
feasible, but for short sampling periods, physically open populations can sometimes be
treated as closed (Pollock, 1982). For example, sampling for a bird population might be
restricted to a time period just prior to nesting, when individuals are not migrating and
natural mortality is minimal. If evidence of biological closure is desired for a physically
open population, then a multistrata sampling and modeling approach can be used to
quantify any losses from the population attributable to death or migration (Hestbeck et al.,
1991; Brownie et al., 1993; Mitro and Zale, 2002). Multistrata model can be
implemented in the computer program MARK (White and Burnham, 1997).
The goal of capture-recapture techniques is to develop estimators of abundance. If the
closure assumption is satisfied, a set of closed-population abundance estimators can be
developed from the capture histories. Estimators based on multiple capture occasions can
be calculated using the computer program CAPTURE (Otis et al., 1978; White et al.,
1982; Rexstad and Burnham, 1991). Included are estimators that are robust to departures
from the equal catchability assumption: behavioral response to capture, temporal
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variability in capture probabilities, and heterogeneity among individuals to capture.
These estimators typically require three or more capture occasions; the Lincoln-Petersen
estimator (Ricker, 1975) can be used for two capture occasions and is robust to temporal
variability in capture probabilities.
An estimator for abundance used when behavioral response to capture is of concern is the
removal estimator developed by Zippin (1956). In removal sampling, animals are
numerically depleted from the closed population by physical removal or marking on
successive capture occasions, such that catch per unit effort decreases proportionately to
the number of animals remaining. Animals are not subject to recapture (or marked
animals are ignored on subsequent capture occasions), thus avoiding behavioral responses
to first capture which may increase or decrease the probability of recapture. Three or
more removal occasions are typically required to estimate abundance. A single removal
occasion can be used in conjunction with a calibrated model to estimate abundance in a
large area by sampling many smaller areas (Mitro and Zale, 2000a). This approach
supports a more rapid assessment of population abundance compared to the multiple
removal occasions techniques.
If the closure assumption cannot be satisfied, the Jolly-Seber estimator for open
populations can be used to estimate population abundance from capture-recapture data
(Jolly, 1965; Seber, 1965). The Jolly-Seber estimator parameterizes the processes of birth
and death, thereby allowing additions to or losses from the population during the
sampling period. The Jolly-Seber abundance estimator can be calculated using the
computer program POP AN (Arnason et al., 1998).
Sampling effort, probability of capture, and population size all influence the precision of
abundance estimates. Estimator precision increases with increasing sampling effort and
capture probability. Greater sampling effort translates into higher capture probabilities;
as more individuals in a population are captured, more marked individuals are recaptured,
providing additional information upon which to base an estimate of abundance.
Sampling effort can be increased by sampling an area more intensively or by sampling on
more occasions. However, as population size increases, precision decreases because a
relatively smaller portion of a population is marked and recaptured for a given amount of
effort.
The number of parameters in an estimator also influences abundance estimate precision,
as well as bias. The goal is to select an estimator that minimizes both bias and precision,
and the most appropriate estimator will depend on the nature of the capture-recapture data
available. If the data indicate a violation of the equal catchability assumption, such as
temporal variability in capture probabilities, then an estimator parameterized for
temporally varying capture probabilities will minimize both bias and precision. Selecting
an estimator with fewer parameters will improve precision but introduce bias; an
estimator with more parameters will be unbiased but imprecise. Estimator selection can
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be aided by using information theoretic criteria, likelihood ratio tests, goodness of fit
tests, and simulation (Burnham and Anderson, 1998; Mitro and Zale, 2002)
Distance sampling - Distance sampling is used to estimate density, and has been used for
populations of birds, mammals (terrestrial and marine), and fish (Buckland et al., 1993).
Distance sampling is equally applicable to estimating the density of inanimate objects
related to animals, such as bird nests or fish spawning redds (Buckland et al., 1993; Mitro
and Zale, 2000b). This technique involves only the sighting of objects (animals, plants,
other) along a line transect or around a point transect. In line transect distance sampling,
an observer moves along a line transect of a study area and records the location, relative
to the line, of each object detected within some distance either side of the line. In point
transect sampling, an observer stands at a fixed point in the study area and records the
location, relative to the point, of each object detected within some distance around the
point.
There are three assumptions necessary for reliable density estimation from line or point
transect sampling (Buckland et al., 1993): 1) objects on a transect are detected with
certainty; 2) objects are detected at their initial location before any movement in response
to the observer; and 3) distances between objects and the transect are measured
accurately. Minimizing deviations from these assumptions will minimize bias in density
estimates. That said, objects can remain undetected without undermining the validity of
the density estimate. Distance sampling theory accommodates decreases in the
detectability of objects as their distance from the line or point transect increases
(Buckland et al., 1993). Perpendicular distances from a line transect (or distances from a
point transect) are "sampled", and the distances are modeled so that detectability can be
estimated. As distance from the line or point transect increases, detectability decreases,
allowing estimation of the effective area sampled and hence density.
In addition to the assumptions above, the position of individual objects in the study area
ideally should be random relative to the line or point transect. If this condition is met,
there is no requirement about how transects are positioned - that is, transects may follow
a random or systematic pattern. If individuals are not randomly distributed, the transects
should be selected randomly (or systematically from a random starting point). Transect
surveys should be designed to avoid sampling effects that are systematic, such as when
transects are placed along streams, roads, or some other physical feature that may
influence the distribution of objects.
Models for estimating density from line or point transect data are provided in the
computer program DISTANCE (Laake et al., 1994). This program uses sample data to
parameterize a detection function, which is used to estimate density. The detection
function describes the distribution of animal locations relative to the line or point
transect, and is selected from a series of models comprising a key function and a series
expansion, the latter which is used to optimize the key function to fit the sample data
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(Buckland et al., 1993). The key function and series expansion that fit the data best can
be selected using a combination ofAkaike's information criterion (AIC) (Akaike, 1973),
likelihood ratio tests, and goodness of fit tests. Density estimate precision depends on
sample size: the larger the sample size, the more information available to describe the
detection function. Buckland et al. (1993) suggest a minimum sample size of 60-80
detected individuals; smaller sample sizes will yield less precise but valid density
estimates.
5.2 Measuring Population Growth
Population growth rate is a quantification of the rate at which population abundance
changes and can be expressed as an intrinsic rate, r, or a finite rate, A (see Section 3). If
the rate of change is constant over some time period t, then (as the solution to Eq. 1):
Nt = N0 ert Eq. 20
and solving for r:
r = --In L Eq. 21
Similarly,
N, = ANM Eq. 5
and solving for A:
1= Eq. 22
Because both r and A can be calculated from ratios of population abundance (Eqs. 22 and
23), direct estimates of the growth rate of field populations can be made using time series
of population abundances estimated using the methods described above. Additionally,
because population growth rate integrates reproduction and survivorship into a scalar
multiplier that defines how a population changes over some time period, it can be
calculated for natural populations using estimates of fecundity and survivorship from
field data and the demographic extrapolation models described in Section 4. Techniques
for both approaches are described below, together with an approach that uses capture-
recapture data.
Estimates from time series analysis - A time series of abundance is simply a sequence of
population sizes through (preferably equally spaced) time. And over a finite length of
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time, population growth rate can be estimated simply as the ratio of the final abundance
to the initial abundance. As with most field-oriented endeavors, however, estimation of
population growth from field data is not as simple as it sounds. Time series analysis for
estimating population growth rate is a method dealing with complexities of field data.
Time series analysis uses the complete sequence of population abundances. In terms of
bias and precision of the resulting estimate of growth rate, it performs best if abundances
are obtained by census or complete enumeration of the population at each time point in
the series; observation error is introduced if abundances are estimated. Additionally,
process error is introduced if stochastic demographic or environmental forces are
operating and reflected in the time series. When observation error predominates, r or A,
can be estimated from the slope of a linear regression of the natural log of population
size, ln(N), versus time (McCallum, 2000). When process error predominates,
abundances may be autocorrelated such that random variations in time periods influence
population size in successive time periods (i.e., errors are associated with successive data
points) and the estimate of standard error will be an underestimate of the true standard
error. If autocorrelation is detected, r or A can be estimated from the mean in the change
in ln(N) between sequential censuses (McCallum, 2000). The Durbin-Watson test can be
used to detect autocorrelation (Sen and Srivastava, 1990).
The approach for addressing autocorrelation in time series is to use differences between
successive observations as the variable for analysis (McCallum, 2000). For population
abundance observations N0, N1? . . ., Nn, mean population growth rate can be estimated as:
r -
I In
N.
i-l-
Eq. 23
which can be rearranged as:
r =
ln(N )-
Eq. 24
Note that only the first and last values of abundance in a time series are used to estimate
f , and the intermediate values do not contribute, which is not a problem if N0 and Nn are
true counts. However, intermediate values will contribute to the estimate of the standard
error of mean growth rate. If only N0 and Nn are used to estimate r, then any error in their
estimation can greatly affect the estimate of r.
The average growth rate of the population, r , is converted to the growth rate of the
average population r by the equation:
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y" __ y
r T
where:
and the estimated standard error of r is:
= . (). If a population is censussed
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immediately before reproduction (prebreeding) then/?-*-1. Field studies are commonly
conducted such that/? is effectively 0 or 1 and one of the survival terms drops out of the
equation for fertility.
Information on reproductive output is a relatively easy demographic parameter to measure
and can be obtained by direct observation of a random sample of individuals in each age-
or stage-class. Estimates of clutch or litter size from observations of captive-bred animals
can also be applied to wild populations (McCallum, 2000), although care must be taken
to ensure that holding or culture conditions do not unintentionally influence the estimates.
For example, female fish in a gravid state can be sampled to determine the number of
eggs produced by age or size class. Many birds have clutch sizes that rarely vary in size.
In a prebreeding census, these numbers are then multiplied by the survival rate through
the remainder of the first year to obtain an estimate of the number of surviving offspring
produced. For example, the clutch size for a bird can be multiplied by rates of hatching
success, survival from hatch to fledging, and survival from fledging through the
remainder of the first year. In wild populations, an estimate of breeding propensity, or the
percentage of females of reproductive age that are breeding, is also required and should
be included in the fertility equation, unless it can be assumed that all individuals of
reproductive age breed in a given year.
Estimation of survival of individuals in a field population is a more difficult problem than
the estimation of fertility. Whereas the fate of every individual can be followed in a
laboratory population, such information may only be available for some fraction of a wild
population, and this information must be used to make inferences about the population as
a whole. There are a number of methods of estimating survival that depend on various
assumptions of detectability of previously identified individuals. If individuals can be
marked and followed with certainty, methods of analysis for known fate data can be used.
Data for individuals that are marked but that may or may not be observed again can be
analyzed using live-recapture or dead-recovery type models. If animals cannot be
marked and later identified, age structure and population size can be used under
restrictive assumptions to estimate survival (McCallum, 2000). The three methods
involving data from marked animals (known fate, live recaptures and dead recovery) are
further discussed below.
Known fate - Animals may be individually tagged with radio transmitters such that the
fate of individuals can be known with certainty through the study period. Survival can be
estimated without the confounding problem of nuisance parameters such as capture
probability, because radio-tagged animals are detected with certainty over time. The data
for each time interval of a known fate study are simply the number of tagged animals
alive and the number dead. For age-specific survival estimates it is necessary to follow
animals tagged at a known age. Known fate data can be analyzed using models in the
computer program MARK (White and Burnham, 1997).
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Live recaptures - The survival of animals that are marked and released and only
reencountered when recaptured alive on subsequent sampling occasions can be estimated
using open population models of the Cormack-Jolly-Seber type (Cormack, 1964; Jolly,
1965; Seber, 1965; Lebreton et al, 1992). Open population models parameterize the
process of survival. Survival rate estimates from live recapture data are actually estimates
of apparent survival: the probability that an animal is alive and has remained in the study
area such that it is available for recapture (i.e., survival times site fidelity). The
assumptions of no tags lost or overlooked, and effectively instantaneous samples relative
to periods between samples (see abundance estimation procedures above), still apply to
open population models for survival estimation. The assumption of equal catchability of
individuals in the population is not as important for survival estimation as it is for
abundance estimation because survival is estimated only for marked individuals. It is
necessary, however, to assume that the survival of marked and unmarked individuals is
the same.
The data for live recaptures is similar to the capture histories described for estimating
abundance. These data can be analyzed using models in the computer program MARK
(White and Burnham, 1997). Open population models for survival analysis require
estimation of survival probabilities and recapture probabilities. These models are flexible
in allowing estimation of time and group effects on survival and recapture probability. In
other words, these parameters can be allowed to vary or be held constant over any or all
time periods or groups. [However, for time-specific models, the estimates of survival and
recapture probability for the final time period are confounded.] Groups may be
identified, for example, by age, sex, geographic location, or treatment. Two-parameter
models can also be used to identify linear trends in a parameter over time, such as a
declining survival rate over the time period of the mark-recapture study. Modeling of
individual covariate effects is also permitted (e.g., individuals identified by size,
condition, body burden).
The approach for analyzing live recapture data should begin with the identification of
biologically plausible models, and may include a global model in which all parameters
are allowed to vary (Burnham and Anderson, 1998). Akaike's information criterion
(AIC) can be used to identify the model or models most strongly supported by the data.
The AIC is a combination of a likelihood value, which measures the discrepancy between
the model and the data, and a penalty term based on the number of parameters in the
model (Burnham and Anderson, 1998; McCallum, 2000). As parameters are added to a
model, the likelihood value will not increase and may decrease, but the penalty term
increases. The model with the lowest AIC has the strongest support from the data and
best describes the survival and recapture rates during the study period given the data.
Model averaging can be used to obtain unconditional parameter estimates; that is,
parameter estimates that are not conditional on one chosen model. In model averaging,
parameters are obtained from all tested models weighted by their AIC.
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Further statistical tests can be performed to obtain a deeper understanding of the data
(Anderson et al., 1995). For example, say AIC is used to select a model and the model
incorporates a linear trend in survival over time. Likelihood ratio tests can be used to
determine whether or not there is significant time-specificity in survival rates, that the
linear trend is significant, and how many parameters should be used to let survival vary
by time. A test can also be conducted to determine the significance of the slope in the
linear trend. Goodness-of-fit tests can be used to test how well a particular model fits the
data.
Dead recoveries - The survival of animals that are marked and released and only
reencountered when recovered dead can be estimated using dead recovery models. Dead
recovery models estimate survival and either reporting probability (the probability an
animal is reported given it has died; White and Burnham, 1997) or recovery probability (a
function of both survival and reporting probability; Brownie et al., 1985). In the Brownie
et al. (1985) model, which uses recovery probabilities, there is no confounding of
parameters for time-specific models. However, modeling a covariate for recovery
probabilities (e.g., recovery as a function of animal size) is not always clear given that
recovery is a function of both survival and reporting probabilities.
In dead recovery studies (also referred to as band-recovery studies), individuals are
banded and recovered at different times, individuals are recovered only one time, and data
may be collected by different people. Band-recovery studies are typically used to
quantify survival for populations subject to harvest, but can be used in any situation in
which individuals are found dead and reported. There can be many more recovery
periods than banding periods in band-recovery studies, as compared to capture-recapture
studies which require an equal number of marking and recapture periods. The
assumptions for band-recovery studies are similar to those for capture-recapture studies:
no band or tag loss, no band effect on survival or recovery, and all banded individuals in
the same cohort have the same survival and recovery rates.
Dead recovery models can be parameterized for study time or group effects and
individual covariate effects as described above for live recapture models. The analysis
procedure of identifying biologically plausible models a priori and testing models using
AIC, likelihood ratio tests, and goodness of fit tests also applies for dead recovery
models.
Direct estimation of "k from capture-recapture data - The population growth rate
parameter A, can also be estimated directly from capture-recapture data using a model by
Pradel (1996). This model is available in the computer program MARK (White and
Burnham, 1997). Capture histories of the live recaptures are required for this model.
Population growth rate A, is estimated from a likelihood equation that simultaneously uses
recruitment parameters and apparent survival parameters. As in the models described
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earlier for live recaptures and dead recoveries, the Pradel model for population growth
rate can be parameterized for study time, group, and individual covariate effects.
5.3 Measuring Population Structure
The structure of a population may be defined in terms of the distribution by size or age of
individuals in a population. A temporally consistent age distribution is a characteristic of
a stable population, or a population at equilibrium. Such populations tend to have a
larger number of smaller or younger individuals and progressively fewer larger or older
individuals. Changes in age distributions over time can indicate instances of excessive
mortality (although they can also indicate episodic recruitment events or particularly
strong recruitment of year classes). If a population is stressed, say by exposure to a toxic
contaminant, the structure of the population may be disrupted. For example, a
contaminant that adversely affects reproduction and recruitment may result in a
population dominated by larger or older individuals. A contaminant that adversely affects
longevity may result in a population dominated by smaller or younger individuals, to a
greater extent than in a stable population.
Knowledge of the age or size structure of a population may show how a population has
been stressed in the past, but may also show how a population can respond in the short-
term if released from the stressor. The short-term or transient dynamics of a population
are heavily influenced by the structure of the population (Caswell, 2001). Transient
dynamics show what changes can be expected in the short run, such as during a recovery
period, whereas asymptotic dynamics of a population show how the population can be
expected to change in the long run.
A representative sample of individuals is necessary for characterizing the age or size
structure of field population. Many species of fish can be accurately aged by counting
annual increments formed in scales, otoliths, or other hard body parts. Such increments
are discernable because of seasonal differences in growth rates. Alternatively to direct
aging procedures, a length-frequency analysis can be performed to assign ages to length
modes. Determining the age of bird or mammal species is more problematic, and usually
requires marking individuals at birth (i.e., a known age) and following them over time.
However, most species can be easily grouped into stages such as juvenile, sub-adult, and
adult stages based on size or other physical characteristics.
5.4 Measuring Population Persistence
Population persistence attributes provide information on the viability of a population, or
the likelihood that a population will persist through some period of time. There are a
number of different persistence attributes (see Section 3), not all of which are easily
estimated for wild populations. However, population viability analysis (PVA) is the
method for estimating the probability that a population of a certain size will persist for a
certain length of time (see Lacy, 1993, 1994). White (2000) describes the data
requirements and techniques for PVAs. These include construction of a realistic
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population model (such as the matrix population model described in Section 4) that
includes fertility and survival components that contribute to population dynamics over
time. Techniques for estimating these parameters are described above. The model should
also include a regulation mechanism, such as density dependence, because persistence
will be overestimated for populations allowed to grow indefinitely. Realistic descriptions
of regulating mechanisms, and accurate field data to parameterize them, are usually
difficult to obtain.
A PVA should also include information about demographic and temporal variation.
Demographic variation is important to consider for small populations. When survival and
births between time steps are treated as random events, then the number of individuals
moving from one stage to the next or entering the population via birth is a random
number. Consider a population with an individual survival rate of 0.5. About 50% of the
individuals in the population will survive to the next time step on average, but
randomness inherent in applying a probability to a finite number of individuals in a
population may preclude exactly 50% surviving. Variation in the number surviving can
be quite large for small populations, and a series of time steps in which less than 50%
actually survive can lead to extinction in small populations versus large populations.
Temporal variation occurs when fertility and survival are random variables that can
change over time in response to environmental condition (White, 2000). For example,
years with harsh weather conditions can result in lower fertility and survival rates
compared to years with mild weather conditions. It can be difficult to obtain field
estimates of temporal variance in demographic parameters; long-term studies are typically
necessary. However, it is acceptable to borrow information from other studies as they
relate to the assessment population, or even from a related species for which long-term
data are available. Data from other studies may be used to construct rules relating
temporal variance in a population parameter to an environmental variable. Note that it is
acceptable to borrow information on the temporal and spatial variance of demographic
parameters but not the parameters themselves. Fertility and survival rate estimates from
stable or increasing populations are inappropriate for use in models for declining
populations.
If a population has a wide geographic distribution (as in Cases 2 and 3 described in
Section 2), then the inclusion of spatial variation in the PVA may be necessary (White,
2000). Spatial variation in fertility and survival rates can occur if there is spatial variation
in the quality of habitat across a landscape. If movement rates are high, then local
populations can become depleted as a result of emigration or replenished as a result of
immigration (Stacy and Taper, 1992). High movement rates may therefore result in high
persistence. The failure to include such variation in a PVA may result in an
underestimate of population persistence.
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Individual heterogeneity or variation in fertility or survival rates may also be included in
PVAs. This type of variation is typically the most difficult to estimate, especially
individual heterogeneity in survival rates. Individual heterogeneity can be quantified
using live recapture data that includes individual covariates, such as some measure of
body condition associated with each marked individual. Rules can then be constructed
relating individual variation in a population parameter to some characteristic of the
individual. With appropriate caveats, estimates of individual heterogeneity may be
borrowed from other studies or related species. If individual heterogeneity is not included
in a PVA then viability may be underestimated.
The major obstacle to PVA is obtaining the data to drive the model (Ruggiero et al.,
1994; White, 2000). Population persistence is a stochastic phenomenon (White, 2000),
requiring complex models that include demographic, temporal, spatial, or individual
variation. A lack of data may suggest that a simpler model should be used, but White
(2000) notes that a lack of data means a lack of information - no valid estimate of
population persistence is possible without adequate information and there is no reason to
believe that an unstudied field population (i.e., lack of information) is any simpler
compared to well-studied populations. The predictive accuracy of several PVA
approaches as used in conservation biology is evaluated by Brook et al. (2000).
5.5 Considering Scalar Issues
As acknowledged earlier, an issue central to assessment of site-specific risks to
populations is the scale or scales at which a population should be evaluated. There is no
single natural scale for ecological studies (Levin, 1992). We may investigate the
characteristics of what can be termed an assessment population (Text Box 1), but an
assessment population is a dynamic concept that needs to be defined in each application.
The question then is what spatial and temporal scales define an assessment population.
Although relevant both to modeling and field-based assessments, the material below
considers scalar issues from the field-based perspective.
The spatial scale at which an assessment population is investigated can be defined based
on biological characteristics of the species and the physical characteristics of the
landscape in which the assessment population occurs. Some populations may be
physically isolated, such as fish in a pond. Some populations may be connected to other
populations in a homogenous or fragmented landscape, such as song birds using forest
habitat. Quantifying the connectedness of populations over a broad spatial scale is
particularly important for estimating population persistence. If immigration and
emigration are negligible, then spatial variation in the landscape or habitat may divide a
population into smaller subpopulations, which may be more vulnerable to local
demographic extinction.
The temporal scale at which an assessment population is investigated is important
because different species have different life histories. Sampling design with regard to
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temporal scale concerns the time increment between samples and the length of the study
(or number of time increments sampled). The time increment between samples or
observations of a population should not be so great such that important dynamics are
unobserved. Time increments should certainly not be longer than the reproductive cycle
of a species but may be shorter if survival is related to ontogenetic changes in an
individual. The length of an assessment may be limited because of decision-making
requirements. However, longevities and the reproductive strategy of the assessment
population should be taken into consideration when interpreting study results and in
making a decision to borrow information from other long-term investigates. For a short-
lived species, multiple generations may be observed in an assessment; for long-lived
species, only a fraction of a generation may be observed. Population-level effects on
long-lived species may therefore be more difficult to detect in assessments of insufficient
duration. Population models may be particularly useful for projecting long-term
responses of long-lived species to stressors.
The field methods described earlier for estimating population attributes and demographic
parameters, such as abundance, fertility, and survival, can be used at most any scale
provided sufficient sampling effort is expended. These methods may also be used at
smaller scales and the results extrapolated over larger scales. For example, abundance
may be estimated in a random selection of small patches of habitat and extrapolated to
areas not sampled (Mitro and Zale, 2000a). Relations between fertility and size or age
may be used to estimate fertility for a population.
5.6 Considering Uncertainty in Field Measurements
The identification and quantification of uncertainty is critical to risk assessment. As
described throughout this section, uncertainty in the estimation of population attributes
and demographic parameters can arise from a number of sources. Variability is also a
characteristic of populations themselves, which respond stochastically to demographics
and environmental conditions. Variability in population attributes cannot be reduced, but
can be estimated. Ignorance in parameter estimates often can be estimated and reduced
by increasing sampling effort and therefore the information available to describe those
parameters.
The methods described earlier for quantifying population attributes and demographic
parameters such as abundance and survival are firmly grounded in statistical theory;
estimation of uncertainty in parameter estimates (also called sampling variance) is
therefore a straight-forward task. The computer programs CAPTURE, MARK, POPAN,
and DISTANCE include estimation of parameter uncertainty. Program MARK also
includes a model averaging capability that quantifies a measure of uncertainty in model
selection, which results in unconditional parameter estimates (i.e., parameter estimates
that are not conditional on one particular model).
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If parameter estimates are extrapolated over larger scales, then additional sources of
uncertainty have to be considered in addition to the uncertainty in the parameter
estimates. A total estimate of uncertainty should include the variation within each
parameter estimate, the variation among parameter estimates, and an extrapolation error
term for making predictions for areas not sampled (Mitro and Zale, 2000a, 2002).
Estimating the uncertainty or stochasticity of the dynamics of a population requires a time
series of estimates for the parameter of interest. If such data are not available for the
assessment population, an estimate of variance can be borrowed from another study of the
species or from investigations of related species. Estimation of temporal or spatial
variation (also called process variation) requires removing the sampling variance from the
series of parameter estimates. Burnham et al. (1987) and White (2000) describe a
procedure for removing sampling variance from a series of estimates to estimate the
underlying process variation.
The uncertainty of parameter estimates can also be incorporated into estimates of
population attributes such as persistence (White, 2000). Models to estimate persistence
have multiple parameters, each with an associated variance; nonzero covariances may
also be present for parameters estimated from the same data (e.g., age-specific survival
rates). The variance of a function of parameters can be estimated using the delta method
or the parametric bootstrap (Efron and Tibshirani, 1993; White, 2000).
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6. Outstanding Research Issues for Superfund and RCRA
In a general sense, the concepts, theories, and methods of population ecology are
sufficiently developed to conduct many kinds of site-specific risk assessment. Despite
this, key uncertainties remain with respect to population-level risk assessment at
Superfund and RCRA sites. Many of these uncertainties have been captured as research
needs identified and communicated by the Superfund program in December 2000.
Similar research needs have been identified through interactions with other Agency
offices and programs. These can be summarized as:
Develop predictive population models to support site-specific risk assessment for
particular species
Develop methods that allow extrapolation of effects on individuals, as measured
in toxicity tests, to populations
Develop methods that support cross-species extrapolations of effect
Develop methods and models to estimate effects on populations from exposure to
multiple stressors
Develop methods and models that support diagnosis of causes of adverse effects
on populations, and that can be used to understand the relative risks of multiple
stressors
Develop approaches to incorporate spatial and temporal variability in stressor
concentrations and distribution in assessment of risks to populations, and to
delimit the spatial scales at which such assessments should be performed
Develop and describe approaches for defining ecological significance, both of
effects on populations and of indicators of those effects measured at lower levels
of biological organization.
In response to many of these research needs, ORD has developed a draft strategic plan to
guide its population-level risk assessment research. The goal of NHEERL's Wildlife
Research Strategy (U.S. EPA, 2004) is to develop scientifically valid approaches for
assessing risks to wildlife and other populations from multiple stressors. Through a
series of EPA's Science Advisory Board reviews and consultations, other EPA peer-
reviews, and discussions with Program Offices that reflect the needs listed above, four
key areas of research have been identified where advances in the science would be
instrumental in improving population-level risk assessment techniques and criteria
methodology. These areas include:
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1. Extrapolation research that improves the basis for predicting toxicological responses
among wildlife and other species and exposure scenarios of concern
2. Coordinated population biology and toxicology research to improve predictions of
population dynamics in spatially-explicit habitats
3. Research to advance techniques for assessing the relative risk of chemical and non-
chemical stressors on wildlife and other populations
4. Research to define appropriate geographical regions/spatial scales for population-level
risk assessments.
Reflecting a conceptual approach to population-level risk assessment that combines
aspects of toxicology, population biology, and landscape ecology, the NHEERL strategy
is focused on three major research objectives:
1. Develop mechanistically-based approaches for extrapolating toxicological data across
species, media, and individual-level response endpoints
2. Develop approaches for predicting population-level responses to stressors. Identify
the responses at the individual level that have the greatest influence on population-
level responses
3. Develop approaches for evaluating the relative risks from chemical and non-chemical
stressors on spatially structured populations across large areas or regions.
The activities communicated in the NHEERL draft research strategy to meet these
objectives are designed to produce methods, models, and findings that will provide
scientifically-credible approaches to EPA Program and Regional Offices, and States and
Tribes for conducting population-level risk assessments and to develop associated
criteria.
In addition to ORD's efforts, the need for improved methods for population-level risk
assessment has been acknowledged by the broader scientific community. SETAC has
taken a lead role in facilitating advancement of the underlying science by organizing an
international workshop (Barnthouse et al., in review) to explore the management context
and goals for protecting populations, key scientific issues relevant to describing
population response to environmental stressors, and the empirical and modeling
approaches that can be used to characterize population-level effects. It also developed
broad guidance for conducting population-level risk assessment in the context of the
Agency's ecological risk assessment guidelines. Working through its Ecological Risk
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Assessment Advisory Group, SETAC continues to pursue related projects, including
collation of examples of population-level risks assessments conducted at hazardous waste
sites. Updates on these projects can be found at
http://www.setac.org/eraag/era_pop_index.htm.
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APPENDIX
ECOLOGICAL RISK ASSESSMENT SUPPORT CENTER REQUEST FORM
Request #0006: How do we make the connection between individual measurements and population
effects; what do we measure?
Requestor: Clarence A. Callahan, Region 9
Problem Statement: How do we make the connection between individual measurements and population
effects; what do we measure? For example, if we measure mortality, what can we say about the ultimate
effect on the population? What can we say about the effect on a population of amphipods if we perform a
laboratory test using amphipods and measure mortality? How do we make the connection between mortality
on the individual and an impact on the population? Can this relationship be shown in both theory and
practice? Of course, the question relates to invertebrates (tending to R-strategy), other animals (tending to K-
strategy) as well as plants.
Background: For several years the general assumption was that toxicity endpoints, even acute effects, e.g.
mortality, were representative of population effects. This is especially true for invertebrate receptors and
assumed for receptors in general. Over the last 10 to 15 years, there seems to have been a leap of faith that
what is true about invertebrates is also true with larger animals. The relationship between measurements at
the individual level and effects at the population level is not generally provided in any ERAs that I have read.
There is generally a statement that "population effects will be addressed" and then a presentation of acute and
sometime chronic testing in single species laboratory tests. In other words, toxicity measures using single
species tests are assumed to be indicative of population effects although the measurement was mortality of
individuals in a laboratory test. This was assumed to be true even when the laboratory test species was not
the same or sometimes even close to the receptor population assumed to be "represented" in the assessment.
If we truly are assessing population level effects, how do we make the connection between individual
measurements and population effects? If we measure mortality, what can we say about the ultimate effect
on the population? What exactly will be the effect on a population of amphipods if we perform a laboratory
test using amphipods and measure mortality? How do we make the connection between mortality on the
individual and the impact on the population? This, I believe has to be shown in both theory and practice if
we continue to maintain this position.
For larger animals, I don't believe that we are capable of doing justice to anything called an ecological risk
assessment at a population level. Then what do we do for sites where larger animals are potentially
impacted? What kinds of studies do we perform? Do we measure individual effects and make that work
somehow, or do we continue to assume that these individual measures relate to population effects?
Expected Outcome: Some text to explain the connection between laboratory testing and field results.
Further explanations about the relationship between the measurement of mortality and the impact to
populations. A list of measurements for laboratory tests that can be related to population effects.
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