SCIENTIFIC REVIEW AND CRITIQUE OF
R. L. PATTERSON'S:
PRODUCTION, MORTALITY, AND POWER-PLANT ENTRAPMENT OF
LARVAL YELLOW PERCH IN WESTERN LAKE ERIE*
D. S. Vaughan and S. M. Adams
Environmental Sciences Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee
for
U.S. Environmental Protection Agency
Region V
February 1981
*Research sponsored by Region V of the Environmental Protection Agency,
under Interagency Agreement 40-650-77 (Task Order No. ORNL/EPA-V5)
with the U.S. Department of Energy under contract W-7405-eng-26 with
Union Carbide Corporation.
By acceptance of this artic.lc, the publisher or
recipient acknawlodjjcs the U S. Govt rnment's
right to retain a non - ex-.iuiiiye, royalty - free
license in and to any copyright covering the
article.
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SCIENTIFIC REVIEW AND CRITIQUE OF
R. L. PATTERSON'S;
PRODUCTION. MORTALITY, AND POWER-PLANT ENTRAPMENT OF
LARVAL YELLOW PERCH IN WESTERN LAKE ERIE
D. S. Vaughan and S. M. Adams
SUMMARY
This report presents a review and critique conducted for EPA,
Region V, of the report, Production, Mortality, and Power-Plant
Entrapment of Larval Yellow Perch in Western Lake Erie. by
R. L. Patterson (1979). Patterson enumerates six objectives for his
study, including:
1. estimate the production of larval yellow perch in 1975-76 in
Michigan and Ohio waters of the western basin of Lake Erie,
2. estimate natural mortality among larval yellow perch for the
25 days following hatching,
3. estimate the number of larval yellow perch entrained and killed in
1975-76 in cooling water used by the Monroe Power Plant,
4. estimate the percentage of total larval production in Michigan
waters lost to the cooling waters used by the Monroe Power Plant,
5. estimate the percent loss in young-of-year recruitment attributable
to entrainment mortality at the Monroe Power Plant,
6. estimate the loss to the yellow perch fishery in western Lake Erie
attributable to entrainment and impingement mortality at the Monroe
Power Plant.
The first objective is met through Patterson's "materials balance"
model (discussed in Sect. 4 of this report). Estimates of natural
mortality for larval yellow perch (objective 2) are not obtained from
the "material balance" model, but are stated without adequate justifi-
cation (Patterson 1979, p. 114). Ranges of estimates of larval yellow
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perch entrained in the cooling water used by the Monroe Power Plant are
provided and combined with subjective weightings for which no justifi-
cation is given; and little explanation is given for the source of data
used in Appendix E of Patterson for estimating the through plant
entrainment mortality (objective 3). Objective 4 is obtained from
objectives 1 and 3; and objective 5 is obtained from objective 4,
assuming no density-dependent mechanism occurs during the larval life
stage. Objective 5 was attempted via the Patterson models 1 and 2.
This report provides a detailed discussion and evaluation of the
data used in the Patterson "materials balance model" and the use of
this model to obtain estimates of larval natural survival and
abundance. A principal deficiency of the Patterson study is the lack
of attention to detail and clarity in presenting the data used in this
model to obtain estimates of larval abundance. An additional defi-
ciency relates to objective 2, in that estimates of the daily instan-
taneous natural mortality parameter p are not estimated, but are given
without adequate explanation or justification.
The two models (models 1 and 2) proposed by Patterson to estimate
long-term impacts on the yellow perch fishery are also critically
evaluated. A problem of significant importance relates to a duality in
meaning of the life-stage survivals, which should represent the
survival of an individual having an average age within its life stage.
The survival must also represent the probability of surviving the
entire life stage because of impacts to later life stages. A secondary
problem relates to the lack of stability in model 1 for the ranges of
life history parameters. Furthermore, the abundance estimates obtained
from the materials balance model are not used in either model 1 or 2.
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The weaknesses and strengths of the Patterson approach, an
introduction to an age structure approach to assessing the long-term
impacts resulting from operating the Monroe Power Plant, and future
data needs to improve further assessments are also present in our
report. The age structure model described in detail in Appendix A will
appear in Quantitative Population Dynamics, edited by D. G. Chapman and
V. F. Callucci (International Cooperative Publishing House, Fairland,
fid.). Ranges of losses to the yellow perch fishery have been estimated
based on this age structure model and entrainment and impingement
estimates from Patterson and C. D. Goodyear (1978). A higher range of
impact estimates were obtained based on C. D. Goodyear's estimates of
entrainment and impingement due to much higher estimates of impinged
yellow perch. However, lack of adjustment in Appendix A of larval
concentrations in western Lake Erie for gear bias is believed to cause
a considerable underestimate of larval abundance and results in an
overestimate of conditional mortality rates and projected losses to the
fishery. On the other hand, the assumption of an equilibrium popula-
tion, when the population is declining, would lead to an overestimate
of age class 0 survival and abundance of later life stages. Additional
assumptions and sources of error are discussed in Appendix A (Sect. 4),
including three sources of error: (1) natural variability in the
environment, (2) errors in the estimation of both model parameters and
inputs, and (3) errors in model structure.
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CONTENTS
Page
SUMMARY ill
1 . INTRODUCTION 1
2. SITE AND PLANT DESCRIPTION 3
3. YELLOW PERCH FISHERY IN WESTERN LAKE ERIE 6
4. LARVAL YELLOW PERCH ABUNDANCE - EVALUATION
OF METHODOLOGIES 9
4.1 Status of Larval Concentration Data 9
4.2 Materials Balance Model of Larval Production 11
4.3 Data Presentation and Reduction 16
5. LONG-TERM IMPACTS ON YELLOW PERCH FISHERY -
EVALUATION OF MODELS 18
5.1 Model 1 19
5.2 Model 2 23
6. DISCUSSION 26
6.1 Weaknesses and Strengths of Patterson's Approach .... 26
6.2 Alternative Age-Structure Approach 27
6.3 Future Data Needs 29
REFERENCES 32
Appendix A. AN AGE STRUCTURE MODEL OF YELLOW PERCH
IN WESTERN LAKE ERIE A-l
Appendix B. MISCELLANEOUS EDITORIAL COMMENTS B-l
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1. INTRODUCTION
Oak Ridge National Laboratory under contract with the U.S.
Environmental Protection Agency, Region V (EPA V), has undertaken a
scientific review and critique of the report by R. L. Patterson
entitled Production, Mortality, and Power-Pi ant Entrainment of Larval
Yellow Perch in Western Lake Erie (Patterson 1979). The following
principal questions (as called for in the EPA task description) were
considered as part of the review and critique:
1. Are the models appropriately applied?
2. Are the assumptions reasonable?
3. What are the weaknesses and strengths of the total approach?
4. What could be done or ought to be done to overcome or more
fully support weaknesses or problem areas?
5. What strengths need to be pointed out or expressed more
fully?
6. Are the estimates of impact about right?
7. What other or better approaches (models or other) might be
pursued for comparative purposes?
8. If additional data are collected, where should more effort
be applied?
9. If the report is unclear or cannot be understood as it now
stands, what information is needed to make it clearer and
more susceptible to independent evaluation?
Considerable overlap exists among the first seven questions, and these
will be addressed as similar problems in the following critique.
Patterson's report follows a logical progression in the develop-
ment of his modeling approach. Data for concentration of larval yellow
perch in the U.S. waters of the western basin of Lake Erie are pre-
sented in Sect. 3. These data are used as input to a "materials
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balance model" to obtain estimates of larval yellow perch mortality and
production (abundance) (Sect. 4). Two models are then described which
assess the loss to the yellow perch fishery attributable to entrainment
and impingement mortality at the Monroe Power Plant (Sect. 5). Long-
term losses to the yellow perch fishery are estimated (model 1) by
using an extention of Horst's (1975) "equivalent adult" model.
In this review and critique, the western basin of Lake Erie and
the Monroe Power Plant are described along with the yellow perch
fishery of Lake Erie. Next, we examine the methodology for estimating
larval abundance used by Patterson and examine models 1 and 2, which
consider the "long-term" effects (i.e., at equilibrium following the
onset of power-plant impact) of entrainment and impingement by the
Monroe Power Plant on the yellow perch fishery in western Lake Erie.
Finally, we summarize the weaknesses and strengths of the modeling
approaches used by Patterson, compare an alternative age structure
approach (see Appendix A) with Patterson's approach, and briefly
discuss future data needs.
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2. SITE AND PLANT DESCRIPTION
The Monroe Power Plant is located on the western shores of Lake
Erie near the city of Monroe, Mich. (Fig. 2.1). Lake Erie is the
2
fourth largest of the Great Lakes by surface area (25,690 km )
(Hartman 1973, Nepszy 1977) and receives about 95% of its total inflow
(Hartman 1973) (annual average of 5465 nT/s) from the three upper
Great Lakes (Lakes Huron, Michigan, and Superior) via the Detroit
River. The annual average outflow to Lake Ontario is about
5720 m /s, implying a theoretical flushing time of approximately
920 days (Hartman).
Lake Erie is naturally divided into three basins (Fig 2.1), the
western basin being the smallest and shallowest. This basin, from
which the Monroe Power Plant receives its cooling water, has about 13%
of the total surface area of Lake Erie, but only 5% of the total volume
(Hartman 1973, Nepszy 1977). The average depth of the western basin
(7.4 m) is only 40% of the average depth of all of Lake Erie (18.5 m).
The western basin has a flushing time of about 60 days (Hartman), and
is considered to have the most important fish spawning and nursery
areas in Lake Erie (Hartman 1973, Nepszy 1977).
The Monroe Power Plant has four coal-fired units with a maximum
expected net capacity of 3150 MW (Detroit Edison Company 1976a).
Unit 1 came on-line in May 1971, and the remaining units began
operation in annual increments: June 1972, March 1973, and May 1974
respectively. Cooling water is obtained from the Raisin River through
an intake canal, which is screened by 3-in.-mesh trash racks and
traveling screens with 3/8-in.-sq. openings. The maximum flow through
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ONTARIO
MICHIGAN
LAKE ST. CLAIR
DETROIT •
MONROE
POWER
PLANT
TOLEDO
OHIO
ORNL-DWG 80-16976 ESD
/
BUFFALO
NEW YORK
CLEVELAND
PENNSYLVANIA
0 20 40 60 80 (km)
•—. ' . • . •. • DISTANCE
0 10 20 30 40 50 (mi)
Fig. 2.1. Drawing of Lake Erie, showing detail of the western,
central, and eastern basins and location of the Monroe Power
Plant.
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the Monroe Power Plant is about 92 m /s, and up to 20% of the water
is recirculated in the winter to prevent icing. Chlorination, lasting
about 30 min, occurs twice daily in the summer and once daily in the
winter. From April 1975 through May 1976 the Monroe Power Plant
operated at about 56% capacity and at about 64% maximum cooling water
flow (59 m /s), resulting in AT's across the condensers of 2 to
16°C (mean 9°C).
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3. YELLOW PERCH FISHERY IN WESTERN LAKE ERIE
Western Lake Erie is in the center of the geographic range of the
yellow perch (Perca flavescens). Spawning usually occurs in late April
and early May as the water temperature reaches 7 to 10°C (Van Meter
1960, Wolfert et al. 1975). Spawning takes place at night and early
morning over submerged vegetation and brush, which anchors the charac-
teristic ribbon-like egg mass (Muncy 1962, Scott and Grossman 1973).
Hatching time varies with temperature, ranging from 6 days at 20°C to
50 days at 5 to 6eC (Ney 1978). Patterson (1979) reports a range of C
to 12 days from spawning until hatching. Yellow perch hatch at about
5 mm in total length, and the yolk sac is absorbed at about 7 mm in
total length (Ney 1978, Ney and Smith 1975). Schneider (1973), while
studying size-selective feeding of yellow perch on zooplankton in
ponds, found the onset of feeding to be a critical phase of life. He
further found that the survival of larval yellow perch and the forma-
tion of year-class strength depend on the density of older perch. The
swimming ability of larval yellow perch is insufficient to sustain
directed movement against wind-driven surface currents (Ney 1978).
Larval yellow perch are initially photopositive and pelagic, but become
demersal at total lengths of about 25 to 40 mm (Ney 1978, Ney and Smith
1975). Larvae are more abundant offshore in western Lake Erie, where
they concentrate near the bottom, while juveniles are common in the
shallow inshore waters (Detroit Edison Company 1976a). Noble (1975)
found that yellow perch mortality rates in Oneida Lake were inversely
proportional to the biomass of young fish and that growth rates were
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not strongly density dependent. Adult yellow perch are active during
the day, with peak movement shortly after sunrise (offshore migration)
and before sunset (onshore migration) (Ney 1978). Growth, fecundity
and survival data for yellow perch are given in Sect. 2.1 of Appendix A.
Yellow perch is one of the two most exploited percid populations
in North America (the other being walleye) (Ney 1978). Marked varia-
tions in year-class strength are characteristic of yellow perch popula-
tions (Hartman 1973, Nepszy 1977). Annual landings for Lake Erie from
1923 to 1972 averaged 2600 metric tons (Hartman 1973). The commercial
harvest of yellow perch rose slowly from 1915 to 1927, averaged 5700
metric tons between 1927 and 1936 (this upsurge attributed to the
decline in lake herring), and increased greatly in the 1950s (primarily
in Canadian waters) (Hartman 1973, Nepszy 1977). Catch per unit effort
was high, with low effort from 1950 to 1970 in the western basin; how-
ever, since 1970, effort has increased in the west and central basins,
while catch per unit effort has decreased in all Canadian waters
(Nepszy 1977).
Attempts to relate yellow perch and walleye year-class strength
fluctuations to environmental and biological variables have been
largely unsuccessful (Ney 1978), although Smith (1977) relates year-
class strength of yellow perch and walleye to climatic factors. Strong
year-classes of yellow perch have been found in 1952, 1954, 1956, 1959,
1962, and 1965, with relatively strong year classes in 1970 and 1975
(Hartman 1973, Nepszy 1977). Coincidental strong year-classes of
walleye have been found in 1959, 1962, 1965, and 1970 (Hartman 1973,
Nepszy 1977). These coincidental strong year-classes may imply either
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a similar environmental mechanism controlling the success of hatch
(such as rate and regularity of water warming during spawning) or a
common controlling predator (rainbow smelt has been suggested) (Nepszy
1977). Wells (1977) has suggested that the sudden decline in yellow
perch in Lake Michigan during the early and mid-1960s was brought on by
the interference of nonnative alewife with yellow perch reproduction.
This decline was preceded by a period of conspicuously high commercial
production, although the sport fishery declined a few years earlier.
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4. LARVAL YELLOW PERCH ABUNDANCE - EVALUATION OF METHODOLOGIES
The purpose of this section is to describe briefly the data
available to Patterson (1979) at the time of his analysis (and listed
in his references), to discuss Patterson's "materials balance model,"
which is used to obtain estimates of larval abundance, and to discuss
the data included in Patterson's (1979, Sect. 3) report in terms of
clarity of presentation and accessibility of data in a form susceptible
to an independent evaluation of his methodology.
4.1 Status of Larval Concentration Data
In 1975 and 1976, under the sponsorship of the U.S. Environmental
Protection Agency, Region V, a sampling program for the western basin
of Lake Erie (U.S. waters) was conducted jointly by the Center for Lake
Erie Area Research (CLEAR), the Michigan Department of Natural
Resources (Michigan DNR), and Michigan State University (MSU). Inves-
tigations by CLEAR included the Ohio waters of the western basin
(Herdendorf et al. 1976, 1977), while the Michigan DNR surveyed the
Michigan waters of Lake Erie (Hemmick et al. 1975, Michigan DNR 1975,
1976). The area near the Monroe Power Plant (Cole 1977) was sampled by
MSU.
The Michigan DNR and CLEAR sampled with nets having different mesh
sizes (471 and 760 y respectively), while MSU used plankton nets with
571-y mesh (C. D. Goodyear 1978). The comparability of the data col-
lected by these agencies is subject to question because gear efficiency
most likely differs between the different sampling gear. Patterson
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10
ignores the question of gear efficiency, both in terms of combining
data from disparate sampling gear and the resultant underestimation of
larval perch concentrations. Numerous papers discuss the problem of
gear efficiency (Schnack 1974, Bjorke et al. 1974, Murphy and
Clutter 1972, Leithiser et al. 1979, Tranter 1968). Inaccuracies in
larval abundance estimates can be introduced by changes in filtration
performance (interaction between net and water), avoidance of sampling
gear (especially by older larvae), and the loss of organisms through
the meshes (extrusion). Filtration performance (including clogging of
nets), avoidance of gear, and extrusion through the mesh will all lead
to an underestimate of the larval concentrations and hence their
abundance.
Patterson (1979; Fig. 2) presents the location of the western Lake
Erie larval sampling stations in 1975 and 1976. Samples were obtained
from five depth zones (6-ft increments from the surface) in Michigan
waters during the periods June 4 through September 5, 1975, and
April 13 through August 3, 1976. Samples were obtained from six depth
zones (2-m increments from the surface) and five sectors (A-E) in Ohio
waters during the periods May 12 through September 8, 1975, and
April 12 through July 7, 1976. Sampling, both day and night, occurred
irregularly over time in both Michigan and Ohio waters, ranging from
weekly to biweekly intervals. Although Patterson (1979, Appendix A)
finds differences between day and night samples, he does not attempt to
adjust upward the concentration estimates to account for greater gear
avoidance in day samples compared with night samples. Patterson notes
the lack of larval yellow perch concentration estimates for Michigan
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11
waters during May 1975. Larval abundance estimates for Michigan waters
in 1975 are suspect because data for the start (and probably the peak)
of the spawning season is lacking.
Entrapment and impingement data for the Monroe Power Plant are
reported by Cole (1977), Detroit Edison Company (1976a, 1976b), and
Hubbell and Herdendorf (1977). An excellent evaluation of the entrain-
ment and impingement data is provided by C. D. Goodyear (1978). This
study found that impinged yellow perch were seriously underestimated
[122,000 according to Detroit Edison Company (1976a) vs her estimate of
626,000]. The possibility also exists that entrapment estimates in
the 1976a report may also be significantly underestimated
(C. D. Goodyear 1978). This underestimate could have occurred because
entrainment sampling was conducted only at 1- and 3-m depths, and the
intake canal is 5 to 7m deep. It is suspected that larvae would be
more abundant near the bottom of the Monroe Power Plant intake canal
(C. D. Goodyear, 1978).
4.2 Materials Balance Model of Larval Production
A brief description of Patterson's "materials balance model" is
given in the Appendix to Appendix A. In this model the abundance of
larval yellow perch is viewed as an integration of several processes,
including (1) production of larvae, h(t); (2) natural mortality during
the larval stage (25 days), m(t); (3) recruitment to the young-of-year
life stage, r(t); (4) net emigration from U.S. waters of the western
basin, v(t); (5) losses due to entrainment of larvae in the cooling
water of the Monroe Power Plant, Eft); and (6) losses due to
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entrainment of larvae by other water users, L(t). The rate of change
•
of larval abundance, N(t), is then given by a linear combination of
these processes [Patterson 1979, Eq. (3)]:
N(t) = h(t) - v(t) - r(t) - m(t) - L(t) - E(t) . (4.2.1)
Total producton is defined as all yellow perch larvae entering or
hatched in the U.S. waters of western Lake Erie, including Maumee Bay
(Patterson 1979, p. 4). The binomial distribution (with parameters m
and q [Eq. (A-l ]} is used to distribute total production over the
spawning period in Michigan and Ohio waters of western Lake Erie.
Losses due to natural mortality are assumed to follow an exponential
decay with a daily instantaneous natural mortality rate, £, while
recruits to the young-of-year life stage (25 days after hatching) are
given by Eq. (A-2). Since Patterson assumes that v(t), E(t), and L(t)
are equal to zero for all values of t, then net emigration and losses
to all cooling water users (including the Monroe Power Plant) are
incorporated among the natural mortality and production expressions.
This modeling approach assumes that the binomial distribution
reasonably reflects the input of yellow perch larvae to Michigan and
Ohio waters during the spawning season. The parameters m and q of the
binomial distribution in Eq. (A-l) are obtained by inspection; that is,
Patterson compares the shapes of curves generated by different combina-
tions of these parameters with the field survey data (larval concen-
tration as a function of the day of year). The parameter d, the period
of time over which spawning is assumed constant, is also obtained by
inspection. The parameters m, q, and d are given in Table 4.1 for Ohio
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13
Table 4.1 Parameter values for Patterson's binomial
distribution of spawning by state waters and year
Ohio waters Michigan waters
Parameter 1975 1976 1975 1976
B
m
q
, d (days) ,
(100-m3 units x 107)
(1!) for x:
5
0.
7
9.
10
393
5
0.
7
9.
10
393
5
0.15
14
0.4976
5
0.
14
0.
15
4976
0 0.5905 0.5905 0.4437 0.4437
1 0.3280 0.3280 0.3915 0.3915
2 0.0729 0.0729 0.1382 0.1382
3 0.0081 0.0081 0.0244 0.0244
4 0.0004 0.0004 0.0022 0.0022
5 0.00001 0.00001 0.0001 0.0001
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and Michigan waters in 1975 and 1976. A comparison of the binomial
coefficients, (^), in Table 4.1 with those given by Patterson
(1979, pp. 82-83) will show that the coefficient given by 0.00001 was
left out of Patterson's analysis for Ohio waters in 1975 and 1976.
Because of the small value of this coefficient, the effect of leaving
it out would be expected to be small. However, the coefficient given
by 0.0022 was left out of Patterson's analysis for Michigan waters in
1975 [but not 1976), and the effect of leaving out this coefficient
could have a more significant effect on predicted larval abundances.
Since the value of 0.0001 was used in place of 0.0022 for the binomial
coefficient for x = 4, and 0 was used in place of 0.0001 for x = 5,
then the relationship between h and p will be biased in some unknown
direction. These coefficients are also missing from the solutions to
Eq. (A-3) as given by Patterson (1979, Appendix F). These errors will
have no effect on Patterson's long-term impacts, since he does not use
estimates of abundance in models 1 or 2 which assess long-term impacts
on the yellow perch fishery (Sect. 5).
In the model, natural mortality is assumed to occur uniformly
during the larval life stage throughout the period of occurrence of
larvae in the western basin. The probability of a larva dying on day 1
of the larval stage is the same as the probability of a larva dying on
day 25 of the larval stage. Furthermore, this probability remains
constant over the entire period of occurrence of larvae. Patterson's
assumption of 25 days for larval development from hatching to recruit-
ment to the young-of-year life stage will affect both the natural
mortality and recruitment terms in Eq. (A-3); that is, increasing the
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15
life-stage duration decreases the dally Instantaneous mortality rate,
p. A decrease (or increase) in p will affect the calibration of the
model. The expression for recruitment [Eq. (A-2)] also assumes that no
density-dependence mechanism occurs during the larval life stage.
Patterson (1979, p. 114) does not estimate natural survival from
his materials balance model, but "judges" that the "overall 25-day
survival is ... in the 2 to 10 percent range." The corresponding
values of p range from 0.156 to 0.092 day . Patterson (personal
communication) argues that an inspection of Figs. 35, 37, 40, and 42
(Patterson 1979) justifies his selection of his range for p (0.09 to
0.16). However, we believe that no unique (p,h) pair is superior to
any other "best" point estimate. The direct relation between p and h
allows one to estimate p or h from the materials balance model, given
an independently obtained estimate of the other parameter. Patterson
(1979, p. 114) points out that this range of estimates of p reflects
net emigration and water intake losses other than these from the Monroe
Power Plant. If the natural mortality is fixed so as to already
reflect these additional losses, then the addition of further terms
having nonzero values to represent these losses will underestimate the
actual larval production.
The larval concentration data that are compared to the model for
various combinations of p and h are assumed to provide unbiased
estimates of these concentrations during the larval production season
for larvae in western Lake Erie. Since these data have not been
adjusted for gear inefficiencies, the resultant estimates of h
(productivity) are likely to be underestimated. In addition, the
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16
estimates based on Michigan waters in 1975 are suspect because sampling
was not conducted during the earlier portions of the production season.
4.3 Data Presentation and Reduction
Patterson does not clearly delineate the four sets of larval con-
centration data that he uses in his materials balance model for obtain-
ing estimates of larval abundance in Michigan and Ohio waters of
western Lake Erie in 1975 and 1976. In order to permit an independent
evaluation of Patterson's methodology, the report should contain the
following information:
1. the raw larval concentration data for Michigan and Ohio waters in
western Lake Erie in 1975 and 1976 (should be presented as an
appendix with uniform format for the two state waters and two years
of data),
2. a description in the main text of how the data were reduced to the
form directly usable in estimating larval production and abundance
(including comparability of Michigan DNR and MSU data, presence of
dead larvae in Lake Erie, gear efficiencies, and pooling of data
over depth and day vs night),
3. a summarization of these reduced data in tabular form by state
water and year.
Most of the raw larval concentration data appear in Patterson's report
in Tables 1 (Michigan waters in 1975), 9 (Michigan waters in 1976), 12A
(Ohio waters in 1975), and 12D (Ohio waters in 1976). Additional lar-
val concentration data appear in Tables 2-7 (MSU night samples in 1975)
and Table A.I (Michigan waters in 1975). It is not clear which data
were used in Patterson's analysis.
No tabular summary of larval concentrations in Michigan waters for
1975 is given for the raw data presented in Tables 1-7 and A.I; only
Fig. 36 gives any indication of the magnitudes of the reduced
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17
concentration data. Tables 9, 12A, and 12D are summarized in
Tables 10, 12C, and 12F respectively. In comparing the raw data pre-
sented in Table 9 with the reduced data presented in Table 10, the raw
data in Table 9 for 6/14-29 were apparently not used in the summary in
Table 10 (Patterson 1979). Further confusion ensues as a result of two
dating systems used interchangeably among Tables 1-12 and Appendixes
A-D (Patterson 1979). Only the "Note" below Table 10 presents a
correspondence between these two dating systems; however, there is
little agreement between the month/day system in Table 9 and the
day-of-the-year system in Table 10.
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5. LONG-TERM IMPACTS ON YELLOW PERCH FISHERY - EVALUATION OF MODELS
In this section we discuss two models which Patterson (1979,
Sect. 5) employs to assess long-term Impacts by entrainment and
Impingement at the Monroe Power Plant on the yellow perch fishery.
Model 1 considers only the entrained and Impinged portion of the yellow
perch population and is an extension of the "equivalent adults"
approach introduced by Horst (1975). Model 2 describes the entire
population of yellow perch and includes a density-dependent component
based on the logistic function. There is no indication that the
estimates of larval abundance are incorporated in either of these
models.
An underestimate of the number of entrained or impinged yellow
perch will cause an underestimate in predicted losses by both models.
Gear inefficiencies in entrainment samples (Sect. 4.1) will lead to an
underestimate of the number of larvae and young-of-year entrained.
C. D. Goodyear (1978) discussed the question of inaccuracies in
impingement estimates and presented estimates of impinged yellow perch
based on actual counts considerably higher than Detroit Edison
Company's estimates (513%). Errors in estimates of survival of
entrained and impinged yellow perch will also cause errors in model
predictions. Patterson (1979, Appendix E) discussed estimation methods
and an example to obtain an entrainment survival of about 0.7, but the
source of the data was not given. Patterson did not discuss
impingement survival.
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5.1 Model 1
Model 1 follows only the subpopulation of the yellow perch
entrained and impinged at the Monroe Power Plant. Model 1 is a mathe-
matically continuous extention to Horst's (1975) "equivalent adults"
approach, which considers the probability of survival from the start of
an entrained or impinged life stage to "adulthood" (usually the first
year of maturity). Horst's model is open-ended in that it assesses
entrainment and impingement losses of a single cohort in terms of
"equivalent adults" and does not provide for any feedback in the form
of a reduced number of adults spawning a reduced number of eggs.
Patterson's model 1, however, closes this loop by describing the rate
of change in abundance of a subpopulation of entrained and impinged
yellow perch as a differential equation [Patterson 1979: Eq. (21)],
which includes a term for the lost reproductive potential. Each
entrained or impinged life stage is adjusted to the age of recruitment
(age class 2), similar to Horst's "equivalent adults." Both the
"equivalent adults" approach and model 1 assume no density-dependent
mechanism.
Patterson presents ranges of estimates for several life-history
parameters: (1 ) fraction of larvae surviving to the young-of-year
stage, e (0.02, 0.1); (2) fraction of young-of-year surviving to age
class 1; s (0.346, 0.575); (3) annual instantaneous fishing mortality
rate, f (0.22, 0.95); (4) annual instantaneous natural mortality rate,
m (0.22, 0.29); and (5) mean annual rate of larval production, Y (375,
3600). These parameters and numbers of fish entrained and impinged are
the sole inputs to model 1. The range of the parameter e was not
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20
estimated, but judged reasonable in Patterson's Sect. 4. The para-
meters s, f, and m are obtained from the literature. The last para-
meter, y , is calculated from the product of hatching success (0.25 to
0.5), number of eggs spawned per sexually mature female (10,000 to
30,000), and the proportion of sexually mature female spawners per
individual (0.15 to 0.24). Patterson assumes a sex ratio of 1:1. A
stable population age structure is assumed in estimating the number of
eggs spawned and the fraction of mature spawning females.
Model 1 [Patterson 1979, Eq.(2D] can be written in the form
N = a(a + b-N) - (m + f)N , (5.1.1)
where a is the number of entrained and impinged yellow perch as age
class 2 "equivalent adults," b is the reproductive potential
™n
(Y.e.s.e ') of age class 2 fish, a is the proportion of age class
2 fish that will die due to natural and fishing causes after six years,
m and f are the natural and fishing annual adult instantaneous mor-
tality rates, respectively, and N and N are the rate of change and
absolute adult population size respectively. In the absence of
entrainment and impingement (a = 0), model 1 is stable if and only if
production perfectly matches mortality (ab = m + f). In this case
the "impacted" population is nonexistent (N = 0). An artifact of the
entrainment and impingement terms appearing as constants in Eq. (5.1.1)
allows for stability when (m + f) exceeds (a-b). Thus, in an
essentially density-independent model, we have feedback which controls
the "impacted" population so as to allow for an "equilibrium" popula-
tion size. However, the range for (m + f) is 0.44 to 1.24, while
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21
the range for (a-b) is 1.23 to 159.86. Since (m + f) is generally
less than (orb), model 1 will generally not approach an equilibrium
population size (Patterson 1979). To obtain equilibrium conditions,
Patterson has resorted to assuming a value for y of 15 (Patterson 1979,
Table 24). Patterson assumes this value after he has already presented
a range of "reasonable" parameter values that does not include this
value. Since early life history survivals (s and e) are usually
poorly known for highly fecund fish, these values rather than y should
be adjusted if "equilibrium" conditions are to be maintained. Also
note that a value for m of 0.29 was used compared with its range of
0.22 to 0.29, and values for f of 0.52 and 0.95 compared with its range
of 0.22 to 0.95 (Table 24, Patterson 1979).
Horst's (1975) "equivalent adults" methodology assumes that all
entrained larvae (or any other life stage that is entrained or
impinged) have just entered that life stage (C. P. Goodyear 1978).
However, larvae that have survived 24 days of the larval life stage
have a much higher probability of surviving to sexual maturity than do
recently hatched larvae. Thus a serious underestimate of the potential
impact due to entrainment by a power plant can result from this
approach without correcting for this source of bias (Adams et al.
1979). In Patterson's model 1 he has adjusted larval survival (e1)
assuming that the mean age of a larva that is entrained is five days.
He (Patterson 1979, Appendix H) provides some justification for this
assumption based on a probabilistic argument. An alternative approach
would be to assume an exponential mortality [Eq. (A-2)] and calculate
the expected age of an individual larva (t):
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22
e"25p[25+
'
where 25 is the duration of the larval stage in days, and p is the
daily instantaneous natural mortality rate. From Eq. (5.1.2) we obtain
as the expected age of an individual larva values ranging from
6 (p = 0.16) to 8 days (p = 0.09), compared with Patterson's (1979,
Appendix H) estimate of 5 days. The expected survival for an "average"
larva to the young-of-year stage would then be given by
e1 = e-tP . (5.1.3)
Patterson (1979, Table 24) obtains as a range for e1 of 0.08 to 0.13
and uses this range in place of e in his analysis. This adjustment
of e might be an acceptable approximation if the larval life stage is
the only entrained or impinged life stage as a result of the operation
of the Monroe Power Plant; however, later life stages are also
entrained and/or impinged. Thus these later life stages (young-of-year
and age classes 1 through 7) should have their survival rates adjusted
similar to that in Eq. (5.1.3). Since model 1 considers only the
entrained and impinged portion of the population, and those yellow
perch lost to entrainment during the larval life stage cannot be
entrained and/or impinged again during a later life stage, larvae
should experience the unadjusted survival when entrained or impinged
during a later life stage. Hence model 1 needs to track separately
each life stage entrained or impinged. In its present form, model 1
cannot account in an adequate manner for power plant impacts occurring
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23
other than at the start of a life stage and can adjust only for the
first life stage entrained or impinged.
In Table 24 (Patterson 1979), identical ranges for the number of
age class 1 (IA1) and age class 2+ (age class 2 and older) (IN)
impinged yellow perch are given (50,000 to 100,000). Since most
impinged fish are younger than those in age class 2 (Sharma and Freeman
1977), the assumption of uniform impingement over all age classes of
yellow perch would lead to an overestimate of the potential impact.
Tables 34 and 35 in Patterson (1979) provide weightings used to combine
estimates of impacts to the yellow perch fishery (Patterson 1979,
Tables 25 to 32) based on the range of parameter values and entrainment
and impingement impacts presented in his Table 24. These weightings
appear highly subjective, and there is no attempt in the Patterson
report to justify them. These weightings imply entrainment and
impingement losses in larvae to be 11,000,000, young-of-year losses to
be 100,000, and losses to both age classes 1 and 2+ to be 67,500.
C. D. Goodyear (1978) suggests that the best estimates for these losses
are 1,351,886 (larvae), 3,614,391 (young-of-year), 181,668 (age
class 1), and 441,159 (age class 2+).
5.2 Model 2
Model 2 considers the entire yellow perch population in Lake
Erie. Patterson maintains the "equivalent adults" approach through his
coefficients for E,, (s-e), E + I (s), and I. (1) [see
—•* y y "
Eqs. (21.1) and (23)]. However, model 2 now introduces a
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24
density-dependent factor into his model in a logistic fashion
(Patterson 1979); from Eq. (23);
(5.2.1)
where K is the habitat carrying capacity (number of adults). This
model results in an S-shaped growth curve of the population which
approaches an equilibrium population size (regulated by its life-
history parameters and K). The levels of entrainment and impingement
will reduce the equilibrium population. Patterson (1979, Table 36)
assumes a value of 5 x 107 for K without any justification pre-
sented. However, Patterson uses model 2 primarily to explore the
effects of varying y on population losses, rather than to provide
specific impact predictions.
Since the coefficient of the density-dependent term in model 2
(S'E-Y) adjusts the population to age class 1 "equivalent adults,"
density dependence is allowed to occur throughout the first calendar
year of life (spawning to December 31). The timing of the density-
dependent mechanism can affect the resultant predicted losses to the
fishery. Power-plant impacts that occur prior to or concurrent with
the density-dependent mechanism will result in less of a reduction to
the fishery than would comparable impacts occurring after the density-
dependent mechanism (Christensen et al. 1977). Allowing the timing of
the density-dependent mechanism during the young-of-year stage
moderates power plant impacts at this stage of development. However,
most density-dependent mechanisms are thought to occur during
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25
critical periods, the most important of these is during the larval life
stage when the yolk sac is consumed (Gulland 1965). If density
dependence occurs during the larval stage, model 2 will tend to
underestimate the actual impact for a specified set of life history
parameters and entrainment and impingement estimates.
In its present form, model 2 suffers from the same duality in the
life-stage survival rates that model 1 suffers from. Either the life-
stage survival values represent an average survival (for an average
aged individual), or they represent survival through the entire life
stage for those that are impacted in a later life stage. Patterson
uses a different range for Y in model 2 than he did in model 1. A
value of 15 was used in model 1, while the values 50, 75, 300, and 1500
were used in model 2 (Table 26, Patterson 1979). This compares with
his original estimated range of 375 to 3600.
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26
6. DISCUSSION
The purpose of this section is to summarize some of the important
weaknesses and strengths of Patterson's approach from Sects. 4 and 5,
to introduce an age structure approach which is compared with
Patterson's approach, and to describe briefly future data needs which
would improve any further analyses of long-term impacts of entrainment
and impingement of yellow perch at the Monroe Power Plant.
6.1 Weaknesses and Strengths of Patterson's Approach
The approach in the Patterson (1979) report consists primarily of
two parts. The first is his materials balance model, which is used to
estimate the larval production parameter, h. Values for the daily
instantaneous natural mortality rate, p, are given without adequate
justification. Larval abundance in Michigan and Ohio waters in 1975
and 1976 are obtained by Eq. (A-4). The estimate for Michigan waters
in 1975 is suspect, since the peak spawning period was apparently
missed. The abundance estimates obtained from this model are not used
in model 1 (or in model 2).
Model 1 is primarily used to address the question of long-term
impacts on the yellow perch fishery due to entrainment and impingement
mortalities of the Monroe Power Plant. The use of model 1 by Patterson
has several flaws, including (1) general lack of stability for the
range in the life-history parameters presented by Patterson and (2) the
duality problem with life stage survival estimates as presently incor-
porated into the model. This second problem also applies to model 2.
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27
6.2 Alternative Age-Structure Approach
A detailed description of an age-structure approach to modeling
the effects of entrainment and impingement at the Monroe Power Plant on
the yellow perch fishery is presented in Appendix A. This approach was
selected primarily because the impacts in question are not uniform in
effect over the life span of yellow perch. As fish grow longer and
swimming capabilities increase, they become less susceptible to power-
plant impacts. Some life stages are more susceptible to plant passage
entrainment mortality than other life stages. Younger fish are
impinged more than older fish, both because of their greater abundance
and greater susceptibility.
The age-structure model in Appendix A uses entrainment and
impingement estimates from Patterson. Our model incorporates a
density-dependent mechanism only during the larval life stage, provid-
ing for a density-independent effect to later life stages. Three
levels of density dependence are considered as well as complete density
independence. Table 8 (in Appendix A) presents a range of potential
annual reductions to the fishery for one year and over six years of
adult impingement. High density dependence implies losses ranging from
0.2 to 2.9%, while low to zero density dependence implies losses rang-
ing from 6.5 to 21.6%. Comparable estimates of losses have since been
obtained using the entrainment and impingement estimates suggested by
C. D. Goodyear (1978): 4.3 to 27.4% (high density dependence) and 55.2
to 83.5% (for low to no density dependence). C. D. Goodyear's (1978)
estimates of impingement losses in later life stages are considerably
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28
higher than Patterson's estimates (based on his weightings); for
example,
Entrainment and/or impingement estimates
Life stage Patterson (1979) C. D. Goodyear (1978)
Larvae 11,000,000 1,351,886
Young-of-year 100,000 3,614,391
Age class 1 67,500 181,668
Age class 2+ 67,500 441,159
Larval concentrations estimated for the U.S. waters of western Lake
Erie are unadjusted for gear avoidance. This bias will carry through
to the abundance estimate of later life stages. If entrainment and
impingement estimates are not biased in the same manner, then the
subsequent impact predictions based on relatively low abundance esti-
mates will be too high. Impingement estimates, which may account for
most of the predicted losses to the fishery, are not subject to gear
bias, since they are based on actual counts, while the abundance
estimates for impingeable life stages are biased low. Therefore, the
projected losses to the fishery based on C. D. Goodyear1s (1978)
entrainment and impingement estimates are believed to be too large.
In our age-structure model we have adjusted survival rates during
the first year of life so as to maintain the population at equilib-
rium. Impacts are introduced as conditional power-plant mortality
rates (Appendix A, Sect. 2.3), which removes the duality problem of
life-stage survivals from which Patterson's models 1 and 2 suffer. In
addition, the density-dependent mechanism is inserted during the larval
life stage, when it is more likely to occur.
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29
Section 4 in Appendix A gives a detailed discussion of the assump-
tions and sources of error to which our age-structure model is sub-
ject. These errors enter into our analysis via (1) natural variability
in the environment, (2) errors in model parameters and inputs, and
(3) errors in model structure. Patterson's models 1 and 2 are subject
to many of these same assumptions and sources of error. It is felt
that the Patterson's models 1 and 2 introduce considerably more error
than does our age-structure model with respect to the third source of
error.
6.3 Future Data Needs
Models are useful in highlighting areas where more or better data
are needed. The precision and accuracy of model predictions can be
improved by emphasizing the collection of data where model assumptions
are felt to be less valid and model predictions are most sensitive.
The impact of the Monroe Power Plant, using a Leslie matrix or age-
structure approach, on the yellow perch population depends greatly on
the conditional mortality rate by life stage. The conditional mor-
tality rate is obtained from the exploitation rate and either the
natural or total mortality rate by life stage (Sect. 2.3, Appendix A),
and the exploitation rate is obtained from the ratio of the number of
yellow perch killed as a result of entrainment and/or impingement to
the total number produced. Inaccuracies in any of these component
parts will result in inaccurate model predictions. It would be
desirable to have better estimates for all of the components of our
model, including (1) yellow perch life-history data for western Lake
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30
Erie based on current environmental conditions (natural mortality by
life stage and adult age classes, age-specific fecundities, and age-
specific sex ratios); (2) estimates of age-specific commercial and
sport fishing mortality rates for the western basin of Lake Erie;
(3) density estimates for each life stage, rather than just larvae, for
the entire western basin of Lake Erie; (4) estimates of gear avoidance
for the sampling gear used in western Lake Erie and the Monroe Power
Plant; and (6) estimates of entrainment and impingement by life stage
and adult age class. The desired data listed above would optimally
improve model predictions, but would be impossible to collect.
C. P. Goodyear (1978) has pointed out that, though greater numbers
of young fish are often entrained or impinged, most of the impact may
be associated with the older entrained or impinged fish. If we con-
sider C. D. Goodyear's (1978) entrainment and impingement estimates
(Sect. 6.2), the losses due to entrainment and impingement of
young-of-year (3,614,391) are considerably larger than those due to
entrainment of larvae (1,351,886). Losses to young-of-year stage would
also occur after the occurrence of density-dependent mortality that
might take place during the larval stage. Therefore, we would argue
for the following list of data needs:
1. density estimates for young-of-year yellow perch for at least
Michigan and Ohio waters of western Lake Erie,
2. continued frequent collection of concentration data for
young-of-year entrained or impinged at the Monroe Power Plant,
3. estimates of entrainment and impingement survival for young-of-year,
4. estimates of gear avoidance (relative to a high-speed sampler) of
young-of-year for sampling gear used in western Lake Erie and the
Monroe Power Plant,
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31
5. yellow perch life history data for western Lake Erie based on
current environmental conditions (especially the natural mortality
rate for young-of-year).
Item 1 is especially important for obtaining accurate estimates of the
abundance of young-of-year yellow perch. Underestimating their abund-
ance will lead to an overestimate of the impact of the Monroe Power
Plant. A mark-recapture study for young-of-year yellow perch would
provide an alternative approach for item 1 and would reduce the data
needs in item 4 to just estimates of gear avoidance of young-of-year
for sampling gear used at the Monroe Power Plant.
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32
REFERENCES
Adams, S. M., H. A. McLain, D. S. Vaughan, G. F. Cada, D. Kumar, and
S. G. Hildebrand. 1979. Analysis of the Prairie Island Nuclear
Generating Station, Intake Related Studies. Report to Minnesota
Pollution Control Agency. Oak Ridge National Laboratory,
Oak Ridge, Tennessee. 235 pp.
Bjorke, H., 0. Dragesund, and 0. Ulltang. 1974. Efficiency test on
four high-speed plankton samplers. pp. 183-200. IN
J. H. S. Blaxter (ed.), The Early Life History of Fish,
Springer-Verlag, Berlin.
Boreman, J. and C. P. Goodyear. In press. Biases in the estimation of
entrainment mortality. IN L. D. Jensen (ed.), Proceedings of the
Fifth National Workshop on Entrainment and Impingement, Ecological
Analysts, Inc., Melville, New York.
Christensen, S. W., D. L. DeAngelis, and A. G. Clark. 1977.
Development of a stock-progeny model for assessing power plant
effects on fish populations. pp. 196-226. IN W. Van Winkle
(ed.), Assessing the Effects of Power-Pi ant-Induced Mortality on
Fish Populations, Pergamon Press, New York. 380 pp.
Cole, R. A. 1977. Entrainment at a Once-Through Cooling System on
Western Lake Erie, Vols. I and II. Institute of Water Research
and Department of Fisheries and Wildlife, Michigan State
University, East Lansing, Michigan, January.
Detroit Edison Company. 1976a. Monroe Power Plant Study Report on
Cooling Water Intake. September.
-------
33
Detroit Edison Company. 1976b. Monroe Power Plant Data Sheets on 1976
Larval Entrainment.
Goodyear, C. D. 1978. Evaluation of 316(b) Demonstration - Detroit
Edison's Monroe Power Plant. Great Lakes Fishery Laboratory, U.S.
Fish and Wildlife Service, Ann Arbor, Michigan. 245 pp.
Goodyear, C. P. 1978. Entrainment impact estimates using the
equivalent adult approach. FWS/OBS-78/65, Fish and Wildlife
Service, Department of the Interior. 14 pp.
Gull and, J. A. 1965. Survival of the youngest stages of fish, and its
relation to year-class strength. Int. Comm. Northwest At!. Fish.
Spec. Publ., (ICNAF) 6:363-371.
Hartman, W. L. 1973. Effects of exploitation, environmental changes,
and new species on the fish habitats and resources of Lake Erie.
Great Lake Fishery Commission. Technical Report No. 22, pp. 1-37.
Hemmick, W., J. Schaeffer, and R. Waybrant. 1975. Larval Fish Survey
in Michigan Waters of Lake Erie, 1975. Great Lakes Studies Unit,
Aquatic Biology Section, Bureau of Environmental Protection,
Michigan Department of Natural Resources.
Herdendorf, C. E., C. L. Cooper, M. R. Heniken, and F. L. Synder.
April 1976. Western Lake Erie Fish Larvae Study - 1975
Preliminary Data Report. CLEAR Technical Report No. 47, The Ohio
State University Center for Lake Erie Area Research, Columbus,
Ohio.
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34
Herdendorf, C. E., C. L. Copper, M. R. Heniken, and F. L. Synder.
March 1977. Western Lake Erie Fish Larvae Study - 1976
Preliminary Data Report, CLEAR Technical Report No. 63. The Ohio
State University Center for Lake Erie Area Research, Columbus,
Ohio.
Horst, T. J. 1975, An assessment of impact due to entrainment of
ichthyoplankton. pp. 107-118. IN S. B. Saila (ed.), Fisheries
and Energy Production: A symposium. Heath, Lexington,
Massachusetts.
Hubbell, R. M. and C. E. Herdendorf. September 1977. Entrainment
Estimates for Yellow Perch in Western Lake Erie 1975-76. CLEAR
Technical Report No. 71, The Ohio State University Center for Lake
Erie Area Research, Columbus, Ohio.
Leithiser, R. M., K. F. Ehrlich, and A. B. Thum. 1979. Comparison of
a high volume pump and conventional plankton nets for collecting
fish larvae entrained in power plant cooling systems. J. Fish.
Res. Board Can. 36:81-84.
Michigan DNR. 1975. Computer Listing of 1975 Larval Fish
Concentrations Sampled in the Western Basin of Lake Erie.
Michigan Department of Natural Resources.
Michigan DNR. 1976. Computer Listing of 1976 Larval Fish
Concentrations Sampled in the Western Basin of Lake Erie.
Michigan Department of Natural Resources.
Muncy, R. J. 1962. Life history of the yellow perch, Perca flavescens,
in estuarine waters of Severn River, a tributary of Chesapeake
Bay, Maryland. Chesapeake Sci. 3:143-159.
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35
Murphy, G. I., and R. I. Clutter. 1972. Sampling anchovy larvae with
a plankton purse seine. Fish. Res. Bull. 70(3):789-798.
Nepszy, S. J. 1977. Changes in percid populations and species
interactions in Lake Erie. J. Fish. Res. Board Can. 34:1861-1068.
Ney, J. J. 1978. A synoptic review of yellow perch and walleye
biology. Am. Fish. Soc. Spec. Publ. 11:1-12.
Ney, J. J., and L. L. Smith, Jr. 1975. First-year growth of the yellow
perch, Perca flavescens, in the Red Lakes, Minnesota. Trans. Am.
Fish. Soc. 104:718-725.
Noble, R. L. 1975. Growth of young yellow perch (Perca flavescens) in
relation to zooplankton populations. Trans. Am. Fish.
Soc. 104:731-741.
Patterson, R. L. 1979. Production, Mortality, and Power Plant
Entrainment of Larval Yellow Perch in Western Lake Erie.
EPA-600/3-79-087. Environmental Research Laboratory, U.S.
Environmental Protection Agency, Duluth, Minnesota. 187 pp.
Schnack, D. 1974. On the reliability of methods for quantitative
surveys of fish larvae, pp. 201-212, IN J. H. S. Blaxter (ed.),
The Early Life History of Fish, Springer-Verlag, Berlin.
Schneider, J. C. 1973. Density dependent growth and mortality of
yellow perch in ponds. Fisheries Research Report No. 1765,
Michigan Oept. of Nat. Res. 18 pp.
Scott, W. B., and E. J. Crossman. 1973. Freshwater fishes of Canada.
Fish. Res. Board Can. Bull. 184, 966 pp.
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36
Sharma, R. K., and R. F. Freeman III. 1977. Survey of Fish Impingement
at Power Plants in the United States. Volume I. The Great
Lakes. ANL/ES-56. Argonne National Laboratory, Argonne,
II linois. 218 pp.
Smith, L. L., Jr. 1977. Walleye (Stizostedion vitreum vitreum) and
yellow perch (Perca flavescens) populations and fisheries of the
Red Lakes, Minnesota, 1930-75. J. Fish. Res. Board
Can. 34:1774-1783.
Tranter, D. J. (ed.). 1968. Zooplankton Sampling. Monographs on
Oceanographic Methodology 2. The UNESCO Press, Paris. 174 pp.
Van Meter, H. D. November 1960. The yellow perch of Lake Erie. Ohio
Conservation Bulletin, pp. 22-23.
Wells, L. 1977. Changes in yellow perch (Perca flavescens) populations
of Lake Michigan, 1954-75. J. Fish. Res. Board Can. 34:1821-1829.
Wolfert, D. R., W. D. N. Busch, and C. T. Baker. 1975. Predation by
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1969-71. Ohio J. Sci. 75(3):118-125.
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A-l
APPENDIX A
AN AGE STRUCTURE MODEL OF YELLOW PERCH
IN WESTERN LAKE ERIE
Douglas S. Vaughan
Environmental Sciences Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37830
ABSTRACT
An age structure model based on life history data (i.e., early
life-stage and age-class survival and age-class-specific fecundity) is
developed for the yellow perch (Perca flavescens) population in the
western basin of Lake Erie. The long-term impact on yellow perch of
entrainment and impingement at the Monroe Power Plant (Monroe,
Michigan) is assessed. Larval abundance estimates are obtained from a
modification of a "materials balance model," while abundance estimates
for later life stages are obtained using life-stage survival esti-
mates. For each life stage, power plant exploitation rates are esti-
mated from entrainment and/or impingement and abundance estimates.
Conditional power plant mortality rates are calculated from exploita-
tion rates and life-stage survival estimates and are incorporated into
the age structure model.
Using side-by-side projections (with and without power plant
impact) of the age structure model, long-term losses of fishery yield
are estimated. One set of projections is made where the age structure
model includes no density-dependent component. Other projections
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A-2
consider the age structure model where the survival term for age class
0 depends on the density of eggs produced that year. The density
dependence is assumed to occur during the larval life stage within age
class 0. Three levels of compensation during age class 0 are con-
sidered. The unknown status of the yellow perch population in western
Lake Erie precludes a precise specification of the level of compensa-
tion. However, heavy fishing pressure on the yellow perch population
in western Lake Erie implies that losses in yield are better repre-
sented by ranges based on little or no compensation (6 to 22%) than by
ranges based on moderate to very strong compensation (0.2 to 2.9%).
Keywords: age structure model, density-dependent, density-
independent, entrainment and impingement, environmental
impact, fish population analysis, Lake Erie, Leslie matrix
model, Monroe Power Plant, yellow perch
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A-3
1. INTRODUCTION
A difficult problem confronting fishery science is that of
assessing the long-term effects of an incremental mortality on a fish
population. This incremental mortality might arise through increased
fishing pressure or through a change in the environment such as a power
plant operation. In the latter case, such mortality is usually assumed
to act independently of the density of the fish population, but is
dependent upon the age (or size) of the fish. Those fish drawn into
the cooling water intakes of power plants and small enough to pass
through the meshes of the debris screens are said to be entrained,
while larger fish entrapped on the surface of the debris screens are
said to be impinged. Mortality results from these processes, although
the actual proportion of fish killed under a particular set of condi-
tions (power plant operation and environmental) has been questioned.
As a result of the age dependence of incremental power plant mortali-
ties, the need for an age structure model to assess long-term impacts
arises.
An age structure (Leslie matrix) model was independently developed
by Bernardelli (1941), Lewis (1942), and Leslie (1945) in order to
follow a female population through time. The Leslie matrix, A(t), is a
square matrix consisting of age-class-specific fecundity factors on the
first row, P-jfji and age-class-specific survivals on the sub-
diagonal, p. (Fig. 1). Usher (1972) suggested introducing the sur-
vival element in the lower right corner of the Leslie matrix to account
for the survival of fish beyond the oldest age explicitly modeled. By
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A-4
representing fecundity factors as shown in Fig. 1, it is assumed that
spawning occurs over a very brief period just prior to the end of the
time period (Emlen 1973). The age structure (a column vector con-
taining age-class-specific abundances), n(t+l), at time t+1 can be
obtained by premulti plying the age structure, n(t), at time t by the
Leslie matrix, A(t), as shown in Fig. 1. Because survival and
fecundity estimates for fish are generally obtained on an annual basis,
a time unit of one year is used. As originally developed, the Leslie
matrix elements were assumed to remain constant over time. Three
mathematical situations can arise: (1) the population will grow expo-
nentially without bounds; (2) the population will decay exponentially
to extinction; or (3) the population is perfectly balanced. Thus, in
this form the behavior of the model is as limited as the exponential
growth model. Any incremental mortality would ultimately drive a
population in the third situation to extinction, unless the excess
mortality was removed before extinction occurred. Survival through the
first year of life is often difficult if not impossible to estimate
with any precision for highly fecund fish populations. Vaughan and
Saila (1976) obtained estimates of survival through age class 0 (the
first year of life) from a Leslie matrix by assuming that the popula-
tion was perfectly balanced situation (3) described above.
The fully defined elements of the Leslie matrix permit one to
project the age structure of a population from one year to the next.
The age structure at time t, n(t), can be converted to the fishery
yield, y(t), by premultiplying n(t) by the diagonal matrix, D, and the
row vector, f. Yield in metric tons (t) is given by the equation:
y(t) = f • D • n(t) • 106 . (1)
-------
A-5
The row vector, £', contains the proportion of each age class lost to
the fishery or age-class-specific fishing exploitation rates. The
diagonal matrix, J£, consists of age-class-specific weights in grams on
the main diagonal and zeros elsewhere.
Since competition during early life stages and cannibalism by
older age classes on younger age classes can result in the density-
dependent regulation of a fish population, density-dependent mechanisms
are incorporated into population models. Gull and (1965) notes that
"most fish have enormous fecundities, and there must be a correspond-
ingly enormous mortality between egg and adult stages." He further
suggests that "most of this mortality is believed to occur in the first
few months of life," and this stage is believed important because "the
regulatory (density-dependent) effects...may occur in this stage."
Survival through the first year of life can be made dependent upon the
number of eggs produced at the start of that year (DeAngelis et al.
1980). However, there is an upper limit of stress to which a popula-
tion may respond in a density-dependent manner, beyond this limit a
population may respond in a density-independent manner (Goodyear
1977). Heavily fished populations may be assumed to be approaching
this limit closely.
In this paper an assessment is made of the losses in yield to the
yellow perch commercial and sport fisheries of western Lake Erie due to
the imposition of incremental age-specific density-independent mor-
tality. In particular, entrainment and impingement mortalities due to
the Monroe Power Plant (Monroe, Michigan) are incorporated into a
Leslie matrix model having density-dependent survival during age
-------
A-6
class 0. Population projections are made (with and without
power-plant-induced mortalities), and annual losses in yield to the
yellow perch fishery are estimated. These estimates of annual losses
in yield are based on no density dependence in age class 0 survival and
on three levels of density-dependent age class 0 survival. Estimates
of losses in yield based on the lowest level of density dependence and
no density dependence are believed to be more representative of the
annual losses that result from the operation of the Monroe Power Plant.
2. METHODS
In this section, four topics are discussed. First, a detailed
description is given of the methods used to estimate the elements in
the Leslie matrix from life history data. Second, a "materials balance
model" developed by Patterson (1979) is modified and used to obtain
estimates of the larval and later life-stage abundances of yellow perch
(Perca flavescens). Third, conditional power plant mortality rates are
determined from estimates of entrainment and/or impingement mortality,
life-stage abundance, and life-stage survival, using a methodology
described by Barnthouse et al. (1979). Finally, the density-dependent
Leslie matrix developed by DeAngelis et al. (1980) is modified to
include incremental density-independent mortalities (i.e., power plant
impacts). These data and model modifications are then used to compare
side-by-side projections (with and without power plant operation) in
order to assess the long-term impacts of the Monroe Power Plant on the
yellow perch population in western Lake Erie.
-------
A-7
2.1 Life History Data. The Leslie matrix model requires the following
information from yellow perch life history data: (1) number of eggs
produced per individual for each sexually mature age class, f.;
(2) probability of surviving from the start of one age class (i-1) to
the start of the next age class (i), p^; and (3) total number of age
classes, N (Fig. 1). Once the Leslie matrix is defined, it can be used
along with estimates of weight at age (both sexes combined) and age
specific fishing exploitation rates (proportion of population removed
by the fishery) to estimate the loss in biomass of the population to
the commercial and sport fisheries.
Estimates of the number of eggs produced per individual for each
age class are obtained from the following sequence. First, a
von Bertalanffy growth function (Table 1, footnote a) is used to
estimate the standard length in millimeters by age class for yellow
perch females [data from Table 7 in Jobes (1952)]. Lower and upper
bounds of the asymptotic 95% confidence intervals, as well as the point
estimates, are estimated for the three parameters of the
von Bertalanffy growth function by nonlinear regression techniques
(Table 1). Standard lengths in millimeters for female yellow perch are
then generated for age classes 1 through 7 for all three cases (lower,
middle, and upper) (Table 2).
Total weight in grams for female yellow perch (W) is calculated
from standard lengths in millimeters (L) using the allometric equation
(Jobes 1952; p. 252),
W = 1.776 x 10-5 L3.015 § (2)
-------
A-8
Table 1. Coefficients of the von Bertalanffy growth function estimated
by nonlinear regression for yellow perch (Perca flavescens) in
Lake Erie from data
Coefficient9
Females only:
L
00
k
t
0
Both sexes combined:
L
00
k
t
0
in Table 7 of
b
Lower
259.3
0.369
0.087
240.4
0.321
-0.052
Jobes (1952)
Middleb
269.9
0.424
0.200
260.3
0.437
0.182
Upper
280.5
0.480
0.314
280.2
0.553
0.416
aLt = L [l-e~ * o'] , where L. equals standard length (in millimeters)
C °° L -I
at age t (in years), and L^ (in millimeters), k (in years" ), and t (in
years) are coefficients of the von Bertalanffy growth function.
bThe middle column is obtained from the point estimates of the parameters
in the von Bertalanffy growth function, while the lower and upper columns
are obtained from the lower and upper bounds, respectively, of the
asymptotic 95% confidence interval.
-------
A-9
Table 2. Life history data for yellow perch (Perca flavescens) of western Lake Erie
Age
class
Standard
length3
(mm)
Total.
weight0
(9)
Fecundityc
(eggs/mature
female)
Fecundity
(eggs/individual)
M
Survival
"V
Fecundity
factor
Lower estimates:
74
131
171
198
217
230
239
Middle estimates:
78
144
188
216
235
247
255
Upper estimates:
1 79
2 156
3 203
4 233
5 251
6 262
7 269
7.7
43.0
95.0
148.6
195.5
233.2
261.8
8.8
56.9
126.0
192.9
247.5
288.3
317.3
9.2
71.8
160.
241.
303.
345.9
374.4
.5
.3
.0
827
5285
12416
20098
27012
32656
37003
960
7147
16828
26621
34821
41044
45508
1003
9180
21838
33891
43295
49940
54387
0
0
4966
8039
10805
13062
14801
0
0
7573
11980
15670
18470
20479
0
0
10919
16946
21648
24970
27193
0.000308
0.75
0.50
0.
0.
0.
.29
.29
.29
0.29
0.000116
0.77
0.61
0.43
0.43
0.43
0.43
0.000034
0.80
0.73
0.64
0.64
0.64
0.64
0
0
2483
2331
3133
3788
4292
0
0
4620
5151
6738
7942
8806
0
0
7971
10845
13855
15981
17404
Calculated using the coefficients of the von Bertalanffy growth function from Table 1
for females only.
°W = 1.776 x 10"5 L3'015, where W is the total weight (g) and L is the standard
length (mm).
CEG6S = 92.045 W1'077, where EGGS is the fecundity (eggs/female) and W is the
total weight (g).
Corrected for immature females, non-spawning mature females and sex ratio.
Survival is from age class i-1 to age class i (i = 1,2 7).
Fecundity factor = fecundity (eggs/individual) x survival.
-------
A-10
where W is the total weight in grams and L is the standard length in
millimeters. This equation was applied to lengths given for each of
the three cases in Table 2.
The fecundity, expressed as the number of eggs produced per
sexually mature female (EGGS), was calculated for each age class from a
weighted average of coefficients from three annual regressions of the
number of eggs on total weight in grams (W) (Sztramko and Teleki 1977,
and Table 1):
EGGS = 92.045 W1-077 . (3)
The weighting used in combining the regression coefficients was by
sample size.
The number of eggs produced per individual of a given age class is
estimated from the product of (1) the fraction of females mature in
that age class, (2) the probability of a mature female spawning,
(3) the age-class-specific sex ratio, and (4) the number of eggs pro-
duced per mature female of that age class (Table 2). No females are
assumed to be sexually mature prior to age class 3, while all females
of age class 3 or greater are assumed to be sexually mature (Patterson
1979). Patterson (1979) indicates a range of 0.8 to 1.0 for the pro-
bability of a mature female spawning. The middle of this range, 0.9,
is used in the middle case, while the lower (0.8) and upper (1.0)
bounds are used in the lower and upper cases, respectively. Also, a
sex ratio of 1:1 was assumed for all age classes (Patterson 1979).
In this analysis each age class is considered to extend from May 31
to the following May 31. In contrast, Patterson (1969), from whom
-------
A-ll
natural and fishing survival are obtained, considered each age class to
extend from January 1 to the following January 1, except for age class
0 which extends from late May to January 1. Annual natural and fishing
survival are from 0.75 to 0.80 and 0.39 to 0.80, respectively, for age
classes 1 through 7 (Patterson 1979). Fishing pressure is introduced
in January to age class 2, so age class 1 survival reflects no fishing
mortality, age class 2 reflects only five months of fishing mortality,
and age classes 3 and older reflect the full amount of fishing mor-
tality. The overall annual survival for age classes 1 through 7 is the
product of annual natural survival and the appropriate annual fishing
survival (Table 2).
The final element needed for the Leslie matrix is survival through
age class 0. Because of the difficulties in obtaining reasonable
estimates of this parameter from field data, estimates are obtained by
assuming a stable population and using Eq. (6) in DeAngelis et al.
(1980). These estimates range from 3.4 x 10" (upper case) to
-4
3.1 x 10 (lower case) with the middle case yielding an estimate of
1.2 x 10"4 (Table 2).
The stable age structures presented in Table 3 are calculated by
first assuming one million eggs were produced and sequentially multi-
plying the number in one age class by the survival value for that age
class to obtain the number in the next age class.
Fishing yield (in metric tons) is calculated using Eq. (1). The
age-class-specific fishing exploitation rates are calculated using the
estimates of natural and fishing survivals in Table 2 (Ricker 1975;
p. 11). The age-class-specific weights in grams are calculated using
-------
A-12
Table 3. Stable age structures and fishing weights and mortalities for
yellow perch (Perca flavescens) in western Lake Erie
Age Age
class structure
(numbers of fish)
Lower estimates:
0 1 000
1
2
3
4
5
6
Middle estimates:
0 1 000
1
2
3
4
5
6
Upper estimates:
0 1 000
1
2
3
4
5
6
000.0
307.5
230.6
115.3
33.4
9.7
2.8
000.0
116.2
89.5
54.6
23.5
10.1
4.3
000.0
34.4
27.5
20.1
12.8
8.2
5.3
Fishing
weights
(g)
_
_
37.7
73.9
111.2
145.1
173.6
_
_
70.9
135.6
193.6
238.8
271.5
_
_
108.9
208.5
287.3
340.6
374.1
Fishing .
mortalities
(u)
0
0
0.079
0.178
0.178
0.178
0.178
0
0
0.192
0.396
0.396
0.396
0.396
0
0
0.287
0.544
0.544
0.544
0.544
Calculated using coefficients of the von Bertalanffy growth function
from Table 1 for both sexes combined, Eq. (2). and weighted by season.
Wishing exploitation rates from Patterson (1979).
-------
A-13
the von Bertalanffy coefficients in Table 1 based on both sexes com-
bined and Eq. (2). Although a year-round fishery for yellow perch
exists, most fishing occurs between spring and fall. A weighted
average of the fish weights is calculated for each age class such that
spring (t) and fall (t+1/2) fish weights each receive a weighting of
0.25, while summer (t+1/4) fish weights receive a weighting of 0.5.
The values calculated for the fishing exploitation rates and the fish
weights by age class are presented in Table 3.
The particular life stage or age class which is stressed has a
great effect on the long-term impact on the population. The early life
history of the yellow perch is broken into four life stages (Patterson
1979): (1) eggs (6-12 days), (2) larvae (25 days), (3) young-of-year
(6 months), and (4) yearlings (1 year). The first three stages and
approximately 5 months of the fourth stage occur during age class 0.
Ranges of these life stage survivals are from Patterson (1979) as shown
in Table 4. The geometric mean survivals of these four stages are
0.35, 0.045, 0.44, and 0.90. These ranges in life stage survivals
imply a range in survival for age class 0 of 0.002 to 0.026 (geometric
mean = 0.006).
The survival rates of these early life stages are difficult to
estimate. Since the range in survivals obtained from the four life
stages is considerably higher than the range in survivals for age class
0 based on a stable population, Patterson's (1979) life-stage survival
estimates are reduced proportionately so as to maintain the population
at equilibrium (Table 4). This assumption of a stable population is
probably not true in the light of declining catch-per-unit-effort (CPUE)
-------
A-14
Table 4. Early life-stage survivals adjusted to maintain the yellow perch
(Perca flavescens) population at equilibrium
Case
Lower
Middle
Upper
Egg
survival
[6 days] a
0.214 (0.50)b
0.156 (0.35)
0.112 (0.25)
Larval
survival
[25 days]
0.006 (0.10)
0.004 (0.045)
0.002 (0.02)
Young-of-year
survival
[6 months]
0.297 (0.58)
0.234 (0.44)
0.181 (0.34)
Yearling
survival
[5 months]
0.815 (0.91)
0.827 (0.90)
0.826 (0.89)
Duration of life stage in brackets.
3Life stage survivals from Patterson (1979) prior to adjustment in
parentheses.
-------
A-15
experienced by the Canadian fishery for yellow perch in Lake Erie
(Nepszy 1977). In fact, the declining CPUE's would indicate that age
class 0 survival assuming a stable population is overestimated based on
current environmental conditions in Lake Erie.
2.2 Life Stage Abundance Estimates. Larval yellow perch concentra-
tions are available for the Ohio and Michigan waters of the western
basin in Lake Erie in 1975 and 1976 (Patterson 1979; Herdendorf et al.
1977a, 1977b) (Fig. 2). A modification of a "materials balance
formulation" (Patterson 1979), described in the Appendix, is used to
obtain estimates of larval yellow perch production for the Ohio and
Michigan waters in 1975 and 1976 (Table 5). United States waters
comprise about 41% of the volume of the western basin of Lake Erie
(Nepszy 1977). Assuming that the Canadian waters are of equal pro-
ductivity to the U.S. waters for yellow perch larvae, the production of
yellow perch larvae for the entire western basin of Lake Erie is 2.45
times the combined production of yellow perch larvae in Ohio and
Michigan waters of the western basin.
g
In the western basin larval production is from 13.8 x 10
(larval survival = 0.006) to 17.2 x 109 (larval survival = 0.002),
Q
mid-estimate is 14.9 x 10 (larval survival = 0.004). The number of
recruits to the young-of-year stage Eq. (A-2) is from 3.4 x 10
(young-of-year survival = 0.181) to 8.3 x 10 (young-of-year
survival = 0.297), mid-estimate is 6.0 x 10 (young-of-year
survival = 0.234). Yearling production estimates are then obtained by
multiplying the number of young-of-year recruits by the corresponding
-------
A-16
Table 5. Estimates of larval yellow perch (Perca flavescens) production
by state, year, and larval survival in Ohio and Michigan
waters of western Lake Erie
State Year
Ohiod 1975
(for Ohio
waters)
1976
Average6
Michiganf 1975
(for Michigan
waters)
1976
Average6
Larval
survival
0.002
0.004
0.006
0.002
0.004
0.006
0.002
0.004
0.006
0.002
0.004
0.006
0.002
0.004
0.006
0.002
0.004
0.006
hb
9.5
8.5
8.0
7.9
7.0
6.6
8.7
7.75
7.3
34.4
25.6
21.5
2.6
2.4
2.2
18.5
14.0
11.85
Production0
(x 109)
6.246
5.589
5.260
5.194
4.603
4.340
5.720
5.096
4.800
2.390
1.783
1.498
0.181
0.167
0.153
1 . 289 •
0.975
0.826
See larval survival column in Table 4.
Method of calculation is described in Appendix; h is the mean total
number of larvae per 100 m of water in the reference volume.
cProduction = d-B-h, where d equals 7 or 14 for Ohio or Michigan
waters, respectively, and B equals 9.393 x 107 or 4.976 x 106 for
Ohio or Michigan waters, respectively, d is the number of days in each
time period, and h is the reference volume in units of 100 m .
Source data for Ohio from Herdendorf et al. 0977a and 1977bX
Arithmetic average of 1975 and 1976 values.
Source data for Michigan from Patterson (1979).
-------
A-17
young-of-year survival. Yearling productivity Is from 0.6 x 107
(annual yearling survival = 0.727) to 2.5 x 107 (annual yearling
survival = 0.688), mid-estimate 1s 1.4 x 107 (annual yearling
survival = 0.713). Adult recruits [Patterson's (1979) age class 2] are
then calculated from the product of yearling production and correspond-
ing annual yearling sur- vival. These estimates range from 0.5 x 107
to 1.7 x 10 , mid- estimate 1s 1.0 x 107. These life-stage produc-
tion estimates assume that the population 1s stable.
2.3 Conditional Mortality Rates. Natural mortality may be expressed
as either the expectation of natural death (the proportion of the
population which dies due to natural causes in the presence of com-
peting sources of mortality) or the conditional natural mortality rate
(the proportion of the population which dies due to natural causes in
the absence of competing sources of mortality) (Ricker 1975). Fishing
mortality may be expressed analogously as either the rate of exploita-
tion or the conditional fishing mortality rate. If fishing mortality
is subsumed into natural mortality, then the "power plant exploitation
rate" or "conditional power plant mortality rate," respectively, may be
discussed. However, it is in the form of the power plant survival rate
(1 - conditional power plant mortality rate) that entrapment and
Impingement estimates are incorporated into the Leslie matrix model.
Because the conditional power plant mortality rate is calculated
from the power plant exploitation rate, it is first necessary to
calculate the power plant exploitation rate. This mortality rate is
equal to the ratio of the number of individuals of a life stage
-------
A-18
entrained and/or Impinged by the power plant to the number of indi-
viduals of that life stage. Production estimates for larvae,
young-of-year, yearlings, and adults are given in the section 2.2.
Entrainment and impingement estimates for these four stages (Patterson
1979) are presented in Table 6. Weightings for the ranges of estimates
of entrainment and impingement for the four life stages (Table 6) are
based on Patterson's (1979) subjective appraisal of the numbers of
larvae, young-of-year, yearlings, and adults that are entrained and/or
impinged by the Monroe Power Plant. These weightings are used to
combine estimates of the conditional power plant mortality rate [see
Eqs. (4) and (5)].
The conditional power plant mortality rate, m, is related to the
power plant exploitation rate, u, by the equation
m
= 1 . (l-A)U/A , (4)
where A is the total fraction of the population removed due to both
"natural" (natural and fishing mortalities) and power plant sources of
mortality (Barnthouse et al. 1979). Assuming that the survival esti-
mates in Tables 2 and 4 reflect both "natural" and power plant mor-
tality, then A equals one minus the survival estimate, and the solution
of Eq. (4) is straightforward. If, however, the survival estimates in
Tables 2 and 4 are assumed to be independent of power plant mortality,
then these survival estimates are conditional "natural" survival
rates. According to Ricker (1975),
1 - A = (1 - m)(l - n) , (5)
-------
A-19
Table 6. Numbers of yellow perch entrained and/or impinged annually at the
Monroe Power Plant with subjective weightings from Patterson (1979)
Life stage (age)
Estimates3
Weightingsb
Weighted mean
of the
estimatesc
Larvae (6-12 days)
Young-of-year (1 month)
Yearlings (7 months)
Adults (19 months)
2 000 000
10 000 000
20 000 000
40 000 000
100 000
50 000
100 000
50 000
100 000
0.18
0.62
0.18
0.02
1.00
0.65
0.35
0.65
0.35
11 000 000
100 000
67 500
67 500
aPages 131-132 in Patterson (1979)
bTables 28-29 in Patterson (1979). These weightings are used to combine
estimates of the conditional power plant mortality rates for the range of
entrainment and/or impingement estimates in this table.
cThe weighted mean of the estimates is the sum of the product of the
estimates and their corresponding weightings.
-------
A-20
where n is the conditional natural mortality rate. Substituting
Eq. (5) into Eq. (4), m now occurs on both sides of the equation. The
resultant equation is transcendental and must be solved by an iterative
technique (Barnthouse et al. 1979).
Estimates of n (or A) are needed for the duration of the life
stages for which conditional power plant mortality rates are to be
estimated. Larval, young-of-year, and yearling survival rates (1-n or
1-A) are given in the previous section with the corresponding pro-
duction estimates. To obtain adult survival rates, two cases of adult
impingement are considered. First, adults are assumed susceptible to
impingement only during the first year of that life stage. In this
case, the one-year survival rates for adults (age 1.6 to 2.6) range
from 0.748 for an adult production of 1.7 x 10 to 0.803 for an adult
production estimate of 0.5 x 10 with a geometric mean of 0.775 for
an adult production estimate of 1.0 x 10 . The second case assumes
that impingement occurs uniformly throughout the adult life stage (age
1.6 through age class 7). Survival estimates for this period range
from 0.0009 for an adult production of 1.7 x 10 to 0.074 for an
adult production of 0.5 x 10 , with a geometric mean of 0.0082 for an
adult production of 1.0 x 10 .
For all four life stages the two sets of estimates (survival as
1-n or 1-A) of the conditional power plant mortality rates were nearly
identical. Weighted averages of estimates of conditional power plant
mortality rates for the four life stages are presented in Table 7 using
the weightings in Table 6.
-------
A-21
Table 7. Conditional power plant mortality rates by life stages and
power plant survival rates used as inputs to the Leslie
matrix model
Conditional power plant mortality
Larvae (6-12 days old)3
Young-of-year (1 month old)
Yearlings (7 months old)
Adults (19 months old)
(1) One year impingement
(2) 6.4 years impingement
Power plant survival rates:
eo
el
One -year impingement:
e2
e3
6.4-year impingement:
e2
e3
Lower
rates:
0.0041
0.0021
0.0033
0.0046
0.0277
0.9959
0.9965
0.9962
0.9973
0.9963
0.9956
Middle
0.0040
0.0032
0.0057
0.0077
0.0326
0.9960
0.9944
0.9935
0.9955
0.9946
0.9948
Upper
0.0039
0.0061
0.0127
0.0166
0.0416
0.9961
0.9886
0.9857
0.9903
0.9899
0.9934
aAges in parentheses represent age at start of life stage.
Power plant survival rates eQ-e3 (see discussion in text) represent the
form in which power plant impact is incorporated into the Leslie matrix
model.
-------
A-22
2.4 Incremental Density -Independent Mortalities. Density dependence
is expressed in the Leslie matrix model for yellow perch through the
survival term for age class 0; that is,
Pl(t) = Ci/[l + C0n0(t)] , (6)
where CQ and C1 are positive constants (De Angel is et al . 1980).
When the population is at equilibrium,
Pie = Ci/M + Conoe) , (7)
where ple and nQe are the equilibrium survival and equilibrium size
(in numbers) of age class 0. ple is calculated from Eq. (6) in
DeAngelis et al. (1980) and nQe is set to one million. Thus, solving
Eq. (7) for C] and substituting this into Eq. (6),
Pl(t) = (1 + C0n0e) Ple/[l + C0n0(t)] . (8)
Note that CQ equal to zero implies no density dependence
(PJ = P]e)- A measure of compensation, XQ (equal to Cnn0e^'
is allowed to range over low (0.01), moderate (1.0), and very strong
(100) levels of assumed compensation.
The conditional power plant mortality rates by life stage cannot
be used directly in the form presented in Table 6. In the present
application of the Leslie matrix model, density dependence is assumed
to occur during the larval life stage. Age class 0 survival, p-,(t),
including power plant impact, is expressed as
p(t) - ei(l + C0n0e) ple/[l + e0CQn0(t)] , (9)
-------
A-23
where eQ is the power plant survival rate for the larval life stage
and e, is the power plant survival rate for the remainder of age
class 0 [young-of-year life stage and first five months of the yearling
life stage (Table 6)]. Power plant impact is introduced into age
class 1 by
p2 = 62 • P2 . (10)
where e2 is the power plant survival rate for age class 1 (the last 7
months of the yearling life stage and first 5 months of the adult life
stage) (Table 6). Finally, power plant impact is introduced into the
adult age classes (2-7) by
Pi = 63 . PJ , (11)
where e., is the power plant survival rate for age class i (Table 6).
The index i is set to 3 for the case where impingement is assumed to
occur only during the first year of the adult life stage (hence only
seven months of impact through impingement occurs during age class 2).
In the case where impingement is assumed to occur uniformly over the
entire adult life stage, i is allowed to run over all integers from 3
through 8 (e^ represents annual power plant survival).
Equation (9) is modified for the case where no compensation is
assumed; that is,
PI = ei • e0 • Pie (12)
where p1, the proportion surviving through age class 0, is inde-
pendent of time and density. Equations (10) and (11) remain unchanged
for the density independent case.
-------
A-24
3. RESULTS
Projections of the yellow perch population for 100 years were made
with and without the power plant impact incorporated into the Leslie
matrix model. The projections with the power plant impact included the
power plant survival rates for the first 40 years (typical duration for
power plant operation) followed by 60 years without the power plant
survival rates. Projections were made for the four levels of compensa-
tion (XQ = 0, 0.01, 1.0, 100) and the three cases based on ranges of
life history data. The relative losses (in %) to the yellow perch
fishery for the two cases of adult impingement are presented in Table 8.
Figure 3 illustrates the reduction in yield to the yellow perch
fishery based on the middle case with one year of adult impingement.
During the first 40 years, when the power plant is operating, the
reduction in yield is monotonic increasing. As the compensation term,
XQ, becomes smaller, the magnitude of the reduction in yield becomes
greater. During the remaining 60 years of the projection, when the
power plant is not operating, the compensation term affects the rate of
return of the population to its equilibrium value (DeAngelis et al.
1980). When the compensation term (XQ) is equal to zero, i.e., no
compensation, the population does not return to its old equilibrium
value, but stabilizes at the population level attained after approxi-
mately 40 years, when the power plant ceases operation. For XQ
greater than zero, different response times are shown. As XQ
increases, so does the time of return to the original equilibrium
population.
-------
A-25
Table 8. Relative annual loss in yield (%) to yellow perch fishery
(both commercial and sport) based on 40 years of power
plant impact followed by 60 years of no power plant impact
Level of compensation3
(XQ)
One-year adult impingement:
0
0.01
1.0
100.0
6. 4 -year adult impingement:
0
0.01
1.0
100.0
Lower
10.4
6.5
0.6
0.2
11.7
7.8
0.8
0.4
Middle6
13.4
9.9
1.1
0.5
14.9
11.4
1.3
0.6
Upper
19.5
16.8
2.6
1.2
21.6
18.9
2.9
1.5
aThe level of compensation ranges from no compensation (XQ = 0; density
independent), to slight compensation (XQ = 0.01), to moderate compensation
(XQ = 1.0), to very strong compensation (XQ = 100).
See Fig. 3 for annual projection of middle case with one year of adult
impingement.
-------
A-26
In Table 8 it is seen that the impact resulting from one year of
adult impingement is smaller than the impact resulting from 6.4 years
of adult impingement, even though equal numbers of adults are assumed
to be impinged in both cases. In the latter case, individuals with
higher reproductive value are impinged. In general, younger fish are
more likely to be impinged than older fish. Thus, annual losses in
yield should lie somewhere between the estimates, based on these two
extreme assumptions concerning adult impingement.
Impacts are seen to be small when a moderate or very strong amount
of compensation is assumed (0.2 to 2.9% loss in yield) (Table 8).
Impacts are more substantial when little or no compensatory reserve is
assumed (6.5 to 21.6% loss in yield). Because yellow perch in the
western basin of Lake Erie are heavily fished (Patterson 1979, Nepszy
1977), it appears that the assumption of little or no compensation will
result in more realistic estimates of long-term losses to the yellow
perch fishery, as compared with estimates based on the assumption of
moderate to very strong compensation.
4. DISCUSSION
Several sources of error enter into this analysis through
(1) natural variability in the environment, (2) errors in the esti-
mation of both model parameters and inputs, and (3) errors in the model
structure. Natural variability results from both temporal and spatial
heterogeneity in the environment. Errors in estimation result not only
from natural variability in the data used to estimate model parameters
and inputs but also from biases or inaccuracies in the data. Since
-------
A-27
models are a simplification of the system modeled, errors in the model
structure can also lead to errors in the analysis.
This modeling exercise assumes no environmental variability
(spatially or temporally) in the western basin of Lake Erie during the
100 years of the model projection. Only in the three density-dependent
cases (Xg = 0.01, 1, 100), where age class 0 survival depends on the
eggs produced that spawning season, does any parameter value change
with time. Because the results of this assessment are presented as a
comparison of projected yields with and without power plant impacts, it
is believed that the effect of the assumption of no environmental
variability is minor.
Errors in the data and simplifying assumptions necessary for some
estimates to be made can cause estimation errors in the model para-
meters and inputs. The data used to estimate the life history para-
meters were obtained for yellow perch in Lake Erie. The growth data
(length and weight) are based on data collected prior to 1952 when
environmental conditions may have differed markedly from current con-
ditions (Jobes 1952). Similarly, the fecundity relationship obtained
from yellow perch in the eastern basin of Lake Erie (Sztramko and
Teleki 1977) may not be representative of yellow perch in the western
basin of Lake Erie. Overestimates of age-specific egg production
(resulting from overestimates of either length, weight, or fecundity)
will cause an underestimate of ple> which in turn will result in an
overestimate of the power plant impact (loss in yield to the yellow
perch fishery). Conversely, underestimating the age-specific egg
production will result in an underestimate of the power plant impact.
-------
A-28
Similarly, overestimating adult survival (natural and fishing survival)
will result in an overestimate of the power plant impact, while under-
estimating adult survival will result in an underestimate of the power
plant impact. Ranges in growth and adult survival (lower, middle, and
upper cases in Tables 3, 4, and 5) are intended to reflect natural
variability and errors in estimating life history parameters. Ranges
in estimates of losses of yield to the yellow perch fishery (Table 8)
account in part for these uncertainties.
Errors in estimating larval concentrations in Ohio and Michigan
waters can result from gear avoidance and/or extrusion by yellow perch
larvae. Underestimates of larval concentration will result in under-
estimates of larval and later life-stage abundances. Overestimates of
the conditional power plant mortality rates will result, followed by
overestimates of the power plant impact. Another weakness in the data
concerns the larval concentration data in Michigan waters in 1975. The
start of the spawning season was missed. This apparently resulted in
_0
very low estimates of q (on the order of 10 ) and high estimates of
h. Overestimates of h (and larval abundance) will lead to underesti-
mates of power plant impacts.
Entrainment estimates will be biased as a result of gear
inefficiencies and/or extrusion. Errors in entrainment estimates are
also introduced by inaccuracies in estimating the proportion of
entrained organisms killed by the power plant. Patterson (1979)
calculates a fraction of 0.7 killed for yellow perch larvae, and he
uses this proportion to reduce the number of larvae entrained to the
number of larvae killed due to entrainment. Likewise, errors in
-------
A-29
estimates of the number of a life stage killed due to impingement are
also introduced as a result of sampling inefficiencies and errors in
impingement survival. Obviously, overestimates of the number of a life
stage killed due to entrainment and/or impingement will result in an
overestimate of the power plant impact. Conversely, an underestimate
of entrainment and/or impingement mortalities will result in an under-
estimate of power plant impact.
Barnthouse et al. (1979) point out two assumptions inherent in
calculating conditional mortality rates: (1) the natural causes of
mortality and power plant impacts act independently of each other, and
(2) mortalities due to natural causes and power plant impacts are con-
stant during the life stage for which they are estimated. The first
assumption is likely to be true, while the latter assumption is likely
violated to some extent. Because of the seasonality often associated
with impingement, power plant impacts associated with a constant
impingement mortality over a life stage will introduce error of unknown
magnitude and direction. Another assumption which introduces error of
unknown magnitude and direction is that of a stable population, which
was assumed twice in this assessment. First, the age class 0 survival
was estimated using this assumption, and, second, later life-stage
abundances were calculated from estimates of larval abundance based on
this assumption. Patterson's (1979) weighting factors are assumed to
provide reasonable estimates of the life-stage-specific conditional
power plant mortality rates based on ranges of entrainment and/or
impingement mortalities. If the weightings cause an overestimate of
the conditional power plant mortality rate, then the power plant impact
-------
A-30
will be overestimated. Conversely, if the weightings cause an under-
estimate of the conditional power plant mortality rate, then the power
plant impact will be underestimated. The range in conditional power
plant mortality rates (Table 7) based on ranges in life history data
will hopefully give a reasonable range of power plant impacts.
The age structure approach to modeling populations provides a
means of assessing the long-term impacts of power plants (or any other
source of density-independent incremental mortality). This is
especially true when the impacts are not uniform over the entire life
span of the population. The major problem in lending realism to age
structure modeling is concerned with the controversial issue of density
dependence (non-age structure models are not free of this problem).
There is no doubt that populations in their natural state, when
moderately stressed, are able to respond in a compensatory manner. It
is also true that populations under large stresses can respond in a
depensatory manner resulting in a population "crash." However, the
main difficulty lies in estimating the coefficients which are used to
express the amount of compensation. In this paper a range of values
for the coefficient of compensation is used, including the assumption
of no compensation. Heavy fishing pressure on the yellow perch
population in western Lake Erie implies that the estimates of loss in
yield are better represented by the ranges based on little or no
compensation (6 to 22%) than by the ranges based on moderate to very
strong compensation (0.2 to 2.9%). However, the unknown status of the
yellow perch population in western Lake Erie precludes a precise
specification of XQ.
-------
A-31
ACKNOWLEDGMENTS
Research was supported by the U.S. Environmental Protection
Agency, Region V, under Interagency Agreement 40-650-77 (Task Order No.
ORNL/EPA-V8) with the U.S. Department of Energy under contract
W-7405-eng-26 with Union Carbide Corporation. I would like to thank
Dr. Lawrence Barnthouse, Benjamin Parkhurst, Dr. Vincent Gallucci, and
Terrance Quinn for their comments on this manuscript.
-------
A-32
LITERATURE CITED
Barnthouse, L. W., D. L. DeAngelis, and S. W. Christensen (1979). An
empirical model of impingement impact. ORNL/NUREG/TM-290 and
NUREG/CR-0639. Oak Ridge National Laboratory, Oak Ridge,
Tennessee.
Bernardelli, H. (1941). Population waves. J. Burma Res. Soc. 31:1-18.
DeAngelis, D. L., L. J. Svoboda, S. W. Christensen, and D. S. Vaughan
(1980). Stability and return times of Leslie matrices with
density-dependent survival: Applications to fish populations.
Ecological Modelling 8:149-163.
Emlen, J. M. (1973). Ecology: An Evolutionary Approach. Addison-
Wesley Publishing Co., Reading, Massachusetts. 493 pp.
Goodyear, C. P. (1977). Assessing the impact of power plant mortality
on the compensatory reserve of fish populations, pp. 186-195.
IN: W. Van Winkle (ed.), Assessing the Effects of
Power-Plant-Induced Mortality on Fish Populations. Pergamon
Press, New York. 380 pp.
Gull and, J. A. (1965). Survival of the youngest stages of fish, and
its relation to year-class strength. Special Publication of the
International Commission for the Northwest Atlantic Fisheries
(ICNAF) 6:363-371.
Herdendorf, C. E., C. L. Cooper, M. R. Heniken, and F. L. Snyder.
(1977a). Western Lake Erie Fish Larvae Study - 1975 Preliminary
Data Report. CLEAR Technical Report No. 47 (revised). The Ohio
State University Center for Lake Erie Area Research, Columbus,
Ohio.
-------
A-33
Herdendorf, C. E., C. L. Cooper, M. R. Heniken, and F. L. Snyder.
(19775). Western Lake Erie Fish Larvae Study - 1976 Preliminary
Data Report. CLEAR Technical Report No. 63. The Ohio State
University Center for Lake Erie Area Research, Columbus, Ohio.
Jobes, F. W. (1952). Age, growth, and production of yellow perch in
Lake Erie. Fishery Bulletin 52:205-266.
Leslie, P. H. (1945). On the use of matrices in certain population
mathematics. Biometrika 33:183-212.
Lewis, E. G. (1942). On the generation and growth of a population.
Sankhya 6:93-96.
Nepszy, S. J. (1977). Changes in percid populations and species
interactions in Lake Erie. Journal of the Fisheries Research
Board of Canada 34:1861-1868.
Patterson, R. L. (1979). Production, mortality, and power plant
entrainment of larval yellow perch in western Lake Erie.
EPA-600/3-79-087. Environmental Research Laboratory, U.S.
Environmental Protection Agency, Ouluth, Minnesota. 187 pp.
Ricker, W. E. (1975). Computation and Interpretation of Biological
Statistics of Fish Populations. Bulletin 191. Department of the
Environment, Fisheries and Marine Service, Ottawa, Canada. 382 pp.
Sztramko, L., and G. C. Teleki. (1977). Annual variation in the
fecundity of yellow perch from Long Point Bay, Lake Erie.
Transactions of the American Fisheries Society 106(6):578-582.
Usher, M. B. (1972). Developments in the Leslie matrix model.
pp. 29-60. IN: J. N. R. Jeffers (ed.), Mathematical Models in
Ecology. Blackwell Scientific Publications, London. 398 pp.
-------
A-34
Vaughan, D. S., and S. B. Sail a. (1976). A method for determining
mortality rates using the Leslie matrix. Transactions of the
American Fisheries Society 105(3):300-383.
-------
A-35
APPENDIX
ESTIMATION OF LARVAL ABUNDANCE
Estimates of larval yellow perch concentrations are available for
the Ohio and Michigan waters of the western basin of Lake Erie in 1975
and 1976 (Patterson 1979; Herdendorf et al. 1977a, 1977b) (Fig. 2).
Patterson (1979) uses a "materials balance formulation" to estimate
larval yellow perch abundance for the Ohio and Michigan waters in 1975
and 1976. He describes the net daily rate of change in larval
•
abundance, Q(t), for a specified volume as a linear function of inputs
and outputs. The sole input considered is the daily production of
larvae within the reference volume, h(t). Outputs considered include
(1) daily net emigration rate, v(t); (2) daily rate of recruitment to
the young-of-year life stage, r(t); (3) daily rate of larval natural
mortality, m(t); (4) daily loss rate of larvae to water usage other
than the Monroe Power Plant, L(t); and (5) daily loss rate of larvae to
entrainment at the Monroe Power Plant, E(t).
Production of larvae is distributed over the spawning season,
h(t), using the binomial probability distribution (Patterson 1979);
i .e.,
h(t) = B - h • () • qx(l-q)m'x , (A-l )
for the time interval TQ + xd to TQ + (x+l)d; where x = 0,1 m;
h(t) is the daily production rate; B is the reference volume in units
of 100 m (9.4 x 10 for Ohio waters and 5.0 x 10 for Michigan
-------
A-36
waters); h is the mean total number of larvae produced per 100 m of
water in the reference volume; m+1 is the maximum number of time
periods over which production occurs (m = 5); q is a parameter which
controls the shape of the binomial distribution; d is the number of
days in each of the time periods (d = 7 for Ohio waters and d = 14 for
Michigan waters); and TQ is the Julian calendar day on which pro-
duction begins (TQ equals 127 and 106 for Ohio waters in 1975 and
1976, respectively, and 120 and 106 for Michigan waters in 1975 and
1976, respectively).
Losses due to natural mortality are assumed to follow an
exponential decay with a daily instantaneous mortality rate, p, based
on the larval life-stage duration of 25 days (Patterson 1979). Since
the losses due to "natural" mortality were adjusted to maintain the
population at equilibrium, the parameter p reflects not only losses due
to natural sources of mortality, but also losses due to entrainment
mortality [E(t) and L{t)] and net emigration [v(t)]. Thus, the terms
E(t), L(t) and v(t) become redundant in the materials balance model.
Further, recruitment of larvae to the young-of-year life stage after 25
days, r(t), is given by,
r(t) = h(t-25)e-25p . (A-2)
/
Hence, the materials balance equation of Patterson (1979) reduces
to:
Q(t) + p • Q(t) = h(t) - h(t-25) • e-25P , (A-3)
where Q(t) is the number of larvae present in the reference volume on
•
day t, and Q(t) is the net rate of change in larval abundance per day
-------
A-37
in the reference volume on day t. Equation (A-3) is easily solvable
over ranges of constant values of h(t) [general solution in Appendix F
of Patterson (1979)]. Daily estimates of Q(t) are obtained from esti-
mates of yellow perch concentrations in Ohio and Michigan waters of
western Lake Erie (Patterson 1979; Herdendorf et al. 1977a, 1977b).
Using estimates of larval survival in Table 4 and the relationship
p = -ln(survival )/25 , Eq. (A-3) contains only two unknowns (h and q).
A consideration of the sum of squares generated by comparing model
predictions over ranges of h and q with the larval concentration data
collected in Ohio and Michigan waters in 1975 and 1976 provides a means
of estimating h and q. Patterson (1979) assumes values for q, but in
this paper both h and q are allowed to vary.
Estimates of h are provided in Table 5 for both Ohio and Michigan
waters in 1975 and 1976 separately and averaged over the two years.
Larval production estimates for the spawning season are calculated from
estimates of h by the relationship,
PRODUCTION = d • B • h . (A-4)
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A-38
"
0,1*1
^2^2
0
0
o o • «/?N-i
ORNL-DWG 73-2999R5
0,1
"
l.t
"
N-M
=A(t)*n(n
4 YEARS (AGE)
nc
f,
Fig. 1. Leslie matrix formulation of life cycle population model. n(t) and
n(t+l) are the population vectors at times t and t + 1, respectively,
Aft) is the Leslie matrix, the Pi's are survival rates, and the
f-j's are fecundities. The bottom part of this figure is designed to
show the relationship of the parameters, Pi and ff, to the age
class numbers, rifff F°>* example, p] is the survival rate from
age class 0 to age class 1.
-------
A-39
ORNL-OWG 60-11092 ESD
DETROIT
• •
MONROE
POWER
PLANT
TOLEDO
CANADA
OHIO SANDUSKY''';'•'•"-
WATERS
0 (0 20 30 40 50 MILES
Fig. 2. Drawing of Lake Erie, showing detail of the western basin and
the location of the Monroe Power Plant.
-------
A-40
ORNL-DWG 80-7555 ESD
90
100
Fig. 3. The reduction in yield to the yellow perch fishery due to
power plant operation based on four levels of compensation.
The level of compensation ranges from no compensation
(X0 = 0; density independent), to slight compensation
(XQ = 0.01), to moderate compensation ()fo = 1.0), to very
strong compensation 0^, = 100). Power plant mortality
occurs for the first 40 years, and no power plant mortality
occurs for the remaining 60 years of the projection. The
projections are based on the middle case with only one year
of adult impingement.
-------
B-l
Appendix B
MISCELLANEOUS EDITORIAL COMMENTS
B.I Main Text
Page Line
3 Footnote 1
79 13
82 30
83
20
83
83
116
121
131
135
29
30
19
7
36
14
(s/r = should be replaced with)
Comment
Appendix 8 s/r Appendix H
N(t) = s/r N(t) =
0 s/r 0.00001; and 365 s/r 169; followed by a
new line: 0 169 < t _< 365
0 s/r 0.00001; and 365 s/r 148; followed by a
new line: 0 148 < t <_ 365
0.0001 s/r 0.0022
0 s/r 0.0001; and 365 s/r 204; followed by a
new line: 0 204 < t < 365
numer s/r number
a = 1 . e-(m+f) T for Eq. (2i.i)
parmaters s/r parameters
the tables s/r Table 33
B.2 Tables
Table
1
2-7
8
Comments
Are the units: no./100 m3?
Source of data? [page 37 is apparently from Cole
(1977)].
Should state that Table 8 is summary of Tables 2-7.
Day of year in Table 8 does not agree with day/month
system in Tables 2-7. Means for Day 142 are off by
less than 0.1% for rows 1, 2, 5, and 6.
-------
B-2
B.2 Tables (cont'd)
Table Comments
9 Breakdown by stage of development unnecessary.
10 Day of year system in Table 10 does not agree with
day/month system in Table 9 (see footnote to
Table 10). Data from 6/14-29 in Table 9 apparently
not used in summary in Table 10.
11 Not needed.
12A-B Table 12B not needed: Sector B of Table 12B - switch
values for 6/21-23 with 7/1-3. Both zones A and B
were not sampled on 5/12-14 (footnote to a Table
12B), why was zone A estimated from zones C-E while
zone B was set to zero? The following errors were
found in Table 12B for sector D:
5/12-14 2.32 s/r 3.48
5/22-25 9.24 s/r 9.57
6/1-4 3.98 s/r 4.06
12C Should reference Table 13 which provided weightings
for combining of Sectors (Table 12B).
12E Table 12E not needed.
12F Under data column: 5/28 s/r 4/28. The following
errors were found for Mean Concentration column:
4/21-23 2.2xlO-3 s/r 5.8xlO~4
5/30 2.13x10-' s/r 9.33x1O'2
Should reference Table 13 which provides weightings
for combining Sectors (Table 12E).
13 This table should be referenced from Section 3 where
it is needed in conjunction with Tables 12A-F.
14 This table should be deleted or referenced from
Section 3 for comparison purposes.
15-16 Not used in analysis.
17 This extensive table could probably appear as an
appendix, although it is not used in analysis; should
be referenced on page 92.
-------
B-3
B.2 Tables (cont'd)
Table
18-21
25-32
33
34-35
Comnents
Should be reduced to just Table 21
Should appear as appendix.
Not referenced from text (see C.I)
Should summarize as single table.
B.3 Figures and Diagrams
Figures Comments
3-7, 9-30
31-34
45
Drop or put in appendix (might put 1 or 2 in text as
examples). Figure 17 not referenced (should be on
page 45).
Of marginal interest.
Marginal; denote as Fig. H.I
Diagrams Comments
A Discussion in Section 2 could be more closely
organized about specific sources of error outlined in
this diagram.
B Subscript left off of E.
B.4 Appendices
Appendix
A
Comments
Where are the data for null hypothesis 2 (bottom sled
tow); with different sampling gear what is the
validity of this test? Missing data point in
Table A.I for Surface Day sample on 5/23.
-------
B-4
B.4 Appendices (cont'd)
B
Sample sizes for depth zones 18 ft - 24 ft, 25 ft and
24 ft - 30 ft (15) are greater than I count from
Table 9 (23 and 13, respectively). Are data missing
from Table 9 for Apr. 26-29, 1976?
For Day 118, second column: n-j s/r i\2- Also,
for Day 118 I count 51 sample points for depth zone
12 ft - 30 ft instead of 55. Data for 6/14-29 in
Table 9 is not worked up.
Data are presumed to come
with respect to Table 11,
deleted. Not called out In
from Table 9.
this appendix
text.
As stated
could be
As pointed out by Patterson, methods 3 and 4 are less
susceptible to biased estimates than methods 1 and 2,
although several potential sources of bias which may
effect methods 3 and 4 have not been addressed
(Boreman and Goodyear 1980). What is the source of
the data in example, how was it collected, and where
were the intake and discharge sampling stations?
Michigan Water, 1976 (using Eq. 10), ranges of t:
189 s/r 190
200 s/r 201
214 s/r 215
Michigan Water, 1975 (using Eq. 9), range of t:
189 s/r 190
Michigan Water, 1975 (using Eq. 9 and 14), range of t:
189 s/r 190
Delete since not used in any analysis.
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