PB84-155993
    Age  Dependent Model of  PCB in a
    Lake Michigan Food Chain
    Manhattan Coll., Bronx, NY
    Prepared  for

    Environmental Research Lab.-Duluth, MN
    Feb 34



U.S.         of Commerce
!1«i*,r.'4 T<»c5 -Rca! Information Serriee

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                                             EPA-600/3-84-026
                                             February 1984
AN AGE DEPENDENT MODEL OF PCB IN A LAKE MICHIGAN FOOD CHAIN
                            by

                     Robert V. Thotaann
                     John P. Connolly
                     Manhattan College
           Environmental Engineering and Science
                   Bronx, New York 10471 .
          Cooperative Agreement No. CR805916010
                      Project Officer

                   William L. Richardson
               Large Lakes Research Station
         Environmental Research Laboratory-Duluth
                Grosse lie, Michigan 48138
               ENVIRONMENTAL  RESEARCH LABORATORY
             OFFICE  OF  RESEARCH  AMD  DEVELOPMENT
            U.S.  ENVIRONMENTAL PROTECTION AGENCY
                      DULUTH,  MM  55804

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                                    TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing)
 \. REPORT NO.
  EPA-600/3-84-026
              3. RECIPIENT'S ACCESSION NO.    _
                     P88 IT   15599 3
4. TITLE AND SUBTITLE
 An  Age  Dependent Model of PCB  in  a  Lake Michigan Food
 Chain
                                                            5. REPORT DATE
                                                               February 1984
              6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)

 R.  V.  Thomann and J. P. Connolly
                                                            a. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
 Manhattan College
 Environmental Engineering and  Science
 Bronx,  New York  10471
                                                             10. PROGRAM ELEMENT NO.
              11. CONTRACT/GRANT NO.
                                                            CR805916
 12. SPONSORING AGENCY NAME AND ADDRESS
 Environmental Research Laboratory
 Office  of Research and Development
 U.S.  Environmental Protection Agency
                     55804
                                                             13. TYPE OF REPORT AND PERIOD COVERED
              14. SPONSORING AGENCY CODE
                EPA-600/03
15. SUPPLEMENTARY NOTES
16. AbSTRACT

 An  age-dependent food chain model that.considers species bioenergetics and toxicant
 exposure through water and food  was developed.  It was  successfully applied to PCB
 contamination in the Lake Michigan lake trout food chain represented by phytoplankton,
 Mysis,  alewife, and lake  trout.   The model indicated  that  for the top predator lake
 trout,  PCB exposure through the  food chain can account  for greater than 99 percent
 of  the  observed body burden.   A  simple steady-state computation indicated that
 ratios  of chemical concentration in predators to that in prey in feeding experiments
 may be  as low as 0.2 and  still result in significant  food  chain transfer.

 It  was  estimated that a criterion specifying that PCB concentrations of all ages of
 lake trout be at or below 5 yg/g (wet weight) in the edible portion would require
 that dissolved PCB concentrations be reduced to somewhere  between 0.5 and 2.5 Wg/1.
 The range reflects uncertainty in the PCB assimilation  efficiency of the species and
 the dissolved PCB concentration.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                               b.IDENTIFIERS/OPEN ENDED TERMS
                           c.  COSATI Field/Group
 8. DISTRIBUTION STATEMENT

  Release to Public
19. SECURITY CLASS (This Report/
  Unclassified
21. NO. OF PAGES
   123,
20. SECURITY CLASS 
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                      NOTICE

This document has been reviewed in accordance with
U.S. Environmental Protection Agency policy and
approved for publication.  Mention of trade names
or commercial products does not constitute endorse-
ment or recommendation for use.
                       11

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                                   CONTENTS
                                                                         Page
Abstract	 IV




Figures	  V




Tables	 IX




Acknowledgements	  X




Section 1.   INTRODUCTION	  1




Section 2.   CONCLUSIONS	  8




Section 3.   RECOMMENDATIONS	 10




Section A.   COMPILATION AM) ANALYSIS OF PCB DATA	 12




Section 5.   AGE DEPENDENT MODEL: THEORY	 27




Section 6.   ESTIMATION OF MODEL FOOD CHAIN INTERACTIONS AND PARAMETERS.. 46




Section 7.   MODEL CALIBRATION	 73




Section 8.   MODEL SENSITIVITY	 88




Section 9.   LAKE TROUT RESPONSE DUE TO REDUCED WATER CONCENTRATION	 99




References	106

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                                  ABSTRACT

     An age-dependent food chain model that considers species bloenergeticc
and toxicant exposure through water and food is developed.   It is success-
fully applied to PCS contamination of the Lake Michigan lake trout food chain
represented by phytoplankton, Mysis, alewife, and lake trout.  The model in-
dicates that for the top predator lake trout, PCB exposure through the food
chain can account for greater than 99 percent of the observed body burden.  A
simple steady-state computation indicates that ratios of chemical concentra-
tion in predators to that in prey in feeding experiments may be as low as 0.2
and still result in significant food chain transfer.
     It is estimated that a criterion specifying i^.at PCB concentrations of
all ages of lake trout be at or below 5 ug/g (wot. "'-'eight) in the edible por-
tion would require that dissolved PCB concentrations be reduced to somewhere
between 0.5 and 2.5 ng/£.  The range reflects uncertainty .In the PCB assimi-
lation efficiency of the species and the dissolved 1-fB concentration.
     This report was submitted in fulfillment of Cooperative Agreement No.
CR805916010 by Manhattan College under the sponsorship of the U.S. Environ-
mental Protection Agency.  This report co'^rs the project period May 1, 1978
to September 30, 1981.
                                    IV

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                                   FIGURES


Number                                                                   Page

   1.   Lake Michigan                                                      2

   2.   Historical trend of PCB concentration in small fish of Lake        3
        Michigan (replotted from Neidermeyer and Hlckey, 1976; also
        data from USF & WLS).

   3.   PCB concentrations Jn lake trout (whole fish), 1971-1979.          5
        ( ) • No. samples,  0 • Arith. mean, A • median. Range »
        + 1 Std. deviation.

   4.   Sampling regions for 1971 fish contaminant survey by Veith        15
        (1973, 1975).

   5.   PCB concentrations (whole fish) as a fvnction of weight,       .   16
        1971 Data from Veith (1975).

   6.   PCB concentrations (whole fish) as a function of % lipid.         17
        1971 Data from Veith (1975).  (Numbers in parentheses are
        fish species, xsee Figure 5 for identification).

   7.   PCB concentrations in echo salmon, 1971-1976.                     19

   8.   PCB concentration in alewife as a function cf age, 1971.          20

   9.   PCB concentration in lake trout ai-- a function of age clasa        21
        for 1971 and 1975.

  10.   Variation of PCB for lake trout from 1971-79 for age              23
        classes 2-6 years.

  11.   Variation of PCb for lake trout from. 1971-79 for age              24
        classes 7-10 years.

  12.   Relationships between PCB and % lipid for Ifike trout froa         25
        different sets.

  13.   Schematic of compartment definition for  a) age dependent         33
        model,  b) simplified steady state model.

  14.   Illustration of meaning of w.(t) and v (t) showing as an          36

        example a 0-i year old and 1-2 year old alewife.

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                             FIGURES (continued)
Number                                                                     Page

  15.   Illustration of equilibrium conditions for concentration of         40
        contaminant in organism.  (a) Exponential increase in organ-
        ism weight, Eq. (11); (b) increase in contaminant body bur-
        den, Eq. (20); (c) increase in contaminant concentration to
        equilibrium (steady state) level, Eq. (21).

  16.   Effect of food chain transfer ratio, f, on ratio of chemi-          45
        cal concentration in top predator from water plus food to
        that from water only.  Equilibrium conditions, constant BCF
        and f ratio along food chain.

  17.   Percent of total Hysis captured in the water column and             49
        fcund in alewife stomach in relation to Hyslo length for
        two sampling dates.  (From Janssen and Brandt, 1980),

  18.   Feeding Interactions specified in the model for alewife and         50
        Hysis.

  19.   Observed Incidence of fish and invertebrates in lake trout          53
        stomachs in relation to lake trout length and computed age.

  20.   Distribution, by sire, of alcwives found in various size            5
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                             FIGURES (continued)


Number                                                                    Page

  27.   Comparison between observed and computed ingestion rates in        68
        relation to wet weight.

  28.   Comparison between observed and computed excretion rates of        71
        PCB in relation to wet weight.

  29.   Comparison of observed PCB concentrations in alewife and lake      74
        trout with calculated concentrations from basic model.

  30.   Average PCB concentration in each of the 4 species included        77
        in the food chain model.  Values indicated are arithmetic
        average over all age classes.

  31.   Computed PCB concentration factor for lake trout due to PCB        79
        uptake from vater and from water and food.

  32.   Coiaputed PCB concentration in lake trout due to PCB uptake         80
        from water and from water and food.

  33.   Comparison of observed PCB concentrations in alewife and lake      83
        trout with calculated concentration from lipid-deper.dent model.

  34.   Comparison of food chain model  and octanol/water partitioning      85
        to llpld tissue of lake trout.

  35.   Coaputed PCB concentration in aleuife from octanol/water par-      86
        titionlng calculation.

  36.   Computed lake trout PCB concentrations at PCB assimilation         89
        efficiencies of 0.65, 0.8, and  0.95.

  37.   Conputed lake trout PCB concentrations at the calibrated ax-       91
        cretion rate and zero excretion rate.

  38.   Computed alewife and lake trout PCB concentrations at dls-         93
        solved PCB concentrations of 2  pg/£, 5 vg/l and 10 Pg/£.

  39.   Computed alewife and lake trout PCB concentrations for models      94
        recalibrated to dissolved PCB concentrations of 2 pg/£ and
        10 pg/1 by alteration of PCB assimilation efficiencies.

  40.   Conputed lake trout PCB concentrations for three trophic           96
        level and four trophic level food chain structures.
                                   Vll

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                              FIGURES (continued)
Number     •                                                              Page

  41.   Computed and observed lake trout PCB concentrations In rela-      98
        tion to wet weight for native trout growth rates (tfl) and
        stocked trout growth rates (02).

  42.   Projected response of different age lake trout to a five-fold    100
        decrease in dissolved PCB concentration - growth rate #1 for
        pre-stocked period.

  43.   Relationships between equilibrium PCB concentration in 11 year   101
        old lake trout and dissolved PCB water concentrations, growth
       •rate #1 = pre-stocked period; growth rate 62 « stocked period.

  44.   Calculated relationship between age class of lake trout and      104
        required dissolved PCB water concentration to meet whole fish
        concentration of 5-10 v-'g/g(w).  Growth rate $2 for stocked lake
        trout.
                                      Vll 1

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                                   TABLES


Number                                                                     Page

   1.   PCS Concentration (Whole Fish) la Lake Trout of Lake Michigan        4

   2.   PCB in Surficial (0-3 ca) Lake Michigan Sediments (1975)            13

   3.   Fraction of Total Alewife Consuseption on Plankton and Each          51
            q Age Class
   4.   Fraction of Total Lake Trout Consumption on Each Mysis and          56
        Alewife Age Class

   5.   Parameter Values Used in Calibration of Modal                       75

   6.   Lake Trout Llpid Content Data Compiled in Relation to Age Class     82

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                               ACKNOWLEDGEMENTS

     Special thanks are due to the USEPA Large Lakes Research Station, Grosse
lie, Michigan for the support to carry out this research effort.   Particular
gratitude is extended to William Richardson for his cooperation in cany areas
of data compilation and evaluation and to Nelson Thomas for his continuing
support and understanding of the basic research aspects of food chain transfer
of toxicants.
     The graduate Research Assistants who also contributed substantially to
this—effort, through their tireless efforts in running and re-running seetn-
ingly endless calculations are Janice Rollwagen and Robert J. ThcT»ann; special
appreciation is extended to them.
     Of course, our colleagues at Manhattan College, specifically Dominic
Oi Toro, Donald 0'Conr->r and Walter Matystik, all helped by their discussions
and direct assistance.  The courteous and patient typing by Eileen Lutoroski
and Margaret Cafarello is also greatly appreciated.

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                                 SECTION 1
                               INTRODUCTION

BACKGROUND
     The fishes of Lake Michigan (Figure 1) have been a matter of study and
concern for a great number of years (Grt. Lakes Basin Comm., 1975;  Int.
Joint Comm., 1978).  The concern was directed toward maintaining a viable
sport and commercial fishery in the face of increased fishing pressures and
predation of the lake trout by the sea lamprey.  Beginning about 10-15 years
ago, concern was expressed over the concentration of potentially toxic sub-
stances in desirable sport and commercial fish.  The elevated levels of DDT
exceeded the guideline value of 5 pg/g(w) (?(w) = grams wet weight) and as a
result DDT was banned in 1972.  Similarly, the elevated concentrations of
polychlorinated biphenyls (PCB) in the fishes of Lake Michigan, particularly
the lake trout (Salvelinus nacaycush) were a matter of significant concern.
Concentrations of PCB in the lake trout in 1971, for example, ranged from
5-20 pg/g(w), substantially above the U.S. Food and Drug Administration (FDA)
guidelines of 5 pg/g(w) in the edible portion of fish.  Several fishing bans
have been issued concerning the consumption of fish contaminated with PCBs.
In 1978 conoercial fishermen harvested more than 43 million pounds of alewifc
for fish neal.  But in 1980, the catch dropped dramatically because of recog-
nition that the PCB concentration of alewives exceeded the FDA guideline of
2 yg/g(w) for fish weal (Anon, 1981).  This particular chemical had been in
use within the Lake Michigan drainage basin for more than 20 years when it
vas restricted in sales (except for minor uses) in 1971.  A full ban was inr
stituted several years later.
     Neiderseyer and Hickey (1976) analyzed the PCB concentration in museum
specimens of small fish from Lake Michigan and observed a marked increase
beginning in the 1950s.  Their results are shown in Figure 2 together with
additional data on PCB concentration from the U.S. Fish and Wildlife Service
(USF&WLS).  Concentration appears to peak in the early 1970s.  The histori-

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                      MICHIGAN
WISCONSIN

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                                                            N
                            GARY

                                INDIANA
                                                   0  25  50  75 100    km
                                                   bnnsrhssgsaj     I
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                       Figure-1.   Lake Michigan

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                               APPROXIMATE TREND
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   1930 1935 1940  1945  1950 1955  1960 1965  1970  1975 1980

                               YEAR

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cal record for PCBs in the top predators of the lake such as the lake trout
is less extensive.  Figure 3 and Table 1 show the general trend in PCB for
the trout (whole fish) for the period 1971-1979 from several sources (Veith,
1975; EPA STORET; USF & WLS; WAPORA, 1981).  As noted previously the concen-
tration of PCB exceeds a guideline level of 5 pg/g(w) although this is for
the edible portion of the fish.  The data indicate that for the years 1971-
77, the mean and median were greater than 13 pg/g(w).  An apparent decline
began in 1978 where mean end median values dropped to 5.8 and 3.3 lJg/g(w)
respectively.  The 1979 data however indicate mean and median values of 10
and 8 pg/g(w).  Across all aga classes therefore there appears to have be^n
some decline in the PCB concentration in the lake trout although the decline
is not dramatic and a longer tern data base is necessary to ascertain the
actual trend.  This is especially true when the variation in the data as
indicated by the standard deviation of Figure 3 is recognized.  Additional
data collected through the Great Lakes Environmental Contamination Survey
(GLECS) in 1975 are for filets only and averaged about 4.5 pg/g(w).
           TABLE 1.  PCB CONCENTRATIONS (WHOLE FISH) IN LAKK TROJT
                             OF LAKE MICHIGAN^

YEAR
1971
1972
1973
197A
1975
1976
1977
1978
1979
MEAN
(Ug/g(w)
13.7
17.9
18.0
17.7
11.7
17.4
13.3
5.8
10.1
STAND.
DEV.
4.5
9.2
1.0
7.9
6.5
17.1
4.4
7.8
7.3
MEDIAN
(Vig/g(w)
13.4
15.4
17.8
20.7
7.3
14.6
14.8
3.3
8.0
NO. OF
FISH
139
1°
30
48
48
40
105
42
182

(1)
    Compiled from Veith (1975), EPA STORET, USF & WLS, and Wapora (1981)

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THE ISSUE OF WATER UPTAKE VS.  FOOD CHAIN TRANSFER
     These data on PCBs in the Lake Michigan fish indicate  a substantial  con-
centration of this substance in the lake trout.   In order to properly under-
stand the mechanisms that give rise to the observed data, it is  necessary to
analyze the data through use of a model of the principal phenomena of chemi-
cal uptake and transfer.  These mechanisms include two principal routes:
     1)  Uptake of PCB directly from water
     2)  Accumulation of PCB through consumption of contaminated food
The significance of the food chain route, i.e. the degree to which a chemical
is accumulated in an organism by predatlon has been the subject  of consider-
able debate and confusion.  For example, Scura and Theilacher (1977) in eval-
uating chlorinated hydrocarbon (CHC) data on a laboratory food chain concluded
that "CHC accumulation is not  a food chain phenomenon but rather the result  of
direct partitioning of the compounds between the seawater and the test organ-
isms."  On the other hand, Welninger (1978) using a model of PCB accumulation
in the lake trout of Lake Michigan concluded that "Direct upteke of PCBs  can
only account for 2-3% of total observed.PCB accumulation by adult lake- trout
although this ruute is more important for juveniles."  Also Thomann (1981),
in analyzing PCB data from a variety of water bodies, concluded  that for  top
predators in the natural environment, the data suggest that the  PCB concen-
tration is about one order of magnitude greater than would  result from uptake
from the water alone.
     It has also been suggested implicitly (Neeley et al.,  1974; Kenaga,  1980)
and explicitly (Neeley, 1979)  that the maximum environmental concentration in
fjsli can be estimated without  recourse to a food chain route. These approaches
assume that uptalce from water is the principal route and for lipid soluble con-
pounds such as the PCBs, the concentration in fish is related directly to the
octanol-water partition coefficient of the compound.  It is assumed in these
approaches then that a first approximation to expected levels of a chemical
can be obtained either from simple partitioning concepts (Neeley et al.,  1974;
Kenaga, 1980) or from a simple model of direct uptake from the water (Neeley,
1979).

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     The issue of whether a simple calculation of uptake of a chenical directly
from the water is sufficient relates to the degree to whi-h such a calculation
would actually reproduce observed field data for important  species such as the
lake trout.  If such a calculation does account for the observed data in the
field, then there is no need for a model that includes a food chain component.
If a simple partitioning calculation fails to reproduce the observed data,
then the principal feature of the food chain must be included.

OBJECTIVES OF RESEARCH
     The principal objectives of this research therefore are to
     1.  develop an age-dependent food chain model of uptake and transfer
         of potentially toxic chemicals
     2.  determine the relative importance of water uptake  and  food chain
         routes of PCS in a Lake Michigan food chain with specific empha-
         sis on lake trout
     3.  test the utility of simple partitioning approaches for PCE that
         do not Include the food chain route
     A.  provide a preliminary projection of response in PCB concentra-
         tion in the lake trout following a reduction in PCB water con-
         centration.
     Although the age-dependent model for transfer of chemicals in aquatic
food chains is calibrated in this work with the PCB data of the Lake Michigan
food chain including the lake trout, a subsidiary and equally important objec-
tive of this research is to provide a general framework that would be appli-
cable in a variety of other problem contexts.

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                                  SECTION 2
                                 CONCLUSIONS

     The contamination of Lake Michigan alewife and lake trout by PCB can be
adequately modeled using an age-dependent computation that considers species
bioenergetics and uptake of PCB from water arid food.  The model successfully
reproduces the age-dependent trends and magnitude of PCB contamination ob-
served in 1971.
     Both the model and the PCB data compiled for this study indicate that
food chain transfer is a significant route of contamination.  Data from thir-
teen species of fi&h suggest an increase in PCB concentration as one proceeds
up the food chain to the top predators.  Transfer of PCB through the food
chain is the major contributor to calculated PCB concentrations, accounting
for greater than 99% of the body burden in adult lake trout.  A simple steady-
state computation indicates that ratios of chemical concentration in predators
to that in prey in feeding experiments may be ss low as 0.2 and still result
in appreciable food chain transfer.
     An empirical relationship between lake trout excretion rate and lipid
content significantly improved the lake trout calibration, suggesting that
lipid tissue is an important factor in PCB dynamics.
     A simple empirical correlation between octanol/water partitioning of PCB
and partitioning between water and fish lipid tissue failed to reproduce the
observed concentrations in alewife and lake trout.  It is concluded that al-
though this simple partitioning approach may be useful in assessing trends,
it cannot estimate actual concentrations, especially in higher trophic level
species, because it does not consider food chain transfer.
     Projections of the response of the lake trout food chain to reduced water
concentrations indicate that a period of about 5 years is needed to reduce
whole body PCB cop.centr.itions in upper nge cl.iss l.Tkc trout.  In order tn II.IVP
the HCB concentratlonr of all flge classes of Inke trout at or below 5 up,/j>(w)
in the edible portion,"it is estimated that the dissolved water concentrations
                                      8

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would have to be between 0.5-2.5 ng/t.  The range results from the uncertainty
of the parameter values in the model.  These water concentrations represent a
75-95% reduction of apparent 1961-1971 water concentrations.  Young age classes
can generally be exposed to higher water PCB concentrations than older age
classes without exceeding the objective of 5 ug/g(w).  As a result, if water
quality projections indicate a lower bound in the achievable PCB water concen-
trations, a size dependent fish consumption guideline can be developed.

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                                  SECTION 3
                               RECOMMENDATIONS

     This- analysis of the PCB contamination of a Lake Michigan food chain has
illustrated gsps of knowledge that add uncertainty to the estimation of the
effect of concentration reductions.  These gaps are most significant in regard
to the compound-related parameters needed by the model, i.e., assimilation
efficiency and excretion rate.  It is therefore recommended that experimental
investigations be conducted to more accurately determine these parameters.  Of
significant value would be relationships, both within and across species, be-
tween these parameters and characteristics of the compound and species, e.g.,
octanol/water partition coefficient and % lipld.
     Additional significant gaps of knowledge are the PCB concentrations of the
invertebrate and plar.kton components of the food chain and accurate estimates
of the water concentration.
     Differences were found between growth rates of pre-stocked and stocked
lake trout.  The model was shown to be sensitive to these differences..  It is .
recommended that lake trout growth rate be investigated to provide an accurate
estimate that will decrease uncertainty in the model projections.
     An empirical relationship between lake trout excretion rate and % lipid
significantly improved the model calibration suggesting that lipld content is
an important factor in accumulation.  It is recocsiended that the model struc-
ture be modified to include a more fundamental description of lipld, possibly
separating the species into lipld and non-lipid components.
     The sediment of Lake Michigan contains a substantial quantity of PCB.
because the sediment responds mnre slowly to reductions in PCB loading than
does the water column, it will have significant PCB concentrations even when
water colicnn concentrations decline to some "acceptable" level.  A significant
question, then, is the extent to which benthic fauna may transfer this sedi-
ment PCB to the pelagic food chain, thus mitigating the concentration reduc-
tion in that food chain.  This question should be addressed by including a
benthic component in the food chain.
                                     10

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     The food chain model was calibrated to data collected in 1971.   Data are
also available through 1979.  These data indicate a decline of lake  trout PCB
concentrations after 1975.  A further calibration of the model, using these
data, would increase confidence in its prediction capability.
     It is also recommended that the model be applied to other chemicals for
which a sufficient.data base exists.  This would test the applicability of
the model as a general framework for assessing the response of the food chain
to toxic substance exposure.

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                                 SECTION 4
                   COMPILATION AND ANALYSIS OF PCS DATA

WATER COLUMN
     The estimation of water column concentrations of PCB in the open waters
of Lake Michigan is difficult because levels during the early 1970s were
apparently lower than the level of detection.  Veith and Lee (1971) reported
from work done in 1970 that the PCB concentration in Lake Michigan water was
below the detection limit of 10 ng/J. (.01 pg/£).   Torrey (1976) and Konasevich
et al. (1978) have summarized the available water data including the earlier
determinations of Veith and Lee, and also Indicated that open water concentra-
tions were below 10 ng/fc.  For some nearshore (.05 km) samples reported in
1972, the concentrations ranged from 12 ng/£ to 56 ng/£.  Values of 30 ng/£
and 
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tions between 2 and 20 ng/g(d) and 12% greater than 20 ng/g(d).  The highest
value measured was 190 ng/g(d).

     TABLE 2.  PCB IN SURFTCIAL (0-3 cm) LAKE MICHIGAN SEDIMENTS (1975)
                          (From Frank et al., 1981)

Whole Lake
Non-Depositional Zones-
Depositional Zones
PCB
Mean
9.7
6.3
17.3
(nR/K(d))
Std. Dev.
15.7
8.1
23.9

     Harbors throughout Lake Michigan have significantly greater sediment PCB
concentrations than the main lake.  As summarized in Konasevich et al. (1978),
Milwaukee Harbor measurements indicated a concentration of 6420 yg/g(d) while
Sheboygan Harbor ranged from .06 to 0.32 vg/g(d).  Thomann and Kontaxis (1981)
in a summary of sediment PCB data for Waukegan Harbor collected by several
laboratories, indicate a range in the harbor spanning five orders of magnitude
from 0.1 to 10,000 pg/g(d).
     These data indicate tViat the sediment of Lake Michigan contain a substan-
tial reservoir of PCB.  The distribution however is not uniform and reflects
past loading of PCB and subsequent distribution throughout the lake with con-
centration in the principal sediment depositional zones.

AQUATIC ECOSYSTEM
     Lover and Intermediate Levels
     No data have been obtained on the PCB concentration in tha phytoplankton
or the smaller zooplankton.  Veith (1973) as reported by Torrey (1976) ana-
lyzed the PCB concentration of the amphipod Pontoporeia in the spring of 1972
and obtained a range from .06 vig/g(v) at 30.5 m to 0.89 yg/g(w) at 8.2 n>.  An
apparent inverse correlation of concentration with distance from shore (in-
creasing depth) was observed.  In the vicinity of Vaukegan, the. concentration
decreased from 0.89 pg/g at 8.2 m to 0.45 vg/g at 30.5 m to 0.34 vg/g at
45.7 o.
                                     13

-------
Fish PCS Data Base-Overview and Summary
     The PCB data for the fishes of Lake Michigan were compiled froa five
principal sources:  a) Veith (1973, 1975), b) USF & WLS, and a Greet Lakes
Environmental Contamination Survey (GLECS) c) the Storage and Retrieval
(STORE!) system of EPA and d) data for 1977-79 obtained fron state agencies
and tabulated by Wapora (1981).  In addition, literature data were evalu-
ated from sporadic sampling conducted by Individual investigators.
     The data reported by Veith (1973, 1975) were obtained in 1971, gener-
ally during the fall at the -Teas shown in Figure 4.  Thirteen species of
fish were taken from the fourteen regions and analyzed for PCBs and analogs
of DDT.  Additional parameters included the weight, length and % fat of the
fish.  Figure 5 and Figure 6 display the summary PCB data of Veith for the
thirteen species as a function of mean species weight and as a function of
mean % lipid.  There is an apparent relationship between weignt and concen-
tration (with the exception of the principal detrital feeders such as carp
and the suckers).  The apparent relationship with weight may reflect differ-
ing positiono in the food chain.  The highest concentration reported was for
the lake trout (£8).  The redhorse sucker (#5), white sucker (i?6), whitefish
(#7) and carp (#9) all have relatively low concentrations of PCB.  This un-
doubtedly reflects the simple food chain structure of these primarily herbiv-
orous and bottom feeding species.  Figure 6 shows no apparent reletionship
between the PCB concentration and the mean species % lipid.  This probably
reflects a confounding of lipid concentration and trophic level position.
Thus, although the bloater (//A) had the highest mean species % lipid (20 +
5.9%), the mean PCB concentration is only 6 Vg/g(w).
     The available PCB deta from the surveys of the USF & WLS extended from
1972-1976.  Bloater chubs and lake trout were obtained off Saugatuck, Michigan
snd coho salmon from east-central Lake Michigan in the area of the Platte
River.  Bloater PCB concentration varied from about 5.7 pg/g(w) in 1972 to
about 3.1 pg/g(w) in 1978 with en cpparent downward trend (see also Figure 2).
     The available GLECS data set (Michigan, 1975) io for surveys and analyses
of PCB conducted in 1975 by the Michigan Department of Agriculture, Michigan
Department of Natural Resources, Michigan Department of Public Health and U.S.-

-------
                     MICHIGAN

                            MANISTIOUE i
WISCONSIN

         GREEN BA Y



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                                INDIANA
                                                   0  25  50 75 100   km
                                                        25    50    75 mi
     Figure  A.   Sampling  regions  for  1971 fish contaminant survey
                by Veith  (1973, 1975).
                                  15

-------
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-------
Food and Drug Administration.  The collections were made throughout the Michi-
gan waters of Lake Michigan.  Twenty seven PCB samples were obtained for the
lake trout and six for burbot in these waters.  The data represent the con-
centration in the filet of the fish and are discussed in the analysis below.
     The STORET data base includes data from a variety of sources including
some samples from Wisconsin and Illinois and other agencies.  The data com-
piled by Wapora (1981) include samples collected up to 1979 and are incor-
porated here to provide a more up-to-date data set.  Zubik et al. (1978) re-
                                     j
ported PCB values for whole freshwater white and longnose mullet from 0.06-
0.71 yg/g(w) for 1975-76.
     The data seta discussed above have been compiled and analyzed with
specific reference to the lake trout and the alewife as a principal food for
the trout.  For the conbined data sets, Figure 3 shows the variation of PCB
from 1971-1979 for the lake trout and Figure 7 shows a similar plot for the
coho salmon.  The lake trout range from 10-20 pg/g(w) while the coho salmon
range from about 8-15 pg/g(w).  No apparent trend exists for the coho while
an apparent decrease occurs in the lake trout beginning after 1976.
     The data were also summarized by age class using weight-age relation-
ships discussed in Section 6, Estimation of Model Food Chain Interactions
and Parameters.  Figure 8 shows the PCB concentration f•. r the alewife in 1971
and indicates that the average concentration was about 5 Vig/g(w).  The PC&  -
concentration is essentially independent of the age of the alewife.
     The lake trout data as a function of age class are shown in Figure 9.
These data were assigned to age classes using growth rates generally repre-
sentative of pre-stocked trout.  Different growth rates end the associated
distribution of PCB with age class are discussed in Section 9.  For 1971,
there is a decided trend towards increasing concentration with age.  The
initial high concentrations of 10-12 pg/g(w) for the 2-3 year old age class
followed by the decline in the 4 year olds may be the result of exposure
to higher water concentrations in in-shore areas.  There is no apparent dif-
ference between the 1971 and 1975 data.
     The distributions of PCB for the lake trout for the years 1971-79 and by

-------
                           LAKE MICHIGAN COKO
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        PCB BODY BURDEN IN  LAKE MICHIGAN  LAKE
           TROUT AS A FUNCTION OF AGE CLASS
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age class are shown in Figures 10 and 11.   There is a clear decline in several
of the upper age classes after 1976 with an apparent leveling off or increase
in 1978 and 1979.   The nine and ten year old age classes still had concentra-
tions of 10 pg/g(w) or greater for these latter years.  The data are therefore
suggestive that there has been some decline in the fish PCB concentration al-
though the decline appears to have leveled off in the upper age classes at
greater than 5 pg/g(w).
     Due to the high lipid solubility of PCBs, one would expect that the PCB
concentration nay be correlated with the lipid content of the lake trout.  Fig-
ure 12 shows the available data.  The relationship is not strong for the Veith
data but is marked for the STORET data.   For this latter data set, the PCB
concentration is about directly proportional to the % lipid.  The GLECS data
are for filet only and also Indicate some tendency toward increasing concen-
trations with increasing lipid content.
     This compilation and analysis of the PCB concentration in the Lake Mich-
igan ecosystem indicates the following:
     1)  Data on PCB arc virtually absent for trophic levels below the fish,
         including zooplankton and phytoplankton
     2)  The data for the fish suggest an increase in PCB concentration as
         one proceeds up the food chain to the top *predators.  Lake trout PCB
         concentrations are the highest  of the top predators
     3)  Across thirteen species there is no apparent relationship between
         PCB concentration and 7. lipid.   For lake trout however, there is
         some evidence for some data bases that indicate increasing PCB con-
         centration with increasing lipid content
     4)  Evaluation of the 1971 and 1975 data by age class for the lake trout
         indicates an approximate four fold increase in concentration of PCB
         from the 4 to 9 year old age classes.
     5)  The lake trout PCB data for 1971-79 appears to indicate a declining
         trend after 1975-76 with some leveling off in 1978 and 1979.

     These summary conclusions regarding the PCB concentration in the Lake
Michigan food chain also indicate the need to develop a modeling structure
                                   22

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        11.  Variation of PCB for lake trout from 1971-79 for age classes
                           7-10 years

-------
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Figure 12.  Relationships between PCB and % lipid for lake fout
          from different sets.
                         25

-------
that will address the aforementioned issues in light of the available  data.
A modeling framework can increase the understanding of the basic  observed
data to help resolve the questions of relative routes in the accumulation
of PCB In the tpp predators.
                                   26

-------
                                  SECTION 5
                         AGE DEPENDENT MODEL: THEORY

PREVIOUS WORK
     A substantial literature exists on compartment models for transfer of
material through food chains and food webs.  The ecological concepts of com-
partment analyses have been reviewed by Dale (1970) and Patten (1971) and ex-
amples of compartment models include Gillet (1974), Hill et al. (1976),
Lassiter et al. (1976), Haefner and Gillet (1976),  and Aoyama et al. (1978).
These approaches incorporate a variety of mechanisms in a timevariable mode.
     Weininger (1978) formulated an age dependent model for PCBs in the lake
trout of Lake Michigan.  In that work, mass balance equations were written
across the age of the trout and included the principal mechanisms of uptake
directly from water and from food.  Uptake from water is functionally depen-
dent on fish respiration and related to the dissolved oxygen transfer across
the gill surfaces.  Food chain transfer is included through feeding on con-
taminated prey where the concentrations of PCB in the food is specified.  Ex-
cretion of PCB is included as a first order loss mechanism and in the actual
calibration of the model to lake trout PCB body burden excretion is assumed
to be zero.  Weininger concluded from his work that direct uptake from water
is small and that the principal route for PCB accumulation in the lake trout
is the food chain.  The model described below builds on this earlier work,
but rather than specifying the food PCB concentration, the model framework is
extended to include calculation of PCB at each level of the food chain.

B10CONCENTRATION AND DEPURATION
     The uptake of a chemical directly from water through transfer across
the gille as in fish or through surface sorption and subsequent cellular  in-
corporation as in phytoplankton is an important route for transfer of toxi-
cants.  This uptake is often measured by laboratory experiments where test
arganisBS are placed in aquaria vith known (and fixed) water concentrations
                                     27

-------
of the chemical.  The accumulation of the chemical over tine is then measured
and the resulting equilibrium concentration in the orger.lsta divided by the
water concentration is termed the bioconcentration factor (BCF).  A simple
representation of this mechanism is given by a mass balance equation around a
given organism.  Thus,

                         of" " Vc * KV'                                  (1)

where v* is the whole body burden of the chemical (yg) , k  is the uptake sorp-
tion and/or transfer rate (£/d-g(w)), w is the weight of the organism (g(w)),
c is the available water concentration (pg/Jt), K is the deeorptlon and excre-
tion rate (d  ) and t is tine.  This equation indicates that the mass input
(pg/d) of toxicant given by k we is offset by the depuration mass loss rate
(VJg/d) given by Kv'.  It is assumed in the mass balance that the rate of
change of the whole body burden is directly proportional to the concentration
of the cheaical in the water.  For PCB, this is a good assumption as shown by
Vreeland (1974) for oysters and Hansen et al. (1974) for pinfish.  For both
these, studies, the resultant PCB concentration in the test animal was linear
to the exposure water concentration.  Eq. (1) Is the proper starting point for
analysis of the mechanisms controlling uptake directly froo water.  The whole
body burden v' is given by

                         v' = vw                                           (2)

where v is the concentration of the chemical (vg/g(w)).  Substitution of (2)
Into (1) gives

                         7^ = k we - Kvw                                  (3)
                         at     u

Expanding the derivative and grouping terns yields
                                                                            (5)
                                     28

-------
where G(d  ) is the net growth rate of the organism, and
                         K1 •= K + G                                   (6)
               then      dv _ k c _ K,v
                         at    u

It is seen that the loss term on tha concentration includes the loss (or gain)
due to the changing weight of the organism during the test and may therefore
be termed an apparent depuration.  The solution to Eq. (7) is
                   k c
               v = ~(1 - exp(- K't)) + vo exp(-K')t                 (8)

where V  is the initial concentration of the chemical in the test organisn.
Note that this expression indicates that the rate of accumulation is a function
of K1, the sum of the depuration rate and the net growth rate.  At equilibrium
or steady state,
                             k c
                         v - -.                                      (9)
and the BCF is given by
                         „   v   ku
The ratio N, the bioconcentratlon factor, is shown here in units Vg/g *
In a form representative of a pseudo dimensionless ratio, the BCF is in typi-
cal units of pg/kg(w) •? Vig/£, i.e. ppb/ppb and then

                         N1 = 1000 N                                 (11)

The BCF is defined from Eq. (10) as the ratio of the uptake rate, k  to the
sum of the depuration and growth rate and represents the ratio of the equilib-
rium steady state chemical concentration to the dissolved water concentration.
It is evident that BCF tests extending over time periods where the weight of
the organism changes are affected by such weight changes.  This effect should

-------
be incorporated in analysis of the test data through Eq.  (8)  or (10).   This
is especially true for analyses of chemical concentration time history data
from independent information on uptake or depuration rates.
     For fish, the primary mechanism for uptake directly  from water is through
transfer of the chemical across the gill surface.   The rate  of transfer can
be calculated from the rate of transfer of oxygen  from water to the blood of
the fish.
     The rate of mass transport of a substance is  given by
               H -    c                                               (12)
where M is the IEHSS transport [vg/d] ,  D is the dif fusivity of the substance
   2                                                             2
[cm /d], A is the effective surface area of gill for transfer [cm ] ,  6 is
the effective thickness of the gill [cm], and c is the concentration  of the
substance in the water [vg/i].  If it  is assumed that the mechanism  for
uptake of the chemical, e.g.  PCB is identical to oxygen uptake then
               rcpCB   DPCB CPCB                                       ....
               \~\~\
where the subscripts PCB and 0  are for the chemical PCB and dissolved
oxygen respectively.  From (13),
               "PCB " cs ^ CPCB

where 6 D D  D/D-.   the ratio of the diffusivity of PCB to that of oxygen.
           rLB  O
From (U),
               "PCB - ku CPCB

where

-------
     The quantity k' represents the mass uptake for the whole fish and has
units, £/d.  Dividing k' by the fish weight gives the uptake rate per unit
weight, i.e.
                              k'
                                                                          (17)
The quantity M  /w is the respiration rate, r, of the fish, i.e.

                         r = MQ /w

where r has units [gO./gCw) - <*]•  The uptake rate for the chemical is there-
fore related to the respiration rate of the organism by

                         k  = B ~^-                                       (18)
This representation is used in the model calibration discussed in the next
section.
     In depuration experiments, the organism is transferred to n tank with
zero toxicant concentration and the time history of the loss of the chemical
is measured.  Eq. (£) then becomes for c=o,

                         v = v  exp(-K')t   '    •                          (19)

or in terms of whole body burden

                         v1 =» VQ' exp(-K)t                                (20)

Again, the weight change of the organism must be properly taken into account.
Eq.(19) can be used to estimate K' and from the net growth rate, the depura-
tion rate K can be obtained.  Or, Eq. (20) can be used directly where the
whole body burden is plotted and the depuration rate obtained from such data.

-------
MODEL FRAMEWORK
     The model utilizes a mass balance of PCS around a defined compartment of
the aquatic ecosystem.  In the most general case,  a compartment is defined as
a specified age class of a specified organism or in the steady state simpli-
fied version discussed below, a compartment is considered as an "average" age
class or range of ages for a given organism.  Figure 13 schematically shows
the compartments.  As indicated in Figure 13(a), each age class of a given
trophic level is considered as a compartment and a mass balance equation can
be written around each such age class.  The zero trophic level is considered
to be the phytoplankton-detrltus component representing one of the principal
sorption mechanisms for incorporating toxicants into the food chain.
     Consider then the phytoplankton, detrital organic material, and other
organisms, all of size approximately <1CO vns as the base of the food chain.
An equation for this compartment is given by a simple reversible sorprion-de-
sorption linear equation as:

                         dv
                         —- = k  c - K v                                (21)
                         dt     uo     o o

where all terras have been defined, the subscript zero refers to the base of
the food chain, and t is real time.
     This simple expression indicates that the concentration at the base of
the rood chain is represented as a balance between the uptake directly from
the water (k  c) and the loss due to desorption and excretion (K V ).  The
            uo                            e                     oo
chemical concentration is the concentration of the average phytoplankton or
detrital particle on a wet weight basis.  Eq. (21) therefore is not a balance
equation for the mass of toxicant in the entire biomass.
     For a compartment above the phytoplankton/detritus level, the mass input
of the toxicant due to ingestion of contaminated food must be included.  This
mass input will depend on  a) toxicant concentration in the food,  b) rate of
consumption of food and  c) the degree to which the ingested toxicant in the
food is actually assimilated into the tissues of the organisms.

-------
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= Compartment number

-------
     The general mass balance equation for the whole body burden  for  a  given
compartment, i, is then similar to Eq.  (1) for water uptake but with  the
additional mass input due to feeding.   Therefore,

               dv!   d(Vtf)    w,dv<    v
-------
where the preference term Is unity.
     The first tenn of Eq.  (25) represents the direct uptake of the chemical
by the organism f.om the water.  The second term represents the flux of the
chemical into the organism through feeding.  Note that the units of this term
are gram of chemical assimilated per gram predator .per day.  The third term
is the loss of chemical due to desorption and excretion from body tissue at a
rate K  plus the change in C"r":entration due to growth of the individual. The
equation pair, (24) and (25), can he solved analytically for the case of known
food concentration and constant coefficients or numerically for time-variable
coefficients.  Norstrom et al. (1976) and Welninger (1978) are examples; in
each case, hovever, the food toxicant concentration ie assumed known.
     The interpretation of w  and n  in Equations (23) and (25) is further
explained in Figure 14.  The variation of the weight (and toxicant concentra-
tion) of a given compartment (i.e. a given age class of a given organism) is
shown with real time.  If as an example, w_ is a 0-1 year old alewife then it
is seen that the weight of this age class nay vary from year to year.  Simi-
larly, the distribution of the toxicant may change from year to year for a
given compartment depending on, for example, the variation in the water column
toxicant concentration.  The specification of the boundaries of a given com-
partment depends on the life cycle of the organism.
     It should be recognized therefore that several of the biological and
toxic parameters of the weight change equation (24)  and the food chain equa-
tion (25) are functions of organism weight within the time interval defined
by the compartment.  One of the principal weight dependent parameters is res-
piration.  Since the uptake of the chemical is dependent on the respiration
through eq. (18) and the specific consumption also depends on the respiration
through eq. (24), the weight dependence of the respiration assumes a signifi-
cant role in the model structure.
     Schmidt-Nielsen (1970) has reviewed 'the relationship between energy util-
ization and body size for an entire size spectrum of organisms.  In addition,
Norstrots et al. (1976), among others, have summarized the literature on res-
piration of fish as a function of weight.  From an energetics viewpoint, the
generalized relationship between respiration and body weight is given by
                                      35

-------
                       1          2         3
                         REAL TIME, years
      o
      \- "
      <••§,
      oc -
      UJ
      o
      O
      X
      o
5>
=0-1 YEAR OLD ALEWIFE

= 1~2 YEAR OLD ALEWIFE
                       i=5
            01234

                         REAL TIME, years


Figure 14.  Illustration of meaning of w (t) and v (t) showing as an example

          a 0-1 year old end 1-2  year old alewife.
                               36

-------
                         R - owY                                        (26)

                                                *u
where R is the kcal respired/day and for 1 kcal "v 1 g(w) aleo Is approxi-
mately equivalent to g(w) respired/day and a and y are empirical constants.
For low routine metabolism,

                         R - c^rwY                                      (27)

Norstrom et al. (1976) suggest the following values for fish at 208C:

                         „   _ n       kcal
                               °'
               and
                                '             os
                                   week - g(w)
                         Y ~ 0.8
The latter estimate for the slope of the relationship between metabolic rates
and body weight is also approximately shown in Schmidt-Nielsen (1970) over a
range fron 10    to 10 g.  The range in y is about 0.75 to 0.9 with a mean
close to 0.75.  See also Section 6, Eq. (53).  Thus, in general

                         R £ a£rw°-8                                    (28)

for R in g(w)/day.  Normalizing this expression by the weight of the organism
gives
                         r' £ a w"'2                                    (29)

where r' ie the fish respiration rate in g(w) respired/g(w)-day and a  is a
constant which may be organism dependent.  In terms of oxygen uptake, the
respiration rate is given approximately by

                         r - 2.7 na r'                                  (30)

where r is in g02/g(w)-day, n is the dry weight to wet weight ratio (g(d)/g(w))
and depends on the species, a  is the carbon to dry weight ratio [g Carbon/g(d)]
                                    37

-------
set at 0.4 in this work and 2.7 is the gO_ utilized/g Carbon.
     Following eq. (18), the chemical uptake rate directly from the water is
then given by
                              2-7 na 6   _Q ,
                         k  - - —  w U^                           (31)
               or
                         ku(w) •= afcw-.2                                 (32)
 .          2.7na
where a,  •»      c
     From Eq. 24, for a growth rate, G, determined from weight-age data, res-
piration from eq. (29) and a constant food assimilation ratio, a, the specific
consumption can be computed as
                                G(w) + r!   G(w) + a w"'2
                         C(w) - - - - i - - —^ -               (33)
                                    &             O

Similarly, the depuration rate is considered es a function of weight, i.e.,
K = K(w).  Thus the general model calculation is given from eqs. (25), (32)
and (33) as
                                                                        (34)

     In this form, it is difficult to understand the behavior of the equation
and the relative importance of each mechanism.  Some additional insight into
the behavior of the equations derived above therefore can be obtained by exam
ining a simple steady state case.

EQUILIBRIUM (STEADY STATE) CONDITION
     The i   compartment around which the mass balance is taken to derive Eq.
(25) is defined as a given age-class of an organism in the food chain.   The
properties of that age-class include the weight change as a result of net
growth, as shown in Eq. (23).  The net growth rate of the age-class can be
considered to be a constant in time, i.e. that the average growth rate of a
                                     38

-------
2 to 5-yr-old top predator is the same from 1 year to the next.  This assump-
tion implies no temporal change in the feeding rate, food availability or res-
piration rate.  Such an assumption may be entirely reasonable for cne lower
levels of the food chain but may be questionable for the top predators.  Never-
theless, considerable insight can be gained into the behavior of the contami-
nant equations by assuming e constant growth rate.  In a similar fashion, the
assumption is made that the uptake, assimilation, and excretion rates are con-
stant within a defined age-class (i.e. a defined compartment).
     The solution to Eq. (24) for constant coefficients is

                         Wi " "

where w   is the initial weight at the beginning of the age-class i.
     The solution to Eq. (22) , the body burden equation under an assumption of
constant coefficients, is
                Ck  c + a     C    ,V  ,)w
                              t
                                                                          (36)
where v' , is the initial contaminant body burden at the beginning of the age-
class i.
     The solution to Eq. (25) is

               k .c + a. .  ,C. . .v  '

                                                                          (37)
                                      + V  exp(-K't).
     Figure 15 shows the form of Eqs. (35)-(37).  The increase in the weight
of ths given age-class is exponential as shown in Fig. (15a), with a constant
net growth rate of G .  Figure (15b) shows the increase in body burden and in-
dicates that no equilibrium le reached,  i.e. the total mass of contaminant in
                                     39

-------
                      AGE CLASS i
                    O)
                    IU
                    5
                                    TIME
                 Q
                 O
                 en
                 <  2
                 2  £
                 2
                 O
                 O
                                    TIME
              - <  °>
              •5 EC  en
              < i—  a.
              O
              O
                 O
                 O
                          EQUILIBRIUM

                         (STEADY STATE)

                        CONCENTRATION
(c)
                                    TIME
Figure 15.  Illustration of equilibrium conditions  for  concentration  of

            contaminant in orgsalsni.   (a) Exponential increase  in  organ-

            ism weight, Eq. (11);  (b)  Increase in contaminant body bur-

            den, Eq. (20); (c) increase in contaminant  concentration  to

            equilibrium (steady state) leve', Eq. (21).

-------
the organism continues to grow as a result of uptake, assimilation,  and increase
in weight.  Indeed, Eq. (36) shows that only if the net growth rate  is zero
(i.e. weight of the organism is a constant) is there an equilibrium  condition
on the body burden.  A constant weight assumption, however, is a particularly
poor one.  Figure (15c) shows that even as weight is increasing exponentially
and the body burden increasing according to Eq. (36), the concentration of the
contaminant approaches a constant value, an equilibrium or steady state condi-
tion.  This equilibrium concentration represents a balance between the inputs
of the contaminant to the organism and the mechanics of excretion and increas-
ing weight of the organism.  This can be seen from Eq. (25) where at equilib-
rium, dv /dt « 0, and

                         K'v. = k .c + a. .  .C. . , v. ,
                           i i    ui     i»i-l i»i-l i-1
or
                                 k .ic + o. .  ,C. . ,v. ,
                            v  = JSi	i,i-l 1,1-LjtzI                 (38)
                             1              K ±

which can also be obtained from Eq. (37) at large t.
     If then it is assumed that the growth and contaminant related coefficients
are constant over the length of time defined by the age-class of the compart-
ment, then an equilibrium or steady state condition in the concentration of the
contaminant is reached.  This is the basis of considering an equilibrium or
steady state model where the time derivative in Eq. (.''S)  is set equal to zero.
     One can also obtain from this line of reasoning the appropriate age-class
interval for each compartment that will guarantee an approximate equilibrium
condition.  If a criteria of 90% of equilibrium is chosen, then the  age inter-
val t  for a compai -.sent Is

                         t  > 2.3/K'                                     (39)
                          a —

For example, for a low excretion rate (e.g. K «• 0.001/d)  and a high  net growth
rate that are representative of the upper levels of the food chain (e.g. G =
0.01/d), t  Ji 3.1 yr.  Therefore if one considers the lower level to be repre-

-------
sentative of an age-class spanning about 0.5 yr and the upper food chain level
to be representative of an age-class spanning about 3 yr, then an equilibrium,
steady etflte concentration will be reached.  Such a concentration will be
approximately independent of the initial concentration at the beginning of the
age-class as can be determined from Eq. (37).  On the other hand, if excretion
is very low, say approximately zero, and if the net weight change G is also
very low, say approximately zero, then Eq. (.39) indicates that the age span
approaches infinity.  This simply implies that an equilibrium condition will
never be reached under those compartment characteristics.  Such cases can
occur for low excretion racis and older top predators.  To summarize, equilib-
rium or steady state implies constant positive net weight change and con >tant
uptake, assimilation, and excretion rates over an age-class interval defined
to guarantee 90% of equilibrium.
     Continuing with this simplification, Eq. (38) can be written as
          \)  — N r + f     \)
          Vi   Nic ^  i.i-1 i-1
             « v.  + v. ,
                iw    if

where N  is the BCF given by
          „       ui      iw
f . . . is a food chain transfer number  (a bioinagnif ication ratio) given by
 1,1— i

                                                                          (42)
and v   and v , are the components of the chemical concentration in organism i
due to uptake from water and food chain transfer respectively.
     The f factor therefore represents the ratio cf the chemical in the preda-
tor due to food chain transfer relative to the chemical concentration of the
prey, i.e.

          '      '
                                     42

-------
iiiAB ratio can be obtained experimentally through feeding experiments where
the water concentration is zero or where enough experimental information is
obtained to calculate f from Eq. (43).  Lieb et al. (1974), in feeding exper-
iments using rainbow trout and Aroclor 1254, obtained a ratio of about 2
Indicating that the approximate equilibrium concentration of the trout was
about twice that of the PCB in the diet.  Note that the meaning of f is con-
trasted to the BCF, the fonaer as a ratio of chemical concentration in preda-
tor to that in food, the latter a ratio of chemical concentration in predator
to that in the water.  Comparisons then of the numerical magnitude of the BCF
(for PCB, order 100 pg/g * V!g/£) and the f factor (for PCB, order 1 vg/g(w) T
1J8/8(W)) can be misleading.
     For example, consider a four step food chain representative of phytoplank-
ton, zooplankton, saall fish and large fish.  The chemical concentration at
each level are then given from Eq. (40) as

                         Vl = N1C                                       (44a)
                         V2 - N2c -f f^Vj                               (44b)
                         V3 = N,c -f f32V2                               (44c)
                         V4 " V + fA3vA                               C44d)

     Successive substitutions beginning with the lowest level and proceeding
to the fourth level give the chemical concentration for tha top predator as

               V4 " V + [f43N3 + f43f32K2 + f43f32f21Nl^C              (45)

                  C V4w + V4f   .
     The first term, V. , represents as before the chemical concentration in
the top predator due to uptake from water only and the second term, v. ... rep-
resents the chemical concentration due to the cumulative transfer of the chem-
ical through the food chain.  Now for PCB, a reasonable assumption is that the
BCF is approximately constant across the food chain.  Therefore,
and Eq. (45) becomes

-------
                                                                          (46)
     The effect rf food chain transfer is now clearly additive to the concen-
tration from water uptake only.  In this model then, there will always be an
increase in chemical concentration in a predator due to food chain transfer.
The degree of relative significance of that transfer is the question, not
whether there is any food chain transfer at all.  Consider the case where f
is a constant across the food chain at a value of 2 (the value obtained by
Lieb et al. (1974) for rainbow trout).  Then

                    v, " [1 + 2 + 4 + 8]v,

                       - 15 v,
                             4w
showing that the concentration of the top predator ie fifteen Clones the level
due just to uptake from water.  The cumulative effect from the lowest level
(phytoplankton) to the top predator can also be seen.
     Figure 16 summarizes the effect of the food chain transfer factor in the
ratio of chemical from water and food to that from water only.  Note that for
f «= 0.5, and a four level food chain, the resultant concentration in the top
predator would be almost twice that from water uptake only.  A vater quality
standard for chemicals that were based solely on water uptake to the food chain
would therefore exceed an attainable chemical concentration by about two times
if the food chain were not taken into account.
     If food chain transfer is considered "significant" at say 20% of the con-
centration due to water only, then the approximate constant f level can be cal-
culated.  Thus if
then f is about 0.2.  If the ratio of chemical concentration in the predator to
that in prey in feeding experiments is therefore only 0.2, there will be an
approximate 202 increase in the top predator over the concentration from wauer
only.  A lower bound of f of about 0.2 is suggested then as the boundary be-
tween significant and non-significant food chain transfer effects.

-------
CC
o
  CC
  a.
  Q.
  O
  Q
  O
  O
  u.
  2 ^
  O

  O
  o
  LU


  Q
CC
O
Q
UJ
cc>
Q- _)
Q. 2
OO
           UJ
         HO
         < H
O
2
O
O
               10
                9
                8

                7

                6
               2.0
               1.2
               1.0
                    NUMBER OF TROPHIC LEVELS INCLUDING

                                      PREDATOR LEVEL: 4.
                                         L
                  0  0.2
                f =
                          0.5         1.0          1.5         2.0

                   CONCENTRATION IN PREDATOR DUE TO

                                FE.EDING ONLY


                      CONCENTRATION IN FOOD (PREY)
Figure 11.   Effect of food chain transfer ratio, f, on ratio of chemical

            concentration in top predator from water plus food to  that

            from water only.  Equilibria conditions, constant BCF and f
            ratio along food chain.

-------
                                 SECTION 6
         ESTIMATION OF MODEL FOOD CHAIN INTERACTIONS AND PARAMETERS

     The accumulation of PCBs In the Lake Michigan food chain is modelled
assuming a four species food chain consisting of phytoplankton, Mysis relicta,
alewife (Alosa pseudoharengus), and lake trout (Salvelinus namaycush).  As
discussed below, this species linkage constitutes the major energy transport
route to the lake trout.  Both Mysis and alewife are viewed as representative
species of the middle levels of the food chain acknowledging that other inver-
tebrates and small fish also contribute to the observed PCB levels in Lake
Trout.  The phytoplankton component of the model is assumed to represent non-
living particulate organic material as well as living plankton.
     Phytoplankton are represented by a single compartment that is assumed to
be in dynamic equilibrium with water column dissolved PCB.  The other species
are separated into discrete age classes.  For any age class growth rate and
predator-prey relationships are constant.  Dynamics of feeding and growth
within an age class are not considered.

FEEDING STRUCTURE
     Hvsis relicta is a crustacean of the order Mysidacea.  It is found in
North America in the deep waters of the Great Lakes, some of the Canadian
lakes, Green Lake of Wisconsin and the Finger Lakes of upper New York State
(Riots, 1966).  It is a filter feeder, feeding primarily on plankton and de-
tritus although it also may seize zooplankton (Mozley and Howtniller, 1977).
     Mysts exhibits a diurnal migration cycle, moving vertically from the
bottom at dusk, feeding in the water column and then returning to the bottom
waters.  Beeton (1960) has described this cycle in Lake Michigan showing that
light and vertical thermal structure control the migration.  As surface light
intensity Increases the height of migration Decreases.  If a sharp therraocline
.is present, the myslds will generally concentrate just below it until their
descent prior to sunrise.

-------
     Mysis are present throughout Lake Michigan and may be found all year at
depths greater than 30 m. (Mozley and Howmlller, 1977).  In winter, popula-
tions may be found at shallower depths.  They are an important link in the
food chain, especially as a forage for fishes (Grossnickle, 1978).
     Morgan and Beeton (1978) found the life cycle of Mysis in Lake Michigan
to be about 16 months for females and slightly longer than 1 year for males.
Females can produce two broods of young, the first at 12 months and the second
at 16 months.  Juveniles are released at distinct intervals throughout the
year with a periodicity of about A months.
     The feeding habits of Lake Michigan Hysis have been determined by exami-
nation of gut contents.  In a qualitative analysis McWilliara (1970) found that
plankton were tha dominant food sourc^, although some cladocerans, copepods
and juvenile nysids were present in Mypis guts.  Grossntckle (1978) found that
vertically migrating niysids in Lake Michigan have nearly empty guts as they
begin their ascent but feed rapidly as they move up in the water column, sug-
gesting that Mysis may be regarded as a pelagic consumer.  Groasnickle also
indicated that the analysis of fecal pellets suggested that feeding was pri-
marily on phytoplankton.  In laboratory experiments he did show, however, that
adult ir.ysids were omnivorous when offered naturally occurring phytoplankton
assemblages and specific zooplankr.cn species.
     The food chain model is structured with four A month age classes of Mysis
reflecting life span and birth frequency.  All classes consume phytoplankton
exclusively.

     Alewife
     The alevife is an anadromous fish fonp.d in the Atlantic Coast waters of
North America.  It also has become established in certain freshwater bodies
including the Finger Lakes of upper New York and all the Great Lakes.  In Lake
Michigan, alewives have increased from their first reported appearance in 1949
to become the cost abundant species (Janssen and Brandt, 1980).  They feed
almost exclusively on Crustacea ranging In size from small copepods and
cladocera to Pontoporeia hoyi and Mysis rellc.ta (Morsell and Norden, 1968).

-------
Algae have been found In alewife stomachs but this ie believed to be inciden-
tal to feeding on zooplankton (Morsell and Norden, 1968).   Alewive8 live
approximately seven years spawning in late June in Lake Michigan (Carlander,
1969).
     An intensive study of the feeding habits of adult alewlves In Lake Mich-
igan (Janssen and Brandt, 1980) showed that they concentrated near the bottom
during the day and migrated to the base of the thennocline at night in a pat-
tern that coincided with that of Mysis.  The authors suggested that the ver-
tical migration of alewife was mechanistically linked to their feeding behavior,
I.e., they were actually following and consuming Mysis.  Based on stomach con-
tent data, the authors concluded that Mysis was the major constituent in the
diet of adult alewlves.  Pontoporela and niicrocrustacean zooplankton were alco
present in alewife stomachs but were much lees common than Myels.  In addition,
average body length of MyjrJjs in alewife stomachs were longer than average body
length of Mysis in the water coluion (Fig. 17), a possible consequence of larger
Mysis being more visible and thus more vulnerable to predation and/or predetloa
on only the layer of large Mysis in the observed vertical segregation of Kysts
by size.
     In the model the alewife component is divided Into 7 eingle year classes.
The feeding structure (Fig. 18) reflects the field observations described
above, young-of the-year alewife consuming phytoplankton end all other age
classes consuming Mysls vlth a bias toward the larger Mysis (Table 3).

     Lake Trout
     The lake trout is a predatory fish found throughout Canada, the Great
Lakes drainage basin and parts of New England, New York, Wisconsin, Minnesota,
and Montana (Carlander, 1969).  Up to the nid-1940's the lake trout was abun-
dant in Lake Michigan and a species of primary Importance to the commercial
fishery.  Beginning in 1946 production dropped catastrophlcally due to over-
fishing and predstion by the eea lamprey.  By the mid-1940's lake trout were
virtually extinct in Lake Michigan.
     In an effort to restore the fishery, sea lamprey production was controlled

-------
  cc
  LU
  CO
  o
  o
  01
  Z
  D
      m
                           -0
o       o      o
CD       TJ-      CM

   HOVWOiS3dlM31VNi
                                   NWOIOO W31VM Nl
Figure  17.  Percent  of  total Mysis captured in the water coluran and

           found in alevlfe stomach in  relation to Hysls length for

           two sacpling dates.  (Frora Janssen and Brandt,  1980).

-------
00
c
OD
2 *»
3 re
o-.ro
O
b
w

m
•o
ro
o
3-
ra

0
o
Q.
(5
O
M
                            PLANKTON
0-4
months
4-8
months
8-12
months
12-16
months
                                                               MYSIS
! o-i
1 year
1-2
years
2-3
years
3-4
years
4-5
years
5-6
years
6-7 |
years
—•- J
                                                              ALEWIFE
C
M*

«l

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TABLE 3.  FRACTION OF TOTAL ALEWIFE CONSUMPTION ON  PLANKTON
                 AND EACH MYSIS AGE CLASS


ALEWIFE
AGE 0-4 MO. 4-8 MO.
CLASS PLANKTON MYSIS MYSZS
0-1 yr .1.0
1-2 yr 1.0
2-3 yr
3-4 yr
4-5 yr
5-6 yr
6-7 7T
8-12 MO. 12-16 MO.
MYSIS MYSIS
1.0
1.0
0.5 0.5
0.5 0.5
1.0

-------
by poisoning larvae and blocking spawning routes and in 1965 lake trout stock-
ing was begun.  Each year several million yearling lake trout are planted at
various sites throughout the lake.
     A summary of lake trout food items in relation to season and lake trout
size (Weininger, 1978) shows that Invertebrates  (largely Mysis reltcta and
Pontoporela hoyi) are the major food items for trout up to 200 ma total length
(approximately 2 years old) and that slewife and to a lesser extent sculpln
and smelt are the major food items for all larger trout.
     Data conplled frca stomach content examinations reported by Wright (1968)
(Fig. 19) also show invertebrates to be the major food source of young trout,
fish the main food source of older trout and alewife the major component of
that fish.
     Also compiled frota data reported by Wright  (1968) is the distribution of
alewife age classes in the lake trout diet (Fig. 20).  These data indicate
that trout eat over a wide range of alewife age  classes and that the range of
age classes consumed increases with the age of the trout.
     The lake trout component of the model is divided into 13 single-year age
classes (Fig. 21).  Reflecting the above data, the first two age classes con-
sume My sis exclusively, the next class consumes  Mysis and first and second
year alevlfe.  Older trout consume alewife exclusively, with an age class dis-
tribution coEziensurate with the stomach content  data presented (Table 4).

BIOLOGICAL PARAMETERS
     Weight-Age Relationship
     The biological parameters required by.the model and described in Section
5 Include growth rate, respiration rate and assimilation efficiency of food.
These parameters must be specified for each age  class of all species other
than phytoplankton used in the model.
     Growth rate, which is a function of both temperature and diet. Is nea-
eured either as the change In length or the change in weight with age.  Length
change with ege may usually be described by an equation of the form (Schnute
and Fournier, 1980):
                                     52

-------
           FREQUENCY OF OCCURENCE OF  FREQUENCY OF OCCURENCE
              FISH IN LAKE TROUT       OF INVERTEBRATES IN LAKE
                  STOMACHS              TROUT STOMACHS
                                               1 1 I I  1  i
            0  10 20 30  40 50 60    0  10 20  30 40 50 60
                          TOTAL LENGTH, cm
            i   i   i   i r T i  i  i  i
            0   1   2   3456  789
I  1  |   | ~7 'T ~f ~1  I  I
0123 456 789
                                AGE. y

          PERCENT OF TOTAL VOLUME OF PERCENT OF TOTAL VOLUME
           FOOD CONSUMED AS FISH AND     OF FISH CONSUMED AS
                INVERTEBRATES               ALEVYIFE
                                                 i i
            0  10 20  30  40 50 60    0  10 20  30 40  50  60
                          TOTAL LENGTH, cm
            I    I   I   I III  i  I  I
            0123 456  789
i	1—i	1  r i i i ni—i
0123  456 789
                                AGE. y
Figure  19.  Observed Incidence of fish ad Invertebrates  in lake trout
           stomachs in relation to  lake trout length and computed age.
                               53

-------
                          ALEWIFE AGE. yr
                          12      34  5678
                20

                10
                                  I  i  I III
                   LAKE TROUT:
                     12.0-19.9 cm.
                     1-2 yr
                   0  24  6 8  1012 14 16 18 20
                          12      34  5678
to
UJ

I
Ul
                20

                10
                      I I I T

                      TROUT:
                   20.O-32.9cm.
                   2-4 yr
              u.
              O
              £C
              Ul
              CO
     '0  2 4  6  8 10 12 14 16  18 20
            12      34 5678
20


10


 0




20
                    i i  i m

                   LAK£ TROUT:
                     33.0-42.9 cm,
                     4-6 yr
                   0  2  4  6  8 10 12 14 16 18 20
                          12      34  5678
                          •  I  I    I  I  I  I I I

                                 LAKE TROUT:

                                   43'.0-64.5 cm.

                                   5-9 yr
                   0  2  4  6  6 10 12  14 16 18 20
                       ALEWIFE LENGTH, cm

Figure 20.  Distribution, by  size, of alevives found In various size
           clesses of lake trout.

-------
 •*!
 •A


 C
 re
 a.
 no


 M-

 3
 o
 3
 n
 n
 n.


 M»
 3
H
o
a.
ro
0-1
year
1-2 j 2-3
vcnri 1 yean
3-4
ysart
4-5
yean
6-6
years
6-7
years
                                                                                                        ALEWIFE
0-1
year
1-2
years
2-3
yean
3-4
years
4-5
years
5-C
yean
G-7
years
7-8
yean
8-9
years
9-10
years
10-11
years
11-12
years
12-13
years
                                                                                                        LAKE TROU
O
c

-------
TABLE 4.  FRACTION OF TOTAL LAKE TROUT CONSUMPTION ON EACH MYSIS
AND ALEWIFE AGE CLASS

•ROUT
AGE 0-4 HO.
:LASS MYSIS
0-1 yr
1-2 yr
2-3 yr
3-4 yr
4-5 yr
5-6 yr
6-7 yr
' 7-8 yr
8-9 yr
9-10 yr
10--11 yr
11-12 yr
12-13 yr
4-8 MO. 8-12 MO. 12-16 MO. 0-1 YR. 1-2 YR. 2-3 YR. 3-4 YR.
MYSIS MYSIS MYSIS ALEWIFE ALEWIFE ALEWIFE ALEWIFE
1.0
1.0
0.5 0.25 0.25
0.2 0.4 0.4
0,2 0.5 0.2
0.2 0.5 0.2
0.25 0.25
0.25 0.25
0.25
0.25



4-5 YR.
ALEWIFE




0.1
0.1
0.25
0.25
0.25
0.25
0.33
0.33

5-6 YR. 6-7 YR.
ALEWIFE ALEWIFJJ






0.25
0.25
0.25 0.25
0.25 0.25
0.33 0.34
0.33 0.34
0.5 0.5

-------
                                      -K A
                                        i )                             (47)
where
                         L. - length at age 1
                         L  = maximum length
                         K  • growth rate constant
                         A  - age

An age-weight relationship may then be obtained from the relationship between
length and weight, w, which is usually of the form (Ricker, 1978):

                         w - a Lb                                       (48)
     The age-weight relationship is usually signoidal (logistic) in shape.
It is most conveniently modeled by computing instantaneous first-order rates
of growth for successive time intervals (Ricker, 1978).
                                              v
     A linear length (L,inm) - age (A,tno) relationship has been observed for
Hysis relicta in Lake Michigan (Morgan and Beeton, 1978):

                         L = 3.0 + 0.91A                                (49)

Combining this relationship with an observed wet weight  (mg) - length  (na)
relationship (Reynolds and DeGraeve, 1972):

                         w - 0.007L2*92                                 (50)

yields the weight-age relationship shown by the solid line in Fig. 22.  This
relationship was approximated in the food chain, model by first-order growth
rates of 0.0193, 0.0107, 0.0073, and 0.0056/d for the successive 4 south
periods indicated by the dashed lines in Fig. 22.
     Growth rates for alevives were determined by fitting first-order  rate
expressions to weight-age data for Lake Ontario alevives reported by Csrlander
(1969).  A rate of 0.00245/d was calculated for the  first 4 age classes and a
rate of 0.00047/d was calculated for the remaining age classes  (Fig. 23).

-------
                                                                          st**TT'!2c!fr:fl
ar    M   sr   or    8     a    £
                  artinom ,30A
0
       BB sgs
                         al
 blioa) qlrianotJfllsT rf Jgn3 t-Jrfgis* bna saa-rf^aasl  s noil
                       bsrfasb) labcai arfj hi baau  as  bno
                                                                              f

-------
       102
en

h-*
X
(D
LU
LU
  2X10°
                                            1
                    1
           0
3456

    AGE, years
8
  Figure 23.  Observed wet veight  in relation to slewife age as compared
             to functional relationship used in the oodel.
                                  59

-------
These rates are low in comparison to both Mysis and lake trout  and  indicate
that the tlevife is a alow growing fish.
     Lake Trout growth rates were calculated using weight-age data  for  trout
from Lake Michigan and Lake Superior that was reported  by Carlander (1969).
As with alevives, two first-order rate expressions were used  (Fig-  24);
0.0058/d for the first two age classes (zero and 1 year olds) and 0.0012/d
then-if^er.  These growth rates are representative of native lake trout since
the data used were gathered prior to 1965, the first year of lake trout stock-
Ing in Lake Michigan.  Hatchery-reared lake trout are faster growing and shorter
lived than the native trout (R. Hess, Illinois Dept. of Conservation personal
communication).
                                                           v
     A recent study of the age-length relationship of fin-clipped  (stocked)
lake trout (Ress and Muench, 1980) indicates growth rates significantly dif-
ferent than those celculated for the native trout.  The weights of  Juvenile,
and young adult trout are substantially higher and weights of the last  two age
classes are lower (Fig. 25).  The weights (g(y)) were calculated from total
lengths Ccn) using a relationship determined from data  compiled in  STORET:

                         w - 0.0063S L3'1125

Calculated growth rates are 0.0026/d for one to four year olds, 0.00072/d for
four to seven year olds, and 0.00024/d for seven to thirteen year  olds.
     The 1971 PCB data, to which the model is calibrated, includes  both native
and stocked trout.  Because the oldest stocked trout is of year class 1964,
all fish that were greater th/m 7 years old in 1971 must be native trout.
Fish 7 years old and younger in 1971 are liksly etocked trout  since their pop-
ulation is far greater than that of native trout.  The calculated  growth rates
therefore suggest that two non-homogeneous populations of trout are included
in  the PCB data set.  Using the calculated growth rates of native  trout will
simulate the population represented by the older trout.  Because thsse trout
exhibit the snaxlcum PCB concentrations they ere the trout calibrated to in
this work.  It io acknowledged that the stocked trout calculated growth rates
are, likely, s»re representative of the younger trout and a comparison of
computed PCB using both estimates of growth rates  is shown In Section 8.
                                       60

-------
         104
         103
      07 102
      h-"
      x
      g
      LU
      H-
      LU
         10°
         10-
                                        i   »    J
JL
             0   1   23456789  10  11  12

                               AGE, years
Figure 24.  Observed vet weight In relation  to lake trout  age es compared

           to functional relationship used  in the model.
                                61

-------
                               O HESS AND MU£NCH (1980)
                               O CAP LANDER (1969)
                          \    I •   I    I    l    I	I	L
                      345678
                        AGE CLASS (years)
9  10  11  12
Figure 25.  Comparison of  lake trout wet weight-age data fron: Carlander
           (1969) and Ress and Huench (1980).  Lines indicate rates
           used in the model.
                              62

-------
     Respiration
     Respiration or metabolic rate is composed of the basal  metabolic rate
(the rate of energy expenditure necessary to sustain life) and  the rate of
energy usage for activity.   The sum of these components,  under  normal condi-
tions, is termed routine metabolise.  Metabolic rate is a function of tem-
perature and size or weight of the. individual.
     The relationship between metabolic rate and temperature Is a complex
function of species and environment.  For a particular species  and environ-
ment the logarithm of basal or standard metabolism (the minimum rate observed)
generally Increases In a parabolic fashion with temperature. Although no
single functional relationship ie capable of describing the  relationship
across species,  within 10*C  of the midpoint of a species normal, environ-
mental temperature range an experimental relationship of  the form:

                              O.OS33(T-T )
                    R   - Re          n                              (51)
                     8t    %
where
                    R   • metabolic rate at temperature,  T(g(w) respired/day)
                     Bt
                    R   » metabolic rate at midpoint tecp.irfiture T
                     Bffi                                           m
approximates the temperature effect (Brett and Graves, 1979).
     As discussed in Section 5, Eq. (26), the relationship  between metabolic
rate, R, and body weight, w, is described by the relationship:

                    R •= ctwY                                            (52)

The values of the coefficients o and y have been the focus  of mu'ch research
with  reported values of y ranging from 0.75 (Kleiber, 1961)  to 0.36  (Glass,
1969).  A review of the field by Heissingsen (as cited by Schnidt-Nielsen,
1970) showed that for poikilotherms y WSB approximately 0.77.
                                     63

-------
     Routine metabolism of free-swimming Myels relicta from an arctic and a
temperate lake has been determined for various body weights at several tem-
peratures (Laoenby and Langford, 1972).  At all temperatures the relation-
ship between respiration and body weight conformed to E
-------
for respiration (g/g/d) ranging from 0.0212  to 0.0278 as fish else and svin
speed increases.  Respiration rates calculated using these values are approx-
imately a factor of 2 lower than those calculated using Eq. 54.   Use of these
lower rates in the model would require a slight Increase in toxicant assimi-
lation efficiency to maintain consistency with observed PCB concentrations in
alewife and lake trout.
     The respiration of lake trout in relation to body weight has been ana-
lyzed by Weininger (1978).  Combining the respiration-weight relationship for
basal metabolism (£q. 52) with a functional  representation of temperature
effects and of activity in terms of swimming speed, Weininger presented the
following general relation:

                         R - ovY eBT e*V                                (55)

where
                         T • temperature (°C)
                         V • avim speed (en/sec)
                       £,$ " empirical constants

Regression using an ejctenslve data set of 183 respiration experiments yielded
an equation that when swim speed is converted to trout length, L(cm), using
the empirical relation (Weininger, 1978):

                         V - 0.46L,                                     (56)

respiration is expressed as .g/g/d, and'temperature is set at 10"C, may be
written as

                         r' - 0.03V-0'295 e°-01L                        (57)

     in the model length, L, Is determined from the weight-length relationship
(Weininger, 1978):

                         £n(L) - 0.296tn(w)  + 1.803                     (58)
                                     65

-------
     Cslculated respiration in relation to body weight for Kyaia, alewlfe,  end
trout IB shown in Fig. 26.  Also shown is a general relationship based on data
for many species of freshwater fish (Winberg, 1956).  Lake trout respiration
levels off at high body weight because of the increasing contribution of 8wln»-
ming activity to respiration.
     Assimilation Efficiency
     The assimilation efficiency of food, as specified in the model,  is the
fraction of food ingested that does not appear In the feces.  It is a function
of the type of food eaten and the rate of consumption.  Elliott (1976) found
that the assimilation efficiency of brown trout eating Caunaarus pulex varied
from 0.86 at 102 of maximum consumption rate to 0.77 at maximum consumption
rate.  He also found that efficiency Increased with temperature and was Inde-
pendent of fish body weight.  In general, assimilation efficiency in carniv-
orous fish ranges from about 0.75 to 0.9 (Brett and Graves, 1979).  The diges-
tibility of plant life (algae, grasses) Is comparatively low and herbivorous
fish consequently have lower assimilation efficiencies.  A summary by Brett
and Graves (1979) indicates a range of 0.16 to about 0.65.  Based on this in-
formation the assimilation efficiencies In the tiodel ware set st 0.8 for lake
trout and alewlfe and 0.3 for Mysis.
     The food ingestion rate (g/g/d) used in the model Is computed as the sum
of the growth and respiration rates non&alized by the food assimilation effi-
ciency.  Fig. 27 shows the ingeetion rate calculated for each species in rela-
tion to body weight.  The discontinuities that are seen ere a consequence of
the change in Inputted growth rate with age.  Also shown are laboratory observed
Ingestion rates for Mysis relicta (Cooper and Goldr-an, 1980) and a field obser-
vation of elewlfe ingestion rate (Weaver, 1975).  The fit of the computed rates
to the data further supports the values used In the model for growth, respira-
tion and assimilation.

PCB PARAMETERS
     The concentration of PCB in the bodies of Mysis, alevlfe, and lake trout
is controlled by the rates at which PCB is adsorbed, metabolized, and excreted.
Each of these rates ie a  function of the species bioenergetlcs.
                                     66

-------
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        c
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                10-2
                10'3
                        MYSIS'
                                       GENERALIZED LOW ROUTINE
                                      METABOLIC RA TE FOR FISHES,
                                              r = 0.03 w-°-2


                                                          ALEWIFE
                                             LAKE TROUT
                                                                      I
                   10-4  1Q-3 1Q-2
                                           10°    101    102
                                       WET WEIGHT, g
                                                     103   104    105

-------
co
      "1
      h«>
      00

      r(
      n>
    ft C.
    eg M.
    r? tn
    n re
    o •••

    C S
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    OC !T>
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    • re
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         JC.

         •5 . 50
            40
            30
   20
   10
         ?   0
         INGESTION RATE AS A FUNCTION OF SPECIES WEIGHT
                        ©
MYSIS

Q
                                   ALEWIFE
                                                  TROUT
              10-4 10-3
                   -2  io-1   10°    io1   io2

                          WET WEIGHT (gms)
                              103    104    105

-------
     Absorption occurs at the gill membrane, skin, and digestive  tract.  The
skin la normally not significant In this  regard and  Is not  considered here.
Adsorption through the gill membrane is assumed to be proportional  to respira-
tion as described in Section 5.   Absorption through  the  lining  of the diges-
tive tract io computed as the product of  the ingestion rate of  PCB  (food inges-
tion rate x pg FCB/gfood) and an assimilation  efficiency for PCB.
     The assimilation efficiency Is the fraction  of  ingested contaminant that
is passed across the gut lining into the  organism.   It is normally  computed
as the ratio of the sum of the measured mass of contaminant In  a  test organism
and the mass excreted to the mass ingested.  However,  it is difficult to accu-
rately determine the mass excreted because significant contaminant  must be
excreted before taessurable dissolved contaminant  concentrations are reached.
As an alternative^ excretion rates determined  from depuration studies may  be
used to estimate the OSES excreted if contaminant concentrations  in the organ-
ism are measured over the duration of feeding.
     Another method to determine assimilation  efficiency is suggested  from the
equilibrium condition described by Eq. (40),   If  there is no uptake from water,
as in most experiments designed to determine assimilation efficiency,  this
equation may be written as:
                                                                         (59)
Solving for the assimilation efficiency yields:

                                v (K  + G )

Thus  if  the feeding rate, C.  ., the food concentration, v , the excretion
                           * > j                           J
rate, K. ,  end the growth  rate, G , are known then the assimilation efficiency
may be calculated from the equilibrium concentration of the organism under
study.
      No  assicilatlon efficiencies of PCB by lake trout, alewife, or Mysis have
been  reported.  The assimilation efficiency for PCB Aroclor 1254 in synthetic
                                    69

-------
food by rainbow trout  has been reported to be  0.68 based on the retention of
ingested PCB over a 32-week test period, assuming no excretion (I-ieb et al.,
1974).  No significant excretion was detected  during a 16-week depuration
•jtudy.  From a study of short-tern PCB Aroclov 1254 uptske from PCB-contaml-
nated phytoplankton (Wyman and O'Connors, 1980),  the PCB assimilation effi-
ciency of the estuarine copepod Arartia tonsa  was calculated to be approximatly
0.2.  This low efficiency relative to the rainbow trout is consistent with the
food assimilation efficiencies discussed previously in this section.  The PCB
assimilation efficiencies used in the tnodf.I are O.j5 for Mysis, 0.7 for ale-
wife, and 0.8 for lake trout.   These values were determined by calibrating the
model to observed PCB in lake  trout and alewife.   Assimilation efficiency was
varied du-f.ing the calibration  because of the uncertainty associated with it.
     Metabolism of PCB is not  significant.  The composition of PCB residues in
rainbow trout (Lleb, et al., 1974} and fathead minnows (DeFoe et al., 1978) vas
found to be essentially identical to the composition of PCB used for the exper-
iment.
     Excretion of PCB may >c estimated froa the ratio of PCB concentration in
the body of a particular species to the concentration «_'f PCB the species is
exposed to in a noa-feeding test, i.e., ihe bioconcentration factor (See Equa-
tion (10)).  If growth is not  significant during the rest because of a low or
zero feeding rate then Eq. CIO) simplifies to
                        K
                    K - ~                                                 (61)

The bioconcentration factor for PCB has beeo shown to be nearly constant over
a wide range of aquatic species at a value, of  approximately 10 Cpg/8. .   •"
I'g/R     ) (ThoDann, AyMi;.  Using this value  and the uptake re.te computed
   ^*^2 c Gr
from the respiration rate CEq. Q.8)) a value for excretion rate nay be calcu-
lated directly.  Fig.  28 compares the resulting excretion rates with rates
measured in ihe laboratory for various species.  Note that no excretion rate
data is avallaMc for large fish such as the adult lake trout.  The values
used in the mcdel are within the reported ranges.  The data in Fig. 28 indi-
cate eigniflcai.t variability of excrerion rate.  Much of  this variability  is
                                    70

-------
c
*f

n>


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do
•
o o
M) O
O a"
H> 0>
3 O
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*"* !9
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r» o
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~ m
C rtJ
re i
rt <
re
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(7) 3
rr
• n
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9
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1 U~'

T
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ji"l
TJ
IU 10-2
*-
^•t
cc

z
o
III. Ill
III 10-3
CC
0
X
LU


m-4
« RAINBOW TROUT
0 f007> A YELLOWPERCH
® FATHEAD MINNOW
0 SPO T
A V '
„ *. PIN FISH
^•>. o CALANUS
f ^^^8%(^^
^r ^^""'''ifc*^
MY SIS

® T*1**1^
X ^^^^ifcfc_
* ^^*fc^-
' * ^fc^
~ ALEWIFE ^^^
**^*^
/***li*^i*t««^_
/ ^^B*»»«!B«a»
^/5/^F 77?0(/r


i i 1 I i i i i i
        10~5  1Q-4
ID"2  TO-'  100   101   102  103

   WET WEIGHT, g
104  105

-------
likely analytical error.  Because PCB civ .•~»:lon rates ere low the decrease
in body burden during most excretion experiments is loss than the uncertainty
of the PCB measurement.                                     •

-------
                                  SECTION 7
                             MODEL CALIBRATION

     The final calibration is the result of a series of model runs that deter-
mined a consistent set of parameter values that vere in agreement  with observed
values and reproduced the observed PCB concentrations in Lake Michigan lake
trout and alevife.  Data for 1971 were used in the calibration.  A constant
dissolved PCB concentration of 5 ng/£ was assumed.  A constant value  implies
that the elev/ife and lake trout sampled in 1971 were exposed to  a  constant  PCB
concentration for their entire lives, vhich for the oldest trout represented
is ten years.  A tine variable dissolved PCB concentration was not used be-
cause no accurate data history exists.  The values assigned to the PCB assimi-
lation efficiency were adjusted to reproduce the observed PCB distribution.
This parameter was chosen ES the calibration variable because of the  uncertainty
of its value relative to the other parameters in the model.  Sensitivity  Letween
adjusting the PCB assimilation efficiency and the dissolved PCB  concentration
was tested and Is discussed in Section 8.
     The basic model presented in Section 5 and a model Including  an  empirical •
function relating lake trout excretion rate to lipld content were  calibrated
to the data.  The lipid-dependent excretion was included because of the ob-
served relationship between lake trout PCB concentration and percent  of body
weight as lipld.  (See Figure 6).

BASIC MODEL
     The cor.parison between observed data and calculated PCB concentrations in
alewife and  lake trout is shown in Fig. 7.9.  The parameter values  used  in the
model and presented in Section 6 are sunrmfirized in Table 5.  The model  repro-
duces the observed dsLfl vlth the exception of the cnrly age classes of  lake
trout.  No combination of parameters was successful at reproducing the  high
PCB values in age class 2 and 3 lake trout while maintaining consistency  vith
reported parameter values and reproducing the observed concentrations in  the

-------
•s, 15
1 10
cy c
^
^ 0
en
z"
O
•
H
H 25
5 20
o
z 15
O
0 10
00
0 c
Q_ °
0
ALE WIFE
-
' ^^J— f— i— 5
^X^J°**| | | | |

123456
AGE CLASS, yr

z./3/cE r/?ot;r T
- • 0 . 	 _
JL^-— "^ [^
T T T ^i>
l i J^T I I

•i ^^ $ '
— 
-------
TABLE 5.  PARAMETER VALUES USED IN CALIBRATION OF MODEL

Parameter
Jrovth Rate (d~ )
lespiratlon Rate a
!g/g/d) Y
;R-awVV) *
'ood Assimilation Efficiency
'CB Assimilation Efficiency
loconcentration Factor fron
•ater 
-------
upper age classes.  A possible explanation of these high values  is  that young
trout may be exposed to higher dissolved PCB concentrations than older trout
because of a tendency to stay In shallow near-shore waters.  This effect is
not simulated by the model because of the assumed constant dissolved PCB con-
centration.
     The data and the model both indicate that PCB concentrations in lake  trout
are 3 to 4 times those in alewife.  The computed increase results from the
higher PCB concentration in lake trout prey (alewife) relat*ve to alewife  prey
(Mysis).  All species in the model accumulate similar PCB concentrations from
dissolved PCB because of the constant relationship maintained between uptake
rate from water and excretion rate (i.e., constant BCF).  Some variation does
occur depending on the influence of growth rate as a concentration  loss mech-
anism.  The increase in computed PCB concentration with increasing  trophic
level (Fig. 30) is a direct consequence of the transfer of accumulated PCB from
one level to the next.  Section 5 discusses this effect in a simple steady
state situation.
     As a further illustrative example, using values consistent with the pre-
ceding discussion, consider a 4 level food chain (see Eq. 45) in which each
level has a bioconcentration factor fron; water of 10  Pg/g * Pg/g ,  ..   and a
                                             _                  W3 u GJT
bioconcentration factor from food of 0.3 x 10  pg/g * Pg/g.  As in  the Lake
Michigan PCB calibration assume that the water concentration is 5 ng/£ and
that the first level of the food chain is exposed only through water thus
achieving a concentration of 0.5 Pg/g.  The second level receives  the same
0.5 Pg/g from water but also receives 1.5 Pg/g from food since it bloconcen-
trates by a factor of 3 the 0.5 Pg/g accumulated by the first level.  It  then
has a concentration of 2 pg/g.  In a similar manner the third level accumu-
lates  0.5 Pg/g from water and 6 pg/g from food and the fourth level accumu-
lates 0.5 pg/g from water and 19.5 pg/g from food.
     From  this example it is evident that even for small accumulation factors "
from food there is a significant geometric increase in the concentration
achieved by ascending levels of the food chain.  Also evident is the increase
in  Importance of uptake from food et ascending levels of the food  chain.   At
the first  level 100X of the accumulated concentration is from water while  by

-------
en
°e>
en
en
=t
Z
O
»-
LU
O
2
O
O
CO
13
12
11
10
 9
6
 5
4
3
2
 1
0
            PHYTO-
          PLANKTON
                      MYSIS
ALEWIFE   LAKE TROUT
   Figure 30.  Average PCS concentration in each of the  '* species
              included in the food chain model.  Values indicated
              are  arithmetic average over all age classes.
                               77

-------
the fourth level only 2.5X of the accumulated concentration is from vater.
The geometric Increase shown by this simple example is also computed by the
calibrated food chain model as illustrated in Fig. 30.
     The relative importance of food and water to the computed PCB accumula-
tion by lake trout is illustrated in Fig. 31.  The PCB accumulated from water
is relatively constant of all age classes at a wet-weight BCF of approximately
      4
2 x 10 .  Including food results in over an order of magnitude higher BCF for
juvenile trout increasing with the concentration in the prey to an approxi-
mately 2 order of magnitude higher BCF for the oldest trout.  Expressing PCB
accumulation in terms of concentration, Fig. 31 shows that greater than 992
of the PCB in adult trout is taken up in food.  The contributions of food and
water to the lake trout calibration are shown directly in Fig. 32.  Again,
the overwhelming Influence of the food component is evident.  Considering the
other species or levels in the model the average fraction of total PCB concen-
tration that Is contributed from food is 0 for phytoplankton, 0.5 for Mysis,
and 0.85 for alewife.

LIPID-DEPENDENT MODEL
     Empirical evidence indicates that the extent of accumulation of organic
chemicals by aquatic species in laboratory studies is related to the lipo-
phillc nature of the chemicals.  The lipophillc nature is normally expressed
as the equilibrium concentration ratio of the chemical partitioned between
noctanol and water, i.e., the octanol-water -oa.'tition coefficient.  A linear
relationship between the log of the BCF and the log of the octanol-water par-
tition coefficient for a wide range of chemicals has been demonstrated for
rainbow trout (Chiou, et al., 1977) and fathead minnows  (Velth, et al., 1979).
     The lipophillc nature of a chemical controls its rate of transport
across the cell membranes of the gut and gills and Its partitioning between
the blood and lipid tissue of an exposed species.  The former affects the
assimilation efficiency of the cheric.nl and the latter affects the apparent
excretion rate of the compound because the sequestering  of chemical in the
llpld tissue slows the r.ite at which the cherrical reaches excreting organs.
The BCF then Increases with the lipophllic nn.turc of  the chcrr.lcnl because of
an increased uptake rate and a decic;i!;cd excretion rate.
                                      78

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     The nechanlsms that relate the BCF tnd lipophillc nature of the  chemical
also suggest that the BCF should be related to the lipid content of the  test
species.  De Foe et al. (1978) found that the BCF of PCB Aroclor 1248 and  PCB
Aroclor 1260 In fathead minnows was directly related to the llpld content  of
the fish and that a nearly constant BCF was obtained when FCB concentrations
were expressed on a llpld basis (pg/g,, ..).  Roberts et al. (1977) reported
that tissue retention ox the Insecticide chlorodane by northern redborse
suckers was directly proportional to the lipid content of the fish.   In  addi-
tion, their data indicated that the assimilation efficiency of chlordane was
directly related to the percent of body weight as lipid while excretion  rate
was inversely related.
     The high llpld-solubillty of PCBs suggests that accumulation r.f  PCBs
should be correlated with the lipid content of the exposed species.   The ana-
lysis of data presented in Section 4 Indicates that across thirteen  species
there 'is no apparent relationship between PCB concentration and % lipid.
However, for the lake trout the data does Indicate increasing PCB concentra-
tion with increasing llpld content.
     To test if an improvement of the lake trout calibration would result,
excretion rate was formulated as an empirical function of the lake trout
lipid content.  Lipid content in relation to lake trout age  (Table 6) was
compiled from the PCB data sources for fishes of Lake Michigan listed in
Section 4.  An inverse power-law relationship between excretion rate and Z
lipid was chosen and the coefficients of the relationship determined by cal-
ibration of the model to the lake trout .PCB data.  The resulting relation-
ship is:

                         K - 	^	z                           (62)
                             6 x 10  (lipid)
where
          K" «• excretion rate used in the basic model.
                                     81

-------
   TABLE 6.  LAKE TROUT LIPID CONTENT TATA COMPILED IN RELATION TO AGE CLASS
Lsi-.e Trout
Age Class
2
3
4
5
6
7
8
9
10
Mean Z
Lipid
8.6
7.0
6.4
6.8
10.8
16.3
18.1
16.3
13.6
Std. Deviation
3.3
3.4
2.9
3.5
4.9
5.8
7.0
9.3
5.5
Max. '
14.8
13.2
12.6
16.0
21.3
50.0
36.2
49.2
45.0
Min.
3.2
1.1
3.5
2.1
1.8
4.0
6.1
1.5
5.7
No. of Points
8
10
16
33
154
i:42
73
70
10

     With this formulation an improvement of the lake trout calibration was
achieved (Fig. 33).  The model still doei not reproduce the early age class
data but does very well at fitting the shape as well as the magnitude of the
later'-data.  This result indicates that lipid content IB important to the
dynaailcs of PCB accumulation in lake trout.  The empirical relationship be-
tween excretion and lipid used here has no fundamental basis but is important
because it points out the significance of lipid content.  A taore mechanistic
formulation would separate each lake trout age class into lipid and non-lipid
components.
                                 *
     The demonstrated importance of lipid content and the observed increase in
lipid content with lake trout age suggests the possibility that the increasing
PCB concentration with lake trout age cicy be explained by partitioning from
water to lipid rather than uptake from food.  Some evlde-.ce, in fact, indi-
cates that field observed contaminant concentrations may be directly estimated
frop. water concentrations using lipid content and the octanol-vater partition
coefficient of the contaminant (Schnoor, 1980).  To test this possibility, the
highest reported octanol-water partition coefficient available in the lltera--
ture (10 '   for HCB) was used with the lake trout lipid content to predict
lake trout PCB concentration.  Following Schnoor (1980) the octanol-water par-
tition coefficient was assumed to be equivalent to the llpid-based BCF
                                     82

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Figure 33.  Cocparlaon of observed PCB Concentrations In alevlfe
           and lake  trout with calculated concentration frora
           lipid-dependent model.
                              83

-------
g,. .. -r Vg/R  t  ).  The resulting PCB concentrations (Fig.  34) calculated
from the equation:
                         V - BCF*c*f.
                                L    L
          where
                        £L - frBCtion of body weight as lipid

vere A to 5 times lower than the data and food chain model cslculutiou for
adult trout and clearly «m unsatisfactory estimation of lake trout contatii-
nation.  The. poor fit results from the failure to consider exposure through
food which, ae shown earlier, io the <5citina-.it contributor of PCB to the top
predator lake trout.  Similarly for the alewife, the simple lipid partition-
ing calculation yields concentrations 2 to 4 times lower than the observed •
data (Fig. 35).  This calculation is closer to the data than the lake ttout
calculation rosslbly because the importance of contaminated food to body
burden is less in the lower trophic level alevife.  It should be noted that
the uncertainty in the dissolved PCB concentration is. such that the. actual
concentration may be as high as 10 ug/i, i.e., twice the concentration used
here, thus doubling the fish PCB concentrations calculated by simple lipid
partitioning.  These high calculated values would corce clcse to observed
alewife concentrations but wou?d Belli be significantly below observed lake
trout concentrations.
     The feet that satisfactory results have previously been achieved with
the simple octanol-water BCF approach may reflect the different focus of
this method relative to the work presented here.  The octanol-vater BCF
approach is based on correlation of data over a rsnge of cheaicals, fish
species and water bodies.  Interpretations are made or. general trends that
include a significant amount of stetlstical variability.  Estimation to
within an order of magnitude of observation is considered satisfactory.  In
contrast, thie work ie focused cm a finer scale where accurate prediction
is jfeecessary to determine the Intact of a specific chemical, on a specific
fishery, in. a specific vrater body.  While the fonaer method is valuable in
assessing trends, the latter is necessary to answer specific questions
about  the management and fate of a given system.

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                PARTITIONING TO LIPiD TISSUE OF LAKE TROUT

                                PERCENT LIPID
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CONCLUSIONS
     The calibration of the age-dependent  food  chain model  to data from Lake
Michigan illustrates several points:
     1.   the model Is capable of reproducing the age-dependent  trends and
          magnitude of PCB contamination observed in Lake Michigan alewife
          and lake trout in 1971.
     2.   transfer of PCB through the food chain Is the major contributor to
          observed PCB concentrations in lake trout, accounting  for  greater
          than 99Z of the body burden in adult  trout.
     3.   an empirical relationship between lake trout  excretion rate and
          lipid content significantly improves  the lake trout calibration,
          suggesting that lipid tissue is  an inportant  factor in PCB dyna-
          mics.
     A.   a simple enpirlcal correlation between octanol-vater partitioning
          of PCB and bloconcentration of PCB falls to  reproduce  the  observed
          concentrations in alewlfe and lake trout.
                                      87

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                                 SECTION 8
                             MODEL SENSITIVITY

     Of the parameter values chosen for calibration of the model  to  the ale-
wife and lake trout PCB data, the values for PCB  assimilation  efficiency, PCS
excretion rate, and dissolved PCB concentration are the least  well known.   It
is thus pertinent to examine the effect of variation of these  parameter values
on the PCB concentrations computed by the model.
     In addition, because the food chain structure leading to  a top  predator
such js ths lake trout is more complex than that  of other species of sport  or
commercial interest, it is useful to examine the  effect of a simpler structure
on the computed concentrations.
     This significance of the differences ±n l«ke trout growth rate  that are
discussed in Section 6 is also examined.

SENSITIVITY OF MODEL TO PCB ASSIMILATION EFFICIENCY
     Very little data ere available that defines  the assimilation efficiency
of toxicants by fish.  As cited earlier, Lieb, et al. (1974) reported that
the PCB Aroclor 1254 assimilation efficiency of rainbow trout  vas approxi-
mately 0.68. An analysis of this data by Veininger (1978) shoved  that for fish
greater than 5.5 g, the assimilation efficiency ranged froa  0.64  to  0.79.   In
a previous modeling study (Thomann,•1981) the PCB assimilation efficiency of
lake trout vas assumed to 0.9.
     A comparison of computed lake trout PCB concentrations  at lake  trout PCB
assimilation efficiencies of 0.95, 0.8 and 0.65 and observed PCB  concentra-
tions is shown in Pig. 36.  The high and low assimilation efficiencies bracket
the estimates noted above and 0.8 is the vslue used In the codel  calibration.
Computed concentration is approximately 4 tg/g lower at the  upper age classes
when the assimilation efficiency is 0.65.  The results at the  0.95 assimila-
tion efficiency reproduce th.e observed data for the clddle age classes fairly
well.
     It la significant that the computed velues at asslcilstlon  efficiencies
                                       88

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0.65 and 0.8 both fall within the obse.rved data since the available experi-
mental data indicate that 0.65 to 0.8 IB the assimilation efficiency range.
The pg/g difference at upper age classes between the two computations,  how-
ever, is substantial because It will effect estimates of the efficiency of
PCB load reductions in lowering lake trout PCB concentrations to below the
FDA action limit of 5 pg/g.  This variability therefore must be considered
in management decisions based on the model's results.

SENSITIVITY OF MODEL TO LAKE TROUT PCB EXCRETION RATE
     The PCB excretion rates used in the calibration are calculated from ob-
served BCFs assuming that the BCF represents the ratio of uptake to excretion
rate (see Eq. 105)).  As shown in Section 6 the resultant values compare well
with rates reported in the literature.  However, there la substantial varia-
bility in the reported rates and some literature data indicate that the PCB
excretion rate is effectively zero (DeFoe et el., 1973; KcLeese et al., 1980).
To examine the influence of this variability on the computed PCB concentra-
tions the excretion rate for lake trout was altered from the values used for
calibration to zero.
     A conparison of computed PCB concentrations in lake trout that have excre-
tion rate specified as zero with computed PCB concentrations from the calibra-
tion is shown in Fig. 37.  Reducing lake trout excretion to zero increases
computed concentrations In adult trout by approximately 3 V-'g/g or 13 percent.
Because this increase results in a less satisfactory fit of the model to ob-
served data, it suggests that either zero excretion rate is unreasonable or
that other parameter values in the model are Incorrectly specified.
     As discussed earlier, PCB assimilation efficiency Is not well defined and
for lake trout could vary at least from 0.65 to 0.8.  Also presented were the
results of lowering the value of lake trout assimilation efficiency from 0.8
to 0.65, I.e., a reduction in adult trout PCB concentrations of approximately
* Pg/8 or 17 percent.  This reduction would more than compensate for the in-
crease resultant from assignment of zero excretion rate.  Therefore, It Is con-
cluded that the uncertainty in assimilation efficiency precludes a judgement as
to the most appropriate of the reported excretion rates.
                                      90

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                                           BaoswJ on BCF of  100 ?
                                       343   3    7   8   9   10  11   12
                                                     CLASS

-------
SENSITIVITY OF MODEL TO DISSOLVED PCB CONCENTRATION
     As discussed in Section 4, the main-lake dissolved PCB concentration
during the early seventies is believed to have been less than  10 ng/i.  A
more precise estimate is unavailable.  In the calibration a value of 5 ng/l
is assumed.
     An examination of the effect of variation of the dissolved  PCB concen-
tration on computed alevife end lake trout PCB concentrations  can be used  to
assess the likelihood that the dissolved PCB concentration was significantly
different than 5 ng/l.  A criteria far calibration of the model  is that the
bloeaergetlc and PCB associated parameter values be in agreement with observed
values.  This criteria is satisfied at a dissolved PCB concentration of 5  ng/l.
If this criteria cannot be met at higher and lower concentrations it suggests
that the concentration cruet have been close to 5 ng/£.
     Assucing dissolved PCB concentrations of 10 end 2 ng/.l alters the conputed
alevife and lake trout PCB concentrations as shovn In Pig. 38.  As expected, at
10 ng/i computed concentrations are tauch greater than observed values and  at 2
ng/i they are much lower than observed values.  To adjust these  consulatlone
to better slnrjlate the data the PCB aesinllatlon efficiency is adjusted since
this parameter exhibits the widest range of observed values, all other para-
neters b-avirg been shovn in Section 6 to be in good agreement  vith experiaental
data.
     At the 2 ng/l dissolved PCB concentration, the nodel failed to  reproduce
the observed data even with asslnllatlon efficiencies for alevife and trout
increased to 0.99 (Fig. 39).  Calculated concentretlone were consistently  low
for alevife and low for upper ege class trout.
     At the 10 ng/£ dissolved PCB concentration, decreasing HyslB assinilation
efficiency to 0.2 (the value reported by Vynan and O'Connors  (1930)  for  the
copepod Acartta torisa) end alewife assitEilation efficiency to 0.45  produced
calculated concentrations essentially Identical to the calibration  at a  dis-
solved PCB concentration of 5 ng/jt (Fig. 39).  Although the assicilfition effi-
ciency of 0.2 for Hysij! ie reasonable, the velue of 0.45  for alewife is  low
relative to available fish data.  However, since no data on riddle  level con-

-------
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  AGE CLASS (years)
       0   t   2   3   4   5   6  7  8  9  10  11  12  13

                         AGE CLASS (years)
   Figure 38.  Coaputed  alewlfe and  lake trout PCS concentrations
              at dissolved PCS concentrations of 2 ug/1, 5 ug/Jt
              end 10 ug/i.
                              93

-------
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LAKE TROUT

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Figure 39.  Computed alevife and  lake trout PCB concentrations for models
           recalibrated to dlss.olved PCB concentrations of 2 ug/i and
           10 ng/£ by alteration of PCB essiclletion  efficiencies.

-------
Burners like alewife are available, the value of 0.45 cannot be considered un-
reasonable and 10 ng/JJ. must be assumed to be a possible value for the dissolved
PCB.
     It may be concluded from the above analysis that the average dissolved
PCB concentration in the main-lake of Lake Michigan was likely in the range
of 5 to 10 ng/£.  The implication of using 5 ng/£ in the calibration is that
a conservative estimate of the loading reduction necessary to achieve a cer-
tain concentration in the food chain vill result from any projection.  Tne
model is linear with respect to dissolved PCB concentration and the undertainty
of the model results will be dliectly proportional to the uncertainty of the
dissolved PCB concentration.  Since an uncertainty in dissolved concentration
of approximately a factor of 2 is suggested by the above analysis a similar
factor must be placed on any prediction mode using the model.

SENSITIVITY OF MODEL TO FOOD CHAIN STRUCTURE
     The lake trout food chain considered here includes four trophic levels.
The geometric i\ crease in PCB contamination vith trophic level demonstrated.
in Section 7 suggests that if the lake trout food chain were, eay, the three
trophic level chain that is exhibited by nany other species then PCB concen-
trations in lake trout would be much less.
     To Illustrate this effect the laVe trout PCB. concentrations vere computed
with Mysls removed from the food chain structure and then with alewife removed
from the food chain structure (Fig. 40).  For both cases there is a dramatic
reduction in lake trout PCB.  At the upper age classes the food chain without
Myjs_is_ has higher concentrations than the food chain without alewife.  This
results from the higher assimilation efficiency of the alewife relative to
Mysis.  At the  lower age classes the food chain withuut alewife '.IBS higher
concentrations because the lake trtut are consuming Hysis^ whereas in the mode
without Mysis they are consuming the lower concentration plankton.
     For adult  trout the loss of a trophic level reduces concentration by a
factor of 5 to  10.  This Illustrates the Importance of food chain transfer
end the significance of a species trophic position on its accumulation of PCB
fron the environment.

-------
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                                   4    5    5    7.8

                                    AGE CLASS (years)
                                                           10   11   12

-------
SENSITIVITY OF MODEL TO LAKE TROUT GROWTH RATES
     As presented In Section 6, native and stocked lake trout in Lake  Michigan
may have different rates of growth based on observed length-age and weight-age
relationships.  The growth rate difference is significant because the  1971  data
used for calibration of the model include fish from both populations.   Fish
greater than 7 years old in 1971 were native to Lake Michigan because  they  were
born prior to the beginning of the stocking program.  Fish less than 7 years
old, that were caught and analyzed for PCB, were likely stocked since  the stocked
population was far greater than the native population.
     Computed PCB concentrations using both sets of growth rates are compared
to each other and observed PCB concentrations in Fig. 41.  Weight, rather than
age class, is used in the figure because the age class divisions are different
for each set of growth rates.  As in the previous calibration figures, com-
puted concentrations using the growth rates for native trout are be.Tow the
data for young trout, high for intermediate age trout and within the data for
the older trout.  The differences between the model and data for the smaller
trout are accentuated by the compressed scale for the early age classes. The
computed concentrations using the growth rates for stocked trout fit the data
for trout up to 3000 g(w) much better then the calibration.  The continued  in-
crease for heavier trout (greater than age 7), however, is not supported by
the data.                                           •                     •   .
     These results indicate that the optimal model calibration would consider .
stocked trout up to about age 7 and native trout thereafter.  This supports
the contention that there are two trout populations with diflerent growth
rates.  An important consequence of this population difference is indicated
by the computation of greater PCB accumulation in stocked trout.  With e' .;cked
trout comprising the bulk of the population in Lake Michigan, the calculated
PCB concentration reduction necessary to reduce lake trout PCB to a specified
level is greater than predicted using native trout growth rates.  This is illus-
trated in Section 9.

-------
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                                                 GROWTH #2
                                                       GROWTH # 7
            1.000    2,000
                              3.000   4,000
                              WEIGHT (g)
                                     6.000
      III j I   1
      02 45 6

      Ul   I
      023
                                   1
     8
I	I
                            1
                                                  10
I   I   i   I   I   1
                            6     7  8  9  10 11  12
                            AGE CLASS (years)
                                                         •GROWTH
                                                         -GROWTH #2
       Figure 41.  Computed and observed lake trout PCB concentrations
                  In relation to wet weight for native trout  growth
                  rates (tfl) and stocked ..Tout growth rates (#2).
                                 98

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                                  JECTION  9
            LAKE TROUT RESPONE DUE TO REDUCED WATER CONCENTRATION

      The objectives of this research as noted  in the  Introduction include a
 preliminary projection of the response in PCB  concentration in the lake trout
 following a reduction in water column concentration.  The purpose of such a
 projection is to determine the approximate dissolved  vater column concentra-
 tion that is necessary to have PCB concentrations in  the edible portion of
 the lake trout below 5 pg/g(w).
      Figure 42 shows the result of a simulation of the  response of the lake
 trout to a five fold decrease in the dissolved PCB concentration.  The time
 history of 3 different year classes is shown.   The dashed lines show the
 simulated PCB concentration after the water concentration is  instantaneously
 dropped from 5 ng/A to 1 ng/Jl.  For the 7-year old lake trout, initially at
 a concentration of about 19 Vg/g(w), there is  a decline for a period of 5
 years to about 6 pg/gCw) at which point the assumed maximum age of the fish
 of 12 years is reached.  The four year old fish is calculated to approach
 4 Pg/g(w) after about a four-five year period  of decrease.  The one year old
 traces out the PCB distribution that is calculated over its life cycle and
. as shown reaches a naxl-juis value of 4 Vg/gCw).  One concludes from this pro-
 jection that when water levels drop from  the assumed  concentration of 5 ng/£
  dissolved to 1 ng/£, that the lake trout will reach  Ecximum  concentrations
 of ebout 4 pg/g(w) on a whole fish basis. A period of about  5 years would be
 required to "clear out" the higher concentrations from the  upper age class
 fish.  The calculations shows in Figure 42 however are for  the growth rate
 of the lake trout for the pre-stocked period.   The time variable response
 under the higher growth rates representing  the period of  extensive stocking
 would be somewhat different although not  markedly so.
      The entire modeling framework for  the  PCB in the lake  trout is  linear to
 the dissolved water concentration.  A  simple  relationship can therefore be
 obtained between lake trout concentration and  the PCB concentration  In  the
 water.  This is shown in Figure A3. As noted  previously  In Section  8 - Model

-------
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 6

 4

 2

 0
        PROJECTED RESPONSE OF DIFFERENT AGE
         LAKE TROUT TO A FIVE-FOLD DECREASE
           IN DISSOLVED PCB CONCENTRATION
             CALCULATED FOR
             5ng/L
             PROJECTED FOR
              1 ng/L
                    1-YEAR OLD
                   i   i   i    t
     0123
                   4   5  6   7   8   9  10 11  12
                    AGE CLASS, years
    Figure 42.  Projected response of different age lake trout
             to a five-fold decrease in dissolved PCB con-
             centration - grovth rate #1 for pre-stocked
             period.
                        100

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                            ESTIMATED RANGE OF
                          1961-1971 CONCENTRATION
                                                          A.
                                       FOR: 8-9 YEAR OLD
                                           (GROWTHRATE #11

                                           7 YEAR OLD
                                           (GROWTH RATE #2)
                                    ESTIMA TED RANGE OF
                                  REQUIRED CONCENTRATION
              0               5              10

               DISSOLVED PCB WATER CONCENTRATION (ng/l)
         C7>
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(GROWTH RA TE #2)
                        ESTIMA TED RANGE OF
                     REQUIRED CONCENTRATION
              0               5              10

               DISSOLVED PCB WATER CONCENTRATION (ng/l)


Figure 43.  Relationship!? between equilibrium PCB  concentration in 11 year
           old lake trout and dissolved PCB water concentrations, growth
           rate i?i - pre-stocked period; growth rate H2 - stocked period.
                                101

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Sensitivity, the 1971 lake trout data using growth rate Si (pre-atocked growth
rate) could be calibrated within an acceptable range of parameters for water
concentrations between 5 and 10 ng/£.  Figure 43(a) shows this calibration
range for the 20 yg/g(w) as observed in the 8-9 year age class and the pre-
stocked growth rate (#1).  As snown in Figure 41, the 20 vg/g(w) also applies
to the 7 year olds under the stocked period growth rate (02).  The calibration
and sensitivity analyses indicate that the dissolved PCS water concentration
for the 1961-1971 period was then probably between 5 and 10 ng/£.
     The objective for PCB concentration in the edible portion of the lake trout
is 5 yg/g(w).  The model calculation is for the PCB concentration in the whole
fish.  Recognizing the variability in the concentration of the edible portion
as a function of the whole fieh (see for example, Figure 9), a range of 5-10
pg/g(w) on a whole fish basis was chosen.  This assumes that the edible portion
concentration is about 50% of the whole fish concentration, a fraction indicated
approximately by the data of Figure 9.  This range is then used to estimate the
required water concentration such that the edible portion would be expected to
be below 5 yg/g(w).  Figure 43(a), shows the linear relationship between whole
fish concentration and dissolved water concentration.  The shaded.area indicates
the region of uncertainty as a result of the calibration uncertainty in the
water concentration.  If whole fish concentrations of 5-10 pg/g(rf) are accept-
able (and are considered to result in edible concentrations less than 5 Vig/g(w)),
then a range of about 1-5 ng/£ dissolved PCB water concentration is necessary.
A 50-90% reduction in the 1971 water concentration would therefore result in
7-9 year old whole fish concentrations of 5-10 Vg/g(w) and edible portion con-
centrations generally less than 5 Vg/g(y).  The degree to which any reduction
in water concentration have been accomplished since 1971 is subject to further
study.
     The situation is slightly different for the older fish (e.g., 11 years old)
under the higher growth rate of the stocked fish.  This Is shown in Figure 43(b)
where it is noted that 20 pg/g(w) in an 11 year old results from only 2.5-5 ng/£
(as contrasted to 5-10 ng/£ under the slower growth rate).  The difference is
attributed to the apparent higher growth rate of the stocked lake trout (see
discussion in Section 8).  For a -similar objective of 5-10 pg/g(w) tn the 11
                                     102

-------
year old fish, Figure 43(b) indicates that the required dissolved PCB water
concentration would have to be in the range of 0.5-2.5 ng/£.  This range
represents a 75-952 reduction of apparent 1961-1971 concentrations.
     It is apparent then that for a f/'X'.-d waiter concentration, the objective
of 5 ug/g(v) in the edible portion may be met by some age classes but not
others. Indeed, the critical age classes are the fish that are generally
older than about 6 years.  The overall relationship between age class and the
required dissolved water concentration to maintain 5-10 ug/g(w) on a whole
fish basis is shown in Figure 44.  The range shown reflects uncertainty in
the PCB assimilation efficiency and dissolved PCB concentration.  As indi-
cated, the older age classes require the lowest dissolved PCB water concentra-
tion to meet the 5-10 ug/g(w) level.  This is Just another representation of
"'gures 42 and 43.  Thus, if a level of 2 ng/£ were obtained, thci> whole fish
6 years and older would have concentrations between 5 and 10 ug/g(w).  Con-
versely, whole fish less than 6 years old would have PCB concentrations less
than 5 ug/g(w).  It Is possible to use a plot such as Figure 44 to develop an
age dependent (or more practically a weight or size dependent) basis for open-
ing up the fishery to consumption.  For example, if projections for the next
10 years indicate that the lowest attainable PCB water concentration is 1 ng/£
because of diffuse and atmospheric sources, then lake trout 8 years or older
(i.e., 3.5 kg or 70 cm) would be prohibited for consumption.  The whole body
concentrations in those fish would be expected to be equal to or greater than
5 ug/g(w).

CONCLUSIONS
     The projections of the behavior of the lake trout food chain to reduced
water concentrations Indicate the following:
     1.   Following reductions in water column PCB concentrations, a period
          of about 5 years is needed to reduce whole body PCB concentrations
          in upper age class lake trout.
     2.   In order to have the PCB concentrations of all age classes of lake
          trout at or below 5 ug/g(w) in the edible portion, it is estimated
          that the dissolved water concentrations would have to be between
          0.5-2.5 tig/£ using growth rates representative of stocked fish.

-------


Q_

Si
O cc
CO I—
£ z
Q UU
O
HI
DC
                                     CONCENTRA TION

                                     10 ng/g, wet weight
2  -
        0
                             468

                             AGE CLASS (years)
  Figure 44.  Calculated  relationships between age  class of lake trout

             and required  dissolved PCB water concentration to aeet

             whole fish  concentration of 5-10 ug/g(w).  Growth rate

             $2 for stocked lake trout.
                               104

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This range represents a 75-95% reduction of apparent 1961-1971 water
concentrations.
Younger age classes can generally be exposed to higher water PCB con-
centrations than older age classes without exceeding the objective  of
5 Pg/g(w).  As a result, if water quality projections indicate a
lower bound in the achievable PCB water concentrations, a size depen-
dent fish consumption guideline can be developed.

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                                      110

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