FINAL DRAFT
Subject to Editorial Review
PRODUCTION, MORTALITY, AND POWER PLANT
COOLIMG WATER ENTRAINMENT OF LARVAL YELLOW
PERCH IN MICHIGANOHIO WATERS OF THE
WESTERN BASIN OF LAKE ERIE IN 1975 AND 1976
IMPACTS UPON STANDING CROP AND THE FISHERY
by
Richard L. Patterson
Large Lakes Research Station
U.S. Environmental Protection Agency
Grosse lie, Michigan
and
School of Natural Resources
University of Michigan
Ann Arbor, Michigan
September 1978

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 t3

in MichiganOhio waters o£ the western basin of Lake Erie alone. Among
these, the 3100 negawatt Detroit Edison power plant located at Monroe, Michi
gan has the largest water pumping capacity. Operating at 50 percent capacity
for one 24 hour period, the Edison plant can pump approximately 4.32x10^
cuaic eters of water through the cooling cycle.
In order to assess the impacts, if any, that the Monroe power plant might
be exerting jpon the yellow perch population and fisheries of western Lake
Erie, a t.ree year field sampling program was undertaken to provide baseline
data on larval perch abundance and entrainment levels'. The purposes of
the analyses of the data are the following: 1. estimate production of larval
yellow perch in MichiganOhio waters of the western basin; 2. estimate natur
al aort3lity of larval yellow perch prior to their recruitment into the
youngofyear stage of development; 3. estimate the number of larval yellow
perch entrair.ed and killed in the cooling water cycle of the Monroe power
plant; 4. estimate the percentage of total larval perch production in Michi
gan waters of the western basin that is lost in the cooling water cycle of
the Mor.roe power plant; 5. estimate the percent loss in youngofyear re
crui.t=eit attributable to entrainment mortality at the Monroe power plant;
6. est:ate the loss to the yellow perch fisheries in western Lake Erie at
tributable 13 impingement and entrainment mortality occurring at the Monroe
power plant.
^Tron lace .:>ril through July in 1975 and 1976, biologists from the Michigan
Depar:~ent of :,'at^ral Resources (MDNR), the Institute of Water Research of
>!l.ch: ;n State University (HSU), and the Center for Lake Erie Area Research
o: the Chio State University (CLEAR) sampled larval fish densities throughout
U.S. acers of the western basin. In 1977, the field observational program
as ccj'jc:cd by CLEAR. Results reported in the present paper are based
•jpon jiyros of 197576 data only.
2

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 10® M^, and Ohio waters: 9 .393 x 10^ M^); the model
parameters are estimated by the method of least squares.
Production of larval yellow perch in U.S. waters of the western basin in
1975 is estimated to have been 2.3x10^3.5x10^, of which 7.0x10^
2.3xl03 are es tinated to have survival for 25 days following hatching.
Production in 1975 in U.S. waters of the western basin is estimated to have
been 1.8x10^2.6x10^ of which 5.3x10^1.8x10^ are estimated to have
been recruited into the youngofyear stage. Yellow perch larval production
in Michigan waters in 1976 declined from 1975 to approximately 2729 percent
of the 1975 level while production in Ohio waters declined to an estimated
8385 percent of the 1975 level. When an estimated 50 percent survival of
youngofyear fishes is combined with the an estimated 210 percent survival
of larvae an estimated 1.05.0 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 in 1975 is approximately 7.4x10^. The estimated
number entrained, however, is nearly double that figure. The estimated
yellow perch larval entrainment at the same plant in 1976 calculated by
Detroit Edison personnel using their own pump samples is approximately
3

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 0.34.7 percent for 1975 and 0.91.5 percent in 1976, considering
Michigan waters only.
It is estimated that the potential long run annual loss to commercial and
sport fisheries is approximately 110,000406,000 pounds. The above value is
the best interval estimate obtainable, and is the result of averaging the
values given in Tables 2532 for different combinations of population para
meters 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
krovn, although the compensatory reserve is believed to be slight. It is
suggested that the differential impact of entrainment and impingement losses
is greatest when the fishery is in a depressed condition, which is the pre
sent situation. The basic reason for this increased impact is that when the
co=oensatory reserve is zero, low numbers of reproductive stock cannot re
place incremental losses to that stock at all. Additional increments of loss
in such a situation can drive the population into an irreversible decline.
If the yellow perch fishery were tightly regulated, and if it rested upon a
large reproductive base, reproductive compensation could conceivably account
for cost, if not all, of the losses caused through entrainment and impinge
Lculations in Appendix 8 indicate that annual losses could prove to be
considerably higher.
4

ment mortality incurred by cooling waters of the Edison power plant at
Monroe.
Objec tives
The following analysis of field data collected in 19751976 is part of a
program sponsored by the U.S. Environmental Protection Agency 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 the present study are: 1) to estimate pro
duction of larval yellow perch in U.S. waters of the western basin in 1975 —
76; 2) to estimate natural mortality among larval yellow perch for the 2030
day period following initiation of the prolarval stage; 3) to estimate the
number of larval yellow perch entrained and killed in cooling water of the
3100 megawatt Edison plant located at Monroe in 197576; 4) to estimate the
percentage of total larval perch production in Michigan waters of the west
ern basin that is lost in the cooling water cycle of the Monroe power plant;
5) to estimate the percent loss in youngofyear recruitment attributable to
entrainment mortality at the Monroe power plant; 6) to estimate 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 pri
mary producers and benthic fauna have been previously reported (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 that are hatched in
5

hURO
RAISIN
RIVER
CANADA
DETROIT
^ /, RIVER
^ OUTFALL
MICHIGAN
DISTANCE ( MILES
WATERS
OTTER
INTERNATIONAL
BOUNDARY
CREEK
OHIO '.VATEss
AU'.'EE
X '.lAU'.IEE
RIVER
STREAM INPUT OF LARVAE
tet Intake losses
SPANNING SOURCES
OF LARVAE
SANDUSKY BAY
\
\ '<$?¦ / .. /
EXCr'xNGE DUE TO MIGRATION
AND CtRCULA TION
Figure 1. Western Lake Erie inputs and losses of yellow perch larvae.

streams are carried into the coastal waters of the western basin by stream
flov. Some are hatched in the Detroit River, Lake St. Clair, or along the
Canadian shoreline and are carried into Michigan waters by large scale basin
water circulation (10). Larvae that are spawned in shoreline waters on the
U.S. side (Figure 1) by adults residing in basin waters undoubtedly comprise
by far 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, extending from the
shoreline outward to the international boundary and eastward to the boundary
of Ohio Zone E" (Figure 2). Thus, any larvae that are collected at sampling
stations within the geographic boundary defined above are considered for pur
poses of the present study to have been produced in the reference volume 
U.S. waters of the western basin. This definition of total production allows
valid conparisons between production and a) natural mortality of larvae, and
b) numbers of larvae entrained by water intakes since the latter two pro
cesses na'ice no distinction between larvae due to their source of entry into
the basin. Secondly, the above definition of production does not require in
dependent estimates of larvae that enter the basin from streams, or embay
nents external to the basin. 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
8.0)xl09 1 arvae may be considered an upper limit to larval yellow perch
production in U.S. waters of the western basin. An alternative approach is
6

HURON RIVER
1 DETROIT >
\ RIVER
^ OUTFALL
CANADA
SANDY CREEK
RAISIN RIVER
INTERNATIONAL
BOUNDARY
MICHIGAN
OHIO

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 in
time is the cumulative effect of integration of the processes of production,
water intake entrainment, natural mortality, migration, and recruitment into
the youngofyear life stage, all of these factors are taken into consider
ation below. The method involves specification of a mathematical model that
incorporates a parameter h of production and a parameter p of natural morta
lity, both of which are estimated numerically from field observations of lar
val densities. The model makes no assumption about joint behavior of pro
duction and natural mortality, i.e., the parameters h and p.
Numerous possible sources of larvae sampling error exist. Perch larvae
tend to move about in clumps, inhabiting beach areas, backwaters, and shal
low embayments. As a result larvae may reach the youngofyear stage without
ever becoming vulnerable to sampling gear. If this occurs, some clumps will
never be sampled during a cruise, a situation that contributes to an under
estimate of abundance. Perch larvae in the western basin exhibit a highly
skewed daytime distribution in the water column, a high percentage being
clustered on or near bottom (Appendix 1). Unless precautions are taken to
sample the bottom concentrations of larvae both the mean and standard error
of the estinate of mean concentration will be in error. Errors in the esti
mate of mean concentration propagate errors in estimates of production and
natural mortality which, in turn, give rise to errors in the estimated per
cent of total production entrained in water intakes and recruitment into the
youngofyear stage.
7

In addition :o errors in estimates of the parameters h and p of produc
tion ,nd natural mortality, modeling errors can also occur which are differ
ent from parameter estimation errors but which may lead to errors in para
meter estimates. Modeling errors occur when incorrect assumptions are made
about the mathematical representation of biotic or environmental processes
that affect larval abundance and therefore, indirectly, estimates of produc
tion and natural mortality. In summary, estimates of production and natural
mortality of larval fishes can be in error due to four major causes shown in
Diagram A below.
Data Collection a.d Disolav
Field surveys of standing crops of larval fishes are reported in (1),
(2), (3), (5), ar.d (6) and provide the data base for estimates of production
and natural mortality of larval yellow perch in 1975 and 1976. Estimates 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
entraiment. Estimates of production and natural mortality of larval fishes
are key requirements for an assessment of the impacts of specific point
sources of larval mortality.
Data on larval perch concentrations shown in graphs and tables below are
based upon measurements taken at 68 stations in Ohio waters and at 20 sta
tions in Michigan waters (Figure 2). In addition special sampling studies
were carried out by the Michigan State University Institute of Water Re
sources. A complete listing of all species concentrations obtained at in
dividual stations on specific cruises can be obtained from (1), (2), (3),
8

Model
Specification
Modeling
Error
Model of
Larval
Abundance
Bias
in
Field Data
Parameter
Estinacion
Error ,
Estimated
Larval Production
and Natural
Mortality
yr
Estimated % Loss
to YoungofYear
Population Due
to Water
Intake Mortality
Diagram A: Sources of Error in Estimation Process
9

(4), (5), and (6). Tables 111 summarize data in references (1), (2), (3),
and (4) relative to yellow perch densities in Michigan waters (also in Fi
gures 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 while
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, a subdivision of Michigan waters into two
surface zones was tentatively defined. Analysis of 1976 data, however, did
not show significantly higher mean concentrations in waters south of the Rai
sin River mouth. Also plotted in Figure 3 for comparison are concentrations
of larval perch sampled in lake waters in the immediate vicinity of the river
mouth and in the upper discharge canal (4, Table B26) of the Detroit Edison
power plant. The lack of data in 1975 on larval perch densities during May
(Figure 7), the earlier part of their period of abundance, created difficulty
in assessing total production and percent natural mortality of larval perch
in Michigan waters for 1975. 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_
on a sampling date V (V^ x^ + • • • + x,.)
10

10?
10'
10°
10
10"
(0) ZERO CONCENTRATION
o MDNR. 1975
a MSU. 1974
i MSU. 1975
6,10,11
\
2Aq
A 10
7 STANDARD ERROR
OF MEAN
— MEAN CONCENTRA TION
IN 06 FT DEPTH USING
MDNR DA TA ONL Y
Stations 2,6,10,11,12
sampled by MSU in
vicinity of power plant
for comparison.
(0)6,10,11,12 (Q) 2,6,10,11,12
(0) 11, 12
J—d L
(0) "\\ \ (0)
&—ADJ6
100 120
140 160 180
TIME (clays)
200 220
Tigure 3. Larval perch concentration in 06 ft. zone
from Raisin River to Maumee Bay (197475).

{ MEAN CON CENTRA TION ± 7 S.E.
(0) ZERO CONCENTRATION
100 120
140 160 180
TIME, days
200 220
Figure 4. Larval perch concentration in 06 ft. zone
from Raisin River to Maumee Bay (1975) .
Data Source: Table 1.

J MEAN CONCENTRATION ± 1 S.E.
(0} ZERO CONCENTRATION
102 
CO
£
o
o
O
f 101 
(0) (0)
10~2 1 1 1 lo oJ •—
100 120 140 160 180 200 220
TIME, days
Figure 5. Larval perch concentration in 612 ft. zone
from Raisin River to Maumee Bay (1975).
Data Source: Table 1.

J MEAN CONCENTRATION ± 7 S.E.
100 120 140 160 180 200 220
TIME, days
Figure 6. Larval perch concentration in 612 ft. zone
from Raisin River to Huron River (1975).
Data Source: Table 1.

SINGLE ST A TtON SAM PL ES FROM TABLES 28
SHOWN FOR COMPARISON
OVERALL MEAN
CONCENTRATION
±1 S.E.
O
O
UJ
O 1Q2
3
100 120 140 160 180 200 220
TIME, days
Figure 7, Mean larval perch concentration in Michigan waters (1975).
Data Source: Table 1.

where:
X = volune of Michigan waters = 4.976x10® •
volume of ith depth zone.
i = 1 corresponds to 01—61 zone: 5.6x10^
i = 2 corresponds to 6 1 —121 zone: 5.1x10?
i = 3 corresponds to 12'18' zone: 8.2x10?
i = 4 corresponds to 18'24' zone: 2.32x10® m3
i = 5 corresponds to 24'30' zone: 1.27x10® M^
x.
i
mean concentration in ith depth zone averaged over all
measurements obtained in that zone for the given sampling
date.
Standard Error _ j (V^
of Mean T
2
S1 + ... + y
(2)
where:
s[ = standard deviation of all n^ measurements obtained in ith
depth zone on the given sampling date.
Sample concentrations obtained in each depth zone are lumped for purposes of
calculating mean concentrations shown in Figure 7. Also plotted in Figure 7
are sample concentrations obtained during night hours by Michigan State Uni
versity biologists. The latter concentrations were sampled in the 61 — 121
depth zone approximately 1 kilometer offshore from the mouth of the Raisin
River (Tables 28). Densities of larval yellow perch obtained at night were
round to be higher than densities obtained during daylight hours and pro
bable causes are discussed in (4). A subsequent statistical analysis of day
mght differences (Appendix 1) showed that the observed differences were
significant (P < .10 for surface and P < .005 for bottom concentrations),
11

indicating that estimates of yellow perch larval abundance or production
based upon densities observed only during daylight hours are biased low.
Larval perch densities measured in 1976 in Michigan waters are listed in
Table 9 and plotted in Figures 914. As would be expected concentrations are
highest in the 0* —6' depth early in the spawning period. An overall mean
concentration for Michigan waters in 1976 is calculated and shown in Table 10
and Figure 13. Before an overall mean concentration for Michigan waters was
calculated, it was determined whether observed differences in mean concentra
tions by depth zone were statistically significant. Tests of significance
for differences (Appendix 2) by depth zone for Michigan waters in 1976 showed
that concentrations in the 01 —121 zone were significantly higher (P < .025)
during the period of observed peak abundance than concentrations measured in
other depth zones. Further, statistical analysis showed that 0' —12' and
12'30' zones could be lumped for purposes of computing mean concentrations
and standard errors. Calculations of mean and standard errors for Figure 13
are shown in Appendix 3. 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 declining level due to a combination of
factors of natural mortality, migration, and net avoidance. As larvae
increase in age to 2030 days, they become progressively more capable of
avoiding capture by sampling gear so that eventually no larvae are observed
in samples (also see Figures 15 and 16 for similar patterns occurring in
Ohio waters in 197576).
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 57 days elapse be
12

« P10
• P6
• PI 1
PO'VER PLAiSiT
• PI 2
• PA
LO'"'E R
DISCHARGE
1 KM
Figure 8. Locations of HSU sampling stations in vicinity
of Monroe Power Plant.
Data Source: Ref.(4).

103
102
101
I
<

103
£ MEAN CONCENTRATION ± 1 S.E.
(O)ZERO CONCENTRATION
100 120
140 160 180
TIME, days
200 220
Figure 10. Larval perch concentration in 612 Et. zone
from Raisin River to Maumee Bay (1976).
Data Source: Table 9.

103
£ MEAN CONCENTRA TION ± 1 S. E.
(0) ZERO CONCENTRATION
TO"2
100 120
140 160 1$0
TIME, days
200 220
Figure 11. Larval perch concentration in 06 ft. zone
from Raisin River to Huron River (1976) .
Data Source: Table 9.

TO3
W2
~ 10
£ MEAN CONCENTRA TtON ±1 S.E.
(0) ZERO CONCENTRATION
I _
10° 
10"' 
102
100 120 140 160 180 200 220
TIME, days
Figure 12. Larval perch concentration in 612 ft. zone
from Raisin River to Huron River (1976).
Data Source: Table 9.

J MEAN CON CENTRA TION ± 1 S.E.
ij) M.S.U. DATA ONLY
REF. VOLUME = 4.976 x 10^ m3
n
E
CD
O
a)
O
E
3
C
1 10"
I—
<
CC
2
LU
(J
z
o
o
1
100 120 140 160 180 200 220
TIME, days
Figure 13. Mean larval perch concentration in Michigan Waters (1976).
Data Source: Table 9.

10:
PROL PRO LARVAE
EPL: EARLY POST LARVAE
LPL. LATE POST LARVAE
10' 
10° 
O
U 10l
TO"2
PROL
100 120
140 160 180
TIME, days
200 220
figure 14.
Mean larval perch concentration in Michigan Waters (1976)
by stage of maturation.
Data Source: Table 9.

fore prolarve develop into an early post larval stage and approximately 10
additional days elapse before the late post larval stage is attained. Yellow
perch larvae are considered for present purposes to be recruited into the
youngofyear stage after 25 days of life (source: R.A. Cole). Figure 14
shows that larval production began approximately on day 102 (April 12, 1976)
and continued at a relatively high rate until approximately 140, a period of
about five weeks. Abundance tapered off, finally terminating between days
190 and 2001.
Mean concentrations of larval perch in Ohio waters of the western basin
for 1975 and 1976 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 12A12E. In the 1976 plot
standard errors on each date are calculated by pooling estimates of mean con
centrations obtained in Zones AE. Figures 1830 show estimated mean concen
trations in the 02 meter and 24 meter depth zones for sectors A, C, and D
for 197576. The plots do not provide a clear picture of which year produced
the highest larval abundance. Even when all depth zones are accounted for
(Figures 1516) the picture remains somewhat clouded but it is indicated that
abundance of perch larvae was lower 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.
13

$ OVERALL MEAN CON CENTRA T/ON ± 7 S.E.
(0) ZERO CONCENTRA T/ON
REF. VOLUME = 9.351 x 109 m3
¦ 1 1 1—j.—i o—1 1—
100 120 140 160 180 200 220
TIME, days
Figure 13. Mean larval perch concentration in Ohio Waters
(1975, Zones AE).
Data Source: Tables 12A and 12B.

102
J OVERALL MEAN CONCENTRATION ±1 S.E.
(0) ZERO CONCENTRATION
REF. VOLUME = 9.351 x 109 m3
1CT
10° 
o
U 1CT1
TO"2
2 2 x 10
100
140 160
TIME, days
200 220
Figure 16. Mean larval perch concentration in Ohio Waters
(1976, Zones AE).
Data Source: Tables 12C and 12D.

J MEAN CONCENTRA TION ± 1 S.E.
(0) ZERO CONCENTRA TION
100 120
140 160 180
TIME, days
200 220
Figure L7. Larval perch concentracion in 02 meter zone,
Maumee Bay (1975).
Data Source: Ref.(5).

J MEAN CONCENTRA TION ± 1 S. E.
(OJ ZERO CONCENTRATION
100 120
140 160 180
TIME, days
200 220
Figure 18. Larval perch concentration in 02 meter zone,
Ohio Area A (1975).
Data Source: Table 12A.

{ MEAN CONCENTRA TION ± 1 S E.
(0) ZERO CONCENTRA TION
O
o
UJ
Jl 1 Ll_0_l 1 1—
120 140 160 180 200 220
TIME, days
figure 19.
Larval perch concentration in 24 meter zone,
Ohio Area A (1975).
Data Source: Table 12A.

J MEAN CONCENTRATION
(0) ZERO CONCENTRATION
n
O
LU
10 2 I 1 l—i iQ b 1 1—
100 120 140 160 180 200 220
TIME, days
Tigurc 20. Larval perch concentration in 02 meter zone,
Ohio Area C (1975).
Data Source: Table 12A.

{ MEAN CONCENTRA T10N ± 7 S.E.
(0) ZERO CONCENTRATION
"—0
o
o
LU
100 120 140 160 180 200 220
TlME, days
Figure 21. Larval perch concentration in 24 meter zone,
Ohio Area C (1975) .
Data Source: Table 12A.

{ MEAN CONCENTRA TION ±1 S.E.
(0) ZERO CONCENTRA TION
102 
n
E
o
o
GJ
E 101 
" 1 1—JLl 'o 1 I I
100 120 140 160 180 200 220
TIME, days
Figure 22.
Larval perch concentration in 02 meter zone,
Ohio Area D (1975).
Data Source: Table 12A.

} MEAN CONCENTRATION ±7 S.E.
(0) ZERO CONCENTRATION
.l_iQ
(0)
100 120 140
160 180
TIME, days
200 220
Figure 23.
Larval perch concentration in 02 meter zone,
Ohio Area D (1975).
Data Source: Table 12A.

(0) ZERO CONCENTRATION
O
o
100 120
(0)j (0)
O—OOO1—
140 160
_L
JL
180
TIME, days
200 220
Figure 24.
Larval perch concentration in 02 meter zone,
Maumee Bay (1976).
Data Source: Ref.(6).

103
J MEAN CONCENTRATION ± 7 S.E.
(0) ZERO CONCENTRATION
102
100 120
(0)\ (0)
o—o—1L
140 160 180
TIME, days
200 220
Figure 25. Larval perch concentration in 02 meter zone,
Ohio Area A (1976).
Data Source: Table 12D.

103
£ MEAN CONCENTRATION ±1 S E.
(0) ZERO CONCENTRA TION
TO2
CO
e
o
o
a
"c 101
o
h
<
cc
I
LL)
o
o
CJ
10° 
10
i _
10
2
100 120 140 160 180 200 220
TIME, days
rigurc 26. Larval perch concentration in 24 meter zone,
Ohio Area A (1976).
Data Source: Table 12D.

£ MEAN CONCENTRATION ±1 S.E.
(0) ZERO CONCENTRATION
100
140 160
TIME,days
Tigure 27. Larval perch concentration in 02 meter zone,
Ohio Area C (1976).
Data Source: Table 12D.

103
102
CO
E
o
o
I 101
D
C
o
h
<
cc
o
z
o
a
10"
10
2
10°
$ MEAN CON CENTRA TION ± 7 S.E.
(0) ZERO CONCENTRATION
(0)
o
100 120 140
(0)\ (0)
—d oL
160 180
TIME, days
200 220
Figure 28. Larval perch concentration in 24 meter zone,
Ohio Area C (1976).
Data Source: Table 12D.

103
J MEAN CONCENTRATION ±1 S.E.
(0) ZERO CONCENTRATION
(0)
O
(0) (0)
J—o—o
100 120
140 160 180
TIME, days
200 220
Figure 29. Larval perch concentration in 02 meter zone,
Ohio Area D (1976).
Data Source: Table 12D.

£ MEAN CONCENTRA TION ± 1 S.E.
(0) ZERO CONCENTRATION
180 200 220
Figure 30. Larval perch conccntation in 24 meter zone,
Ohio Area D (1976).
Data Source: Table 12D.

Factors Affecting Larval Abundance
It is not within the scope of the present analysis to elucidate the rela
tive influences of biotic and environmental factors which determine larval
production and subsequent strength of the year class. For present purposes
it is sufficient to summarize 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 either di
rectly in basin waters or by having first been transported into basin waters
from tributaries, estuaries, and shallow erabayments along the shoreline.
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 few days of life, although larvae exhibit very early
a pattern of diurnal vertical migration in the water column which is undoubt
edly not entirely passive (4). Subsequent to a two to four week period of
relatively intense production, yellow perch spawning activity rapidly drops
to a low level but can occur even into midsummer. Since MichiganOhio
waters of the western basin form an open system, water and biota are ex
changed with the Canadian portion of the western basin and the central basin
of Lake Erie. Water, biotic, and abiofic materials are fed into Michigan
OhLO waters from numerous streams and two large rivers. Ninetyfive percent
of the stream flow into the western basin is supplied by the Detroit River
and yellow perch larvae are known to be transported into the western basin
by the Detroit River (personal communication, G. Fritz, also see Table 14).
Vithdrawls for municipal and industrial uses represent losses of both water
14

and whatever is suspended in the water, including fish larvae (11). No at
tempt was made to estimate separately the additions of larvae into the basin
from streams or rivers. Such estimates are not strictly necessary because
larval concentrations measured directly in basin waters at several points in
time will include additions of larvae from streams and rivers provided they
roach the zones in which sampling occurs prior to recruitment into the juve
nile stage.
Approaches to Modeling Larval Production and Abundance
Ichthyoplankton abundance can be described by simulation of the spawning
population or by time variable mathematical functions fitted to abundance
measurements. Functional forms involving polynomials, rational functions,
or exponentials may be assumed in which one or more parameters in the func
tion are estimated from the data. One such model is specified by an equation
of the form:
A(t) = /lP(tx)•s(t,x) dx
o
where:
A(t) = 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:
A( t) = V.C./k'e^^'.Cle^) dx
15

where:
A(t) = larval abundance at time t
V = volume of reference basin (number of 100 M3 units)
C = Mean total number of larvae per 100 deposited in
reference volume during period of production
a
mortality related parameter
k = normalizing constant.
B = production related parameter
Difficulties of this approach are: a) the parameters may not be interpretable
in terns of biological or environmental processes, b) conservation of larval
numbers need not be guaranteed. The approach followed below is based upon a
materials balance for the net daily rate of change of larvae in a reference
volune. Each source or sink for addition or removal of larvae is represented
by an individual terra and after dividing both sides of the equation by the
size of the reference volume a differential equation expressing the net rate
of change in concentration is obtained. The equation contains two para
meters, representing production and natural mortality of larvae. Concentra
tions in Michigan and Ohio waters are analyzed separately; therefore, two
different reference volumes are used below.
A Material Balance Model of Larval Abundance
A material balance formulation for the net daily rate of change in larval
abundance for a specified reference volume is:
N(t) = h(t)  v(t)  r(t)  m(t)  L(t)  E(t)
(3)
16

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
entrainraent 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).
n(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 (Mich
igan 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.
17

Natural mortality is assumed to be a force operative on all larvae alike where
the chance of a given larva surviving a short interval t of time is p • At,
i.e., proportional to the length t. This assumption leads to a first order
decay of the surviving population and the exponential survival function eP1.
Equivalently, natural mortality is assumed to be proportionalto abundance:
ra(t) = p*N(t) (A)
from which one deduces, upon solving the equation
N(t) =  m(t) =  p*N(t),
N(t) = N(0)e~P.t.
Thus, the proportion of larvae surviving t days following hatching on day 0 is:
N(t) _ pt
N(0) " e *
The mortality parameter, p, is estimated by fitting a solution to equation (3)
to field based estimates of mean concentration of larvae in Michigan and Ohio
waters separately. The assumption that p is a constant is interpreted to mean
that the totality of conditions in a given year that produces larval mortality
remains unchanged. On the average, throughout the months MayAugust, the frac
tion of remaining larvae that do not survive from one day to the next fluctu
ates about a constant p. This is equivalent to the assumption of conditional
independence of the natural mortality rate on larval production within a given
spawning season, 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
Mic'i iganOhio waters of the basin and by larvae transported into the basin from
18

tribut.iries, estuaries and across the international boundary from Canadian
waters^. Approximately six to twelve days following spawning, eggs hatch and
an individual yolksac or "pro" larvae begins day 1 of its life. It is evident
from examination of field samples (Figure 14) that production builds up to a
peak very rapidly, remains at an elevated level for a period ,of time, decreases
to a very low level for an additional period, then ceases altogether. Any
mathematical function h(t) used to describe larval production should distribute
the prolarval input over approximately the same period that prolarvae are
observed in the reference volume. The function h(t) should peak at approxi
mately the same time that peak production is estimated to occur in the refer
ence volume, and it should exhibit rate of change characteristics suggested by
field data (Figures 1316). Finally, it should contain a parameter describing
productive intensity which can be estimated from field data. A function which
meets the above criteria is:
B*h*('Q)*q® (lq)m~0
B'h'C^'q^ (lq)m~l
Bh'(2)*q^ (lq)ra2
(0 < t < T \
— — o'
(To t < T0 + d)
(T0 + d < t < T0 + 2d)

where:
ra +¦ 1 = maximum number of time periods in which production can occur,
d = number of days in each of the m + 1 time periods of larval
produc tion.
q = parameter which determines the time period in which production
function peaks. (0 < q < 1). q and m jointly determine the
spread or skewness of the production function over the period
of larval abundance,
h = production parameter or mean total number of larvae deposited
per 100 cubic meters of water in reference volume. The
parameter h directly influences the amplitude of the production
rate.
= day on which production begins.
= maximum number of days that production occurs.
B = number of 100 unit volumes of water in reference volume.
(= 4.976 x 10^ for Mich igan waters)
(= 9.393 x 10^ for Ohio waters when Mauraee estuary is
included; 9.351 x 10^ if zones A,B,C,D, and E alone are
cons idered).
n
(x) = binomial coefficient.
Total larval production for d consecutive days in period x in the reference
volume is therefore:
dBhCi) qX"l • (lq)ra~x+l
(x= 1,2, ••• , m+ 1)
20

Total larval production is distributed over the periods 1,2, •••, m+1) in the
reference volume and suras to:
m+1 m
Z d»B«h*(x_i) qx_1 • (lq)m_x+l =
x=l
m+1 m
= dBh E (xi) qXl.(lq)mx+l
x=l
From probability theory:
ra+1 . m
xIi qx~1m~x+1 = i.
so that total production in the reference volume during the period of abund
ance for any given year is:
Total Production = d>B«h (5)
The function h(t) has the shape of a series of stairsteps 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 function defined by
(5) must reflect these discontinuities by being solved explicitly and sepa
rately for each of the ra+1 subintervals of time during which production can
occur.
The parameters q and m 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 approxi
21

raately 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 produc
tion parameter, h, obtained by fitting (by least squares) the solution to
equation (3), containing h and p, to the estimated concentrations in the refer
ence 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 estimated
to have commenced between May 1 and May 10 and continued at a high rate until
approximately May 21 (day 144) followed by a rapid decline. Larval perch are
fully recruited (by assumption) into the youngofyear stage 25 days following
their day of production. Larval abundance peaks approximately on day 144 so
that nearly all production must have occurred on or before that date. Inspec
tion of tables of the binomial probability function shows that when m = 5 and
q = 0.10, and setting d = 7, 59% of production occurs in the first seven days
of production, and 33% occurs from the seventh to fourteenth day, or a total
of 92% by the fourteenth day of production. If production commences on day
127, the fourteenth day of production occurs on day 144, the day of approxi
mate peak larval abundance, and the 35th and final day of production occurs on
day 162, twenty five 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 probability
function corresponding to m = 5 and q = 0.10 the following production function
is obtained as a special case of equation (5):
22

h(c) = <
0
0. 5905•B«h
0.3230Bh
0.0729 *B *h
O.OOSl'Bh
0.0004«B*h
0
0 < t < 127 (=T \
— — 0/
127 < t < 134 (=Tq + d)
134 < t < 141 (=Tq + 2d)
141 < t < 148
148 < t < 155
155 < t < 162
162 < t < 365
(7)
where:
B = 9.393 x 10?
d = 7
Other combinations of ra and q were tested but none yielded a distribution which
so adequately fit the field observations on the spread and apparent timing of
peak production. That is, equation (7) together with alternatives generated
by varying p, d, and m, were compared by substitution into equation (3). Equa
tion (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 functions may be necessary in or
der to select the function which most adequately describes the actual but un
known time dependent introduction of larvae into the reference volume. The end
result is a more reliable estimate of total production and the conditional re
lationship of natural mortality to total larval production.
Analyses following the same lines as the preceding case led to production
functions describing larval perch production for the three remaining cases:
23

Production in Ohio Waters: 1976
0
h(t) = *<
0.5905Bh
0.32S0B'h
0.0729Bh
0.0031B *h
0.0004 B«h
0
B = 9.393 x 10?
d = 7
0 £ t 1 106
106 < t < 113
113 < t £ 120
120 < t £ 127
127 < t < 134
134 < t < 141
141 < t < 365
Production in Michigan Waters: 1975
0
0.4437 «B *h
0.3915Bh
h(t) = < 0.1382•B*h
0.0244 «B«h
O.OOOlBh
0
B = 4.976 x 106
d = 14
0 < t < 120
120 < t < 134
134 < t < 148
148 < t < 162
162 < t < 176
176 < t < 190
190 < C < 365
24

Production in Michigan Waters: 1976
h(t)
0
0 <
t
<
106
0.4437•B*h
106
<
t
< 120
0.3915'B*h
120
<
t
< 134
0.1332Bh
134
<
t
< 148
0.0244B'h
148
<
t
< 162
0.0022*B*h
162
<
t
< 176
0.0001B'h
176
<
t
< 190
0
190
<
t
< 365
(10)
B =4.976 x 106
d = 14
Recruitnent into the YoungofYear Stage
Following a period of maturation lasting from 20 to 30 days, the surviving
larvae are recruited into the first juvenile stage of development or youngof
year stage. (The length of the larval stage is defined as D = 25 days for all
calculations following below). Upon consideration of the effect of natural
mortality upon the number of youngofyear recruits the recruitment rate, r(t),
is approximately equal to a time translation of the production rate, h(t), re
duced m amplitude by the factor e~^5p which accounts for natural mortality
that occurs during the 25 day period of maturation. Therefore."
r(t) = h(t25)e~25P
By not taking into account in (11) the fact that larvae which are killed due
to water intake cntrainment or other point sources of loss will not be re
cruited into the youngofyear stage the estimate of recruitment provided by
equation (11) nay be slightly exaggerated. Although equation (11) accounts
25

for removal of larvae that survive 25 days from the total pool existing at
time t, the actual effect represented by equation (11) that is observed in the
field is a reduction in the number of 2030 day old larvae captured by sampling
gear due to their enhanced ability to avoid capture. The ability of larvae to
avoid capture by sampling gear does not jump from zero to 100 percent effec
tiveness at the exact age of 25 days so that equation (11) is only an approxi
mate representation 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 func
tion of their size is not attempted.
Emi^ration
The term v(t) accounts for lateral emigration of larvae across the inter
national boundary and between Michigan and Ohio waters. The patterns of cir
culation 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
which are produced along the Michigan shoreline can be removed from Michigan
waters in as few as two days. Larvae produced in Mauraee Bay are transported
into both Michigan and Ohio waters but under normal southwest wind conditions
during late spring most are exported into Michigan waters. Larvae which enter
the western basin from the Detroit River are transported into Michigan waters
as velL. Thus, both inandout migration of larvae occurs in Michigan
waters^. Numerical studies suggest that by ten days after larvae are
hatched wLthin one kilometer of the Michigan shoreline, up to fifty percent
*I:i—i;iit:on is accounted for in the production term h(t).
26

could be transported into international waters unless removed by mortality or
unless their own lateral swimming motion counteracts water circulation. It is
estimated that for the case of Michigan waters net out migration of perch lar
vae occurs but may not be more than 510 percent of total production. Large
numbers of larvae are lost through natural mortality by the time they would
otherwise reach the 24'30' depth zone near international waters after having
been hatched along the Michigan shoreline. A total net loss due to emigration
reduces abundance on any given day and consequently will affect 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 circul
ation in the western basin (10) indicate a net loss of larvae from Ohio waters
due to advective transport. Perch larve exercise vertical migration in the
water column (4) soon after hatching and as a result they become vulnerable to
transport by near surface currents which carry them into the midwaters of the
basin. As they settle to the bottom, however, their direction of transport is
reversed and move further into MichiganOhio waters. Numerical studies indi
cate that considerable mixing of larvae from separate spawning areas can
occur. It is difficult to establish with confidence a numerical percentage of
larvae that are transported out of Ohio waters due to movement by the water
column but simulation studies (10) suggest that it is less than five percent.
Lateral migration of larvae due to their own locomotion occurs but the
extent to which it influences migration out of or into OhioMichigan waters is
unknown.
In the numerical analyses conducted in the present study emigration is
assumed to be zero:
v(t) =0 (0 c t < 365) (12)
27

The effect of this assumption is to cause any net loss in abundance due to
emigration to be confounded with production and natural mortality. That is,
if emigration causes a reduction in abundance but is assumed to be zero (in
the specification 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 assuming that:
v(t)0 leads to an underestimate 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 underestimating water intake entrainment mortality. It is be
lieved that larval emigration losses are at most 5 to 10 percent of total pro
duction, so that if the production parameter h can be estimated assuming v(t) =
0, then emigration can be approximately accounted for by adding ten percent to
the value of h.
28

Larval Losses Due to Entrainment in the Monroe Power Plant Cooling Water Intake
Ichthyoplankton concentrations have been sampled at numerous locations in
the immediate 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 due to entrainmnet effects is estimated by multiplying daily consump
tion of water by mean concentration of live larvae in the cooling water col
umn, multiplying that product by the fraction of live larvae killed in the
entrainment cycle, and summing the result over all days in which larvae are
known to be present in the water column:
number larvae killed = 2 (daily cooling water usage) x
in given year due to days in period (concentration of live larvae) x
(13)
cooling water of larval (fraction of live larvae
entrainment abundance killed)
Various estimates of total numbers killed in a given year can be obtained, de
pending upon how the terms on the right hand side of equation (13) are esti
mated. Appendix 5 illustrates four methods of estimating fraction of live lar
vae killed due to the entrainment process. Daily cooling water usage is pro
bably the nost accurately known as records are maintained at power plants from
which daily usage rates of cooling water (Figure 31) can be obtained.
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) sampling gear. Fi
gures 32 and 34 shows concentrations sampled in 1974, 75, and 76 at stations
located as shown in Figure 8. Mean concentrations for the 06' depth zone in
the Raisin River  Maumee Bay area for 1975 and 1976 are also plotted for cora
29

parison purposes. The lines shown in Figure 33 represent upper and lower
values of larval concentrations used to estimate the number of larvae en
trained during the period of abundance in 1975. It might be argued that Sta
tion 2, located in the upper discharge represents the most uniformly mixed sec
tion of the water column and, therefore, should provide the most unbiased mea
surements on concentrations of larvae in the cooling water. However, substan
tial statistical fluctuations in larval concentrations occur at Station 2 as
well as all other stations (Table 16 and Figure 34) and, therefore to ignore
observations 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 re
cord of daily cooling water usage (Figure 31) lower and upper estimates of num
bers entrained in 1975 were 2,726,000 and 14,262,000, respectively. Based upon
an estimate that 20 percent of yellow perch larvae entering the cooling cycle
are either dead or dying (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 5 and using larval mortality data published by Cole (4,
Table 9), estimates of the percentage of larvae killed due to the entrainment
process are:
lOOp = 100 (1  ^ • ~) = 65
(Method 3) (1975 data)
and
I00p . 100 a  i . 5.)  72
(Method 4) (1975 data)
30

DATA SOURCE
• 1975 (Re f. 10)
x 1976 (Ref. 9)
70,000
60,000
>
5 50,000
CO
E
§ 40,000 p
X X xxx
• X
',••1
o
U_
30,000
20,000
10,000
X X
120
XX XXX
140 160
TIME, days
180
Figure 31. Daily cooling water pumping rate at Edison Plant,
Monroe, Michigan (May to July, 197576).
Data Source: 1975  Ref.(10); 1976  Ref.(9).

Therefore, using an estimate of 70 percent mortality of live larvae due to en
trapment, 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 published by Detroit Edison (7) in 1975 showed peak
densities to occur 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  160 than the
values indicated by the solid lines in Figure 33. The mean daily rate of loss
estimated to have occurred in 1975 is:
0 (0 < t < 125)
134,000 (125 < t _< 132)
265,764 (132 < t < 141)
E(t) = < 126,500 (141 < t < 148)
66,361 (148 < t < 156)
21,209 (156 < t < 170)
L 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. Entrainment of larval yellow
perch in 1976 was estimated by Detroit Edison personnel using their own pump
sampled data (9) to have been 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 (that were calculated by Detroit Edi
son) were divided by daily volume of cooling water (Figure 32) to obtain esti
mates of mean concentrations of larvae in the cooling water column. These
31

103
102
101
t
<
oc 10°
10
1
10
2
^A
2 ad 12
o
° 70A, 2
° 10
^A
77 A
72
O DETROIT EDISON PUMP
SAMPLES 1976
+ MSU DISCHARGE CANAL,
1976
A MSU, 1974
~ MSU. 1975
O MDNR 06 FT DEPTH ZONE
* MEAN CONC., 1975
O MDNR 06 FT DEPTH ZONE
2 A MEAN CONC, 1976
A
A6
+ O
(0) INDICATES ZERO
CONCENTRA TION
~ 2
CO
A 2
O,
O
+
o
c+
72
+
72
SEE FIG. 8 FOR
LOCATION OF
SAMPLING STATIONS
B Y NUMBER
o
2
6,10.11
2 0^>
10
(0) 11.12
J A I—
(0) 6,10.11,12
(0)7 7 ^
100 120 140
JSHAOJO
160 180
TIME, days
0 O
2,6,10,11.12
o
J I
200 220 240
Figure
32. Larval perch concentration in vicinity
Plant cooling water intake (see Figure 8
for locations of sampling stations).
of Monroe

~ ME A SUREMENTS OB TAI NED IN THE
VICINITY OF COOLING WA TER INTAKE
HIGH ESTIMATE
LOW ESTIMATE
100 120 140
160 1 80
TIME, days
200 220
Figure 33. Larval perch concentrations estimated in Monroe Plant
cooling water (1975).
Data Source: Ref.(4).

estimates are then compared to measurements of concentrations of larval perch
in the upper discharge obtained by MSU (Figure 34). A statistical test of
significance of the difference in the mean values of the two sets of concen
trations shows no significant difference. 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 Edison's 1975 estimate, as a percentage of
total production in Michigan waters. In 1975, an estimated total of 2.9x10®
 5.2x10® perch larvae were produced in Michigan waters. Detroit Edison
estimated that 5.0 x 10^ perch larvae were entrained in 1975, or 1.0%  1.7%
of the estimated production in Michigan waters. In 1976, production declined
to an estimated 8.4x10?  1.4x10? so that the percentage of production
estimated to have been entrained (based upon D.E. estimates) is 0.2%  0.4%,
about 222 of the percentage for 1975. This comparison suggests that Detroit
Edison's estimate of number of larvae entrained in 1976 may be low. If per
centage of production that is entrained in 1976 were the same as in 1975, the
estimated number entrained in 1976 increases to 8.4x10^2.4x10^. Combining
data from Figures 31 and 34, using equation 13, yields an estimate of numbers
killed due to the entrainment cycle of 195,000  2,827,000.
fvntrainnent bv 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 are
published in (11) of numbers of yellow perch larvae entrained by all 18 intakes
in 19/576 and are reproduced in the present report as Tables 1821. Com
bining the estimated mean daily pumping rates given in (11) with estimates of
32

102 
cn
£
o
o
o
C 101 
o
H
<
CC 10°
f
2
LU
U
o
o
10' 
10"2
o PLANT INTAKE PUMP SAMPLES
(Data source, Ref. 9)
+ UPPER DISCHARGE SAMPLES
(Data source, Ref. 4.)
_L
HIGH ESTIMATE
LOW ESTIMATE
100 120
140 160 180
TIME, days
200 220
Figure 34. Larval perch concentrations estimated in Monroe Plant
cooling water (1976).
Data Source: Ref.(4).

the respective 0'—51 depth zones, the author estimated total numbers of larval
yellow perch losses attributable to all power plant operations in MichiganOhio
waters of the western basin to be the following:
Intake 1975 1976
Michigan
Fermi 48,0001,100,000 261,0003,300,000
Monroe 1,432,0009,833,000 195,0002,827,000
Whiting 827,0001,525,000 74,0001,251,000
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 1321 and the above estimates of total losses attributable to all
power plant operations became available after the numerical analysis of pro
duction was completed, the assumption made for purposes of the analyses is:
L(t) = 0
Overall estimates of production can be adjusted by adding estimated losses
due to water intake entrainment mortality.
Analytical Solution to the Differential Equation of Balance for Larval Concen
tration
The equation of balance for larval perch assumes the form
N(t) + p*N(t) = h(t)  h(t25)*e~25p  E(t) (16)
upon substituting 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 Mich
igan 1976  are given in Appendix 6. Equations (A6.7), (A6.9), (A6.ll),
33

(A6.13), and (A6.15) in Appendix 6 were programmed with the parameters h and p
permitted 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 Estinating Parameters h and p
The parameters h (number of perch larvae added to every 100 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 "pre
dicted" value of larval concentration (number of larvae per 100 cubic meters of
water in the reference volume at a given time) given by the solution to Equa
tion (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:
{l N 1 1 h
N ]_^B ^Ci) ~ estimated mean cone. on day t^)2 > (17)
Following the least squares criterion the combinations of h and p which mini
mize the M.S.E. (for a given reference volume and year) are shown in Figures
35, 37, 40, and 42. If either h or p is selected in advance the value of the
A
other that minimizes M.S.E. can be obtained from the appropriate Figure. If h
and p are two values selected by minimizing mean square error in a given case,
Chen from Equation (6), total larval production and 25day survival for the
given reference volume and year is estimated as:
Total Production = d'B'h (13)
34

£ 0.12
<
cc
>
b 0.10
i
<
i—
O 0.03
<
§ 0.06
I—
<
z
> 0.04
<
o
z
<
LU
0.02
0
4.21
3.64 4.09
3.14 3.52
• • •
/
2.71 3 00 ~ '4.12
4.35
CURVE 01
IN FIG. 36
2.37 2.38 2.57 ,'3.56
• • • • " •
y
2.29 2.14 2 23 ,'3.06 3.84
• •••••
2.38 2.05 1.99 ,'2.65 3.38
• • • • •
2 67 2.13 1.89 ,'2.35 3.17
• •••••
~
2 41 1.95 ~ '2.14 2.78
• • • • •
2.22 ~ '2.03
• • •
CURVE 02 IN FIG. 36
I I l l l I I l I I i
1.0 1.4 1.8 2.2 2.6 3.0
PRODUCTION PARAMETER (/?)
Figure 35. Model prediction error for combinations of mortality and
production parameters (Ohio, 1975).

10?
n
E
o
o
o
r>
r~
C
3
C
O
h
<
cc
H
z
LU
CJ
z
o
CJ
CURVE 01.
p  0.09, h = 3.0
PRODUCTION = 1.97 x 109
YOy RECRUITS =
2.08 x 103
0— MEASURED
— PREDICTED
_ CUR VE 02
..
CURVE 02:
p = 0 04, h = 1.5
PRODUCTION = 9.86 x 103
YOY RECRUITS =
3.63 x 108
ASSUMPTIONS.
v[t) = Q
£(r) = 0
Lit) 0
140 160 180
TIME, days
200 220
Figure 36. Predicted vs. estimated larval perch concentrations for
two production  mortality parameter combinations
(Ohio, 1975).
Data Source: Tables 12A and 12B.

>
\
_l
<
I
cc
o
Z>
I—
I <
^ cc
>
_1
<
Q
z
<
UJ
LU
0.20
0.13
0.16 
0.14 
0.12 
0.10 
0.03 
0.77»°i74 .^.°69
~
• •
0 84
0.78 •
0.73 / '' /
0.78 ~*' * 0.73
0 85 0.78 ~ 0 79 /
* * CURVE M2
0.81 / 0 82 IN FIG. 38
• / • • •
0 85 ^ 0.87
t / • •
0 89 ' 0 87
0 99
CURVE Ml IN FIG. 38
4.0 5.0 6.0 7.0 8.0 9.0 10.0
PRODUCTION PARAMETER (h)
Figure 37. Model prediction error for combinations of
mortality and production parameters
(Michigan, 1975).

n
O
O
(U
JD
E
3
C
<
cc
I
z
LU
(J
2
O
CJ
0— MEASURED
— PREDICTED
CURVE M2.
p = 0.19, h = 9.5
PRODUCTION = 6.61 x 10s.
YOY RECRUITS =
5.29 x 106.
CURVE Mh
p = 0.08, h = 4.0,
PRODUCTION =
x 108
Y RECRUITS
77 x 107
ASSUMPTIONS
L(t) = 0
v{t) = 0
E(t) = 0
10"1
TO"2
120
140 160 180
TIME, days
Figure 38. Predicted vs. estimated larval perch concentrations
for two production  mortality parameter combinations
(Michigan, 1975).
Data Source: Table 1.

1010
o.
109
CUR VE 01 IN FIG. 36.
(25DA Y SUR VIVAL = 2.08 x 108)
CURVE 02 IN FIG. 36.
(25DA Y SUR VIVAL = 3.63 x 108)
/
D
CURVE M2 IN FIG. 38.
(25DA Y SURVIVAL = 5.29 x 106)
108
CURVE Ml IN FIG. 38.
(25DA Y SUR VIVAL = 3.77 x 107)
10
10*
_L
0 10 20 30 40 50 60
PERCENT SURVIVAL FOR 25 DAYS
70
Figure 39. Plausible larval perch production  survival
combinations in Western Basin (1975).

0 16
s.014
LLl
c 0.12
>
H
< 0.10
fr
ee
o
5 O.so
<
cc
Z)
5 005
z
>
^ 0 04
Q
Z
<
0.02
0

/
/
*
—
~
4 90
'
S
4 38 4 75 ''
• • /
4 21 4 64 /
* /
3 70 4 08 /
3 48 3 55 / 4 63^\
—
* ~ * * CURVE 01
3 12 308 /4 07 4 81 ,N F,Q 4J
/
2 51 2 84 ,'3 56 4 29

• • / • • • *5 21
2 28 2 34 /3 11 3 84

• i ^ • . • 4 78
2 17
2 10 ,'2 75 3 45
— •
• • • • • 4 34
2 22 1 96
— • «
/ 2.45 3 16
2 00 /
— .• •
~ # * *
2 07
T 94/'
— • •
. CURVE 02 IN FIG 41
2 12
i
2 77
l t l l 1 i t I I f i
1.0 1.4 1 8 2.2 2 6 3.0
PRODUCTION PARAMETER {h)
3.4
Figure AO. Model prediction error for combinations of
mortality and production parameters (Ohio, 1976).

10:
O— MEASURED
PREDICTED
10'
10°
10
1
0
CURVE 01.
j ~ p = 0 09, h = 2.6
PRODUCTION = 1.71 x 109.
r /r^sl YOY RECRUITS = 1.8 x 108
/!
CUR VE 02
p = 0.02, h= 1.2
PRODUCTION = 7.89 x 108
YOY RECRUITS = 4.78 x 10s
(CM (2 2 x 103)
 0—0
ASSUMPTIONS
E(t)= 0
= 0
 0
100 120 140 160 180 200 220
TIME, days
Figure 41. Predicted vs. estimated larval perch concentrations for
tvo production  mortality parameter combinations
(Ohio, 1976).
Data Source: Tables 12C and 12D.

>
H
_i
<
h
cc
O
<
QC
D
h
<
Z
>
_J
<
Q
Z
<
UJ
0.24
0.20
0.16
LJJ
< 0.12
cc
0.08
0.04
0
0.610
0.784 0.348/ 1.15
4 52 2.55 1.18 1.04,
4.19 2.04 1.37
. 2.34
1.81 CURVE Ml IN
FIG. 43.
2.98
J L
CURVE M2 IN
FIG. 43.
i i i i i i '
J L
0 0.4 0.8 1.2 1.6 1.8 2.0 2.4
PRODUCTION PARAMETER {h)
Figure A2. Model prediction error for combinations of
mortality and production parameters
(Michigan, 1976).

102
r>
E
o
o
CD
JD
E
3
c
H
<
QC
h
Z
LLl
o
101
10°
O
u 10"1
TO"2
O— MEASURED
— PREDICTED
CURVE Ml
p = 0.16, h = 2.0
PRODUCTION = 1.39 x 10s
YOY RECRUITS = 2.55 x 106
CURVE M2: p = 008,h = 1.1
PRODUCTION = 7 66 x 107
T YOY RECRUITS =
1.04 x 107
•A 
ASSUMPTIONS.
F(f) = 0
Mf) = 0
/ (r) = 0
100 120
140 160 180
TIME, days
JL
200 220
Figure A3. Predicted vs. estimated larval perch concentrations for
two production  mortality parameter combinations
(Michigan, 1976).
Data Source: Table 9.

CURVE 01 IN FIG. 41.
yOy RECRUITS = 1.8 x 10s
!> 1010
109
CURVE 02 IN FIG. 41.
YOY RECRUITS =
4.78 x 108
OHIO WA TERS
CURVE Ml IN FIG. 43.
YOY RECRUITS = 2.55 x 106
CURVE M2 IN FIG. 43.
YOY RECRUITS = 1.04 x 10?
MICHIGAN WATERS
107
0 10 20 30 40 50 60
PERCENT SURVIVAL FOR 25 DAYS
70
Figure 44. Plausible larval perch production  survival
combinations in Western Basin (1976).

° o w
> H <2
<
<
I—
CO
DQ ^ X
< > I
m cc o
O 3 I
cc GO ^
Q.
0.40
0.30 
0.20 
0.10
0
N DAILY NA TURA L
MORTALITY RATE, p = 0.09
ME A N DAILY NA TURA L
MORTALITY RATE, p = OAS
J I L
0 5 10 15 20
MEAN AGE AT TIME OF ENTRAPMENT, days
Figure 45. Plausible relationship between mean age of larvae at entrainment and
fraction of larvae lost due to entrainment that would have
survived to reach yoy stage.

and:
number of yoy recruits =
= 25 day survival =
= d.B.h.e~25*P (19)
Estimation of h and p proceeds for a given reference volume and year by defin
ing a rectangular network of (h,p) pairs. The prediction error variance is
numerically evaluated for selected (h,p) combinations and recorded as shown in
Figures 35, 37, 40, and 42. The finer the mesh of the grid (the closer to
gether the (h,p) combinations) the more precisely can the parameter combina
tions that minimize prediction error variance be estimated. For example, in
Figures 35 and 40 the haxis is graduated in increments of 0.2 which corres
ponds to an increase in total larval production in the reference volume of
(0.2) (7) (9.393x10^) = 1.31 x 10^ larvae. Therefore, any term on the right
ft
hand side of equation (16) that is less than 10 percent of 1.31 x 10 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 give
the values of p that approximately minimize M.S.E. for given values of the pro
duction 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 i.e.,
biologically unrealistic. For the cases of Michigan waters: in 1975 the
conbmation of (h,p) that minimized M.S.E. is located on the boundary of the
i;rid (n = 9.5, p = .19); for Michigan 1976 the optimum occurs at an interior
35

point of Che grid (h = 2.0, p = .16). A value of p = .19 corresponds Co a
25day survival of 0.9 percenC and p = .16 corresponds Co 1.8 percenC survival
for 25 days. These survival percentages are probably coo low on biological
grounds buC in addicion Chey also reflecC Che lumping of emigraCion and other
water intake losses, L(t), into natural mortality. Overall 25day survival is
judged to be in the 210 percent range. It is clear from the analysis that
production in Ohio waters is much greater than in Michigan waters. It also
appears that changes in production from one year Co the next which are on the
order of 1520 percent are detecCable. IC is reporCed in (12) Chat OcCober
1976 Crawls in the western basin indicated a sevenfold decline in youngof
year perch abundance from October 1975. Inspection and comparison of Figures
35 and 40 suggest that larval production may have declined from 1975 to 1976
in Ohio waters (peak mean abundance was lower in 1976) but it is improbable
based upon the present study, that a sevenfold drop in 25 day larval survival
occurred from 1975 to 1976. If yoy recruitment did, in fact, experience a
sevenfold decrease the hypothesis is therefore suggested that yellow perch
year class strength is heavily influenced during the late post larval phase of
development. The broken lines which mark the M.S.E. estimates of p for fixed
values of h in Figures 35, 37, and 40 should not be interpreted as defining re
lationships between production and 25 day survival because: a) each line is
based upon data collected in a single year only, and b) the slopes are so
steep that net 25 day survival actually decreases as production increases.
Modeling error can affect the locations of (h,p) pairs which minimize
prediction error variance. It was pointed out above that emigration, v(t),
could be on the order of five to ten percent of production and Chat entrain
36

ment mortality, L(t), from water intakes is estimated to be tens of millions.
Both v(t) and L(t) were assumed to be zero for the computer runs described in
the present report. If L(t) and v(t) are programmed as positive functions the
graph of the resulting solution to equation (16) of larval balance will
slightly improve the fit of the model for the case of Ohio 1975 (Figure 36).
It is not clear by simple inspection of the graphs of the other solutions (Fi
gures 38, 41, and 43) whether increasing L(t) and v(t) will cause the predicted
concentrations to more closely fit the estimated concentrations. In any case,
a first order correction can be made to estimates of production obtained by as
sunlng L(t) = v(t) = 0, by adding the estimates of total water intake morta
lity 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). While small differences in the prediction error
variance were observed between the two cases, the numerical values of E(t) were
so small relative to the interval length on the h~axis (Figure 37) that no de
tectable differences for the locations of M.S.E. values of p were observed. As
before a first order correction to production can be obtained by adding total
estimated water intake mortality and total estimated emigration to previously
estimated values of total production. The question of correcting estimates of
production for nodeling errors committed by assuming L(t) = E(t) = 0 is some
what 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 ton percent of total production, the correction could be as great as 2x10^
1arvne.
37

Estimates of Production and Natural Mortality
Single point estimates of production and natural mortality obtained by lo
cating 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 above. On the basis of the above method, however, larval sur
vival over a 25day period following hatching has been estimated to be between
2 and 10 percent. If two million female spawners each deposit nine thousand
eggs and if hatching success is 25 percent a total of 4.5 billion larvae are
hatched. Ten percent survival for 25 days produces an initial youngofyear
population of 450 million. Two percent survival over the same period reduces
the population after 25 days to 90 million. The range of larval production
for which a 25day survival of 210 percent is optimum in the M.S.E. sense is
obtained from Figures 35, 37, 40, and 42 and is the following:
Michiean Waters, 1975
Z Surviving 25 days: 2% 10%
Estimated value of h: 7.5 4.2
Estimated production: 5.2x108 2.9x108
Estimated number surviving
natural mortality 25 days: 1.0x10? 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
7. Surviving 25 days: 2% 10%
Estimated value of h: 2.0 1.2
Estimated production: 1.4x108 8.4x10?
Estimated number surviving
natural mortality 25 days: 2.8x106 8.4x106
Z (killed due to entrainment
on 5th day of life) esti
mated to have otherwise
survived 25 days: 5.5 17.7
38

Ohio Water. 1975
% Surviving 25 days:
Estimated value of h:
Estimated production:
2%
4.5
3.0x109
10%
3.0
2.0x109
Estimated number surviving
after 25 days:
6.0x107
2.0xl08
Ohio Waters. 1976
% Surviving 25 days:
Estimated value of h:
Estimated production:
2%
3.8
2.5x109
102
2.6
1.7x109
Estimated number surviving
after 25 days:
5.0x107
1.7x108
Estimates of production for other 25day survival percentages can be obtained
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, Figures 35, 37, 40, and 42
clearly illustrate this point^. If larval production is high the M.S.E.
estimate of the nean daily natural mortality rate results in lower 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 recruitment requires that marginal recruitment into the yoy
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 concerns
the estimation of larval production and natural mortality for the years 1975
76. The percent loss in recruitment into the youngofyear class attributable
to entrainment mortality at the Monroe power plant is a more realistic measure
of iip.ict than percent loss of larval production because it takes into account
nitur.il mortality of larvae as well as larval production.
\n ostiintc of lean daily natural mortality rate of 0.13 (3.9 percent survival
tor J3 davs) is obtained from Tabic 11 by dividing the difference in peak con
centrations of EPL and PROL by 27 days.
39

Estimated percent loss in nuraer of yoy recruits =
R R R
100 ( °a" !) = 100 (1  gi) (20)
' o o
where:
R0 = number of yoy recruits in Michigan waters in the
absence of the Monroe power plant operation.
= nuraber of yoy recruits in Michigan waters in the
presence of the Monroe power plant operation.
In 1975:
= l.OxlO7 " 2.9xl07
Ro = Rl + r2
where:
R2 = nunber of live larvae killed due to entrainraent that
would have survived 25 (days mean age at entrainraent =
5 days).
Estimated number killed due to entrainraent mortality in 1975 =
= 1.5xl06  S.OxlO6
Percent (killed due to entrainraent on 5th day of life) estimated
to have otherwise survived 25 days =
= 5.5%  17.7%
r2 = 1.5x106x055  8.0xl0^x.177 =
= 3.25xl04  1.42xl06
Therefore, the estimated percent loss in number of yoy recruits is:
Rl R1 10 io7
100 ( 1  =) = 100 (1 =—7r) = 100 (1 ^ r) to
Ro R1 + R2 I.0x10 + 8.25x10
40

9 Q*10
100 (1 : t) = 0.8% to 4.7%
2.9x10 + 1.42x10
In 1976:
= 2.78xl06 ~ 8.4xl06
r2 = 0.46x106*.055 " 0.7xl06x.l77 = 2.53xl04  1.24xl05
Therefore, the estimated percent loss in number of yoy recruits is:
100 (1 j^) = 100 (1 
2.78xl06
o
2.78xl06 + 2.53xl04
8 4v1 f)
100 (1 ^ ?) = 0.9% to 1.5%
8.4x10 + 1.24x10
Analysis of Losses to Standing Crop and the Fishery
The equations of balance for a population are composed of terras that mimic
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 obtained which can then be
studied by variation of process parameters.
In the following, an equation of balance is defined which incorporates lar
val production, larval survival, youngofyear survival, natural mortality of
subadults and adults, and fishing mortality. Estimates of population para
meters are provided which permit a numerical analysis of the impact upon catch
as a result of variations in any of these factors.
Define the following variables and parameters:
N(t) = adult population size (age class II and older fishes)
in year t. [no individuals).
41

N(t) = net annual instantaneous rate of change in adult popu
lation size in year t. [no. • yr.1].
f = mean annual instantaneous mortality rate from commercial
and sport fishing. [yr.1].
m = menn annual instantaneous mortality rate due to causes
other than fishing, entrainment, and impingement.
[yr."1].
Y = mean annual rate of larvae production per individual
in population size N. [no. larvae • individual 1 •
yr. ] .
£ = annual fraction of larvae surviving environmental
forces of mortality for first 25 days to reach young
of year stage. [y.o.y. • larvae1].
s = 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.1].
e n = annual fraction of age class I subpopulation that
survives nonfishing causes of mortality to be re
cruited into adult population. [adults • subadults1].
K = habitat carrying capacity of adult population
[no. adults].
T = maximum life length of adult fishes.
E, = annual loss of larval fishes due to power plant entrain
*" — I
meat. [larvae • yr. J.
Ey = annual loss of youngofyear due to power plant entrain
ment . [y.o.y. • yr. 1 ].
Iy = annual loss of youngofyear due to power plant impinge
ment . [y.o.y. • yr. 1 ].
1^ = annual loss of age class I fishes due to power plant
LTip ingement. [subadults • yr.1].
I\j = 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].
= annual loss of fLshes in age class I and older due to
power plant impingement. [adults • yr.1].
42

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
minus
annual rate of loss of adults which have survived the maximum age T.
In equation forn:
N = ciR  (ra + f) N (21)
or:
N = CiR  (m + f) *N  IA (21.1)
where:
a = i _ e(ra + 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 that is lost annually due to
power plant entrainraent and impingement mortality, including its reproductive
potent ial.
The inferences made about impacts of entrainraent and impingement mortality
will depend upon how one represents or models Rj the recruitment terra in
equations (21) and (21.1).
In the following, the hypothetical subpopulation of fishes absent as a re
sult of entramment and impingement mortality of larvae, juveniles, subadults,
43

and adults will be analyzed using equation (21) as the basic expression for
which the following recruitment model is considered:
Model 1:
R = E . c . s . e™ + (entrained larvae component)
+ E%f . s . e~m + (entrained y.o.y. component)
+ I . s . e® + (impinged y.o.y. component)
+ 1^. . etn + (impinged subadult component)
+ * (impinged adult component)
+ Y • N(t) . £ . s . e™ (reproductive potential component)
Thus, if:
R = recruitment of individuals into age class II group; recruitment
is expressed by the equation:
R = [I%, + em (IA1 + s (I + Ey + £ (E£ + Y • N(t))))] (22)
y.o.y.
s V
A1
r
&
JO
©
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 calcu
44

lating a steady state population size together with fishing harvest for differ
ent 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 hypo
thetical subpopulation of fishes not present due to entrainment and impingement
mortality. The analysis of the second model is limited to a small number of
combinations of population parameters, and is included to provide an indication
of the potential compensatory effects within the perch population in Lake Erie.
Model 2:
R = s * E * Y • N(t) (1  ) 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 = s[e • (y • N(t) (1   E0)  (E + I )] (23)
K x, y y
Model 2 incorporates a parameter, K, representing the habitat carrying ca
pacity for the population. The carrying capacity may change slowly over time
as water quality and interspecific factors of competition change. The carry
ing capacity represents the upper limit of the attainable size of the popula
tion. 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 value,
45

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 popula
tion parameters, as well as losses to the population represented by the terms
E^, ly, Ey, and 1^. The dynamics of recruitment in equation (23) are such
that the population increase follows an Sshaped curve, approaching its equil
ibrium value. The rate of population increase slows down as population den
sity increases, due to a reduced rate of recruitment of larvae into the ju
venile stage. Equation (23) is, no doubt, the simplest way to introduce com
pensation for population density into the dynamics of recruitment . It should
be noted in equation (23) that the product £ • y (number of larvae per indivi
dual surviving to enter youngofyear stage) is multiplied by the compensation
term (1  —), rather than E or y alone. Thus, the expression e • y • (1  ^
K K.
is used to approximate the actual, but unknown function e(N) • y(N) describing
larval survival at 25 days following hatching of eggs. Further, there is no
attenpt 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 En, E , and I are constant throughout, but can be varied
X, y >
from one calculation of equilibrium population to the next.
The effect of entrainment or impingement mortality is analyzed by modeling
the whole population rather than the subpopulation of entrained and impinged
fishes as in the earlier case. Although the quadratic term in equation (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.
^Other quantitative expressions for representing compensatory effects of high
larval mortality are currently in use (20). Research and modeling of compen
satory processes is active.
46

Solutions to Equations
Substituting equation (22) into (21) and solving for N, one obtains:
N(t) = N(0)e~Bt + ct /*" R(x)e^(t~x) dx (24)
o
where:
B=m+fa«s*E«Y» em,
R(x) = I (x) + e~m[I (x) + s(I (x) + E (x) + e • E.(x))]
N A1 y y *¦
and:
N(0) = initial population size.
I (x), I (x). I (x), E.(x) and E (x) may be constants or functions of the
N A1 y x, y
time parameter x. As time t increases, the contribution of the initial popu
lation level N(0) diminishes exponentially. The integral term is an exponen
tially weighted moving average of the contributions of successive recruitments
R(x) in year x in which more distant additions R(x) contribute an exponen
tially decreasing proportion to the total population. If one is interested in
a steady state condition, as t approaches infinity, N(t) approaches, under ap
propriate conditions on R(x),
M _ liiit rt _ , N B(tx) ,
N  a f R(x)e dx
t  «> o
This is the steady state value of the size of the hypothetical subpopulation
lost due to entrninment and impingement mortality. In the following, all im
pingement and entrainment functions are assumed to be constants, and therefore
independent of time. Therefore, R(x) = R = constant.
For this case :
N(t) = [N(0)  " Rlefc + 5 * R (25)
p P
where R is defined above, and:
a = 1  e"(m + *6
^Diensionnl analysis verifies that d'Cs'yc m and (m + f) are conparable
quant it ies
47

where:
t  I = 6.
Equation (25) shows no steady state unless m + f > cfE'S'ye111, i.e., 8 > 0,
which must be true on the average in the environment or the population would
explode. When 3 > 0, the steady state population is:
a —
3 ' R
Model 2 of recruitment is exercised by substituting equation (23) into
equation (21.1) and solving the differential equation:
N = aR  (m + f) • N  I =
= n .s • e »v *N •( 1  —)  a*s »(E + I + e • E )  I 
' K y y & A
where:
 (ra + f) »N
a = 1  e"(m + f)*7
Collecting coefficients of N®, N^, N^:
M = aN2 + bN + c (26)
where:
Zf S * E • Y , , , r\
a =  — L, b = ct'S'C'Y  (m + f)
and:
Solving!
c =  (a*s*(E + I + e • E0) + I ).
y y x, A
N(t) = A +
BA
, . Non a(BA)t
1 ~ e
o
(27)
48

where:
Nq = initial population size
Thus:
c
A
a
and:
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 disturb
ance. 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„, E , I . and I. are sufficiently
£ y y A
large.
Estinates of Entrainment and Impingement Mortality
Cole (4) gave the following 95 percent confidence interval estimates of the
numbers of yellow perch larvae potentially entrained at the Monroe power plant
in 1973, 1974, and 1975 (millions of larvae):
Estimated Number Entrained (millions) Year
Three estimates obtained by the author of numbers of perch larvae entrained in
the power plant cooling waters in 1975 using sampled concentrations of larvae
obtained by Cole in the river channel and in the upper discharge channel, and
(1) 0 < 2.2 < 5.1
(2) 59.6 < 83.1 < 111.5
(3) 13.7 < 29.3 < 44.9
1973
1974
1975
usmg volumes of cooling water published in (7) are:
49

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 en
trained in 1975 (7) which includes prejuveniles or youngofyear fishes. Since
prejuveniles were not counted separately, it is assumed that combined youngof
year mortality due to entrainment and impingement is:
Iy + E = 100,000
This assumption is probably conservative in view of the estimated total
number entrained as reported by Detroit Edison. Based upon Cole's 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 that are entrained,
the estimates of numbers of larvae entrained can be reduced to E^, an estimate
of live larvae killed due to entrainment:
E? (millions killed)
(1) 0  2.856 (1973)
(2) 33.38  62.44 (1974)
(3) 7.672  25.14 (1975)
(4) 1.526  7.986 (1975)
(5) 1.338  11.68 (1975)
(6) 10.86 (1975)
(D.E.) 2.816 (1975)
(7) 0.53 (1976)
(D.E.) 0.36 (1976)
Table 22. Estimates of Entrainment Caused Larval Mortality
50

Estimated Impingement Mortality
Detroit Edison published the following estimates of numbers of fishes
killed due to impingement (7):
(Iv + IaI + Ia) Year
165,365 (excluding Jan.,
Feb., Mar.) 1972
215,032 1973
152,857 1974
171,641 (excluding April
and May) 1975
Table 23. Estimated Impingement Mortality
It is impossible to estimate the individual terms Iy, IA^, Iy from the
data shown above. Therefore, for computational purposes, the quantities IA
and 1^ (adult and subadult mortality, respectively) are each permitted to
assume the values 0, 50,000, and 100,000 independently, so that the sum 1^ +
1^ ranges from 0 to 200,000. When the sura 1^ + 1^ is combined with the
earlier assumption of Iy + Ey = 100,000, it is clear that total impingement
mortality will range over the values shown above.
Estimates of Population Parameters
c: annual fraction of larvae surviving natural environmental forces of
mortality to reach voungofvear stage.
The methodology underlying the estimate o£ E, the annual fractional rate
of survival of larvae from natural environmental forces of mortality to reach
youngofycar stage (25 days after date of hatching), is based upon the
analysis of larval production in U.S. waters of the western basin of Lake Erie
shown above and resulted in an estimate of £ in the rangel:.
^"It is shown in Appendix 8 that the percentage of entrained larvae that would
have survived for 25 days had they not been entrained increases with age at
cntrain^ient and may reach 25%.
51

0.02 < e £ 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 succes
sive years (1972, 1973, 1974, 1975) yield estimates of annual youngofyear
survival fractions of 0.12, 0.19, and 0.33, respectively, using the ratio^:
y.o.v. survival yearlings C.P.E. in year (t)
fraction y.o.y. C.P.E. in year (t1)
The nonthy instantaneous mortality rates, a, corresponding to annual survival
fractions of 0.12 and 0.33 are, respectively,
_ 1_ In .12 = 0.177
12
and
1 In .33 = 0.092
Q = ~ 12
In turn, the monthly instantaneous rates 0.177 and 0.092 yield six months sur
vival fractions which are, respectively,
s = e~l77(6) = 0.346
and
3 = e.092(6) = 0.575.
Thus, the fraction of youngofyear that survives (approximately 6 months) to
2
be recruited into the yearling stage or age class I is :
0.34 £ s £ 0.58.
f: annual instantaneous fishing mortality rate from commercial and sport
fishing.
Based upon an estimate that 20 to 40 percent of all perch vulnerable to
fishing gear will be harvested annually by commercial or sport fisherman (A.
\\ constant coefficient of catchability is assumed.
2
It is reported in (22) that research on postlarval yellow perch mortality
indicates a si:: month survival of approximately 0.49, a value well within
the interval (.34, .58).
52

Jensen, personal communication, 1976), the instantaneous annual fishing morta
lity rate is estimated to be between 0.22 and 0.51. However, it is reported
in (22) that during the period 196878, total annual mortality may have risen
to 70Z. If the annual natural mortality fraction holds at 25%, the implica
tion follows that the instantaneous annual fishing mortality rate may have in
creased to 0.95. Therefore, it is estimated as:
.22 < f < 0.95
m: annual instantaneous natural mortality rate of yellow perch.
The Great Lakes Fishery Laboratory, U.S. Fish and Wildlife Service reports
an estimated natural mortality rate lying in the range^:
0.22 < m < 0.29
Other data relating to natural mortality of yellow perch are reported in
(14) and (15).
y: nean annual rate of larvae production per individual in the subpopu
lat ion.
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 nge class I and older. By definition:
Y = hatching success • number eggs deposited per sexually mature
female spawner
• number sexually mature female spavners per
individual in subpopulation.
It is reported by Scholl (personal communication, 1977) that hatching
success for yellow perch in Lake Erie ranges between 25 and 50 percent:
^"Reference (22) and W. L. Hartman, personal communication, 1976.
53

.25 < hatching success < .50
The number o£ eggs deposited per sexually mature female is reported to range
between 10,000 and 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 female
spawns during her lifetime, the number of age classes included in the subpopu
lation, 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 subpopulation can be
calculated.
To do so, N2 is used to denote the number of individuals entering age
class II under equilibrium conditions. Based upon information provided by the
Ohio Division of Wildlife (12) on sexual maturation of yellow perch of
different ages, it is 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 of any age class are females, that a sexually
mature female spawns in any given year with probability Ps, that fishing
mortality commences with age class III individuals, and that the equilibrium
number of age class I individuals is the fraction of sexually mature
female spawners in the subpopulation of age class II and older fishes may be
calculated from the following:
Number of Individuals Number of Female Spawners Age Class
~ Q II
PoPfN, e~(2m + f) HI
Nie"(3n + POcNieOm + 2f) iv
+ 3f) pspf:4e(4m + 3C) V
Nie(" + pspfN1e~(5m + Af) Vl
+ 5f) osp£N1e(6m + 5f) vu
5A

The fraction of the subpopulation that is sexually mature female spawners may
be defined as:
number of sexually mature female spawners per individual
in subpopulation (age class II  VII) =
r Cm + f) 5(m + f).
PsPf[e + ¦ ¦ • • + e
[1 + e~^n + + + e~5(m + f)j
An important inference that follows is that the fraction of the subpopula
tion that consists of sexually mature females drops as the fishing and natural
mortality rates increase. For example, if f = m = 0.22, the above fraction
is x .60 but if f = m = .52, the fraction drops to pg • p^ x .35. By
assuming that fifty percent of each age class consists of females, and that
the probability of spawning by any given sexually mature female is .8  1.0,
and using the ranges of m and f estimated above, the number of sexually mature
females per individual in the subpopulation consisting of all fishes in age
class II and older is calculated to vary between 0.153 and 0.239."
number of sexually mature female
0.15 < spawners per individual in < 0.24
~ subpopulation (age class IIVII)
Therefore, the parameter y is estimated to lie in the range:
(0.25) (10,000) (0.15) = 375 < y < (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, Y'E's'e m,
follows:
namely:
(375) (0.02) (0.22) (0.75) < Yes'e~m < (3600) (.10) (.58) (.80)
1.23 < ycs'e~m  167.5
55

In the long run, it is required that the mean rate of addition of recruits
to the subpopulation 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 by using as input the continued
annual losses of larvae, juveniles, and adults incurred from entrainment and
impingement mortality. When the reproductive potential of this population is
taken into consideration, and assuming 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 of this hypothetical population. Given its
size, one estimates the annual yield to sport and commercial fishermen by
multiplying the estimated equilibrium value of N by the annual fishing
mortality fraction 1e^.
A computer program was written and sizes, N, of an equilibrium population
and (1 —e~^) N, loss in yield, were calculated:
N = ct,S"1,[lM + e~m(s(E 0 •£' + 100,000) + I,,)]
N x. A1
(m + f)6
cl = 1  e
£' = fraction of larvae ]ost to entrainment that is estimated
to have survived to reach youngofyear stage, had they
not been entrained,
(? = i+ f  a* s •£'• Y*em (2 > 0 is required for equilibrium)
where:
and:
56

e' : .08, .13
s: .42, .50
f: .52, .95
m: .29
Y: 15
E£: 2xl06, IOxIO6, 20xl06, 40xl06
IN: 0, 50,000, 100,000
IA1: 0, 50,000, 100,000
Table 24. Values of Population Parameters and Entrainment
and Impingement Mortalities Used in Calculation of
Potential Impact on Population Size
Calculations of potential losses in yield for different combinations shown
in Table 24 above are given in Tables 2532 below. The parmaters m and y are
held constant in each case.
The value y ~ 15 is held constant and recognizes only a modest reproductive
potential of the population of fishes lost due to entrainment and impingement
mortality. The values of s, and f form eight combinations each of which
corresponds to one of the tables. In each case a constant loss of youngof
year due to entrainment and impingement (ly + Ey) is set equal to 100,000 in
dividuals. Three levels of losses of yearlings and adults (1^1 + are con~
sidered (0, 1x10^, 2x10^) and in each case the loss is split equally (1^ =
1^) between those two stages. All losses in yield are expressed in units of
pounds of fish, assuming 3.5 fish per pound. The entries in Tables 2532 are
calculated from equation 2835, respectively, each of which is a special case
57

of Che equation given above for potential reduction in annual yield under
equilibrium conditions. The coefficients of IN, IA^, and in equations 2835
are the factors that 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 translates into a
potential annual loss to the fisheries of 1x10^ x .007 = 7000 pounds.
l\i + :N
e'
II
l/i
OO
o
II
.42; f =
.52
200,000
68262
124262
194262
334262
100,000
45262
101262
171262
311262
0
22262
78262
148262
288262
2.0 10.0 20.0 40.0
E^: (millions)
Table 25. Estimated Potential Loss in Yield (pounds)
Loss in yield: 0.263 I + 0.197 I + 0.007 E£ + 8262 (28)
1A1+ :N
£' =
o
CO
cn
II
.42; f =
.95
200,000
52116
93259
144687
247544
100,000
34387
75530
126959
229816
0
16658
57801
109230
212087
2.0 10.0 20.0 40.0
E^: (millions)
Table 26. Estimated Potential Loss in Yield (pounds)
Loss in yield = 0.203 I + 0.152 I + .005 E + 6373 (29)
58

i\i ~ in
e1
11
o
00
CO
II
50; f = .52
200,000
84643
156643
246643 426643
100,000
57193
129193
219193 399193
0
29743
101743
191743 371743
2.0
10.0
20.0 40.0
E^: (millions)
Table 27. Estimated Potential Loss in
Yield (pounds)
Loss in yield:
0.314 IN +
0.235 IA1 +
0.009 E£ + 11743
I \1 + IN
e'
= .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^: (millions)
Table 28. Estimated Potential Loss in Yield (pounds)
Loss in yield = 0.221 IN + 0.165 IA1 + 0.007 E£ + 8265 (31)
59

i\i + In
£' =
.13; s =
.42; f =
52
200,000
163144
347144
577144
1037144
100,000
113494
297494
527494
987494
0
63844
247844
477844
937844
2.0
10.0
20.0
40.0
E£: (millions)
Table 29. Estimated Potential Loss in
Yield (pounds)
Loss in yield = 0
568 IN + 0
.425 Iai +
0.023 Eo
+ 17844
In + I \j
£' =
.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^: (millions)
Table 30. Estimated Potential Loss in
Yield (pounds)
Loss in yield = 0
279 IN + 0
209 Iai +
0.011 Ej,
+ 8765
60

l\\ + Im
£'
= .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
E^: (millions)
Tabla 31. Estimated Potential Loss
Loss in yield = 1.32 + 0.987 1^1
20.0
in Yield (pounds)
+ 0.064 E^ + 49368 (34)
I\1 + I\j
£ '
= .13; s =
.50; f =
.95
200,000
106590
242590
412590
752590
100,000
76690
212690
382690
722690
0
46790
182790
352790
692790
2.0 10.0 20.0 40.0
E^: (millions)
Table 32. Estimated Potential Loss in Yield (pounds)
Loss in yield = 0.342 IN + 0.256 IA1 + 0.017 + 12790 (35)
Since the annual loss in yield is never constant even under equilibrium
conditions, the estimates given in Tables 2532 are reduced to estimates of a
single weighted mean annual loss for each of the two values of £' that were
selected. In order to carry out this reduction, a probability distribution
must be assigned to the values appearing in Tables 2528 and Tables 2932.
61

Such an assignment should give recognition to the estimates contained in
Tables 22 and 23. It should also reflect estimates of recent fishing pressure
and youngofyear survival which are assumed to be independent of each other.
Based upon an interpretation of Tables 22 and 23, the following distribution
of weights is assigned to each table entry for each of the four Tables 2528.
The distribution is applied again to Tables 2932, so that two weighted mean
estimates of potential annual loss in yield are obtained.
wt:
.25
XA1 + TN
each
s  f
combination
200,000
.016
.054
.016
.002
100,000
.029
.101
.029
.003
0
0
0
0
0
Er
2.0
10.0
20.0
40.0
Wt:
.045
155
.045
005
Table 33. Probability Weights Assigned to Each Table Entry.
The entries m the main body of the tables are obtained by multiplying
each combination s  f) by the respective weights contained in
the marginal distributions on E^, 1^ + 1^, and s  f. The marginal distribu
tions assigned to E^, + 1^, are given in Tables 34 and 35.
62

XAI + JN
Wt. Assigned .
200,000
.35
100,000
.65
0
0
Table 34. Marginal Probability Distribution
Assigned to 1^ + 1^
ES,
Wt. Assigned
40x10
.02
20x10
.18
10x10
.62
2x10
.18
Table 35. Marginal Probability Distribution
Assigned to
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 e' = .08 and e' = .13, respectively. Therefore, the potential mean
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 reduction in total harvest over a
63

period of years is expected. If fishing pressure is increased in an attempt
to oaintain 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 coupled with excessive harvests, could tip the yellow
perch fisheries into an irreversible decline. It is clear from examination of
catcheffort and stock assessment data collected for the past twenty years
that the combined yellow perch harvest has been declining for the past 79
years, and the population presently is in a depressed condition. The major
reasons for this condition are over exploitation and poor recruitment, but the
fact remains that entrainment and impingement mortality from power plant
cooli.ng 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
Immediate effect upon the harvest would be a reduction, 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,
entrainment and mpingeraent mortality will actually increase in absolute terms
(numbers entrained and impinged), rather than decrease. The differential
npact of entrainment and impingement mortality, however, would be lessened,
due to the presence of a larger reproductive base. Thus, the impact of a
given level of entrainment and impingement mortality upon the yellow perch
population is nost severe when the population is in a depressed condition, as
64

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
increase, a point is reached 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. Denoting the compensation
fraction by <5, the actual loss in yield is estimated as:
actual loss in yield = potential loss x (1 —

36). Note from equation (26) that the compensatory term affects the rate of
recruitment into the age class I subpopulation which is:
a*s*E*Y*N*(l  7)
K.
the rate of recruitment per individual into the age class I and older popula
tion is:
ti N>
a* s •£•,• (I 
Since compensation undoubtedly occurs separately through the terras y and
£, implying that both Y and £ are functions of N, the above expression may be
considered to be a first order representation of some actual but unknown com
pensatory mechanism operative in the population.
It is seen in Table 36 that if reproductive potential is high (y = 300 
1500), compensation can effectively eliminate the effects of entrainment and
impingement 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 popula
tion under conditions of high fishing pressure and moderate losses due to en
trainment 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 7 gives an indication of the statistical variation in the equili
briuu population level as £ and y fluctuate from year to year. Although his
torical data on year class strength suggests that annual larval survivals are
correlated so that annual fluctuations may be less than the value calculated,
natural environmental factors creating large variations in population size are
sufficient to nask smaller systematic annual losses imposed by man.
66

Annual
Y
ZA
E + I
y y
f
Harvest (lbs
1500
0
0
0
.37
4,312,660
1500
lxlO5
lxlO5
lxlO7
.37
4,311,976
1500
lxlO5
lxlO5
lxlO7
.52
5,625,718
1500
lxlO5
lxlO5
2xl07
.37
4,311,082
1500
lxlO5
lxlO5
2xl07
.52
5,624,922
300
lxlO5
lxlO5
lxlO7
.37
3,885,591
300
lxlO5
lxlO5
lxlO7
.52
4,957,475
300
lxlO5
lxlO5
2xl07
.37
3,882,235
300
lxlO5
lxlO5
2xl07
.52
4,952,952
300
0
0
0
.37
3,890,979
75
0
0
0
.37
2,309,674
75
lxlO5
lxlO5
lxlO7
.37
2,272,832
75
lxlO5
lxlO5
lxlO7
.52
2,431,838
75
lxlO5
lxlO5
2xl07
.37
2,249,305
75
lxlO5
lxlO5
2xl07
.52
2,393,347
50
0
0
0
.37
1,255,471
50
lxlO5
lxlO5
lxlO7
.37
1,145,857
50
lxlO5
lxlO5
lxlO7
.52
0
50
lxlO3 
lxlO5
2xl07
.37
1,064,052
50
lxlO5
lxlO5
2xl07
.52
0
Table
36. equilibrium Harvest Under Different Conditions of
Fishing
Prcs
sure, Reproductive
Potential, and
Entrainment
and Impingement
Losses: K =
5xl07; e = .08
; s = .26; m
= .37
67

REFERENCES
I. Larval Fish Survey in Michigan Waters of Lake Erie, 1975. Prepared by W.
Hcmmick, 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 ot Lake Erie. Michigan Department ot 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. Entrainraent at a OnceThrough Cooling System on Western Lake
Erie, Vols. I and II, Institute of Water Research and Department of
Fisneries and Wildlife, Michigan State University, East Lansing,
Michigan, January, 1977.
5. Hcrdendorf, 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. , The Ohio State University Center for Lake Erie Area
Research, Columbus, Ohio, April 1976.
6. Hcrdendorf, 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. o3, 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. Polgnr, T.T. Striped Bass Ichthyoplankton Abundance, Mortality, and
Production Estimation for the Potomac River Population. Proceedings of
uie Commence 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.

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
Entrainnent, Large Lakes Research Station, U.S.E.P.A., Grosse lie,
Mi.cni.gan, August 1977.
11. 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 Ohio's 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 Gro'n
Road, Grosse lie, Michigan, p. 22.
14. Brazo, D.C., Tack, P.I., and Liston, C.R. Age, Growth and Fecundity of
Yellow Perch, , 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, W.L. 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. Hcang, 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, \.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.

20. Van Winkle, W., Christensen, S.W., Kauffman, G. Critique and Sensitivity
Analysis of the Compensation Function Used in the LMS Hudson River
Striped Bass Models, Environmental Sciences Division Publication No. 944,
Oak Ridge National Laboratory, December 1976, pp. 830.
21. Cardlner, K.D. 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, Grosse He, Michigan, dated 32378.

TABLE 1
Observed Densities of Larval Yellow Perch
in Michigan Waters: 1975
Data Source: Ref. (2).
Depth Zone
Volume Represented
Date
n rl
iJUU
Stations
106 M3
6/46/5
6/96/12
6/186/24
O'n'
18
5.6
0.64
0
19
0,3.19,3.19,
0,0,0,0,0
3.19,0.46
20
46.33
3.90
6 ' — 12 '
1
0.42
7.13
0
6.20
4
51
0
0
0.53
0.35
1
0.42
0
0
0
11
6.06
5.01
14
4.98
1.57
12118'
8
0
0
0
0
12
82
1.11
0
15
5.99
2.10
17
1.10
11.45
18'2A '
5
0.62
0
0.37
1.04
9
232
0.40
0
0.57
0
13
0
0
16
0
0.72
24 * — 30'
6
0
0
0
0.31
10
0.36,0,0,0
0.68
127
1.72,0.66,
„_ , , „6 3
1.57,0.94,
Total: 497.6 x 10 M
0.99

TABLE 1 (Continued)
Depth Zone
Date
j
Stations
6/307/2
7/147/16
7/287/30
8/118/14
0'6'
18
0
0
0
0
19
0,0,0,0,0,
0
0
0
20
0
0
0
0
61121
1
0
3.00
0
0
0.33
0.33
0
0
4
0
0.36
0
0
0
0.32
0
0
7
0
0
0
0
0
0
0
0.35
11
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
12'181
8
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0.35
0
18'241
5
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
24'301
6
0
0.35
0
0
0
1.22
0
0
10
0,0,0,0,0,
0
0
0.38

at ii
~
18
19
20
m
1
A
7
11
14
"Us"
8
12
15
17
zM
5
9
13
16
^30
6
TABLE 1 (Continued)
Date
9/29/5
0
0
0
0
0
0
0
0
0
0
0
0
0
0 Note: When two values are given for a
0 single station on a given date,
0 the lower and upper values are
0 measurements at the bottom and
0 top of the water column, respec
0 tively. If a single value is
0 given, it is an average repre
0 senting the entire water column,
usually not more than three feet
— in depth.
0
0
0
0
0
0
0
0
0
0
0

TABLE 2
Results of Night Sampling by MSU on May 21, 1975
(// Perch Larvae/100 M^)
Integrated Tow
1
Replication No.
2 3 4
5
Statistics
X 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
Surface
1
Replication No.
2 3 4
5
Statistics
x 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
Mid Depth
1
Replication No.
2 3 4
5
Statistics
x 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
Bottom
1
Replication No.
2 3 4
5
Statistics
x s
Pro L.
Post L.
21.7 11.3 5.7 11.0 9.0
24.8 5.7 0 8.2 6.0
11.7 6.00
8.9 9.37

TABLE 3
Results of Night Sampling by MSU on May 22, 1975
(// Perch Larvae/100 M"^)
Integrated Tow
Replication No.
Statistics
1
2 3 4
5
x 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
Surface
Replication No.
Statistics
1
2 3 4
5
x s
Pro L.
0
0 0 0
0
0 0
Post L.
0
0 0 0
0
0 0
Mid Depth
Replication No.
Statistics
1
2 3 4
5
X 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
Bottom
Replication No.
Statistics
1
2 3 4
5
x s
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

TABLE 4
Results of Night Sampling by MSU on May 23, 1975
(# Perch Larvae/100 M"^)
Integrated Tow
1
Replication No.
2 3 4
5
Statistics
x s
Pro L.
Post L.
7.2
8.4
5.0 8.3 6.0
23.6 15.4 25.0
2.4
14.4
5.8 2.26
17.4 6.90
Surface
1
Replication No.
2 3 4
5
Statistics
x s
Pro L.
Post L.
0
0
3.2 0 3.3
0 0 0
0
0
1.3 1.78
0 0
Mid Depth
1
Replication No.
2 3 4
5
Statistics
x s
Pro L.
Post L.
5.8
8.7
0 5.8 5.5
11.9 5.8 5.5
5.4
10.7
4.5 2.52
8.5 2.86
Bottom
1
Replication No.
2 3 4
5
Statistics
x s
Pro L.
Post L.
5.9
29.7
6.5 6.4 10.9
22.6 16.0 38.2
5.8
14.5
7.1 2.15
24.2 9.88

TABLE 5
Results of Night Sampling by MSU on June 16, 1975
(// Perch Larvae/100 M^)
Integrated
Tow
Replication No.
Statistics
1
2
3
4
5
x" s
Pro L.
0
0
0
0
0
0 0
Post L.
8.8
8.6
i 17.9
1.0
12.1
9.7 6.14
Surface
Replication
No.
Statistics
1
2
3
4
5
x s
Pro L.
0
0
0
0
0
0 0
Post L.
2.9
0
2.8
0
0
1.1 1.56
Mid Depth
Replication
No.
Statistics
1
2
3
4
5
x" s
Pro L.
* 0
0
0
0
0
0 0
Post L.
2.5
5.1
8.9
0
7.3
4.8 3.59
Bottom
Replication
No.
Statistics
1
2
3
4
5
x" s
Pro L.
0
0
0
0
0
0 0
Post L.
9.5
17.4
4.9 14.2
10.1
11.2 4.78

TABLE 6
Results of Night Sampling by MSU on June 18, 1975
(// Perch Larvae/100 M^)
Integrated Tow
Replication No.
Statistics
1
2
3 4
5
x" s
Pro L.
0
0
0 0
0
0 0
Post L.
1
1
5.1 2.1
1.9
2.2 1.69
Surface
Replication No.
Statistics
1
2
3 4
5
x s
Pro L.
0
0
0 0
0
0 0
Post L.
0
0
0 0
0
0 0
Mid Depth
Replication No.
Statistics
1
2
3 4
5
x s
Pro L.
"o
0
0 0
0
0 0 
Post L.
0
0
0 15.1
0
3.0 6.75
Bottom
Replication No.
Statistics
1
2
3 4
5
X s
Pro L.
0
0
0 0
0
0 0
Post L.
2.4
7.3
i 9.3 17.2
15.9
10.4 6.15

TABLE 7
Results of Night Sampling by MSU on June 19, 1975
(// Perch Larvae/100 M^)
Integrated
Tow
Replication No.
Statistics
1
2
3
4
5
x s
Pro L.
0
0
0
0
0
0 0
Post L.
2.2
0
2.2
0
0
0.9 1.2
Surface
Replication No.
Statistics
1
2
3
4
5
x s
Pro L.
0
0
0
0
0
0 0
Post L.
0
0
0
0
0
0 0
Mid Depth
Replication No.
Statistics
1
2
3
4
5
Y s
Pro L.
0
0
0
0
0
0 0
Post L.
0
0
0
0
0
0 0
Bottom
Replication No.
Statistics
1
2
3
4
5
x" s
Pro L.
Post L.
0 0 0 0 0
8.7 2.6 10.0 0 0
0 0
4.3 4.8

TABLE 8
Sunmary of Night Sampling Results by MSU in MayJune 1975
(// Perch Larvae/100 M"^)
Day
142
143
144
168
170
171
(1)
Intcg.
Tow
33.48
19.90
23.14
9.68
2.22
0.88
(2)
Surface
(S)
29.00
0
1.30
1.14
0
0
(3)
Mid
Depth
on
57.66
3.62
13.02
4.76
3.02
0
(4)
Bottom
(B)
20.68
35.12
31.30
11.22
10.42
4.26
(5)
Avg. of
S,M,B
35.78
12.91
15.21
5.71
4.48
1.42
(6)
Avg. of
(l)+<5)
34.63
16.41
19.18
7.70
3.35
1.15

TABLE 9
Observed Densities of Larval Yellow Perch
in Michigan Waters: 1976
Data Source: (3,4)
Depth Zone
and
MDNR
Stations
Volume Represented
Prol.
4/13
MDNR
EPL
LPL
0' 6'
(10b M3)
18
19
20
5.6
0
0
0
0
0
0
0
0
0
6'12'
1
4
7
11
14
51
12 ' — 13'
8
12
15
17
82
18' 24 '
5
9
13
16
232
24'30 '
6
10 127
3
Note: All concentrations are in units of ///100 M .
Note: Tor MDNR data: When two values are recorded at a single station and
date, upper and lower values denote measurements at surface and bot
tom, respectively.
Note: No entry denotes no sample available.
Note: MSU samples taken only in general vicinity of MDNR stations.

TABLE 9 (Continued)
Depth Zone
A/2627
A/27
4/28
4/28
and
MDNR
MSU
MDNR
MSU
Stations
Prol
EPL
LPL
Total Larvae
Prol
EPL
LPL
Total Larvae
0
1
o
18
0
0
0
586.5,49.7,
11.7
36.1,12.9
19
0.911
0
0
3.7,23.6,
29.0,18.6
20
0
0
0
5.0,51.8,
26.1
64.4
61 12 1
1
0
0
0
1.18
0
0
4
0.878
0
0
0.392
0.784
0
7
1.32
0
0
2.74
0
0
11
0.9
11.5
14
6.9,102.9,
130.1
142.9
12' 18'
8
3.3
0.439
0
0
0.392
0
0
0
12
0
0
0
0
0.413
0
0
8.0
15
17
18 '241
5
1.7,0
0
0
0
1.0,0
0
0
0
5.0,1.0
9
0
0
0
1.0,4.1
0
0
0
0,0,0
13
0
0
0
0
0
0
0
2.1
16
o
1

TABLE 9 (Continued)
Depth Zone
and
Stations
Prol
4/29
MDNR
EPL
LPL
4/29
MSU
Total Larvae
Prol
5/14
MDNR
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
9.38
0
0
0
0
0
0
0
0
4.8
9.2
12 *IS'
8
12
15
17
1.78
8.63
0.909
9.59
0
0
0
0
0
0
0
0
3.7
2.1
0
13'24 1
5
9
13
16
0.957
0
0
0"
0
0
0
0
24'30' !
6
10

TABLE 9 (Continued)
Depth Zone
and
Stations
Prol
5/161
MDNR
EPL
8
LPL
5/16
MSU
Total Larvae
5/18
MSU
Total Larvae
0' 6 1
18
19
20
0
2.2,0
0
1.1,0
6 1 121
1
4
7
11
14
1.84
0
0
0
0
0
0
0
0
0
0
0
0
0
f—•
f
1
o;
8
12
15
17
1.9
0
0
0
18'24 '
5
9
13
16
0.0,1.0
4.7,3.2
0
0
1.0,0,1.6
0,3.0
0
'30'
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

TABLE 9 (Continued)
5/24 5/26
Depth Zone
5/24
MSU
5/2526
MSU
and
MDNR
Total
MDNR
Total
Stat iorvs
Prol
EPL
LPL
Larvae
Prol
EPL
LPL
Larvae
0' 6 1
13
0
47.7
0
3.0,1.0
1.1,2.1
19
0.456
1.37
0
20
0
1.95
0
0,29.5,
0.8,3.4,
7.3
6.5,2.6
6'12'
1
0.303
0.303
0
0.710
1.07
0
4
0
0
0
0
1.96
0
7
0
0
3.44
0
1.60
0
11
0,0
0
0.878
0
0.9,2.8,
0
1.57
0
2.7
14
0
0
5.24
1.9,1.0,
0,0,5.7
0
1.12
0
0,0
12 ' 13 '
8
2.0
0
0
0
3.0
0
0.784
0
12
0,1.0
0
0.439
0
0
0
0
0.392
15
0
0
0.878
0
0.344
0
17
0
1.32
0
0
0
0
CM
1
CO
*
5
9.7
0
9
0
0
0
0
1.96
0
13
1.0,1.9,
0
0.439
0
4.0
0
0.784
0
0,0,4.5
16
0
0
0
0
0
0
24'301
6
0
12.3
0
0
12.5
0
10
0
0
0
0
0
0

TABLE 9 (Continued)
Depth Zone
6/7
6/8
and
MDNR
MDNR
Stations
Prol
EPL
LPL
Prol
EPL
LPL
0' 6'
18
0
0
0
19
0
1.37
0
20
0
0
4.39
6' — 121
1
0
0
0
0
0.797
0
4
0
0
0
0
0
0
7
0
0
0
0
0
0
11
0
0
0.505
0
0.459
0
14
0
0
0
0
0
0
121181
8
0
0
0
0
0
0
12
0
0
0
0
0.358
0
15
0
0
0
0
0
0
17
0
0
0
0
0
0.437
18124'
5
0
0
0
0
0.392
0
9
0
0
0
0
0.858
0
13
0
0.478
0
0
0.08
0
16
0
0
0
0
0
0
24'30'
6
0
0
0
0
0
0
10
0
4.45
0
0.909
0.454
0

TABLE 9 (Continued)
6/14 6/21 6/26
Depth Zone
MSU
MSU
MSU
and
Total
Total
Total
Stations
Larvae
Larvae
Larvae
0' 61 
0,3.3
0,0,0,0,0
0,0
0,0,0,0,0,0
0,0,0,0,0
0
0,0,0,2.0
0
61121
0
0
121IS'
0
0
0
0
18'24 '
0
0
0,0,0,0,0,0
0,0,0,0,0,(
24 ' — 30 '
0,0,14.4,12.4
0,0,0,0,0,0,(
0,0,0

TABLE 9 (Continued)
Depth Zone
and
Stations
Prol
6/29
MDNR
EPL
LPL
01 61
18
19
20
0
0
0
0.636
0
0
0
0
0.488
6' 12'
1
4
1
11
14
12'18'
8
12
15
17
13'2i '
5
9
13
16
24 *30'
6
10

TABLE 9 (Continued)
Depth Zorie
7/6
7/9
7/1920
and
MDNR
MDNR
MDNR
Stations
Prol
EPL
LPL
Prol
EPL
LPL
Prol
EPL
LPL
o'6'
18
0
0
0
0
0
0
19
0
0
0
0,0,0
0,0,0
0,0,0
0,0
0,0
0,0
20
0
0
0
0
0
0
6'12'
1
0
0
0.583
0
0
0.583
0
0.516
0
0
0
0
0
0
0
0
0.967
0
4
0
0
0
0
0.392
0
7
0
0
0
0
0.439
0
11
0
0
0
0
0
0
14
0
0
0
0
0
0
12118'
8
0
0
0
0
0.516
0
12
0
0
0
0
0
0
15
0
0
0
0
0
0
17
0
0
0
0
0
0
18124 '
5
0
0
0
0.350
0
0
9
0
0
0
0
0
0
13
0
0
0
0
0
0
16
0
0
0
0
1.09
0
24130'
6
0
0.583
0
0.406
0
0
10
0
0
0
0
0
0

TABLE 9 (Continued)
Depth Zone
7/21
7/28
8/3
and
MDNR
MDNR
MDNR
Stations
Prol
EPL
LPL
Prol
EPL
LPL
Prol
EPL
LPL
0' 6 1
18
0
0
0
19
0
0
0
20
0
0
0
6 '12'
1
4
0
0
0.334
0
0
0
7
0
0
0
No yellow perch
0
0
0
after 8/3.
11
0
0
0
0
0
0
14
0
0
0
0
0
0
12'181
8
0
0
0
0
0
0
12
0
0
0.369
0
0
0
15
0
0
0
0
0
0
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
18'24' 1
5
0
0
0
0
0
0
9
0
0
0
0
0
0
13
0
0
0
0
1.76
0
16
0
0.388
0
0
0
0
24130'
6
0
0
0
0
1.70
0
10
0
0
0
0
0
0

TABLE 10
Mean Concentration of Yellow Perch in
Michigan Waters: 1976
Day Mean Standard Error (S.E.) Mean + 1 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
Not e: Day 120 = 1 May.
Data Source: Table 9
Calculations given in Appendix 3.

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
153
0.041
0.386
0.056
0.483
138
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

TABLE 12A
Means and Standard Deviations of Larval Perch
Concentrations in Ohio Zones AE, 1975
Data Source: Reference (5)
Depth Zone
Sector
A
1
2
3
4
5
6
n
Time
X
s
X
s
X
s
X
s
X
s
X
s
May 1214












May 2225
15.75
n=8
13.08
7.00
n=4
8.72
5.00
n=4
3.56






June 14
12.12
n=8
8.1
4.75
n=4
4.65
1.25
n=4
0.96






June 1117
18.37
n=8
51.57
1.50
n=4
3.00
0
n=4
0






June 2123
2.75
n=8
3.99
0
n=4
0
0
n=4
0






July 13
0
0
0
0
0
0






July 1115
0
0
0
0
0
0






Aug. 14
0
0
0
0
0
0






Aug.27
Sept. 8
0
0
0
0
0
0
_
_
_

TABLE 12A (Continued)
Depth Zone
Sector
B
Tine
1
2
3
4
5
6
X
s
X
s
X
s
X
s
X
s
X
s
May 1214












May 2225






1.25
n=4
2.5
0.50
n=4
0.58
1.50
n=4
3.0
June 14






0
n=2
0
0
n=2
0
1
n=2
1.41
June 1117






0
0
0
0
0
0
June 2123






0
0
0
0
0
0
July 13






0
n=2
0
0.25
n=4
0.50
0
n=2
0
July 1115






0
0
0
0
0
0
Aug. 14






0
0
0
0
0
0
Aug. 27
Sept. 3






0
0
0
0
0
0

TABLE 12A (Continued)
Depth Zone
sector
C
Time
1
1
1
1
b
X
s
X
s
3T
s
X
s
X
s
X
s
May 1214
49.5
n=10
156.53
78.5
n=6
139.3
0.5
n=6
1.22
0
n=4
0
0
n=4
0


May 2225
614.12
n=8
1732
72.12
n=8
115.0
3.33
n=6
6.74
4.5
n=4
4.8
10.5
n=4
17.8


June 14
2.94
n=8
8.11
1.94
n=8
1.77
2.0
n=6
3.63
0.5
n=4
0.58
0.25
n=4
0.50


June 1117
0
n=8
0
0.31
n=8
0.37
0
n=6
0
0
n=4
0
0
n=4
0


June 2123
0.37
n = 8
0.98
0.17
n=8
0.11
0
n=3
0
0
n=2
0
0
n=2
0


July 13
0
0
0
0
0
0
0
0
0
0


July 1115
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



TABLE 12A (Continued)
Depth Zone
aeccor
D
l
i
a
j
t>
Time
s
Y
s
Y
s
s
•x
s
Y
s
May 1214
0.25
n=4
0.5
6.0
n=4
12.0
0
n=4
0
0.75
n=4
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
June 2123
0
0
0
0
0
0
0
0
0
0
0
0
July 13
0
0
0
0
0
0
0
0
0
0
0
0
July 1115
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

TABLE 12B
Dace
Estimated Abundance of Larval Perch
in Ohio Zones AE, 1975
Sector
B C
5/1214
5/2225
6/14
6/1117
6/2123
7/13
7/1115
8/14
8/27 to 9/8
1.09x10 *
2.41xl0?
1.35xl07
1.19xl07
1.53xl06
0
0
0
0
0**
3.05x10'
1.06xl07
0
0
2.43xl0€
0
0
0
2.05x10
4.14x10
2.30x10'
7.56x10"
4.95x10"
0
0
0
0
8
8
3.32x10
9.24x10'
3.98xl07
9.95x10"
0
0
0
0
0
3.47x10
2.21x10
7.72xl07
5.02x10"
0
0
0
0
0
8
*: Estinatcd by using average concentrations in Zones C,D and E.
**: Zone B not sampled on 5/1214.

TABLE 12C
Estimated Mean Concentration in Ohio Waters,
1975 (Zones AE)
Date
Mean
Concentration.
(Mo. per 100 M )
Standard Error
(S.E.)
Mean + 1 S.E.
5/1214
2.38
1.93
(4.5xlO1, 4.31)
5/2225
8.36
2.74
(5.62, 11.10)
6/14
1.75
6.3xl0_1
(1.12, 2.38)
6/1117
1.51xl0_1
6.6xl0_1
(0, 8.Ixl0_1)
6/2123
2.22xl0~2
8.7xl0~2
(0, l.lxlO"1)
7/13
2.60xl02
1.5xl0"2
(l.lxlO2, 4. Ixl0~2)
7/1115
0
0
8/14
0
0
8/27 to 9/8
0
0

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;iay 1
6.9xl06
4.9xl06
3.9xl06
0
0
0
May 811
1.3xl06
9.3xl05
2.6xl06
0
0
0
May 2023
7.9xl05
0
b.3xl05
0
0
0
May 30 (Partial)






June 79
0
7.0xl05
0
0
0
0
June 1925
0
0
0
0
0
0
June 30July 7
0
0
0
0
0
0

TABLE 12D (Continued)
Sector B \ Depth
\ Zone
Date \
1
2
3
4
5
6
Apr. 1216
0
0
0
Apr. 2123 (Partial)



Apr. 28>!ay 1
0
0
0
May 811
A.OxlO6
2.AxlO6
1.6xl0?
May 2023
0
0
0
May 30 (Partial)



June 79
3.9xl06
0
0
June 1925
0
0
0
June 30July 7
0
0
0

TABLE 12D (Continued)
Sector C \ Depth
\ Zone
Date \
1
2
3
A
5
6
Apr. 1216
0
0
0
0
0
Apr. 2123 (Partial)
5.4xl04
0
0
0
0
Apr. 28May 1
3. OxlO6
2.6xl08
2.6xl08
5.7xl07
2.4xl06
May 811
7.9xl05
1.2xl06
l.lxlO6
7.6xl06
1.2xl06
May 2023
4.3xl05
4.3xl06
6.3xl06
/r
1.9x10
3.6xl06
May 30 (Partial)





June 79
0
0
0
0
0
June 1925
0
0
0
0
0
June 30July 7
0
0
0
0
0

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)






Apr. 28May 1
2.3xl06
6.8xl06
3.lxlO5
1.7xl0?
1.5xl07
8.0xl06
May 811
5.9xl05
5.3xl06
2.8xl06
8.7xl06
8.9xl07
3.5xl0?
May 2023
1.8xl05
1.8xl05
6.1xl05
1.4xl07
l.OxlO7
0
May 30 (Partial)
0
6.0xl04
A.6x10^
0
0
1.6xl06
June 79
0
6.0x10^
0
0
0
0
June 1925
0
0
0
0
0
0
June 30July 7
0
0
0
0
0
0

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. 28May 1
0
0
5.5xl06
6.9xl0?
0
0
May 811
6.0xl05
1.5xl06
3.9xl07
2.3xl0?
5.8xl0?
1.3xl08
May 2023
3.5x10^
l.OxlO6
3.5xl06
3.3xl06
3.6xl06
3.8xl06
May 30 (Partial)
0
6.6xl05
0
0
1.8xl06
0
June 79
0
0
0
0
0
0
June 1925
0
0
0
0
0
0
June 30July 7
0
0
0
0
0
0

TABLE 12E
Estimated Abundance of Larval Perch
in Ohio Zones AE, 1976
Date
Sector
C
4/1216
4/2123
4/28 to 5/1
5/811
5/2023
5/30
6/79
6/1925
6/30 to 7/7
0
0
1.57xlO?
4.83>;10£
1.22x10£
7.0x10"
0
0
0
2.24xlo'
0
3.9xl06
0
0
0
5.4x10*
5.83x10
1.19xl07
1.65xl07
0
0
0
8
4.94x10
1.41x10
2.50x10'
6.26xlOC
6.0x10*
0
0
8
7.45x10
2.52x10"
1.52x10'
2.46xlOC
0
0
0

TABLE 12F
Estimated Mean Concentration
in Ohio
Waters, 1976 (Zones
AE)
Date
Total Abundance
Mean
Concentration
(No. per 100 M^)
Estimated
Standard
Error*
Mean +
1 Standard
Error
4/1216
0
0
4/2123
5.4xl04
2.2xl0~3
1.32xl0~3
(8.8x10"4,3.5x10_3)
4/28 to
5/1
7.23xl08
7.72
3.31
(4.41, 11.0)
5/811
4.32>:108
4.62
1.79
(2.83, 6.41)
5/2023
5.79xl07
6.19xl0_1
2.04xl0_1
(4.1xl0"1,8.2xl0~1)
5/30
8. 7 2 x 10 6
2.13xl0_1
8.42xl0~2
(1.3xl0_1,2.97xl0_1
6/79
4.66xl06
4.98xl0~2
4.04xl0~2
(9.4xl0~3,9.0xl0~2)
6/1925
0
0
0
6/30 to
7/7
0
0
0
^Standard Error estinated from mean concentrations across sectors on a given
date, except for 4/28 to 5/1.

TABLE 13
Water Volumes
(from
in Ohio Waters
Ref. 5) (cubic
of Western Basin
meters)
Sector
Depth
\ Zone
1
2
3
4
5
6
Total
A
5.73xl07
9.3xlO?
1.71x10®
0
0
0
3.21x3 0®
B
0
0
0
7.7 7x10®
9.72x10®
1.06xl09
2.81xl09
C
2.17xl0?
2.44x10®
6.3xl08
7.63x10®
4.73x10®
0
2.13xl09
D
7.15xl07
2.41xlO?
6.lOxlO7
2.48x10®
8.29x10®
6.38x10®
1.8 IxlO9
E
7.02xl06
2.94xlO?
1.17x10®
2.60x10®
3.57x10®
1.51xl09
2.28xl09
F 4.28xl06 2.26xlO? 1.01x10® 3.46x10® 6.53xl08 1.71xl09 2.84xl09
TOTAL
9.745xlO? 4.131xl08 1.08xl09 2.394xl09 3.284xl09 4.918xl09 1.22xlOJ°

TABLE 14
Concentrations of Larval Yellow Perch
at Station 2 in Canadian Waters
Data Source: Ref. (2,3)
3
Date Concentration (it/100 M )
1976 Bottom Surface
51776 11.82
52576 8.56 6.59
6376  0.78
7976 0.74
72176 1.86
1975
61875
0.64
0

TABLE 15
Yellow Perch Larval Concentrations
Sampled in Immediate Vicinity
of Power Plant
Station Number
Date 6 10 11 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
Data Source: Table B26, Vol. II, Ref. (4).

TABLE 16
Coefficients of Sampling Variation
Associated with Mean Concentrations
Contained in Table 15
Station Number
Date 6 10 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
Data Source: Table B31, Vol. II, Ref. (4).

JOi
.51
! 1—1
181
135
136
137
139
143
144
146
148
152
153
154
156
153
159
161
162
163
164
165
166
168
172
TABLE 17
Estimated Number of Yellow Perch Larvae
Entrained by Monroe Power Plantl in 1976
Mean Concentration
Estimated Number Flow Larv.
Entrained (24 hr) 100 M^/day ///100
45,488
36,469
0.21
36,645
33,445
0.22
161,831
28,892
0.93
10,364
33,445
0.05
0.22
9,768
24,434
0.40
10,219
30,552
0.33
3,987
24,434
0.16
8,372
24,434
0.34
1,395
24,434
0.06
2,991
30,552
0.10
0
24,434
0
7,471
18,316
0.41
13,356
24,434
0.55
12,545
24,434
0.51
15,947
24,434
0.65
5,183
24,434
0.21
997
24,434
0.04
2,391
18,316
0.13
2,813
18,316
0.15
6,578
24,434
0.27
3,940
24,434
0.16
5,982
30,552
0.20
60,668
36,632
1.66
30,699
48,868
0.63
10,759
54,948
0.20

Dat
173
175
179
180
182
187
188
189
193
194
196
197
198
199
200
201
203
207
208
210
213
214
216
220
221
223
224
225
226
227
TABLE 17 (Continued)
Mean Concentration
Estimated Number Flow Larv.
Entrained (24 hr) 100 MVday #/100
1,913
54,948
0.03
20,672
67,184
0.31
41,825
67,184
0.62
14,408
67,184
0.21
13,285
61,066
0.22
3,898
67,184
0.06
12,278
67,184
0.18
5,847
67,184
0.09
4,722
67,184
0.07
3,508
67,184
0.05
15,476
67,184
0.23
5,977
73,264
0.08
3,586
73,264
0.05
7,876
73,264
0.11
1,793
73,264
0.02
4,782
73,264
0.06
8,368
73,264
0.11
1,195
73,264
0.02
1,275
73,264
0.02
1,275
73,264
0.02
1,195
73,264
0.02
0
0
1,195
73,264
0.02
0
0
0
0
2,953
54,948
0.05
0
0
0
0
0
0
0
0

TABLE 17 (Continued)
Date
Estimated Number
Entrained (24 hr)
Flow
100 M3/day
Mean Concentration
Larv.
ff/100 M3
228
649,691
Estimates Based Upon Detroit Edison Data on Estimated Number Entrained
Per Day and Flow Rates.
Data Source: Ref. (9)

Michigan
TABLE 18
Water Intake Specifications
Data Source: Ref. (11)
Intake
Lake Sector
Depth Zone
Pumping Rate
(100 Mfyday)
Ferni (P)
Monroe (P)
Siting (P)
Monroe City
M
M
M
M
12
12
12
34
9274
78299
11671
303
Subtotal
99547
Ohio
Acme (P) R
Bayshore (P) R
DavisBesse (P) C
Camp Perry C
East Harbor
State Park D
Erie Industrial
Park C
Kelleys Island E
Lakeside
Association E
JIarblehead E
Oregon A
Port Clinton C
PutInBay D
Sandusky E
Toledo A
R 14716
R 28342
2 818
2 9.5
3 3
2 8
2 3
2 8
2 4.5
3 160
2 57
2 5
4 404
3 303
Subtotal 44841
Total 144388
(P)  Power Plant

TABLE 19
Larvae Entrainment Estimates
1975
Data Source: Ref. (11)
Entrainment Estimate
Intake Point Sample Depth Zone
Michigan
Fermi (P) 61,000 349,000
Monroe (P) 531,000 2,940,000
Whiting (P) 268,000 439,000
Monroe City 2,100 69,200
Subtotal 862,700 3,797,200
Ohio
Acne (P)*  2,340,000
Bayshore (P) 1,686,300 4,510,000
DavisBesse (P)**
Camp Perry 9,000 14,800
East Harbor State Park 200 900
Erie Industrial Park 7,200 11,900
Kelleys Island 900 400
Lakeside Association 700 1,000
Marblehead 400 600
Oregon 2,800 6,900
Port Clinton 1,200 88,700
PutInBay 1,500 300
Sandusky 2,600 61,500
Toledo 50,900 124,000
Subtotal 1,763,700 7,161,000
Total 2,626,400 10,958,200
(P) 
;k _
** ,
Power Plant
N'o fish caught at sampling station in 1975
DnvisBcsse not operating in 1975

TABLE 20
Larvae Entrainment Estimates
1976
Data Source: Ref. (11)
Entrainment Estimate
Intake Point Sample Depth Zone
Michigan
Femi (P) 265,300 728,000
Monroe (P) 1,625,700 6,150,000
Whiting (P) 1,520,600 917,000
Monroe City 6,300 544,600
Subtotal 3,417,900 8,339,600
Ohio
Acne (P)*  24,200,000
Bayshore (P) 1,181,400 46,600,000
DavisBesse (P) 17,200 334,000
Camp Perry 12,300 3,900
East Harbor State Park 700 400
Erie Industrial Park 9,600 3,100
Kelleys Island 400 300
Lakeside Association 2,300 900
Marblchead * 2,100 500
Oregon 6,600 6,200
Port Clinton 47,500 23,200
PutInBay 300 29,200
Sandusky 94,200 270,100
Toledo 118,400 112,200
Subtotal 1,493,000 71,584,000
Total 4,910,900 79,923,600
(P)  Power Plant
*  No fish caught at sampling station in 1976.

TABLE 21
Ranges of Entrainment Losses
Intake 1975 1976
Michigan
Fermi (P) 61,000349,000 265,000728,000
Monroe (P) 531,0002,940,000 1,636,0006,150,000
Whiting (P) 268,600439,000 917,0001,521,000
Monroe City 2,10069,200 6,300544,600
Ohio
Acme (P) 02,340,000 024,200,000
Bavshore (P) 1,690,0004,510,000 1,180,00046,600,000
DavisBesse (P)*  17,200334,000
Camp Perry 9,00014,8000 3,90012,300
East Harbor State
Park 200900 400700
Erie Industrial Park 7,20011,900 3,1009,600
Kellevs Island 3001,000 300400
Lakeside Association 7001,000 9002,300
Marblchead 400600 5002,100
Oregon 2,8006,900 6,2006,600
Port Clinton 1,20088,700 4,70023,200
PutIn3ay 3001,500 3002,900
Sandusky * 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.

Appendix 1
STATISTICAL TESTS OF SIGNIFICANCE FOR DIFFERENCE IN
CONCENTRATIONS OF LARVAL YELLOW PERCH IN THE WESTERN BASIN
OF LAKE ERIE IN HAY AND JUNE 1975
Data Sources: Ref. (2,4,5)

Introduction and Summary
Accurate estimates of abundance of larval yellow perch 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 reliability
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 nonuniform
distribution varies diurnally. Nine statistical tests of significance follow
below which deal with differences in larval concentrations observed 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 differences in
concentration was detected between surface and bottom during daylight hours.
Significant surface  bottom differences in larval concentrations 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 accurately
estimate larval concentrations and abundance. It is important to note in

Table 2 that bottom sled tows yielded substantially higher concentrations 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 1:
Mean daytime concentrations at surface and near bottom in Michigan waters
are equal.
Alternative: Concentration near bottom is greater.
Data:
xs = 1.97* xB = 2.43
ss = 3.99 sB = 4.28
n
48 n = 48
Test Statistic Value:
2.43  1.97 _ 0.46
t_ "> .2^~0 84
(4.28) (3.99) ,
[ 43 48 J
(4 .28 )2 (3.99)2
. _L«L !£_i_ .2.
(4.28) 2 (3 .99) .2
1 48 J 1 48 1
0.54
49 49
0. 5088
0.0052
 2 = 95
x. = sample nean
s. = sample standard deviation

Result: Since t ^ _ g.527 for 95 d.f., the null hypothesis is
supported 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 under the null
hypothesis.
Null Hvnothesis 2:
Mean daytime concentrations at surface and on bottom in Michigan waters
are equal.
Alternative: Concentration on bottom is greater.
Data:
x<3 = 1.97 Xg = 5.83
ss = 3.99 sB = 4.52
n = 48 n = 15
(bottom sled tow)
Test Statistic Value:
5.83  1.97 3.86
? 0 1 30
.(4.52T (3.99) X
1 L5 48 J
= 2.97
(4.52)2 (3.99)2 2
d.f. = [ » * *8 ; 2 =
(4.52) 2 (3.99) .2
1 15 J 1 48 1
16 49
2.8686
0. 1182
2 = 22
Result: Since t = 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 = 2.97 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:
xs = 5.28 xB = 18.83
ss = 11.18 sB = 16.13
n = 30 n = 30
Test Statistic Value:
18.33  5.28 _ 13.55 _ , ,fi
t~ « « — O CO """ J . / u
(16.13) (11.18) 4 J
1 30 + 30 J
d.f. = 164,84 j—  2 = 53
(16.13)2 (11.18) 2
1 30 J 1 30 J
31 31
Result: Since = 2.70 for 40 degrees of freedom and ^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:
*N = 5.28 xD = 1.97
sN = 11.18 sD = 3.99
n = 30 n = 48
Test Statistic Value:
5.28  1.97 _ 3.31 _ .
t 2 2 2 12
(11.18) (3.99) A
1 30 48 J
,(U.18)2 + (3.99)2,2
d.f. = — —  2 = 35.99  2 = 34
.( 11.18) .2 .(3.99) i2
1 30 J 1 48 J
31 49
Result: Since t gg = 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 ^ =
1.70 and 1.68 for 30 and 40 degrees of freedom, respectively.
Null Hvoothesis 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.
Data:
= 18.83 xD = 5.83
SN = 1613 sD = 4.52
n = 30 n = 15

Test Statistic Value:
18.83  5.83 13.00 , 1A
t = ^ T~ = TT7 = 4,10
(16.13) (4.52) A
1 30 15 J
(16.13)2 (4.52)2 2
( 1A 1C J
d.f. = — —  2 = 39.61  2 = 38
.(16.13)^,2 ,(4.52),2
30 15
31 16
Result: Since t = 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 Zone A of Ohio waters at the surface and
bottom are equal.
Alternative: Concentration at the surface is greater than concentration
at the bottom.
Data:
*s 3 14.15 xB = 8.00
Ss =32.85 sB = 13.67
n = 20 n = 20
Test Statistic Value:
14.15  8.00 6.15
(32.85)2 (13.67)2 796
20 + 20
= 0.77

ars are
. ternative: Dayt*.
Data:
= 38.31
sg = 104.82 sg =
n  42 ri = 42
Test Statistic Value:
h = 38.31  1.69 _ 36.62 _
r(104.82)2 + (8WA ' 1623 '
1 42 42
d. f.
(104.82)
42
(8.70) 2
42 J
,(104.82) .2
1 42 '
43
43.59  2 = 42
i
(8.70) .2
42
43

Result: Since t = 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.
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:
"*3 = 6.58 xs = 0.51
sg = 10.64 Sg = 0.90
n = 36 n = 37
Test Statistic Value:
6.58  0.51 6.07 . ,,
t = = ir~ = = 341
(10.64) (0.90) 4
1 36 37 J
(10.64)2 (0.90)22
t 36 + 37
d.f. = ^  r—  2 = 37.51  2 = 36
. (10. 64) . 2 .(0.90) ,2
1 36 1 1 36 1
37 37
Result: Since t = 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:
= 9.03 xs = 0.31
s3 = 14.97 sg = 0.64
n = 32 n = 32
Test Statistic Value:
9.03  0.31 = 8.72 =  ?q
(14.97) (0.64) 4
1 32 32 1
.(14.97)2 (0.64)^2
32 32 J
d.f. =  T  2 = 32
r(14.97K2 r(0.64)72
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.

TABLE Al.l
MEASURED CONCENTRATIONS OF LARVAL YELLOW PERCH
IN MICHIGAN WATERS (1975).
Night
Day
Date
Surface
Near Bottom
Surface
Near Bottom
5/21
24.4, 33.8,
46.5,
17.0, 5.7,

—
20.8, 34.6,
19.2,
15.0
32.5
5/22
o
o
o
o
o
40.7,
70.3, 24.5
1.1, 0, 3.2, 8.4
0, 1.0, 4.1, 8.9,
26.1,
14.0
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
5/23
0, 3.2, 0, 0
35.6,
29.1, 22.4,
1.1, 2.4, 1.1,
1, 4.2, 6.4, 9.9,
49.1,
20.3
3.8, 1.1, 1.2,
0, 1.0, 8.9, 7.2,
8.9, 6.7, 0, 2.2,
0, 0, 15.0, 18.9
4.1, 11.7
6/16
2.9, 0, 2.8,
9.5,
17.4, 4.9,
0, 0, 0, 0,
0.9, 0, 0, 0,
o
o
14.2,
10.1
0, 0, 0, 0,
o
o
o
o
0, 0, 1.0, 0
o
o
o
6/13 0, 0, 0, 0, 0 2.4, 7.3, 9.3
17.2, 15.9
6/19
0, 0, 0, 0, 0 8.7, 2.6, 10.0,
o,
0,
0,
0,
0,
0,
0,
0,
o
o
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
0,
0,
0,
0
x = 5.28
s = 11.18
n = 30
x = 18.83
s = 16.13
n = 30
x = 1.97
s = 3.99
n = 48
x = 2.43
s = 4.28
n = 48
Data Source: R.A. Cole, Institute of Water Research, Department of
Fisheries and Wildlife, Michigan State University:
Ref. (4).

TABLE A1.2
FORMULAE FOR TESTING EQUALITY OF POPULATION MEANS
Null Hypothesis: Population Means Are Equal, Variances of Populations Assumed
To Be Unknown and Not Necessarily Equal.
Test Statistic*:
X1 
x2
—2
+
L»i
s2~]^
2
m2
Distributed approximately as Student's t with:
r2
si
2i
S2
2
Lmi
ml_
1
/SM2
+
2
m
1 + 1
^2 + 1
V = Degress of Freedom (d.f.)
*Johnson & Leone, Statistics and Experimental Design in Engineering and the
Physical Sciences, Vol. 1, p. 226, Wiley, 1964.

Appendix 2
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
0'6' 17 57.3 134
61121 18 24.6 46.7
12'IS' 15 2.62 3.28
181241 25 0.63 1.26
24130' 15 0.45 0.49
Null Hypothesis 1:
There is no significant difference in mean concentrations in the 016'
and 6'12* depth zones during April 2629, 1976.
Alternative: Mean concentration in 0'—6' zone is greater.
Test Statistic and d.f.:
Given in Appendix 1, Table A1.2
Test Statistic Value:
= 57.3  24.6 = 32J „
>2 ,,, ,,2i% 34.3 U,y;5
[~( 134)2 (46 . 7 )2"T
L 17 18 J
Rl34)2 (46.7)2~]2
L 17 18 J
M2 ¥4)
,2 ^s2n2
, f _ — _ o _ 1386261 .
d.f. . . 2  62752
13 19
Result: Calculated value of t not significant at 10 percent level.
Null hypothesis is accepted.
One concludes that the 0'—61 and 6 * — 12* depth zones can be lumped for
purposes of computing mean larval concentration in Michigan waters. The
renaming depth zones are lumped into a second group.

Appendix 3
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^ x^ +
Standard 1 2 S1 2 ^2A
error: (S.E.)~ VT ^V1 n1 + 2 n2
where:
xx = mean concentration in 01 —121 zone
n^ 3 sample size in 01 — 12 * zone
s~ = sample variance in 0* —121 zone
x2 = mean concentration in 12'—30' zone
n,, = sample size in 12'30' zone
ry #
s~ = sample variance in 12'30' zone
= volume in 0' —12' zone
V2 3 volume of 12'30' zone
= total volume
Day 118 (4/2629)
n, = 35 n = 55
1 2
x^ = 40.5 x^ = 1.16
a1 = 100 s 2 = 2.14
Vx = 0.566 x 108 V2 = 4.41 x 10 VT = 4.976 x 108
1 (0.566 x 108 x 40.5 + 4.41 x 108 x 1.16) = 5.63
4.976 x 108
 . _ I „ ,„8,2 (100)2 . /f ,, in8v2 (2.14)2 A
S.E. =» j [(.566 x 10 ) x —T7— + (4.41 x 10 ) x — ]  1.94
4.976 x 108 35 55
Mean concentration + 1 S.E. = 5.63 + 1.94 = 3.69, 7.57

Dav 136
= 14 1*2 = 31
x. = 0.562 x„ = 2.17
i ^
s1 = 0.943 s 2 = 3.86
4.976 x 108
(0.566 x 108 x 0.562 + 4.41 x 10& x 2.17) = 1.99
n  _ 1 „ in8.2 (.943)2 8 2 <3.86)2,
S.E. = g [(.566 x 10 ) x —r,— + (4.41 x 10 ) x — J
4.976 x 108 14 31
Mean concentration + 1 S.E. = 1.99 + 0.624 = 1.37, 2.61
Dav 145
n =36 n2 = 31
x^ =* 3.94 X2 = 191
s = 8.87 s 2 = 3.37
x =  (0.566 x 108 x 3.94 + 4.41 x 108 x 1.91) = 2.14
4.976 x 10
1  ,n8»2 (8.87)2 ,JJ,2 (3.37)2,
S.E. = J [(.566 x 10 ) x —57— + (4.41 x 10 ) x —r, J
4.976 x 108 36 31
Mean concentration + 1 S.E. = 2.14 + 0.56 = 1.58, 2.70
Dav 158
= 13 n2 = 20
x
1
0.579 x2 = 0.471
Sj = 1.17 s2 = 0.996
7 ¦ r (0.566 x 108 x 0.579 + 4.41 x 108 x 0.471) = 0.483
4.976 x 10

I ,.8,2 (1.17)2 . ,, ,, ,„8,2 (0.996)^,4
S.E. = r [(0.566 x 10 ) x —— + (4.41 x 10 ) x ^ J = 0.201
4.976 x 103 13
Mean concentration + 1 S.E. = 0.483 + 0.201 = 0.282, 0.684
Dav 188
= 15 n2 = 20
x^ = 0.133 X2 = 0.147
3 = 0.225 s2 = 0.287
~ ~ 1 (0.566 x 108 x 0.133 + 4.41 x 10® x 0.147) = 0.145
4.976 x 108
1 r,~ ,„8X2 (0.225)2 /f ,, ,«8X2 (0.287)2^ _ n n^7
S.E. = j [(0.566 x 10 ) x r?— (4.41 x 10 ) x —~t; ' = UUJ/
4.976 x 10
Mean concentration + 1 S.E. = 0.145 + 0.057 = 0.088, 0.202
Dav 201
n^ = 13 n2 = 8
^ = 0.140 x2 = 0.213
sl =» 0.285 * s2 = 0.562
x = (0.566 x 108 x 0.14 + 4.41 x 108 x 0.213) = 0.205
4.976 x 10
S.E.  [(0.566 xlO8)2 x (°:283) + (4.41 x 108)2 x (Q'^62) ft = 0.176
4.976 x 103 13 8
Mean concentration + 1 S.E. = 0.205 + 0.176 = 0.029, 0.381

Day 209
= 5 = 20
x^ = 0 X2 = 0126
s1 = 0 s 2 0.392
x = T (4.41 x 108 x 0.126) = 0.112
4.976 x 10
S.E.  [(4.41 x 108)2 x (°'q92) ]H = 0.078
4.976 x 10
Mean concentration + 1 S.E. = 0.112 + 0.078 = 0.034, 0.190

Appendix 4
SAMPLE CALCULATION OF MEAN CONCENTRATIONS OF PROLARVAE (PROL),
EARLY POSTLARVAE (EPL), AND LATE POSTLARVAE (LPL) IN
MICHIGAN WATER IN 1976

April 2730 (Day 118)
Let Cj, = total mean concentration of larvae in Michigan waters on
day 118, 1976.
= 5.63
C = concentration o£ prolarvae on day 118
r RuL
= C x mean fraction PROL.
T
Mean fraction PROL = ^ (56.6 x X^ + 441 x X2)
where:
= fraction PROL in 012 ft. zone.
X2 = fraction PROL in 1230 ft. zone.
X1 = 2.17 + 0.06 + 0 = 0973
1.29
X2 ~ 1.29 + 0 + 0 1*°°
Mean fraction PROL = , , (56.6 x 0.973 + 441 x 1.0)
497.6
= 0.997
CPROL=5'63 *J>.9975.61
Cepl = concentration of early post larvae on day 118.
= CT x mean fraction EPL.
Mean fraction EPL = ^ ^ ^ (56.6 x y^ + 441 x y^)
where:
y^ = fraction EPL in 012 ft. zone
y2 = fraction EPL in 1230 ft. zone
0.06
1 2.17 + 0.06 + 0
. = 9 = o
2 1.29 + 0 + 0
= 0.027

Mean fraction EPL = ^ (56.6 x 0.027 + 441 x 0)
= 0.003
Crm = 5.63 x 0.003 = .017
LrL
= concentration of late post larvae on day 118.
= Cj x mean fraction LPL.
Mean fraction LPL = j ^ (56.6 x Z^ + 441 x Zy)
where:
Z^ = fraction LPL in 012 ft. zone.
= fraction LPL in 1230 ft. zone.
Z = 2  o
1 2.17+ 0.06 +0
Z = 2 = o
2 1.29 + 0 + 0
;*.ean fraction LPL = ^ (56.6 x 0 + 441 x 0) = 0
= 5.63 x 0 = 0

Appendix 5
ESTIMATING PERCENT MORTALITY OF
ENTRAINED LARVAE

Method I.
Let Ne = estimated number of live larvae entrained on a given day.
Let = 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) nl
100 p = 100 ^ — = 100 (1  jp) (A5.1)
E E
Equation A5.1 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 x^. = mean concentration of live larvae in cooling water entering
plant on the given day.
Let ^ =
mean concentration of live larvae entering upper discharge
canal on the given day from plant discharge.
Then,
XL
100 p = 100 (1  —) (A5.2)
XE
Methods (1) and (2) defined above use concentrations of live larvae only
and can be used only when
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

Method 3.
Let ^ ancj x^. jje defined as before. Let Dg 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
v J) y v J)
100 p = 100 (1  ) "100 (1  — • * nE) (A5.3)
*E XE L
+ °E
x D
Equation (A5.3) differs from (A5.2) by an adjustment factor E + E
*L °L
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,
D_
°E + *EX °E °L + XL,
100 p = 100 (1  ^r ) = 100 (1  r * jr— ) (A5.4)
L L E XE
°L + XL
Example
To illustrate the application of these four methods, consider the
hypothetical data displayed in Table I. Following Table 1 are the four

calculations 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 entrainment
mortality i9 lost. For example, sampling variation may result in a low count
of live larvae entering the plant which will lower the estimate of entrainment
mortality. A high count of dead larvae at the discharge, however, indicates
that there may have been substantial larval mortality as a result of
entrainment. The inclusion of counts of dead as well as live lrvae will use
all the available information related to entrainment mortality. Methods 1 and
2 are modified (in methods 3 and 4) to incorporate both live and dead larval
counts so that the base population is the entire entrained population for a
given species. As noted by equation (A5.3) 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 reversed. 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 fron 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 numerical 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 recommended, therefore, that the
average of the two values be used as the estimate of larval mortality due to
entrainment. 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,
incidentally, 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.

COOLING WATER VOLUMES AND LARVAL CAPTURE DATA
HYPOTHESIZED FOR EXAMPLE 1
TABLE 1
Daytime hrs: 0500  2100 (5 a.m.  9 p.m.)
Avg. cooling water inflow: 2100 c.f.s.
Vol. sampled (plant intake)
130 cu. meters
live pro larvae 15
dead pro larvae 3
live post larvae 4
dead post larvae 1
Vol. sampled (upper discharge)
75 cu. meters
live pro larvae 2
dead pro larvae 12
live post larvae 2
dead post larvae 8
Nighttime hrs: 2100  0500 (9 p.m.  5 a.m.)
Avg. cooling water inflows: 1100 c.f.s.
Vol. sampled (plant intake)
28 cu. meters
live pro larvae 63
dead pro larvae 15
live post larvae 28
dead post larvae 4
Vol. sampled (upper discharge)
48 cu. meters
live pro larvae 10
dead pro larvae 80
live post larvae 8
dead post larvae 31

Calculations
Anit. of cooling water flowing
into the plant in daytime from
0500 to 2100
3,404,800 cubic meters
Amt. of cooling water flowing
into the plant in nighttime
from 2100 to 0500
1,783,466 cubic meters
Calculation of%
# live pro larvae (daytime)
3404800 = 392 861
ld x
# live post larvae (daytime)
3404800 _ ,,,
4 x —— = 104,763
t live pro larvae (nighttime)
1783466 _ , nnQ
63 x 28— 4,012,798
# live post larvae (nighttime)
28 x = 1,783,466
Calculatin of
ne = 6,293,888
# live pro larvae (daytime)
2 x MOWOO . 90 794
0 live post larvae (daytime)
2 x 3^800 . 9o m
# live pro larvae (nighttime)
10* ll§^, 371i555
48
# live post larvae (nighttime)
8 „ = 2,7,244
Nl = 805,387

Method 1
100 p = 100 (1~6293888) = 100 (1 " 12796)
= 87.204%
Method 2
_ 3404800 15 + 4 1783466 ,63 + 28,.
E " 3404800 + 1783466 1 1.3 + 3404800 + 1783466 K 0.28
= (.65625) < (14.615) + (.34375) • (325) =
9.5911 + 111.72 = 121.31
„ _ 3404800 ,2 + 2. 1783466 10 + 8
'L ~ 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  L°^0~) = 100 (1  .13511) = 100 (.86489)
= 86.489%
Method 3
De = (.65625) (^pp) + (.34375) (^ *gA) = 2.0192 + 23.3256
= 25.345
D = (.65625) (" * 8) + (.34375) (^VtI^ = 17.500 + 79.492
L 0.75 0.4o
= 96.992
,00 p . 100 :i . ^ . ^4^, , 100 (1  0.13511 • \l)ill,\2l6U9l2>

Method 4
= 100 (1  (0.13511) (1.2934))
= 100 (1  .179 75)
82.525%
inn  inn n 25345 96.992 + 16.389,
100 p 100 (1 96 992 * 25.345 + 121.31
= 100 (1  .2613 (.773))
= 79.80Z

Appendix 6
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_25P  E(t) (A6.1)
(t lto> 0)
Equation (A6.1) is of the form:
«
N(t) + C*N = F(t) (t>to>0). (A6.2)
where:
C = constant;
F(t) = function of time.
The general solution to (A6.2) is:
_ J/ V ~C*(t~t ) —C'(t~t ) t J rj \ C.(Zt ) i { KC O \
N(t)  N(t ;e o + e o FIZ; e o dz (A6.3;
o tJ
o
(t > t )
— o'
and therefore (A6.1) has the solution given by (A6.3).
If F(t) happens to be independent of the parameter t} say F(t) = F, then
(A6.3) becomes:
x c.(tt ) A F . c.(tt k
N(tj = N(t )e o + r (1  e o) (A6.4)
o C
(t > t \
— o>
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 = C£ an(j F = F^
(i = I, n). Equation (A6.4) is:

N(t) =<
C (ft ) F
N(t )•e 0 + i • (1  e 1 ° )
C1
(to < t < ti)
C '(tt.) F. C,*(tt.)
N' (t x) • e 2 1 f ' (1  e 2 1 )
< t < t2)
C *(tt ) F C '(tt )
N(t,)*e J 1 + 7T ' (1 " e J) L
l C3
(t2 < t < t^)
C (tt .) F C (tt .)
^ \. n a1 n *., n n l
N(t .)*e + — (1  e
n L o
n
(tnl

Michigan Water, 1976 (using Equation 10)
r o
0.4437'h
0.3915h
(0.3915  0.4437 e"25p).h
(0.1382  0.4437 e~25p)h
(0.1382  0.3915 e"25p)«h
(0.0244  0.3915 e_25P)h
(0.0244  0.1382 e~25P).h
(0.0022  0.1382 e_25P)*h
(0.0022  0.0244 e25P)»h
(0.0001  0.0244 e"25P)*h
(0.0001  0.0022 e"25P)h
 0.0022* he"25P
 0.0001»h•e_2^P
0
(B = 497.6 xlO4; E(t) = 0)
£[N(t) + p N(t)] =<
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
(A6.6)

The solution to Equation (A6.6) following the format of Equation (A6.5) is:
N(t) =0 0 < t < 106
N(t) = N(106)e"p(t"106) + 0.4437 ( —)(le~p(t106)) 106 < t < 120
P
N(t) = N(120)e~p(t~120) + 0.3915 ( —) (le"p( t_106)) 120 < t < 131
P
N(t) = N(131)e~p(t_131) + (0.3915  0.4437.e"25p)(—)(le"p(t"131)) 131 < t < 134
P
N(t) = N(134).e"p(t"l34) + (0.1382  0.4437 •e"25p) (—) (le"p( t_134)) 134 < t < 145
P ~~
N(t) = N(145).e"p(t 145) + (0.1382  0.3915e~25p) ( —) (le"p( t145)) 145 < t <
148
P
N(t) = N(148)e"p(t"L48) + (0.0244  0.3915 .e"25p) (—) (le"p( C U8)) 148 < t < 159
P
N(t) = N(159)e"p(t 159) + (0.0244  0.1382,e 25p)( —)(le P(t"159)) 159 < t < 162
P
N(t) = N( 162) •e_p( C L62) + (0.0022  0.1382.e 25p) (—) (le"p( t_162) 162 < t < 173
P ~
N(t) = N(173)*e"p(t~173) + (0.0022  0.0244 te~25p) (—) (le"p( t173 ^) 173 < t < 176
P ~
N(t)
= N( 176) • e~p( t176) + (0.0001  0.0244e 25p)( —)(le P(t_176)) 176 < t < 187
P
N(t) = N(187).e"p(C 187) + (0.0001  0.0022 »e 25p)( —)(le p(t 18?)) 187 < t <
189
P
N(t) = N(139).e"p(C 189) + 0.0022 *e 25p ( —)(le~p(t 189)) 189 < t < 200
P
N(t) = N( 200) •e~p( t200) + 0.0001.e"25p ( —)(le P(t_200)) 200 < t < 214
P
N(t) = N(214).e"p(C"214) 214 < t < 365
(A6.7)

Ohio Waters, 1975 (using Equation 7)
0
0.5905'h
0.328'h
0.0729'h
0.0081h
(0.0081  0.5905*e"25p).h
(0.0004  0.5905'e"25p).h
(0.0004  0.328e_25P)*h
0.328.e"25P.h
 0.0729e~25P«h
 0.0081'e2^P*h
 0.0004e_25Ph
0
i[N(t) + p• N(t) ] =<
0 < 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
(A6.8)
(B = 9.393 x 107; E(t) = 0)
The solution to Equation (A6.8) following the format of Equation (A6.5) is:
N(t) =0 0 < t < 127
N(t) = (0.5905H — )(le P(t~127))
P
127 < t < 134
N(t) = N(134)e"p(t~134) + (0.328)(—)(le"p(t 134)) 134 < t < 141
P
N(t) = N(141).e~p(t~141) +
(0.0729)( —)(le P(t"141)) 141 < t < 148
P
N(t) = N(148)e~p(t_148) + (0.0081)( —)(le~p(t"148)) 148 < t £ 152
P

N(c;
N(e) = NCl20).e~p(t_i'
H(t) = H(127).e"P(t""7)
; e + <0.008l)(

N(t) = N( 131)e p(t"131> + (0.0O8I  0.5905,e~25p)(^)(ie~P(t_ 131 >n,,
'v p e ) 131 < t _< 134
N(t) = N( 134)• e P(c*134) + (0.0004  0.5905,e~23p)(^)M ~p(t134h
M p Mi e ) 134 < t < 138
N(C> = N(138).e~p(t138) + (0.0004  .328.e"25P)(^Hi "PU138>
M p Mi~e ' 138 < t < 141
N(t) = N(141).e~p(t~141)  0.328.e"25p (!^v, pCt141),
P n 6 ' 141 < t < 145
N(t) = N(l45)«e P^C 1+5^  0.0729.e~25p f~)(l ~p(t145).
p ' 145 < t < 152
N(t> = N(L52).e"pCtI52) _ Q 0Q81 25p tvB . p(t152).
P M 6 3 152 < t < 159
N(t)  N(l59).ep(t"15^ . 0.0004.e~25p (^)d ~P(t159),
P 6 ' 159 < c < 166
N(t) = N(166)ep(tL66)
166 < t < 365
(A6.ll)

Michigan Water, 1975 (using Equation 9)
0
0.4437* h
0.39 L5« h
(0.3915  0.4437e"25P)h
(0.1382  0.4437«e~25p),h
(0.1382  0.3915'e"25P)'h
(0.0244  0.3915.e"25P)»h
(0.0244  0.1382*e~25p)*h
(0.0001  0.1382.e"25P).h
(0.0001  0.0244.e"25p).h
 0.0244•e2^P«h
 O.OOOl'e2^?^
0
[N(t) + pN'(c)] = <<
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
(A6.12)
(B = 497.6 x 104; E(t) = 0)
The solution to Equation (A6.12) following the format of Equation (A6.5)
is:
N(t) = 0
N(t) = 0.4437 ( — )(le~P (t"120))
P
0 < t _< 120
120 < t < 134
N(t) = N(134)e"p(t"134) + 0.3915 ( —)(le p(t I34))
P
134 < t < 145
N(t) = N(145)e"p(t_145) + (0.3915  0.4437.e"25p)( —)(1e p(t 145) 145 < t < 148
P
N(t) = N(148).e"p(C~148) + (0.1382  0.4437 • e~25p) ( —) (le~p( t_148)) 148 < t < 159
P
N(t) = N(159).e"p(t~159) + (0.1382  0.3915 'e~25p) ( —) (le~p( C 159)) 159 < c 1 162
P

N(t) = N(162)e"p(t"I62) + (0.0244  0.3915 .e~25p) le"p( t_162)) 162 < t < 173
N(t) = N( 173)e~P^+ (0.0244  0.1382«e 25p)(^^)(le P^t 17"^) 173 < t <_ 176
N(t) = N(176).e"p(t_176) + (0.0001  0 .1382 .e~25p) (^) (le~p( t_1?6 >) 176 < t < 187
N(t) = N(187).e~p^t~187^ + (0.0001  0.0244«e 25p)(^)(le l87^) 187 < t £ 189
N(t) => N(139).e"P^t1"89^  0.0244*e 25p (^)(le P^C 189^) 189 < t < 201
N(t) = N(20l)e"p^t201^  (0.0001)«e~25p (^)(le P^C 201^) 201 < t < 215
N(t) = N(215).e"p(t~215) 215 < t < 365
(A6.13)

Michigan Water, 1975 (using Equations 9 and 14)
[N
N(t) + p • N' (t) ] = <
0
0 <
t
<
120
0.4437* h'B
120
<
t
<
125
0.4437'h'B  0.027
125
<
t
<
132
0.4437'hB  0.053
132
<
t
<
134
0.3915hB  0.053
134
<
t
<
141
0.3915«hB  0.025
141
<
t
<
145
(0.3915  0.4437e_25P)hB
 0.025
145
<
t
<
148
(0.1382  0.4437«e~25P)'h»B
 0.013
148
<
t
<
156
(0.1382  0.4437.e"25P)hB
 0.004
156
<
t
<
159
(0.1382  0.3915e"25P)«h'B
 0.004
159
<
t
<
162
(0.0244  0.3915e"25P)hB
 0.004
162
<
t
<
170
(0.0244  0.3915e"25P)hB
170
<
t
<
173
(0.0244  0.1382e~25P)hB
173
<
t
<
176
(0.0001  0.1382'e"25p)h*B
176
<
t
<
187
(0.0001  0.0244e"25p)*h*B
187
<
t
<
189
 0.0244'e~25P*h*B
189
<
t
<
201
 0.0001 e~25P*h'B
201
<
t
<
215
0
215
<
t
<
365
(B = 497.6 x 10^; E(t) given by Equation 14) (A6.14)
The solution to Equation (A6.14) following the format of Equation (A6.5)
is:
N(t) = 0
N(t) = 0.4437 — (1e p(t 120))
P
0 < t < 120
120 < t < 125
N( t) = N(125)e"p(t_125) + (0.4437  (1H5)(1_e"P(t_125>) 125 < t < 132
h B p

•Ht) = N( 173)*e r
«(t>  »(176)..I><'»6) , (Q 0()o
N(t) = N{187)e~p(t"187)
+ (0.0001  0.0244
» ¦ N(189).eP 201^
215

Appendix 7
APPROXIMATE VARIANCE OF EQUILIBRIUM POPULATION
AS A FUNCTION OF REPRODUCTIVE POTENTIAL AND LARVAL SURVIVAL

Using Taylor's Expansion, one approximates Var(B) as:
Var (B)  (IV fl2 ~ (fV o2
oE £ dY
where the derivatives are evaluated at y = 50 and £ = .08.
Let e = .08, s = .26, m = .37, y = 50
K = 5xl07, E„ = lxlO7, E = 250,000
z y
a = .04, a = 25
e y
Now:
B = ^ {K + —  iHtOJi + [ (K + —  + h)fy
2 y as£y y assy y Ey
Then:
3B . 1 faff)K . , J_, + 1 [( h _ (mff)K. 2 _ i A V %
3e 2 asy e2 2 Y assy ' ky ey "
r2(k + —  (nH~f)K) ziEUll)
y as£y 2
as£y
 4K( J^)]}
yE
B 1 {_ h + + i + f£ _ OjffjK 2 _ h + fjr *
3y 2 y2 qscy2 2 y asey y Ey
y asEy 2 2
' y asEy
y ey

3B 1 r. 74 5107 . 1 r/c ,„7 , 107 .74107N 2 00 1A7 ,10? , 2.5lo\,Js
3l= 2 {+U^22 * 3064 + 2 [(5*10 + W ~ r03376) " 20,10 (50~~ 4 ) 1 *
7 , ,(.74) 5107 , 451072.51051
* 1(2(10 3041665) ( .0827008 + 32 }
= {44.7399107 +  (1014(18.525849)  101A (.525)]1* • [1014(385.1383 + 1014 (1.5625) ]
= ^ 44.73959*107 + ——(3866958) = 45.155526'10?
2104.242740
(^)2 = 1014 2039.0215
o£
3.262434
o = (.04) = .0016
80 1 / 1q7 . .745107 . 1 r/c ,n7 . 107
3e ~ 2 2500 51.688 2 [(5 10 50
.74510 2
1.03376 '
7 ,10 . .02510
2010' (^ +
)]
,•) /c in7 A 10^. .745107, 10L . 745107.
50 1.03376 ),( 2500 51.688 ^
+ 4w (wL+^w)]}
'2500
200
^ {107(.0711S334) + ^ [1014(2.0759988  1014(.525)] ** 
oy I l
• [1014(2.8816654)(.071183346) + 10I4(.0105)]} =
14
= \ {107 (. 07118334) +^1562658^10—] = . 20873133107
10622645511
(^)2 = 1014(.043568768)
0~ » (25)2 = 625

(V 02  10U27.23042
3y y
Var(B) = 101A(27.23048 + 3.262434)
= 101A(30.493214)
STD. DEV. B = 10?«5.52206609 = 55,220,661

Appendix 8
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 pop
ulation 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 youngoEyear stage, by definition, since they are at that stage at
the time of entrainment. The fraction of larvae which are at some inter
mediate age at the time of entrainment that would be expected to survive
to reach youngofyear is estimated as follows.
Define the following variables and functions.
X1 = a geometrically distributed random variable with
parameter p^, defined on the positive integers,
which denotes the age (in days) of larvae upon
,entering the reference volume.
h^(x^) = probability function of X^.
Pl^1 ~ Pl>Xl 1 Xi = I'2, *'"
0 otherwise
= a geometrically distributed random variable with
parameter 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.

It is estimated above that the fraction of larvae that survive natural
mortality for 25 days and hence are recruited into the youngofyear pop
ulation 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 youngofyear stage, by definition, since they are at that stage at
the time of entrainment. The fraction of larvae which are at some inter
mediate age at the time of entrainment that would be expected to survive
to reach youngofyear is estimated as follows.
Define the following variables and functions.
= a geometrically distributed random variable with
parameter p^, defined on the positive integers,
which denotes the age (in days) of larvae upon
^entering the reference volume.
h^(x^) = probability function of X^.
= 1,2,
otherwise
X2 = a geometrically distributed random variable with
parameter pdefined on the positive integers,
which denotes the number of days that larvae are
in residence in the reference volume upon entering
the entrainment cycle.

It is estimated above that the fraction of larvae that survive natural
mortality for 25 days and hence are recruited into the youngofyear pop
ulation 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 youngofyear stage, by definition, since they are at that stage at
the time of entrainment. The fraction of larvae which are at some inter
mediate age at the time of entrainment that would be expected to survive
to reach youngofyear is estimated as follows.
Define the following variables and functions.
X1 = a geometrically distributed random variable with
parameter p^, defined on the positive integers,
which denotes the age (in days) of larvae upon
^entering the reference volume.
h^(x^) = probability function of X^.
Pl(l " xi = 1,1> '' •
0 otherwise
= a geometrically distributed random variable with
parameter p£, 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.

It is estimated above that the fraction of larvae that survive natural
mortality for 25 days and hence are recruited into the youngofyear pop
ulation 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 youngofyear stage, by definition, since they are at that stage at
the time of entrainment. The fraction of larvae which are at some inter
mediate age at the time of entrainment that would be expected to survive
to reach youngofyear is estimated as follows.
Define the following variables and functions.
X^ = a geometrically distributed random variable with
parameter p^, defined on the positive integers,
which denotes the age (in days) of larvae upon
,entering the reference volume.
h^(x^) = probability function of X^.
xx = 1,2, ..
otherwise
X^ = a geometrically distributed random variable with
parameter 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.

It is estimated above that the fraction of larvae that survive natural
mortality for 25 days and hence are recruited into the youngofyear pop
ulation 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 youngofyear stage, by definition, since they are at that stage at
the time of entrainment. The fraction of larvae which are at some inter
mediate age at the time of entrainment that would be expected to survive
to reach youngofyear is estimated as follows.
Define the following variables and functions.
X^ = a geometrically distributed random variable with
parameter p^, defined on the positive integers,
which denotes the age (in days) of larvae upon
^entering the reference volume.
h^(x^) = probability function of X^.
p (1  p,)^"1 x = 1,2, ...
¦s .
I 0 otherwise
X^ = a geometrically distributed random variable with
parameter P2, 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.

= Probability function of .
P2(l  p2)x2_1
0
^2 1 > 2, . • •
otherwise
Y = X^ + X^ 1 = 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:
f pl p2 v v
— K1 ~ P9)  (l  p,)y] y = 1,2, ...
P2 2 1
g(y) = <
0 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:
Prob(S/p) = Z g(y) x e~P(^ ^ =
y=l
Pl ?2f " P2>  25
= \ [1  (e (1  p„); ]
pl"p2 i_l  ep(l  p ) 2

is p,
, also plott^
p
P1
P2

.09
.99
.98
1.03
.16
.99
.98
1.03
.09
.99
.50
2.01
.U
.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
Estimated Fraction of Larvae Killed Due to Entrainment That Would Have
Survived to Reach YoungofYear Stage as a Function of Age at
Entrainment
Table A8.1

A numerical study of larval transport within the Western Basin (10)
suggests the plausibility of the geometric distribution as a model of lar
val 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 be
lieved to be a reasonable value in the absence of data showing actual ages
or lengths at the time of entrainment. The preceding calculations indi
cate that 17.7% of larvae 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.
 