EPA/600/R-11/023
ERASC-016 F
February 2011
ASSESSMENT OF METHODS FOR ESTIMATING RISK TO BIRDS FROM
INGESTION OF CONTAMINATED GRIT PARTICLES
by
Richard Bennett, Dale Hoff and Matthew Etterson
U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research Laboratory
Mid-continent Ecology Division
Duluth. MN
Ecological Risk Assessment Support Center
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH
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NOTICE
This document has been subjected to the Agency's peer and administrative review and
has been approved for publication as an EPA document. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.
Preferred Citation:
Bennett, R, D. Hoff and M. Etterson. 2011. Assessment of Methods for Estimating Risk to Birds from Ingestion of
Contaminated Grit Particles. U.S. Environmental Protection Agency, Ecological Risk Assessment Support Center,
Cincinnati, OH. EPA/600/R-11/023.
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TABLE OF CONTENTS
Page
LIST OF TABLES v
LIST OF FIGURES vi
AUTHORS, CONTRIBUTORS AND REVIEWERS vii
INTRODUCTION 1
SOIL AND GRIT INGESTION BY BIRDS: WHO, WHY AND HOW MUCH? 1
ESTIMATING RISKS FROM SOIL AND GRIT INGESTION BY BIRDS 3
EPPO scheme 3
Luttik and de Snoo (2004) 6
Peddicord and LaKind (2000) 7
REVISED MODEL FOR ESTIMATING PROBABILITY OF INGESTING LEAD
PARTICLES OR PESTICIDE GRANULES 9
THE IMPORTANCE OF ESTIMATES OF GRIT RETENTION TIME 11
Use of grit retention time in estimating grit ingestion rates 12
Use of grit retention time to estimate internal dose 15
Summary on the use of grit retention time 18
SPECIES PRIORITIZATION IN ASSESSING RISK TO BIRDS FROM
CONTAMINATED PARTICLES 19
Dietary class 20
Size of particles 20
Number of particles 21
Qualitative considerations across species prioritization categories 22
USING GIONFRIDDO AND BEST (1996) DATA SET TO PARAMETERIZE MODEL 22
Estimating mean number of particles ingested per day 22
AN APPROACH FOR ESTIMATING RISK OF MORTALITY FROM INGESTING
LEAD PARTICLES 24
RANGE OF PARTICLE SIZES: IMPLICATIONS TO RISK ASSESSMENTS 27
CONCLUSIONS 28
REFERENCES 29
in
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TABLE OF CONTENTS cont.
Page
APPENDIX A. EXAMPLE SPREADSHEET CALCULATIONS USING THE
REVISED MODEL FOR ESTIMATING PROBABILITY OF INGESTING LEAD
PARTICLES 46
APPENDIX B. GRIT RETENTION TIME EXPRESSED AS AN EXPONENTIAL
FUNCTION 49
APPENDIX C. DESCRIPTION OF THE SIMULATION MODEL Pr (nd + l \ nd) 54
IV
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LIST OF TABLES
No. Title Page
1. Studies of Avian Grit Retention in Gizzards with Estimates of Mean and Median
Retention Times 32
2. Data Summary Table of Dietary Classes, Mean Particle Counts, Mean Particle
Size, and Body Masses of Avian Species Sampled for Gizzard Analyses in
Gionfriddo and Best (1996) 33
3. Data Summary Table of Dietary Classes, Percent Occurrence of Grit, and Mean
Grit Particle Counts by Size Class of Avian Species Sampled for Gizzard
Analyses by Luttik and de Snoo (2004) 35
4. Mean (± Standard Deviation) of Percent Occurrence of Grit and Number of Grit
Particles Found in Gizzards at Necropsy by Dietary Class from Gionfriddo and
Best (1996) and Luttik and de Snoo (2004) 37
5. 95% Upper Confidence Limit of the Mean Estimates for Number of Particles
Found in the Gizzards of Avian Species 38
6. Input Parameters for Simulation Model 39
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LIST OF FIGURES
No. Title Page
1. Illustration of the Mean and Median Particle Retention Times Based on Two
Exponential Functions with Rate Parameters of 0.693 and 0.25 40
2. Comparison of the Proportion of Particles Retained in Mallard Gizzards Over
Time as Observed for Calcareous Grit, Quartzite Grit, and Doses of Five No. 6
Lead Shot in Surviving Birds Without Signs of Lead Poisoning and in Birds that
Died 41
3. Relationship Between Mean Grit Size and Mean Body Mass 42
4. Distribution of Mean Size of Grit Particles Found in the Gizzards of Avian
Species from Gionfriddo and Best (1996) 43
5. Relationship Between Mean Number of Grit Particles Found in the Gizzards of
Avian Species and Their Body Mass 44
6. Distribution of Mean Number of Grit Particles Found in the Gizzards of Avian
Species 44
7. Sample Model Output for Northern Bobwhite Using Parameters in Table 6 45
8. Sample Model Output for Brown-headed Cowbird Using Parameters in Table 6 45
VI
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AUTHORS, CONTRIBUTORS AND REVIEWERS
AUTHORS
Richard Bennett, Dale Hoff and Matthew Etterson
U.S. Environmental Protection Agency
Office of Research and Development
National Health and Environmental Effects Research Laboratory
Mid-continent Ecology Division
Duluth, MN
CONTRIBUTORS
Sharon Thorns
U.S. Environmental Protection Agency
Region 4
Atlanta, GA
REVIEWERS
Sherry K. Krest
U.S. Fish and Wildlife Service
Annapolis, MD
Robert Luttik
National Institute for Public Health and the Environment (RIVM)
Bilthoven, The Netherlands
Richard K. Peddicord
Dick Peddicord & Company, Inc.
Heathsville, VA
ACKNOWLEDGMENTS
The first draft of this document was internally (within EPA) reviewed by Christopher
Salice (EPA Office of Prevention, Pesticides and Toxic Substances) and Jill Awkerman (Office
of Research and Development [ORD]/National Health and Environmental Effects Research
Laboratory. Programmatic review was conducted by Katie Matta of EPA Region 3, a Trichair of
EPA's Ecological Risk Assessment Forum.
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INTRODUCTION
In June 2006, the Ecological Risk Assessment Forum (ERAF) submitted a request to
ORD's Ecological Risk Assessment Support Center (ERASC) to evaluate the effectiveness and
utility of the European Plant Protection Organization (EPPO) Risk Assessment Scheme for Plant
Protection Products (i.e., pesticides) for its ability to estimate the degree of exposure to songbirds
from contaminants in soil. Specifically, are methods and information used for understanding
avian exposure to pesticide granules useful for estimating the probability of ingesting other
contaminated particles such as lead shot or fragments?
An important route of chemical exposure in many ecological risk assessments is the
ingestion of chemicals on or in sediments, soil and small gravel (i.e., grit). Several approaches
have been developed to address this route of exposure in risk assessments. The particular focus
for this white paper is to evaluate approaches available for estimating the risk to birds from
ingestion of lead shot or other lead fragments (hereafter referred to as lead particles). There are
many similarities between lead particle ingestion and the ingestion of pesticide granules as grit or
food items. More specifically, the paper focuses on two primary issues affecting avian exposure
to lead—the rate of ingestion of lead particles by birds and the length of time lead particles are
retained and eroded in avian gizzards to release a dose of lead to target organs. In this white
paper, we briefly discuss soil and grit ingestion by birds, review several published approaches for
estimating the rate of ingestion of lead particles or pesticide granules, and examine the important
sources of uncertainty in parameter estimates for approaches to estimating exposure to lead
particles. We recommend an approach for improving the estimation of lead particle exposure to
birds in ecological risk assessments. This paper does not comprehensively review the toxicity of
lead in birds, but does demonstrate an approach for estimating the risk of mortality from
ingesting lead particles.
SOIL AND GRIT INGESTION BY BIRDS: WHO, WHY AND HOW MUCH?
Many bird species ingest soil, sediment and small gravel while feeding—either
inadvertently (e.g., sandpipers probing for invertebrates on mudflats or woodcock ingesting
earthworms) or intentionally (e.g., as a source for minerals, to reduce gastric disturbances or gut
acidity, or as grit for aiding digestion) (Beyer et al., 1994; Beyer and Fries, 2002; Gionfriddo and
Best, 1999). The amount of soil and sediment ingestion can vary greatly among species and for
some species can represent several percent of the total daily food ingestion rate (Beyer et al.,
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1994; Beyer and Fries, 2002). The deliberate ingestion of small gravel and soil particles for use
as grit also varies considerably among species depending on their diet composition and feeding
behaviors. In some cases, hard seeds or pieces of insect exoskeletons serve as grit (Gionfriddo
and Best, 1999). In addition to variation in the amount of grit ingested each day, species vary in
their preferences based on grit size, shape, surface texture and color (Best and Fischer, 1992;
Best and Gionfriddo, 1991, 1994; Gionfriddo and Best, 1996, 1999). For each species, grit
selection also varies among individuals based on seasonal diet composition, age and nutritional
and reproductive status (Gionfriddo and Best, 1999). Consequently, soil and grit ingestion rates
are a function of many interacting factors.
It is very difficult to measure soil and grit ingestion rates directly in wild birds. However,
soil and grit ingestion rates can be estimated from other available measurements. The most
common published measurement of grit consumption by wild birds is a count of number of
soil/grit particles in gizzards at the time of necropsy, often categorized by particle size (Best and
Gionfriddo, 1991; Gionfriddo and Best, 1996; Luttik and de Snoo, 2004). Sometimes the
amount of soil/grit in the gizzard is expressed as a measured mass or volume, rather than as a
count of particles (Gionfriddo and Best, 1999). Another method of estimating the percentage of
soil in the diet is calculating it as a function of the concentration of acid-insoluble ash in scat
samples (Beyer et al., 1994; Beyer and Fries, 2002).
The amount of soil and grit in gizzard samples reflects a sample at one point in time, and
the amount at any point in time is a function of the soil/grit ingestion rate and the amount of time
soil/grit particles of different sizes are retained in the gizzard before being passed to the
intestines. The two processes of soil/grit ingestion and retention in the gizzard are not
independent. For grit particles in particular, several studies have shown that these two processes
interact somehow to maintain a certain amount of grit in the gizzard, presumably in an attempt to
maximize digestion efficiency (Best and Stafford, 2002). This is observed in controlled
laboratory studies where, as the amount of grit ingested increases, so does the amount eliminated
from the gizzard (i.e., retention time decreases). Conversely, if the amount of grit ingested is
restricted, birds can retain grit in the gizzard for extended periods. Gionfriddo and Best (1999)
present examples of extended grit retention times (up to 1 year) during periods of reduced grit
availability. The exact mechanisms of grit retention in the gizzard are unknown, but several
studies have made consistent observations about the relationship between ingestion rates and grit
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retention times (Gionfriddo and Best, 1999). However, rather than a constant turnover of grit
particle out of the gizzard, Trost (1981) observed in mallards (Anas platyrhynchos) that the
majority of grit particles were contained in only 5% of the fecal pellets, indicating that the
gizzards may periodically evacuate their contents. The high variability in gizzard grit counts
among individuals within a species observed by Gionfriddo and Best (1996) may also indicate
that the relationship between ingestion rates and grit retention times is quite dynamic.
ESTIMATING RISKS FROM SOIL AND GRIT INGESTION BY BIRDS
Because of the intentional and unintentional ingestion of soil and small gravel particles,
there is a risk of exposure to toxic chemicals, such as when ingesting soils containing chemical
residues or mistakenly selecting pesticide granules or lead shot as grit or food (Gionfriddo and
Best, 1999; Beyer and Fries, 2002). Several procedures have been developed to estimate the risk
of chemical ingestion via these nonfood routes of exposure and will be discussed in this section.
There are many similarities in the procedures developed to estimate the risk of ingesting
particles, such as pesticide granules or lead shot, but there are also differences in how
information (e.g., grit retention time) is used. Pesticide granules pose an acute toxicity risk, so
the emphasis is on estimating the probability or possibility that enough granules could be
consumed in a short period of time (i.e., one day) to be acutely lethal. For pesticides, grit
retention time is only used in combination with gizzard count data to estimate the daily grit
ingestion rate. Ingested lead shot or lead fragments, on the other hand, need to be eroded in the
gizzard over a period of days or weeks to be toxic, so estimates of retention time are used not
only in estimating particle ingestion rates, but also in assessing whether or not they will be
retained long enough to pose a risk of toxicity.
EPPO scheme
For pesticides the Environmental Risk Assessment Scheme for Plant Protection Products.
Chapter 11: Terrestrial Vertebrates, published by the European and Mediterranean Plant
Protection Organization (EPPO, 2003), provides a simple procedure for categorizing the risk to
birds and mammals from ingestion of pesticides as granules, seed treatments and sprayed
products. This scheme considers the ingestion of pesticide granules consumed accidentally as
part of soil ingestion and intentionally as part of grit selection. The risk from various pathways
of exposure is calculated using simple risk quotients based on an estimated exposure (i.e., the
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daily dose expected as a function of application rate, soil or grit ingestion rates, etc.) divided by a
toxicity value.
For granules ingested accidentally as soil, the EPPO scheme estimates risk based on the
overall pesticide concentration in soil contributed by the presence of granules. The daily dry soil
dose (DDSD) is calculated (using a look-up table) as a daily dose based on the pesticide
concentration in soil as a function of application rate and the estimated percentage of the diet
consisting of soil. The DDSD is divided by a toxicity value (e.g., LD50 for short-term risk or
lowest no-observed-effect dose [NOED] from a chronic reproduction test for long-term risk) to
calculate an exposure-toxicity ratio (ETR). The magnitude of the ETR is used to categorize the
risk as high, low, or uncertain.
For granules ingested intentionally as grit, the daily granule dose (.DGD) is calculated as:
DGD (mg/kg body wt./d) = DGI x [G„rface/(SPmrface + Gmrface)] x Gloading (Eq. 1)
where:
DGI = daily grit ingestion rate,
Gsurface = number of pesticide granules at surface per unit area,
SPsurface = number of granule-sized soil particles at surface per unit area, and
Ghading = the amount of active ingredient in one granule.
The procedure estimates exposure (i.e., DGD) under reasonable worst-case and most
likely case scenarios. A key assumption in this model is that each pesticide granule and natural
grit particle has an equal probability of being selected and ingested (i.e., there is neither
preference for, nor avoidance of, lead particles). The DGD is divided by a toxicity value (e.g.,
LD50 for short-term risk or lowest NOED from a chronic reproduction test for long-term risk) to
calculate an ETR which also is used to categorize risk.
The risk quotient approach provides a means for classifying the risk of ingesting a toxic
dose from pesticide granules ingested as grit. The risk classification is intended to be protective
of all species. Because of the use of conservative assumptions, it is not intended for use in
estimating the probability of ingesting a specific number of granules, although it is possible to
obtain crude estimates. Removing the Grading term from the equation above provides a simple
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estimate of the overall mean number of pesticide granules ingested each day based on the daily
grit ingestion rate multiplied by the proportion of granule-sized particles that are pesticide
granules. To accomplish this, the EPPO scheme estimates the daily grit ingestion rate (DGI)
using estimates of the number of grit particles in gizzards of necropsied birds (geometric means
of predominantly granivorous species or 90th percentile of distribution of species) multiplied by a
conversion factor. A conversion factor of 4.2 was used and represented the inverse of the grit
turnover rate (expressed in days), also known as grit retention time, from a study with house
sparrows {Passer domesticus) fed diets containing various concentrations of grit particles
(Fischer and Best, 1995). Their estimated grit retention time of 0.24 days represents one of the
shortest reported retention times in the literature and possibly reflects the conditions of this
specific experiment. Silica granules were mixed into a canned dog food (i.e., much softer than
usual sparrow diet) at concentrations that would average from 4 to 64 granules per bird per day.
Birds were necropsied over an 8-day period to determine the number of grit particles in the
gizzard at death in relationship to estimated daily grit consumption. The cautions presented on
the representativeness of this conversion factor are the same as presented in Stafford and Best
(1999).
Best and Stafford (2002) expanded on the work of Fisher and Best (1995) by more
precisely delivering specific doses of grit particles to both house sparrows and bobwhite (Colinus
virginianus) fed either the same soft dog food diet or a grain diet. They concluded that the initial
study in Fischer and Best (1995) "may not have accurately represented the relationship between
grit consumption and grit retention" and stated that both species "eliminated large amounts of
grit at the higher dose levels but retained most of the grit at lower levels, which suggests that
birds need a certain amount of grit in their gizzard, perhaps to maximize efficiency of digestion."
Hence, the EPPO scheme uses a very short estimate of retention time which increases the
estimated daily grit ingestion rate. The estimate of retention time in the paper by Fischer and
Best (1995) is considerably shorter than information from other studies and reviews and results
in a relatively conservative risk index for use in pesticide screening assessments.
When the chemical of concern may be ingested accidentally with soil as well as ingested
intentionally as grit particles, these two routes of exposure may be independent and thus additive
in terms of estimating a total exposure dose. However, birds may ingest a wide range of particle
sizes from very fine soil particles to larger grit particles that may be 1 or more mm in size. It is
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very difficult to separate accidental soil ingestion from intentional grit ingestion when there is
overlap in the particle size ranges. In assessments of gizzard contents, Best and Gionfriddo
(1991) and Luttik and de Snoo (2004) considered only particles >0.1 mm and >0.5 mm,
respectively, as possible grit particles in their counts. However, in estimating percent soil
ingestion, Beyer et al. (1994) used a method for calculating acid-insoluble ash content in feces
that does not discriminate soil particle sizes. Consequently, estimates of percentage of soil in the
diet may overlap somewhat with estimates of grit ingestion rates due to the differences in the
methods used. Avian risk assessments of lead exposure will need to consider these two possible
routes of exposure (i.e., accidental soil ingestion and intentional grit ingestion) in light of
site-specific information on the nature of lead availability. In other words, is the lead available
primarily as dissolved lead in soil, lead shot or fragments, or a combination?
Luttik and de Snoo (2004)
As mentioned above, the EPPO scheme can be modified to produce a simple estimate of
the overall mean number of pesticide granules ingested each day based on the daily grit ingestion
rate multiplied by the proportion of granule-sized particles that are pesticide granules. Luttik and
de Snoo (2004) present a model for estimating the probability of birds and mammals consuming
0, 1 or more pesticide granules per day while accidentally or intentionally ingesting soil particles.
The model uses a binomial distribution and calculates the probability of selecting N pesticide
granules based on a probability mass function. Estimates are required of the number of
granule-sized particles ingested each day by a species and the proportion of granule-sized soil
particles that consists of pesticide granules. As in the EPPO model, a key assumption is that
each pesticide granule and natural grit particle has an equal probability of being ingested. The
model can be simplified as follows to estimate the probability (Pr) of selecting a specific number
of pesticide granules in a day:
(Eq. 2)
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where
N = the number of pesticide granules ingested per day,
T = the total number of granule-sized particles ingested per day, and
P = the proportion of the total number of granules and granule-sized soil particles at
the surface that are pesticide granules.
[Note: The exclamation mark represents a factorial. Nfactorial, written as N\, equals the
product of all positive integers from 1 to N. For example, 31 = 1x2x3.]
Unlike the approach used in the EPPO scheme above, the method presented by Luttik and
de Snoo (2004) calculates the probability of ingesting N or more granules each day. Because the
focus of the Luttik and de Snoo (2004) approach is on the risk from acutely toxic pesticides in or
on granule products, the approach does not consider grit retention time.
Peddicord and LaKind (2000)
The Peddicord and LaKind (2000) model was specifically developed to estimate the
probability that birds at a recreational shooting range would ingest at least one lead shot/particle
during their lifetime. Their model could be viewed as a simpler version of the binomial model of
Luttik and de Snoo (2004), though there are three important differences in approach.
First, it estimates the proportion of grit-sized particles that consists of lead shot or
fragments, both on the shooting range itself and in off-site habitat used by each species, with an
estimate of fraction of foraging time spent on-site vs. off-site. Thus, it takes into account that an
animal's foraging area may encompass more than just the site of concern, whether that is a
shooting range or an agricultural field treated with pesticides.
Second, it purports to estimate the number of grit particles selected and retained in the
gizzard in a lifetime. It does this using the following equation:
N = Y(DJDp) (Eq.3)
where
N = number of grit particles selected and retained in the gizzard in a lifetime,
Y = number of years a bird lives,
De = number of days per year that a bird forages in the area, and
Dp = retention time for a shot in the gizzard (days).
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However, while the equation includes the life span in years and the number of days per
year at the site of concern, it does not incorporate information on the number of particles
ingested per day—only their retention time. By not including information on particle ingestion
rates, the model presented in Peddicord and LaKind (2000) does not accomplish its stated goal of
estimating the probability of a bird ingesting at least one lead particle in its lifetime.
Consequently, the model, as presented, severely underestimates the number of particles selected
and retained in the gizzard. The equation would accomplish its stated goal by adding a term for
the mean number of particles in gizzards at time of necropsy. As noted previously, gizzard
counts have been reported in the literature for many species. Dividing the mean number of
particles in the gizzard by particle retention time provides a simple estimate of the number of
particles ingested per day and results in the following modified equation:
N = Y x De x (G/Dp) (Eq. 4)
where
G = mean number of particles in gizzard at time of necropsy.
Third, the Peddicord and LaKind (2000) model does not estimate the probability of
ingesting exactly 1 or 2 or more lead particles, as in Luttik and de Snoo (2004). However, it
estimates the probability that none of the ingested particles in a lifetime is a lead particle, and
then estimates the probability of ingesting 1 or more lead particles as 1 minus the probability of
ingesting no particles [i.e., Pr (>1) = 1 -Pr (0)]. In this regard, using the same assumptions
about the rate of grit ingestion and the proportion of particles that are lead, the Peddicord and
LaKind (2000) and Luttik and de Snoo (2004) models calculate the same probability of ingesting
1 or more lead particles or pesticide granules.
If the Peddicord and LaKind (2000) model were modified, as in Eq. 4, to correctly
estimate the number of particles selected and retained in the gizzard over a specified time period,
there is another aspect of the model to consider in risk assessments. By attempting to estimate
the probability that birds would ingest at least one lead shot/particle during their lifetime, where
maximum life span is used (7), the model results in a conservative estimate of exposure for a
simple screening process. However, a risk manager may need more discreet time frames in
exposure estimates for developing risk mitigation strategies. By using the maximum life span,
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the model attempts to calculate the risk over a period of time that is far longer than the life span
of most individuals of the population. Consequently, the risk to most individuals is greatly
overstated. Risks from ingesting lead particles would be more meaningful in risk assessment if
expressed as a function of shorter time frames. For example, if the objective is to assess risks to
populations, presenting risks on an annualized basis would be more effective since other inputs
in a population model are typically expressed annually. In this case, that is easily accomplished
by dropping the Y parameter from Eq. 4 to estimate the number of particles selected and retained
in the gizzard per year. Shorter time frames also may be appropriate in meeting other
management objectives, and this is discussed further below.
REVISED MODEL FOR ESTIMATING PROBABILITY OF INGESTING LEAD
PARTICLES OR PESTICIDE GRANULES
We developed a revised model for estimating the probability of ingesting lead particles
that integrates some features of the Luttik and de Snoo (2004) and Peddicord and LaKind (2000)
models, while addressing some of the issues discussed as well. Most importantly, it provides a
means of estimating the probability of ingesting lead particles over any specified time frame.
While the following section focuses on the probability of ingesting lead particles, the model also
is useful for estimating the probability of ingesting pesticide granules when the same
assumptions are met. The model runs in Microsoft® Excel. The input parameter cells are those
with blue backgrounds. Other cells contain definitions or model calculations and should not be
changed. An example set of calculations from the spreadsheet model is included in Appendix A.
For each species, an estimate of the number of grit particles ingested each day is required.
This parameter is rarely measured directly. The most commonly available data on avian grit
ingestion are typically counts of grit particles in the gizzard at necropsy, which represents a
snapshot in time of grit usage. A very simple deterministic way to estimate overall grit ingestion
rates is shown below as Eq. 5:
. . , ... Mean # grit-sized particles/gizzard _
Grit particles ingested/day = (Eq. 5)
Mean grit retention time (days)
Information in the literature concerning grit retention time is highly variable, so it may be
appropriate to examine the responses under different estimated retention times.
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The model is set up to examine the probability of ingesting lead particles during an
exposure period that can range from 1 day (if interested in daily exposure probability) to the
maximum number of days each year on the site of concern. In cases where the assumed
retention time of individual lead particles may be too short to cause toxicity (or where more than
one lead particle may be needed to cause toxicity), the revised lead model could be used to
examine the probability of ingesting multiple lead particles over a specified exposure period.
The total number of grit particles ingested per exposure period is calculated by multiplying the
daily ingestion rate by the number of days selected. A rounding function is used to express the
total number of grit particles per exposure period (T) as a whole number.
As in the Peddicord and LaKind model, our revised model considers that the foraging
range of a species may include both the contaminated area of interest (i.e., on-site), as well as
surrounding uncontaminated or less contaminated habitat (i.e., off-site). Also, it uses the same
simple estimate of the proportion of foraging activity on-site. The proportion of grit-sized
particles from all foraging sites that is lead particles (P) is calculated as:
Like the models discussed previously, the revised model uses a simple estimate of the
proportion of available grit-sized particles consisting of lead particles (based on site-specific
information) and assumes that each lead particle and natural grit particle has an equal probability
of being ingested (i.e., there is neither preference for, nor avoidance of, lead particles). Best and
Gionfriddo (1991, 1994) reported that particle characteristics such as shape, texture and color
can affect avian preferences for various types of grit particles. We found no information
suggesting that avian species might prefer or avoid lead shot or lead fragments relative to other
grit types. The assumption of equal acceptance among particle types remains a source of
(Eq. 6)
where
Pon-site = proportion of grit-sized particles available on-site that is lead particles,
Poff-site = proportion of grit-sized particles available off-site that is lead particles, and
F = proportion of foraging activity on-site.
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uncertainty in all of these models estimating the probability of ingesting lead or pesticide
particles.
The model then calculates the probability (Pr) of ingesting N lead particles during an
exposure period. Probabilities are calculated for N = 0 through 8 particles using the same
probability mass function presented in Luttik and de Snoo (2004):
N = the number of lead particles ingested during exposure period,
T = the total number of grit-sized particles ingested during exposure period, and
P = the proportion of the total number of lead and grit-sized soil particles at the
surface that are lead particles.
Just as in Peddicord and LaKind (2000), the revised model calculates the probability of
ingesting one or more lead particles by essentially calculating 1 minus the probability that none
of the particles ingested is lead [i.e., Pr (>1) = 1 -Pr (0)].
THE IMPORTANCE OF ESTIMATES OF GRIT RETENTION TIME
The estimates used for grit retention time, whether based on assumptions or
measurements in published studies, have a great influence on the revised model estimates of the
probability of ingesting lead particles. Since T, the number of particles ingested in a specified
time period, is part of an exponent in the model, the model results are very sensitive to variations
in T. Also, the daily grit ingestion rate is inversely related to input parameter estimates for grit
retention time. Consequently, the estimates for grit retention time indirectly have considerable
influence on model outcomes of the probability of ingesting lead particles. The significance of
estimates of grit retention time is an artifact of not having direct measurements of grit ingestion
rates for wild birds.
Estimates for retention time also are very important in the assessment of the degree of
risk posed by lead particles to various species. The toxicity of lead particles is related to the
length of time the particles are retained and eroded in the gizzard. McConnell (1967) found that
(Eq. 7)
where
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lead shot retained in the gizzards of bobwhite quail or mourning doves (Zenaidura macroura)
were eroded to a small fraction of their original size within 2 to 3 weeks. Bellrose (1959) set a
20-day limit for waterfowl to void ingested lead particles or die. Consequently, under conditions
where grit is retained only briefly (e.g., less than a few days), the risks of lead poisoning may be
reduced, but these risks increase with increasing estimates of the retention time of lead particles
because more of the particle is eroded and taken up in the blood. In this case, estimates of
retention time have a direct bearing on estimates of the internal dose of lead from eroded
particles and the overall characterization of risk from lead poisoning.
These two issues related to retention time (i.e., estimating ingestion rates and internal
dose) are not independent and are discussed further in the following sections.
Use of grit retention time in estimating grit ingestion rates
As mentioned above, grit retention time is highly variable and depends on a number of
factors including the rate of grit ingestion, the characteristics of the diet, and the nature of the grit
particles themselves (see review by Gionfriddo and Best, 1999). Even within an individual bird,
when a group of identical grit particles is inserted into the gastrointestinal tract at one time, they
are not all retained for the same period of time and then voided. Initially particles are eliminated
very rapidly, but then the elimination of the remaining particles slows significantly (Fischer and
Best, 1995). For example, house sparrows voided 50% of particles in the first 24 hours, but 32%
of particles remained for more than 13 days. In red-winged blackbirds (Agelaius phoeniceus),
90% of particles were voided in the first 24 hours. In other experiments house sparrows with
unlimited access to quartz grit were switched from quartz to feldspar. Six hours after the switch,
sparrow gizzards contained 40% feldspar/60% quartz, and after 24 hours contained
88% feldspar/12% quartz (Gionfriddo and Best, 1995). However, several of the quartz particles
still remaining after 24 hours were retained for up to 30 days. Trost (1981) and King and
Bendell-Young (2000) reported a similar pattern in mallards and described the grit retention rates
as exponential functions. Consequently, while the models described above for estimating the
probability of ingesting particles use a point estimate for grit retention time, the fate of any
particular particle in the gizzard can be highly variable (e.g., voided almost immediately or
retained for days or weeks). In reviewing the literature for information on grit retention time it
also is important to determine if the authors have reported an estimate of the retention time for a
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group of particles as the median (i.e., time until 50% of particles are voided), mean, maximum
(i.e., time until all particles are voided), or some other type of expression of retention time.
Estimates of mean grit retention time are most appropriate for estimating grit ingestion rates, and
this is discussed further below.
As mentioned previously, one of the shortest grit retention times reported in the literature
is 0.24 days for house sparrows (Fischer and Best, 1995). Although this is expressed essentially
as a mean retention time, it is based on a study with a high rate of grit ingestion and an atypically
soft diet for the species. The results with sparrows and red-winged blackbirds presented by
Fischer and Best (1995) indicate that birds consuming soft diets may not need much, if any, grit
to aid digestion. Consequently, grit particles that are ingested by these birds are eliminated
rapidly from the gizzard. The relatively low particle counts in gizzards of insectivorous birds
(see Species Prioritization section below) may be a function of this short retention time as well as
a lesser incentive for ingesting grit in the first place.
At the other extreme, Gionfriddo and Best (1999) discuss that during periods of reduced
grit availability (e.g., snow cover during winter), birds have the ability to retain grit in their
gizzards for extended periods of time. Many of the examples discussed are used to illustrate that
it is possible for birds to maintain grit in the gizzard for digestion even when grit is limited in
availability, but these examples tell us little about more typical conditions when grit availability
is not a limiting factor. One of the longest examples (9 months) in Gionfriddo and Best (1999) is
based on a study by Robel and Bisset (1979) where bobwhite quail were maintained in
environmental chambers for 9 months without access to grit, but at necropsy birds still had some
of the original grit from an earlier housing arrangement retained in their gizzards. Most of these
examples are not a reflection of mean grit retention time, and several reflect experimental
manipulation of grit availability.
There are few actual estimates of median or mean grit retention time in birds. Mateo and
Guitart (2000) estimated the half-life (i.e., median retention time) for calcareous grit in mallards
as 1.4 days. They also used information from Trost (1981) to estimate the half-life for quartzite
grit as 3.1 days in mallards. Experiments with house sparrows dosed with quartz grit suggest a
median grit retention time of approximately 0.5 day (Gionfriddo and Best, 1995). Best and
Stafford (2002) found that on a more typical seed diet the grit retention time of sparrows and
bobwhite quail decreased as the number of silica grit particles in the gavage dose increased. For
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daily doses between 72 to 144 silica particles per day, sparrows and bobwhite on seed diets had
mean grit retention times of approximately 1 day. Lower doses resulted in mean retention times
of >1 day. The weight of grit consumed each day by rufous-collared sparrows (Zonotrichia
capensis) on a seed diet was approximately the same as the weight of grit in gizzards of
field-collected sparrows, suggesting a mean grit retention time of approximately 1 day
(Lopez-Calleja et al., 2000).
If we assume that the retention of ingested grit particles in avian gizzards can be modeled
as a negative exponential function, as reported in Trost (1981) and King and Bendell-Young
(2000), then observations from various studies of the proportion of grit particles remaining at
specific time periods can be used to estimate the mean and median grit retention times. As new
grit particles are ingested each day, some of the particles are passed through the gizzard
relatively rapidly while the rate of passage for the remainder of the particles slows considerably.
By describing the retention time as an exponential function, as illustrated in Figure 1, a rate
parameter (X) is calculated for each distribution that can be used to estimate the mean and
median retention time. Mean retention time equals 1/X, while the median equals ln(2)/A or
0.693IX. For a more thorough discussion of the mathematical relationships of exponential
functions and examples of their use, see Appendix B. For an example of how this may be
applied to reported observations, consider a study by Fischer and Best (1995) where wild house
sparrows were captured, dosed with 5 silica particles each, and released to the wild. These
sparrows were collected 1, 4, 7, 10 and 13 days postdosing to count the number of silica particles
retained in the gizzards. They observed that 50% of the silica particles were remaining after
24 hours. If the retention of these grit particles follows an exponential function, the rate
parameter (k) equals 0.693 days 1, resulting in a mean retention time of 1.44 days and a median
of 1 day. Additional estimates of mean and median particle retention times based on published
observations are presented in Table 1.
A critical aspect of this assumption is that each ingested particle has an equal probability
of being voided from the gizzard at any particular time. When ingested particles vary in their
physical characteristics (i.e., size, shape, texture), the gizzard may selectively retain certain
particles over others. Selective retention becomes an issue in studies of grit retention times
because investigators need to be able to identify the grit particles consumed (or dosed) at a
particular point in time from those particles consumed later. To do this, investigators may
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change the type of particle or some other particle characteristic (e.g., color) used so that they are
recognizable. In some cases, however, the recognizable characteristics of particles also can
affect their retention probability, and thus change the pattern of retention over time from that
estimated using an exponential function. For example, while the house sparrows dosed with
silica particles (Fischer and Best, 1995) voided 50% of silica particles in the first 24 hours,
sparrows collected on days 4, 7, 10 and 13 postdosing all retained about 1/3 of the dosed silica
particles (Figure 1). An exponential function with a rate parameter of 0.693 day 1 indicates that
virtually all the dosed particles would have been voided by 7 days postdosing. These study
results suggest that even if silica particle retention initially followed an exponential function, the
remaining silica particles were selectively retained by the gizzard over other naturally available
grit particles for an extended period. Fischer and Best (1995) similarly observed that while
dosed red-winged blackbirds voided 90% of silica particles in the first 24 hours, the remaining
10% was retained in the gizzard for up to 13 days (i.e., no additional loss of silica particles
observed after 24 hours). The extent to which gizzards are selective in retaining individual grit
particles and how it occurs are unclear (Gionfriddo and Best, 1999).
A consistent observation amongst researchers studying grit ingestion rates and grit
retention times is that these parameters are highly variable among birds and within a bird over
time due to a variety of factors discussed above. In general, when grit availability is not limited,
birds are routinely replenishing grit and mean grit retention times may range from less than 1 day
to several days, though this observation is based on limited studies with only a few species. As
mean grit retention times become shorter, daily grit ingestion rates increase, resulting in an
increased probability of ingesting a lead particle (or other type of toxic particle). However, as
retention times increase, even though the probability of ingesting a lead particle decreases, the
estimated internal dose from an ingested lead particle may increase.
Use of grit retention time to estimate internal dose
Once a lead particle is ingested, it must be eroded in the gizzard before the lead can be
taken up in the blood. As mentioned above, the complete erosion of a lead particle may take up
to several weeks in some species. If grit retention times are relatively short and an ingested lead
particle is voided within hours of ingestion, the risk may be small. However, even when the
median grit retention time is relatively short, some fraction of ingested particles has been
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observed to remain in the gizzard for many weeks (Gionfriddo and Best, 1995; Trost, 1981).
Consequently, even if all ingested particles have an equal probability of being retained, any
individual ingested lead particle has a small probability of being retained significantly longer
than the mean retention time. The probability that a particle is retained for a specified period of
time can be calculated using the exponential functions illustrated in Figure 1. If the mean grit
retention time is assumed to be 1.44 days (X = 0.693), each particle has a probability of 0.5 of
being retained each day and one can calculate the probability that a particular particle could be
retained for more than X days. For example, there is a 0.125 probability that a particle will be
retained 3 days (proportion of particles remaining at 3 days = 0.125) and a 0.0078 probability at
7 days. If the mean retention time is assumed to be 4 days (X = 0.25), the probability that a
particle would be retained for >3 or >7 days is 0.47 and 0.17, respectively. However, if gizzards
selectively retain lead particles longer than other types of natural grit particles, lead particles may
have an even greater probability of being retained long enough to pose a risk to birds, even if
mean grit retention times in general are relatively short. This section examines the literature on
retention time of lead particles in gizzards.
McConnell (1967) reported that bobwhite quail and mourning doves dosed with lead shot
expelled shot in their feces at regular intervals starting 3 days after dosing and continuing up to
22 days. In the shot excreted by bobwhite, there was no noticeable deterioration in the first
week, but by 10 days shot were eroded to 1/2 of their original size and to 1/6 original size by
day 22. In doves, shot excreted after 6 days were eroded to 1/2 their original size and to 1/6
original size after day 17.
Mourning doves dosed with 4 No. 8 lead shot had an average of 2.3 shot remaining in the
gizzard at necropsy 34 days later (Buerger et al., 1986). These doves were fed a diet of 95%
cracked corn, 5% commercial pigeon diet, and <1% oyster shell grit. Kendall et al. (1982)
developed a prediction equation to estimate the percent of lead shot remaining (i.e., not yet
eroded) in the gizzard of ringed turtle doves (Streptopelia risoria) overtime (i.e., percent of lead
shot remaining = 97.8 - 4.24 x time (days), R = 0.88). They observed that approximately 70%
of a 110 mg No. 6 lead shot was eroded in a dove's gizzard in 14 days.
Acutely dosed mallards and black ducks (Anas rubripes) voided or completely eroded all
ingested lead shot within 21 days after dosage (Chasko et al., 1984). Mortality was directly
related to the length of lead particle retention time, and lead retention times were highly variable
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among individuals receiving the same dose. Lead particle retention times were shortest for
asymptomatic birds, intermediate for birds showing signs of lead poisoning, and longest for birds
that eventually died (Chasko et al., 1984). During the experiment, ducks were fed a diet of
natural foods including seeds, aquatic plants, small fish and aquatic invertebrates, including
small snails, crabs and mussels. There is no mention of additional grit sources.
Vyas et al. (2001) reported considerably shorter lead shot retention times in
brown-headed cowbirds (Molothrus ater). Seven of 10 cowbirds on a predominantly seed diet
survived being dosed with a single No. IVz lead shot, with six birds excreting the shot within
24 hours and one within 48 hours. Three of 10 cowbirds died within 24 hours. All three birds
exhibited signs of lead poisoning and retained the dosed shot either in their gizzard or intestines.
As little as a single lead shot may also cause mortality in other avian species. Pain and
Barnett (1988) observed 60% mortality in black ducks dosed with a single No. 4 lead shot. All
birds died within 6 days and retained the dosed shot in their gizzard. No mortality was observed
in mallards dosed with a single No. 4 shot (Pain and Barnett, 1988). Four of 27 ring-necked
ducks (Aythya collaris) dosed with a single No. 4 lead shot died 14 to 21 days after dosing, with
peak blood lead levels observed one week after dosing. Mourning doves dosed with a single
No. 8 lead shot suffered 24% mortality over a 34-day period (Buerger et al., 1986), compared to
60% and 52% mortality in doves receiving two or four shot, respectively.
The trend observed in the above papers reporting on the retention of lead shot in avian
gizzards suggests that lead particles are typically retained for at least several days in many
species and as long as three weeks. It is very difficult to directly compare this information with
the information on mean and median grit retention times discussed in the previous section
because of the differences in experimental procedures and species tested. In most of the
literature on lead exposure there is no mention of access to alternative sources of grit.
Consequently, the retention of lead shots may or may not be extended in these studies due to lack
of access to other sources of grit. Conversely, hard grit particles have been shown to increase the
rate of lead shot erosion. Also, the rate of lead particle erosion is faster for individuals
consuming a hard diet (e.g., cereal grains) than a soft diet (e.g., varied plant and animal diet)
(Chasko et al., 1984).
Three studies with adult mallards can be combined to provide a comparison of the
retention times of lead versus more natural grit types—calcareous grit (Mateo and Guitart, 2000),
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quartzite grit (Trost, 1981) and lead shot (Chasko et al., 1984). Mateo and Guitart (2000) and
Trost (1981) quantitatively described the retention of grit particles as exponential functions with
mean retention times of 2.04 and 4.46 days, respectively (Figure 2). Chasko et al. (1984) dosed
mallards with five No. 6 lead shot. Of the six dosed mallards, four survived without signs of
toxicity while two died. The birds that died retained all the dosed shot for at least a week and
retained 60% of shot at death. The retention time of lead shot in asymptomatic birds was
somewhat longer than was observed with calcareous and quartzite grit, at least initially
(Figure 2). If we were to assume that retention of lead shot in the asymptomatic mallards
follows an exponential function, we could calculate the rate parameter for observations at day 3,
7, 10 and 14. If retention followed an exponential function the estimated X values at the four
observations would be approximately equal. However, the calculated rate parameters increased
over time (i.e., X = 0.10, 0.11, 0.16 and 0.21 at 3, 7, 10 and 14 days, respectively), indicating that
the exponential function was not an adequate description of the lead particle retention because
these X values suggest retention times were decreasing. One possible explanation is that as lead
shot are eroded and become smaller, their probability of being retained in the gizzard decreases.
This explanation needs to be tempered by the small sample sizes and the comparisons among
dissimilar studies. However, the consistent trend from this comparison and other studies cited
above is that lead shot may be retained in gizzards longer than other types of grit and that birds
that die of lead poisoning may retain lead shot longer than those that survive. Consequently,
assuming that the retention times for lead particles are equal to those of other grit particles may
lead to an underestimation of risk.
Sanderson and Irwin (1976; as cited in Trost [1981]) found that steel shot was retained
significantly longer than lead shot. While steel shot is retained longer than lead shot and natural
grit, it does not necessarily follow that grit and lead shot are retained at the same rate. The
difficulty in comparing the retention times of grit and lead shot relates to the toxic effects caused
by lead when sufficient lead shot are ingested to study retention quantitatively.
Summary on the use of grit retention time
While grit retention time is an important parameter for calculating the amount of grit
consumed daily and for estimating the risk to birds from ingestion of lead particles, there are few
studies that directly measure mean or median grit retention time. For purposes of using estimates
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of grit retention time to calculate grit ingestion rates in birds, a review of published literature
indicates that grit retention time can be relatively short (i.e., <1 day to a few days) when grit
availability is not limited and relatively long (e.g., up to a year) if grit availability is very limited.
The shorter the retention time, the higher the grit ingestion rate and, thus, the higher the
probability of ingesting a lead particle. However, once a lead particle is in the gizzard, the
literature indicates that in many species lead particles can be retained for days to weeks and can
be almost completely eroded in less than 3 weeks. Whether or not lead particles are
preferentially retained in gizzards over natural grit is difficult to determine. However, several
studies indicate that birds dosed with lead shot retained the shot in their gizzards long enough to
cause toxicity and death. Even if lead particles are not preferentially retained, the skewed
distribution of retention times for individual particles (i.e., Trost, 1981), described as a negative
exponential function, suggests that an individual lead particle may be voided very quickly or
could be retained long enough to cause toxicity, even if the median grit retention time is
relatively short.
SPECIES PRIORITIZATION IN ASSESSING RISK TO BIRDS FROM
CONTAMINATED PARTICLES
A key component of ecological risk assessment's (ERA) problem formulation is the
development of a conceptual site model (CSM) (U.S. EPA, 1997). In developing the CSM,
investigators identify pathways of exposure linking contaminated media to receptors representing
foraging guilds (e.g., insectivorous passerine) and then choose specific receptors of concern
(ROC) within each foraging guild in order to develop exposure models. When ingestion of
contaminated particles is a consideration within the CSM, it is important to note that the number
and size of grit particles will vary by species and foraging guild. This will influence the
probability of avian species ingesting contaminated particles. By comparing the foraging and
grit use habits of birds with the physical characteristics of the contaminated particles, it may be
possible to focus quantitative risk characterization on a fewer number of species to decrease
overall uncertainty in the assessment. Gionfriddo and Best (1996) examined the gizzards of
35 different species (with 5 or more gizzards per species) from the midwestern United States and
documented the frequency of occurrence of grit within each set of gizzards, the mean and median
number of particles (> 0.1 mm), and the particle size (Table 2). To illustrate the variation in grit
use frequency and number of particles, consider that within this data set, occurrence of grit
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ranged from 0 to 100% while mean grit counts per gizzard ranged from 0-281. Similarly, Luttik
and de Snoo (2004) presented the frequency of grit occurrence, mean number of grit particles,
and particle size for 27 avian species in The Netherlands (Table 3). Due to differences in the
methods used in these two studies it is difficult to merge the databases, but data from these
studies will be summarized to help investigators prioritize ROCs when considering the
importance of contaminated particles ingested as grit for representative receptors in the CSM.
Dietary class
Dietary class (or foraging guild) can have a significant influence on the occurrence and
numbers of grit found in the gizzards of bird species (Gionfriddo and Best, 1996). The most
common proposed function of grit within the gizzards of birds is for the mechanical grinding of
food (Gionfriddo and Best, 1999). Therefore, birds in avian trophic guilds consuming hard plant
(e.g., seeds) and animal material tend to have a higher frequency of grit usage relative to birds
that have a soft diet. Gionfriddo and Best (1996) found grit in nearly all of the gizzards (94%)
from six granivorous species, while Luttik and de Snoo observed grit in 100% of gizzards from
seven granivores (Table 2). Similarly, grit was observed in most of the gizzards collected from
omnivorous species in both studies, compared to only 40% in nine insectivorous species
(Gionfriddo and Best (1996). The nongranivore dietary class in Luttik and de Snoo (2004)
represents a diverse collection of species with the waterfowl species ingesting significantly more
grit particles than other species in the class. Gionfriddo and Best (1996) reported that the
number of grit particles was significantly different among dietary classes (ANOVA, p < 0.001,
see Table 4).
Size of particles
Mean body size has a significant influence on the size of grit particles that avian species
ingest (Gionfriddo and Best, 1996; Figure 3, p < 0.0001, R2 = 0.66). Luttik and de Snoo (2004)
reported that the mean size of grit particles increased with mean body size for the granivorous
species, but not among the nongranivorous species. By quantifying the size of contaminated grit
particles, investigators can further focus the assessment and measurement endpoints on specific
avian species. Of the 35 species sampled by Gionfriddo and Best (1996), 89% of the species had
mean particle sizes less than 1.9 mm (Table 2, Figure 4). In his masters thesis, Edwards (2002,
Virginia Tech) sifted several soil samples from a public shooting range near Blacksburg Virginia
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in the George Washington-Thomas Jefferson National Forest and found that more than 90% of
the shot found was number 6 to number 8 pellets (2-3 mm). In this example, an investigator
would focus the species of concern towards species most likely to ingest this size of particles
(Figure 4): killdeer, mourning dove, rock dove, ring-necked pheasant and American crow.
Conversely, Edwards also noted that within 30 meters of the firing line at the range there was a
higher incidence of lead fragments ranging down in size to 0.01 mm. The firing line area was a
small fraction of the range as a whole, but to the extent that it would be occupied by other
species of smaller size, those species may also be of concern.
Number of particles
As a result of factors discussed in earlier sections of this document, the number of
particles ingested by different species and individuals within species can vary considerably at
any given time. From the Gionfriddo and Best (1996) data set (replicated in Table 2) it is
noteworthy to view the standard deviations around the mean number of particles found in the
gizzards of the various avian species. In most instances, the standard deviation is larger than the
mean value (e.g., house sparrow, mean number of particles = 281, standard deviation = 476,
n = 146). Based on the species from Gionfriddo and Best (1996), regressing body mass with
mean number of particles yields no significant or identifiable relationship (Figure 5). Although
no discernable relationship between body mass and number of particles could be found, an
obvious cluster of points is observed in bird species with masses between 10 and 100 grams
having less than an average of 50 particles in their gizzards (Figure 5). This data translated into
histogram format (Figure 6) illustrates that only five of 35 species in the data set were found to
have an average number of particles greater than 50 in their gizzards. Those species were rock
dove, fox sparrow, ring-necked pheasant, American tree sparrow and house sparrow.
Conversely, Luttik and de Snoo (2004) reported that the mean number of grit particles
was related to body weight (logio particle number = 1.21 * logio (body wt.), R = 0.66, n = 27).
However, this analysis included all particles, including fine soil particles. Also, this relationship
was dominated by the species of the diverse nongranivore category that included several
waterfowl species that consumed large amounts of fine soil or sediment material. This illustrates
that across a diverse set of species, the ingestion of particles ranges from those that intentionally
ingest grit particles to those that ingest particles incidental to their feeding activity.
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Consequently, the number of grit particles ingested is influenced by multiple factors, including
diet composition, body weight, and foraging behavior.
Qualitative considerations across species prioritization categories
Considering across these various factors (dietary class, contaminated particle size and
average number of particles ingested) influencing the probability of species ingesting
contaminated particles, certain inferences can be drawn depending on the habitat setting and
CSM involved. For example, if the particle contamination is primarily lead shot (which is
typically larger than 2 mm) in upland settings, one would want to choose a granivorous species
like a rock dove and/or ring-necked pheasant. Nearly all the individuals within these species will
use grit, the grit size found in their gizzards is consistent with contaminated particle size, and
their gizzards typically contain a high number of particles. This rationale is one that would be
used when a risk assessor is seeking a species with a relatively high probability of being exposed
to a contaminated particle. The habitat setting, physical characteristics of the contaminated
particles, and other aspects of the problem formulation in the risk assessment (e.g., assessment
and measurement endpoints) will influence how one might use these factors in prioritizing
species of concern when assessing the risk of contaminated particles to avian species.
USING GIONFRIDDO AND BEST (1996) DATA SET TO PARAMETERIZE MODEL
Estimating mean number ofparticles ingested per day
In the revised lead model (Eq. 7), the number of particles ingested per unit time (T) is a
quotient of the mean number of particles per gizzard divided by the mean grit retention time
(Eq. 5). Although the Gionfriddo and Best data set does not attempt to represent the mean
number of particles found in their gizzard samples as a particle ingestion rate, we feel that this
robust data set of randomly collected individuals per species is a reasonable source of
information identifying the number of particles at any given time that may be in the gizzards of
birds. If we assume that that number (although variable) could be replicated at another point in
time, an ingestion rate can be estimated.
Given the large variation observed in gizzard counts among individuals, the use of point
estimates for the number of gizzard grit particles in model calculations is intended to reflect the
probability of ingesting lead particles across a large population of birds and is less useful for
estimating the probability that individuals may ingest a lead particle. A prudent adjustment of
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the average number of particles found in the gizzards of individuals in the Gionfriddo and Best
(1996) data set would be to calculate a 95% Upper Confidence Limit (UCL) of the mean from
the mean and standard deviation values given in Table 2. This calculation was completed by
using the following equation taken from a U.S. EPA OSWER guidance document (U.S. EPA,
2002):
95% UCL \ - a = mean + Tvai x ^cr/yfn^j (Eq. 8)
where
mean = mean number of particles/gizzard at time of necropsy
Tvai = from a table of critical values of the Student's t distribution. The(l-a)th
percentile of the Student's t distribution with n -1 degrees of freedom
a = standard deviation and
yfn = the square root of the number of observations.
In the example cited earlier for house sparrow, the mean number of grit particles found in
the gizzards of 146 individuals was 281, and the standard deviation was 476. When this
information is used to parameterize Eq. 8, the following result is yielded:
95% UCL = 281 + 1.6554 x (476/12.08) = 346 particles (Eq. 9)
This computation assumes a normal distribution of the number of grit particles found in
the gizzards of a number of individuals per species. Little information is available to determine
the robustness of this assumption. Table 5 shows the upper 95% UCL calculated in this manner
for all species in the Gionfriddo and Best (1996) data set. These values may be substituted for
the mean number of particles ingested in Eq. 5. Using these estimates, and a range of retentions
times as discussed in previous sections, reasonable daily particle ingestion rates can be calculated
to parameterize Eq. 7.
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AN APPROACH FOR ESTIMATING RISK OF MORTALITY FROM INGESTING
LEAD PARTICLES
Thus far this paper has focused on approaches for estimating exposure, i.e., the
probability of ingesting toxic particles such as lead shot or pesticide granules. In the case of lead
particles, the probability of mortality due to particle ingestion is a function of both the rate of
lead particles ingested and their cumulative retention time in the gizzard. This may occur if a
single lead shot is retained long enough to cause death or if the cumulative exposure from
multiple ingested shot within a certain time period is sufficient to result in death.
One approach for estimating the risk of mortality from ingesting lead particles is to
estimate the cumulative exposure to lead particles in the gizzard for a specific time period and to
compare the estimate to a critical value indicative of death. To do this we can calculate the
number of particle-exposure-days, which is defined as the cumulative number of days that one or
more particles is retained in the gizzard within a specified period of days. For example, one lead
particle retained for 6 days and three particles each retained for 2 days within a 6-day period both
represent six particle-exposure-days. A death occurs when the number of particle-exposure-days
exceeds some critical amount, expressed as a particle-exposure-days, within a specified time
period of w days.
To model this process we developed a simulation strategy in three broad steps (described
in more detail in Appendix C). The first step is to develop a probability model for the number of
lead particles in the gizzard of a bird on any given day, conditional on the number of lead
particles in the gizzard the previous day. Development of the probability model requires six
assumptions:
1. Gizzard load of grit particles is fixed,
2. Birds pass any given grit particle from the gizzard with a fixed daily probability,
3. Lead particles are passed at the same rate as other natural grit particles,
4. Gizzard grit contents are replenished to a fixed load of grit particles daily,
5. Lead particles are acquired during replenishing in proportion to their
concentration in the environment (i.e., there is neither preference for, nor
avoidance of, lead particles), and
6. Particle-exposure-day is an adequate expression of cumulative exposure over a
specified period of time.
In reality, the gizzard load varies due to factors that are not well understood, and it is not known
if lead particles are selected in proportion to their occurrence and retained at the same rate as
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natural grit particles, but these assumptions are made to provide a starting point for estimating
potential exposure. With the above assumptions we formulate a stochastic matrix (M) giving the
probability distribution for the number of lead particles in the gizzard on any given day,
conditional on the number of particles that were in the gizzard the previous day (Appendix C).
The second step is to use the probability model above to simulate a time-series of grit
particles in the gizzards of individual birds within an exposed population over an ecologically
relevant time period. For example, the time period may range from a few days for some migrant
species passing through a site to all or most of the year for year-long resident species at a site.
This requires an assumption about the distribution of lead particles in the gizzard at the start of
the time series. In this version of the model we assume that there are no lead particles in
gizzards at the start of the time series (i.e., m = 0).
The simulation model has eight inputs, of which seven are required (q and RT are
redundant):
rid = number of lead particles in the gizzard at the start of day d, assuming birds
arrive at a site with no lead particles in their gizzard, i.e., m = 0,
G = mean gizzard load expressed as the total number of particles in the gizzard at a
time,
RT = mean retention time (in days) for a particle in the gizzard,
q = l/RT = daily probability that a particle is voided,
(a, w) = ordered pair representing a fatal dose of toxic particles, where a bird will die if
it experiences at least a particle-exposure-days within a period of w days
S = the length of time (in days) that birds use the habitat, and
B = the number of birds to simulate.
The third step is to track the number of simulated birds for which the number of particle-
exposure-days exceeds some critical amount within a specified window of time. In this step,
each particle is assumed to reside in the gizzard in units of a full day (an exposure day) and a
running total of particle-exposure-days is tracked within a moving window of w days beginning
on day d—w. On each day, any female that exceeds a total of a particle-exposure-days within w
days is assumed to have died of lead poisoning and is removed from the simulation. If d < w
then exposure days are tracked back to day 1 only. The number of dead birds at the end of the
time series divided by the number birds simulated (B) is the probability of mortality during the
full time period (S). The value selected for B does not necessarily reflect the population size at a
25
-------
particular site. The higher the value of B used in the simulations, the more precise the estimated
probability of mortality will be.
To illustrate the simulation model, we provide examples of model output using northern
bobwhite (Colinus virginianus) based on information in McConnell (1967) and brown-headed
cowbird (Molothrus ater) based on information in Vyas et al. (2001). Input data for both
simulations are found in Table 6.
In McConnell (1967) northern bobwhite died when 52 particle-exposure-days had been
accumulated in a 20 day period. For bobwhite foraging on a contaminated site for 90 days where
lead particles accounted for 2% of total particles, the probability of death by the end of the
season was estimated to be 7.6% (Figure 7). In other words, 7.6% of the bobwhite feeding at this
site for 90 days would be expected to have died due to lead exposure. The longer birds remain
on a contaminated site, the higher their overall probability of achieving a lethal exposure.
Brown-headed cowbirds died after one particle-exposure-day in a one-day period (Vyas et al.,
2001). For cowbirds foraging at a contaminated site for 45 days with lead accounting for 0.1%
of the total particles, the estimated probability of death was substantially higher (36%) even with
a much lower concentration of lead in the environment (i.e., 1 in 1000 particles) and a shorter
total period of exposure (Figure 8). This is due to the lower critical threshold for cowbirds
(1 particle-exposure-day over a 1-day window), but also due to the faster gizzard turnover rate.
In its current form, the model also outputs a graph showing the cumulative probability of death
as a function of time at the contaminated site (Figures 7 and 8).
The primary limitation to the use of this simulation model is that several input parameters
are highly variable or there is little empirical data on which to base parameter estimates. In the
model, the terms for mean gizzard load (G) and mean retention time (RT) are the same as in the
revised model for estimating the probability of ingesting lead particles discussed above.
Evidence presented above suggests that both model inputs may vary greatly due to factors such
as diet composition, availability of grit, and grit characteristics. Also, very few studies have
empirically measured mean retention time, and those studies have been under laboratory
conditions (Table 1), so there is considerable uncertainty in deriving estimates of mean retention
time for field scenarios. Additionally, although examples exist for parameterizing a (particle-
exposure-days) and w (critical time period of exposure), these parameters are not reported in
studies and must be estimated from available information. Also, the critical value a probably
26
-------
varies as a function of w, but we have insufficient data to speculate on the form of those
relationships. Thus the number of species for which this model can be parameterized directly
with empirical data is limited. Because of the uncertainty surrounding several of the input
parameters, the simulation model currently is best used as a tool to explore the relationships
among input parameters and to evaluate model outputs under a variety of assumptions about
input parameters. Additional research would be needed to understand how model mortality
estimates are influenced by bias in input parameter estimates.
The model above has three other important limitations. First, simulations are only
feasible with gizzard loads up to about 250 particles due to limitations in MATLAB software on
the size of matrices. Thus the model cannot be applied to species such as waterfowl in its current
form because of their ingestion of larger amounts of grit particles. Second, the model does not
track additional mortality that would occur due to particles persisting in the gizzard after the end
of the season. Thus the mortality estimates are biased low, especially for birds with long gizzard
residence times. The first two limitations could be addressed through revisions to the model if
necessary. Third, in reality, the rate of particle erosion is a function of their size and shape, yet
at this point the model does not consider particle size and there is little data on which to
incorporate size-related erosion rates into the model. Additional research would be required to
address this limitation.
RANGE OF PARTICLE SIZES: IMPLICATIONS TO RISK ASSESSMENTS
Contaminants in soils exist in a wide variety of particle sizes and more often exist as part
of the soil matrix. To reiterate a point discussed earlier regarding the EPPO scheme models for
soil and grit ingestion, when the chemical of concern may be ingested accidentally with soil as
well as ingested intentionally as grit particles, these two routes of exposure may be independent
and thus additive in terms of estimating a total exposure dose. However, because birds may
ingest a wide range of particle sizes, from very fine soil particles to larger grit particles (i.e.,
>1 mm in size), it is very difficult to separate accidental soil ingestion from intentional grit
ingestion when there is overlap in the particle size ranges. The soil ingestion estimates by Beyer
et al. (1994) are based on a method where the size range of particles included an overlap with the
information of grit size preferences by Best and Gionfriddo (1991) and Luttik and de Snoo
(2004). Consequently, estimates of percentage of soil in the diet may overlap somewhat with
estimates of grit ingestion rates due to the differences in methods used to calculate the estimates.
27
-------
Each site-specific risk assessment of lead should consider these two possible routes of exposure
in light of site-specific information on the nature of lead availability (i.e., does the lead exist
primarily as dissolved lead in soil, lead shot and fragments, or a combination?). At firing ranges
where larger lead particles are more common, the probability that some species are ingesting
lead particles as grit increases. To use models for estimating the probability of ingesting lead
particles as grit, we need measurements of the proportion of grit-sized particles on the surface
made up of lead particles or a means of estimating this proportion. When information is
available on the lead particle size distribution at a site, this can be compared to the distributions
of preferred grit particles for various avian species to determine which species have the greatest
overlap. For example, if the lead at a site is predominately in the form of No. 8 lead shot
(—2.3 mm), this helps focus on the subset of species typically ingesting grit particles in this
range; many of these species would not be inadvertently ingesting particles of this size as soil,
but would be more likely to intentionally select these particles as grit. In this case, the models
for estimating the probability of ingesting lead particles as grit may be the most appropriate
method for estimating exposure. On the other hand, if the lead particles at a site are variable in
size and predominantly smaller (say <1.5 mm), it would be difficult to separate lead ingested
through accidental soil ingestion from intentional grit ingestion. In this case, estimating
exposure via the grit ingestion models would likely overlap to some extent with estimates based
on soil ingestion methods, and investigators would need to develop a weight-of-the-evidence
case, using available site-specific information, in order to estimate exposure potential. When
using grit ingestion models, investigators need to consider the nature of the contamination in the
soil matrix within the conceptual site model.
CONCLUSIONS
In this paper we reviewed several approaches for estimating the probability of ingesting
contaminated particles such as pesticide granules or lead particles (i.e., shot or bullet fragments),
and all of these approaches are strongly influenced by the estimate of daily grit ingestion rate,
which is not measured directly. The daily grit ingestion rate can be estimated using the number
of grit particles found in gizzards at a point in time and an estimate of the grit retention time (i.e.,
length of time that grit particles are retained in the gizzard). However, grit retention times have
only been measured in a few controlled studies with a few species, and empirical evidence
28
-------
indicates that grit retention times can vary considerably due to factors such as diet composition,
availability of grit, and grit characteristics. Consequently, estimating the probability of ingesting
contaminated particles depends heavily on assumptions made about grit retention times. Also,
all of these approaches assume that contaminated particles, whether they are pesticide granules
or lead fragments, are ingested in proportion to their availability in the environment (i.e., there is
neither preference for, nor avoidance of, contaminated particles), but there is little empirical
information about whether birds actively prefer or avoid contaminated particles, which could
result in an underestimation or overestimation, respectively, of the probability of exposure.
In addition to approaches for estimating the probability of ingesting contaminated
particles, we presented an approach for using this information to estimate the probability of
mortality from the ingestion of lead particles. Mortality from the erosion of lead particles is a
function of the number of lead particles ingested and the length of time each particle is retained
in the gizzard. In the approach presented, the estimate of the grit retention time is used not only
to estimate the daily grit ingestion rate of a species, but also to estimate the length of time
ingested particles are retained and eroded in the gizzard. A model was developed to determine if
the cumulative number of days that one or more particles was retained in the gizzard was
sufficient to cause mortality. However, several input parameters are highly variable or there is
little empirical data on which to base parameter estimates. Consequently, the model currently is
best used as a tool to explore the relationships among input parameters and to evaluate model
outputs under a variety of assumptions about input parameters. However, additional research
would be needed to understand how uncertainty in input parameters affects mortality estimates
from the model.
REFERENCES
Bellrose, F.C. 1959. Lead poisoning as a mortality factor in waterfowl populations. 111. Nat.
Hist. Sur. Bull. 27:235-288.
Best, L.B. and D.L. Fischer. 1992. Granular insecticides and birds: Factors to be considered in
understanding exposure and reducing risk. Environ. Toxicol. Chem. 11(10): 1495-1508.
Best, L.B. and J.P. Gionfriddo. 1991. Characterization of grit use by cornfield birds. Wilson
Bull. 103(l):68-82.
Best, L.B. and J.P.Gionfriddo. 1994. House sparrow preferential consumption of carriers used
for pesticide granules. Environ. Toxicol. Chem. 13(6):919-925.
29
-------
Best, L.B. and T.R. Stafford. 2002. Influence of daily grit consumption rate and diet on gizzard
grit counts. J. Wildl. Manage. 66(2):381-391.
Beyer, W.N., E.E. Connor and S. Gerould. 1994. Estimates of soil ingestion by wildlife. J.
Wildl. Manage. 58(2):375-382.
Beyer, W.N. and G.F. Fries. 2002. Toxicological significance of soil ingestion by wild and
domestic animals. In: Handbook of Ecotoxicology, 2nd ed., D.J. Hoffman, B.A. Rattner, G.A.
Burton Jr. and J. Cairns Jr., Eds. Lewis Publishers, Boca Raton, FL. p. 151-166.
Buerger, T.T., R.E. Mirarchi and M.E. Lisano. 1986. Effects of lead shot ingestion on captive
mourning dove survivability and reproduction. J. Wildl. Manage. 50(1): 1-8.
Chasko, G.G., T.R. Hoehn and P. Howell-Heller. 1984. Toxicity of lead shot to wild black
ducks and mallards fed natural foods. Bull. Environ. Contain. Toxicol. 32(4):417-428.
Dunning, J. B. 1993. CRC Handbook of Avian Body Masses. CRC Press, Boca Raton, FL.
Edwards, D.H. 2002. Lead distribution at a public shooting range. Masters Thesis, Virginia
Tech University, Blacksburg, VA.
EPPO (European and Mediterranean Plant Protection Organization). 2003. Terrestrial
vertebrates, Chapter 11. In: Environmental Risk Assessment Scheme of Plant Protection
Products. Bull. EPPO. 33:147-149. Available at
http://archives.eppo.org/EPPOStandards/PP3_ERA/pp3-ll(2).pdf.
Fischer, D.L. and L.B. Best. 1995. Avian consumption of blank pesticide granules applied at
planting to Iowa cornfields. Environ. Toxicol. Chem. 14(9):1543-1549.
Gionfriddo, J.P. and L.B. Best. 1999. Grit use by birds: A review. In: Current Ornithology,
Vol. 15, V. Nolan Jr., E.D. Ketterson and C.F. Thompson, Eds. Kluwer Academic/Plenum
Publishers, New York, NY. p. 89-148.
Gionfriddo, J.P. and L.B. Best. 1995. Grit use by house sparrows: Effects of diet and grit size.
The Condor. 97(1): 57-67.
Gionfriddo, J.P. and L.B. Best. 1996. Grit-use patterns in North American birds: The influence
of diet, body size, and gender. Wilson Bull. 108(4):685-696.
Kendall, R. J., P.F. Scanlon and R.T. Di Giulio. 1982. Toxicology of ingested lead shot in
ringed turtle doves. Arch. Environ. Contam. Toxicol. 11(3):259-263.
King, J.R. and L.I. Bendell-Young. 2000. Toxicological significance of grit replacement times
for juvenile mallards. J. Wildl. Manage. 64(3):858-862.
Luttik, R. and G.R. deSnoo. 2004. Characterization of grit in arable birds to improve pesticide
risk assessment. Ecotoxicol. Environ. Saf. 57(3):319-329.
30
-------
Lopez-Calleja, M.V., M. Soto-Gamoa and E.L. Rezende. 2000. The role of gastolites on
feeding behavior and digestive efficiency in the rufous-collared sparrow. The Condor.
102(2):465-469.
Mateo, R. and R. Guitart. 2000. The effects of grit supplementation and feed type on steel-shot
ingestion in mallards. Pre. Vet. Med. 44(3):221-229.
McConnell, C.A. 1967. Experimental lead poisoning of bobwhite quail and mourning doves.
Pro. Ann. Conf. Southeast. Assoc. Game Fish Comm. 21:208-219.
Pain, D.J. and B.A. Rattner. 1988. Mortality and hematology associated with the ingestion of
one number four lead shot in black ducks, Anas ribripes. Bull. Environ. Contam. Toxicol.
40(2):159-164.
Peddicord, R.K. and J.S. LaKind. 2000. Ecological and human health risks at an outdoor firing
range. Environ. Toxicol. Chem. 19(10):2602-2613.
Robel, R.J. and A.R. Bisset. 1979. Effects of supplemental grit on metabolic efficiency of
bobwhites. Wildl. Soc. Bull. 7:178-181.
Sanderson, G.C. and J.C. Irwin. 1976. Effects of various combinations and numbers of lead:iron
pellets dosed in wild-type captive mallards. Final Report. U.S. Fish and Wildlife Service.
Contract 4-16-0008-914. 136 pp.
Stafford, T.R. and L.B. Best. 1999. Bird response to grit and pesticide granule characteristics:
Implications for risk assessment and risk reduction. Environ. Toxicol. Chem. 18(4):722-733.
Trost, R.E. 1981. Dynamics of grit selection and retention in captive mallards. J. Wildl.
Manage. 45(l):64-73.
U.S. EPA. 1997. Ecological Risk Assessment Guidance for Superfund: Process for Designing
and Conducting Ecological Risk Assessments. Interim Final. U.S. Environmental Protection
Agency, Office of Solid Waste and Emergency Response. EPA/540/R-97/006.
U.S. EPA. 2002. Calculating Upper Confidence Limits for Exposure Point Concentrations at
Hazardous Waste Sites. U.S. Environmental Protection Agency, Office of Solid Waste and
Emergency Response. OSWER 9285.6-10.
Vyas, N.B., J.W. Spann and G.H. Heinz. 2001. Lead shot toxicity to passerines. Environ.
Pollut. 111(1):135-138.
31
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Table 1. Studies of Avian Grit Retention in Gizzards with Estimates of Mean and Median Retention Times.
Study Description and Reference
Species
Time
Since
Dose
(days)
Proportion
of Initial
Dose
Remaining
Rate
Parameter
or X
(days-1)
Mean
Retention
Time
(days)
Median
Retention
Time
(days)
Birds were dosed with 5 silica particles, released to
the wild, and collected at various time intervals
postdosing (Fischer and Best, 1995).
House sparrow
1
0.50
0.693
1.44
1.00
Red-winged
blackbird
1
0.1
2.303
0.43
0.30
Birds with access to quartz grit were switched to
feldspar grit and euthanized at specific time
intervals. The proportion of two grit types in
gizzards was recorded (Gionfriddo and Best, 1995).
House sparrow
0.25
0.6
2.043
0.49
0.34
1
0.12
2.120
0.47
0.33
Birds were dosed with 25 green quartzite particles,
and particles passed in feces were counted over a
24-day period (Trost, 1981).
Mallard
Multiple measurements
0.224a
4.46
3.09
Ducklings with access to one color of grit were
switched to another color and euthanized at specific
time intervals. The weight of original color grit was
recorded (King and Bendell-Young, 2000).
Mallard
Multiple measurements
0.48b
2.08
1.44
Birds with access to calcareous grit were switched to
siliceous grit and euthanized at specific time
intervals. The weight of calcareous grit remaining
was recorded (Mateo and Guitart, 2000).
Mallard
Multiple measurements
0.49c
2.04
1.42
"Trost (1981) expressed retention of quartzite particles as a negative exponential function with a 4-day interval retention rate of 0.408, which is equivalent to a
daily rate parameter (X) of 0.224 days \
bKing and Bendell-Young (2000) expressed retention of grit particles as an exponential function with "grit turnover rate" of 0.02/hr, which is equivalent to a
daily rate parameter of 0.48 days \
c Mateo and Guitart (2000) expressed retention of calcareous grit as an exponential function with a daily rate parameter of 0.49 days-1.
-------
Table 2. Data Summary Table of Dietary Classes, Mean Particle Counts, Mean Particle Size, and Body Masses of Avian
Species Sampled for Gizzard Analyses in Gionfriddo and Best (1996).
i
!
i
! Average
I #of
j Particles
\ Median #
! Mean
!
Average Mass (g)
i
Species
j Dietary
I Class
j Percent j Number
I Occurrence I Sampled
sd
1 of
[ Particles
j Size
j mm.
I Females
Males 1
Non- j
specified 1
Combined \
Rank
j Percentage
I of Species
Northern Oriole
j Omnivore
! o
| 5
| 0
0
i 0
| 0
j
j
33.6 |
33.6 I
1
| 3%
Yellow-rumped Warbler
| Insectivore
| 0
! 5
I 0
0
1 0
I 0
! 12.2
12.9 |
j
12.55 |
2
| 6%
House Wren
i Insectivore
57
! 7
1 3
5
1 1
I 0.3
10.9 j
10.9 |
3
j 9%
Cedar Waxwing
j Frugivore
| 20
i 20
i 9
40
i 0
! 0-3
j 33.1
30.6 |
31.85 |
4
j 11%
Hermit Thrush
j Omnivore
! 83
| 6
! 14
17
f 6
! 0-3
31 1
31 I
5
j 14%
Common Yellowthroat
i Insectivore
i 21
i 14
! 21
1
1 0
! 0.3
| 9.9
10.3 j
10.1 j
6
I 17%
American Tree Sparrow
j Granivore
| 100
| 8
1 267
212
| 203
| 0.4
j
20.1 |
32.3 !
20.1 I
7
| 20%
i 23%
Fox Sparrow
j Granivore
1 100
j 5
I 102
88
| 93
I 115
j
32.3 |
8
Lark Sparrow
1 Omnivore
| 100
! 5
I 42
50
| 22
I 116
j
29 |
29 |
9
| 26%
House Sparrow
j Granivore
| 98
! 146
! 281
476
I 97
I 01
| 27.4
28 |
27.7 |
10
j 29%
Dickcissel
i Omnivore
! 25
! 28
I 4
18
1 0
1 08
| 24.6
29.3 j
j
26.95 [
11
| 31%
American Robin
j Omnivore
| 44
j 43
I 12
26
I o
I 08
|
77.3 j
77.3 j
12
| 34%
Song Sparrow
1 Omnivore
j 93
| 14
I 14
15
1 8
1 08
j 20.5
21 I
20.75 j
13
| 37%
Common Grackle
j Omnivore
| 57
| 47
I 10
21
j 1
! 0.9
| 100
127 j
113.5 |
14
I 40%
Chipping Sparrow
j Omnivore
| 95
i 20
! 12
16
I 7
! 0.9
|
j
12.3 |
123 I
15
| 43%
Vesper Sparrow
j Omnivore
| 86
| 125
I 12
14
I 8
I 0.9
| 24.9
26.5 |
25.7 \
16
j 46%
Red-Headed
Woodpecker
1 Insectivore
! 57
| 27
j 31
59
t 2
j 0.9
f 0.9
5
!
j
71.6 |
71.6 |
17
| 49%
Indigo Bunting
| Omnivore
8!
21
1 35
91
I 4
14.1
14.9 |
14.5 |
18
51%
European Starling j Omnivore 36 56 | 21 j 85 j 0 J 1 j 79.9 84.7 ; 82.3 ^ 20 57%
-------
Table 2. cont.
Species
I Dietary
1 Class
I Percent j Number
j Occurrence jj Sampled
Mean#
of I
Particles j
sd
I Median #
j of
; Particles
! Mean
i Size
1 mm.
|
j Females
Average Mass (g
j Non-
Males j specified
) I
1 Combined [
Rank
Percentage
of Species
Brown-headed Cowbird
i Omnivore
| 52
I 175
10 I
30
I 1
| 1
I 38.8
49
1 439 I
19
54%
European Starling
j Omnivore
! 36
I 56
21
85
I 0
| 1
! 799
84.7
1 82-3 I
20
57%
Northern Cardinal
i Omnivore
| 73
i 22
40 I
82
i 6
j 1
! 439
45.4
i 44.65 j
21
60%
Savannah Sparrow
i Granivore
| 100
1 21
41 j
102
1 20
I 1
j 19.5
20.6
| 20.05 1
22
63%
Red-winged Blackbird
j Omnivore
| 73
I 82
I7 |
61
1 4
i 1.1
1 4i-5
63.6
52.55 |
23
66%
Barn Swallow
j Insectivore
| 22
1 23
I
4
I °
j 1.2
18.6
| 18-6 1
24
69%
Horned Lark
I Omnivore
| 99
I 69
11 1
13
1 8
I 1.2
I 30.8
31.9
1 305 I
25
71%
Eastern Kingbird
1 Insectivore
| 24
I 29
!
4
1 0
| 1.3
39.5
1 39-5 I
26
74%
Western Meadowlark
i Insectivore
| 44
1 9
2 I
3
I 0
! 1.4
| 89.4
106
I 977 I
27
77%
Yellow-billed Cuckoo
j Insectivore
j 44
1 9
3 I
6
1 0
j 1.6
64
I 64 I
28
80%
Blue Jay
j Omnivore
! 85
I 20
55 I
42
I 15
j 1.6
86.8
| 86.8 ]
29
83%
Northern Bobwhite
1 Omnivore
! 90
I 75
49 1
106
I 12
! 1.8
178
! 178 !
30
86%
Killdeer
j Insectivore
! 93
1 28
8 I
9
1 5
1 19
1 101
92.1
i 96.55 I
31
89%
Mourning Dove
i Granivore
! 68
I 40
10 1
16
I 3
| 2.1
| 115
123
| II9 I
32
91%
Rock Dove
| Omnivore
| 100
| 15
69 1
43
I 60
1 2.3
542
! 542 !
33
94%
Ring-necked Pheasant
1 Granivore
| 100
I 37
151 I
190
t 88
i 2.3
I 953
1317
I II35 I
34
97%
American Crow
j Omnivore
| 53
1 64
49 |
156
i 2
| 2.9
1 438
458
I 448 I
35
100%
sd = standard deviation.
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Table 3. Data Summary Table of Dietary Classes, Percent Occurrence of Grit, and Mean Grit Particle Counts by Size Class
of Avian Species Sampled for Gizzard Analyses by Luttik and de Snoo (2004).
Species
Scientific Name
Dietary Class
Number
Sampled
Percent
Occurrence
Mean Number of Grit Particles Per Bird
<0.25 mm
0.25-0.5 mm
0.5-0.75 mm
>0.75 mm
Linnet
Carduelis cannabina
Granivore
2
100
0
11
7
93
Goldfinch
Carduelis carduelis
Granivore
1
100
0
20
6
37
Twite
Carduelis flavirostris
Granivore
1
100
0
0
1
121
Greenfinch
Chloris chloris
Granivore
8
100
14
47
10
85
Woodpigeon
Columba palumbus
Granivore
20
100
13
5
1
207
Chaffinch
Fringilla coelebs
Granivore
8
100
19
26
4
61
Brambling
Fringilla montifringilla
Granivore
1
100
0
9
1
187
House sparrow
Passer domesticus
Omnivore
11
100
519
218
32
147
Tree sparrow
Passer montanus
Omnivore
1
100
127
44
6
71
Grey partridge
Perdix perdix
Omnivore
25
100
1,566
378
37
639
Pheasant
Phasianus colchicus
Omnivore
16
100
408
98
10
204
Skylark
Alauda arvensis
Nongranivore
6
100
1,610
423
45
172
Mallard
Anas platyrhynchos
Nongranivore
11
100
50,250
15,903
1,827
1,959
White-fronted goose
Anser albifrons
Nongranivore
1
100
77,419
24,707
2,974
5,348
Greylag goose
Anser anser
Nongranivore
5
100
144,889
73,931
9,999
11,202
Bean goose
Anser fabalis
Nongranivore
1
100
85,216
40,827
5,462
5,395
Meadow pipit
Anthus pratensis
Nongranivore
9
22
106
38
5
1
Carrion crow
Corvus corone
Nongranivore
13
92
13,348
4,268
497
214
Jackdaw
Corvus monedula
Nongranivore
1
100
25,340
7,425
823
482
-------
Table 3. cont.
Species
Scientific Name
Dietary Class
Number
Sampled
Percent
Occurrence
Mean Number of Grit Particles Per Bird
<0.25 mm
0.25-0.5 mm
0.5-0.75 mm
>0.75 mm
Reed bunting
Emberiza schoeniclus
Nongranivore
3
33
42
11
1
0
Black-headed gull
Larus ridibundus
Nongranivore
8
75
1,134
419
54
42
White wagtail
Motacilla alba
Nongranivore
3
33
0
8
2
1
Magpie
Pica pica
Nongranivore
11
64
1,969
615
71
26
Starling
Stumus vulgaris
Nongranivore
10
20
1,301
342
35
3
Blackbird
Turdus merula
Nongranivore
10
80
33,629
6,094
448
32
Song thrush
Turdus philomelos
Nongranivore
10
90
833
236
26
17
Lapwing
Vanellus vanellus
Nongranivore
2
100
3,877
919
89
32
u>
C\
-------
Table 4. Mean (± Standard Deviation) of Percent Occurrence of Grit and Number of Grit
Particles Found in Gizzards at Necropsy by Dietary Class from Gionfriddo and
Best (1996) and Luttik and de Snoo (2004).
Dietary Class
N*
% Occurrence of Grit
Mean # of Grit Particles in Gizzardb
Gionfriddo and Best (1996)
Granivore
6
94 ± 13
142± 113
Insectivore
9
40 ±27
7.8 ± 10.9
Omnivore
19
70 ±28
24 ± 19
Luttik and de Snoo (2004)
Granivore
7
100
134 ± 55
Omnivore
4
100
471± 405
Nongranivore
16
76 ±31
13,966 ± 26,110
a N represents number of species in each class.
b In Luttik and de Snoo mean number of particles represent the total particles >0.25 mm.
37
-------
Table 5. 95% Upper Confidence Limit of the Mean Estimates for Number of Particles
Found in the Gizzards of Avian Species.
Species
Number
Sampled
Mean # of
Particles
sd
T-value
95% UCL
Northern Oriole
5
0
0
2.1318
0
Yellow-rumped Warbler
5
0
0
2.1318
0
Barn Swallow
23
1
4
1.7171
2
Eastern Kingbird
29
1
4
1.7011
2
Western Meadowlark
9
2
3
1.8595
4
House Wren
7
3
5
1.9432
7
Yellow-billed Cuckoo
9
3
6
1.8595
7
Dickcissel
28
4
18
1.7033
10
Killdeer
28
8
9
1.7033
11
Cedar Waxwing
20
9
40
1.7291
24
Brown-headed Cowbird
175
10
30
1.6537
14
Common Grackle
47
10
21
1.6787
15
Mourning Dove
40
10
16
1.6849
14
Horned Lark
69
11
13
1.6676
14
American Robin
43
12
26
1.6820
19
Chipping Sparrow
20
12
16
1.7291
18
Vesper Sparrow
125
12
14
1.6572
14
Hermit Thrush
6
14
17
2.0150
28
Song Sparrow
14
14
15
1.7709
21
Red-winged Blackbird
82
17
61
1.6639
28
Common Yellowthroat
14
21
1
1.7709
21
European Starling
56
21
85
1.6730
40
Red-Headed Woodpecker
27
31
59
1.7056
50
Blue Jay
20
35
42
1.7291
51
Indigo Bunting
21
35
91
1.7247
69
Northern Cardinal
22
40
82
1.7207
70
Savannah Sparrow
21
41
102
1.7247
79
Lark Sparrow
5
42
50
2.1318
90
38
-------
Table 5 cont.
Species
Number
Sampled
Mean # of
Particles
sd
T-value
95% UCL
American Crow
64
49
156
1.6694
82
Northern Bobwhite
75
49
106
1.6657
69
Rock Dove
15
69
43
1.7613
89
Fox Sparrow
5
102
88
2.1318
186
Ring-necked Pheasant
37
151
190
1.6883
204
American Tree Sparrow
8
267
212
1.8946
409
House Sparrow
146
281
476
1.6554
346
sd = standard deviation.
Table 6. Input Parameters for Simulation Model.
Parameter
Definition
Northern
Bobwhite
Brown-
headed
Cowbird
G
Gizzard load (i.e., number of grit particles in gizzard)
49
10
P
Proportion of grit-sized lead particles in environment
0.02
0.001
RT
Mean retention time for grit in gizzard (= 1 iq)
4 days
1 day
q
Daily probability that a grit particle is removed from the
gizzard (= 1 /RT)
0.25
1
a
Critical number of particle-exposure-days
52
1
w
Critical time window for experiencing a exposure days
20
1
S
Length of season that bird uses the contaminated
environment
90 days
45 days
B
Number of birds simulated
10,000
10,000
39
-------
X = 0.693, MRT = 1.44 d
X = 0.25, MRT = 4 d
~ house sparrow
Median retention time
Mean retention time
0.4
0.3
0
1
2
3
4
5
6
7
8
9
10
Days
Figure 1. Illustration of the Mean and Median Particle Retention Times Based on Two
Exponential Functions with Rate Parameters of 0.693 and 0.25. MRT = mean
retention time. Red triangles represent the observed proportion of silica grit
remaining in house sparrow gizzards as a function of time postdosing (Fischer and
Best, 1995).
40
-------
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
*
*
% A
Calcareous grit,X = 0.49
- ¦ Quartzite grit,X = 0.224
~ Asymptomatic (5 shot)
X Dead (5 shot)
*
*
- -A
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Days
Figure 2. Comparison of the Proportion of Particles Retained in Mallard Gizzards Over
Time as Observed for Calcareous Grit (solid line), Quartzite Grit (dashed line),
and Doses of Five No. 6 Lead Shot in Surviving Birds Without Signs of Lead
Poisoning (solid triangles, n = 4) and in Birds that Died (six-point stars, n = 2).
41
-------
3.5
y = 0.4989*Ln(x) - 0.8684
E 2.5
E
-------
3
2.5
E
1 2
o
N
* 1.5
0.5
0
American crow •
Ring-necked pheasant
Rock dove
Mourning dove -
Killdeer
S * *
~ ~ ~ r
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Percentage of species
Figure 4. Distribution of Mean Size of Grit Particles Found in the Gizzards of Avian
Species from Gionfriddo and Best (1996).
43
-------
300
250
200
te 150
100
50
~ ~ ~ ~ ~~
~ ~ ~ 4 ~ * £ a
^ ~ ~~~ #
10
100 1000
Mean body mass (g)
10000
Figure 5. Relationship Between Mean Number of Grit Particles Found in the Gizzards of
Avian Species and Their Body Mass.
300
House sparrow
Tree sparrow -
<0 250
o
0
1 200
a
Ring-necked pheasant
O) 150
•s
c 100
3
Fox sparrow
Rock dove
50
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Percentage of species
Figure 6. Distribution of Mean Number of Grit Particles Found in the Gizzards of Avian
Species.
44
-------
0©E
Exposure model
G = 49 gizzard capacity (G > 0)
P = 0.02 proportion of grit at soil surfance that is lead (0 < P < 1)
- Grit retention-
ci - 0.25 daily probability of particle removal (0 < q < 1)
RT = 4 average retention time (RT > 0)
B = 10000 Sample Size (B > 0,10,000 recommended)
critical particle exposure
critcal window (w > 0)
season length (S > t)
- Output
O overlay graphs Probability of death:!
40 50
Day of season
Figure 7. Sample Model Output for Northern Bobwhite Using Parameters in Table 6.
Exposure model
G = 10 gizzard capacity (G > 0)
P = 0.001 propDrtion of grit al soil surfance that is lead (0 < P < 1)
Grit retention-
q - 1 daily probability Df particle retroval (0 < q < 1)
RT = 1 average retenticn time (RT > 0|
B = 10000 Sample Size (B >0,10,000 recommended)
Effects model
pha = 1 criticel particle exposure c
W = j 1 critca window (w > 0)
S = : 45 season length (S >t)
O overlay graphs Probability of death:
20 25
Day of season
Figure 8. Sample Model Output for Brown-headed Cowbird Using Parameters in Table 6.
45
-------
APPENDIX A. EXAMPLE SPREADSHEET CALCULATIONS USING THE REVISED
MODEL FOR ESTIMATING PROBABILITY OF INGESTING LEAD PARTICLES
The probability of ingesting N lead particles is calculated for a scenario based on northern
bobwhite with an overall average number of grit particles in the gizzard of 49 and a mean grit
retention time of 1.4 days. The scenario is based on feeding 100% of the time during a 1-day
period on a contaminated site where 1% of the available grit-sized particles is a lead particle.
Under this scenario, there is a 70% probability that no lead particles would be ingested
during the 1-day period and a 30% probability of ingesting 1 or more lead particles, including a
25% probability of ingesting 1 lead particle and a 4% probability of ingesting 2 particles.
The spreadsheet model also includes a Factorial Worksheet to explain the factorial
calculations, especially for scenarios where the number of grit particles ingested is very high.
46
-------
APPENDIX A: Revised Model for Estimating the Probability of Ingesting N Lead Particles by Birds Species Bobwhite Revised 3/10/09
Parameter
Parameter code
I I I
Estimate particle ingestion rate using
mean number of grit particles in gizzards
divided by estimated retention time in
days
Mean # grit-sized particles/gizzard
G
49
ENTER PARAMETER ESTIMATES ONLY IN BLUE CELLS
Mean particle retention time (i.e., mean #days particle
retained in gizzard)
RT
1.4
Daily particle ingestion rate (i.e.. mean # particles
ingested/day)
DPIR = G/RT
35
Alternative estimate of DPIR
0
Choose number of days of exposure
period to consider—ranging from 1 (if
interested in daily risk) to the maximum
number of days/year at site of
concern—to estimate particle ingestion
rate for total exposure period
# days in exposure period
D
1
Exposure period particle ingestion rate (i.e.. mean #
particles ingested/exposure period)
EPPIR = DPIR x D
35
Rounded-up particle ingestion rate/exposure period (7)
T =
Roundup (EPPIR)
35
Proportion of grit-sized particles available
on-site that are lead
# Lead particles per unit area
^-ON
10,000
Total # grit-sized particles per unit area
7~on
1,000,000
Prop of lead particles on-site
P ON = L ON^7ON
0.01000
Alternative method of estimating P0n
0
Proportion of grit-sized particles available
off-site that are lead
# Lead particles per unit area
/-OFF
0
Total # grit-sized particles per unit area
7"off
1,000,000
prop or lead particles orr-site
^OFF = l-offl7"oFF
0
Alternative method of estimating P0ff
0
Prop of foraging time on-site
F
1
Proportion of lead particles from all foraging sites
P = poti * F + Port
x (1 - F)
0.01
# of lead particles ingested/exposure period
N
0
1
2
3
4
5
6
7
8
Calculate components of the probability
mass function for each # of ingested lead
particles
PN
1.00000000
0.01000000
0.00010000
0.00000100
0.00000001
0.00000000
0.00000000
0.00000000
0.00000000
(1 -pf-»
0.70344769
0.71055323
0.71773053
0.72498034
0.73230337
0.73970037
0.74717209
0.75471929
0.76234271
7! UN I x (T - N)\) (see note on FACTORIAL worksheet)
1
35
595
6545
52360
324632
1623160
6724520
23535820
Probability of ingesting N lead particles
during exposure period
Pr (/v) = rri !{ni x (7 -/vim x p"x (1 - pi7"-"
Pr (/V)
0.70344769
0.24869363
0.04270497
0.00474500
0.00038343
0.00002401
0.00000121
0.00000005
0.00000000
Same probabilities as previous line expressed in scientific notation
7.0345E-01
2.4869E-01
4.2705E-02
4.7450E-03
3.8343E-04
2.4013E-05
1.2128E-06
5.0751 E-08
1 7942E-09
Peddicord and LaKind calculates prob of ingesting >1 lead particle as 1 minus probability of
consuming 0 lead particles
1 - Pr (0)
0.29655231
-------
Factorial Worksheet
The probability mass function includes factorials in a term expressed as T\/(N I x (7~ - A/)!)
where:
T = the total number of grit-sized particles ingested during the specified exposure period, and
N = the number of lead particles ingested during the specified exposure period.
Excel only calculates factorials up to 1701
For species with high grit ingestion and exposure periods of many days, T can easily exceed 170.
The formulas for N =0 through 8 have been simplified because algebraically many of the values in the numerator and denominator cancel.
N T\/(N\x (T - N)\)
0 n/(0! x(T - 0)\) = T 1/(1 x T\) = 1 Note: 0! = 1
1 n/(1! x (r - 1)1) = 771 = T
2 7~!/(2! x (f - 2)!) = (7~ x (T - 1))/(1 x 2)
3 7~!/(3! x (f - 3)!) = (7~ x (T - 1) x (T - 2))/(1 x 2 x 3)
4 7~!/(4! x (T- 4)\) = (T x (T - 1) x (T- 2) x (T - 3))/(1 x 2 x 3 x 4)
5 ri/(5! x (T- 5)!) = (f x (T- 1) x (f- 2) x (T - 3) x (f- 4))/(1 x2x3x4x5)
6 ri/(6! x (T- 6)!) = (r x (f - 1) x (r- 2) X (r- 3) X (r- 4) X (r- 5))/(1 X2x3x4x5x6)
7 ri/(7! x (T- 7)\) = (7~ x (r- 1) x (r- 2) x (r- 3) X (r- 4) X (r- 5) X (r- 6))/(1 x2x3x4x5x6x7)
8 n/(8l X (T- 8)l) = {T X (r- 1) x (T- 2) x (f - 3) x (T- 4) x (f - 5) x (T - 6) x (f - 7))/(1 x2x3x4x5x6x7x8)
Example if T = 20:
N T\f(N\x(T-N)\)
0
201/(01 x (20)
) =
1
1
201/(1! x (19)
) = 20/1 =
20
2
20!/(2! x (18)
) = (20 x 19)12 =
190
3
20!/(3! x (17)
) = (20 x 19 x 18)/6 =
1140
4
20!/(4! x (16)
) = (20 x 19 x 18 x 17)/24 =
4845
5
20!/(5! x (15)
) = (20 x 19 x 18 x 17 x 16)/120 =
15504
6
20!/(6! x (14)
) = (20 x 19 x 18 x 17 x 16 x 15)/720 =
38760
7
20!/(7! x (13)
) = (20 x 19 x 18 x 17 x 16 x 15 x 14)/5040 =
77520
8
20!/(8! x (12)
) = (20 x 19 x 18 x 17 x 16 x 15 x 14 x 13)/40320 =
125970
-------
APPENDIX B. GRIT RETENTION TIME EXPRESSED AS AN EXPONENTIAL
FUNCTION
Trost (1981) and King and Bendell-Young (2000) both described the probability of grit
particles being retained in a gizzard as an exponential function. If we assume that an exponential
function generally describes grit retention times in birds, we can use observations of the
proportion of grit particles retained in the gizzard after specific periods of time to estimate mean
and median grit retention times for a species.
For the first example, consider the house sparrows dosed with five silica grit particles and
released by Fischer and Best (1995). The sparrows on average voided 50% of ingested particles
in the first 24 hours (i.e., 50% probability that the time for a particle to be voided will be between
0 and 24 hours).
Consider the exponential random variable. Let P be the probability. The parameter X is
the random variable corresponding to a specific elapsed time before a particle that we are
interested in is voided (days). Lower case x represents the many possible choices forX that are
defined by the probability mass function, f(x).
The exponential random variable is a continuous random variable defined by the
parameter X > 0.
ifx>0
if x< 0
Assuming the time to void the particle is distributed as an exponential random variable,
¦Ax a
= -e
0
i - e~*
a > 0
49
-------
Taking the first example of the 50% probability that the time for a particle to be voided
will be between 0 and 24 hours (1 day), we can solve for the rate parameter X.
0.5 = P {X < 1}
1 -Ax -Ax
0.5 = f Xe dx = -e
0
e"A =0.5
X = 0.693 day"1
The expectation of the exponential random variable is MX. The expectation is the
expected value or a weighted value that considers the magnitude of the possible values for the
retention time multiplied by the probability that the retention time assumes that value. The
expectation can give an idea of what the mean retention time might be. In the case of the
sparrow the mean retention time was 1.44 (1/0.693) days. The median retention time is equal to
ln(2)!X or 1.0 day.
For a second example, consider the house sparrows whose grit access was switched from
quartz to feldspar (Gionfriddo and Best, 1995). There was a
1. 40% probability that the quartzite grit particle was voided within the first 6 hours.
2. 88% probability that the quartzite grit particle was voided within the first 24 hours.
Solving again for X for each of the measures of retention time,
0.4 = P {X < 0.25} = f^25 Xe~Xx dx = 1 - e~°'25X
0.6 = e~°-25X
X = 2.04 day"1
1 -A
= 1- e
0
50
-------
0.88 = P {X < 1} = \lQ^e Xx dx =1- e A
0.12 = e"A
X = 2.12 day"1
The mean retention time measured in the house sparrow study using the quartz/feldspar
was about 0.5 days. The differences in the estimates for the two house sparrow studies could
reflect the conditions of the experiment or the types of grit used.
Sometimes, when there are multiple observations of the proportion of grit retained at
specific time periods, the calculated rate parameters (X) differ considerably—suggesting that the
exponential function may not appropriately describe the temporal pattern of grit retention over
all time periods. This may occur when the probability of particle retention changes because the
gizzard selectively retains or passes certain types of particles. An example of this occurred in the
house sparrow experiment by Fischer and Best (1995). In addition to reporting that 50% of the
silica particles remained after 1 day, the authors observed that 32% of the particles were retained
13 days postdosing in sparrow gizzards.
0.32 = P {X > 13}
co -2x
0.32 = | Xe dx
13
-13A
0.32 = e
X = 0.0876 day"1
This observation produces a much lower estimated rate parameter (0.0876 day 1 vs.
0.693 days *) and, consequently, a higher estimate of mean retention time (11.4 days vs.
1.44 days). Since Fischer and Best (1995) observed the same percentage of silica grit retained
-AX
= —e
°0 -13/1
= e
13
51
-------
from day 4 to day 13, an exponential function is not a good description of the process of grit
retention during this period.
A similar pattern was observed by Fischer and Best (1995) for red-winged blackbirds. In
the blackbirds 90% of the dosed silica particles were voided within the first 24 hours, but the
remaining 10% of the particles were retained through day 13 postdosing.
0.9 = P {X < 1} = foAe~Xx dx =1- e~A
e~A = 0.1
X = 2.3 day"1
0.1= P {X > 13} = QAe~Axdx = e"13A
0.1=e"m
X = 0.177 day"1
The two estimates of X are not very close for the red-winged blackbird, probably
reflecting that after an initial period where the dosed silica particles were rapidly voided from
blackbird gizzards, a small proportion of the silica particles were selectively retained.
Consequently, the exponential function seems to provide a useful description of grit retention
rates under conditions when each particle has an equal probability of being voided from the
gizzard at any particular time period. However, when the physical characteristics of a particular
grit particle (or type of particles) lead to selective retention within the gizzard, the exponential
function may underestimate the retention time at certain time periods.
If one assumes that all ingested particles have an equal probability of being retained,
including lead particles, an exponential function can be used to estimate the probability that an
ingested lead particle is retained for a specific period of time. To do this we define the critical
number of days required for a lead particle to be retained to cause mortality of a bird as C. For a
given X we can estimate the probability that a particle is retained for C or more days as:
52
-------
P {X > C}= Qle Axdx = e CA
For example, consider that a bird has a mean grit retention time of 1.4 days:
X = 1/1.4 days = 0.7143 day"1
Assume C is 7 days, i.e., it takes 7 days for a particle to be eroded enough to cause harm.
P {X > 7} = l^Xe^dx = e-7 x 0-7143 = 0.00 67
Consequently, if lead particles have an equal probability of being retained and grit
retention time is relative short (i.e., 1.4 days), then there is <1% probability that the lead particle
is retained in the gizzard for 7 or more days.
53
-------
APPENDIX C. DESCRIPTION OF THE SIMULATION MODEL Pr (nd + x \ nd)
Let:
rid = number of lead particles in the gizzard at the start of day d. By convention, n\ = 0.
y = number of particles removed from the gizzard during one time-step (i.e., 1 day).
x = number of lead particles remaining after y total particles are removed during one
time-step (x = rid —y)-
z = number of lead particles added back to the gizzard during one time-step.
G = gizzard capacity expressed as the total number of particles in the gizzard at a time.
pi = Pr (n = i - 1), thus pt is the probability of a given value for n, where 1 < z < G + 1.
Nd = {Pr (rid = i~ !)}> where z indexes the columns of Nd- Thus, Nd is a row-vector with
G + 1 columns. By convention, Ni has a 1 in the first column and zeros elsewhere.
We wish to use information about rid, y, z and G to predict the number of lead particles in
the gizzard from one day to the next. In other words, we want a probability model of the form
p (nd +11 »d) or, equivalently Nd + \ = f {Nj). We make the following assumptions about
processes:
1. Birds replenish their full gizzard daily and gizzard capacity is fixed.
2. Birds void particles daily with probability q. Thus, y~ binomial(G,q)
3. Toxic particles are equally likely to be voided as nontoxic particles. Thus,
x ~ hypergeometric (nd, nd - y, G).
4. Particles are picked up proportionally to their concentration in the environment.
Thus, z ~ binomial(y,P), where P is the proportion of grit-sized particles that are
toxic.
To anticipate problems with computer time, we will develop the model in matrix notation
to take advantage of M ATLAB. In the development below, we condition on y, then marginalize
over its distribution.
First, we need a matrix Xy =Pr (x | iy , v, G) that gives the conditional probabilities
for having x lead particles remaining in the gizzard after a day given that y total particles were
removed, of which nd-x were lead.
54
-------
What does Xy look like?
1. Its rows correspond to different values for rid.
2. Its columns correspond to different values for x.
3. The cells give the transition probabilities from w^to x conditional on G and y.
Therefore, row i of Xy gives the hypergeometric distribution for having x=j— 1 toxic
particles remaining in the gizzard conditional on starting with nd = i -1 particles. More
generally:
Pr (x = j - 1 | nd = i - 1, y, G)
fl-1 ^
J -1 -
'G - i +
,y-t + J)
fG^
(Eq. CI)
where
Now let us define another matrix Zy = Pr (nd + x \ x9 y, r) that gives the conditional
probabilities for having rid+1 lead particles in the gizzard after picking up y particles given that
the bird was left with x particles after the removal step.
What does Zy look like?
1. The rows of Zy correspond to the starting points x.
2. Columns of Zy correspond to the ending points rid+
3. The cells give the transition probabilities from x to rid+1 conditional on>>.
Therefore, row i of Zy gives the binomial distribution for picking up i = nd +1 — x toxic
particles out ofy particles picked up. More generally:
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where
Zy = \pr {nd +1 = J -1 I X = ; -1, .y, p) = K 1 P{j~i] (l-P)(,,"> + iH(Eq.C2)
Pr (nd + i = j - 1 | x = i - 1, y, P) = 0 if
\nd
1 nd
+ 1
+ 1 < x
Finally, we marginalize over j/:
Pr {nd + l| nd) =M = lLXyZyPr (y | G' ?)
(Eq. C3)
To estimate the number of lead particles in the gizzard on an arbitrary day d > 1, we can
use powers of M\
Particle-Exposure-Days
The model (Eq. C4) alone gives only the daily probability of uptake, elimination and
retention of lead particles. It does not attempt to estimate the probability of death associated
with a given time-series of gizzard contents. However, we can use M (Eq. C4) to estimate the
probability that a bird ingests a fatal dose of toxic particles, given some information on what
constitutes a lethal exposure. Below we develop a simulation model of fatality due to ingested
particles.
The model uses M, together with a random number generator, to simulate the progress of
birds picking up and ejecting lead particles over the course of a season. To do so, we define an
exposure day to have occurred when a single particle resides in the gizzard for a day. The basic
strategy of the simulation model is to track the total number of exposure days that occur within a
fixed period of time. All parameters for the model are as previously defined, except:
1. (a, w) = ordered pair representing a fatal dose of toxic particles. Thus a bird will die
if it experiences at least a exposure days within a period of w days.
2. S = the length of time that birds use the habitat.
3. B = the number of birds to simulate.
(Eq. C4)
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Assuming that birds enter the habitat on day 1 with no lead particles in their gizzard, the
matrix M is used to generate a time series of particle counts in the gizzard over the full S-day
season. As the simulation proceeds, the cumulative number of exposure days (in the previous w
days) is tracked, and simulated birds are assumed killed if their exposure exceeds (a, w).
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