&EPA
United States
Environmental Protection
Agency
Environmental Research
Laboratory
Duluth MN 55804
EPA600 379087
Aiujust 1979
Research and Development
Production,
Mortality, and
Power Plant
Entrainment of
Larval Yellow
Perch in Western
Lake Erie

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This document is available to the public through the National Technical Informa
tion Service, Springfield, Virginia 22161..

EPA600/379087
August 1979
PRODUCTION, MORTALITY, AND POWER PLANT
ENTRAINMENT OF LARVAL YELLOW PERCH
IN WESTERN LAKE ERIE
by
Richard L. Patterson
Large Lakes Research Station
Environmental Research LaboratoryDuluth
Grosse lie, Michigan 48138
and
School of Natural Resources
University of Michigan
Ann Arbor, Michigan 48109
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA 55804

DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory
Duluth, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views
and policies of the U.S. Environmental Protection Agency, nor does mention
of trade names or coninercial products constitute endorsement or reconunenda
tion for use.
ii

FOREWORD
The Great Lakes with their large reservoir of water are subjected to
many uses. Not only do they support abundant aquatic life, provide
drinking water, recreation, transportation and waste assimilation, but
their water is also used in industrial processes. Quite often it is very
difficult to access the impact of one use upon another. This report has
attempted to synthesize thedata from many investigations into an analysis
of the impact of the use of cooling water on the production of fish. It is
through analyses such as those that have been performed in this report that
we will be guided in making decisions on the management of the Great
Lakes.
J. David Yount, Ph.D.
Deputy Director
Environmental Research LaboratoryDuluth
111

ABSTRACT
This study assessed impacts of the Monroe Power Plant upon the yellow
perch population of Western Lake Erie caused by entrainment and impingement
of larvae and older fishes in the plants open cycle cooling system in
197576. Data analyzed in the study were collected by the Michigan Depart
ment of Natural Resources, the Center for Lake Erie Area Research of the Ohio
State University, and the Institute of Water Research of Michigan State Uni
versity. Estimates of total numbers of perch larvae entrained, total perch
production, the natural mortality rate of perch, and the percentage of perch
production that was entrained by the Monroe Power Plant were obtained for
197576. Impingement estimates were obtained from data supplied by the power
plant. The above estimates consider only effects that occur in the same year
in which entrainment and impingement occurs. Impacts may occur in subsequent
years which include a depression of fish stocks and reduced yields to the
fishery. Losses to the standing stocks and fisheries were estimated using a
method which falls into a category known as the equivalentadult type
which provided estimates of the longrun annual depression of yellow perch
standing stocks and the yellow perch fisheries. A numerical model was
developed which incorporated several population parameters including entrain
ment and impingement losses, and natural mortality rates for larvae, young
ofyear, and juveniles, and fishing mortality rates.
iv

CONTENTS
Foreword iii
Abstract iv
Figures V i .
Tables ix
Acknowledgement Xi
1. Introduction and Summary 1
2. Objectives . . . . 4
3. Data Collection and Display . . . . 9
4. Methods . . . . 77
5. Results and Discussions 119
References 139
Appendices
A. Statistical tests of significance for difference in
concentrations of larval yellow perch in the western
basin of Lake Erie in Nay and June 1975 142
B. Statistical tests of significance for differences in
concentrations of larval yellow perch in depth zones
in Michigan waters in 1976 . 152
C. Calculation of mean concentration and standard errors
f or yellow perch larvae in Michigan waters in 1976 . . 154
D. Sample calculation of mean concentrations of pro
larvae (PROL), early postlarvae (EPL), and late post
larvae (LPL) in Michigan waters in 1976 158
E. Estimating percent mortality of entrained larvae . . . 160
F. Solutions to first order equations of larval balance
for Michigan and Ohio waters, 1975 and 1976 167
C. Approximate variance of equilibrium population as a
function of reproductive potential and larval survival 180
H. Relationship between age of larvae at entrainment and
reduction of young of year population due to entrainment . 183
V

FIGURES
Number Pag
I Western Lake Erie inputs and losses of yellow perch larvae . . S
2 Western Lake Erie larval sampling stations in 197576 . . . . 6
3 Larval perch concentration in 0 to 6 ft. zone from
Raisin River to Maunlee Bay (19741975) 32
4 Larval perch concentration in 0 to 6 ft. zone from
Raisin River to Mauniee Bay (1975) 33
5 Larval perch concentration in 6 to 12 ft. zone from
Raisin River to Mawnee Bay (1975) 34
6 Larval perch concentration in 6 to 12 ft. zone from
Raisin River to Huron River (1975) 35
7 Mean larval perch concentration in Michigan waters (1975) . . 36
8 Locations of MSU sampling stations in vicinity of Monroe
Power Plant 38
9 Larval perch concentration in 0 to 6 ft. zone from
Raisin River to Maumee Bay (1976) 39
10 Larval perch concentration in 6 to 12 ft. zone from
Raisin River to Maumee Bay (1976) 40
11 Larval perch concentration in 0 to 6 ft. zone from
Raisin River to Huron River (1976) 41
12 Larval perch concentration in 6 to 12 ft. zone from
Raisin River to Huron River (1976) 42
13 Mean larval perch concentration in Michigan waters (1976) . . 43
14 Mean larval perch concentration in Michigan waters (1976)
by stage of maturation 44
15 Mean larval perch concentration in Ohio waters (1975,
Zones AE) 46
vi

Larval perch concentration in 0 to 2 meter zone, Ohio
Area A (1975)
Larval perch concentration in 2 to 4 meter zone, Ohio
Area A (1975)
Larval perch concentration in 0 to 2 meter zone, Ohio
Area C (1975)
Larval perch concentration in 2 to 4 meter zone, Ohio
Area C (1975)
Larval perch concentration in 0 to 2 meter zone, Ohio
Area D (1975)
Larval perch concentrations in 2 to 4 meter zone, Ohio
Area D (1975)
Larval perch concentration in 0 to 2 meter zone, Maumee
Bay (1976)
Larval perch concentration in 0 to 2 meter zone, Ohio
Area A (1976)
Larval perch concentration in 2 to 4 meter zone, Ohio
Area A (1976)
Larval perch concentration in 0 to 2 meter zone, Ohio
Area C (1976)
Larval perch concentration in 2 to 4 meter zone, Ohio
Area C (1976)
Larval perch concentration in 0 to 2 meter zone, Ohio
Area D (1976)
Larval perch concentration in 2 to 4 meter zone, Ohio
Area D (1976)
Daily cooling water pumping rate at Edison Plant
Monroe, Michigan (May to July, 197576)
Larval perch concentration in vicinity of Monroe Plant
cooling water intake
vii
Number
Page
16
Mean larval
perch
concentration
in
Ohio
waters
(1976,
Zones AE)
47
17
Larval perch
concentration in 0
to
2 meter
zone,
Maumee
Bay (1975)
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
62
. . . 63
. . 64
. 65
66
67
68
. 69
. . . 70
. 71
. . 72
. . . 73
. . 74
. . . 75
. . as
89

Number Page
33 Larval perch concentrations estimated in Monroe Plant
cooling water (1975) 90
34 Larval perch concentrations estimated in Monroe Plant
cooling water (1976) 91
35 Model prediction error for combinations of mortality
and production parameters (Ohio, 1975) 104
36 Predicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Ohio,1975) 105
37 Model prediction error for combinations of mortality
and production parameters (Michigan, 1975) 106
38 Predicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Michigan, 1975) 107
39 Plausible larval perch production survival combinations
in Western Basin (1975) 108
40 Model prediction error for combinations of mortality and
production parameters (Ohio, 1976) 109
41 Predicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Ohio,l976) 110
42 Model prediction error for combinations of mortality and
production parameters (Michigan, 1976) ill
43 Preicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Michigan,1976) 112
44 Plausible larval perch production survival combina
tions in Western Basin (1976) 117
45 Plausible relationship between mean age of larvae at entrain
ment and fraηtion of larvae lost due to entrainment that
would have survived to reach yoy stage 186
viii

TABLES
Number Page
1 Observed densities of larval yellow perch in Michigan
waters: 1975 10
2 Results of night sampling by MSU on May 21, 1975 13
3 Results of night sampling by MSU on May 22, 1975 14
4 Results of night sampling by MSU on May 23, 1975 15
5 Results of night sampling by MSU on June 16, 1975 . . . . 16
6 Results of night sampling by MSU on June 18, 1975 . . . . 17
7 Results of night sampling by MSU on June 19, 1975 . . . . 18
8 Summary of night sampling results by MSU in MayJune 1975 19
9 Observed densities of larval yellow perch in Michigan
waters: 1976 20
10 Mean concentrations of yellow perch in Michigan waters:
1976 30
11 Estimated mean concentration of larval perch in Michigan
waters, 1976, by stage of development 31
l2A Means and standard deviations of larval perch concentra
trations in Ohio Zones AE, 1975 48
12B Estimated abundance of larval perch in Ohio Zones
AE,1975 53
12C Estimated mean concentration in Ohio waters, 1975
(ZonesAE) 54
l2D Estimated abundance of larval perch in Ohio Zones
AE, 1976 (by depth zone) 55
l2E Estimated abundance of larval perch in Ohio Zones
AE,1976 60
ix

Number Page
12F Estimated mean concentration in Ohio waters, 1976
(ZonesAE) 61
13 Water volumes in Ohio waters of western basin 93
14 Concentrations of larval yellow perch at station 2
inCanadianwaters 94
15 Yellow perch larval concentrations sampled in immediate
vicinity of power plant . 95
16 Coefficients of sampling variation associated with
meanconcentrations 95
17 Estimated number of yellow perch larvae entrained by
Monroe Power Plant in 1976 96
18 Water intake specifications . . . 99
19 Larvae entrainment estimates, 1975 100
20 Larvae entrainment estimates, 1976 101
21 Ranges of entrainment losses 102
22 Estimates of entrainment caused by larval mortality 126
23 Estimated impingement mortality 127
24 Values of population parameters and entraiment dnd
impingement mortalities used in calculation of
potential impact on population size 131
25 Estimated potential loss in yield (pounds) 132
26 Estimated potential loss in yield (pounds) 132
27 Estimated potential loss in yield (pounds) . . . . 133
28 Estimated potential loss in yield (pounds) 133
29 Estimated potential loss in yield (pounds) . . . . 133
30 Estimated potential loss in yield (pounds) . . . . 134
31 Estimated potential loss in yield (pounds) . . . . 134
32 Estimated potential loss in yield (pounds) . . . . 134
33 Probability weights assigned to each table entry . 135
x

Number Page
34 Marginal probability distribution . . . . 135
35 Marginal probability distribution 135
36 Equilibrium harvet under different conditions of fishing
pressure, reproductive potential, and entrainment and
impingement 138
A.l Measured concentrations of larval yellow perch in
Michigan waters (1975) 150
A.2 Formulae for testing equality of population means . . . 151
Li Cooling water volumes and larval capture data
hypothesized for example E.l 163
H.1 Estimated fraction of larvae killed due to entrainment
that would have survived to reach youngofyear stage
as a function of age at entrainment 185
xi

ACKNOWLEDGEMENTS
The author expresses his gratitude to Mr. Nelson Thomas, Chief of the
Large Lakes Branch, Large Lakes Research Station, for his strong support and
encouragement without which this project could never have been completed.
Appreciation is expressed to Ms. Debra Caudill for her perserverance and
patience with the author in typing a difficult manuscript.
The author thanks Dr. John Paul of the Large Lakes Research Station and
Dr. Al Jensen of the University of Michigan School of Natural Resources, for
reviewing technical content of earlier drafts of the manuscript. Thanks also
are extended to scientists at the Fish and Wildlife Laboratory, U.S. Fish and
Wildlife Service, Ann Arbor, Michigan, and the Ohio Department of Natural
Resources, Sandusky, Ohio, for reviewing the manuscript at earlier stages of
preparation.
The author also expresses his appreciation to Dr. Ed Herdendorf and Larry
Morris of the Center for Lake Erie Area Research, The Ohio State University,
for their considerable assistance in data interpretation throughout the
study.
x l i

SECTION 1
INTRODUCTION AND SUMMARY
The yellow perch population of Lake Erie has fluctuated widely over the
past forty years as evidenced by commercial catch statistics and field sur
veys taken by the Ohio and Michigan Departments of Natural Resources and the
U.S. Fish and Wildlife Service (12,19). Any occurrence of an increased ju
venile recruitment rate (due to operation of compensatory factors associated
with reproduction) has been insufficient to offset limiting factors such as
higher fishing pressure (including pressure on yearlings), increased inter
specific competition, and deterioration of the microhabitat of larvae and ju
venile fishes. Field surveys show the occurrence of strong year classes only
at very irregular intervals (17,19), between which these strong classes may
be separated by as much as seven years. Strong year classes have repeatedly
occurred, however, as the result of several interacting population and envi
ronmental factors, rendering the assignment of causes to fluctuations in year
class sizes tentative at best. This is not to say that no relationships
exist between reproduction, growth, standing crop, fishing, and natural mor
tality. It is all too well known that heavy natural predation combined with
heavy fishing pressure will deplete Great Lakes fish stocks to the point of
an irreversible decline. Power plants that employ open cycle, oncethrough
cooling water systems are also known to cause losses of large numbers of lar
vae and youngofyear fishes by entrainment and impingement, although their
impact upon the yellow perch fishery of Lake Erie has not been previously in
vestigated. Eighteen municipal and industrial water intakes have been iden
tified in MichiganOhio waters of the western basin of Lake Erie alone.
Among these, the 3100 megawatt Detroit Edison power plant located at Monroe,
Michigan has the largest water pumping capacity. Operating at 50 percent
capacity for one 24 hour period, the Edison plant can pump approximately
4.32xl0 6 cubic meters of water through ih coo1j g _ cycle .
In order to assess the impacts that the Monroe power plant might be
exerting upon the yellow perch population and fisheries of western Lake Erie,
a three year field sampling program was undertaken to provide baseline data
on larval perch abundance and entrainment levels. The purposes of the
iFrom late April through July in 1975 and 1976, biologists from the Michigan
Department of Natural Resources (MDNR), the Institute of Water Research of
Michigan State University (MSU), and the Center for Lake Erie Area Research
(CLEAR) of the Ohio State University sampled larval fish densities through
out U.S. waters of the western basin. In 1977, the field observational pro
gram was conducted by CLEAR. Results reported in the present paper are
based upon analyses of 197576 data only.
1

analyses of the data are as follows: 1. estimate production of larval yellow
perch in MichiganOhio waters of the western basin; 2. estimate natural mor
tality of larval yellow perch prior to their recruitment into the youngof
year stage of development; 3. estimate the number of larval yellow perch en
trained and killed in the cooling water cycle of the Monroe power plant; 4.
estimate the per_££nXa$e of total larva] pprrh p^ri^yiinn in Michigan waters
of the western basin that is lost in the cooling water cycle of the Monroe^
power plant; 5. estimate the percent loss in youngofyear recruitment attri
butableto entrainment mortality at the Monroe power plant; 6. estimate the
TOSS toThe yoJTLr«j pgrrh fighprjjgg in upqfPrn Lake Erie attributable to
impingement and entrainment mortality occurring at the Monroe power plant.
Estimates of production and natural mortality of yellow perch larvae are
obtained by formulating and solving a materials balance model of larval con
centration (or abundance) which incorporates two parameters: htotal larval
production in a season per 100 cubic meters of water in the reference volume;
pmean daily natural mortality rate. The model describes the time variation
of mean larval concentration throughout the reference volumes (Michigan
waters: 4.976 x 108 M3, and Ohio waters: 9.393 x 109 M3); the model para
meters are estimated by the method of least squares.
n of larval^ellow perch in U.S. waters of the western basin in
(Tl975 Is estimated to havebeen 2.3xlo93.5xlQ9. of which J^.OxlQ72.3xl08 are
^stimated to have survived fqr__2J_dgyf ff»T»«nri'ng hatching. Production in
f^Jglft^in U.S. waters of the western basin is estimated to have been 1.8x10^
2.6x10^ of which S^lxlO^LSxlO^ are estimated to have been recruited into
the youngofyear stage. Yellow perch larval production in Michigan waters
in 1976 declined to approximately 27 to 29 percent of the 1973 level whereas
production in Ohio waters declined to an estimated 83 to 85 percent of the
1975 level. When an estimated 50 percent survival of youngofyear fishes is
combined with the an estimated 2 to 10 percent survival of larvae an esti
mated 1.0 to 5.0 percent of larvae survive to be recruited into the yearling
stage of development.
The number of larvae estimated to have been lost due to entrainment at
the Monroe power plant inQ^ZVis approximately 7.4x10^. The estimated
number__enJ»ainoHJ however, is nearly double that figure. The estimated yel
low perch larval entrainment at the same plant in 1976 calculated by Detroit
Edison personnel using their own pump samples is approximately 650,000. It
is estimated that yellow perch larval losses attributable to the power plant
in 1976 were between 195,000 and 2,827,000.
The percentage loss of recruitment of yellow perch into the youngof
year stage due to entrainment mortality at the Monroe plant is estimated to
be 0.8 to 4.7 percent for 1975 and 0.9 to 1.5 percent in 1976, considering
Michigan waters only.
It is estimated that the potential long run annual loss to commercial and
sport fisheries is approximately 110,000 to 406,000 pounds. The above value
is the best interval estimate obtainable and is the result of averaging the
values given in Tables 25 through 32 for different combinations of population
parameters and fishing mortality. The most basic assumption underlying the

analysis is that combined pressures on the yellow perch population will not
be so severe as to exhaust the reproductive stock. The effects of compensa
tory mechanisms possibly operative in the yellow perch population are un
known, although the compensatory reserve is believed to be slight. The dif
ferential impact of entrainment and impingement losses may be greatest when
the fishery is in a depressed condition, which is the present situation.
The basic reason for this increased impact is that when the compensatory re
serve is zero, low numbers of reproductive stock cannot replace incremental
losses to that stock at all. Additional increments of loss in such a situa
tion can drive the population into an irreversible decline. If the yellow
perch fishery were tightly regulated, and if it rested upon a large repro
ductive base, reproductive compensation could conceivably account for most,
if not all, of the losses caused through entrainment and impingement morta
lity incurred by cooling waters of the Edison power plant at Monroe.
1 Calculations in Appendix 8 indicate that annual losses could prove to be
considerably higher.
3

SECTION 2
OBJECTIVES
The following analysis of field data collected in 19751976 is part of a
program sponsored by the U.S. Environmental Protection Agency (U.S. EPA) to
assess the impacts of electrical power generating plants using opencycle,
oncethrough cooling on the aquatic communities of the western basin of Lake
Erie.
The particular objectives of thepresent study are: I) to estimate pro
duction of larval yellow perch in 197576 in U.S. waters of the western
basin; II) to estimate natural mortality among larval yellow perch for the
20 to 30 day period following initiation of the prolarval stage; III) to
estimate the number of larval yellow perch entrained and killed in 197576
in cooling water of the 3100 megawatt Edison plant located at Monroe; IV) to
estimate the percentage of total larval perch production in Michigan waters
of the western basin that is lost in the cooling water cycle of the Monroe
power plant; v) to estimate the percent loss in youngofyear recruitment at
tributable to entrainment mortality at the Monroe power plant; VI) to esti
mate the loss to the yellow perch fishery in western Lake Erie attributable
to impingement and entrainment mortality occurring at the Monroe power plant.
Impacts upon primary producers and benthic fauna have been previously re
ported (4) and are not discussed below.
Difficulties of Estimating the Effect of Water Intake Mortality Upon Larval
Fish Survival
Yellow perch larvae enter U.S. waters of the western basin of Lake Erie
from a variety of sources (Figure 1). Some larvae hatched in streams are
carried into the coastal waters of the western basin by stream flow. Some
are hatched in the Detroit River, Lake St. Clair, or along the Canadian
shoreline and carried into Michigan waters by large scale basin water cir
culation (10). Larvae spawned in shoreline waters on the U.S. side (Figure
1) undoubtedly comprise the largest proportion of the total. The term total
production is defined here as all pro and post yellow perch larvae entering
or hatched in U.S. waters of the western basin, including Maumee Bay, ex
tending from the shoreline outward to the international boundary and eastward
to the boundary of Ohio Zone E (Figure 2). Thus, any larvae collected at
sampling stations within the geographic boundary defined above are considered
herein to have been produced in the U.S. waters of the western basin. This
definition of total production allows valid comparisons between production
and a) natural mortality of larvae, and b) numbers of larvae entrained by
water intakes, since the process of entrainment and natural mortality are not
4

Figure 1. Western Lake Erie inputs and losses of yellow perch larvae.
RAISIN
RIVER
4
0
/
I
Ό
I
10
I
I
..
DISTANCE (MILES I
20
c 2
OHIO WATERS
BOUNDARY
N
STREAM INPUT OF LARVAE
RIVER
WATER INTAKE LOSSES
SPAWNING SOURCES
OF LARVAE
EXCHANGE DUE TO MIGRA TION
AND CIRCULA TION
SANDUSKYBAY .
5

\\ CETR T.
\OUTFALL
S
B
OHiO
SA.fPLINGZOIEBOUNDARY
PORT . GE..
I I
10
DISTA.CE (. 1 ILES
20
NTE RNATIONAL
BOUNDARY
.
S
Figure 2. Western Lake Erie larval sampling stations in 197576.
S \ DY
R ;Sv RIVER
. O.ROE
PO.. ER
S
S
MI C H GA N
S
A
I .,
/
op
RIVER
Sc
OHIO
SI. .1PLIVG ST T/Q JS
\
D.
\OH!O
\
7
0/ /
IS  /
0
RIVER
6

functions of larval source of entry into the basin. Moreover, the above de
finition of production does not require independent estimates of larvae that
enter the basin from streams or embayments external to it. If such estimates
are, in fact, available then an estimate of the component of production due
to basin spawners is possible.
If a direct approach is taken toward estimating production by basin
spawners, the number of female spawners is multiplied by the number of larvae
produced per female spawner. The resulting estimate of approximately (7.0 to
8.0)xlO 9 larvae may be considered an upper limit to larval yellow perch pro
duction in U.S. waters of the western basin. An alternative approach is
developed below for estimating production and natural mortality which uti
lizes measurements of larval densities rather than estimates of numbers of
adult spawners and fecundity. Since abundance of larvae at any instant is
the net integrative effect of production, water intake entrainment, natural
mortality, migration, and recruitment into the youngofyear life stage, all
of these factors are considered below. The method involves specification of
a mathematical model that incorporates a parameter h of production and a
parameter p of natural mortality, both of which are estimated numerically
from field observations of larval densities. The model makes no assumption
about joint behavior of production and natural mortality, i.e., the para
meters h and E
Numerous possible sources of larvae sampling error exist. Perch larvae
tend to move about in clumps, inhabiting beach areas, backwaters, and shallow
embayments. As a result larvae may reach the youngofyear stage without be
coming vulnerable to sampling gear. If this occurs, some clumps will never
be sampled during a cruise; this contributes to an underestimate of abun
dance. The daytime distribution of perch larvae in the water column in the
is s w with ig1 percentage clustered on or near bottom
tions of larvae both the mean and standard error of the estimate of mean
concentration will be in error. Errors in the estimate of mean concentration
propagate errors in estimates of production and natural mortality which, in
turn, give rise to errors in the estimated percent of total production en
trained in water intakes and recruitment into the youngofyear stage.
In addition to errors in estimates of the parameters h and of produc
tion and natural mortality, modeling errors different from but leading to
errors in parameter estimates may also occur. Modeling errors occur when
incorrect assumptions are made about the mathematical representation of
biotic or environmental processes which cause biased estimates of larval
abundance and therefore, indirectly biased estimates of production and
natural mortality. In sunmiary, estimates of production and natural mortality
of larval fishes can be in error due to four major causes shown in Diagram A.
7

Model
( icatio )
Model of
Larval
Abundance
Modeling \
Diagram A:
Sources of Error in Estimation Process
Estimated
Larval Production
and Natural
Mortality
Errors in
Estimating
Larval
Mortality in
Water
Intakes
Estimated % Loss
to YoungofYear
Population Due
to Water
Intake Mortality
8

SECTION 3
DATA COLLECTION AND DISPLAY
Field surveys of standing crops of larval fishes provide the data base
for estimates of production and natural mortality of larval yellow perch in
1975 and 1976. Estimates of the numbers of larval fishes entrained and
killed in cooling water of the Edison plant at Monroe (4,6,7,9) provide the
data base for estimating entrainment mortality and percentage of total annual
production of larval yellow perch lost due to entrainment. Estimates of pro
duction and natural mortality of larval fishes are key requirements for an
assessment of the impacts of specific point sources which produce larval
mortality.
Data on larval perch concentrations shown in the graphs and tables below
are based upon measurements taken at 68 stations in Ohio waters and at 20
stations in Michigan waters (Figure 2).l In addition, special sampling
studies were conducted by the Michigan State University Institute of Water
Resources. A complete listing of all species concentrations obtained at in
dividual stations on specific cruises can be obtained from Cole (4), Hemmick,
et al. (1), Herdendorf, et al. (5,6), and the Michigan Department of Natural
Resources (2,3). Tables 1 through 11 summarize data in references (1), (2),
(3), and (4) relative to yellow perch densities in Michigan waters (see also
Figures 37). Water circulation in the western end of the basin is such that
a large proportion of water from the Maumee estuary, driven by southwest
winds, moves northeast into the Michigan zone from May to September whereas
bottom waters from the Detroit River outfall move southwest along the bottom
to replenish surface waters in the Michigan zone. Since larval densities
measured at individual stations in 1975 were higher in the Maumee estuary and
near the beaches between the Maumee estuary and the Raisin River than in
waters north of the Raisin River, Michigan waters were tentatively subdivided
into two surface zones. Analysis of 1976 data, however, did not show signi
ficant differences in mean concentrations between waters south of the Raisin
River mouth and waters north of the mouth. Figure 3 compares concentrations
of larval perch sampled in lake waters in the immediate vicinity of the river
mouth with those in the upper discharge canal (4, Table B26) of the Detroit
Edison power plant. The lack of data on larval perch densities during May
1975 (Figure 7), earlier in their period of abundance, made it difficult to
assess total production and percent of natural mortality of larval perch in
1 Depth zones in Michigan waters are reported in the English system of units
to conform to the original data set. Calculations and results are reported
in the metric system.
9

TABLE 1. OBSERVED DENS ITIES OF LARVAL YELLOW PERCH
EN MICHIGAN WATERS: 1975
Data Source: Ref. (2)
Depth Zone
and
Stations
Date
6/4 6/5
6/9 6/12
6/18 6/24
0 6
18
19
20
0.64
0,3.19,3.19,
3. 19,0 .46
46.33
0
0,0,0,0,0
3.90
612
._________________
1
4
7
1].
14
0.42
0
0
0.53
0.42
0
7.13
6.20
0
0.35
0
0
6.06
5.01
4.98
1.57
1218
8
12
15
17
0
0
0
0
1.11
0
5.99
2.10
1.10
11.45
1824
5
9
13
16
0.62
0.37
0.40
0.57
0
1.04
0
0
0
0
0
0.72
24 30
6
10
0
0
0
0.31
0.36,0,0,0
0.68
1. 72,0. 66,
1.57,0.94,
0.99
10

TABLE 1 (coNTINuED)
Depth Zone
and Date
Stations 6/30 7/2 7/14 7/16 I 7/28 7/30 8/11 8/14
06
18
19
20
0
0,0,0,0,0
0
0
0
0
0
0
0
0
0
0
612
1
4
7
11
14
0
0.33
0
0
0
0
0
0
0
0
3.00
0.33
0.36
0.32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.35
0
0
0
0
1218
8
12
15
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.35
0
0
0
0
0
0
0
18 24
0
5
9
13
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2430
6
10
0
0
0,0,0,0,0
0
0.35
1.22
0
0
0
0
0
0
0
0.38
0
11

TABLE 1 (cONTINUED)
Note : When two values are given
for a single station on a
given date, the lower arid
upper values are measure
ments at the bottom and
top of the water column,
respectively. If a single
value is given, it is an
average representing the
entire water column,
usually not more than three
feet in depth.
4
7
ii
14
0
0
0
0
0
0
0
0
12
15
17
0
0
0
0
0
0
0
9
13
0
0
0
0
0
0
16
12

TABLE 2. RESULTS OF NIGHT SAMPLING BY MSU ON MAY 21, 1975.
(# Perch Larvae/100 M 3 )
Integrated Tow
1
Replication No.
2 3 4
5
Statistics
1 s
Pro L.
Post L.
19.2
20.2
11.0 8.4 7.2
35.5 22.7 21.0
10.1
12.3
11.1 4.63
22.3 8.37
1
Surface
Replication No.
2 3 4
5
Statistics
1 s
Pro L.
Post L.
14.0
10.4
15.0 11.9 24.2
18.8 7.9 10.4
5.9
26.6
14.2 6.61
14.8 7.77
1
Mid Depth
Replication No.
2 3 4
5
Statistics
1 s
Pro L.
Post L.
50.8
45.2
36.6 37.2 30.6
30.5 14.3 22.3
11.9
8.9
38.8 8.54
24.2 14.29
1
Bottom
Replication No.
2 3 4
5
Statistics
1 s
Pro L.
Post L.
21.7
24.8
11.3 5.7 11.0
5.7 0 8.2
9.0
6.0
11.7 6.00
8.9 9.37
13

TABLE 3. RESULTS OF NIGHT SAMPLING BY MSU ON MAY 22, 1975.
(# Perch Larvae/100 M 3 )
Integrated Tow
Replication No.
Statistics
1
2 3 4
5
1 s
Pro L.
7.0
9.5 7.9 2.1
9.7
7.2 3.09
Post L.
15.3
15.5 9.1 13.7
9.7
12.7 3.06
1
Surface
Replication No.
2 3 4
5
Statistics
1 s
ProL.
0
0 0 0
0
0 0
PostL.
0
0 0 0
0
0 0
1
Mid Depth
Replication No.
2 3 4
5
Statistics
1 s
Pro L.
0
0 0 2.9
0
0.6 1.3
Post L.
6.2
2.9 6.1 0
0
3.0 3.08
1
Bot torn
Replication No.
2 3 4
5
Statistics
Pro L.
13.6
17.6 9.2 20.3
2.8
12.7 6.94
Post L.
27.1
52.7 15.3 5.8
11.2
22.4 18.65
14

TABLE 4. RESULTS OF NIGHT SAMPLING BY MSU ON MAY 23, 1975.
(# Perch Larvae/l0O M 3 )
Integrated Tow
Replication No.
Statistics
1
2
3 4
5
5
Pro L.
7.2
5.0
8.3 6.0
2.4
5.8 2.26
Post L.
8.4
23.6
15.4 25.0
14.4
17.4 6.90
1
2
Surface
Replication No.
3 4
5
Statistics
5
Pro L.
0
3.2
0 3.3
0
1.3 1.78
PostL.
0
0
0 0
0
0 0
1
2
Mid Depth
Replication No.
3 4
5
Statistics
s
Pro L.
5.8
0
5.8 5.5
5.4
4.5 2.52
Post L.
8.7
11.9
5.8 5.5
10.7
8.5 2.86
1
2
Bottom
Replication No.
3 4
5
Statistics
s
Pro L.
5.9
6.5
6.4 10.9
5.8
7.1 2.15
Post L.
29.7
22.6
16.0 38.2
14.5
24.2 9.88
15

TABLE 5. RESULTS OF NIGHT SAMPLING BY MSU ON JUNE 16, 1975.
(# Perch Larvae/100 N 3 )
Integrated Tow
Replication No.
Statistics
1
2
3 4
5
1 s
ProL.
0
0
0 0
0
0 0
Post L.
8.8
8.6
17.9 1.0
12.1
9.7 6.14
1
2
Surface
Replication No.
3 4
5
Statistics
s
ProL.
0
0
0 0
0
0 0
Post L.
2.9
0
2.8 0
0
1.1 1.56
1
2
Mid Depth
Replication No.
3 4
5
Statistics
1 s
ProL.
0
0
0 0
0
0 0
Post L.
2.5
5.1
8.9 0
7.3
4.8 3.59
1
2
Bot torn
Replication No.
3 4
5
Statistics
1 s
ProL.
0
0
0 0
0
0 0
Post L.
9.5
17.4
4.9 14.2
10.1
11.2 4.78
16

TABLE 6. RESULTS OF NIGHT S NPLING BY MSU ON JUNE 18, 1975.
(# Perch Larvae/100 M 3 )
Integrated Tow
Replication No.
Statistics
1
2
3 4
5
1 s
ProL.
0
0
0 0
0
0 0
Post L.
1
1
5.1 2.1
1.9
2.2 1.69
1
2
Surface
Replication No.
3 4
5
Statistics
1 s
ProL.
0
0
0 0
0
0 0
PostL.
0
0
0 0
0
0 0
1
2
Mid Depth
Replication No.
3 4
5
Statistics
1 s
ProL.
0
0
0 0
0
0 0
Post L.
0
0
0 15.1
0
3.0 6.75
1
2
Bottom
Replication No.
3 4
5
Statistics
1 s
ProL.
0
0
0 0
0
0 0
Post L.
2.4
7.3 9.3 17.2
15.9
10.4 6.15
17

TABLE 7. RESULTS OF NIGHT SAMPLING BY MSU ON JUNE 19, 1975.
(# Perch Larvae/100 N 3 )
Integrated Tow
Replication No.
Statistics
1
2
3 4
5
s
ProL.
0
0
0 0
0
0 0
Post L.
2.2
0
2.2 0
0
0.9 1.2
1
2
Surface
Replication No.
3 4
5
Statistics
s
ProL.
0
0
0 0
0
0 0
PostL.
0
0
0 0
0
0 0
1
2
Mid Depth
Replication No.
3 4
5
Statistics
s
ProL.
0
0
0 0
0
0 0
PostL.
0
0
0 0
0
0 0
1
2
Bot toni
Replication No.
3 4
5
Statistics
s
ProL.
0
0
0 0
0
0 0
Post L.
8.7
2.6
10.0 0
0
4.3 4.8
18

TABLE 8. SUMMARY OF NIGHT SAMPLING RESULTS BY MSU IN MAYJUNE 1975
(# Perch Larvae/lOU M 3 )
Day
142
143
144
168
170
171
(1)
Integ.
33.48
19.90
23.14
9.68
2.22
0.88
Tow
(2)
Surface
29.00
0
1.30
1.14
0
0
(S)
(3)
Mid
Depth
57.66
3.62
13.02
4.76
3.02
0
(M)
(4)
Bottom
20.68
35.12
31.30
11.22
10.42
4.26
(B)
(5)
Avg. of
35.78
12.91
15.21
5.71
4.48
1.42
S , M, B
(6)
Avg. of
34.63
16.41
19.18
7.70
3.35
1.15
( 1)+(5)
19

TABLE 9. OBSERVED DENSITIES OF LARVAL YELLOW PERCH
IN MICHIGAN WATERS: 1976.
Data Source: (3,4)
Depth Zone
and
MDNR Stations
4/13
NDNR
Prol. EPL LPL
0 6
18
19
20
0
0
0
0
0
0
0
0
0
612
1
4
7
11
14
1218
8
12
15
17
1824
5
9
13
16
24 30
6
10
Note : All concentrations are in units of #/100 M 3 .
Note : For MDNR data: When two values are recorded at a single station
and date, upper and lower values denote measurements at surface
and bottom, respectively.
Note : No entry denotes no sample available.
Note : MSIJ samples taken only in general vicinity of MDNR stations.
20

TABLE 9 (CONTINUED)
Depth Zone
and
Stations
4/2627
}IDNR
Prol EPL LPL
4/27
MSU
Total Larvae
4/28
MDNR
Prol EPL LPL
4/28
MSU
Total Larvae
O6
18
19
20
0
0.91]
0
0
0
0
0
0
0
586.5,49.7
36. 1, 12.9
3.7,23.6,
29.0,18.6
5.0,51.8,
64.4
11.7
26.1
612
1
4
7
11
14
0
1.18
0
0
0
0
0.9
6.9,102.9,
142.9
0.878
0.392
1.32
2.74
0
0.784
0
0
0
0
0
0
11.5
130.1
1218
8
12
15
17
3.3
0
0.439
0.392
0
0.413
0
0
0
0
0
0
0
0
0
8.0
1824
5
9
13
16
1.7,0
1.0,0
1.0,4.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.0,1.0
0,0,0
2.1
2430
6
10
1.0,0
0,0
0.9,0
0
0
0
0
0
0
0.9,1.0
1.1,0
0
21

TABLE 9 (coNTINuED)
Depth Zone
and
Stations
4/29
MDNR
Prol EPL LPL
4/29
14SU
Total Larvae
5/14
I4DNR
Prol EPL LPL
5/14
MSU
Total Larvae
0 6
18
19
20
54.8
0
0
0
2.73
0
0
6 12
1
4
7
11
14
1.53
9.01
0.329
9.88
0
0
0
0
0
0
0
0
4.8
9.2
12 18
8
12
15
17
1.78
8.68
0.909
9.59
0
0
0
0
0
0
0
0
3.7
2.1
0
1824
5
9
13
16
0.957
0
0
0
0
0
0
0
2430
6
10
22

TABLE 9 (CONTINUED)
Depth Zone
and
Stations
5/1618
MDNR
Prol EPL LPL
5/16
MSU
Total Larvae
5/18
MSU
Total Larvae
0 6
18
19
20
0
2.2,0
0
1.1,0
6 1.2
1
4
7
11
14
1.84
0
0
0
0
0
0
0
0
0
0
0
0
0
1218
8
12
15
17
1.9
0
0
0
1824
5
9
13
16
0.0,1.0
4.7,3.2
0
0
1.0,0,1.6
0,3.0
0
2430
6
10
4.1,0,2.2
0,1.0,3.3
15.4
3.0,0, 1.2
3.3,16.3,0
1.1
23

TABLE 9 (coNTINUED)
Depth Zone
and
Stations
5/24
MDNR
Prol EPL LPL
5/24
MSU
Total Larvae
5/2526
MDNR
i Prol EPL LPL
5/26
MSU
Total Larvae
06
1
18
19
20
0
0.456
0
47.7
1.37
1.95
0
0
0
3.0,1.0
0,29.5,
7.3
1.1,2.1
0.8,3.4,
6.5,2.6
612
1
4
7
11
14
0,0
0,0,5.7
0.303
0.710
0
0
0
0
0
0
0
0
0.303
1.07
0
1.96
0
1.60
0.878
1.57
0
1.12
0
0
0
0
3.44
0
0
0
5.24
0
0.9,2.8,
2.7
1.9,1.0,
0,0
1218
8
12
15
17
2.0
0,1.0
0
0
0
0
0
0
0
0
0
0.784
0.439
0
0
0.344
1.32
0
0
0
0
0.39
0.878
0
0
0
3.0
0
18 24
5
9
13
16
9.7
1.0,1.9
4.0
0
0
0
0
0
0
0
1.96
0.439
0.784
0
0
0
0
0
0
0
0
0
0,0,4.5
24 30
6
10
0
0
0
0
12.3
12.5
0
0
0
0
0
0
24

TABLE 9 (coNTINuED)
Depth Zone
and
Stations
6/7
MDNR
Prol EPL LPL
6/8
MDNR
Prol EPL LPL
0 6
18
19
20
0
0
0
0
1.37
.0
0
0
4.39
6 12
1
4
7
11
14
0
0
0
0
0
0
0
0
0
0
0
0.797
0
0
0
0
0
0.459
0
0
0
0
0
0
0
0
0.505
0
0
0
1218
8
12
15
17
0
0
0
0
0
0
0
0
0
0
0
0.358
0
0
0
0
0
0
0
0
0
0
0
0.437
1824
5
9
13
16
0
0
0
0
0
0
0
0
0
0.392
0
0.858
0.478
0.08
0
0
0
0
0
0
0
0
0
0
2430
6
10
0
0
0
0.909
0
0
4.45
0.454
0
0
0
0
25

TA BLE 9 (CoNTINuED)
Depth Zone
and
Stations
6/14
MSU
Total Larvae
6/21
NSU
Total Larvae
6/26
MSU
Total Larvae
06
0,3.3
0
0,0,0,0,0
0,0,0,0,0,0
0,0,0,0,0
0,0,0,2.0
0,0
0
612
0
0
12lS
0
0
0
0
1824
0
0,0,0,0,0,0
0
0,0,0,0,0,0
2430
0,0,14.4,12.4
0,0,0
0,0,0,0,0,0,0
26

TABLE 9 (cONTINUED)
Depth Zone
and
Stations
6/29
IIDNR
Prol EPL LPL
0 6
18
19
20
0
0
0.636
0
0
0
0.488
612
1
4
7
11
14
1218
8
12
15
17
18 24
5
9
13
16
2430
6
10
27

TABLE 9 (cONTINUED)
Depth Zone
and
Stations
7/16
MDNR
Prol EPL LPL
7/9
MDNR
Prol EPL LPL
7/1920
MDNR
Prol EPL LPL
0 6
18
19
20
0
0
0
0
0
0
0
0
0
0
0,0,0
0,0
0
0
0,0,0
0,0
0
0
0,0,0
0,0
0
612
1
4
7
11
14
0
0
0
0
0.583
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.392
0
0.439
0
0
0
0
0.583
0
0
0
0
0
0
0
0
0
0
0
0.516
0.967
0
0
12 18
8
12
15
17
0
0
0
0
0
0
0
0
0
0.516
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1824
5
9
13
16
0
0.350
0
0
0
0
0
0
0
0
0
0
0
0
0
1.09
0
0
0
0
0
0
0
0
2430
6
10
0
0.406
0
0
0.583
0
0
0
0
0
0
0
28

TABLE 9 (coNTINUED)
Depth Zone
and
7/21
MDNR
7/28
MDNR
8/3
MDNR
Stations
06
Prol
EPL
LPL
Prolj EPL
LPL
Prol
EPL
LPL
18
19
20
0
0
0
0
0
0
0
0
0
612
1
4
7
11
14
0
0
0
0
0
0
0
0
0.334
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
No yellow perch
after 8/3.
1218
8
12
15
17
0
0
0
0
0
0
0,0,0
0,0
0,0,0
0,0
0
0
0
0
0
0
0,0,0
0,0
0,0,0
0,0
0
0
0.369
0
0
0
0,0,0
0,0
0,0,0
0,0
1824
5
9
13
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.76
0.388
0
0
0
0
0
2430
6
10
0
0
0
0
0
1.70
0
0
0
0
0
0
29

TABLE 10. MEAN CONCENTRATIONS OF YELLOW PERCH IN
MICHIGAN WATERS: 1976
Day
Mean
Standard Error (S.E.)
Mean ±
S.E.
104
0
0
118
5.63
1.94
3.69,
7.57
136
1.99
0.624
1.37,
2.61
145
2.14
0.56
1.58,
2.70
158
0.483
0.201
0.282,
0.684
188
0.145
0.057
0.088,
0.202
201
0.205
0.176
0.029,
0.381
209
0.112
0.078
0.034,
0.190
Note : Day 120 = 1 May.
Data Source: Table 9
Calculations given in Appendix C.
30

TABLE 11. ESTIMATED MEAN CONCENTRATION OF LARVAL PERCH IN
MICHIGAN WATERS, 1976, BY STAGE OF DEVELOPMENT.
Early Late
Pro Post Post
Date Larvae Larvae Larvae Total
104 0 0 0 0
118 5.61 0.02 0 5.63
136 0.80 1.19 0 1.99
145 0.04 2.06 0.04 2.14
158 0.041 0.386 0.056 0.483
188 0.033 0.103 0.009 0.145
201 0 0.202 0.003 0.205
209 0 0.095 0.017 0.112
215 0 0 0 0
31

(0) ZERO CONCENTRATION
o MDNR, 1975
MSU, 1974
o MSU, 1975
102 6A
12
E 06
o 10 2
0
z 10 10
U)
 1 110 hA
E 10
a12 1STANDARD ERROR
C 6A ..OFMEAN
Z  MEAN CONCENTRATION
0
IN 06 FT DEPTH USING
MDNR DATA ONLY
io 12A
I Stations 2,6,10,11,12
z 012
sampled by MSU in
o 6,lOjl
vicinity of power plant
o 2 A for comparison.
0
101
(0)6,10,11,12 (0)2,6,10,11,12
(0) 11,12 (0) 11
1 0 2 ___________A____________ ( 0 )
100 120 140 160 180 200 220
TIME (days)
Figure 3. Larval perch concentration in 0 to 6 ft. zone
from Raisin River to Maumee Bay (19741975).
2
o2
A10
32

MEAN CONCENTRATION ± 1 S.E.
(0) ZERO CONCENTRA TION
102
C.,
E
0
 101
E
C
z
0
H
< iriO
U 
I
z
uJ
0
z
0
0
101 
(0) (0) (0)
j 0 __
100 120 140 160 180 200 220
TIME, days
Figure 4. Larval perch concentration in 0 to 6 ft. zone
from Raisin River to Mauinee Bay (1975).
Data Source: Table 1.
33

MEAN CONCENTRATION ±1 S.E.
(0) ZERO CONCENTRA TION
102
E
0
0
E 101
0
I
10o.
I
z
w
0
z
0
0
101 
(0) (0)
102 I I 01 I
100 120 140 160 180 200 220
TIME, days
Figure 5. Larval perch concentration in 6 to 12 ft. zone
from Raisin River to Maumee Bay (1975).
Data Source: Table 1.
34

102
C,,
E
0
0
:i.b01
< 100
cr
z
uJ
0
z
0
101
220
TIME, days
Figure 6. Larval perch concentration in 6 to 12 ft. zone
from Raisin River to Huron River (1975).
Data Source: Table 1.
102
100 120 140 160 180 200
35

101
100
101
102
10s
100
200 220
TIME, days
Figure 7.
Mean larval perch concentration in Michigan waters (1975).
Data Source: Table 1.
E
0
0
I  .
E
C
2
0
I
cr
H
z
w
0
z
0
0
120 140 160 180
36

Michigan waters for that year. Mean larval concentrations shown in Figure 7
are obtained as weighted averages of concentrations sampled over all depth
zones for which data are available on a given date:
Mean Concentration 1 (1)
on a sampling date (V 1 x 1 + + V 5 x 5 )
where:
VT = volume of Michigan waters = 4.976x10 8 M 3 .
V. = volume of ith depth zone.
63
1 1 corresponds to 0 6 zone: 5.6x10 M
i 2 corresponds to 612 zone: 5.lxlO 7 M 3
I = 3 corresponds to 1218 zone: S.2x10 M
, ,, 8 3
= 4 corresponds to 18 24 zone: 2.32x10 M
83
1 = 5 corresponds to 24 30 zone: l.27xl0 M
x 1 = mean concentration in ith depth zone averaged over all
measurements obtained in that zone for the given sampling
date.
2 2
Standard Error (V l + + V S 5 )h/2 (2)
of Mean T n 1 n 5
where:
sj standard deviation of all n 1 measurements obtained in itb
depth zone on the given sampling date.
Sample concentrations obtained in each depth zone are aggregated for purposes
of calculating mean concentrations (Figure 7). Also plotted in Figure 7 are
sample concentrations obtained at night. The latter samples were collected
in the 6 to 12 depth zone approximately 1 kilometer offshore from the mouth
of the Raisin River (Tables 28). Densities of larval yellow perch obtained
at night were found to be higher than those obtained during the day and pro
bable causes are discussed by Cole (4). A subsequent statistical analysis
of day to night differences (Appendix A) showed that they were significant
(P < .10 for surface and P < .005 for bottom concentrations), indicating that
estimates of yellow perch larval abundance or production based upon densities
observed only during daylight hours are low.
Larval perch densities measured in Michigan waters in 1976 are listed in
Table 9 and plotted in Figures 9 through 14. Concentrations are highest in
the 0 to 6 depth early in the spawning period. A 1976 overall mean concen
tration for Michigan waters is calculated and shown in Table 10 and Figure
37

L4 E I
P12
IL
N
Figure 8.
Locations of NSL sampling stations in vicinity
of Monrot Power Plant.
Data Source: Ref.( ).
.P o
.Pii
jo

102
101
100
101
102
100 120 140 160 180 200 220
TIME, days
Figure 9. Larval perch concentration in 0 to 6 ft. zone
from Raisin River to Maumee Bay (1976).
Data Source: Table 9.
(O)
I
10
MEAN CONCENTRA TION ± 1 S.E.
(0) ZERO CONCENTRA TION
C.,
E
C
C
1 .
E
C
0
F
a:
I
z
w
0
z
0
0
I I
39

10
102
101
10°
101 
102 
100
MEAN CONCENTRATION ± 1 S.E.
(0) ZERO CONCENTRA TION
200 220
TIME, days
Figure 10.
Larval perch concentration in 6 to 12 ft. zone
from Raisin River to }laumee Bay (1976).
Data Source: Table 9.
C )
E
0
0
a)
E
2:
0
F
cr
I
z
w
0
z
0
0
(0) (O)
(0)
120 140 160 180
40

C ,,
E
0
0
a,
E
C
z
0
I
c
F
z
w
0
z
0
0
10
MEAN CONCENTRA TION ± 1 S. E.
(0) ZERO CONCENTRATION
101
100
101
102
100 120 140 160 1 0 200 220
TIME, days
Figure 11. Larval perch concentration in 0 to 6 ft. zone
from Raisin River to Huron River (1976).
Data Source: Table 9.
102
(0)
(0)
41

10
102
101
100
101
102
E
0
0
E
C
z
0
F
cc
F
z
w
0
z
0
0
TIME, days
Figure 12. Larval perch concentration in 6 to 12 ft. zone
from Raisin River to Huron River (1976).
Data Source: Table 9.
100 120 140 160
180 200 220
42

102
101
100
101
c v )
E
0
0
C)
E
C
z
0
z
w
0
z
0
0
102
100 120 140 160 180 200 220
TIME, days
Figure 13. Mean larval perch concentration in Michigan waters (1976).
Data Source: Table 9.
43

102
r) ir
E
0
0
a,
E
C
Z ir O
o
F
F
z
w
0
z
0
o 101
100 120 140 160 180 200 220
TIME, days
Figure 14. Mean larval perch concentration in Michigan waters (1976)
by stage of maturation.
Data Source: Table 9.
102
44

13. Before an overall mean concentration for Michigan waters was calculated,
it was determined that observed differences in mean concentrations by depth
zone were statistically significant. Tests of significance for differences
(Appendix B) by depth zone for Michigan waters in 1976 showed that concentra
tions in the 0 to 12 zone were significantly higher (P < .025) during the
period of observed peak abundance than concentrations measured in other depth
zones. Furthermore, statistical analysis showed that 0 to 12 and 12 to
30 zones could be aggregated to compute mean concentrations and standard
errors. Calculations of mean and standard errors for Figure 13 are shown in
Appendix C. Figure 13 presents a typical picture of the temporal variation
in larval abundance: a rapid buildup occurs due to a high production rate
followed by a decline due to natural mortality, migration, and net avoidance.
As larvae increase in age to 20 to 30 days, they become progressively more
capable of avoiding capture by sampling gear, so that eventually no larvae
are observed in samples (see also Figures 15 and 16 for similar patterns
occurring in Ohio waters in 1975 to 76).
Concentrations shown in Figure 13 on any given date represent the sum of
prolarvae, early post larvae, and late post larvae. A disaggregation of
these data corresponding to the three stages of larval development (for each
sampling date) is plotted in Figure 14. Approximately five to seven days
elapse before prolarvae develop into an early post larval stage and approxi
inately 10 additional days elapse before the late post larval stage. For pre
sent purposes, yellow perch larvae are considered to be recruited into the
youngofyear stage after 25 days of life. Figure 14 shows that larval pro
duction began approximately on day 102 (April 12, 1976) and continued at a
relatively high rate until approximately day 140, a period of about five
weeks. Abundance tapered off, finally terminating between days 190 and 200.1
For 1975 and 1976, mean concentrations of larval perch in Ohio waters of
the western basin exhibited temporal variations similar to those shown in
Michigan waters (Figures 15 and 16). The mean values shown in Figures 15 and
16 are weighted averages of concentrations in Zones A,B,C,D, and E. The tem
poral patterns of abundance are similar for both years, although peak produc
tion occurred approximately three weeks earlier in 1976 and was possibly
lower in 1976 than in 1975. Means and standard errors are calculated by fol
lowing equations (1) and (2) and using Tables l2A12E. In the 1976 plot
standard errors on each date are calculated by pooling estimates of mean con
centrations obtained in Zones A through E. Figures 18 to 30 show estimated
mean concentrations in the 0 to 2 meter and 2 to 4 meter depth zones for sec
tors A, C, and D for 197576. The plots do not clearly show which year pro
duced the highest larval abundance. Even when all depth zones are accounted
for (Figures 15 and 16) the picture remains somewhat clouded but it is indi
cated that perch larvae were less abundant in 1976 than in 1975, based upon
comparison of mean concentrations.
In order to incorporate observations obtained by the MSU Institute of Water
Research (Table 9) into Figure 14 it is assumed that the proportions of
larvae in each developmental stage obtained from analysis of MDNR observa
tions holds as well for MSUIWR observations.
45

102
101
100
OVERALL MEAN CONCENTRATION ± 1 S.E.
(0) ZERO CONCENTRATION
REF. VOLUME = 9.351 x iO m 3
(0)
I I
10
102
100 120 140 160 180 200 220
TIME, days
Figure 15. Mean larval perch concentration in Ohio waters
(1975, Zones AE).
Data Source: Tables 12A and 12B.
C)
E
C
C
a,
E
C
z
0
I
z
w
0
z
0
0
(0)
46

102
100 120 140 160 180
TIME, days
Figure 16.
Mean larval perch concentration in Ohio waters
(1976, Zones AE).
Data Source: Tables 12C and 12D.
OVERALL MEAN CONCENTRA TION ± 1 S.E.
(0) ZERO CONCENTRATION
REF. VOLUME= 9.351 x 10 m 3
102
101
100
101
C.,
E
0 )
E
C
z
0
I
m
I
z
w
0
z
0
0
(2.2 x iO )
200 220
47

TABLE 12A. MEANS AND STANDARD DEVIATIONS OF LARVAL PERCH
CONCENTRATIONS IN OHIO ZONES AE, 1975.
Data Source: Reference (5)
Sector
A
1
2
Depth Z ne
3 4
5
6
Time
x
s
x
S
X
S
X
S
X S
X
S
May l214

May 2225
15.75
13.08
7.00
8.72
5.00
3.56
n=8
n4
n4
June 14
12.12
n8
8.1
4.75
n4
4.65
1.25
n4
0.96
June 1117
18.37
n=8
51.57
1.50
n4
3.00
0
n=4
0
June2l23
2.75
n8
3.99
0
n4
0
0
n=4
0
Ju ly l3
0
0
0
0
0
0
Ju1y111
0
0
0
0
0
0
Aug.14
0
0
0
0
0
0
Aug. 27
Sept.8
0
0
0
0
0
0

48

TABLE 12A (CONTINUED)
Depth Z ne
Sector
B
Time
2
3
4
5
6
x
s
x
s
x
S
x
S
x
S
x
S
May l214




May 2225
1.25
n=4
2.5
0.50
n=4
0.58
1.50
n=4
3.0
June l4
0
0
0
0
1
1.41
n2
n=2
n2
Junel l17
0
0
0
0
0
0
June2l23
0
0
0
0
0
0
July l3
0
n2
0
0.25
n4
0.50
0
n=2
0
Ju lyll15
0
0
0
0
0
0
Aug.14
0
0
0
0
0
0
Aug. 27
S pt.3
0
0
0
0
0
10
49

TABLE 12A (CONTINUED)
Depth Zbne
Sector
C
1
2
3
4
5
6
Time
x
s
x
s
x
S
x
s
x
S
x
S
May 1214
49.5
156.5
78.5
139.3
0.5
1.22
0
0
0
0
n10
n=6
n6
n=4
n=4
May 2225
614.12
1782
72.12
115.0
3.33
6.74
4.5
4.8
10.5
17.8
n=8
n=8
n=6
n4
n=4
June 14
2.94
n=8
8.11
1.94
n8
1.77
2.0
n6
3.63
0.5
n4
0.58
0.25
n4
0.50
June 1117
0
n8
0
0.31
n8
0.37
0
n6
0
0
n 4
0
0
n=4
0
June 2123
0.37
n8
0.98
0.17
n8
0.11
0
n3
0
0
n=2
0
0
n=2
0
Ju ly l3
0
0
0
0
0
0
0
0
0
0
Julyll15
0
0
0
0
0
0
0
0
0
0
Aug.14
0
0
0
0
0
0
0
0
0
0
Aug. 27
Sept.3
0
0
0
0
0
0
0
0
0
0
50

TABLE 12A (CONTINUED)
Sector
D
Time
1
2
Depth Zdne
3 4
5
6
x
s
x
s
x
s
x
s
x
s
x
s
May 1214
0.25
n4
0.5
6.0
n4
12.0
0
n4
0
0.75
n4
1.5
0
n=2
0
0
n=2
0
May 2225
5.0
n=4
10.0
0.87
n=4
1.5
12.25
n=4
14.2
6.0
n=4
7.7
5.5
n=4
4.1
3.75
n=4
7.5
June 14
1.25
n=4
1.26
0.25
n=4
0.50
17.25
n=4
21.47
0.75
n=4
0.96
1.75
n=4
1.71
2.0
n=4
2.45
June 1117
0
0
0
0
0
0
0
0
0.12
n=4
0.25
0
0
June2l23
0
0
0
0
0
0
0
0
0
0
0
0
July l3
0
0
0
0
0
0
0
0
0
0
0
0
Julyll15
0
0
0
0
0
0
0
0
0
0
0
0
Aug.14
0
0
0
0
0
0
0
0
0
0
0
0
Aug. 27
Sept.3
0
0
0
0
0
0
0
0
0
0
.
.0
0
51

TABLE 12A (CONTINUED)
Sector
E
Time
1
2
Depth Z
3
ne
4
5
6
x
s
x
s
x
s
x
s
x
s
x
s
May 1214
7.75
n4
15.5
0.33
n=6
0.82
0.75
n=4
1.5
0.75
n4
1.5
0
0
0
0
May 2225
5.75
n4
10.84
11.92
n6
26.47
13.5
n4
17.6
13.75
n=4
16.3
5.25
n4
5.5
9.75
n=4
14.93
June 14
0.5
n=4
1.0
0.25
n4
0.5
1.0
n=4
0.82
1.0
n2
0
1.5
n=4
3.0
4.5
n+
6.45
June 1117
0
0
0.25
n=4
0.29
0
0
0
0
0.12
n=4
0.25
0
0
June2l23
0
0
0
0
0
0
0
0
0
0
0
0
Ju lyl3
0
0
0
0
0
0
0
0
0
0
0
0
Julyll15
0
0
0
0
0
0
0
0
0
0
0
0
Aug.14
0
0
0
0
0
0
0
0
0
0
0
0
Aug. 27
Sept.3
0
0
0
0
0
0
0
0
0
0
0
0
52

TABLE 12B. ESTIMATED ABUNDANCE OF LARVAL PERCH IN
OHIO ZONES AE, 1975.
Sector
Date A B C D E
5/1214 1.O9x10 7 * 2.05x10 8 2.32x10 6 3.47x10 6
5/2225 2.41x10 7 3.O5x1O 7 4.14x10 8 9.24x1O 7 2.21x10 8
6/14 1.35x10 7 1.06x1 0 7 2.30x1 0 7 3.98x10 7 7.72x10 7
6/1117 1.19x10 7 0 7.56x10 5 9.95x1 0 5 5.02x10 5
6/2123 1.58x10 6 2.42x1O 6 4.95x10 5 0 0
7/13 0 0 0 0 0
7/1115 0 0 0 0 0
8/14 0 0 0 0 0
8/27to9/8 0 0 0 0 0
*: Estimated by using average concentrations in Zones C, D and E.
: Zone B not sampled on 5/1214.
53

TABLE 12C. ESTIMATED MEAN CONCENTRATION IN OHIO WATERS,
1975 (zONES AE).
Mean
Concentration Standard Error
Date (No. per 100 M 3 ) (S.E.) Mean ± S.E .
5/1214 2.38 1.93 (4.5x10 1 , 4.31)
5/2225 8.36 2.74 (5.62, 11.10)
6/14 1.75 6.3x1O (1.12, 2.38)
6/1117 1.51x10 1 6.6x1O (0, 8.Ox1O )
6/2123 2.22x10 2 8.7x10 2 (0, 1. 1x1O )
7/13 2.60x10 2 1.5x10 2 (1.1x10 2 , 4.1x10 2 )
7/1115 0 0
8/14 0 0
8/27 to 9/8 0 0
54

TABLE 12D. ESTIMATED ABUNDANCE OF LARVAL PERCH IN OHIO ZONES AE,
1976 (BY DEPTH ZoNE).
Data Source: Reference (6)
Sector A \ Depth
\ Zone
Date
1
2
3
4
5
6
Apr. 1216
0
0
0
0
0
0
Apr. 2123 (Partial)
0
0
0
0
0
0
Apr. 28 May 1
6.9x10 6
4.9x10 6
3.9x10 6
0
0
0
May 811
1.3x10 6
9.3x10 5
2.6x10 6
0
0
0
May 2023
7.9x10 5
0
4.3x10 5
0
0
0
May 30 (Partial)

June 79
0
7.0x10 5
0
0
0
0
Junel925
0
0
0
0
0
0
June 30July 7
0
0
0
0
0
0
55

TABLE 12D (coNTINuED)
Sector B\ Depth
\ Zone
Date
.
1
2
I
3 4

5
Apr. 1216
0
0
0
Apr. 2123 (Partial)
Apr. 28Mayl
May 811
0
4.0x10 6
0
2.4x10 6
0
1.6x10 7
Nay2O23
0
0
0
May 30 (Partial)
June 79
3.9x10 6
0
0
June 1925
0
0
0
June 30July 7
0
0
0
56

TABLE 12D (cONTINuED)
Sector C \ Depth
\ Zone
Date \
1
2
3
4
5
6
Apr. 1216
0
0
0
0
0
Apr. 2123 (Partial)
5.4x10 4
0
0
0
0
Apr. 28 May 1
3.0x10 6
2.6x10 8
2.6x10 8
5.7x10 7
2.4x10 6
May 8li
7.9x10 5
l.2x10 6
l.1x10 6
7.6x10 6
l.2x10 6
May 2023
4.3x10 5
4.3x10 6
6.3x10 6
l.9x10 6
3.6x10 6
May 30 (Partial)
June79
0
0
0
0
0
Junei925
0
0
0
0
0
June 30July 7
0
0
0
0
0
57

TABLE 12D (cONTINuED)
Sector D \ Depth
\ Zone
Date \ 1 2 3 4 5 6
Apr.1216 0 0 0 0 0 0
Apr. 2123 (Partial)
6 6 5 7 7 6
Apr. 28 May 1 2.3x10 6.8x10 3.lxlO l.7x10 l.5xlO 8.OxlO
May 811 5.9x10 5 5.3x10 6 28x10 6 8.7x10 6 8..9x10 7 3.5x10 7
May 2023 l.8x10 5 1.8x10 5 6.1x10 5 l.4x10 7 l.0x10 7 0
May 30 (Partial) 0 6.OxlO 4 4.6x10 6 0 0 l.6xl0 6
June 79 0 6.0x10 4 0 0 0 0
Junel925 0 0 0 0 0 0
June 30July 7 0 0 0 0 0 0
58

TABLE 12D (CONTINUED)
Sector E \ Depth
\ Zone
Date
1
2
3
4
5
6
Apr. 1216
0
0
0
0
0
0
Apr. 2123 (Partial)
Apr. 28 May 1
0
0
5.5x10 6
6.9x10 7
0
0
May 811
6.0x10 5
l.5x10 6
3.9x10 7
2.3x10 7
5.8x10 7
l.3x10 8
May 2023
3.5x10 4
l.0x10 6
3.5x10 6
3.3x10 6
3.6x10 6
3.8x10 6
May 30 (Partial)
0
6.6x 10 5
0
0
l.8x10 6
0
June79
0
0
0
0
0
0
June 1925
0
0
0
0
0
0
June 30July 7
0
0
0
0
0
0
59

TABLE 12E. ESTIMA TED ABUNDANCE OF LARVAL PERCH
IN OHIO ZONES AE, 1976.
Date
A
B
Sec tor
C
D
E
4/1216
0
0
0
0
0
4/2123
0
5.4x1 0 4
4/28 to
5/1
1.57x10 7
0
5.83x10 8
4.94x10 7
7.45x10 7
5/811
4.83x10 6
2.24x10 7
1.19x10 7
1.41x10 8
2.52x10 8
5/2023
1.22x10 6
0
1.65x10 7
2.50x10 7
1.52x10 7
5/30
6.26x10 6
2.46x10 6
6/79
7.0x10 5
3.9x10 6
0
6.0x10 4
0
6/1925
0
0
0
0
0
6/3Oto
7/7
0
0
0
0
0
60

TABLE 12F. ESTIMATED MEAN CONCENTRATION IN OHIO WATERS,
1976 (ZONES AE).
Date
Total
Abundance
Con
(No.
Mean
centration
per 100 M 3 )
Estimated
Standard
Error*
Mean + 1
Standard
Error
4/1216
0
0
4/2123
5.4x10 4
2.2x10 3
1.32x10 3
(8.8x10 4 , 3.5x10 3 )
5/28 to
5/1
7.23x10 8
7.72
3.31
(4.41, 11.0)
5/811
4.32x10 8
4.62
1.79
(2.83, 6.41)
5/2023
5.79x10 7
6.19x1O
2.O4x1O
(4.1x10 , 8.2x10 )
5/30
8.72x10 6
2. 13xlO
8.42x10 2
(1.3x10 , 2.97x10 )
6/79
4.66x10 6
4.98x10 2
4.04x10 2
(9.4x10 3 , 9.0x10 2 )
6/1925
0
0
0
6/30 to
7/7
0
0
0
*
Standard Error estimated from mean concentration across sectors on a given
date, except for 4/28 to 5/1.
61

E
0
0
I
a,
E
C
z
0
F
a:
I
z
w
0
z
0
0
102
101
100
10i
100 120 140 160 180 200 220
TIME, days
Figure 17. Larval perch concentration in 0 to 2 meter zone,
Maumee Bay (1975).
Data Source: Ref.(5).
102
62

102
101
100
101
10_2
100 120 140 160 180
TIME, days
Figure 18.
Larval perch concentration in 0 to 2 meter zone,
Ohio Area A (1975).
Data Source: Table 12A.
MEAN CONCENTRATION ± 1 S. E.
(0) ZERO CONCENTRA TION
C. )
E
cD
I
c
E
z
C
H
H
z
uJ
0
z
0
0
(0)
200 220
63

102
C )
E
0
C
 101
E
C
0
F
< 100
F
z
uJ
C)
z
0
C) 101
102
100
TIME, days
Figure 19. Larval perch concentration in 2 to 4 meter zone,
Ohio Area A (1975).
Data Source: Table 12A.
MEAN CONCENTRA TION ± 1 S.E.
(0) ZERO CONCENTRA TION
120 140 160 180 200 220
64

102
C ,
E
o ) 1r 1
 I,
E
C
z
0
H
<100
H
z
LU
0
z
0
10
102
100 120 140 160 180 220
TIME, days
Figure 20. Larval perch concentration in 0 to 2 meter zone,
Ohio Area C (1975).
Data Source: Table 12A.
200
65

102
C..)
E
C
a)
E 10
z
0
H
cr 100
I
z
LU
0
z
0
0
10i
100 120 140 160
TIME, days
Figure 21. Larval perch concentration in 2 to 4 meter zone,
Ohio Area C (1975).
Data Source: Table 12A.
102
180 200 220
66

102
101
100
101
102
C.,
E
Q
Q)
E
0
F
I
w
0
z
0
0
Figure 22.
TIME, days
Larval perch concentration in 0 to 2 meter zone,
Ohio Area D (1975).
Data Source: Table 12A.
100 120 140 160 180 200 220
67

102
101
100
101
102
100 120 140 160
180 200 220
TIME, days
Figure 23.
Larval perch concentrations in 2 to 4 meter zone,
Ohio Area D (1975).
Date Source: Table 12A.
68
C,,
E
0
0
I
I
E
C
z
0
I
I
z
w
0
z
0
0

10
102
10 1
100
101
102
100
120
160 180 200 220
TIME, days
Figure 24.
Larval perch concentration in 0 to 2 meter zone,
Maumee Bay (1976).
Data Source: Ref.(6).
(0) ZERO CONCENTRA TION
0
E
0
0
I
a)
0
E
C
0
I
a:
I
z
w
C)
0
0
(0)
30uC
140
(0)
69

C.,
E
0
0
E
C
z
0
I
I
z
w
0
z
0
0
10
102
101
100
101
10.2
100
220
TIME, days
Figure 25. Larval perch concentration in 0 to 2 meter zone,
Ohio Area A (1976).
Data Source: Table l2D.
120 140 160 180 200
70

1O
102
E
Q
 ir i
E
C
z
0
H
cr 100
H
z
LU
0
z
0
0
101
TIME, days
Figure 26. Larval perch concentration in 2 to 4 meter zone,
Ohio Area A (1976).
Data Source: Table 12D.
102
100 120 140
71

10
102
101
100
101
(V)
E
0
0
Q)
E
C
0
F
a:
I
z
w
0
z
0
0
Figure 27.
100
TIME,days
Larval perch concentration in
Ohio Area C (1976).
Data Source: Table 12D.
0 to 2 meter zone,
102
72

100 120 140 160
TIME, days
Figure 28.
Larval perch concentration in 2 to 4 meter zone,
Ohio Area C (1976).
Data Source: Table 12D.
c )
E
a)
E
C
z
0
H
a:
F
z
LU
0
z
0
0
10
102
101
100
101
102
180 200 220
73

10
102
101
100
10i
C .,
E
0
0
w
E
C
z
0
F
c x
I
z
w
0
z
0
0
Figure 29.
100
Larval perch concentration in 0 to 2 meter zone,
Ohio Area D (1976).
Data Source: Table 12D.
102
TIME, days
74

10
102
101
100
101
E
a)
o
E
C
z
0
F
cr
I
w
0
z
0
0
Figure 30.
100 120 140 160 180
Larval perch concentration in
Ohio Area D (1976).
Data Source: Table 12D.
2 to 4 meter zone,
102
200 220
75

Factors Affecting Larval Abundance
It is not within the scope of this analysis to elucidate the relative
influences of biotic and environmental factors which determine larval
production and subsequent strength of the year class. For present purposes,
it is sufficient to suiwnarize all such influences in terms of production (as
defined above), natural mortality, recruitment into the youngofyear stage,
entrainment by water intakes, and migration due to transport by the water
column. Larval production occurs from hatching of eggs spawned directly in
basin waters or in tributaries, estuaries, and shallow embayments which feed
into basin waters. Perch larvae are transported initially from spawning beds
into deeper waters by water motions and later by their own locomotion as
well. Lateral movement is passive for the first days of life, although lar
vae exhibit very early a pattern of diurnal vertical migration which is un
doubtedly not entirely passive (4). After a two to four week period of rela
tively intense production, yellow perch spawning activity rapidly drops, but
it can occur even in midsuniner. Since MichiganOhio waters of the western
basin form an open system, water and biota are exchanged with the Canadian
portion of the western basin and the central basin of Lake Erie. Water,
biotic, and abiotic materials are fed into MichiganOhio waters from numerous
streams and two large rivers. The Detroit River supplies ninetyfive percent
of the total stream flow and transports yellow perch larvae into the western
basin. Withdrawals for municipal and industrial uses cause losses of both
water and its suspended constituents, including fish larvae (11). No
separate estimates were made of numbers of larvae entering the basin from
streams or rivers. Such estimates are not strictly necessary because mea
surements of larval concentrations in basin waters at several points will
include larvae from streams and rivers, provided they reach the sampling
zones prior to recruitment into the juvenile stage.
76

SECTION 4
METHODS
Approaches to Modeling Larval Production and Abundance
Ichthyoplankton abundance, can be quantified by simulating the spawning
population or by using time variable mathematical functions fitted to abun
dance measurements. Functional forms involving polynomials, rational func
tions, or exponentials may be assumed in which one or more parameters in the
function are estimated from the data. One such model is specified by an
equation of the form:
t
A(t) = I P(tx).s(t,x) dx
0
where:
ACt) = larval abundance at time t (t > o),
P(y) = instantaneous larval production rate at time
instant y (y > o)
s(t,x) = fraction of larvae produced in time interval
tx, tx + dx) that survive a time interval
of length x.
A variation of the above is:
t
A(t) = V.C.fk.e (tx).(1..eIBx) dx
where:
ACt) = larval abundance at time t
V = volume of reference basin (number of 100 M 3 units)
C = Mean total number of larvae per 100 M 3 deposited in
reference volume during period of production
cx = mortality related parameter
k = normalizing constant.
= production related parameter
77

Difficulties with this approach are: a) the parameters may not be inter
pretable in terms of biological or environmental processes, b) conservation
of larval numbers is not necessarily guaranteed. The approach followed be
low is based upon a materials balance for the net daily rate of change of
larvae in a reference volume. Each source or sink f or addition or removal
of larvae is represented by an individual term; after both sides of the
equation are divided by the size of the reference volume, a differential
equation expressing the net rate of change in concentration is obtained.
The equation contains two parameters, representing production and natural
mortality of larvae. Concentrations in Michigan and Ohio waters are
analyzed separately; therefore, two distinct reference volumes are used.
A Material Balance Model of Larval Abundance
A material balance formulation for the net daily rate of change in lar
val abundance for a specified reference volume is:
N(t) h(t) v(t) r(t) m(t) L(t) E(t) (3)
where:
N(t) net daily instantaneous rate of change in larval abundance
in specified reference volume on day t. (0 < t < 365).
N(t) = number of larvae in reference volume on day t. (0 < t < 365).
E(t) = daily rate of loss of larvae from reference volume due to
entrainment by condensor cooling waters of Edison power plant
at Monroe, Michigan.
L(t) = daily rate of loss of larvae in reference volume due to
withdrawal of water by other industrial and municipal water
intakes.
h(t) daily rate of addition of larvae to reference volume (daily
production rate).
r(t) daily rate of recruitment of larvae in reference volume into
the first juvenile stage of development (assumed to occur after
25th day of life following hatching).
rn(t) = daily rate of loss of larvae in reference volume due to
natural mortality.
v(t) = daily net emigration of larvae across boundary of reference
volume due to water transport or larval locomotion.
Losses Due to Natural Mortality
Environmental conditions, natural predation and biotic factors which
cause mortality among yellow perch larvae within the reference volumes
78

(Michigan waters and Ohio waters of western basin) are represented by a
natural mortality parameter p:
p = mean daily fractional mortality rate for yellow perch larvae
within the specified reference volume.
Natural mortality is assumed to be a force operative on all larvae alike
where the chance of a given larva surviving a short interval At of time is
p At, i.e., proportional to the length At. This assumption leads to a
first order decay of the surviving population and the exponential survival
function ePt. Equivalently, natural mortality is assumed to be propor
tional to abundance:
m(t) = pN(t) (4)
from which one deduces
N(t) = m(t) =
N(t) = N(O)eP.t.
Thus, the proportion of larvae surviving t days following hatching on aay 0
is:
N(t ) Pt
N(0) e
The mortality parameter, p, is estimated by fitting a solution to equation
(3) to separate field based estimates of mean concentration of larvae in
Michigan and Ohio waters. The assumption that p is a constant is inter
preted to mean that total conditions that produce larval mortality in a
given year remain unchanged. On the average, throughout the months May to
August, the fraction of remaining larvae that do not survive from one day to
the next fluctuates about a constant p. This is equivalent to the assump
tion that the natural mortality rate on larval production within a given
spawning season is conditionally independent, but it implies nothing about a
possible variation in p from one year to the next, which may reflect changes
in larval production or other biotic or environmental factors.
Production of Yellow Perch Larvae
Larval production occurs from the hatching of eggs spawned directly in
MichiganOhio waters of the basin and by larvae transported into the basin
from tributaries, estuaries and across the international boundary from
Canadian waters. Approximately six to twelve days following spawning,
eggs hatch and an individual yolksac or prolarvae begins the first day of
Limits on annual production are estimated in terms of numbers of female
spawners, number of eggs deposited, population size of species, and
hatching success. An upper limit is estimated to be approximately 7 to 8
billion.
79

its life. It is evident from examination of field samples (Figure 14) that
production rapidly builds up to a peak, remains elevated for a period of
time, decreases to a low level for an additional period, then completely
ceases. Any mathematical function h(t) used to describe larval production
should distribute the prolarval input over approximately the same period in
which prolarvae are observed in the reference volume. The function h(t)
should peak at approximately the same time that peak production is estimated
to occur in the reference volume, and it should exhibit rate of change
characteristics suggested by field data (Figures 13 to 16). Finally, it
should contain a parameter describing productive intensity which can be
estimated from field data. A function which meets the above criteria is:
o (O

Tj = maximum number of days that production occurs.
B = number of 100 M 3 unit volumes of water in reference volume.
( 4.976 x 106 for Michigan waters)
( 9.393 x l0 for Ohio waters when Maumee estuary is
included; 9.351 x l0 if zones A,B,C,D, and E alone are
considered).
( ) = binomial coefficient.
Total larval production for d consecutive days in period x in the reference
volume is therefore:
d.B.h.( i) qXl (1_q)m
(x = 1,2, .. , m + 1)
Total larval production is distributed over the periods 1,2, , m+1) in
the reference volume and sums to:
m+l
d .B.h .( i) qXl (l_q)mX4l
x= 1
m+l
d.B .h E xl qxl.(l_q)mx+l
x1
From probability theory:
m31
qXl (1_q)in = 1,
x1
so that total production in the reference volume during the period of abund
ance for any given year is:
Total Production = d .Bh (6)
The function h(t) has the shape of a series of stair steps which can be
upstairs, downstairs or up and down stairs, depending upon the values
of m and q. The height of each step is proportional to the value of h.
Since h(t) as defined by equation (5) contains m+1 discontinuous steps the
particular solution to equation (3) which incorporates a production func
tion defined by equation (5) must reflect these discontinuities by being
solved explicitly and separately for each of the m+l subintervals of time
during which production can occur.
The parameters q and in are determined together on a trial and error
basis (visual inspection aided by computer calculations) by selecting values
which cause h(t) to exhibit a similar production gradient and to peak at
approximately the same time that larval abundance is estimated to reach a
maximum. The values selected for q and m can indirectly affect the value
of the production parameter, h, obtained by fitting (by least squares) the
solution to equation (3), containing h and p, to the estimated concentra
81

tions in the reference volumes shown in Figures 7, 13, 15, and 16. As q
and m are estimated, values of d are determined by inspection of Figures 7,
13, 15, and 16 (one value of d for each case) so that the quantity (m+l) .d
matches the length of the period over which larval production is estimated
to have occurred.
Production in Ohio Water: 1975
From inspection of field survey data and Figure 15, production is esti
mated to have commenced between May 1 and May 10, continued at a high rate
until approximately May 21 (day 144), and then declined rapidly. Larval
perch are fully recruited (by assumption) into the youngofyear stage 25
days after their day of production. Larval abundance peaks on approxi
mately day 144, so that nearly all production must have occurred on or be
fore that date. Tables of the binomial probability function show that when
m = 5 and q 0.10, and setting d = 7, 59 percent of production occurs in
the first 7 days, and 33 percent occurs from the 7th to 14th day, or a
total of 92 percent of production by the 14th day. If production commences
on day 127, the 17th day of production occurs on day 144, the day of ap
proximate peak larval abundance, and the 35th and final day of production
occurs on day 162, 25 days prior to the day on which all larvae are assumed
to have been fully recruited into the youngofyear stage (after inspection
of field sampling records). Therefore, by selecting the binomial pro
bability function corresponding to m = 5 and q = 0.10, the following pro
duction function is obtained as a special case of equation (5):
0 0

equation (3). Equation (7) produced a much superior fit when the resulting
solution to equation (3) was matched to the data shown in Figure 15. (See
Figure 36 for optimum values of p for selected values of h). It is clear,
therefore, that numerical analysis of two or more candidate production func
tions may be necessary in order to select the function which most adequately
describes the actual but unknown time dependent introduction of larvae into
the reference volume. The end result is a more reliable estimate of total
production and the conditional relationship of natural mortality to total
larval production.
Analyses following the same lines as the preceding case led to produc
tion functions describing larval perch production for the three remaining
cases:
Production in Ohio Waters: 1976
o O

B = 4.976 x io6
d = 14
Production in Michigan Waters: 1976
0 0

(11) is only an approximation of the process of net avoidance. Since a
more accurate specification of an avoidance function cannot be verified,
further refinement of equation (11), taking into account ability of larvae
to avoid capture as a function of their size, is not attempted.
Emigration
The term v(t) accounts for emigration of larvae across the inter
national boundary and between Michigan and Ohio waters. The patterns of
circulation of the water mass in the western basin are known and studies of
larval transport using a hydrodynamic model of Lake Erie (10) suggest a net
export of larvae out of Michigan territorial waters. Numerical studies show
that larvae produced along the Michigan shoreline can be removed from Michi
gan waters in as few as two days. Larvae produced in Maumee Bay are trans
ported into both Michigan and Ohio waters, but under normal southwest wind
conditions during late spring, most are exported into Michigan waters. Lar
vae which enter the western basin from the Detroit River are transported in
to Michigan waters as well. Thus, both inandout migration of larvae oc
curs in Michigan waters. (Inmigration is accounted for in the production
term h(t).) Numerical studies suggest that by the tenth day after larvae
are hatched within one kilometer of the Michigan shoreline, up to fifty per
cent could be transported into international waters unless they are killed
or their own lateral swimming motion counteracts water circulation. It is
estimated that for Michigan waters net out migration of perch larvae occurs
but may not be more than 5 to 10 percent of total production. Large numbers
of larvae are lost through natural mortality before they reach the 8 to 10
meter depth zone near international waters after having been hatched along
the Michigan shoreline. A total net loss due to emigration reduces abun
dance on any given day and consequently affects estimates of the parameter
h. Larval concentrations sampled in Ohio waters (5), and in zone F
(Canadian waters) combined with numerical simulation studies of water cir
culation in the western basin (10) indicate a net loss of larvae from Ohio
waters due to advective transport. Soon after hatching, perch larvae
migrate vertically in the water column (4), and as a result they become
vulnerable to transport by nearsurface currents which carry them into the
midwaters of the basin. As they settle to the bottom, however, their
direction of transport is reversed and they move further into MichiganOhio
waters. Numerical studies indicate considerable mixing of larvae from
separate spawning areas. It is difficult to establish with confidence a
percentage of larvae that are transported out of Ohio waters due to move
ment by the water column, but simulation studies (10) suggest that it is
less than five percent.
Lateral migration of larvae by selflocomotion occurs but the extent to
which it influences migration from or to OhioMichigan waters is unknown.
In the numerical analyses conducted in this study, emigration is
assumed to be zero:
v(t) = 0 (0 < t < 365) (12)
85

The effect is that any net loss in abundance due to emigration is con
founded with production and natural mortality. That is, if emigration
causes a reduction in abundance but is assumed to be zero (in the speci
fication of the term v(t)) the estimated value of the production parameter
h can be biased low. If an upper limit is placed upon emigration by as
sulning that:
v(t) 0 leads to an underesti
mate of total production but may have no effect at all on the estimate of
mean daily natural mortality fraction. The underestimation of emigration
has exactly the same effect as the underestimation of mortality from water
intake entrainment. It is believed that larval emigration losses are at
most 5 to 10 percent of total production, so that if the production para
meter h can be estimated assuming v(t) 0, then emigration can be approxi
mately accounted for by adding 10 percent to the value of h.
Larval Losses Due to Entrainment in the Monroe Power Plant Cooling Water
Intake
Ichthyoplankton concentrations have been sampled at numerous locations
in the ininediate vicinity of the cooling water intake of the Detroit Edison
power plant at Monroe (4); (also see Figure 8). The number of yellow perch
larvae killed by entrainment is estimated by multiplying daily consumption
of water by mean concentration of live larvae in the cooling water column,
multiplying that product by the fraction of live larvae killed in the en
trainment cycle, and sunining the result over all days in which larvae are
known to be present in the water column:
number larvae killed (daily cooling water usage) x
in given year due to days in period (concentration of live larvae) x
cooling water of larval (fraction of live larvae
entrainment abundance killed) (13)
Various estimates of total numbers killed in a given year can be obtained,
depending upon how the terms on the right hand side of equation (13) are
estimated. Appendix E illustrates four methods of estimating fraction of
86

live larvae killed due to the entrainment process. Daily cool{ng water
usage is probably the most accurately known as records from which daily
usage rates of cooling water (Figure 31) can be obtained are maintained at
power plants.
Measurement of the concentration of larvae in the cooling water column
is most subject to error and depends upon: a) location of the sampling
station; b) frequency of sampling; c) time of day of sample; and, d) sam
pling gear. Figures 32 and 34 show concentrations sampled in 1974, 1975,
and 1976 at the stations shown in Figure 8. Mean concentrations for the 0
to 6 depth zone in the Raisin River Mauinee Bay area for 1975 and 1976
are also plotted for comparison purposes. The lines shown in Figure 33
represent upper and lower values of larval concentrations. These values
are used to estimate the number of larvae entrained during the period of
abundance in 1975. It might be argued that Station 2 located in the upper
discharge area represents the most uniformly mixed section of the water
column and therefore should provide the most unbiased measurements on con
centrations of larvae in the cooling water. However, substantial statisti
cal fluctuations in larval concentrations occur at Station 2 as well as at
all other stations (Table 16 and Figure 34); therefore, to ignore observa
tions obtained at other stations is to make less than optimum use of the
information contained in the full set of measurements. Based upon the
upper and lower limits of concentration shown in Figure 33 and upon the
published record of daily cooling water usage (Figure 31), lower and upper
estimates of numbers entrained in 1975 were 2,726,000 and 14,262,000, re
spectively. Based upon an estimate that 20 percent of yellow perch larvae
entering the cooling cycle are either dead or dying using data published by
Cole (4, Table 9), the number of live larvae entrained is estimated to be
between 2,180,800 and 11,409,600. Following methods 3 and 4 outlined in
Appendix E and using larval mortality data published by Cole (op. cit.),
estimates of the percentage of larvae killed due to the entrainment process
are:
loop 100 (1 . ) 65 (Method 3) (1975 data)
and
loop ioo (1 . ) = 72 (Method 4) (1975 data)
Therefore, using an estimate of 70 percent larval mortality due to entrain
ment, the lower and upper estimates of live larvae entrained and killed are
1,526,560 and 7,986,720, respectively, inspection of perch larval concen
trations in cooling water, which Detroit Edison published in 1975 (7) showed
peak densities on day 156, approximately 25 days after the peak plotted in
Figure 33, suggesting that larval perch concentrations in the cooling water
column may have been substantially higher in the period 130 to 160 days than
the values indicated by the solid lines in Figure 33. The mean daily rate
of loss estimated to have occurred in 1975 is:
87

DATA 3URCE
1975 (Ref.1O)
1976 (Ref. 9)
70,000
x X XXX
60,000
.
> .. C
(0
50,000
E
40,000
X XXX
30,000 x
C X C X C X
20,000
10,000
I I I
120 140 160 180
TIME, days
Figure 31. Daily cooling water pumping rate at Edison Plant
Monroe, Michigan (May cO July, 197576).
Data Source: 1975 Ref.(1O); 1976 Ref.(9).
88

10
DETROIT EDISON PUMP
SAMPLES 1976
+ MSU DISCHARGE CANAL,
1976
A MSU, 7974
102 6 A 0 MSU, 1975
C )
E 2 2 o MDNRO6FT DEPTH ZONE
0 2 MEAN CONC., 1975
o 10 MDNR 06 FT DEPTH ZONE
2A MEAN CONC., 1976
0 )
1O hA 6
A (0) INDICATES ZERO
+ 0 o CONCENTRA TION
0
+ 02
SEE FIG. 8 FOR
A 2 LOCATION OF
100  12 SAMPLING STATIONS
0
I +
2 + 12 0 BYNUMBER
w 0
o 0
2 2A,.. A
o  L J
o 6,70,1110
101
0 0
2,6,10,11,12
(0) 6,10,1
(0)11,12 (0)11
1 0_2  A I
100 120 140 160 180 200 220 240
TiME, days
Figure 32. Larval perch concentration in vicinity of Monroe
Plant cooling water intake (see Figure 8
for locations of sampling stations).
89

102
E
0
C
 101
E
C
z
0
I
lAo
I
z
w
0
z
0
0
101
102
100 120 140 160 180 200 220
TIME, days
Figure 33. Larval perch concentrations estimated in Monroe Plant
cooling water (1975).
Data Source: Ref.(4).
90

o PLANT INTAKE PUMP SAMPLES
(Data source, Ref. 9)
+ UPPER DISCHARGE SAMPLES
(Data source, Ref. 4.)
+
ESTIMATE
____ _____ 0
0
I +
I + 0
/ 00
0
0: TIMA
100 120 140 160 180 200 220
TIME, days
Figure 34. Larval perch concentrations estimated in Monroe Plant
cooling water (1976).
Data Source: Ref.(4).
II
E
C
C
a)
c
E
C
z
0
F
cc
F
z
uJ
0
z
0
0
102
101
100
101
102
91

0 (0 < t < 125)
134,000 (125 < t < 132)
265,764 (132 < t < 141)
E(t) = 126,500 (141 < t < 148) (14)
66,361 (148 < t < 156)
21,209 (156 < t < 170)
0 (170 < t < 365)
Analysis of concentrations of larval yellow perch collected at the same sta
tions over the same period in 1974 (Table 15) indicates that a larger
number of larval perch may have been entrained in 1974. Using their own
pump sampled data (9), Detroit Edison personnel estimated entrainment of
larval yellow perch in 1976 at 650,000, a drop of nearly one order of
magnitude from 1975. This estimate was checked in two different ways.
First, the daily estimates of numbers of larvae entrained (calculated by
Detroit Edison) were divided by daily volume of cooling water (Figure 32)
to obtain estimates of mean concentrations of larvae in the cooling water
column. These estimates were then compared to measurements that MSU ob
tained of concentrations of larval perch in the upper discharge (Figure
34). A statistical test revealed no significant difference in the mean
values of the two sets of concentrations. A second method of checking the
plausibility of the estimate of 650,000 perch larvae entrained in 1976
consists of comparing this figure to Detroit Edisons 1975 estimate, as a
percentage of total production in Michigan waters. In 1975, an estimated
total of 2.9x10 8 to 5.2xl0 8 perch larvae were produced in Michigan waters.
Detroit Edison estimated that 5.0 x 106 perch larvae or 1.0% to 1.7% of
the estimated production in Michigan waters were entrained in 1975. In
1976, production declined to an estimated 8.4xl0 7 to l.4x10 7 , so that the
percentage of production estimated to have been entrained is 0.2% to 0.4%,
about 22 percent of the 1975 percentage. This comparison suggests that
Detroit Edisons estimate of number of larvae entrained in 1976 may be low.
If percentage of larvae produced and entrained in 1976 were the same as in
1975, the estimated number entrained in 1976 would increase to 8.4x10 5 to
2.4x10 6 . A combination of data from Figures 31 and 34 and the use of equa
tion 13, yield an estimate of 195,000 to 2,827,000 killed due to the en
trainment cycle.
Entrainment by Other Industrial and Municipal Water Intakes
A total of 18 municipal and industrial water intakes have been located
in MichiganOhio waters of the western basin of Lake Erie (11). Estimates
of numbers of yellcM perch larvae entrained by all 18 intakes in 1975 to
1976 are reproduced in the present report as Tables 18 to 21 (11). A corn
bination of the estimated mean daily pumping rates given in (11) with esti
mates of larval concentrations in the respective 0 to 6 depth zones re
vealed the following estimated total numbers of larval yellow perch losses
92

TABLE 13. WATER VOLUMES IN OHIO WATERS OF WESTERN BASIN.
(From Ref. 5) (cubic meters)
N Depth
N Zone
Sect oi N
A
B
C
D
1
5.73x io
0
2. 17x io
7. 15x10 7
7.02x 106
2
9.3x1O 7
0
2.44x 108
2.41x10 7
2. 94x10 7
2.26x
4. 131x1O
E
3
1.71x10 8
0
6.3x10 8
6. lOx 10
1. 17x10 8
1. 0 lx 108
1.08x 10
4
0
7. 77x10 8
7.63x 108
2 .48x10 8
2. 60x10 8
3. .46x 108
2. 394x10 9
5
0
9. 72x10 8
4.73x 108
8 .29x10 8
3. 57x10
6.53x 108
3 .284x10 9
6
0
1. 06x
0
6 .38x10 8
1.5 lx 10
1.71x10 9
4. 918x10 9
F
4.28x10 6
TOTAL
9.745x10 7
Total
3.21x10 8
3.21x10 9
2. 13x10 9
l.S lxlO 9
2.28x10 9
2. 84x io
1.22x10°

TABLE 14. CONCENTRATIONS OF LARVAL YELLOW PERCH AT
STATION 2 IN CANADIAN WATERS.
Data Source: Ref. (2,3)
Da
te
Concentration (#/100 M 3 )
Bottom Surface
1976
51776
11.82
52576
8.56
6.59
6876
0.78
7976
0.74
72176
1.86
1975
61875
0.64
0
94

TkBLE 15. YELLOW PERCH LARVAL CONCENTRATIONS SAMPLED
IN INNEDIATE VICINITY OF POWER PLANT.
Data Source: Table B26, Vol. II, Ref. (4).
Station Number
Date 6 10 1]. 12 2
51074 90.8 37.6 0 0 57.6
52974 5.0 15.3 10.7 6.2 0.2
61174 8.0 0.2 0 1.1 20.8
62174 0 0 0 0 1.3
51275 48.1 28.0 10.5 65.5 33.4
6275 0.2 0.2 0.2 0.6 2.2
62575 0 0 0 0 0
TABLE 16. COEFFICIENTS OF
WITH MEAN CON
Data Source: Table B
S LlNG VARIATION
CENTRAT IONS.
31, Vol. II, Ref.
ASSOCIATED
(4).
Date
6
10
Station Number
11
12
2
52974
43.8
39.4
45.5
64.1
78.1
61174
47.0
244.9
0
164.7
34.7
51275
110.1
63.7
43.9
39.0
49.3
6275
306.2
244.9
113.9
173.3
95.6
95

TABLE 17. ESTIMATED NUMBER OF YELLOW PERCH LARVAE
ENTRAINED BY MONROE POWER PLANT IN 1976.
Data Source: Ref. (9)
Estimated
Date Entrained
Numb
(24
er
hr)
Flow
100 M 3 /day
Mean Concentration
Larv.
#1100 M 3
108114 45,488 36,469 0.21
115120 36,645 33,445 0.22
121127 161,831 28,892 0.93
128134 10,364 33,445 0.05
135 0.22
136 9,768 24,434 0.40
137 10,219 30,552 0.33
139 3,987 24,434 0.16
143 8,372 24,434 0.34
144 1,395 24,434 0.06
146 2,991 30,552 0.10
148 0 24,434 0
152 7,471 18,316 0.41
153 13,356 24,434 0.55
154 12,545 24,434 0.51
156 15,947 24,434 0.65
158 5,183 24,434 0.21
159 997 24,434 0.04
161 2,391 18,316 0.13
162 2,813 18,316 0.15
163 6,578 24,434 0.27
164 3,940 24,434 0.16
165 5,982 30,552 0.20
96

TABLE 17 (coNTINuED)
Estimated
Number
Flow
Mean Concentration
Larv.
Date Entrained
(24
hr)
100 M 3 /day
#/100
M 3
166 60,668 36,632 1.66
168 30,699 48,868 0.63
172 10,759 54,948 0.20
173 1,913 54,948 0.03
175 20,672 67,184 0.31
179 41,825 67,184 0.62
180 14,408 67,184 0.21
182 13,285 61,066 0.22
187 3,898 67,184 0.06
188 12,278 67,184 0.18
189 5,847 67,184 0.09
183 4,722 67,184 0.07
194 3,508 67,184 0.05
196 15,476 67,184 0.23
197 5,977 73,264 0.08
198 3,586 73,264 0.05
199 7,876 73,264 0.11
200 1,793 73,264 0.02
201 4,782 73,264 0.06
203 8,368 73,264 0.11
207 1,195 73,264 0.02
208 1,275 73,264 0.02
210 1,275 73,264 0.02
213 1,195 73,264 0.02
214 0 0
216 1,195 73,264 0.02
220 0 0
221 0 0
97

TABLE 17 (cONTINuED)
Date
Estimated
Entrained
Numb
(24
er
hr)
Flow
100 M 3 /day
Mean Concentration
Larv.
#/100 M 3
223
2,953
54,948
0.05
224
0
0
225
0
0
226
0
0
227
0
0
228
0
0
649,691
Estimates based upon Detroit Edison data on estimated number entrained
per day and flow rates.
98

TABLE 18. WATER INTAKE SPECIFICATIONS.
Data Source: Ref. (11)
Pumpin
Intake Lake Sector Depth Zone (100 M /
Rate
day)
Michigan
Fermi (P) M 12 9274
Monroe (P) M 12 78299
Whiting (P) M 12 11671
Monroe City M 34 303
SUBTOTAL 99547
Ohio
Acme (P) R R 14716
Bayshore (P) R R 28342
DavisBesse (P) C 2 818
Camp Perry C 2 9.5
East Harbor
State Park D 3 3
Erie Industrial
Park C 2 8
Kelleys Island E 2 3
Lakeside
Association E 2 8
Marblehead E 2 4.5
Oregon A 3 160
Port Clinton C 2 57
PutInBay D 2 5
Sandusky E 4 404
Toledo A 3 303
SUBTOTAL 44841
TOTAL 144388
(P) Power Plant
99

Intake
Michigan
TABLE 19. LARVAE ENTRAINMENT ESTIMATES, 1975.
Data Source: Ref. (11)
Entrainment Estimate
Point Sample Depth Zone
Fermi (P)
Monroe (P)
Whiting (P)
Monroe City
Ohio
61,000
531,000
268,000
2,100
349,000
2,940,000
439,000
69,200
Acme (p)*
Bayshore (F)
DavisBesse (P)**
Camp Perry
East Harbor State Park
Erie Industrial Park
Kelleys Island
Lakeside Association
Marblehead
Oregon
Port Clinton
PutInBay
Sandu sky
To 1 edo
1,686,300
9,000
200
7,200
900
700
400
2,800
1,200
1,500
2,600
50,900
2,340,000
4,510,000
14,800
900
11,900
400
1,000
boo
6,900
88,700
300
61,500
124,000
SUBTOTAL
1,763,700
7,161,000
TO TAL
2,626,400
10,958,200
(P) Power Plant
* No fish caught at sampling station in 1975.
DavisBesse not operating in 1975.
SUBTOTAL 862,700 3,797,200
100

TABLE 20. LARVAE ENTRAINMENT ESTIMATES, 1976.
Data Source: Ref. (11)
Entrainment
Estimate
Intake Point Sample
Depth Zone
Michigan
Fermi (P)
Monroe (P)
Whiting (P)
Monroe City
265,300
1,625,700
1,520,600
6,300
728,000
6,150,000
917,000
544,600
Ohio
SUB TOTAL
Acme (p)*
Bayshore (P)
DavisBesse (P)
Camp Perry
East Harbor State Park
Erie Industrial Park
Kelleys Island
Lakeside Association
Marblehead
Oregon
Port Clinton
PutInBay
Sandu sky
To 1 edo
3,417 ,900
1,181,400
17,200
12,300
700
9,600
400
2,300
2,100
6,600
47,500
300
94,200
118.400
8,339,600
24,200,000
46,600,000
344,000
3,900
400
3, 100
300
900
500
6,200
23,200
29,200
270, 100
112,200
SUB TOTAL
TOTAL
1,493,000
4,910,900
71,584,000
79,923,600
(P) Power Plant
* No fish caught at sampling station in 1976.
101

TABLE 21. RANGES OF ENTRAINMENT LOSSES
Intake
1975
1976
Michigan
Fermi (F)
61,000349,000
265,000728,000
Monroe (P)
Whiting (F)
531,0002,940,000
268,600439,000
1,636,0006,150,000
917,0001,521,000
Monroe City
2, 10069,200
6,300544,600
Oh io
Acme (P)
02,340,000
024,200,000
Bayshore (P)
1,690,0004,510,000
1,180,00046,600,000
DavisBesse (p)*
17,200334,000
Camp Perry
9,00014,800
3,90012,300
East Harbor State Park
200900
400700
Erie Industrial Park
7,20011,900
3, 1009,600
Kelleys Island
3001,000
300400
Lakeside Association
7001,000
9002,300
Marblehead
400600
5002, 100
Oregon
2,8006,900
6,2006,600
Port Clinton
1,20088,700
4,70023,200
PutInBay
3001,500
3002,900
Sandu sky
2,60061,000
94,000270,000
Toledo
50,800124,000
112,000118,000
(P) Power Plant
* DavisBesse not in operation during 1975.
Range of larvae entrainment by Michigan and Ohio water intakes. Data based
upon both point sample and depth zone entrainment.
102

attributable to all power plant operations in MichiganOhio waters of the
western basin:
Intake 1975 1976
Michigan
Fermi 48,0001,100,000 26 1,0003,300,000
Monroe 1,432,0009,833,000 195,0002,827,000
Whiting 827,0001,525,000 74,0001,25 1,000
Ohio
Acme 497,0001,700,000 520,0001,363,000
Bayshore 879,0002,500,000 733,0001,850,000
DavisBesse 17,000334,000
TOTAL 3,683,00016,658,000 1,800,00010,925,000
Since Tables 18 to 21 and the above estimates of total losses attributable
to all power plant operations became available after the numerical analysis
of production was completed, the assumption made for purposes of the analy
ses is:
L(t) = 0 (15)
Overall estimates of production can be adjusted by adding estimated losses
due to entrainment in water intakes.
Analytical Solution to the Differential Equation of Balance for Larval
Concentration
The equation of balance for larval perch assumes the form
N(t) + p.N(t) = h(t) h(t25).e 25 P E(t) (16)
with the substitution of equations (4), (5), (11), (12) (14) and (15) into
equation (3). The expressions for h(t) and E(t) depend upon the reference
volume and the year being considered. Solutions to Equation (16) for five
cases Ohio 1975 and 1976, Michigan 1975 with and without entrainment
mortality, and Michigan 1976 are given in Appendix F. Equations (F.7),
(F.9), (F.ll), (F.13), and (F.15) were programmed permitting the parameters
h and p to range over assigned values as shown in Figures 35, 37, 40, and
42. Specific solutions as illustrated in Figures 36, 38, 41, and 43 are
obtained for each specific (h, p) combination.
Method of Estimating Parameters h and p
The parameters h (number of perch larvae added to every 100 M 3 of
water in the reference volume in a given year), and p (mean daily natural
mortality rate of perch larvae in the reference volume in a given year) are
estimated by the method of least squares. For a given combination of h and
p, the predicted value of larval concentration (number of larvae per 100
103

0.12 4.21
3.64 4.09
S S
>
0.10 3.14 3.52
2.71 3.00 /4.12
I . . . S
2.37 2.38 2.57 ,3.561 .35
00.08 . . . .
S S S S S S
2.29 2.14 2.23 ,3.06 3.84
2.38 2.05 1.99 / 2.65 3.38
S S S S
0.06  / CUR VE 01
2.67 2.13 1.89 /2.35 3.17
< S . . . INFIG.36
/
Z 2.41 1.95 ,2.14 2.78
J
2.22 ,2.03
> 0.04
S S
C
z 0.02 CURVEO2/NFIG.36
w
0 I I I I I I I I I I
1.0 1.4 1.8 2.2 2.6 3.0
PRODUCTION PARAMETER (h)
Figure 35. Model prediction error for combinations of mortality and
production parameters (Ohio, 1975).
104

102
100
CURVE 01:
p = 0.09, h = 3.0
PRODUCTION = 1.97 x 109
Y 0 V RECRUITS =
2.08 x 108
.CURVEQ2
I
I
0 MEASURED
PREDICTED
CUR VE 02:
p = 0.04, h = 1.5
10
E
C
a)
E
C
z
0
H
c
H
z
uJ
0
z
o10
TIME, days
Figure 36. Predicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Ohio, 1975).
Data Source: Tables 12A and 12B.
102
100 120
PRODUCTION 9.86 x 108
 YOY RECRUITS
3.63 x 108
I
140 160 180
A SSUMP TI ONS:
v(t) = 0
E(t) = 0
L (t) = 0
0
200 220
105

0.20
0.74 ,0.69
0.77. . .
078 4
. . . .
0.18. .
0.73 / /
0.78 . 0.73
0. 84 /
H 0.85 0.78 , 0.79 /
0.16 . CURVEM2
0.81 0.82 /AFJG.38
., . .
0.85 / / 0.87 0.99
0.14 S
W 0.89 0.87
1 ._I . S
Zc
0.12
/
C
z 0.10
w
/ CLJRVEM1/NF/G.38
0.08
I I
4.0 5.0 6.0 7.0 8.0 9.0 10.0
PRQDUCT ON PARAMETER (Ii)
Figure 37. Model prediction error for combinations of
mortality and production parameters
(Michigan, 1975).
106

102 
101 
100
101
102
100
0
0
MEASURED
PREDICTED
CURVE M2:
p = 0.19, h = 9.5.
0 PRODUCTION = 6.61 x 108.
/
YOY RECRUITS
5.29 x 106.
CURVE Ml:
p=0.08 ,h=4.0,
PRODUCTION =
2.79 x 108.
YOY RECRUITS
3.77 x iO
)
1
ASSUMPTIONS:
L(t)=0
v(t)0
E(t)=0
I
I
120 140 160 180 200
TIME, days
220
Figure 38. Predicted vs. estimated larval perch concentrations
for two production mortality parameter combinations
(Michigan, 1975).
Data Source: Table 1.
E
0
0
E
C
z
0
I
a:
I
z
w
0
z
0
0
0
107

1010
CUR VEO7 INFIG. 36.
(25DAYSURVIVAL 2.08x 708)
/ CUR yE 02 IN FIG. 36.
I .
CUR yE M2 IN FIG. 38.
SsN,, (25.DA Y SURVIVAL = 5.29 x 706)
C CUR VEM1 IN FIG. 38.
Z 8 (25DAY SURVIVAL = 3.77x 70 )
10
I
0
0
0
cr
a
J
> 1fl7 
J
106
0 10 20 30 40 50 60 70
PERCENT SURVIVAL FOR 25 DAYS
Figure 39. Plausible larval perch production survival
cotnbinations in Western Basin (1975).
108

2.51 2.84 ,3.56 4.29
521
2.23 2.34 ,3.11 3.84
, 4.78
2.17 2.10 ,2.75 3.45
. .434
: 2 . o,/ ;o7 .3.16
 1.94, . CURVE 02 IN FIG. 41.
2.12 2.77
I I I I I_ I t __ I  I  I 1
1.8 2.2 2.6 3.0 3.4
PRODUCTION PARAMETER (h)
Figure 40. Model prediction error for combinations of
mortality and production parameters (Ohio, 1976).
,
/
z .
w
H
>
F
J
F
0
J
H
z
>
J
z
uJ
0.16
0.14
0.12
0.10
0.80
0.06
0.04
0.02
0
4.90
.
/
4.38 475
,
.
4.21 4.64
.
3.70 4.08 ,
3.48 3.55 ,6 .
. S
/ CUR VEO1
3.12 3.08 ,4.07 4.81 IN FIG. 41.
S
/
1.0 1.4
109

102
0 MEASURED
PREDICTED
CURVE 01:
io /P0.O9i  2 .6
E 7 PRODUCT/ON 1.71 x iO .
YO Y RECRUITS = 1.8 x 108,
I  CURVE 02:
I
p=0.02,h=1.2
C PRODUCTION = 7.89 x 108
100 YOYRECRUITS4.78x 108
F I
I ASSUMPTiONS:
o I 
2 I
o I v(t) O
o
10  L(t)=0
I
I
S
(0) (2.2 x 10s) (0) (0)
102 O 1 ob
100 120 140 160 180 200 220
TIME, days
Figure 41. Predicted vs. estimated larval perch concentrations for
two production mortality parameter combinations
(Ohio, 1976).
Data Source: Tables 12C and 120.
1
S
S
I
110

>
H 0.24
J
H
020
C
J
<0.16
LU
<<0.12
Z 0
>
J
0.08
z
LU
U
0 .0.4 0.8 1.2 1.6 1.8 2.0 2.4
PRODUCTION PARAMETER (h)
Figure 42. Model prediction error for combinations of
mortality and production parameters
(Michigan, 1976).
0.6 10
.
0.;84 0.348/5
. .
4.52 2.55
S S
/\
1.18 1.04/ 1.81
S S
1.37/ 2.98
S
4.19 2.04
S S
CUR VEM1 IN
FIG. 43.
3.46
CURVE i142 IN
FiG. 43.
7.59
2.34
I I I
1 _ I I I I I I I I I
111

102
T ME,days
Figure 43. Predicted vs. estimated
two production mortality
(Nichigan,
Data Source:
larval perch concentrations for
par meter combinations
1976).
Table 9.
CURVE Ml:
0 MEASURED
p = 0.16, h = 2.0
PREDICTED
PRODUCT/0N 1.39 x 108
YOY RECRUITS = 2.55 x 106
C .,
E
Q
C
E
C
z
0
I
H
z
w
0
z
0
0
CURVEM2: p=0.08,h=1.1
PRODUCTION = 7.66 x 10
YO Y RECRUITS =
1.04 x 10
101
100
101
ASSUMPTIONS:
E(t) = 0
v(t) =
L(t)=
0
0
102
100 120 140 160 180 200 220
112

cubic meters of water in the reference volume at a given time) provided by
the solution to Equation (3) is compared to a mean concentration estimated
from field data analysis (plotted in Figures 7, 13, 15, and 16). The Mean
Square Error, M.S.E.(h,p) , is by definition:
N
M.S.E. h,p) = ( N(tj ) estimated mean conc. on day t 1 ) (17)
N 1=1
Following the least squares criterion, the combinations of h and p which
minimize the M.S.E. (for a given reference volume and year) are shown in
Figures 35, 37, 40, and 42. If either h or is selected in advance, the
value of the other that minimizes M.S.E. can be obtained from the appro
priate figure. If h and p are two values selected by minimizing Mean Square
Error or MSE in a given case, then from Equation (6), total larval produc
tion and 25day survival for the given reference volume and year is esti
mated as:
Total Production = dBh (18)
and:
number of yoy recruits =
= 25 day survival =
= d.B.h.e 25 P (19)
For a given reference volume and year, estimation of h and p proceeds by
defining a rectangular network of (h,p) pairs. The prediction error
variance is numerically evaluated for selected (h,p) combinations and re
corded as shown in Figures 35, 37, 40, and 42. The finer the mesh of the
grid (the closer together the (h,p) combinations) the more precisely the
parameter combinations that minimize prediction error variance can be
estimated. For example, in Figures 35 and 40 the haxis is graduated in
increments of 0.2; this graduation corresponds to an increase in total lar
val production in the reference volume of (0.2) (7) (9.393x10 7 ) = 1.31x 10 8
larvae. Therefore, any term on the right hand side of equation (16) that is
less than 10 percent of l.31x10 8 , or about 13 million larvae, is not
likely to produce any difference in the pair (h,p) that minimizes M.S.E.
The broken lines shown in Figures 35, 37, and 40 show the values of p that
approximately minimize M.S.E. for given values of the production parameter
h. It was initially anticipated that a unique global optimum pair (h,p)
would be identified for each case analyzed. Such optima are shown for Ohio
waters: h = 1.5, p 0.04 for Ohio 1975, and h = 1.2, p = 0.02 for Ohio
1976. However, a value of p = 0.04 corresponds to a 25day survival (yoy
recruitment) of 36.8 percent, a value considered to be too high, that is,
biologically unrealistic. In Michigan waters: the 1975 combination of
(h,p) that minimized M.S.E. is located on the boundary of the grid (h =
9.5, p = .19); for Michigan 1976 the optimum occurs at an interior point of
the grid (h = 2.0, p = .16). A value of p = .19 corresponds to a 25day
survival of 0.9 percent and p = .16 corresponds to 1.8 percent survival for
113

25 days. These survival percentages may well be too low from a biological
standpoint; they also reflect the lumping of emigration and water intake
losses, L(t), into natural mortality. Overall 25day survival is judged to
be in the 2 to 10 percent range. It is clear from the analysis that produc
tion in Ohio waters is much greater than in Michigan waters. It also ap
pears that changes in production on the order of 15 to 20 percent from one
year to the next are detectable. It is reported in (12) that October 1976
trawis in the western basin declined sevenfold in youngofyear perch abun
dance from October 1975. Comparison of Figures 35 and 40 suggest that lar
val production may have declined in Ohio waters from 1975 to 1976 (peak mean
abundance was lower in 1976), but based upon this study, it is improbable
that a sevenfold drop in 25 day larval survival occurred from 1975 to 1976.
If yoy recruitment did, in fact, decrease sevenfold, it may be hypothe
sized ye1lc perch year class strength is heavily influenced during the late
post larval phase of development. The broken lines in Figures 35, 37, and
40 which mark the M.S.E. estimates of p for fixed values of h should not be
interpreted as defining relationships between production and 25day survi
val because: a) each line is based upon data collected in a single year
only, and b) the slopes are so steep that net 25day survival actually de
creases as production increases.
Modeling error can affect the locations of (h,p) pairs which minimize
prediction error variance. Emigration, v(t), could be on the order of 5 to
10 percent of production and that entrainment mortality, L(t), from water
intakes is estimated to be in the tens of millions. Both v(t) and L(t) were
assumed to be zero for the computer runs described in this report. If L(t)
and v(t) are progranined as positive functions, the resulting solution to
equation (16) of larval balance will show a slighty improvement in the fit
of the model for Ohio 1975 (Figure 36). It is not clear by simple inspec
tion of the graphs of the other solutions (Figures 38, 41, and 43) whether
increasing L(t) and v(t) will cause the predicted concentrations to fit the
estimated concentrations more closely. In any case, a first order correc
tion to estimates of production can be made by assuming L(t) = v(t) = 0, and
by adding the estimates of total water intake mortality and total emigration
to the estimates of production for each case. Two cases were analyzed for
Michigan 1975 waters: E(t) = 0 (Figure 38), and E(t) specified by equation
(14). Whereas small differences in the prediction error variance were ob
served between the two cases, the numerical values of E(t) were so small
relative to the interval length on the haxis (Figure 37) that no detect
able differences for the locations of M.S.E. values of p were observed. A
first order correction to production can be obtained by adding total esti
mated water intake mortality and total estimated emigration to previously
estimated values of total production. Correcting biases in estimates of
production caused by modeling errors (by assuming that L(t) = E(t) 0) is
somewhat academic inasmuch as total larval production can only be estimated
to within tens of millions for Michigan waters and hundreds of millions for
Ohio waters. However, if larval emigration out of the reference volume is
as much as ten percent of total production, the correction could be as great
as 2xl0 8 larvae.
114

Estimates of Production and Natural Mortality
Single point estimates of production and natural mortality obtained by
locating those (h,p) combinations that minimize prediction error variance
can lead to estimates that are unrealistic due to a combination of errors
outlined in Diagram A (p. 8). On the basis of the above method, however,
larval survival over a 25day period following hatching has been estimated
to be between 2 and 10 percent. The range of larval production for which a
25day survival of 2 to 10 percent is optimum in the M.S.E. sense is ob
tained from Figures 35, 37, 40, and 42 and is the following:
Michigan Waters, 1975
% Surviving 25 days: 2% 10%
Estimated value of h: 7.5 4.2
Estimated production: 5.2xl0 8 2.9x10 8
Estimated number surviving
natural mortality 25 days: l.0x10 7 2.9x10 7
% (killed due to entrainment
on 5th day of life) esti
mated to have otherwise
survived 25 days: 5.5 17.7
Michigan Waters, 1976
% Surviving 25 days: 2% 10%
Estimated value of h: 2.0 1.2
Estimated production: l.4x10 8 8.4x1O 7
Estimated number surviving
natural mortality 25 days: 2.8xlO 6 8.4x10 6
% (killed due to entrainment
on 5th day of life) esti
mated to have otherwise
survived 25 days: 5.5 17.7
Ohio Waters, 1975
% Surviving 25 days: 2% 10%
Estimated value of h: 4.5 3.0
Estimated production: 3.0x10 9 2.0x10 9
Estimated number surviving
after 25 days: 6.OxlO 7 2.OxlO 8
Ohio Waters, 1976
7. Surviving 25 days: 2% 10%
Estimated value of h: 3.8 2.6
Estimated production: 2.5xlO 9 1.7xl0 9
Estimated number surviving
after 25 days: 5.OxlO 7 1.7xl0 8
115

Estimates of production for other 25day survival percentages can be ob
tained from Figures 39 and 44. It is clear from the above that recruitment
into the youngofyear class is more sensitive to the natural mortality
rate than to the number of eggs that are hatched in a given year. When the
M.S.E. criterion is used to match mortality and production rates this point
is clearly illustrated in Figures 35, 37, 40, and 42. If larval produc
tion is high, the use of M.S.E. estimate of the mean daily natural mortality
rate results in lower numbers for recruitment into the youngofyear class
than for cases where larval production is lower. It may be argued that a
realistic relationship between larval production and youngofyear recruit
ment requires that marginal recruitment into the youngofyear class must be
a nonnegative function of larval production. It is pointed out that the
present analysis does not deal with this question but only with the estima
tion of larval production and natural mortality for the years 1975 to 1976.
The percent loss in recruitment into the youngofyear class attributable to
entrainment mortality at the Monroe power plant is a more realistic measure
of impact than percent loss of larval production because it takes into ac
count natural mortality of larvae as well as larval production.
Estimated percent loss in numer of yoy recruits =
K _ R 1 K 1
100 ° ) = 100 (1 ) (20)
where:
= number of yoy recruits in Michigan waters in the
absence of the Monroe power plant operation.
R 1 = number of yoy recruits in Michigan waters in the
presence of the Monroe power plant operation.
In 1975:
R 1 = l.0x10 7 2.9xl0 7
= R 1 + R 2
where:
R 2 = number of larvae that would have survived 25 days
in the absence of entrainment.
Estimated number killed due to entrainment mortality in 1975 =
= 1. SxlO 6 8. OxlO 6
Percent (killed due to entrainment on 5th day of life) estimated
to have otherwise survived 25 days =
116

CURVE 01 IN FIG. 41.
Y0Y RECRUITS = 1.8 x io
/ CURVE M2 IN FiG. 43.
0 Y0YRECRUITS= 1.04 x 10
GANWATERS
I I I I I I
40 50 60
PERCENT SURVIVAL FOR 25 DAYS
Figure 44.
Plausible larval perch production survival
combinations in Western Basin (1976).
CURVE 02/N FIG. 41.
YQY RECRUiTS =
4.78 x 108
J
>
c
C
0
L .
E
C
z
0
I
0
0
0
C
j
>
1010
10
108
OHIO WATERS
CUR VE Ml IN FIG. 43.
YOY RECRUITS 2.55 x 106
10
0 10 20 30
70
117

= 5.5% 17.7%
R 2 = l.5x 10 6 x.055 8.Ox lO 6 x. 177 =
8.25x 10 4  l.42x 10 6
Therefore, the estimated percent loss in number of yoy recruits is:
R R 7
100 (1 = 100 R + R = 100 (1 l.OxlO ) to
o 1 2 l.OxlO + 8.25x10
7
100 (1 2.9x10 6 = 0.8% to 4.7%
2.9x10 + l.42x10
In 1976:
= 2.78x10 6 8.4xl0 6
R 2 = 0.46x 10 6 x.055 0.7x10 6 x.177 = 2.53x10 4 1.24xl0 5
Therefore, the estimated percent loss in number of yoy recruits is:
R R 6
100 (1 !) = 100 (1  R = 100 (1 2.78x10 4 ) to
R 2 2.78x10 + 2.53x10
100 (1  8.4x 10 6 ) = 0.9% to 1.5%
8.4x10 + 1.24x10
118

SECTION 5
RESULTS AND DISCUSSIONS
Analysis of Losses to Standing Crop and the Fishery
The equations of balance for a population are composed of terms that
parallel or reflect its life processes. Each term reflects assumptions about
the dynamic behavior of a component process. When all processes are coupled
through an equation of balance, temporal fluctuations in population are ob
tained which can then be studied by variation of process parameters.
In the following, an equation of balance which incorporates larval pro
duction, larval survival, youngofyear survival, natural mortality of sub
adults and adults, and fishing mortality is defined. Estimates of popula
tion parameters which permit a numerical analysis of the impact upon catch
as a result of variations in any of these factors are provided.
Define the following variables and parameters:
N(t) = adult population size (age class II and older fishes)
in year t. [ no. individuals].
N(t) = net annual instantaneous rate of change in adult popu
lation size in year t. [ no. yr. .
f = mean annual instantaneous mortality rate from commercial
and sport fishing. [ yr.].
m = mean annual instantaneous mortality rate due to causes
other than fishing, entrainment, and impingement.
[ yr. 1 ].
= mean annual rate of larvae production per individual
in population size N. [ no. larvae individuaF 1
yr. 1.
= fraction of larvae surviving environmental forces
of mortality for first 25 days to reach youngof
year stage. [ y.o.y. larvae].
119

$ = annual fraction of youngofyear that survive until
December 31 (of year in which they are produced) to be
recruited into age class I (also referred to as year
ling or subadult stage). [ subadults y.o.y. ].
e = annual fraction of age class I subpopulation that
survives nonfishing causes of mortality to be re
cruited into adult population. [ adults . subadults].
K = habitat carrying capacity of adult population
[ no. adults].
T = maximum life length of adult fishes.
= annual loss of larval fishes due to power plant entrain
ment. [ larvae yr.].
E = annual loss of youngofyear due to power plant entrain
ment. [ yo.y. yr. ].
I annual loss of youngofyear due to power plant impinge
ment. [ y.o.y. . yr.].
1 A1 = annual loss of age class I fishes due to power plant
impingement. [ subadults yr. 1 ].
annual loss of adults (age class II and older fishes)
due to power plant impingement. [ adults . yr. 1 ].
L = annual larvae production rate. [ larvae . yr. ].
1 A annual loss of fishes in age class I and older due to
power plant impingement. [ adults . yr.J.
The verbal statement of population balance can be expressed as:
net annual instantaneous rate of change in population level
equals
annual rate of recruitement of subadults into age class II
minus
annual instantaneous rate of loss of stock due to fishing
minus
annual instantaneous rate of loss of stock due to nonfishing mortality
120

minus
annual rate of loss of adults which have survived the maximum age T.
In equation form:
N aR(m+f)N (21)
or:
N aR (in + f)N (21.1)
where:
a 1 e(m+ f) (T 1)
Equation (21.1) defines a balance of the surviving population and equation
(21) defines a balance on the segment of the population lost annually due to
power plant entrainment and impingement mortality, and includes its lost
reproductive potential.
The inferences made about impacts of entrainment and impingement morta
lity will depend upon how one represents or models R, the recruitment term
in equations (21) and (21.1).
In the following, the hypothetical subpopulation of fishes absent as a
result of entrainment and impingement mortality of larvae, juveniles, sub
adults, and adults will be analyzed using equation (21) as the basic expres
sion for which the following recruitment model is considered:
Model 1:
R = E , . s ein + (entrained larvae component)
+ E . s . ein + (entrained y.o.y. component)
+ I . . s . e + (impinged y.o.y. component)
+ 1 A1 ein + (impinged subadult component)
+ 1 N + (impinged adult component)
+ y N(t) . s . e (reproductive potential component)
Thus, if:
R = recruitment of individuals into age class II group; recruit
ment is expressed by the equation:
R = [ IN + em (TA1 + S (i + Ey + c (E + y N(t))))} (22)
121

Diagram B: Conceptual Model of Hypothetical Population
A numerical analysis of the size of the unrealized subpopulation of
fishes follows by substituting equation (22) into (21), solving for N, and
calculating a steady state population size together with fishing harvest for
different feasible combinations of population parameters. Diagram B is a
flow chart of the resulting materials balance.
A second model of recruitment was also considered in which equation (21)
represents the net balance for the surviving population rather than the
hypothetical subpopulation of fishes not present due to entrainment and im
pingement mortality. The analysis of the second model is limited to a small
number of combinations of population parameters and is included to indicate
the potential compensatory effects within the perch population in Lake Erie.
Model 2:
R = s N(t) (1 N(t) ) reproduction and recruitment
prior to adjustment for en
trainment and impingement.
s e E , entrained larvae component.
s (E + I ) entrained and impinged young
ofyear component.
Thus, recruitment is expressed by the equation:
R = sEC (i N(t) (1 N(t) ) E ,) (E + i fl (23)
Model 2 incorporates a parameter, K, representing the habitat carrying
capacity for the population. The carrying capacity may change slowly over
time as water quality and interspecific factors of competition change. The
carrying capacity represents the upper limit of the attainable size of the
population. If the population is in a state of dynamic equilibrium, it will
always be at a level below the carrying capacity. As the carrying capacity
changes, the equilibrium level of the population will adjust itself to a new
122

value, again below the new value of K. The amount by which the equilibrium
value of the population lies below the carrying capacity depends upon the
other population parameters, as well as losses to the population represented
by the terms E , I , E , and 1 A The dynamics of recruitment in equation
(23) are such that the population increase follows an Sshaped curve,
approaching its equilibrium value. The rate of population increase slows
down as population density increases, due to a reduced rate of recruitment
of larvae into the juvenile stage. Equation (23) is, no doubt, the simplest
way to introduce compensation for population density into the dynamics of
recruitment. It should be noted that in equation (23) the product E
(number of larvae per individual surviving to enter youngofyear stage) i .
multiplied by the compensation term (1 ), rather than or y aloneJ
Thus, the expression e (1 is used to approximate the actual, but
unknown function E(N) y(N) describing larval survival at 25 days following
hatching of eggs. Furthermore, there is no attempt in equation (23) to
model changes in entrainment and impingement mortality brought about by
fluctuations in larval production from one year to the next. The terms
E , and I are constant throughout but can be varied from one calculation of
equilibrium population to the next.
The effect of entrainment or impingement mortality is analyzed by model
ing the whole population rather than the subpopulation of entrained and im
pinged fishes as in the earlier case. Although the quadratic term in equa
tion (23) creates the Sshaped curve of population change as it approaches
equilibrium, a more important characteristic of the equation for present
purposes is the manner in which the equilibrium value of the population is
limited by the population parameters and by entrainment and impingement
losses.
Solutions to Equations
Substituting equation (22) into (21) and solving for N, one obtains:
t
N(t) = N(O)e t + a I R(x)e (t ) dx (24)
where:
fa s e e , 2
R(x) = IN(X) + e [ I (x) + s(I (x) + E (x) + . E (x))}
Al y y
and:
N(O) initial population size.
1 Other quantitative expressions for representing compensatory effects of
high larval mortality are currently in use (20). Research and modeling of
compensatory processes is active.
2 Dimensional analysis verifies that acsye m and (m + f) are comparable
quantities.
123

IN(x), IAl(x), I (x), Ej(x) and E (x) may be constants or functions of
the time parameter x. As time t increases, the contribution of the initial
population level N(O) diminishes exponentially. The integral term is an
exponentially weighted moving average of the contributions of successive
recruitments R(x) in year x in which more distant additions R(x) contribute
an exponentially decreasing proportion to the total population. If one is
interested in a steady state condition, as t approaches infinity, N(t) ap
proaches, under appropriate conditions on R(x),
limit t (tx)
N_tχ af R(x)e dx
0
This is the steady state value of the size of the hypothetical subpopula
tion lost due to entrainment and impingement. In the following, all im
pingement and entrainment functions are assumed to be constants and there
fore independent of time. Therefore, R(x) = R = constant.
For this case
N(t) = [ N(O) }e t + R (25)
where R is defined above, and:
= I e(
where:
T I. = 6.
Equation (25) shows no steady state unless m + f > c Es y e m , i.e.,
> 0, which must be true in the environment on the average or the popula
tion would explode. When > 0, the steady state population is:
Model 2 of recruitment is exercised by substituting equation (23) into
equation (21.1) and solving the differential equation:
N= aR(m+f) NIA
= c scyN.(l ) cts(E + I + E E ) A
(m + f) .N
where:
1 e(m + f).7
Collecting coefficients of N°, N 1 , N 2 :
NaN 2 +bN+c (26)
124

where:
_______
a K ,bc .s.FJ.1(m+f)
and:
c = (as(E + I + E ) + IA).
Solving:
BA
N(t) = A + B N (27)
o a(BA)t
+ N A e
where:
N 0 = initial population size,
Thus:
A =  B 1 ,
and:
B =   [ : /(b)2  4C ]
The equilibrium value of the population is B, assuming B < A. The value
of the coefficient a indicates rate of recovery of the population from a
disturbance. A negative value of b indicates extinction of the population.
Such a condition occurs if the combined natural and fishing mortality rate
exceeds the reproductive potential of the population. The population can
also decline until It reaches zero if the loss terms E , I)7 and 1 A are
sufficiently large.
Estimates of Entrainment and Impingement Mortality
Cole (4) estimated the following 95 percent confidence intervals of the
numbers of yellow perch larvae potentially entrained at the Monroe power
plant in 1973, 1974, and 1975:
Estimated Number Entrained (millions) Year
(1) 0 <2.2 <5.1 1973
(2) 59.6 <83.1 <111.5 1974
(3) 13.7 <29.3 <44.9 1975
125

Using sampled concentrations of larvae obtained by Cole in the river channel
and in the upper discharge channel and volumes of cooling water published in
(7), the author obtained the following three estimates of numbers of perch
larvae entrained in the power plant cooling waters in 1975.
Estimated Number Entrained (millions) Location of Measurement Year
(4) 2.72 14.26 river channel near mouth 1975
(5) 2.39 20.85 upper discharge 1975
(6) 19.4 lake waters near river mouth 1975
(7) 0.94 1976
The Detroit Edison Company reports an estimated 5,029,000 perch larvae
entrained in 1975 (7) which includes prejuveniles or youngofyear fishes.
Since prejuveniles were not counted separately, it is assumed that combined
youngofyear mortality due to entrainment and impingement is:
+ Ey = 100,000
This assumption is probably conservative in view of the estimated total
nuther entrained as reported by Detroit Edison. Based upon Colets estimate
of 20 percent of perch larvae either dead or dying prior to entrainment and
using an estimate of 70 percent mortality of live perch larvae entrained,
the estimates of numbers of larvae entrained can be reduced to E , an esti
mate of live larvae killed due to entrainment:
TABLE 22. ESTIMATES OF ENTRAINMENT CAUSED BY LARVAL MORTALITY.
E2,
(millions killed)
(1)
02.856
(1973)
(2)
33.3862.44
(1974)
(3)
7.67225.14
(1975)
(4)
1.5267.986
(1975)
(5)
1.33811.68
(1975)
(6)
10.86
(1975)
(D.E.)
2.816
(1975)
(7)
0.53
(1976)
(D.E.)
0.36
(1976)
Estimated Impingement Mortality
Detroit Edison published the following estimates of numbers of fishes
killed due to impingement (7):
126

TABLE 23. ESTIMATED IMPINGEMENT MORTALITY.
(i + 1 A1 + IA)
Year
165,365 (excluding
Jan.,
Feb., Mar.)
1972
215,032
1973
152,857
1974
171,641 (excluding
April
and May)
1975
It is impossible to estimate the individual terms I 7 1 A1 A from the
data shown above. Therefore, for computational purposes, the quantities A
and 1 A1 (adult and subadult mortality, respectively) are each permitted to
assume the values 0, 50,000, and 100,000 independently, so that the sum A +
Al ranges from 0 to 200,000. When the sum A + Al is combined with the
earlier assumption of I + E = 100,000, it is clear that total impingement
mortality will range over the values shown above.
Estimates of Population Parameters
e: fraction of larvae surviving natural environmental forces of morta
lity to reach youngofyear stage .
The methodology underlying the estimate of E, the fractional rate of
survival of larvae from natural environmental forces of mortality to reach
youngofyear stage (25 days after date of hatching), is based upon the
above analysis of larval production in U.S. waters of the western basin of
Lake Erie and resulted in an estimate of E in the range 1 :.
0.02 < s < 0.10
s: fraction of youngofyear that survives to be recruited into age
class I .
Data (7) indicating abundance of youngofyear and yearlings in 4
successive years (1972, 1973, 1974, 1975) yield estimates of annual young
ofyear survival fractions of 0.12, 0.19, and 0.33, respectively, using the
ratio 2 :
y.o.y. survival = yearlings C.P.E. in year (t )
fraction y.o.y. C.P.E. in year (tl)
1 1t is shown in Appendix H that the percentage of entrained larvae that
would have survived for 25 days had they not been entrained increases with
age at entrainment and may reach 25%.
constant coefficient of catchability is assumed.
127

The monthy instantaneous mortality rates, a, corresponding to annual sur
vival fractions of 0.12 and 0.33 are, respectively,
a 1 in .12=0.177
12
and
a 1 in .33 = 0.092
12
In turn, the monthly instantaneous rates 0.177 and 0.092 yield six months
survival fractions which are, respectively,
s = e 77(6) = 0.346
and
s = e 092(6) = 0.575.
Thus, the fraction of youngofyear that survives (approximately 6 months)
to be recruited into the yearling stage or age class I is 1 :
0.34 < s < 0.58.
f: annual instantaneous fishing mortality rate from commercial and
sport fishing .
Based upon an estimate by Jensen (School of Natural Resources, Univer
sity of Michigan) that 20 to 40 percent of all perch vulnerable to fishing
gear will be harvested annually by commercial or sport fisherman, the in
stantaneous annual fishing mortality rate is estimated to be between 0.22
and 0.51. However, it is reported in (22) that during the period 1968 to
1978, total annual mortality may have risen to 70 percent. If the annual
natural mortality fraction holds at 25 percent, the implication follows that
the instantaneous annual fishing mortality rate may have increased to 0.95.
Therefore, it is estimated as:
.22 < f < 095
m: annual instantaneous natural mortality rate of yellow perch .
The Great Lakes Fishery Laboratory, U.S. Fish and Wildlife Service 2
reports an estimated natural mortality rate in the range:
1 1t is reported in (22) that research on postlarval yellow perch mortality
indicates a six month survival of approximately 0.49, a value well within
the interval (.34, .58).
2 Reference (22) and W.L. Hartman. (Great Lakes Fishery Laboratory, U.S. Fish
and Wildlife Service).
128

0.22 < m < 0.29
Other data relating to natural mortality of yellow perch are reported in
(14) and (15).
: mean annual rate of larvae production per individual in the subpopu
lation .
In model 1, the subpopulation for which y is estimated includes all
fishes in age class II and older. In model 2, the subpopulation estimated
includes all fishes in age class I and older. By definition:
y = hatching success number eggs deposited per sexually mature
female spawner
number sexually mature female spawners per
individual in subpopulation.
It is estimated by Scholl (Division of Wildlife, Ohio Department of
Natural Resources) that hatching success for yellow perch in Lake Erie
ranges between 25 and 50 percent:
.25 < hatching success < .50
The number of eggs deposited per sexually mature female in Lake Ontario is
reported by Scott and Crossinan (23) to vary between 2,000 and 90,000 with
an estimated average of 23,000. For the present calculation pertaining to
Lake Erie, it is therefore assumed that the number of eggs deposited per
sexually mature female ranges from 10,000 to 30,000.
The number of sexually mature female spawners per individual in the sub
population is variable and depends upon the mean number of times that a fe
male spawns during her lifetime, the number of age classes included in the
subpopulation, and the mean mortality rates from both natural causes and
fishing. Given equilibrium population conditions and assuming that the
subpopulation of interest consists of all fishes in age class II and older,
the number of sexually mature female spawners per individual in the sub
population can be calculated.
To do so, N 2 is used to denote the number of individuals entering age
class II under equilibrium conditions. Based upon Ohio Division of Wildlife
(12) information on sexual maturation of yellow perch of different ages, it
can be assumed that no age class II females are sexually mature and that all
females in age classes III and older are sexually mature. Assuming that a
fraction Pf of any age class are females, that a sexually mature female
spawns in any given year with probability that fishing mortality com
mences with age class III individuals, and that the equilibrium number of
age class I individuals is N 1 , we may calculate the fraction of sexually
mature female spawners in the subpopulation of age class II and older
fishes from the following:
129

Number of Individuals Number of Female Spawners Age Class
N 1 em 0 II
+ f) p p N e( 2 m + f) iii:
N e ) p p N e( 3 m + 2f) iv
1 ,, .. sf1
NieY+m + 3f) p p N 7 e( 4 rn + 3f) v
I S i. .L
N e Sm + ) p p N e( 5 m + 4f) vi
N 1 e( 6 m + Sf) pSpfNle( 6 m + 5f) VII
The fraction of sexually mature female spawners in the subpopulation may be
defined as:
number of sexually mature female spawners per individual
in subpopulation (age class II VII) =
(e_(m + f) . . . . e 5 + f)
sf + +
ii + e(m + f) + . . . + e5( + f)]
It may then be deduced that the fraction of the subpopulation consisting
of sexually mature females drops as the fishing and natural mortality rates
increase. For example, if f = m = 0.22, the above fraction is Pf x .60
but if f = m .52, the fraction drops to P Pf x .35. By assuming (a) that
fifty percent of each age class consists of females and (b) that the
probability of spawning by any given sexually mature female is .8 to 1.0, and
by using the ranges of m and f estimated above, we calculate the number of
sexually mature females per individual in the subpopulation consisting of all
fishes in age class II and older to vary between 0.153 and 0.239:
number of sexually mature female
0.15 < spawners per individual in < 0.24
subpopulation (age class hVu)
Therefore, the parameter I is estimated to lie in the range:
(0.25) (10,000) (0.15) = 375 < < (0.50) (30,000) (0.24) = 3600.
The estimated mean number of recruits into age class II per year per
individual in the subpopulation under equilibrium conditions, I.E.s.em,
follows:
(375) (0.02) (0.22) (0.75) < y.E.s .em < (3600) (.10) (.58) (.80)
name ly:
1.23 < y.cse < 167.5
Sex ratios among yellow perch do not remain constant at 50:50 across age
classes. This assumption may be an overestimate of the actual percentages
of females in the older age classes. Recent data on sex ratios of yellow
perch in Lake Erie are unavailable.
130

In the long run, the mean rate of addition of recruits to the subpopula
tion must not exceed the total mean rate of removals.
Impacts of Entrainment and Impingement Mortality
The reduction in yield from age class II and older yellow perch in
MichiganOhio waters of the western basin has been estimated by calculating
an equilibrium size of a subpopulation created with the use of the con
tinued annual losses of larvae, juveniles, and adults incurred from entrain
ment and impingement mortality as input. When the reproductive potential of
this population is taken into consideration, when it is assumed that such a
population is subject to the same biological processes and environmental
pressures as the surviving population, one can use the parameter estimates
given above together with equation (25) to estimate the size N of this
hypothetical population. One then estimates the loss in annual yield tQ
sport and commercial fishermen by multiplying the estimated equilibrium
value of N by the annual fishing mortality fraction ier.
A computer program was written and sizes, N, of an equilibrium popula
tion and (le ) N, loss in yield, were calculated:
N = + e_m(s(EQ + 100,000) + IA1)]
where: (m + f)6
= fraction of entrained larvae estimated to have survived
to reach youngofyear stage.
and:
= m + f a*s.s.y.em (13 > 0 is required for equilibrium)
TABLE 24. VALUES OF POPULATION PARAMETERS AND ENTRAINMENT AND IMPINGEMENT
MORTALITIES USED IN CALCULATION OF POTENTIAL IMPACT ON POPULATION SIZE.
:
.08, .131
s:
.42, .50
f:
.52, .95
m:
.29
y:
E :
15
2x10 6 , lOxlO 6 , 20xl0 6 ,
40x10 6
IN:
0, 50,000, 100,000
I i:
0, 50,000, 100,000
Calculations of potential losses in yield for combinations shown in
Table 24 are given in Tables 2532. The parmaters m and y are held con
stant in each case.
1 Calculations given in Appendix H provide a bases for setting E = .08 and
13.
131

The value y = 15 is held constant and provides a modest reproductive po
tential of the population of fishes lost due to entrainment and impingement.
The values of c, s, and f form eight combinations each of which corresponds
to one of the tables. In each case a constant loss of youngofyear due to
entrainment and impingement (ly + E ) is set equal to 100,000 individuals.
Three levels of losses of yearlings and adults ( Al + 1 N) are considered (0,
1x10 5 , 2x10 5 ) and in each case the loss is split equally (IN = 1 A1)
between yearlings and older fishes. All losses in yield are expressed in
pounds of fish, assuming 3.5 fish per pound. The entries in Tables 2532
are calculated from equations (28) to (35), respectively. 1
The coefficients of N 1 A1 and E in equations (28) to (35) convert
annual losses of fishes in each of the three stages (due to entrainment and
impingement) into reductions in yield to the fisheries.
Thus, for example, an annual loss of 1 million larvae converts into a
potential annual loss of lxlO 6 x .007 = 7000 pounds to the fisheries.
Th.BLE 25. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
E : (millions)
Loss in yield 0.203 N + 0.152 1 A1 + .005 Ei + 6373
(29)
Each of the equations (28) to (35) is a special case of the equation for N
given above, namely the size of the hypothetical population of equivalent
adults lost due to entrainment and impingement.
Al + N
= .08; s = .42; f = .52
200,000
100,000
0
68262
45262
22262
2.0
124262 194262 334262
101262 171262 311262
78262 148262 288262
10.0 20.0 40.0
Ei: (millions)
Loss in
yield: 0.263
1 N + 0.197 1 A1 + 0.007 E 2 , + 8262
TA3LE
26. ESTIMATED
POTENTIAL LOSS IN YIELD (POUNDS).
1 A1 + N
.08; s = .42; f = .95
200,000
100,000
0
52116
34387
16658
93259 144687 247544
75530 126959 229816
57801 109230 212087
(28)
2.0 10.0 20.0
40.0
132

TABLE 27. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
Ej: (millions)
Loss in yield = 0.568 N + 0.425 + 0.023 E + 17844 (32)
Al + N c = .08: s = .50: f = .52
200,000 84643 156643 246663 426643
100,000 57193 129193 219193 399193
0 29743 101743 191743 371743
2.0 10.0 20.0 40.0
E : (millions)
Loss in yield: 0.314 N + 0.235 1 A1 + 0.009 E + 11743
TABLE 28. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
A1 1 N c=.08;s=.50;f=.95
200,000 60865 116865 186865 326865
100,000 41565 97565 167565 307565
0 22265 78265 148265 288265
2.0 10.0 20.0 40.0
E 2 : (millions)
Loss in yield = 0.221 Ό + 0.165 + 0.007 E + 8265
TABLE 29. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
I j +IN = .13; s = .42; f = .52
200,000 163144 347144 577144 1037144
100,000 113494 297494 527494 987494
0 63844 247844 477844
(30)
(31)
2.0 10.0 20.0 40.0
133

TABLE 30. ESTIMATED POTENTIAL LOSS IN YiELD (PouNDs).
E 9 ,: (millions)
Loss in yield = 0.342 1 N + 0.256 + 0.017 Ej+ 12790 (35)
Since the annual loss in yield is never constant even under equili
brium conditions, the estimates given in Tables 2532 are reduced to esti
mates of a single weighted mean annual loss for each of the two values of C
that were selected. In order to carry out this reduction, a probability
distributixt nnist be assigned to the values appearing in Tables 2528 and
Tables 2932. Such an assignment should give recognition to the estimates
contained in Tables 22 and 23. It should also reflect estimates of recent
1 A1 + N = .13; s .42; f = .95
200,000 79565 167565 277565 497565
100,000 55165 143165 253165 473165
0 30765 118765 228765 448765
2.0 10.0 20.0 40.0
E 9 : (millions)
Loss in yield = 0.279 N + 0.209 1 A1 + 0.011 E + 8765
TABLE 31. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
iA1 IN c=.13;s=.50;f =.52
200,000 408068 920068 1560068 2840068
100,000 292718 804718 1444718 2724718
0 177368 689368 1329368 2609368
2.0 10.0 20.0 40.0
E : (millions)
Loss in yield = 1.32 N + 0.987 + 0.064 E + 49368
TABLE 32. ESTIMATED POTENTIAL LOSS IN YIELD (POUNDS).
Al + T N s = .13; s = .50; f .95
200,000 106590 242590 412590 752590
100,000 76690 212690 382690 722690
0 46790 182790 352790 692790
(33)
(34)
2.0 10.0 20.0 40.0
134

fishing pressure and youngofyear survival which are assumed to be inde
pendent of each other. Based upon an interpretation of Tables 22 and 23,
the following distribution of weights is assigned to each table entry for
Tables 2528. The distribution is applied again to Tables 2932, so that
two weighted mean estimates of potential annual loss in yield are obtained.
TABLE 33. PROBABILITY WEIGHTS ASSIGNED TO EACH TABLE ENTRY.
+ N
each
.088 200,000 .016
.162 100,000 .029
0 0 0
E : 2.0
Wt: T .045
Wt:
(s,f)
.25
combination
.054
.101
0
.016
.029
0
.002
.003
0
10.0
20.0
40.0
.155
.045
.005J
The entries in the main body of the tables are obtained by multiplying
each combination (E 2 ,, 1 A1 + N s, f) by the respective weights contained
in the marginal distributions on Ej, 1 A1 + N and (s, f). The marginal
distributions assigned to Eu,, I + N are given in Tables 34 and 35.
TABLE 34. MARGINAL PROBABILITY DISTRIBUTION
ASSIGNED to 1 A1 +
+ N Wt. Assigned
200,000 .35
100,000 .65
0 0
TABLE 35. MARGINAL PROBABILITY DISTRIBUTION
ASSIGNED to Ej.
Ej Wt. Assigned
40xl0 .02
20x 10 6 .18
10x10 6 .62
2x10 . 18
The overall weighted mean estimates of the potential annual loss in
fishery yield are approximately 110,000 pounds and 406,000 pounds for the
cases = .08 and E = .13, respectively. Therefore, the potential mean
135

annual loss is estimated to be 110,000406,000 pounds. An annual loss
yield of 100,000 pounds is not great when compared to a realized annual
yield of 5 to 6 million pounds and would be extremely difficult if not
impossible to detect by statistical methods applied to standing crops or
harvests, except locally. However, it has been demonstrated that losses
due to impingement and entrainment must occur and an average actual reduc
tion in total harvest over a period of years is expected. If fishing pres
sure is increased in an attempt to maintain catch, as has occurred in recent
years, the fisheries are perturbed in the direction of overexploitation and
an eventual drop in harvest due directly to power plant impacts cannot be
rectified by biological compensation. The estimates given above apply only
to the Monroe power plant. With additional plants with oncethrough cooling
being situated in the western basin, it is easily seen that their combined
pressure on the fisheries will be substantial, and, when this is coupled
with excessive harvests, it could tip the yellow perch fisheries into an ir
reversible decline. It is clear from examination of catch effort and stock
assessment data collected for the past twenty years that the combined yellow
perch harvest has been declining for the past seven to nine years, and the
population is presently in a depressed condition. The major reasons for
this condition are over exploitation and poor recruitment, but the fact re
mains that entrainment and impingement mortality from power plant cooling
waters is exercising an impact upon the fisheries. If fishing pressure by
Canada and the U.S. were relaxed by 10 percent per year, the inunediate
effect would be a reduction of the harvest, but over a period of years the
population would recover a substantial portion of its reproductive base and
yields would increase above present levels. Under such conditions, entrain
ment and impingement mortality will actually increase in absolute terms
(nuubers entrained and impinged), rather than decrease. The differential
impact of entrainment and impingement mortality, however, would be lessened,
due to the presence of a larger reproductive base. The impact of a given
level of entrainment and impingement mortality upon the yellow perch popula
tion is most severe when the population is in a depressed condition, as is
the present situation. This analysis, based upon equation (25), is valid
only so long as there is sufficient reproductive stock to maintain an
equilibrium population in the presence of the array of natural mortality,
fishing mortality, and entrainment and impingement mortality. As losses in
crease, a point is reached at which where an equilibrium population is not
possible and the fishery collapses.
Effects of Compensation
Effects of compensation, if any, by the surviving population may already
be accounted for in the losses estimated above. If the compensation frac
tion is denoted by , the actual loss in yield is estimated as:
actual loss in yield = potential loss x (1cS) = (le ) N (1cS) (36)
where:
0<6<1
136

and:
N =  N + e_m (I + s(E E + 100,000))]
The present level of compensation by yellow perch in Lake Erie is un
known in numerical terms but may well be at its maximum, if it occurs at
all. In order to obtain some indication of the degree to which compensa
tory mechanisms might mitigate the combined impacts of overexploitation, en
trainment and impingement mortality, and adverse environmental conditions
resulting in poor survival of larvae and youngofyear, a simplistic model
of recruitment (Model 2) defined by equation (23) was solved (equation 27))
and a set of calculations were made assuming equilibrium conditions in the
population (Table 36). Note from equation (26) that the compensatory term
affects the rate of recruitment into the age class I subpopulation which is:
N
cxs E yN(l
the rate of recruitment per individual into the age class I and older popu
lation is:
Since compensation undoubtedly occurs separately through the terms y and
6, implying that both y and c are functions of N, the above expression may
be considered to be a first order representation of some actual but unknown
compensatory mechanism operative in the population.
Table 36 indicates that if reproductive potential is high (y = 300
1500), compensation can eliminate the effects of entrainment and impinge
ment losses. However, when reproductive potential is low (y = 75), com
pensation is much less effective. As reproductive potential decreases even
further (y = 50), compensation cannot prevent a total collapse in the popu
lation under conditions of high fishing pressure and moderate losses due to
entrainment and impingement mortality. This analysis of compensatory
effects suggests that under the present conditions of a depressed yellow
perch fishery, the effect of any additional compensatory reserve operative
in the population is slight if it exists at all.
Appendix G indicates the statistical variation in the equilibrium pop
ulation level as 6 and y fluctuate from year to year. Although historical
data on year class strength suggests that annual larval survivals are cor
related so that annual fluctuations may be less than the value calculated,
natural environmental factors creating large variations in population size
are sufficient to mask smaller systematic annual losses imposed by man.
Evidence contradicting the presence of compensation within yellow perch
populations is cited in (Smith 1977, JFRBC 34(10): 17741783.
137

TABLE 36. EQUILIBRIUM HARVEST UNDER DIFFERENT CONDITIONS OF FISHING
PRESSURE, REPRODUCTIVE POTENTIAL, AND ENTRAINMENT AND IMPINGEMENT.
LOSSES: K = 5x10 7 ; E = .08; s = .26; m .37.
Annual
1 1 A E + I E , f Harvest (lbs.)
1500 0 0 0 .37 4,312,660
1500 1x10 5 1x 10 5 1x10 7 .37 4,311,976
1500 1x10 5 lx lO 5 1x 10 7 .52 5,625,718
1500 1x10 5 1x10 5 2x10 7 .37 4,311,082
1500 1x10 5 1x1 0 5 2x 10 7 .52 5,624,922
300 1x10 5 1x 10 5 1x10 7 .37 3,885,591
300 1x10 5 1x 10 5 1x10 7 .52 4,957,475
300 1x10 5 1x10 5 2x10 7 .37 3,882,235
300 1x10 5 ]x10 5 2x10 7 .52 4,952,952
300 0 0 0 .37 3,890,979
75 0 0 0 .37 2,309,674
is ixl.0 5 1x1 0 5 1x10 7 .37 2,272,832
75 1x1 0 5 1x10 5 1x10 7 .52 2,431,838
75 1x10 5 1x10 5 2x10 7 .37 2,249,305
75 1x1 0 5 1x1 0 5 2x10 7 .52 2,393,347
50 0 0 0 .37 1,255,471
50 1x10 5 1x10 5 1x10 7 .37 1,145,857
50 1x10 5 1x10 5 1x1 0 7 .52 0
50 1x10 5 1x10 5 2x10 7 .37 1,064,052
50 lxiO 5 2x10 7 .52 0
138

REFERENCES
1. Larval Fish Survey in Michigan Waters of Lake Erie, 1975 . Prepared by
W. Heimnick, J. Schaeffer, and R. Waybrant, Great Lakes Studies Unit,
Aquatic Biology Section, Bureau of Environmental Protection, Michigan
Department of Natural Resources.
2. Computer Listing of 1975 Larval Fish Concentrations Sampled in the
Western Basin of Lake Erie . Michigan Department of Natural Resources.
3. Computer Listing of 1976 Larval Fish Concentrations Sampled in the
Western Basin of Lake Erie . Michigan Department of Natural Resources.
4. Cole, R.A. Entrainment at a OnceThrough 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 1977.
5. Herdendorf, C.E., Cooper, C.L., Heniken, M.R., Snyder, F.L. 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, April 1976.
6. Herdendorf, C.E., Cooper, C.L., Heniken, M.R., Snyder, F.L. 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, March 1977.
7. Detroit Edison Company. Monroe Power Plant Study Report on Cooling
Water Intake , September 1976.
8. Polgar, T.T. Striped Bass Ichthyoplankton Abundance, Mortality, and
Production Estimation for the Potomac River Population . Proceedings of
the Conference on Assessing the Effects of Power Plant Induced
Mortality on Fish Populations, sponsored by Oak Ridge National
Laboratory, Energy Research and Development Administration, and
Electric Power Research Institute, Gatlinburg, Tenn., May 36, 1977,
pp. 109125.
139

9. Detroit Edison Company. Monroe Power Plant Data Sheets on 1976 Larval
Entrainment .
10. Paul, J.F. and Patterson, R.L. Hydrodynamic Simulation of Movement of
Larval Fishes in Western Lake Erie and their Vulnerability to Power
Plant Entrainment , Large Lakes Research Station, U.S.E.P.A., Grosse
Ile, Michigan, August 1977.
ii. Hubbell, R.M. and Herdendorf, C.E. Entrainment Estimates for Yellow
Perch in Western Lake Erie 197576 . CLEAR Technical Report No. 71,
The Ohio State University Center for Lake Erie Area Research.
Columbus, Ohio, September, 1977.
12. Lake Erie Research Unit Staff, Status of Ohios Lake Erie Fisheries ,
Ohio Division of Wildlife, Sandusky, Ohio, 1177, pp. 7, 12.
13. Patterson, R.L. An Outline of Quantitative Procedures for Analyzing
Larval Fish Abundance Data From Western Lake Erie , June 1976, U.S.
Environmental Protection Agency, Large Lakes Research Station, 9311
Groh Road, Grosse lie, Michigan, p. 22.
14. Brazo, D.C., Tack, P.1., and Liston, C.R. Age, Growth and Fecundity
of Yellow Perch, Petc.a ave ,ce.n.6, in Lake Michigan Near Ludington,
Michigan , Proc. Am. Fish. Soc., 104, 1975, p. 727.
15. Ricker, W.E. Abundance, Exploitation, and Mortality of the Fishes of
Two Lakes . Invest. Indiana Lakes Streams, 1974, 2:345448.
16. Jobes, F.W. Age, Growth, and Production of Yellow Perch in Lake Erie ,
Fishery Bulletin 70, U.S. Fish and Wildlife Services, Vol. 52, 1952.
17. Hartman, WL. Effects of Exploitation, Environmental Changes, and New
Species of the Fish Habitats and Resources of Lake Erie , Great Lakes
Fishery Commission, Technical Report No. 22, April 1973, p. 34.
18. Heang, T.T. Populations and Yield of Yellow Perch and Catfish in
Saginaw Bay, Lake Huron . Unpublished report, Summer 1975, School of
Natural Resources, University of Michigan, pp. 15.
19. Muth, K.M. Status of Major Species in Lake Erie, 1976 Commercial Catch
Statistics, Current Studies and Future Plans , U.S. F.W.S., presented at
Great Lakes Fishery Commission Meeting, Columbus, Ohio, March 910,
1977, p. 10.
140

20. Van Winkle, W., Christensen, S.W., Kauffman, G. Critique and Sensi
tivity Analysis of the Compensation Function Used in the LMS Hudson
River Striped Bass Models , Environmental Sciences Division Publication
No. 94Li , Oak Ridge National Laboratory, December 1976, pp. 830.
21. Carlander, lCD. Handbook of Freshwater Fishery Biology , Brown and
Company.
22. Memorandum from T.A. Edsall, U.S. Fish and Wildlife Service, Great
Lakes Fishery Laboratory, Ann Arbor, Michigan to Nelson A. Thomas,
Chief, Large Lakes Research Station, Crosse lie, Michigan, dated
32378.
23. Scott, W.B. and Crossman, E.J. Freshwater Fishes of Canada , Bulletin
184, Fisheries Research Board of Canada, Ottawa, 1973, p. 758.
141

APPENDIX A
STATISTICAL TESTS OF SIGNIFICANCE FOR DIFFERENCE IN
CONCENTRATIONS OF LARVAL YELLOW PERCH IN THE WESTERN BASIN
OF LAKE ERIE IN MAY AND JUNE 1975
Data Sources: Ref. (2,4,5)
Introduction and Summary
Accurate estimates of abundance of larval yellow percn depend upon the
attainment of unbiased estimates of mean concentrations in the water column
obtained at frequent intervals throughout a six week period beginning
approximately May 1, of a given year. Many factors influence the reli
ability and accuracy of such estimates including sampling frequency, time,
location, and equipment. Field samples obtained by teams from the Michigan
State University Institute of Water Research and Ohio State University
Center for Lake Erie Area Research suggest that larval yellow perch are
highly nonuniformly distributed in the water column and moreover, this non
uniform distribution varies diurnally. Nine statistical tests of signifi
cance follow below which deal with differences in larval concentrations ob
served to exist between the surface and bottom of the water column during
hours of both daylight and darkness. These tests indicate that substantial
day night differences exist at both the top and bottom of the water column
in Michigan waters of the western basin. One important exception occurs in
the vicinity of the mouth of the Maumee River where no significant differ
ences in concentration was detected between surface and bottom during day
light hours. Significant surface bottom differences in larval concentra
tions exist in most Ohio waters in which yellow perch spawning occurs.
The above results indicate that it is necessary to sample the water
column at both surface and bottom during hours of darkness in order to ac
curately estimate larval concentrations and abundance. It is important to
note in Table 2 that bottom sled tows yielded substantially higher concen
trations of larval perch than nets towed near bottom in the same general
vicinity.
Tests of Hypotheses Concerning Significance of Observed Differences in Mean
Concentrations
Null Hypothesis l
Mean daytime concentrations at surface and near bottom in Michigan
waters are equal.
142

Alternative: Concentration near bottom is greater.
Data:
1.97* XB = 2.43
= 3.99 s 8 = 4.28
n 48 n 48
Test Statistic Value:
 2.43 1.97 0.46
 [ (4.28)2 + (3.99)2 ½  0.84  0.54
48 48
( 4.28)2 + ( 399)2
48 48
d.f. = 2 2 2=
( 4.28 ) 2 + r( ) 2
48 48
49 49
0.5088 2 95
0.0052
Result: Since t 70 = 0.527 for 95 d.f., the null hypothesis is sup
ported by the data, i.e., there is more than a 30 percent chance that
random effects alone could produce a value of t = 0.54 unoer the null
hypothesis.
Null Hypothesis 2 :
Mean daytime concentrations at surface and on bottom in Michigan waters
are equal.
Alternative: Concentration on bottom is greater.
Data:
= 1.97 XB 5.83
s = 4.52
n = 48 n = 15
(bottom sled tow)
* = sample mean.
s. = sample standard deviation.
143

Test Statistic Value:
+ ( 399)2 2
48
+ ( 399)2 2
_______ 48
49
Result: Since t 995 = 2.82 for 22 d.f., the null hypothesis is not
supported by the data, i.e., there is less than a onehalf percent chance
that random effects alone could have produced the value of t 4.97 under
the null hypothesis.
Null Hypothesis 3 :
Mean nighttime concentrations at surface and near bottom in Michigan
waters are equal.
Alternative: Concentration near bottom is greater.
Data:
( 11. 18)2 2
+ 30
31
5.83 1.97
( 4.52)2
15
t =
d.f. =
+ ( 399)2½
48
3.86
1.30
= 2.97
( 4.52)2
15
( 4.52)2 2
15
16
2.8686
0.1182 2 22
= 5.28 = 18.83
= 11.18 = 16.13
n 30 n 30
Test Statistic Value:
18.83 5.28 13.55
3.58 3.78
( 16.13)2
30
t =
d.f. =
+ ( 11.18)2 ½
30
164.84
r( 16 13)2 2
30
31
2 53
144

Result: Since t 995 = 2.70 for 40 degrees of freedom and t 995 2.66
for 60 degrees of freedom, the null hypothesis is not supported by the
data, i.e., there is less than a onehalf percent chance that random
effects alone could have produced the value of t 3.78 under the null
hypothesis. The observed value of t is highly significant.
Null Hypothesis 4 :
Mean surface concentrations during daytime and nighttime in Michigan
waters are equal.
Alternative: Surface concentration at nighttime is greater than surface
concentration during daytime.
Data:
XN 5.28 = 1.97
11.18
n 30 n 48
Test Statistic Value:
5.28 1.97 = 3.31 = 1 56
r(h1 .18) 2 + ( 3.99)2 ½ 2.12
30 48
( 11.18)2 + ( 399)2 2
d.f. = 2 2 2=35.992=34
r(h1 18 ) 2 (3.99 ) 2
30 48
31 49
Result: Since t 90 1.31 and 1.30 for 30 and 40 degrees of freedom,
respectively, the null hypothesis is not supported by the data at the ten
percent level of significance. However, there is no reason to reject the
null hypothesis at the five percent level of significance since t 95 =
1.70 and 1.68 for 30 and 40 degrees of freedom, respectively.
Null Hypothesis 5 :
Mean bottom concentrations during daytime and nighttime in Michigan waters
are equal.
Alternative: Bottom concentration at nighttime is greater than bottom
concentration during daytime.
145

Data:
XN = 18.83
XD = 5.83
= 16.13
= 4.52
ii = 30
Test Statistic Value:
n = 15
t = 18.83
( 16. 13)2
30
5.83
+ ( 4.52)21½
15
13.00
3.17 4.10
+ ( 4.52)2 2
+ 1(4.52)212
________ 15
16
Result: Since t 995 = 2.75 and 2.70 for 30 and 40 degrees of freedom,
respectively, the data do not support the null hypothesis at the onehalf
percent level of significance. There is less than a onehalf percent
chance that random effects alone could produce the value t 4.10 under
the null hypothesis. The observed value of t is highly significant.
Null Hypothesis 6 :
Mean daytime concentrations in
bottom are equal.
Alternative: Concentration at
at the bottom.
Data:
Zone A of Ohio waters at the surface and
the surface is greater than concentration
i c : 5 = 14.15
= 8.00
s = 32.85
n 20
Test Statistic Value:
SB = 13.67
11 20
6.15
7.96
d.f. =
( 16. 13)2
30
( 16.13)212
30
31
2 39.61 2 = 38
t =
14.15 8.00
, (32.85)2 2
20
+ ( 13.67)2
20
146

( 32.85)2
20
( 32.85)2 2
20
21
+ ( 13.67)2 2
+ [ (13.67)]2
Result: Since t 80 = 0.856 for 26
provide evidence for rejecting the
of significance, that is, there is
random effects alone would produce
hypothesis. The observed value of
degrees of freedom, the data do not
null hypothesis at the 20 percent level
more than a twenty percent chance that
a value of t 0.77 under the null
t is not highly significant.
Null Hypothesis 7 :
Mean daytime concentrations at the
waters are equal.
surface and bottom in Zone C of Ohio
Alternative: Daytime concentration at bottom is greater.
Data:
n
= 42
xs
n = 42
Test Statistic Value:
1(104.82)2
42
(lo4.82)2 2
42
43
+ ( 8.70)2 2
+ ( 870)22
43
Result: Since t 975 2.02 and 2.00 for 40 and 60 degrees of freedom,
respectively, the data do not support the null hypothesis at the 2.5
percent level of significance, that is, there is less than a 2.5 percent
chance that random effects alone would produce the value t = 2.26 under
the null hypothesis.
d.f. =
2 28.06 2 = 26
= 38.31
= 104.82
SB
= 1.69
= 8.70
ss
t
d. f.
38.31
[ (104.82)
42
1.69
(8.70)2 ½
42
36.62
16.23
2.26
2 = 43.59 2 42
147

Null Hypothesis 8 :
Mean daytime concentrations at the surface and bottom in Zone D of Ohio
waters are equal.
Alternative: Daytime concentration at bottom is greater.
Data:
Test Statistic Value:
[ (10.64 )
36
( 10.64)212
36
37
+ (O.9O) 2
r(0.9 0) 2 j2
+ 36
37
Result: Since t 995 2.75 and 2.70 for 30 and 40 degrees of freedom,
respectively, there is less than a 0.5 percent chance that random effects
alone would produce a value of t 3.41 under the null hypothesis. The
test statistic is highly significant.
Null Hypothesis 9 :
Mean daytime concentrations at the surface and bottom in Zone E of Ohio
waters are equal.
Alternative: Daytime concentration at bottom is greater.
Data:
XB
9.03
i:
=
0.31
5 B
=
14.97
s
=
0.64
n
=
32
n
=
32
XB = 6.58
SB = 10.64
n = 36
6.58
0.51 6.07
(0.90)2 ½ 1.78
[ (10.64)
t
d.f. =
3E s = 0.51
s = 0.90
n = 37
= 3.41
2 = 37.51 2 = 36
148

Test Statistic Value:
9.03 0.31 = 8.72 = 3 29
( 14.97)2 ( 0.64)2 ½ 2.65
32 32
( 14.97)2 + ( 0.64)22
d.f. = 32 32 2 32
( 14.97)22 ( 0.64)22
32 + 32
33 33
Result: The value of t 3.29 is highly significant at the 0.5 percent
level for 32 degrees of freedom, i.e., it is highly improbable that random
effects alone would produce the observed value of t.
149

TABLE A.1.
MEASURED CONCENTRATIONS OF LARVAL YELLOW PERCH
IN MICHIGAN WATERS (1975).
Day Night
Date Surface Near Bottom Surface Near Bottom
5/21 24.4, 33.8
20.8, 34.6,
32.5
46.5, 17.0, 5.7,
19.2, 15.0
40.7, 70.3, 24.5
26.1, 14.0
1.1,
3.8,
8.9,
2.2,
2.4, 1.1,
1.1, 1.2,
6.7, 0,
4.1, 11.7
6/16 2.9, 0, 2.8
0, 0
9.5, 17.4, 4.9,
14.2, 10.1
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 1.0, 0
0.9, 0, 0, 0,
0, 0, 0, 0,
1.7, 0, 0, 0
6/18 0, 0, 0, 0,
0
2.4, 7.3, 9.3
17.2, 15.9
8.7, 2.6, 10.0,
0, 0
Data Source: R.A. Cole, Institute of Water Research, Department of Fisheries
and Wildlife, Michigan State University: Ref. (4).
5/22 0, 0, 0, 0,
0
5/23 0, 3.2, 0,
0
35.6, 29.1, 22.4
49.1, 20.3
1.1,
0, 3.2,
8.4
0,
1.0,
4.1,
o.9,
0,
0,
3.1,
15.7,
0,
1.0,
5.3,
5.4,
0,
0,
1.0,
16.9
1,
1.1,
4.1,
9.8
1, 4.2, 6.4, 9.9,
0, 1.0, 8.9, 7.2,
0, 0, 15.0, 18.9
6/19 0, 0, 0, 0,
0
x= 5.28
s = 11.18
n= 30
0, 0,
0, 0,
0, 0,
= 18.83
S = 16.13
n= 30
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0
= 1.97
S 3.99
n 48
0, 0,
0, 0,
0, 0
2.43
4.28
48
x=
s=
150

TABLE A.2. FORMULAE FOR TESTING EQUALITY OF POPULATION MEAI S
Null Hypothesis: Population Means Are Equal, Variances of Populations
Assumed To Be Unknown and Not Necessarily Equal.
Test Statistic*:
t =
2 2
[ s 1 +
[ m 1 m 2
Distributed approximately as Students t with:
r 2 2,2
[ 2 + . j
= ml  2
in 1 +l 512+1
= Degrees of Freedom (d.f.)
*Johnson & Leone, Statistics and Experimental Design in Engineering and the
Physical Sciences , Vol. 1, p. 226, Wiley, 1964.
151

APPENDIX B
STATISTICAL TESTS OF SIGNIFICANCE FOR DIFFERENCES IN
CONCENTRATIONS OF LARVAL YELLOW PERCH IN DEPTH ZONES
IN MICHIGAN WATERS IN 1976
Data Source: Table 9
Date: April 2629, 1976
Data:
Sample
Sample Sample Standard
Size Mean Deviation
Depth Zone m I s
17 57 3 134 00
612 18 24.6 46.7
1218 15 2.62 3.28
1824 25 0.63 1.26
2430 15 0.45 O.49
Null Hypothesis 1 :
There is no significant difference in mean concentrations in the O6
and 612 depth zones during April 2629, 1976.
Alternative: Mean concentration in O6 zone is greater.
Test Statistic and d.f.:
Given in Appendix A, Table A.2
Test Statistic Value:
57.3 24.6 32.7
t f(134)2 + (46.7)21½   0.95
17 18 J
152

[ 1342 + (46.7)212
d f 17 18 .1 2 1386261 2 20
(l34)2\2 ((467)2 2 62752
\ 17 1 18 )
18 19
Result: Calculated value of t not significant at 10 percent level.
Null hypothesis is accepted.
One concludes that the 06 and 6l2 depth zones can be lumped for
purposes of computing mean larval concentration in Michigan waters. The
remaining depth zones are lumped into a second group.
153

APPENDIX C
CALCULATION OF MEAN CONCENTRATION AND STANDARD ERROR
FOR YELLOW PERCH LARVAE IN MICHIGAN WATERS IN 1976
Data Source: Table 9
Mean concentration on specified day = (V 1 + V 2 2 )
2 2
Standard = L C 2 + 2
error: (S.E.) VT 1 n 1 2
where:
mean concentration in Ol2 zone
sample size in O12 zone
s sample variance in O12 zone
= mean concentration in 123O zone
= sample size in 1230 zone
= sample variance in 1230 zone
V 1 volume in O12 zone
V 2 = volume of 1230 zone
V = total volume
Day 118 (4/2629)
ni = 35 a 1 = 55
= 1.16
100 s 2 = 2.14
V 1 = 0.566 io8 V 2 = 4.41 x io8 VT = 4976 10
154

= 1 8 (0.566 x io8 x 40.5 + 4.41 x 10 x 1.16) = 5.63
4.976 x 10
S.E. = 1 8 [ (.566 ( 1oO)
4.976 x 10
+ (4.41 x 108)2 x ( 2; 4)2]½ 1.94
Mean concentration + 1 S.E. = 5.63 + 1.94 = 3.69, 7.57
Day 136
n 1 = 14 = 31
X 2 = 0.562 X 2 2.17
s 1 = 0.943 s 2 = 3.86
= 1 (0.566 x io8 x 0.562 + 4.41 x io8 x 2.17) = 1.99
4.976 x 10
S.E. 1 [ (.566 x 108)2 ( 943)2
4.976 x 1O 14
+ (4.41 x10 8 ) 2 ( 3.86 ) 0.624
Mean concentration + I S.E. 1.99 + 0.624 1.37, 2.61
Day 145
36 n 2 31
3.94 = 1.91
s 1 = 8.87 s 2 3.37
= 8 (0.566 x io 8 394 + 4.41 io 8 x 1.91) = 2.14
4.976 x 10
155

1 ( 8.87 )
SE. = 8 [ (.566 36
4.976 x 10
+ (4.41 x10 8 ) 2 ( 3 37)2 ½ 0.56
X 31
Mean concentration + 1 S.E. 2.14 + 0.56 = 1.58, 2.70
Day 158
= 13 20
= x 2 = 0.471
s = 1.17 s 0.996
1 2
1
= (0.566 x 10 x 0.579 + 4.41 x 10 x 0.47 1) = 0.483
4.976 io 8
2
1 _________
S.E. = [ (0.566 108)2 ( 1.17 )
X 13
4.976 x i0
+ (4.41 108)2 ( 0.996)21½ = 0.201
20
Mean concentration + 1 S.E. 0.483 + 0.201 0.282, 0.684
Day 188
= 15 = 20
0.133 x 2 = 0.147
a = 0.225 s 0.287
1 2
I
(0.566 x io8 x 0.133 + 4.41 x 108 0.147) = 0.145
4.976 x 1O
[ (0.566 x 108)2 ( 0.225)2
1 __________
x 15
S.E. = 4.976 x io8
+ (4.41 108)2 ( 0.287)2]½ = 0.057
20
156

Mean concentration + 1 S.E. = 0.145 + 0.057 0.088, 0.202
Day 201
= 13 = 8
= 0.140 x 2 = 0.213
s 1 = 0.285 S 2 = 0.562
8 (0.566 x 10 x 0.14 + 4.41 x 1O x 0.213) = 0.205
4.976 x 10
S.E. [ (0.566 x10 8 ) 2 x ( 0.285)2
4.976 x 10
+ (4.41 x 1o82 x ( 0.562)2 ½ 0.176
Mean concentration + 1 S.E. 0.205 + 0.176 = 0.029, 0.381
Day 209
= 20
0 x 2 0.126
s 1 = 0 s 2 0.392
8 (4.41 10 x 0.126) 0.112
4.976 x 10
S.E. 1 [ (4.41 108)2 ( 0.392) ] = 0.078
4.976 x 10
Mean concentration i s.c. = 0.112 0.078 0.034, 0.190
157

APPENDIX D
SAMPLE CALCULATION OF MEAN CONCENTRATIONS OF PROLARVAE (PROL),
EARLY POSTLARVAE (EPL), AND LATE POSTLARVAE (LPL) IN
MICHIGAN WATERS IN I976
April 2730 (Day 118)
Let CT = total mean concentration of larvae in Michigan waters on
day 118, 1976.
= 5.63
CPROL = concentration of prolarvae on day 118
= CT x mean fraction PROL.
Mean fraction PROL 49 6 (56.6 x X 1 + 441 x X 2 )
where:
X 1 = fraction PROL in 012 ft. zone.
X 2 fraction PROL in 1230 ft. zone.
x 2.17 0 973
12.17+0.06+0
x 1.29 100
21.29+0+0
Mean fraction PROL = 49 6 (56.6 x 0.973 + 441 x 1.0)
= 0.997
CPROL 5.63 x 0.997 = 5.61
CEPL concentration of early post larvae on day 118.
CT x mean fraction EPL.
158

Mean fraction EPL 4976 (56.6 x y 1 + 441 x y 2 )
where:
= fraction EPL in 012 ft. zone
fraction EPL in 1230 ft. zone
0.06
= 2.17 + 0.06 + 0 = 0.027
0
= 1.29 + 0 + 0
Mean fraction EPL = 49 6 (56.6 x 0.027 + 441 x 0)
= 0.003
C = 5.63 x 0.003 = .017
EPL
CLPL concentration of late post larvae on day 118.
= CT x mean fraction LPL.
Mean fraction LPL 49 6 (56.6 x Z 1 + 441 x Z 2 )
where:
fraction LPL in 012 ft. zone.
fraction LPL in 1230 ft. zone.
0 0
2.17 + 0.06 + 0
0 0
1.29 + 0 + 0
mean fraction LPL = 49 6 (56.6 x 0 + 441 x 0) 0
CLPL 5.63 X 0 0
159

APPENDIX E
ESTIMATING PERCENT MORTALITY OF
ENTRAINED LARVAE
Method 1 .
Let NE = estimated number of live larvae entrained on a given day.
Let NL = estimated number of live larvae entering upper discharge
canal from plant discharge on the same day.
Then, estimated percent mortality, 100 p, on that day is:
NE NL
100 p = 100 N 100 (1 (E.l)
E
Equation E.l requires knowledge of volume of cooling water on the given
day.
The following method of estimating percent mortality on a given day can be
applied using only knowledge of sample concentrations of live larvae en
trained and discharged.
Method 2 .
Let XE = mean concentration of live larvae in cooling water entering
plant on the given day.
Let XL = mean concentration of live larvae entering upper discharge
canal on the given day from plant discharge.
Then,
X
100 p = 100 (1 ) (E.2)
XE
Methods (1) and (2) defined above use concentrations of live larvae only
and can be used only when XL < XE.
160

Method 3 which follows below contains an adjustment which permits the in
clusion of counts of dead as well as live larvae which removes the re
striction XL < XE.
Method 3 .
Let XL and XE be defined as before. Let DE and DL denote the mean
concentrations of dead larvae that are entrained and discharged from the
power plant in the cooling water, respectively on the given day. Then per
cent mortality due to entrainment, 100 p, is:
XL
x. D x x D
100 p = 100 (1 + L = 100 (1 E + E ) (E.3)
XE X xL+DL
XE + DE
x +D
Equation (E.3) differs from (E.2) by an adjustment factor E E
+ DL
which utilizes Counts of both live and dead larvae collected at the intake
and outlet and also adjusts for different size samples collected at the in
take and outlet.
A fourth method, similar to method 3, uses sample ratios of dead larvae to
total larvae.
Method 4 .
Let all variables be defined as given above. Then,
DE
D x D D x
100 p = 100 (1 E+ E ) = 100 (1 D + XE (E.4)
DL + XL
Example
To illustrate the application of these four methods, consider the nypo
thetical data displayed in Table E.1. Following Table E.1 are the four cal
culations of estimated percent mortality of larvae due to entrainment which
are 87.204, 86.489, 82.525, and 79.797 percent, respectively. Methods 1 and
2 are equivalent provided the mean concentrations in method 2 are calculated
as shown in the example. The base population in both methods 1 and 2 is
live larvae which is a subset of the total entrained population. Since
methods 1 and 2 do not incorporate counts of dead larvae, information about
161

entrainment mortality is lost. For example, sampling variation may result
in a low count of live larvae entering the plant which will lower the esti
mate of entrainment mortality. A high count of dead larvae at the dis
charge, however, indicates that there may have been substantial larval mort
ality as a result of entrainment. The inclusion of counts of dead as well
as live larvae will use all the available information related to entrain
ment mortality. Methods 1 and 2 are modified (in methods 3 and 4) to incor
porate both live and dead larval counts so that the base population is the
entire entrained population for a given species. As noted by equation (E.3)
the ratio of live larvae discharged to live larvae entrained is multiplied
by an adjustment factor which incorporates counts of dead larvae that are
entrained and discharged. The effect can be to either increase or decrease
the estimated percentage of larval mortality due to entrainment. In the
above hypothetical example the calculated percentage was reduced. Method 4
is similar to method 3 but the roles of dead and live larval counts are re
versed. In method 4 dead larvae receive the same emphasis that live larvae
received in method 3. Different percentages result, however, since counts
of dead larvae entrained and discharged from the plant are different from
counts of live larvae entrained and discharged from the plant. In the
above example the estimated percentage of larval mortality resulting from
entrainment given by method 4 is smaller than that given by method 3. In
another example, the magnitudes of the percentages given by the two methods
could be reversed. Just as a comparison of live larval counts before and
after entrainment can be used as the basis for estimating mortality due to
entrainment, a comparison of dead larval counts can be used in a manner
exactly analogous, (methods 3 and 4) but which results in different numer
ical values for the estimate because the counts are not the same. There
should be no theoretical reason why method 3 should be preferred over
method 4 or vice versa. It is reconunended, therefore, that the average of
the two values be used as the estimate of larval mortality due to entrain
ment. In the above example, the estimated mortality due to entrainment is
therefore, 1/2 x (82.525 + 79.797) = 81.161 percent. It is noted, inci
dentally, that the ratio of dead larvae to live plus dead larvae at the
discharge is not a satisfactory method of estimating larvae mortality due
to entrainment as it fails to compensate for larval mortality due to
sampling.
162

TABLE E.l. COOLING WATER VOLUMES AND LARVAL CAPTURE DATA
HYPOTHESIZED FOR EXAMPLE E. 1.
Daytime hrs: 0500 2100 (5 a.m. 9 p.m.)
Avg. cooling water inflow: 59.5 Cu. meters per sec.
Vol. sampled (plant intake) Vol. sampled (upper discharge)
130 cu. meters 75 cu. meters
live pro larvae 15 live pro larvae 2
dead pro larvae 3 dead pro larvae 12
live post larvae 4 live post larvae 2
dead post larvae 1 dead post larvae 8
Nighttime hrs: 2100 0500 (9 p.m. 5 a.m.)
Avg. cooling water inflows: 31.1 cu. meters per sec.
Vol. sampled (plant intake) Vol. sampled (upper discharge)
28 Cu. meters 48 cu. meters
live pro larvae 63 live pro larvae 10
dead pro larvae 15 dead pro larvae 80
live post larvae 28 live post larvae 8
dead post larvae 4 dead post larvae 31
163

Calculations
Amt. of cooling water flowing
into the plant in daytime from 3,404,800 cubic meters
0500 to 2100
Amt. of cooling water flowing
into the plant in nighttime 1,783,466 cubic meters
from 2100 to 0500
Calculation of NE
# live pro larvae (daytime) 15 x 3404800 = 392,861
130
# live post larvae (daytime) 4 x 3404800 = 104,763
130
# live pro larvae (nighttime) 63 x 1783466 = 4,012,798
28
# live post larvae (nighttime) 28 x 1783466 = 1,783,466
28
NE = 6,293,888
Calculation of NL
I live pro larvae (daytime) 2 x 2404800 = 90,794
75
I live post larvae (daytime) 2 x 3404800 = 90,794
75
# live pro larvae (nighttime) 10 x 1783466
48 371,555
I live post larvae (nighttime) 8 x 1783466
48 297,244
NL = 805,387
164

Method 1
805387
100 p = 100 (1 6293888 = 100 (1 .12796)
= 87.204%
Method 2
3404800 ( 15 + 4 1783466 63 + 28 )
XE 3404800 + 1783466 1.3 + 3404800 + 1783466 0.28
= (.65625) . (14.615) + (.34375) (325) =
9.5911 + 111.72 = 121.31
3404800 2 + 2 1783466 10 + 8
XL 3404800 + 1783466 .75 + 3404800 + 1783466 0.48
= (.65625) (5.3333) + (.34375) (37.5) =
3 4999 + 12.890 = 16.3899
16.3899
100 p = 100 (1 12l.31 = 100 (1 .13511) = 100 (.86489)
= 86.489%
Method 3
3+1 15χ4
DE = (.65625) 1.3 + 0.28 2.0192 + 23.3256
= 25.345
( 12 + 8 ) + 80 + 31
DL = (.65625) 0.75 0.48 = 17.500 + 79.492
= 96.992
XL XE D
_______ 121.31 + 25.345
100 p = 100 (1 + D = 100 (1 0.13511 16.3899 + 96.992 =
165

= 100 (1 (0.13511) (1.2934))
100 (1 .179 75)
82. 525%
Method 4
25.345 96.992 + 16.389
100 p = 100 (1 96.992 25.345 + 121.31 )
= 100 (1 .2613 (.773))
= 79.80%
166

APPENDIX F
SOLUTIONS TO FIRST ORDER EQUATIONS OF LARVAL BALANCE
FOR MICHIGAN AND OHIO WATERS, 1975 AND 1976
Given:
N(t)  p N(t) + h(t) + f(t) + (h(t25) +f(t25))e 25  E(t) (F.1)
(t > t > 0)
0
Equation (F.l) is of the form:
N(t) + C N = F(t) Ct > t > 0). (F.2)
0
where:
C constant;
F(t) = function of time.
The general solution to (F.2) is:
N(t) N(t)eC tto) + e (t_to)tft F(Z) eC t) dz (F.3)
(t > t 0 )
and therefore (F.1) has the solution given by (F.3).
If F(t) happens to be independent of the parameter t, say F(t) = F, then
(F.3) becomes:
N(t) N(t )e(tto) + (1 e t_to (F.4)
0 C
Ct > t 0 )
If the definitions of the parameter C or the function F(t) are specific to
subintervals of time as are the cases represented by Equations (7), (8), (9),
and (10) above, then for subinterval i, let C = Cj and F = F
(i = 1, ..., n). Equation (F.4) is:
167

c (tt ) F C .(tt )
1 0 1 1 0
N(t ).e + (1 e )
0 C 1
(to < t < t 1 )
c (tt ) F c (tt )
(Nt ).e (1 e )
2
N(t) = Ct 1 < t < t 2 )
C (tt ) F C (tt )
N(t ).e (1 e )
3
(t 2 < t < t 3 )
C (tt ) F C (tt )
n nI n n ni
N(t ).e + (1 e
ni C
n
(tn_i < t < t ) (F.5)
Writing down the balances defined by Equation (F.i) for each of the cases
represented by Equations (7)(lO) above, the following differential equations
of balance and their solutions are obtained.
168

Michigan Water, 1976 (using Equation 10 )
0
0.4437 h
0.3915 h
(0.3915 0.4437
(0.1382 0.4437
(0.1382 0.3915
(0.0244 0.3915
(0.0244 0. 1382
(0.0022 0. 1382
(0.0022 0.0244
(0.0001  0.0244
(0.0001 0.0022
 0.O022he 25
0.0001he 25
Lo
(B = 497.6 x10 4 ;
e 25 ) h
e 25 ) h
e 25 ) h
e 25 ) h
e 25 ) h
e 25 ) h
e 25 ) h
e 25 ) i
e 25 ) h
0 < t < 106
106 < t < 120
120 < t < 131
131 < t < 134
134 < t < 145
145 < t < 148
148 < t < 159
159 < t < 162
162 < t < 173
173 < t < 176
176 < t < 187
187 < t < 189
189 < t < 200
200 < t < 214
214 < t < 365
The solution to Equation (F.6) following the format of Equation (F.5) is:
N(t) 0 0 < t < 106
p(t10 6 ) hB
N(t) = N(106)e + 0.4437 ()(1 P(t10 6 ))
e
p
106 < t < 120
p( t120)
N(t) = N(120)e + 0.3915 (  )(1 P(t106))
e
p
120 < t < 131
[ N(t) + pN(t) I
E(t) = 0)
(F.6)
169

p(t131) 25p h.B
N(t) = N(131).e + (0.3915  0.4437.e )(_)(1_e_P(t_131))
p
131 < t < 134
437e )(
N(t) = N(134).e t_134) + (0.1382 0.4 . 25 . )(l_e t_134))
134 < t < 145
03915e )(
N(t) = N(145) e p(t 145) + (0.1382 l_e t 145))
145 < t < 148
N(t) = N(148) e p(t 148) + (0.0244 0.3 25p hB P(t14 8 ))
915 e )()(1e
p
148 < t < 159
N(t) = N(159) e p(t 159) + (0.0244 O.1382 25 ( )(l_e t_159))
e )
p
159 < t < 162
01382e )(
N(t) = N(162).e Pt 162) + (0.0022 . 25 ) )(1_e_ t_162)
162 < t < 173
N(t) = N(173).e ) (t 173) + (0.0022 25p hB p(t173)
0.0244e )()(1e 
p
173 < t < 176
00244e )(
N(t) = N(176) .e p(t 176) + (Qo 1 25p )(l_e(t_176))
176 < t < 187
00001 00022e )(
N(t) = N(187).e)(t 187) + 25p !)(l_e (t_187))
187 < t < 189
0022 e (__)(l_e (t _189))
N(t) = N(189).e) t 189) + 0 25p hB
p
189 < t < 200
170

p(t200)
N(t) N(20O) e + O.O0O1 e
200 < t < 214
N(t) = N(214).eP(t 214)
25p ()(I_e t_2°°))
p
214 < t < 365
127 < t < 134
(F.7)
Ohio Waters, 1975
(using Equation 7)
1
0
0. 5905 h
0. 328 h
0. 07 29
O.0081h
(0.0081 0.59O5e 25 )h
(O.OOO4  0.59O5e 25 )h
 [ N(t) + pN(t)]
(0.0004  0.328.e 25 ).h
0.328 e 25 h
O.O729e 25 h
0.0081e 25 h
O.O0O4e 25 h
0
(B = 9.393 x io ; E(t) = 0)
The solution to Equation (F.8) following the format of
N(t) = 0 0 < t < 127
N(t) (O.5905)( _ )(l_e_1 t_127))
p
O < t < 127
127 < t < 134
134 < t < 141
141 < t < 148
148 < t < 152
152 < t < 155
155 < t < 159
159 < t < 162
162 < t < 166
166 < t < 173
173 < t < 180
180 < t < 187
187 < t < 365
(F.8)
Equation (F.5) is:
N(t) = N(134).e P(t 134) + (O. 3 28)( )(1_e P ( 134))
p
134 < t < 141
171

N(t) = N(141) .eP(t 141) + (0.072 9 ) )(l_eP(t141))
p
141 < t < 148
N(t) = N(148).e p(t 148) + (O.OO81)( )(l_e (t_148))
p
148 < t < 152
N(t) = N(152).e p(t 152) + (0.0081 O.59O5.e25P) L )(l_e t 152))
p
152 < t < 155
N(t) = N(155)e p(t 155) + (0.0004 O.59O5e25P)( )(l_e t 155))
p
155 < t < 159
N(t) = N(159)e p(t 159) + (0.0004  O.328 .e25P)( )(l_e t 159))
p
159 < t < 162
p(t162) 25
N(t) N(162)e 0.328e (L )(l_e (t_162))
p
162 < t < 166
N(t) = N(166) p(t 166) 0.0729. 25p (hB . _e(t_166))
e
166 < t < 173
p(t173) 2
N(t) = N(173) .e 0.0081e 5 ( )(l_e t_173))
p
173 < t < 180
N(t) N(180).e t 180) 0.00O4e 25 )(l_e t_18°))
p
180 < t < 187
N(t) N(187).eP(t 187)
187 < t < 365 (F.9)
172

0. 5905
0. 328
0. 0729
o < t < 106
106 < t  113
113 < t < 120
120 < t < 127
127 < t < 131
131 < t < 134
134 < t < 138
138 < t < 141
141 < t < 145
145 < t < 152
152 < t .: 159
159 < t < 166
166 < t < 365
(F. 10)
of Equation (F.5) is:
Ohio Waters, 1976 (using Equation 8 )
0
0.0081h
(0.0081  O.5905e 25 )h
(0.0004 0.5905.e 25 ) .h
4 [ Nt) + pN(t)J =<
(0.0004 O.328.e 25 ).h
0.328.e 25 r.h
25p
0.0729.e .h
25p
0.0081 .e
25 p
L 0.0004 e .h
0
(B = 9.393 x lo 7 ; E(t) = 0)
The solution to Equation (F.lO) following the format
N(t)0 0

p( t131)
N(t) = N(131).e + (0.0081 O.59O5.e25P)( )(l_e t 131))
p
131 < t < 134
14(t) = 14(134) .e p(t 134) + (0.0004 O.59O5e25P)( )(l_e t 134))
p
134 < t < 138
p(t138)
N(t) = N(138)e + (0.0004 .328e25P)( )(l_e t 138))
p
138 < t < 141
N(t) = N(141).eI (t 141) 0.328.e 25 T ( )(l_e t 141))
p
141 < t < 145
p(t145) 25 p h.B (1_et _145 ))
14(t) = N(145).e 0.0729 .e ()
p
145 < t < 152
N(t) = N(152).e p(t 152) o.oo . 25p hB ( le_P(t_152))
e ()
p
152 < t < 159
N(t) = N(159) P(t 159) 0. 25p hB (l_e t159))
0004 e ()
p
159 < t < 166
14(t) = N(166).e t 166)
166 < t < 365 (F.11)
174

Michigan Water, 1975 (using Equation 9 )
0.4437 .h
0.3915h
25p
(0.3915 0.4437e )h
25p
(0.1382 0.4437.e ).h
25 p
(0.1382 0.3915.e )h
25 p
(0.0244 0.3915e )h
25p
(0.0244 0.1382 e ) h
(0.0001  0.1382e )h
25p
(0.0001  0.0244e )h
25 p
0.0244e h
25 p
25 p
0.0001 .e
Lo
(F. 12)
(F.5) is:
0
[ N(t) + pN(t)] =
0 t < 120
120 < t < 134
134 < t < 145
145 < t < 148
148 < t < 159
159 < t < 162
162 < t < 173
173 < t < 176
176 < t < 187
187 < t < 189
189 < t < 201
201 < t < 215
215 < t < 365
(B = 497.6 x io ; E(t) = 0)
The solution to Equation (F.12) following the format of Equation
N(t) 0 0 < t < 120
h.B p (t_120))
N(t) 0.4437 (,(1e
p
120 < t < 134
N(t) = N(l ) .e tl34) + 0.3915 ( )(l_et 34))
p
134 < t < 145
p(t145) 25p )( 1 P(t 1.45)
N(t) = N(145).e + (0.3915 0.4437e )
p
145 < t < 148
N(t) = N(148) .e p(t 148) + (0.1382 0.443 25 )(l_e t 48))
7e )
p
148 < t < 159
175

N(t) = N(159).e t 159) + (0.1382 0.391 2 SP)( .!)(le P(t_15 9 ))
5e
p
159 < t < 162
N(t) = N(162)e p(t 162) + (0.0244 O.3915.e25P)( )(l_e t_162))
p
162 < t < 173
N(t) = N(173).e p(t 173) + (0.0244
173 < t < 176
N(t) = N(176) e p(t 176) + (0.0001 O.l382.e25P) !)(l_e t 176))
p
176 < t < 187
N(t) N(187).e P (t 187) + (00001 O.O244.e25P) )(l_e t 187))
p
187 < t < 189
N(t) = N(l89).e ptt 189) 0.0244.e 25 )(l_e t_189))
p
189 < t < 201
N(t) = N(201) p(t 201) (0.0001) 2 5 j (hB)( 1 _P(t_201))
e
p
201 < t < 215
N(t) N(215).e t 215)
215 < t < 365 (F.13)
176

Michigan Water, 1975 (using Equations 9 and 14 )
120 < t < 125
p(t125) 0.027
N(t) = N(125)e + (0.4437 h.B )()(l_e t125))
125 < t < 132
[ N(t) + p.N(t)} =
0
0

N(t) = N(132) e p(t 132) + (0.4437 0.053 ( )(l_e_ t_132))
hB
132 < t < 134
N(t) N(134).eP(t 134) + (0.3915 0.053 (l_e(t134))
hB
134 < t < 141
N(t) = N(141) e p(t 141) + (0.3915 0.025
hB )( )(l_e (t_141))
p
141 < t < 145
N(t) = N(145) e p(t 145) + (0.3915 0.443 25p 0.025 hB (l_e_P(t145))
7.e hB
145 < t < 148
N(t) = N(148),e (t_148) + (0. 1382 0.443 0.013 h.B (l_e_ t_148))
7.e h B
148 < t < 156
N(t) N(156)eP(t 156) + (0.1382 25p 0.004 h.B (l_e (t_150))
Q 4437.e hB
156 < t < 159
N(t) = N(159).e p(t l59) + (0.1382 0.391 25p 0.004 hB (1_e_ t_159))
5 .e hB
159 < t < 162
N(t) = N(162).e t_162) + (0.0244 0.391 25p 0.004 hB (l_e_1 t_162))
5.e hB
162 < t < 170
N(t) N(170) .e t 170) + (0.0244 0.3915 _25P)c )(1_e (t_170))
p
170 < t < 173
N(t) = N(173).e p(t 173) + (0.0244 0.138
2.e
p
173 < t < 176
178

N(t) = N(l76).e_ t176) + (0.0001  O.l382.e25P)( )(l_e t176
p
176 < t < 187
N(t) = N(187)e p(t 187) + (0.0001  O.O244.e25P)( )(l_e t 187))
p
187 < t < 189
N(t) = N(189) .e (t189) O.0244 25p hB _P(t 1 8 9))
e ()(1e
p
189 < t < 201
N(t) = N(201) p t 201) 25p hB _P(t_201))
e 0 0001 e ()(1e
p
201 < t < 215
N(t) N(215).e t 215)
215 < t < 365 (F.15)
179

APPENDIX C
APPROXIMATE VARIANCE OF EQUILIBRIUM POPULATION AS A
FUNCTION OF REPRODUCTIVE POTENTIAL AND LARVAL SURVIVAL
Using Taylors Expansion, one approximates Var(B) as:
B2 2 B2 2
Var(B) = () a + () a
c 6
where the derivatives are evaluated at y = 50 and c .08.
Let 6 = .08, s = .26, m = .37, y = 50
K = 5xl0 7 , E , = lxlO 7 , E = 250,000
a 6 .04, a, 1 25
Now:
B = {K + ( m+f)K + [ (K + ( m+f)K)2  4K(_& +
2 y ct sEy LSE , 1
Then:
= _ ( m+f)K + I [ (K + ( m+f)K)2 +K( +
aE 2 ctscy 2 1 ascy y y
[ 2(K + ( m+f)K) ( (m+f)K )
y as y 2
a s 61
E
 4K( ..1)]}
IC
= ! + ( m+f)K + ! [ K + ( m+f)K)2  4K( & +
2 2 2 2 y c s y y 6,1
I S
180

E
( m+f)K E ( m+f)K )
[ 2(K + ctss 2
c scy
E E
 4K( 
) E y
1 . 74 510
+ 12.922 .0064
+ [ (51o + 1O 7 . 74l0 2 2010 (10 + 2.510 ½
i5 1.03376 50 4
[ (2(10 4.3041665) ( 74) 5b0 4 510 .2.51O }
.0827008 + .32
= 44.73991O + (1014(18.525849)_1014(.525)]_Ό
. [ 1o14 (385.1383 + io14 (1.5625)]
= 44.7395910 + 1014(386.6958 ) = 45.155526 10
2 10 .4.242740
B 2 1o 14 2039.0215
(5 ) =
L B2 2= 14
10 3 262434
2 )2 = .0016
a = (.04
C
1 1O 7 74510 1 7 + . 74510 2
2 2500 + 51.688 + 2 1.03376
. 025
2010 ( +
[ 2(s .1o +  . 74510 . 74.5.10 )
50 1.03376 2500 + 51.688
181

+ 4 5 1X 7 .O25.lO )}}
25OO + 200
= 1o .o71183 . + [ 1014(2.0759988 1014(.525)]
By 2 2
[ 1o14.(2.8816654).(.o71183346) + 1o 14(.olos)]}
= [ 1o (.o7118334) + 21562658.1O14 = .2O873133 1O
1o . 6226455 11
(B)2 = 1o 14.o43568768
By
= (25)2 = 625
I BB 2 2 014.27.23042 I
I () 0 = 1
Var(B) = 1014(27.23048+ 3.262434)
= 1014(30.493214)
STD. DEV. B = 10 5.52206609 = 55,220,661
182

APPENDIX H
RELATIONSHIP BETWEEN AGE OF LARVAE AT ENTRAINMENT AND
REDUCTION OF YOUNG OF YEAR POPULATION DUE TO
ENTRAINMENT
It is estimated above that the fraction of larvae that survive natural
mortality for 25 days and hence are recruited into the youngofyear popu
lation is between 2 and 10 percent of total production. Therefore, the
fraction of larvae lost due to entrainment mortality that would be expected
to have survived to reach the youngofyear stage would also be between 2
and 10 percent provided they are in their first day of life at the time of
entrainment. At the other extreme all larvae which are in their 25th day
of life at the time of entrainment would have survived to reach youngof
year stage, by definition, since they are at that stage at the time of en
trainment. The fraction of larvae which are at some intermediate age at
the time of entrainment that would be expected to survive to reach youngof
year is estimated as follows.
Define the following variables and functions.
X 1 = a geometrically distributed random variable with
parameter p 1 , defined on the positive integers,
which denotes the age (in days) of larvae upon
entering the reference volume.
h 1 (x 1 ) = probability function of X 1 .
p)x 1 1 x 1 = 1,2,
0 otherwise
X = a geometrically distributed random variable with
2 parameter p 2 , defined on the positive integers,
which denotes the number of days that larvae are
in residence in the reference volume upon entering
the entrainment cycle.
h 2 (x 2 ) = probability function of X 2 .
xl
p 2 p 2 ) 2 x 2 = 1,2,
1 0 otherwise
183

Y = X 1 + X 2 l = a random variable denoting the age (in days) of
larvae upon entering the entrainment cycle.
g(y) probability function of Y.
One easily verifies that:
(1 )Y (1 1 )Y y = 1,2,
g(y) =4
otherwise
p = mean daily natural mortality rate of larval
yellow perch.
0.09 < p < 0.16.
(S/p) = conditional event that entrained larvae would have
survived in reference volume until 25th day of life,
given that the mean daily natural mortality rate = p.
The probability of occurrence of the event (S/p) is:
25
E g(y) x eP 25 Y) =
y= 1
er(l p 2 )
e (l p 2 )
e (lp) 5
2 (e (l p 1 )) 2 1
1 e (1 p 1 )
E(Y) mean age of larvae upon entering the entrainment
cycle =
= 1. + L  1.
p 1 p 2
Prob(S/p) is defined as the fraction of larvae lost due to entrainment
that would have survived to reach youngofyear stage, given that the
mean age of the larval population entering the entrainment cycle is
E(Y) = L + 1
p 1 p 2
25
11 (e (l p 2 )) I
Prob(S/p) =
p 1 p 2 f
= p 1 p 2
0
184

and that the mean daily natural mortality rate of larvae in the reference
volume is p. Table H.l below shows the relationship between Prob(S/p)
and E(Y), also plotted in Figure 45.
TABLE H.l. ESTIMATED FRACTION OF LARVAE KILLED DUE TO ENTRAINMENT
THAT WOULD HAVE SURVIVED TO REACH YOUNGOFYEAR STAGE AS A
FUNCTION OF AGE AT ENTRAINMENT
p 1
p 2
E(Y)
Prob(S/p)
.09
.99
.98
1.03
.116
.16
.99
.98
1.03
.020
.09
.99
.50
2.01
.127
.16
.99
.50
2.01
.026
.09
.99
.20
5.01
.177
.16
.99
.20
5.01
.055
.09
.99
.10
10.01
.241
.16
.99
.10
10.01
.116
.09
.99
.07
14.31
.26
.16
.99
.07
14.31
.125
.09
.99
.05
20.01
.24
.16
.99
.05
20.01
.12
A numerical study of larval transport within the Western Basin (10) sug
gests the plausibility of the geometric distribution as a model of larval
residence time in basin waters prior to entrainment at the Monroe power
plant, at least for larvae within a radius of a few miles of the cooling
water intake. The mean residence time in basin waters prior to entrainment
appears to be on the order of 13 days for larvae within a three mile radius
of the intake and increases with linear distance from the intake. A mean
age of entrained larvae of approximately 5 days is believed to be a rea
sonable value in the absence of data showing actual ages or lengths at the
time of entrainment. The preceding calculations indicate that 17.7% of lar
vae that are 5 days old when entrained would have survived 25 days when the
mean daily natural mortality rate is p = .09. The percentage drops to 5.5%
when p = .16 (Figure 45).
185

0.40
LL
0 0 w
> Q3Q MEA N DA IL Y NA TURA L
Hj MORTALITY/?ATE,p=O.09
(I)
<> 0.20
ci c o
iTY p=O
ODI
aw 0.10
a 0..
0
0 5 10 15 20
MEAN AGE AT TIME OF ENTRAINMENT, days
Figure 45. Plausible relationship between mean age of larvae at entrainment and
fraction of larvLre lost due to entrainment that would have
survived to reach yoy stage.

TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA600/379O87
3. RECIPIENTS ACCESSION NO.
4. TITLE AND SUBTITLE
Production, Mortality, and Power Plant Entrainment
of Larval Yellow Perch in Western Lake Erie
5. REPORT DATE
August 1979 issuing date
6.PERFORMINGORGANIZATIONCODE
7. AUTHOR(S)
Richard L. Patterson
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
SMIE AS BELOW
10. PROGRAM ELEMENT NO.
1BA769
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS 13. TYPE OF REPORT AND PERIOD COVERED
ENVIRONMENTAL RESEARCH LABORATORYDULUTH Final 19751978
OFFICE OF RESEARCH AND DEVELOPMENT 14.SPONSORING AGENCY CODE
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA 55804 EPA 600 03
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This study assessed impacts of the Monroe Power Plant upon the yellow perch
population of Western Lake Erie caused by entrainment and impingement of larvae and
older fishes in the plants open cycle cooling system in 197576. Data analyzed
in the study were collected by the Michigan Department of Natural Resources, the
Center for Lake Erie Area Research of the Ohio State University, and the Institute
of Water Research of Michigan State University. Estimates of total numbers of perch
larvae entrained, total perch production, the natural mortality rate of perch, and
the percentage of perch production that was entrained by the Monroe Power Plant were
obtained for 197576. Impingement estimates were obtained from data supplied by the
power plant. The above estimates consider only effects that occur in the same year
in which entrainment and impingement occurs. Impacts may occur in subsequent years
which include a depression of fish stocks and reduced yields to the fishery. Losses
to the standing stocks and fisheries were estimated using a method which falls into
a Category known as the equivalentadult type which provided estimates of the
longrun annual depression of yellow perch standing stocks and the yellow perch
fisheries. A numerical model was developed which incorporated several population
parameters including entrainment and impingement losses, and natural mortality rates
for larvae, youngofyear and juveniles, and fishing mortality rates.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
C. COSATI Field/Group
Fishes, Lakes
Lake Erie
06/F
18. DISTRIBUTION STATEMENT
RELEASE UNLIMITED
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
199
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 22201 (Rev. 477)
US GOVTRNMENT PR NTINGOFFICF 1971 557.O6O /5415
187
 