United States
Environmental Protection
Agency
Environmental
Research Laboratory
Duluth MN 55804
EPA-600/3-78-036
April 1978
vxEPA
Research and Development
Size Dependent Model
of Hazardous Substances
in Aquatic Food Chain
Ecological Research Series
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2 Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials. Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
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aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/3-78-036
April 1978
SIZE DEPENDENT MODEL OF HAZARDOUS SUBSTANCES
IN AQUATIC FOOD CHAIN
by
Robert V. Thomann
Manhattan College
Bronx, New York 10471
Contract No. R803680030
Project Officer
William L. Richardson
Environmental Research Laboratory - Duluth
Grosse He, Michigan 48138
ENVIRONMENTAL RESEARCH LABORATORY - DULUTH
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA 55804
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DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory -
Duluth, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of
trade names or commercial products constitute endorsement or recommendation
for use.
ii
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FOREWORD
The presence of Hazardous Substances In the environment is a major
concern of the U.S. Environmental Protection Agency. One research goal of
the Environmental Research Laboratory-Duluth is to develop quantitive
methods for describing the transport and fate of hazardous substances in the
freshwater environment, particularly the Great Lakes. High levels of
persistant organic chemicals in Great Lakes fish are threatening their
usefulness as a resource by jeopardizing the associated recreation and
commercial fishing industries.
This report presents an innovative approach to tracking hazardous
substances in freshwater ecosystems. It is a first attempt to conceptulize
a very complex process. Additional research is required at this point to
test and verify the hypothesis presented. The purpose of reporting this
research in its infancy is to stimulate thinking by the research and
management communities.
William L. Richardson
Environmental Scientist
Large Lakes Research Station
iii
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ABSTRACT
In order to incorporate both bioaccumulatlon of toxic substances direct-
ly from the water and subsequent transfer up the food chain, a mass balance
model is constructed that introduces organism size as an additional indepen-
dent variable. The model represents an ecological continuum through size de-
pendency; classical compartment analyses are therefore a special case of the
continuous model. Size dependence is viewed as a very approximate ordering
of trophic position.
The analysis of some PCB data in Lake Ontario is used as an illustration
of the theory. A completely mixed water volume is used. Organism size is
considered from 100 ym to 10 ym. PCB data were available for 64 ym net
hauls, alewife, smelt, sculpin and coho salmon. Laboratory data from the
literature were used for preliminary estimates of the model coefficients to-
gether with the field data. The analysis indicated that about 30% of the
observed 6.5 yg PCB/gm fish at the coho salmon size range is due to transfer
from lower levels in the food chain and about 70% from direct water intake.
The model shows rapid accumulation of PCB with organism size due principally
to decreased excretion rates and decreased biomass at higher trophic levels.
The analysis indicates that if a level of 5 yg PCB/gm at 10 ym is sought,
total (dissolved and particulate) water concentration would have to be about
36 ng/1 or about 66% of the present 55 ng/1.
iv
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CONTENTS
Page
Foreword ill
Abstract iv
Figures vi
Tables vil
Acknowledgments viii
1. Introduction 1
2. Conclusions 3
3. Recommendations 4
4. The Generalized Model 5
Compartment Approach 5
Continuous Model 7
5. The Completely Mixed Water Volume Case 14
Steady State 15
Constant Coefficients 16
Variable Coefficients 19
6. Data Analysis 22
Laboratory Data Analysis - 22
Water Uptake and Excretion - Some Illustrations ... 22
Field Data Analysis - PCB's in Lake Ontario 28
Available Data on Lake Ontario 28
References 36
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FIGURES
Number Page
1 The Continuous Environment and Discrete Approximation ... 6
2 Range of Prey Size for Alewife Larval Stage and Juvenile-
Adult Age Groups 0-IV, Lake Michigan 9
3 Distribution of Toxicant in One-Dimensional Physical
and Ecological Space 10
4 Schematic of General Model for Single Completely Mixed
Water Volume 12
5 Density Function, ¥ and Distribution Function S 12
6 a) The Toxicant Density Function, b) The Biomass Density
Function, and c) The Bioaccumulation Function 18
7 A Three Region Model a) Variation of Biomass Density
b) Components of Bioconcentration Factor 20
8 Variation of PCB Uptake With Organism Size, From Water
Only 24
9 Variation of PCB and DDT Excretion With Organism Size ... 24
10 Lake Ontario Mass Density as a Function of Organism Size . 32
11 Analysis of PCB's in Lake Ontario 34
vi
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TABLES
Number Page
1 Form of Hazardous Substance Transport Equation
for Different Water Body Types 13
2 Range of Organism Sizes 23
3 Explanation of Symbols for Figure 8, PCB Concentration
Factors 25
4 Explanation of Symbols for Figure 9, PCB Excretion
Rates 26
5 Some Relationships Between Uptake and Excretion
and Organism Size 29
6 Some Data for Lake Ontario PCB Concentration (Arochlor
1254 Equivalent) 30
7 Coefficients Used in Analysis of PCB Data with
Steady State Size Dependent 35
vii
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ACKNOWLEDGMENTS
This work was completed during a sabbatical leave from Manhattan College
to which a grateful acknowledgment is made. An additional acknowledgment
is gratefully recognized to Hydroscience, Inc., Westwood, New Jersey, who
during the leave provided financial support from research and development
funds as well as other direct and indirect staff support. This research in
addition was supported by the U.S. Environmental Protection Agency through
the Large Lakes Research Station at Grosse Isle under a research grant to
Manhattan College. Such financial support was further complemented by the
encouragement and insight from Drs. Wayland Swain and Nelson Thomas and
Mr. Bill Richardson.
Special thanks are due to Drs. Dominic DiToro, and Donald J. O'Connor
of Manhattan College and John L. Mancini and John St. John of Hydroscience,
Inc., who provided a valuable forum for discussion and important insights
into model behavior.
viii
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SECTION 1
INTRODUCTION
The presence of hazardous substances in the aquatic food chain is a
problem of rapidly developing dimensions and magnitude. Passage of the Toxic
Substances Control Act of 1976, unprecedented monetary fines, and continual
development of data on lethal and sub-lethal effects attest to the expansion
of control on the production and discharge of such substances. On the other
hand, new product production and the ever present potential for insect and
pest infestations with attendant effects on man and animal result in contin-
uing demand for product development. As a result of this confrontation, con-
siderable effort has been devoted in recent years to the development of pre-
dictive schemes that would permit an a priori judgment of the effects of a
given substance on the environment.
In this paper, a model is presented that is focused specifically on the
aquatic ecosystem and the transport and accumulation of hazardous substances
in the aquatic food chain. Specific toxicological effects are not included
in this work; the emphasis is on the fate of the substance in the aquatic
ecosystem. The primary motivation for the development of the model is to
place in a generalized framework, the large amount of work in laboratory,
field, and mathematical experiments of hazardous substances in the food
chain.
The literature on the transport of hazardous substances generally begins
by assigning to the ecological system a series of compartments positioned in
space and time. The concept of a compartment arises from a grouping of eco-
logical properties, species or types (e.g., "phytoplankton", "fish"). The
continuum of the environment is replaced by finite, discrete, interacting
trophic levels. The details of each compartment need not be specified and
internal mechanisms are not necessarily examined. Attention is usually di-
rected towards a portion of the ecosystem, the degree of specificity .of com-
partments depending heavily on the aims of the investigator. The ecological
concepts of compartment analyses have been reviewed by Dale (1970), and
Patten (1971). Examples of compartment models in food chain studies of haz-
ardous substances include Gillet (1974), Hill et. al., (1976), Lassiter, et.
al., (1976) and Hoefner and Gillet (1976).
Compartment analyses provide a great deal of flexibility and can incor-
porate reasonably complicated food webs. However, the basic difficulty with
viewing the food chain problem in a compartment sense is that any general un-
derlying theoretical framework may be masked by the choice of the compart-
ment. The discretization of the aquatic food chain obscures the "continuous"
nature of the ecosystem. Futhermore, if there are m ecological variables
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(ecological compartments) positioned at n spatial locations, there are a
total of m x n compartments and m x n equations (differential or algebraic)
to be solved. Thousands of equations can easily result. The thrust of this
work therefore is the formalization of a generalized unified framework for
the transport of substances in the food chain. Discretization of ecological
space into compartments would therefore be a special case or approximation of
the general theory.
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SECTION 2
CONCLUSIONS
As a result of the research reported on herein, the following conclu-
sions can be drawn.
1. The one-dimensional aquatic food chain can be visualized as a con-
tinuum using organism length as an independent variable.
2. The mass balance of a toxicant being both absorbed directly from
the water and transported up the food chain by predation, using an
organism length representation, results in a single partial differ-
ential equation, the properties of which are well-known.
3. This equation in principle permits rapid solution for the distribu-
tion of the toxicant throughout the food chain without resort to
classical compartment analysis and resulting sets of equations.
However, the size dependent model in its present form, does not
permit detailed analysis on any one segment of the ecosystem.
4. The size dependent model provides a framework for uptake, feeding
and excretion data by aquatic organisms coupled to the physical
properties of the water body (flow, volume) and the chemical pro-
perties of the toxicant (photo-oxidation, vaporization).
5. An illustration is provided by PCB concentration over the size
range from 100 ym to 10 ym. Using the observed PCB distribution
in a food chain of Lake Ontario, a calibration of the model coef-
ficients indicates that 67% of the observed 6.5 yg/gm in coho
salmon is from direct uptake from the water phase and 33% from the
food chain route.
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SECTION 3
RECOMMENDATIONS
It is recommended that additional hazardous substances be investigated
within the size dependent model structure to determine food chain accumula-
tion patterns. Such substances might include cadmium, mercury, and mirex,
among others. Additional problem settings should also be investigated in-
cluding small lakes or embayments, and river and estuarine systems.
Further, it is suggested that the relationship of the size dependent
model and compartment models be investigated together with the interaction of
the size dependent model and biomass models.
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SECTION 4
THE GENERALIZED MODEL
The principal questions that prompted this line of research into a gen-
eralized hazardous substance model are: "If compartments represent discrete,
homogenous entities in ecological space, what is the continuous analog of
this approximation? Since compartment analyses often represent differential
equations around previously chosen trophic levels what is the suitable math-
ematical framework that would represent ecological space as a continuum rath-
er than discretized levels?" Figure 1 illustrates the question by analogy to
the often-made discrete approximation to a continuous water body for analysis
of dissolved substances in the water. Continuous space is replaced by a se-
ries of discrete regions in space and mass balance equations are written
around each region in space for the substance of interest. Similarly in eco-
logical compartment analyses, mass balance equations are written around a se-
ries of individual "regions" thereby describing the transport and cycling of
the substance in the food chain. For a toxicant, the relevant measure is the
mass of toxicant per unit biomass at that level.
COMPARTMENT APPROACH
Therefore, for compartment analyses, one lets
at location j and
, mass toxicant v
ij mass trophic level i
,,, ,mass of trophic level i,
M. . = I , f )
ij volume of water
also at location j. Then v. M = s.. is the mass of toxicant of level i re
lative to the volume of water at location j . In one-dimensional food chains
(excluding food webs for the moment) , for a volume of water V. , the rate of
change of the mass of the toxicant is given by: ^
+ advection + dispersion + sources - sinks
where K and K. are transfer rates [T ] into and out of level i.
i~ J. » i ii
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\
CONTINUOUS
DISCRETE APPROXIMA TION
CONTINUOUS
DISCRETE APPROXIMA 7VO/V
(a) Transport of substance in water.
(b) Transport of substance in food chain.
Figure 1. The Continuous Environment and Discrete Approximation
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If it is assumed temporarily that the mass/volume of each trophic level is
constant and that there is a single completely mixed volume, then Equation
(1) becomes:
, dV
Mi if = si-i,i Vi - siiv i + wi
i
where M± = M± V = trophic level mass, S^ ± = KI_I 1 M^, S±i = Kj_iMj_ and
W. = external sources and sinks. (Advective and dispersive terms can, of
course, be included). Now, it is noted that Equation (2) is identical to the
mass balance equation that results for a finite difference approximation for
water quality variables in physical space. In Equation (2), however, physi-
cal space is replaced by trophic space or ecological space. The question
posed earlier is thus made specific by Equation (2), i.e., what is the under-
lying continuous equation of which Equation (2) is an approximation?
The subscript i in Equation (2) essentially represents some ecological
variable in continuous trophic space. Therefore, in reality, Equation (2)
represents a mass balance around some region in ecological space represented
by an ecological coordinate. Such a coordinate would be distinct from the
usual physical coordinates of length, width and depth of a water body. A
generalized model would proceed by writing a mass balance equation that incor
porates both physical and ecological space. Such a derivation is part of a
class of models generally referred to as "Population Balance Models^" because
of their use in describing age distributions. A detailed review of such
models is given by Himmelblau and Bischoff (1968) and Rotenberg (1972).
CONTINUOUS MODEL
Following these authors, consider a function + 4 + aK«+ j, if
where v - dx/dt, v = dy/dt, v - dz/dt and v. = d?./dt, the time rate of
" Jr Z 11
change of the property i. Equation (3) is the general mass balance equation
for a toxicant in m+3 space and can be compared to the usual three-dimensional
-------
mass balance equation written only in physical space. In the case of food
chain modeling, a relevant metric must be chosen that can represent position
in trophic space. One such measure is the size or length of the organism
which through suitable allometric relationships can be related to the mass of
the organism (see Eberhardt, 1969). The choice of organism size as a suita-
ble metric in trophic space is advantageous from a field sampling point of
view. That is, it is considerably less difficult to fractionate samples by
size than by weight. Nets and filters can be easily used to divide a food
chain by size. An example of the continuous nature of the ecosystem is shown
in Figure 2. The overlapping size preferences of various stages of the ale-
wife illustrates the role that organism size plays in food chain transfers.
Futhermore, if there is no change in species composition, the length metric
may be related to the lipid content of organisms which may be of value in the
modeling of lipophilic compounds.
Of course, the use of an overall length metric does not permit a dis-
tinction to be made between organism types. Therefore, fish larvae and large
crustaceans look the same to this metric: "a centimeter is a centimeter".
It should be recognized also that introducing size dependence as an indepen-
dent variable greatly oversimplifies a complex ecosystem. Such dependence
implies that larger organisms prey on smaller organisms which is obviously
not always true. The framework given below, however, in principle permits
different size class interactions, but this is not pursued in this work. For
certain problem contexts, organism size may be very roughly correlated to
trophic position, but it is recognized that in general, trophic status and
organism size are not related. The approach here is to introduce an ecolog-
ically reasonable simplification into existing model structures to provide
additional analytical insight.
Conceptually, incorporation of other ecological properties is readily
accomplished in Equation (3) but obviously at the sacrifice of analytical
simplicity. The idea then is to describe the transport of a hazardous sub-
stance by how much of the total mass of the substance is located at various
size ranges of organisms and in various locations in physical space. For
organism size and one physical dimension, say longitudinal distance, Figure 3
shows the nature of ¥. As indicated, ¥ is a density function of the toxicant
for positions x and property C- The transport with organism size is consid-
ered as one-dimensional and not branched, such as in a food web. For a one-
dimensional food chain
Y = s f(L,t)
where s = mg toxicant/liter and f dL = fraction of total mass of toxicant
between trophic length L and L + dL, so that ¥ has units [mg toxicant/liter-
organism length]. Note that since ¥ is a continuous density function, the
amount of toxicant mass at a specific size is zero; only over some range of
organism size is there a non-zero amount of toxicant mass. This is a conse-
quence of the assumption that biological space is described by a continuum of
organism size. The special case of single organism aquaria experiments is
easily derived from this general view.
For a one dimensional size distribution and using the standard disper-
sion and advective terms in physical space, Equation (3) becomes
8
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SIZE RANGES OF ALEWIFE AND ALEWIFE PREY-LAKE MICHIGAN
(MORSELL AND NORDEN, 1968; NORDEN, 1968)
A. Alewife (predator)
ALEWIFE
LARVAL STAGES
AGE GROUPS
102 SIZE.pm i
B. Prey of larval alewife
CLADOCERANS
I I I I I II I I I I I I I I I
M: SIZE, jum
C. Prey of juvenile—adu/t alewife
COPEPODS
(1 mm)
CRUSTACEANS
(PONTOPOREIA)
CLADOCERANS
Figure 2. Range of Prey Size for Alewife Larval Stage and Juvenile-Adult
Age Groups 0-IV, Lake Michigan
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Density of toxicant in
physical and ecological space
Ecological space (e.g.
organism length) £
Fraction of toxicant in
JK \ region Ax,
Figure 3. Distribution of Toxicant in One-Dimensional
Physical and Ecological Space
10
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aw 3 3 S S 3W 3 PW
f1 + -5^- (v Y) + ^ (v V) + ^ (v T) + -^ (E —) + x1 (E I1)
dt ox x dy y dz z ox x x oy ydy
' "^\E T\ ) + TTT" (v_ i) = S (x,y,z,L,t)
dz zdz oL L
where v , v , v are net advective velocities in xyz, respectively, E , E
X y Z X V
and E are dispersion coefficients in xyz space, S represents the sources and
z
sinks of ^ and v = dL/dt, the "transfer velocity" with which the toxicant
L
is transported up the food chain represented by the metric, L.
A separate equation is necessary for the water phase of the toxicant and
is given by
If- + •£ (v c) + ^ (v c) + TT- (v c) •+ ^ (E |% + / (E |£)
3t 3x x ' %y y 3z z 3x x9x 3y "*"
r\ i\ °°
+ TT— (E —) = W (-x v 7 t} 4- r
-------
CONTINUOUS ECOLOGICAL SPACE IN WATER COLUMN
ORGANSIM SIZE, /urn
Pyto-
Silts—clays plankton Zooplankton Fish
\ " I
EXCHETION ABSORPTION
MASS
INPUT
<•-.
TOXICANT IN WA TER
Figure 4. Schematic of General Model for Single Completely Mixed Water Volume
_
0)
ea
o
"x
o
•*->
en
E
MASS TOXICANT IN
REG I ON L-L
-------
able, L, results in an added dimensionality to each equation. Thus, the com-
pletely mixed case, (which without L, would be represented by an ordinary
differential equation) is represented by a partial differential equation.
Similarly, the one-dimensional river case now also includes the additional
ecological dimension resulting in a time variable partial differential equa-
tion in two dimensions. In this work, the completely mixed water volume is
considered in some detail in order to develop the concepts and explore in a
preliminary way, the meaning and determination of the model parameters and
behavior.
TABLE 1
FORM OF HAZARDOUS SUBSTANCE TRANSPORT EQUATION
FOR DIFFERENT WATER BODY TYPES
Water Body Type Assumptions General Equation
Lake or Bay Completely Mixed 3¥ 3 L _ _,, .
Volume - V V3t V *T ^ 't}
River One-dimensional- 3¥_ :
no dispersion dt i
Estuary One-Dimensional- ^1 + 1 ^ + 1 ^_ (E A£i.)
Dispersive, advective 3t A 3x A 3x x 3x
S(x,L,t)
13
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SECTION 5
THE COMPLETELY MIXED WATER VOLUME CASE
If in Equations (4) and (5) the water body is assumed to be well mixed,
with no gradients in concentration, then the governing equation for V, the
toxicant density function is
v V
V (fr + ~^L" } = QTin " Q¥ +W'(L)-S'(L) (8)
where Q = mass transport through volume V, VF. = the input density function,
W'(L) = sources of ¥ and S'(L) = sinks of ¥. Equation (8) can be recognized
as an advective equation or maximum gradient equation identical to that used
in analysis of river systems but here derived for continuous organism size in
a completely mixed volume. Since the equation has no dispersion terms, there
is no "mixing" in the food chain.
The left hand side terms represent the rates of change of the density of
the substance with time and organism size. The first term on the right hand
side of Equation (8) is the mass transport of the density of the substance
entering the volume. This would include the mass of toxicant distributed in
the phytoplankton, zooplankton, and fish entering the completely mixed volume
V.
The mass transport Q is a quantity that reflects the transport of the
entire food chain and in general may be a function of L. For the passive
regions of the food chain (e.g. non-motile phytoplankton), Q represents the
water flow. For active regions (e.g. migratory fish), Q represents the
transport of toxicant out of the volume due to the velocity of those particu-
lar regions. The sources and sinks are discussed below. The behavior of
equations such as Equation (8) is well known. Solutions to distributed
sources and sinks, variable coefficients and time variable situations are all
obtainable. However, to provide a starting point some further assumptions
are in order. Assume that:
1) the uptake of the toxicant is proportional to the water concentra-
tion c and the biomass along L,
2) excretion of the toxicant occurs from the entire food chain accord-
ing to first-order kinetics on ¥,
3) yin = 0, i.e. there is no input of toxicant mass associated with
the food chain.
14
-------
The assumption of proportional uptake to the water concentration is par-
ticularly important since it implies linearity with input loads. The litera-
ture on laboratory experiments for the upper levels of the food chain appears
to justify this assumption. (For example, see Hansen et al, 1974, and
Vreeland, 1974 for the linear uptake of PCB's with water concentration for
pinfish and the American oyster.) However, in the micron and sub-micron
range of particles (e.g. clays), the adsorption phenomenon is not necessarily
linear and often varies logarithmically over wide ranges. For the descrip-
tion of a toxicant in the food chain however, the assumption appears reason-
able, at least for the higher levels.
Under these assumptions, Equation (8) becomes:
JW 3^T
V(ft + ^L > = •Q(L)>t' ' K(L)V
-------
dv V
jf- + K'f = ku(L)m(L)c (11)
OO
c=±[f + / K^dL] (12)
where K1 = Q/V + K = 1/t + K
° (13)
(for t = V/Q, the detention time)
and G = Q/V + A + / k m dL (14)
Ll
In general, all coefficients are functions of L. Thus the detention time t
represents the detention time of the entire food chain as well as the water.
Note that Equation (11) is an ordinary differential equation while its cou-
pled water equation is an algebraic equation that is easily solved once ¥ is
known. Several important special cases of Equations (11) and (12) can now be
explored.
CONSTANT COEFFICIENTS
Consider the organism size as divided into a series of regions each with
constant coefficients but each region is still continuous. The continuous
nature of the region distinguishes it from a compartment where a discretiza-
tion is performed. Also assume that the mass density function m(L) is a con-
stant in each region. Then Equation (11) for region i is:
v d¥i
Li cuT + KVi - kui mic l-l...r (15)
Equation (12) is:
i T, r L.
L -VL ) ^un (16)
Li
or c = -=[— + I K..s ] (16a)
lj V 11
r
and G = Q/V +A+ r /•, JT /,,, x
I Jk mdL (16b)
1-1 L± U
If it is temporarily assumed that the water concentration is fixed and known,
or that the contribution to c from the food chain is small, then the equa-
tions can be considered decoupled. The solution to Equation (15) for the
first region therefore is:
16
-------
me
VL
for LX 1 L 1 L2
(17)
where the subscripts for region 1 have been dropped and Y - is the initial
value obtained from the preceding region in the food chain. The first term
in Equation (17) represents the uptake from the water by the specific region
of the food chain and subsequent transfer up the food chain via the velocity
v . The second term represents the input of the toxicant from the preceding
food chain region and subsequent transfer. Equation (17) can also be written
as:
k c
v = rr- (1 - exp(-K'(L-L1))) + Y ,/m., exp(-Kf(L-L.)) (18)
K- 1 01 L£ 1
VL VL
where v hr.s units (Mass(Toxicant)/Mass(Biomass), i.e., a bioaccumulation fac-
tor. The quantity v is a measure often used in assessing levels of hazardous
substarces in the food chain for possible regulatory action. Figure 6 shows
the relationship between V, m and V. Note that the second term involves the
mass density for the region between L., and L-, m.., which indicates that as
the mass density decreases with increasing movement up the food chain, the
initial condition of the toxicant will be altered by the ratio of the adja-
cent biomass density. This can be seen if it is assumed that V has reached
its equilibrium value in the region preceding L^ to L». Then:
v ku c m01
01 " K>01
and VL = k C/K'Q- *s t*ie bioaccumulation factor in the region L to LI . Then
in Equation (18):
_ V- , ^01
K' L 1 1 m12 LI
This equation shows the effect of the varying biomass density along the food
chain. A 50% decrease of mass density from region LQ to L., doubles the ini-
tial bioaccumulation factor in region L- to L?.
The difficulty with the simple model of Equation (19) is that the bio-
mass density function is usually decreasing rapidly with L. Thus a large
number of regions would be required or abnormally unrealistic discontinuities
would occur at the boundaries of the ecological regions. A simple extension
of Equation (15) is to assume that:
mi(L) = (mo)iexp(-(b/v)1L) (20)
17
-------
V= 1////77
CO
CO
(c)
TOXICANT/LITER
MG BIOMASS/LITER
ACCUMULATION
I
ORGANSIM SIZE,
Figure 6. a) The Toxicant Density Function, b) The Biomass Density
Function and c) The Bioaccumulation Function
18
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Thus, the differential equation is now forced by an exponentially decreasing
biomass density function which eliminates discontinuities at region bound-
aries. The solution for a given region is:
k cm
) - exp (-K'L/VL» + ^expCK'L/v^ (21)
but since m is given by Equation (20) ,
\y k c
- = v = gTI£ (1 - exp(-((K'-b)/vL)L)) + V1exp(-((K'-b)/vL)L) (22)
Note that this equation is identical in form to Equation (18) except that the
coefficient K' is reduced by b. Equation (22) is to be preferred since there
are no mass discontinuities and hence a "smooth" calculation can be made of
the bioaccumulation factor as a function of trophic length. The structure
and meaning of Equation (22) is displayed in Figure 7.
As shown in Figure 7, three ranges of organism size are assumed. The
variation of the mass density is given by the three exponential functions in
Figure 7 (a). The two components of the bioconcentration factor given by
Equation (22) are shown: the effect due to food chain transport from the
preceding region and the effect due to uptake from the water and subsequent
accumulation within the region.
The water equation associated with this case is given from Equation (16)
together with Equations (20) and (21). Equations (16) and (22) form the
basic steady state model. These coupled equations can then be solved using
an iterative approach on the water concentration for given external input
conditions. Successive application of Equation (22) through any number of
regions in ecr Logical space permits computation of the distribution of the
bioaccumulation of the toxicant. Equation (16) which includes the external
mass input of the toxica.it, W, permits the concentration of the "maximum
permissible" discharge so as not to exceed toxicant levels at any point in
the food chain. Furthermore, these equations incorporate the physical as
well as biochemical interactions, as for example, between water detention
time, selective uptake and variable excretion. Yet, the entire food chain is
easily computed via Equation (22) in contrast to the special case of homoge-
neous compartments which requires simultaneous solution of algebraic equa-
tions.
VARIABLE COEFFICIENTS
It is known that the metabolism of organisms is related to the size or
mass of the organism (Eberhardt 1968, 1969). Norstrom et al. (1976) in their
work on a model of bioaccumulation recognized and incorporated, for example,
a log-log relationship of methylmercury and PCB clearance rates for fish over
the weight range of 1-300 gms. Additional extensions of these and other data
are discussed below where it is indicated that a log-log relationship of
clearance rate with organism length is justified. Further, since the veloc-
ity of transfer up the food chain is related to the grazing or predation
rate, it is reasonable to assume that v also depends on the organism length.
19
-------
REGIONS OF CONSTANT COEFFICIENT
(CLEARANCE, UPTAKE, WASH-OUT)
REGION 1 REGION 2 REGION 3
ORGANISM SIZE,
REGION 1
REGION 2
REGION 3
Q.
Q.
CC
e?
< .2
cc x
h- o
z *"
^ O)
LU c
o 3
"Z.
o
o
o
CO
I I
TOTAL BIOCONCENTRATION
BIOCONCENTRA TION FROM WA TER
| UPTAKE WITHIN REGION \
BIOCONCENTRATION FROM
PRECEDING REGION
ORGANISM SIZE, urn
Figure 7. A Three Region Model a) Variation of Biomass Density
b) Components of Bioconcentration Factor
20
-------
The uptake rate for some substances might also be expected to be related to
the size of the organism, as for example, through the mass of lipids which in
turn would result in differential solubilization of a substance.
Obviously, with all coefficients varying as complicated functions of or-
ganism size, a direct analytical solution of all functions of interest would
become cumbersome and unwieldy. However, the lessons learned in modeling
advective water quality systems can be applied here. The principal lesson
learned there is that for many practical applications the problem is best
handled by assuming constant coefficients over certain regions in space as in
the previous case. Since the variation in key parameters is significant over
ecological space, the preceding case can be extended to include logarithmi-
cally varying coefficients together with variable biomass density. The re-
sulting solutions can then be integrated numerically.
Thus let: b..
K - a-jL I (23a)
VL = a2L 2 (23b)
m = a3L 3 (23c)
The mass balance equation in V is then:
+ (Q/V + K)f = k a,L J c (24)
«"j U j
with K and VL given by (23a) and (23b) and k assumed constant. This equa-
tion is a variable coefficient linear equation with a variable distributed
input. The solution (see, for example, Thomann, 1972) is given by:
(25)
where: - -u*o
- L J ) (25a)
(25b)
ai = 1 + bl ~b2 (25c)
a2 = al/0t 1E2 (25d)
If data were available on the power laws of Equation (23), then Equation (25)
provides the density of the toxicant throughout the food chain without resort
to the designation of constant regions.
21
-------
SECTION 6
DATA ANALYSIS
LABORATORY DATA ANALYSIS
The continuous model, which uses trophic length as a measure of ecologi-
cal dimensionality provides a framework for a vast array of experimental data
that have been obtained on the fate of hazardous substances. The laboratory
experiments generally fall into three categories:
1) Bioconcentration and clearance tests using single organisms
2) Uptake and subsequent transfer from one organism to a second (and
third) organism in a "one-dimensional" aquarium test
3) Aquaria simulations of "model" ecosystem food webs.
In each category, the test may include input of the hazardous substance
directly into the water, indirectly through sediment that has a fixed concen-
tration of the toxicant or through "spiked" food. In terms of the continous
model, these laboratory experiments appear as delta functions along the orga-
nism size scale and permit estimates of model parameters at fixed organism
lengths. Thus, if an experiment is conducted on the uptake and clearance
rates of mature Daphnia magna, this provides an estimate for the given sub-
stance at an L of about 4,000 ym (4mm). The model indicates that if labora-
tory data of the first category are plotted as functions of organism size
then estimates of k (L) and K(L) can be obtained. Data of the second catego-
ry permit estimates of VT(L) and data of the third category permit determina-
tion of all the model coefficients under a simplification of a complex web to
a one-dimensional system.
Table 2 shows the range of sizes for different components of the aquatic
system. From the bacterial level to the higher organisms of large animals
and man, the total range is some six orders of magnitude. Although there is
considerable overlap in the components (especially between mature forms of
one component and immature forms of another), various regions of the length
scale do admit of some approximate ecological interpretation.
WATER UPTAKE AND EXCRETION - SOME ILLUSTRATIONS
As an illustration, data have been compiled on the variation of PCB
water uptake and clearance rates. The relationship with length of the organ-
ism is shown in Figures 8 and 9 and Tables 3 and 4. From Equation (22) and a
single organism length, the water uptake data as reported in the literature
represents the ratio of uptake to clearance, k /K = N, the bioconcentration
function. Figure 8 indicates a range of bioconcentration factors with orga-
22
-------
TABLE 2
RANGE OF ORGANISM SIZES
Component
Approx. Size
Dimension (ym)
Physical
Medium Clay
Silt
Sand
Biological
Virus, poliomyelitis
Bacteria
Fungi
Protozoa
Flagellates
Clliates
Algae, Blue-green
Diatoms, green algae
Zooplankton-rotifers
Nauplii
Crustaceans
Fish; small, immature
Fish; medium, juvenile
Fish; large, mature
Man - 6 ft.
0.5 - 1
1-20
20 - 150
0.25
0.5 - 3
2-20
10 - 50
30 - 200
5-20
10 - 100
50 - 200
100 - 500
400 - 4000
1000 - 104(lmm-lcm)
104 - 105(lcm-.lm)
105 - 106(0.1m-lm)
10
6.25
23
-------
102
gs io1
o~£
2 £
u- a
z a 10°
g "
1 1 1 §
o *-
^>
-------
TABLE 3
EXPLANATION OF SYMBOLS FOR FIGURE 8
PCB CONCENTRATION FACTORS
Symbol Organism or Organism Group
PCB Analyzed
Reference
• Spot (Leiostomus xanthurus) Aroclor 1254
O Mayfly nymth (Ephemera danica) Clophen A 50
d. Oyster (Crassostrea virginica) Isomer Mixture
$ Pinfish (Lagodon rhomboides) Aroclor 1016
Spot (Leiostomus xanthurus)
Aroclor 1254
Minnow (Cyprinodon variegatus) Aroclor 1254
Aquatic invertebrates; midge,
scud, mosquito larvae, stonefly
dobsonfly, crayfish
Daphnia magna
Pink shrimp (Penaeus duorarum)
Protozoa (Tetrahytnena
pyriformis)
Algae (Chlorella)
Aroclor 1254
Aroclor 1254
Aroclor 1254
Aroclor 1254
Clophen A 50
Marine phytoplankton - natural Isomer Mixture
assemblage
Particulates - Duwamish Estuary
- Hudson River
Moriarty (1975)
Sodergren and
Svensson (1973)
Vreeland (1974)
Hanson et al
(1974)
Duke and Dumus
(1974)
Hansen et al
(1973)
Sanders and
Chandler (1971)
Sanders and
Chandler (1971)
Nimmo et al
(1971)
Cooley et al
(1972)
Sodergren (1977)
Biggs et al
(1977)
Hafferty et al
(1977)
Unpublished
(1)
All tests on whole organisms or corrected to whole organisms
25
-------
TABLE 4
EXPLANATION OF SYMBOLS FOR FIGURE 9
PCB EXCRETION RATES
Organism or
Symbol Organism Group
Excretion
Measurement PCB Analyzed
IT
V
Pinfish (Lagodon whole
rhomboides) organism
Yellow perch whole
(Perca flavescens) organism
Bacteria whole
(Aerobacter organism
aerogenes, Bacillus
subtilis)
Aroclor 1016
Aroclor 1254
DDT
Reference
• Spot (Leiostomus
xanthurus)
i Man
f)l Rhesus monkey
whole
organism
Adipose
tissue
-
Aroclor 1254 Moriarty
(1975)
DDT Moriarty
(1975)
Allen et al
(1974)
Hansen et al
(1974)
Norstrom et al
(1976)
Johnson and
Kennely (1973)
CD
(2)
Note that some DDT excretion factors have been included
Estimated from field data
26
-------
nism size and except for one point does not appear to show any functional re-
lationship with size. If that point is accepted, however, then a rough ap-
proximation for the bioconcentration factor is:
NPCB ' PCB *-°1L'7 <26)
for L in m and k /K in (gm/1) and N___ is the bioconcentration factor for
U rUD
PCB in yg PCB/gm wet wt v yg/1. The bioconcentration factor could also be
taken as a constant over the entire size range at a value of approximately 50
yg PCB/gm T yg/1. This implies that k and K have the same slope in L. Also,
as an approximation, from Figure 9,
-------
of a toxicant onto mlcroparticles. Such an extension, however, is not ex-
plored here.
Table 5 summarizes some relationships of k /K and K; the bioconcentra-
tion factor and the excretion rate for different substances. Note should be
taken of the fact that the range of organism sizes over which data were avail-
able limits the overall comparison of the relationship between the substances.
Nevertheless, the accumulation of methyl mercury (as a function of length) is
somewhat less relative to PCB and DDT. Thus, at L = 10 ym, the k /K ratio
for mercury is 3.9 in contrast to the PCB ratio of 32 at the same length.
FIELD DATA ANALYSIS - PCB's IN LAKE ONTARIO
The laboratory data discussed above provide estimates of k and K as a
function of organism size. In the basic steady state model of Equation (22),
the parameters v and b must also be known. At present, it appears that ex-
perimental data are not available to permit independent estimation of the
velocity transfer coefficient, v which would require feeding experiments
ij
over a range of organism size. Nevertheless, estimates of b/v can be ob-
L
tained from field data on the distribution of biomass with particle size.
With data available and the toxicant concentration for various levels in the
food chain, an estimate can be made of the components of Equation (22) al-
though such an estimate will not be completely independent of the data it-
self. The analysis of the modeling framework at this stage therefore does
not constitute a verification of the model, but a type of first calibration.
The primary benefit of such an analysis is that it places the available field
and laboratory data in an analytical framework to gain further insight into
the nature of the accumulation of hazardous substances in the food chain. In
order to illustrate the use of the model in this type of setting, the concen-
tration of PCB's in Lake Ontario is analyzed.
AVAILABLE DATA ON LAKE ONTARIO
As part of the IFYGL Program, Haile et al. (1975) have obtained data on
the PCB concentrations in Lake Ontario fish, water, sediment, net plankton,
Cladophora and benthos. Their results together with data obtained by the
Ontario Ministry of the Environment (1976) are summarized in Table 6. The
data on a wet weight basis show a general bioaccumulation of PCB's from the
smaller organisms to the larger coho salmon. The data on the salmon are
generally from inshore stations while the data on net plankton and the ale-
wife group include both inshore and open lake stations. As noted by Haile
et al. (1975), the water data includes both dissolved and micro-particulate
fractions. However, following the work of Zitko (1974) who showed that PCB's
on suspended solids can be bioaccumulated by juvenile Atlantic salmon, it is
assumed that the total PCB concentration in the water is available to the
food chain. The size ranges in Table 6 that were assigned to each component
are somewhat arbitrary, although realistic. As noted in Section V, such a
division is simply a convenience in computing the simpler steady state model
of Equation (22).
28
-------
TABLE 5
SOME RELATIONSHIPS BETWEEN UPTAKE AND EXCRETION AND ORGANISM SIZE(1)
K = a2L
Substance al
PCB
DDT
.01
.45
bl
0.70
0.35
a2
80
15.8
b2
-.80
-.64
Size Range of
Data (urn)
104-105'5
10°-106
(2)
References
1-8
1,2,5,9,
,10,11
NJ
SO
Methyl Mercury
132
-.90
10-10
1,12-18
(1)
ku/K ~ Pg/gm wet wt yg/1; K - I/day; L - ym
(2)
References: 1. Moriarity (1975)
2. Sodegren and Svensson (1973)
3. Vreeland (1974)
4. Hansen et al (1974)
5. Duke and Dumas (1974)
6. Hansen et al (1973)
7. Haque et al (1974)
8. Norstrom et al (1976)
9. Reinert et al (1974)
10. Johnson and Kennedy (1973)
11. Johnson et al (1971)
12. de Freltas et al (1974)
13. Livingston (1975)
14. Hartung (1976)
15. Sloan et al (1974)
16. Hardcastle and Mavichakana (1974)
17. Burrows and Krenkel (1973)
18. Cross et al (1973)
-------
TABLE 6
SOME DATA FOR LAKE ONTARIO
PCB CONCENTRATION (AROCHLOR 1254 EQUIVALENT)
Component
Std. Assumed Range of
Average Deviation Organism Size
(yg/gm(wet wt»
(ym)
(1)
Net Plankton
(64 ym mesh)
Alewife, smelt
slimy sculpin
(1)
Coho Salmon
(2)
0.72 0.35 100 10
3.24 2.14 104 2.5-105
6.47 2.85 2.5-105 106
Water (1,3)
55.4
21.1
(1) Haile et al (1975) (2) Ont. Min. Env. (1976)
(3) Concentration in ng/1, dissolved
+ particulate, <64ym
30
-------
Data on biomass throughout the entire food chain are somewhat limited
especially in the upper trophic levels. This is due partly to the difficulty
of obtaining reliable estimates for fish biomass. However, at the lower end
of the organism size scale, data are available from particle counts given by
Stoermer et al. (1975) and from acoustical measurements made by McNaught et
al. (1975). Stoermer1 s data cover the range from 5 to 150 ym and McNaught 's
data span the region from 800 ym to about 5,000 ym. The lower range there-
fore provides data on particle density in the region <64 ym, the mesh size
used by Haile et al. (1975). The data for 800 ym to 5,000 ym provide biomass
information on the net plankton.
The estimated mass density function is obtained from
m... = i - l....n (29)
1+1
where c. ... is the concentration (e.g. number particles/100 ml) in the size
1 y 1/T"1
range L. to L (ym), 1 is the total number of size ranges and m is the
mass density for the region in concentration units/ym, plotted at the end of
the region. Figure 10 shows a semi- log plot of the mass density estimates as
a function of particle size. As shown, the results of this limited analysis
of the particle and acoustical data indicate regions where one might assume an
exponential decrease in biomass density as given by Equation (20) . Note also
that the biomass. density drops by several orders of magnitude over the range
of the data. The slope of the density function, b/vT [ym ] is a ratio of
Li
model coefficients required by Equation (22). The quotient represents the
ratio of biomass respiration to the rate at which biomass is transferred up to
higher trophic levels via predation. The model requires the slope of the den-
sity function over the entire length scale. Thus, the data of Figure 10, were
used to extrapolate the slope of the density function out to the upper limit
of 10 ym. This is admitedly a hazardous (?) extrapolation and illustrates
the need to obtain biomass data throughout the food chain. The relationship
for the mass slope using Figure (10) is therefore:
b/v. =6.3 L"1'05 (30)
Li
for b/v in [ym]~ and L in ym. Equation (30) was used to estimate b/v for
Li Li
the food chain Equation (22).
The organism size range for Lake Ontario was divided into three continu-
244 5 56
ous regions: 10 -10 ym; 10 -2.5 10 ym; 2.5 10 -10 ym. These regions are not
compartments in the classical sense but are rather continuous domains with
constant coefficients. Estimates of k , K for PCB's were used from Figures 8
u
and 9 in Equation (22) to obtain a good correlation to the observed data.
This provided estimates of the coefficient groupings:
k /(K'-b) and (K'-b)/vT
U Li
31
-------
8
o
o
CO
o
\-
CL
u_
O
a:
LU
CO
ID
Z
4
2
0
2
•4
-8
• Slope = 0.175 [jum'1]
i\
: \-
55lope = 0.06 [/um'1] E
3.
o
Q
Data from
- Stoermer et al. (1975)
Station No. 45
_ 5/2/72-5/5/72
I I I I I I !
0
20 40 60
Data from McNaught
etal. (1975)
Slope = 8.33 X 10'4 [jurrT1 ]
80 0
ORGANISM SIZE,
2000
4000
Figure 10. Lake Ontario Mass Density as a Function of Organism Size
32
-------
The first group, k /(K'-b) was used to obtain an estimate of K'-b which to-
gether with the second coefficient K'-b/vT was used to obtain VL> Then,
given b/vT from the mass density data, b was estimated. This value was then
Li
used with the original estimate of K'-b to close the estimation procedure on
K'. The "free" parameter was therefore v but an external check on the mag-
J-i
nitude of v_ was provided by the b/v_ ratio from the biomass data.
L Lt
The results of applying Equation (22) to the PCB data of Table 6 are
shown in Figure 11 and the associated coefficients are given in Table 7. The
two principal mechanisms of the steady state model are shown in Figure 11.
The uptake directly from the water and subsequent transfer (the first term of
Equation (22)) is seen to increase with increasing organism size". ^At the
upper levels, the excretion rate is low, transfer velocity has increased and
a rapid rise is calculated for the PCB concentration. Figure 11 also shows
the residual PCB transferred from lower food chain levels. Again, because of
the decreased excretion rate, increased transfer velocity through the food
chain and the reduced mass density at the higher levels, PCB concentrations
are retained over the larger segments of the food chain.
Figure 11 shows that for the salmon, about 33% of the observed 6.5 Ug
PCB/gm fish is due to transfer from lower levels in the food chain and about
67% from direct uptake. The build-up of PCB's therefore in the Lake Ontario
ecosystem is postulated to be due to a complex interaction between water up-
take rate, excretion rate, rate of transfer through the food chain and de-
crease of mass density with organism size. It should also be recalled that
the toxicant concentration in the food chain is linearly related to the water
concentration which in turn (Equation 23) is linearly related to the input
PCB mass loading. In principle, then, one could estimate the required input
loading such mat a given level of PCB concentration would not be exceeded in
any region of the food chain. However, sufficient data are not yet available
on the present input to Lake Ontario to permit such a definitive calculation.
Before such a calculation is made it would be preferable to estimate the
water concentration independently of the measured values given input mass
loading and estimates of removal rates.
However, one can estimate the total water (dissolved and microparticu-
late) concentration that would be necessary so as not to exceed certain
levels in the food chain, if the coefficients used herein are considered rea-
sonable. If 5 yg PCB/gm wet wt. is used at 10 ym as a level, than the water
concentration would have to be about 36 ng/1 or about 667, of the present 55
ng/1.
33
-------
OJ
-p-
10
QJ
cn
8 4
Q_
05
OBSERVED DATA
±7 STD DEVIATION
TOTAL ACCUMULATION
ABSORPTION
DIRECTL Y
FROM WATER
103 104
ORGANISM SIZE,
105
106
REGION 1, 64-At MESH HAUL
REGION 2 | REGION 3
ALEWIFE, SMELTS, SCULPIN SALMON
Figure 11. Analysis of PCB's in Lake Ontario
-------
TABLE 7
COEFFICIENTS USED IN ANALYSIS OF PCB DATA WITH
STEADY STATE SIZE DEPENDENT MODEL
Trophic Region
Coefficient 102-104ym 104-2.5-105ym 2.5-105-106ym
Water Uptake - k 0.5 0.38 0.23
-1 U
(gms/1-day)
Excretion - K1 0.05 0.0072 0.0025
(day)'1
Transfer Velocity - VT 12 190 728
Li
(ym/day)
Biomass Respiration - 0.01 0.0024 0.001
b (day)'1
(K'-b)/vL 3-10"3 2.5-10'5 2-10~6
(ym)'1
ku/(K'-b) 13.4 79 158
(gm/1)'1
35
-------
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Anonymous. 1976. Ontario Research Program to Monitor PCB Levels. July 2,
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14
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Cross, F.A. et al. 1973. Relation Between Total Body Weight and Concentra-
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36
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37
-------
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600/9-76-016. pp. 619-623.
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-78-036
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Size Dependent Model of Hazardous Substances in Aquatic
Food Chain
5. REPORT DATE
April 1978 issuing date
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Robert V. Thomann
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Manhattan College
Bronx, New York 10471
10. PROGRAM ELEMENT NO.
IBA608
11. CONTRACT/GRANT NO.
R803680030
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory-Duluth, MN
Office of Research and Development
U.S. Environmental Protection Agency
Duluth, Minnesota 55804
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA-600/03
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A model of. toxic substance accumulation is constructed that introduces organism size as
an additional independent variable. The model represents an ecological continuum
through size dependency; classical compartment analyses are therefore a special case of
the continuous model. Size dependence is viewed as a very approximate ordering of
trophic position.
The analysis of some PCB data in Lake Ontario is used as an illustration of the
theory. A completely mixed water volume is used. Organism size is considered from
100 ym to 10 urn. PCB data were available for 64 ym net hauls, alewife, smelt, sculpin
and coho salmon. The analysis indicated that about 30% of the observed 6.5 Ug PCB/gm
fish at the coho salmon size range is due to transfer from lower levels in the food
chain and about 70% from direct water intake. The model shows rapid accumulation of
PCB with organism size due principally to decreased excretion rates and decreased
biomass at higher trophic levels. The analysis indicates that if a level of 5 yg
PCB/gm at 10s ym is sought, total (dissolved and particulate) water concentration would
have to be about 36 ng/1 or about 66% of the present 55 ng/1.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Hazardous Materials
Contaminants
rfater Pollution
Mathematical Models
Lakes
Great Lakes
PCB
Food Chain
57H
48G
43F
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
47
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
40
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