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This is to certify that the

thesis entitled

THE EFFECTS OF IMPINGEMENT AND ENTRAINMENT
BY THE J. R. WHITING PLANT ON YELLOW PERCH, PERCA FLAVESCENS,
COMMERCIAL AND SPORT FISHERIES IN LAKE ERIE

 

presented by
RICHARD MICHAEL STANFORD

has been accepted towards fulfillment
of the requirements for

Ph.D degreein Fisheriesj Wildlife

§%/Jfl .2L\

Major professor

Date May 12, 1980

 

0-7639

- fiv-< .. ._._.,.4- v...— V A

 

 

 

 

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THE EFFECTS OF IMPINGEMENT AND ENTRAINMENT
BY THE J. R. WHITING PLANT ON YELLOW PERCH, PERCA FLAVESCENS,
COMMERCIAL AND SPORT FISHERIES IN LAKE ERIE

 

By

Richard Michael Stanford

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Fisheries and Wildlife

1980

ABSTRACT

THE EFFECTS OF IMPINGEMENT AND ENTRAINMENT
BY THE J. R. WRITING PLANT ON YELLOW PERCH, PERCA FLAVESCENS,
COMMERCIAL AND SPORT FISHERIES IN LAKE ERIE

 

By

Richard Michael Stanford

This study assesses the bioeconomic effects of the J. R. Whiting

power plant on the yellow perch, Perca flavescens, commercial and sport

 

fisheries in the Michigan waters of Lake Erie. The impact of impingement
(fish killed on plant intake screens) and entrainment (egg and larval
mortality inside the plant during cooling) is estimated to be a 1.7 per-
cent annual reduction in the yellow perch population size. The value

of this loss is estimated to be $10,710/year. The annual economic value
of angling at the plant site is derived from a demand schedule and es-
timated to be $7,720.

During 1978-79 a roving creel survey was conducted in Monroe County
to improve the angling catch and effort data utilized in the surplus
production model to estimate the size of the yellow perch population.
Anglers caught 509,001 yellow perch with 29,411 angler days effort. Mail
surveys by the Michigan Department of Natural Resources (MDNR) apparently
have been overestimating these numbers by a factor of about 4. Therefore,
past MDNR estimates of catch and effort are adjusted for use in the

surplus production model of the perch population.

Richard Michael Stanford

The surplus production model is applied to both the yellow perch
commercial and sport catch and effort data from the Lake Erie waters
of Michigan. The yellow perch population size in the Monroe area, es-
timated from the surplus production model, is approximately 1.074 x1010
fish. The Leslie matrix, a density-independent mathematical model, then
simulates the effects of the J. R. Whiting power plant impingement and
entrainment on this population over the plant's 50-year life expectancy
(1952-2002). The combined effect of impingement and entrainment over
the 50 years of plant operation represents an annual 1.7 percent re-
duction in the yellow perch population size.

A 1.7 percent reduction per year in the yellow perch sport fisheries
catch from impingement and entrainment results in a simple total economic
loss of $535,500 over 50 years of plant Operation, assuming a value of
$1.50 per pound for perch. In contrast, the total potential market
value of angling at the plant site during the same time period was es-
timated to be $386,000. Yet, anglers were willing to pay a maximum of
$1,545,000 (total social value) to keep the plant site in existence for
angling. In the long run (life expectancy of the plant) the economic
losses of the plant to the fisheries seem to outweigh the economic

fisheries benefits in the marketplace, but not in overall social values.

Dedicated to my wife,

Linda Oliphant Stanford

ii

ACKNOWLEDGMENTS

An expression of sincere gratitude is extended to all members of
the Fisheries and Wildlife faculty who provided me with the opportunity
to pursue graduate studies. I appreciate the assistance, counsel, and
personal encouragement of Dr. Daniel R. Talhelm, my advisor and re-
search supervisor. I would also like to thank the other members of
my doctoral committee, Dr. Charles R. Liston, Dr. Milton H. Steinmueller,
and Dr. Alvin L. Jensen for their advice and constructive criticism.

Mr. Gale C. Jamsen and Mr. Ned Fogle of the Michigan Department of
Natural Resources graciously furnished vital information pertaining
to the yellow perch sport fishery. Dr. Thomas J. Horst, Stone and
Webster Engineering Corporation, willingly devoted time to explain the
theoretical implications of the mathematical models utilized in this
study. Dr. Dennis Gilliland, Department of Statistics and Probability,
Michigan State University, served as a consultant regarding the creel
survey. Dr. Pui Kei Wong, Department of Mathematics, Michigan State
University, verified the results of my population simulations and
eigenvalue analysis.

A special acknowledgement is reserved for the creel survey inter—
viewers: Jack Melkerson, Greg Curtis, Kathy Mooney, William Dimond,
Charles Kotz, John Klewicki, and Pat Betcher. They worked diligently
to collect data even under adverse weather conditions. Doug Kononen
and Wei-Chung Lin deserve mention for their competent computer-programming
assistance.

iii

Finally, I am indebted to Consumers Power Company for the financial
support which has made this study possible. I am especially grateful
to the personnel of the Department of Environmental Sciences, parti—
cularly Dr. John Z. Reynolds, Dr. Ibrahim H. Zeitoun, and Mr. John A.
Gulvas who provided necessary information concerning the J. R. Whiting

plant.

iv

TABLE OF CONTENTS

Page

LIST OF TABLES O O ....... O ....... O O O O 0 O 0 O ....... O O ....... O O O O O O O O O O Vii

LIST OF FIGURES O O 0 0 O O O O O O 000000 O O O O O O ....... O O O O O O O 00000 O 00000000 ix
CHAPTER

I. INTRODUCTION ... .................. . ........................ 1

II. LITERATURE REVIEW: HISTORY AND THEORY .................... 5

1. Roving Creel Surveys .............. .................... 5
2. Population Models ....... .......................... 15
3. Population Life History of Yellow Perch ............. .. 26
4. Demand and Supply for Outdoor Recreation ............. . 29
Introduction ........................ .......... ..... 29
Defining Demand and Supply ............. . ....... .... 30
5. Description and Operation of the J. R. Whiting
Plant ..... ....... .. ....... . .................... .. ..... 33
III. METHODS .. .................. . .............................. 37
1. Roving Creel Survey ........... .......... . ... ......... 37
2. Surplus Production and Leslie Matrix Models .. ......... 44
3. Price and Demand Equations for the J. R. Whiting
Plant Site ................ ..... . ..... ........... ...... 51
Data Collection . ....................... . ........... 51
Price and Demand Equations ..... .................... 51
IV. RESULTS AND DISCUSSION .. ...... ............................ 54
1. Roving Creel Survey ............... ....... . ............ 54
2. Surplus Production and Leslie Matrix Models and
Sensitiviy Analysis ...... ..... . ..... ...... ............ 59
Surplus Production . ............................ .... 59
Leslie Matrix ..... ........................ . ....... . 62
Sensitivity Analysis ........... . ................... 71

3. Price Equations, Demand Analysis, and Consumer
Surplus .... ........ ......... .......... ....... ....... 73
Price Equations .................................. 73
Demand Analysis .................................. 73

Consumer Surplus ..... . ........................... 79
V. CONCLUDING OBSERVATIONS .. ....... . ..... ........ .......... 81
APPENDICES

A GENERAL CREEL SURVEY QUESTIONNAIRE ........ . ............. 84
B PARAMETER ESTIMATION OF THE SUPRLUS PRODUCTION MODEL,

AND A PLOT OF OBSERVED YIELDS VERSUS PREDICTED YIELDS ... 85
C DATA SHEET FOR RECORDING BOAT COUNT INFORMATION . ........ 89
D STATISTICAL ANALYSIS OF BOAT FISHERMEN TOTAL ANGLER

DAYS .0. ........ ......OIOOOOOOOC ....... O ...... O 0000000000 90
E WHITING PLANT SITE QUESTIONNAIRE ........................ 93
F ESTIMATED CATCH AND EFFORT BY SPORTS FISHERMEN IN LAKE

ERIE WATERS OF MONROE COUNTY FROM FEBRUARY, 1978 TO

JANUARY, 1979 WITH PERIODS I, II, AND III COMBINED . ..... 97
G ESTIMATED CATCH AND EFFORT BY ANGLERS AT THE J. R.

WHITING PLANT SITE FROM FEBRUARY, 1978 TO JANUARY, 1979

WITH PERIODS I, II, AND III COMBINED .................... 98
H DESCRIPTION AND APPLICATION OF THE DATA FROM THE CREEL

SURVEY, BOAT COUNT, AND J. R. WHITING PLANT SITE
QUESTIONNAIRES 00............OOOOOOOOOOOOO00.0.0.0...COO. 99

I COMMON AND SCIENTIFIC NAMES OF FISH SPECIES CAUGHT IN
MONROE COUNTY 0.00.0.0.........OOCOOICCOOOOOOCO ..... 0.0.0102
J ANNUAL REDUCTION IN THE YELLOW PERCH POPULATION FROM

THE COMBINED EFFECTS OF IMPINGEMENT AND ENTRAINMENT .....103

LIST OF REFERENCES 000... ..... ooooooooooo oooooo o ooooo oo ....... 00.107

vi

Table

10.

F1.

G1.

LIST OF TABLES

Page
Life Table of Yellow Perch of Western Lake Erie
and Lake Huron ................................ ........... 27
Yellow Perch Sport Catch and Effort Estimates from
the Roving Creel Survey in Monroe County from February
1978 to January 1979 ....... ..... .............. ..... ...... 56
Yellow Perch Sport Fisheries Data Reported for Michigan
Waters of Western Lake Erie . ....... ...................... 57

Yellow Perch Commercial Fisheries Data Reported for
Michigan Waters of Western Lake Erie ..................... 60

Estimates of the Parameters k, K, and q for the
Commercial and Sport Surplus Production Models . .......... 61

Yellow Perch Population Estimate in the Michigan Waters
of the Western Basin of Lake Erie by Age ................. 63

The A_Matrix with Survivorship and Fecundity Estimates
of the Existing Natural Population and Initial Population
by Age Class .......... ............. ............. ......... 66

Number of Yellow Perch Impinged and Entrained by Age
at the J. R. Whiting Plant from March, 1978 to February,
1979 ......OOIOOOOOOOO......OIOIOOOOOIOCOO ...... .... ...... 67

Fifty-Year Simulated Loss to the Yellow Perch Population
in the Michigan Waters of Lake Erie ...................... 68

Price Equation Coefficients for Fishing at the J. R.
Whiting Plant Site from February, 1978 to January, 1979 .. 77

Estimated Sport Fishing Catch and Effort for Monroe
County Waters of Lake Erie from February, 1978 to January,
1979 00...........OIOOOOOCO... ........... O ....... 00.0.0... 97

Estimated Catch and Effort at the J. R. Whiting Plant
Site from February, 1978 to January, 1979 ... ........ ..... 98

vii

Table

II.

J1.

 

Page

Common and Scientific Names of Fish Species Caught in
Monroe County from February, 1978 to January, 1979 ....... 102

Annual Simulated Percentage Loss in the Yellow Perch

Population Prior to Stabilization from the Combined
Effects of Impingement and Entrainment ................... 103

viii

LIST OF FIGURES

Figure . Page

1. Percent of anglers on a stream or lake who have
been or will be interviewed in relation to the time
of interview; all anglers stay three hours each and

arrive randomly ............................. ............ 10
2. A normal supply curve (A) and a supply curve for

angling with a given travel time requirement (B) . ....... 31
3. An angling demand curve traced out by supply curves

(prices) and quantities of angling for anglers

residing at hypothetical locations A and B ............ .. 34
4. J. R. Whiting plant site ................. ............... 35
5. Map of western Lake Erie ............. ........ ........... 38
6. General system block diagram ......................... ... 45
7. Estimated equilibrium yield and effort relation (para—

bola), and regression of yield on effort (solid line).
The points are observed yield and effort values from
1960 to 1969 for the commercial fishery ................. 64

8. Estimated equilibrium yield and effort relation
(parabola), and regression of yield on effort (solid
line). The points are the observed yield and effort
values from 1970 to 1977 for the sport fishery .... ...... 65

9. New growth rate of Lake Erie yellow perch for each
respective change in survivorship within each age
Class O.......O......0.0.00.00.00.00......OOOOOOOOOOOOOO. 72

10. Price curve, Period I, showing the user cost of angling
as related to travel time to the J. R. Whiting plant
Site .....IOOCOOOOOOOOOOOO ..... O ........... 0.... ......... 74

11. Price curve, Period II, showing the user cost of

angling as related to travel time to the J. R. Whiting
plant SiteOOIIOOICOOOOOOOOOOOOOO 00000 OOOOOOOOOOOOCOOO... 75

ix

Figure Page

12. Price curve, Period III, showing the user cost of
angling as related to travel time to the J. R.
Witing plant Site 0....0.0.0.0.........OOCOOIOOOOOOOOOO 76

13. Demand curves for non-salmonid fishing at the J. R.
Whiting plant site during Periods I, II, and III ....... 78

B1. Observed yields (solid line) and yields predicted
by the surplus production model (dashed line) for the
commercial fishery. The solid horizontal line is MSY .. 87

BZ. Observed yields (solid line) and yields predicted by
the surplus production model (dashed line) for the
sport fishery. The solid horizontal line is MSY ....... 88

I. INTRODUCTION

Concern in the United States regarding cooling systems of power
plants originally centered on the potential impact of their thermal
effluent. Recently, however, a major topic of study has been the impact
on fish populations resulting from mortality of fish eggs and larvae
carried by the cooling waters through the plant (entrainment) and from
mortality of juvenile and adult fish trapped on intake screens (impinge-
ment) (Van Winkle, 1977).

Increasingly, scientists and engineers are realizing the importance
of improving their ability to assess the effects of impingement and
entrainment on fish populations. Recently, in relation to power plant
sites, they have proposed that mathematical or simulation models be
employed to evaluate these effects.

In this study, the surplus production and Leslie matrix models were
applied to estimate the effects of impingement and entrainment by the
J. R. Whiting plant on the yellow perch pOpulation.iJ1the Michigan waters
of Lake Erie. The surplus production model estimates the harvestable
biomass and harvestable numbers in the population from catch and effort
data of the commercial and sport fisheries. The Leslie matrix model
projects the future number of fish and the age distribution of the
population.

Parameters of the surplus production model are estimated from catch

and effort data. Traditionally catch and effort information has been

supplied by governmental agencies, varying from state to state, respon-
sible for natural resources. In Michigan, the Department of Natural
Resources (MDNR) surveys licensed anglers by mail to estimate total catch
and effort by species in established statistical (geographical) districts.
These surveys have overestimated catch by as much as a factor of 5
(Rybicki and Keller, 1978). Therefore, a roving creel survey was con-
ducted in Monroe County. The catch and effort estimates of this survey
are compared with those of the MDNR.

Commercial catch and effort data in Michigan deserve the same scru-
tiny as the sport estimates, but there are no known studies questioning
their accuracy. The type of investigation that is needed can be seen
in the work of Schaaf and Huntsman (1972). In a marine fishery, they
studied the Atlantic menhaden commercial fishing fleet, observed its
improved fishing efficiency, and by necessity, redefined a unit of effort.
Subsequently,theyuapplieda.stockrrecruitment model to this fishery and
they determinedthat the menhaden resource was overexploited.

Another factor contributing to the suspected inadequacy of Great
Lake commercial catch and effort statistics may be MDNR fishing rules
such as Michigan R299.884(1970), which prohibits commercial fishing
of yellow perch with gill nets in the Michigan portion of Lake Erie. The
MDNR initiated a zone management plan which eliminated gill netting in
Lake Erie. Consequently carp has become the dominant species caught by
Michigan commercial fishermen in Lake Erie.

Power plants not only have direct positive effects such as providing
electric power, but they may also incidentally provide access points

and angling sites for fishermen. To assess the value of angling at a

 

plant site a demand schedule for angling at the site must be estimated.
This will measure in dollars the willingness of anglers to exchange
their resources for various amounts of angling. The demand for angling
at the J. R. Whiting plant site was estimated using a method developed
by Clawson and Knetsch (1966). A demand curve is estimated from the
cost per visit, the travel distance to the angling site, and the visit
rates (angler days/1000 capita) for each travel distance zone.

This dissertation is part of an overall Consumers Power report.
The main objective of the overall report is to estimate the economic
value lost to anglers (beyond the sc0pe of this dissertation) resulting
from impingement and entrainment. In order to estimate this economic
loss the results of my research are necessary. The primary objectives
of my dissertation are to:

1. Estimate the total yellow perch pOpulation size (numbers)

in the Michigan waters of Lake Erie utilizing two surplus
production models (sport and commercial).

2. Estimate the percent reduction in numbers of juvenile and
adult yellow perch from impingement and entrainment after '
the total population size in numbers has been determined.

3. Estimate the economic value of angling provided by the
plant site based on a demand schedule.

In this dissertation, Chapter II is a brief historical and theo—
retical review concerning 1) catch and effort estimations from roving
creel surveys, 2) the development of population models, 3) the approaches
employed by resource economists for estimating demand, 4) the life

history of the yellow perch, Perca flavescens, and S) the description

 

and operation of the J. R. Whiting plant. Chapters III, IV, and V
are the methods, results and discussion, and concluding observations,

respectively.

II. LITERATURE REVIEW: HISTORY AND THEORY

1. Roving Creel Surveys

 

A paucity of information exists regarding roving creel surveys.
Most investigators collect catch and effort data at access points in
the fishery and obtain information from anglers regarding completed
fishing trips. In many inland areas access points may not be readily
available. For example, it is difficult to encounter all anglers,
particularly those located along a path of stream flow only accessible
via private property. This difficulty of locating anglers led to the
development of the roving creel survey.

Robson (1960) outlined a detailed creel census procedure for esti-
mating catch per unit effort (CPE), total effort, and thus total harvest,
using stratified random sampling. This method, however, was found to
be inefficient in the field. Sampling areas had to be small to allow
a complete census of anglers during any sampling period, thus precluding
its use on bodies of water where many access points are present. Field
personnel were inefficiently used since they were stationery and depen-
dent on anglers coming to them.

Hayne (1966, 1972) utilized the stratified random sampling approach.
However, he also introduced a roving investigator into the sampling
scheme so field personnel could actively contact anglers. This pro-
cedure is adaptable and versatile in many field situations and is appli-

cable in both access point and roving creel surveys. The basic features

of this approach are:

1.

The entire period for which the fishery is to be surveyed is
divided into time blocks. The amount of fishing expected

to take place within these blocks should be similar.

Each time block is divided into non—overlapping sampling
units.

Probabilities of expected fishing pressure are assigned to
the sampling units. The sum of the probabilities assigned
to the sampling units within any given block equals 1.0.
Sampling units are randomly chosen within each block based
on the above sampling probabilities. The probability that
sampling will actually be done during any given sampling
unit is proportional to the amount of fishing expected to
occur during that unit.

Sampling on the water body is comprised of counts and inter-
views. Counts of fishermen are done as quickly as possible,
preferably being made for the entire body of water from
some vantage point. It may be necessary to divide large
lakes into sections. The sections, like the sampling units,
are randomly chosen with probability proportional to the
amount of fishing expected to occur in the sections. After
counts are made fishermen are interviewed. Information
gathered from them must include time spent fishing and
weight of fish caught so total harvest can be estimated.

The probability assigned a sampling unit or lake section, x,

equals the number of units of expected fishing effort in

sampling unit or lake section, x, divided by the total number

of expected units of fishing effort of all sampling units

or lake sections (probability proportional to size).

Malvestuto, Davies, and Shelton (1978) conducted a roving creel
survey with nonuniform probability sampling employing the techniques
of Hayne (1966, 1972). They estimated catch and effort at a Georgian
reservoir and indicated that there was no significant difference be-
tween the mean catch/effort for completed trips measured through access
points and the mean catch/effort of incompleted trips measured with
the roving survey.
Talhelm (1972) developed a roving creel survey technique for

interviewing anglers on inland streams. His method, which also may
be applied to lake shore anglers, was used in this study. Talhelm's
survey method incorporates a few of the same concepts as Hayne (1966,
1972), but instead of counting alltfiuaanglers and then interviewing them,
the anglers were interviewed as soon as they were contacted. Information
concerning angling hours,angler days, catch in numbers and pounds,
species composition, and other pertinent information was gathered. In
this tehcnique, it is assumed that all anglers on a lake or stream
segment could be interviewed at any selected point in time on a sample
day. Each stream or lake segment is sampled at several points in
time on its sample day. At each selected point in time, the interviewer
travels the length of the lake or stream interviewing all anglers en-
countered. If there were a large number of anglers, making it impossible
to interview all of them, then every second or third angler would be

interviewed. The probability of finding each angler is proportional

to 1) his length of stay in that area, 2) the number and distribution
of the point samples throughout the day, and 3) the length of day. It
is assumed that anglers know how long they will remain in the area on
the sample day.

It is not possible for one or two interviewers to administer a
ten-minute questionnaire to all anglers at one point in time on a lake
or stream. Therefore, the interviewer starts at one end of each lake
or stream segment and systematically samples the entire segment, inter-
viewing each angler encountered along the way. Talhelm (1972) defines
this sample as a traverse. One traverse is statistically treated as
a sample of the entire stream or lake segment at one point in time. In
fact, each point on the stream or lake segment is sampled at a particular
point in time. Assuming the composition of the angling population
does not change significantly over the period of the traverse, the
result is essentially the same as a sample at one point in time. The
interviewer does not interview anglers who leave as he approaches a
point or anglers who arrive at a point just after he passes that point.
Anglers encountered more than once within an area sampled on a par—
ticular sample day are not re-interviewed.

Since more anglers may be distributed throughout an area at a
particular time of day, as opposed to other times of the day, the effec—
tiveness of each traverse is maximized by spacing the traverses at equal
time intervals from one another throughout the sample day. Each traverse
is viewed as the midpoint of a segment of an equally divided sampling
day, and the interviewers attempt to traverse the area at least three

times a day. For example, assuming a 12-hour day, the three segments

of the day would be approximately 4 hours long: 6:00-10:00, 10:00-2:00,
and 2:00-6:00. The number of hours of each segment depends on the angling
day length. In this example, the area would be traversed at equal

time intervals as close as possible to 8:00, 12:00, and 4:00.

On a particular sample day an interviewer traverses a given area
along a well-defined route. The interviewer follows this path iden-
tically for each traverse during the sample day. The route within
each area is in a north—south direction. When a particular area is
sampled on another sample day, the interviewer should start his first
traverse at a different geographic point (selected randomly) from the
one sampled in that area on a previously sampled day. Three starting
points were chosen within each area: the most northerly and southerly
points and a point midway between both of these. This is done so that
most areas are sometimes traversed early and sometimes late for the
duration of the entire creel survey.

If it is assumed that anglers are distributed throughout the day
in a random pattern, the likelihood of encountering them can be deter-
mined. Figure l (Talhelm, 1972) is a graph which enables a researcher
to ascertain the percent of 3-hour anglers on a stream (or lake) who
have been interviewed in relation to the time of interview during
a 9-hour angling day (0 to 9). Specifically, the isosceles triangle
ABC indicates the instantaneous percentage of 3-hour anglers who will
be or have been interviewed at any specific point in time. For example,
if one traverse is performed during an entire 9—hour angling day
and it is initiated at T=3, then 100 percent of the 3-hour anglers who

arrive on the stream or lake between 0 and 3 would be interviewed.

 

10

 

 

(3

 

 

 

hD-—J

I 1

ad»
All
"1

I
4

(fl
0’

TIME IN HOURS IN RELATION TO ANGLING DAY LENGTH

Figure 1.

Percent of anglers on a stream or lake who have been
or will be interviewed in relation to the time of
interview; all anglers stay three hours each and
arrive randomly.

11

Half of the 3-hour anglers (ABC is half the area AFDC) who are on the
stream or lake from 0 to 6 are interviewed and none from 6 to 9.

A second traverse at T=6, along with the traverse at T=3, would
result in 50 percent of the anglers being interviewed from O to 3
(half retangular area AFBG), 100 percent from 3 to 6 (entire area
GBDC), and 50 percent being interviewed from 6 to 9 (CDE is half the
area since an area equivalent to AFB is placed atop CDE). The percentage
of 3-hour anglers interviewed or the probability of encountering these
anglers during the entire 9-hour day given two traverses (at T=3 and

T=6) would be 662/3

percent (4 of 6 possible areas of Figure 1). Both
of the above examples assume random arrival and departure of anglers
during the 9—hour day, and before 0 and after 9 (open-ended).

If the angling day is assumed to begin exactly at 0 and end exactly
at 9 (close-ended), then all 3-hour anglers prior to time 3 would be
interviewed. This shifts AB to AFB during the first 3-hour period,
and an area equivalent to AFB is placed atOp CDE. This indicates that
100 percent of all anglers would be interviewed (traverses at T=3 and
T=6) during the 9—hour angling day.

The geometrical representation for estimating the percentage of
3—hour anglers interviewed or the probability of encountering 3—hour
anglers during the 9-hour angling day with traverses at T=3 and T=6

(Figure 1) can also be expressed mathematically (Talhelm, 1972). The

probability of encountering 3-hour anglers is:

 

-—— (equivalent to the
x 9 3 geometric solution)

12

where
mi = number of traverses on sampling day i,
ij = total fishing hours on sampling day i by interviewed
angler j,
xi = length in hours of the angling day on sampling day i.

The total number of angling hours (qi) on a stream or lake during angling
day i is given by equation (1) which is separated into forms (A) and

(B):

v
a = 2 ——————~—— - h.. = v x (A)

Form (A) is used under the condition that the probability of encountering

these interviewed anglers is less than 1.

where
ai = angling hours on day 1,
vi = number of different interviews on day i where the proba-
bility of encountering these interviewed anglers is less
than 1.
n.
1
bi = 2 h,, (B)
j=1 13

Form (B) is employed under the condition that the probability of en-
countering anglers equals 1.

where

0"
II

angling hours on day 1,

number of different interviews on day i where the proba-

:3
II

bility of encountering these interviewed anglers equals

1.

13

The summation of equations (A) and (B) gives:
n
q. = v x + 2 h . , (1)

Form (A) is used to calculate the number of angling hours of interviewed

angler j if m oli < xi (probability of encounter is less than 1).

i ij
Form (B) is employed if mi - hij :_xi (probability of encounter = 1).
For example, if angler j reports angling hours (hij) = l, and x1 = 12

and m1 = 3, then the probability of encountering l-hour anglers would
be:

probability (encounter) = mi - h. 3 ° 1 1

The number of angling hours represented by interviewed angler j would

%§.= 4), If angler j reportslqj : 4 the

probability of encounter would equal 1. Therefore, form (B) would

be 4 (form (A)) (SITZT' 1=

be used, and the number of angling hours would equal hij'
The total number of angler days or visits/day (ADi) on angling day

i is estimated by equation (2) which is separated into forms (C) and

(D):
V.
1 xi
c. = Z ————————- , if for a particular interviewed (C)
1 . m, ° h.
J=1 1 1j
O <
angler j, mi hij xi.
where
c1 = angler days on day i.
D.
1 xi
d. = Z = n., if for a particular interviewed (D)
1 j=1 mi ° hij 1

angler j, mi - h. > x,.

14

where
di = angler days on day i.

The summation of equations (C) and (D) gives:

V
AD = 2 —-—-——— + n. (2)

Usually all shore anglers encountered could be interviewed. See Appen-
dix H for an explanation of how the occasionally skipped angler is
entered into equations (1) and (2).

Equations (1) and (2) assume an open-ended fishery. These equations
may underestimate total angling hours or angler days because the sport
fishery acts like a close-ended fishery instead of an open-ended fishery,
but since angling occurs at night underestimates may result. Therefore,
to compensate for this underestimation, a correction factor must be
subjectively introduced by multiplying the correction (C.F.) times
equations (1) and (2) (Talhelm, 1972). For example:

“i

q. = v x (C.F.) + Z hij (C.F.) (3)

1 i i ._
(3;) J-1

C.F. = 1 + a fractional adjustment which allows for the proba-
bility that total angling hours or angler days are
underestimated.

The C.F. is equivalent to shifting AB to some position approaching
AFB in Figure l.

Angling hours, angler days, and catch were computed for each
sampling day in each area, then seasonal estimates were calculated by
proportionally expanding the sample results to the population of days

involved during the survey.

15

2. Population Models

 

Frequently fishery biologists must decide whether or not restrictions
or regulations must be imposed on fishing effort within a particular
fishery. Often these regulations are initiated to prevent overexploi—
tation of a fish stock. In the future, with increasing demand for fish
as a food source or for recreation, it is likely that increased regulation
will be needed. Biologists and other concerned professionals (economists,
lawyers, etc.) must ensure that the most suitable measures be introduced.
Management of fisheries depends on accurate biological and socioeconomic
information about a fish stock to ensure that the consequences of manage-
ment action satisfy those directly involved in the fishery.

In predicting the consequences of a management action, fishery
biologists must model the fish population. Models consist of mathe—
matical expressions which represent the events that occur in the fish
stock. The results of models assist managers in predicting the effect
of management actions, such as controls on the amount of fishing or
the sizes of fish caught. If the model is useful management actions
can be analyzed and the results predicted by the model will correspond
reasonably well to what would actually occur in practice.

Two models commonly used by fishery biologists are: 1) the logistic
surplus production model which treats the population as a whole, con-
sidering the changes in biomass without reference to its structure
(age composition, growth, etc.) (Graham, 1935; Schaefer, 1957) and
2) the dynamic pool model which considers the population as the sum
of its individuals and deals with the growth and mortality rates of

these individuals (Baranov, 1918; Beverton and Holt, 1957; Ricker, 1958).

16

The logistic surplus production model treats the population as a
single variable, biomass. The simplest types of data (catch and
effort) are used in its application. Only relative abundance, measured
in terms of catch per unit of effort, is needed to determine the
harvestable biomass of a fish stock. The logistic model is based on
a generalized logistic population growth equation. In the logistic
growth equation the biomass of a population will tend to increase until
the population has reached the limit of the carrying capacity of the
environment. The rate of increase will be determined solely by the

current biomass of the population, expressed mathematically as:

d_B
dt

= f(B). (4)
Limits to f(B) are set by the fact that it will be zero when the
population is zero and at equilibrium. At equilibrium the population
will tend to stabilize in the absence of exploitation. As the pOpulation
increases from an initial size close to zero the rate of increase will
rise to amaximum at some intermediate value and then decrease. A plot
of the population growth rate against population abundance forms a
parabolic curve if it is assumed that the exponent of the generalized
logistic growth equation equals 2.

If fishermen remove an amount of biomass from a fish stock during
year, t, equal to its natural increase, then the biomass available for
year, t+1, will be identical to that during year, t. This biomass
removal could be repeated each year indefinitely; this removal is termed

surplus production or sustainable yield. In the equations for the

surplus production model, the change in yield is a function of fishing

l7

effort and stock size or biomass (Equation 5) and change in biomass is

equal to growth minus harvest or yield (Equation 6).

where

dY
a? ' ‘153 (5)
LB = kB-kB2 —qEB (6)
dt T

Y = yield (or catch) in pounds or numbers

t = time in years

q = catchability coefficient

E = fishing effort (fishing gear used per time period)

B = harvestable biomass or numbers of the population (biomass
is in pounds)

k = population growth constant

K environmental carrying capacity

The assumptions of the surplus production model are:

1.

5.

6.

Model is deterministic (no random variables), it describes
the average situation.

Age structure is stable.

Time lags are ignored.

Catchability is constant over years and population sizes.
POpulation over the area of interest is a single stock.

Surplus production is a parabolic function of biomass.

The parameters q, K, and k of the logistic model are estimated

from the catch and effort data of commercial and sport fisheries.

Several methods of fitting the surplus production curve have been de-

veloped including a method for linearizing equation (6) (Schaefer, 1957).

18

A multiple linear regression analysis can be utilized with this method
if more than three years of data are available. This study employs

the Schaefer method since the assumption that fisheries must be in
equilibrium is not required (See Chapter III). The parameter estimates
(estimated by ordinary least squares) from this method were then varied
and substituted into a computerized systematic search routine to

find parameter values which minimize the residual sum of squares
(Jensen, 1976). Further details are in Appendix B. Jensen (1976)
discussed other methods some of which require the fishery to be in
equilibrium. Schaefer (1954) proposed an equilibrium approximation
method that was further discussed by Gulland (1969) and Fox (1975).
Several equilibrium equations were derived by Gulland and Fox for the

surplus production model such as:

2 2

Y = qKE-R E (7)

e 7?-
These equilibrium relations are linearized easily. However, these
methods may not work well for fisheries which are never in equilibrium.
Finally, for the non-equilibrium fishery Pella and Tomlinson (1969)
developed a method of numerically integrating equation (5) instead of
approximating it as Schaefer (1957) did. Substituting Pella and
Tomlinson's solution of the integration of equation (6) into equation
(5) gives an equation for yield as a function of time which can be
integrated numerically for given values of the parameters K, q, and k.
A computer search routine is then applied to find values of the param-

eters which minimize the residual sum of squares. This method works

well with data points on both sides of the maximum sustained yield point

19

of the surplus production curve. Since the data points in this study
were scattered to one side of the maximum sustained yield point of the
surplus production curve, Pella and Tomlinson's method was not employed.

Dynamic pool models consider the population of fish as the sum
of its individual members, rather than a single unit. Growth and death
rates of these individuals are analyzed. Logistic models assume that
the rate of growth, death rates from causes other than fishing, and
the number of young fish recruited to a fishery each year are constant
and independent of the abundance of the stock, or the amount of fishing.
Logistic models also assume that individual fish of the same age do
not differ among themselves regarding their rate of growth or suscep-
tibility to capture by fishermen using various types of fishing gear.
These assumptions can be relaxed and replaced by more realistic, yet
more complex, dynamic pool models.

The ideal analytical approach of dynamic pool models for estimating
total yield of a stock would be to consider one cohort of fish through-
out its life. However, in a steady state (constant fishing and mortality
rates), the average yield in a year from all year classes present would
be equaltx>the yield from any one cohort during its life. The assumptions
of the dynamic pool model involving the simple algebraic expression of
yield are:

1. The instantaneous fishing and natural mortality coefficients

are constant.

2. Recruitment is constant.

3. Fish grow isomorphically (fish have the same shape throughout

life). Otherwise the cubic exponent in equation (10) may not

be totally valid.

20

The actual calculations require a mathematical expression for the

growth of the individual fish. The algebra is easier if the expression
of growth canlxacombined easily with an expression for the number of
fish. The latter can be obtained from mortality rates. In mathematical

terms the change in numbers is given by:

§%-= —ZN (8)
where
N = cohort or year class numbers of fish,
Z = F + M = instantaneous total mortality coefficient,
F = instantaneous fishing mortality coefficient,
M = instantaneous natural mortality coefficient.

If 2 is constant, the differential equation can be solved to give:

-M(tC - tr) - (F + M)(t - tc)

Nt = Re (9)
where

Nt = number of fish alive at time, t,

R = number of recruits annually,

tc = age fish become vulnerable to the fishing gear,

tr = age of recruitment into the fishery.

A convenient mathematical expression of growth which fits a wide range
of ages is the von Bertalanffy growth curve, used by Beverton and Holt
(1957). This expresses the weight in the form:

-k’(t - t )
ww(1 — e ° )3 (10)

8
II

where

2
II

average weight of a fish at age, t,

21

W» = average asymptotic weight of a fish,
k’ = growth coefficient,
to = time when the length of a fish is theoretically zero.

This expression for weight combined with the expression for numbers,

provides the formula for yield

t1 -(I~‘ + M)(t - ta) 3 -nk(t - to)

Y = F .r wae z nae dt (11)
tc n=0

where

t1 = maximum age attained,

U6 = 1,

U1 = -3,

Ué = 3,

U3 = -l.

Cubing the parenthetical expression in equation (10) gives these U;
constants in equation (11). Other more complicated algebraic expressions
of yield are possible but will not be discussed. The essential point
is that the yield may be limited by management agencies either by con—
trolling the amount of fishing (F), or the age of first capture (tc).

To make a calculation of yield it is necessary to have estimates
of several parameters in the yield equation. The parameters relating
to growth of the individual fish (WA, k, to) are easily calculated if
the age of the individual fish can be determined from scales or otoliths.
The pattern of growth plus some knowledge of the general biology and
behavior of the fish can provide an estimatecfi tr’ The natural mortality
coefficient, M, is difficult to estimate directly. Usually only the

total mortality, 2, is easily measured. Various techniques are used

22

to separate Z into fishing and natural mortality. The effect of management
measures can depend quite critically on the natural mortality. Re-
cruitment is frequently not explicity estimated, but rather the yield
is expressed as the yield per recruit, Y/R. Recruitment is difficult
to estimate directly. For many fisheries, the best recruitment esti—
mates are obtained by multiplying Z times Y and dividing both by F.
Recruitment is often determined by dividing Y/R into the observed

value of the yield. The reason Y/R is calculated is that in a number
of fisheries annual recruitment fluctuations vary very widely. The
fluctuations appear almost random and quite independent of fishing.

The most important reason for expressing the results as Y/R is that in
the simple yield model it is assumed that recruitment is unaffected by
the amount of fishing, or the abundance of the parent stock. The
relationship between stock and recruitment can take many forms (asymp-
totic, dome-shaped, or parabolic curves) which in turn may have very
different effects on the shape of the curve of total yield against the
amount of fishing. It may also be difficult to determine the true form
of the stock-recruitment curve for a particular stock of fish.

The surplus production model was selected for use in this dis-
sertation because the data available (catch and effort) could be readily
applied. The simplicity of application of the logistic surplus pro-
duction model enabled this investigator to conduct two other analyses
simultaneously, a creel survey and an economic evaluation of the plant
site. The major disadvantages of utilizing the logistic model include:
1) several assumptions in the model are unverifiable (e.g. whether

the plot of yield versus effort is in fact a parabolic curve), 2)

23

accurate parameter estimates are difficult, and 3) the basic equations
are not easily modified to make the model more realistic. Given the
harvestable biomass (or numbers) estimated from this model, life

history information, and the percent of the total catch by weight of

each age class with trapnets (percentage often ranges between 50 and

65 percent depending on effort), the population size was estimated

(See Chapter III). After estimating the yellow perch population size
(number) using the surplus production model, the Leslie matrix model

was employed to simulate power plant effects (impingement and entrainment)
on this population through time.

The Leslie matrix model was introduced by Leslie (1945). It has
been extensively used in demography but overlooked by ecologists until
recently. Saila and Lorda (1977) discussed the advantages and dis—
advantages of this model. The advantages of this discrete time model
include its computational straightforwardness and consideration of
age structure without assuming a stable age distribution.

The major disadvantage of the Leslie matrix model is that it implies
a linear (density-independent) stock—recruitment relationship, since
compensatory mechanisms (density dependent) are ignored; it also
requires estimation of a large number of parameters. In this case,
compensation refers to changes in birth rates and death rates in re-
sponse to changes in population density.

The mathematical structure of the Leslie matrix model is:

24

no f0 f1 ° fx-l fx n0
n1 so 0 o 0 n1
n2 = 0 s1 0 o x n2
(12)
n t+l o o s o n
x x-l x t
__ __ I... _ _. ....J

 

 

 

 

 

 

The column vector Nt is the population number by age class at time t;
the nx elements correspond to the number of individuals at each of

X + 1 ages. The X + l by X + 1 population projection matrix A_has
elements in the first row corresponding to the reproductive potential
or eggs produced per adult (fecundity). The elements of the subdiagonal
correspond to the age specific survival (number of males and females
alive at the end of a one-year period relative to the number alive at
the beginning of a one-year period). If sufficient information for a
species exists to estimate the age-specific fecundity and survivorship
parameters in the population A matrix, then the population growth rate,
A, can be determined by eigenvalue analysis. The intrinsic rate of
increase or so-called finite population growth rate, A, is defined as
the rate of increase per individual per unit of time. The population
growth rate (A) is the positive real eigenvalue (A) of the matrix.

If A8 1.0, then the population is most likely stable or in equilibrium.
The model also permits a detailed analysis of short term predictions
(period of 50 years or less) of the population dynamics under the as-

sumption of constant fecundity and survivorship rates.

25

A sample calculation for one iteration of the Leslie matrix model

would be:
no(t+l) = fon0(t)+f1nl(t)+ °°°°+ fxnx(t).
n (t+l) = S n .
l o o
n2(t+l) = Slnl.
nx(t+l) = Sx-lnx-l'
where
nx = number of age x fish
fx = fecundity of age x fish

3 = survivorship of age x fish

Given the initial population (equivalent to Nt above) calculated
from the surplus production model, survivorship, fecundity, and impinge—
ment and entrainment mortality rates, the following will be determined
in this study utilizing the Leslie matrix model:

1. Effects on all age classes, especially adults, affected by

power plant operation.

2. The effects of impingement and entrainment on yellow perch
stocks during the expected life of the plant (50 years).

3. Changes in the population growth rate resulting from dif-
ferential survival rates of the different age classes as a
consequence of power plant operation.

A sensitivity analysis will also be conducted to test the effect

of changes in the elements of the A_matrix (survival rates) on the

population growth rate.

26

3. Population Life History of Yellow Perch

 

The scientific literature and commercial fisheries statistics were
reviewed to determine the population life history and structure (age

composition, growth, etc.) of the yellow perch, Perca flavescens. This

 

information formed the basis for parameterizing the pOpulation models.

The yellow perch is a North American freshwater fish (Family
Percidae). It occurs naturally from Nova Scotia south to the Florida
panhandle, north to western Pennsylvania,west to eastern Kansas, north-
west to Montana, north to Great Slave Lake (Northwest Territories)
and southeast to James Bay, Quebec, and New Brunswick. The yellow perch
has also been introduced successfully in most states to the south and
west (Scott and Crossman, 1973).

The yellow perch spawns in the spring, usually during April and
May, but spawning may be extended into July. The adults migrate shore-
ward into the shallow areas of lakes. Spawning occurs at night and
early morning, usually near rooted vegetation, submerged brush, or fallen
trees, and occasionally over sand or gravel. The food of yellow perch
changes with their increase in size from immature insects to small
fish (Keast and Webb, 1966).

The reported sex ratio of yellow perch varies. El—Zarka (1959)
reported that on the average female yellow perch constituted 38 percent
of the spawning runs in Saginaw Bay, while Lake Huron had from 83 per-
cent in age 2 to 23 percent in age 6 from 1943 to 1955. Table 1 contains
sex ratios reported from Lake Huron.

Commercial fisheries data on Lake Erie indicate that age 6 is the

oldest age class (Jobes, 1952). Both El-Zarka (1959) and Jobes (1952)

27

Awnafiv noumnmz can occum ”Ammma .uoonmV sowamuuoEuH u Hm>fi>u=mm

Ammmav mxumwuam

 

 

q
Amomfiv umBom mam wumnmm
mm o

Ammmfiv n h~.H

0 mm. qwm.mo oqm mom 0

Nmfimm. om. wmo.sq mmm omm m

Nammm. as. Nso.w~ mom NRA s

amenfi. om. mm~.nfi me n- m

Nummo. <\z o oqa mm N

Nmmwo. <\z 0 mu m H

mNHHo. <\z o mama oz mama oz 0
AmemEmm mmamsmm AmHmEmw\mwwmv AEEV AEwV Aumomv
mam moamev coaumanmom mo zuwccnoom nuwcmq vumvcmum ucwfioz ow<

mHm>H>u=m ecowuuoaoum m N ~

 

 

.counm mxmq mam ofium mxmq cumumoz mo noumm soHHmw mo manmh oMHA .H manme

28

state that the majority of females are not sexually mature until age
3 in Lakes Huron and Erie. Yellow perch become highly vulnerable to
sport fishing at age 2. Age was determined by scale samples taken
during the creel survey in Monroe County.

Survivorship of each age class of yellow perch in the western
basin of Lake Erie can be estimated using age frequency distribution
provided by Jobes (1952). Stone and Webster, Inc. (1978) estimated
survival by a least squares regression of the natural log of the number
commercially collected for ages 2 to 6 against the log of the age;
survival of age 1 was assumed equal to age 2. For age 0 fish the
indirect method of Vaughan and Saila (1976) was used to estimate the
survival rate from egg to age 1; these were the only survival rates
available for Lake Erie yellow perch (Table 1).

Fecundity and average weight as well as length (L) information
were estimated by Sheri and Power (1969) and Jobes (1952) respectively

(Table l). Formulae for fecundity (F) and weight (W) are:

Log F = 3.769 + 0.004 w
10

w = 1.776 x 10'51.3'015
The percent of the total commercial trapnet catch by weight of each
age class of western Lake Erie yellow perch was estimated by Muth (1978).
The percentage of females in each age class and the fecundity estimates
reported by El—Zarka and Sheri and Power respectively are lower than
those of other investigators. For this reason the El-Zarka and Sheri

and Power data were used in this study. These lower estimates result

in a smaller population size for year, t, when the Leslie matrix is iterated.

29

This in turn maximizes the adverse power plant induced mortality effects
of impingement and entrainment on the yellow perch population.

The yellow perch has economic importance to man both commercially
and recreationally. The yellow perch is sold almost everywhere. It
inhabits a vast territory and aggregates near shore especially in the
spring; it usually stays in shallow water of less than 30 feet, although
it may be found in deeper water. These facts make it readily accessible
to fishermen. Leach and Nepszy (1976) state that the population of
yellow perch in the western basin of Lake Erie is currently unstable,
since the exploitation of yellow perch stocks has intensified since
the decline of the blue pike and walleye in the 1950's. Variability
in year class strength has been characteristic of perch populations
in western Lake Erie since the 1950's. Strong year classes were re-
cruited in 1959, 1962, l965, and 1970. Since 1970 the year classes
of yellow perch in western Lake Erie have not been strong, resulting

in a depressed commercial resource (Leach and Nepszy, 1976).

4. Demand and Supply for Outdoor Recreation

 

Introduction

 

Most demand studies of outdoor recreation have focused on travel
costs as a primary variable influencing visitation (Korson, 1979).
Hotelling (1949), Trice and Wood (1958), and Clawson (1959) defined
broad geographic zones around the recreation site, and assumed that
money and travel costs determined the quantity of use at visited sites.
The amounts of participation associated with each level of travel costs
are employed to derive a demand curve for a single unique recreation site

(Clawson, 1959).

30

Defining Demand and Supply

 

Consumers respond to decreases and increases in the relative price
of a product by increasing or decreasing their consumption of that
product respectively. A demand curve summarizes this behavior. Demand
is defined as a schedule of the maximum quantities purchased (per unit
of time) at every possible price over a particular period of time,
holding other influences on demand constant.

The demand for angling is similar to the above price—quantity
schedule, but prices here are not determined by typical market forces.
Rather the "price" of angling represents the cost of angling in terms
of the money and time resources required of the angler for participation
in angling activities. Angling demand relates costs (prices) of
participation to the amounts (quantities) of participation. For in—
stance, if the price of angling increases, the aggregate quantity of

use (days) enjoyed by anglers will decrease, ceteris paribus. An

 

angler day is defined as any part of a day an angler fished. "Demand

for a particular type of angling is the willingness of anglers to

exchange their resources for that type of angling" (Talhelm, 1973b).
Other factors influence demand. These factors change the shapes

and positions of demand curves, and consequently participation rates

of angling. Dwyer, et al. (1977) states "that influences such as

availability and quality of alternative forms of angling, and the

nonhomogeneous tastes and income in the population should be considered."
The quantity of a good offered for sale by producers depends on

the expected price in the marketplace. Curve A in Figure 2 represents

a typical supply curve; it is a price-quantity relationship which shows

31

 

I: A
z
a
a:
m
a.
'33 8
Lu
2
a:
ti

 

 

QUANTITY "SUPPLIED"

Figure 2. A normal supply curve (A) and a supply curve for
angling with a given travel time requirement (B).

32

the given quantities of goods which will be produced (per unit of time)

at various prices during a specified time period, ceteris paribus

 

(Talhelm, 1973b).

The supply of angling recreation is different since consumers
are also the producers of angling activity. Anglers exchange their
personal time and monetary resources for angling activity. The price
of procuring a unit of angling is determined by the monetary and time
costs of transportation to the site and by other costs. Therefore,
angling supply is defined as the minimum price at which each quantity
of a particular kind of angling use is available at an angling site
during a specified time period (Talhelm, 1973b).

Angling "price equations" express angling costs as a direct function
of travel time or distance (Talhelm, 1978). The leading sources of
angler costs incurred to produce angling are: 1) travel time value
necessary to participate in angling, 2) transportation, 3) monetary
cost of food and lodging, 4) direct expenditures for fees, licenses,
and equipment, and 5) value of time spent angling.

Visitation rates to a particular recreation site are not influenced
solely by monetary costs, but also by the time restraints of reaching
the site. Greater travel distance increases the time and monetary
cost of travel and reduces the recreational time available in a given
time period (Talhelm, 1972). Under conditions of perfectly flexible
substitution of work and non-work activities, the Opportunity cost
(e.g. expense of opportunities foregone) of time should equal the
lowest current wage rate after taxes (Talhelm, 1972, 1978). It may also

equal the potential wage rate one could have earned by reallocating time

33

and effort to other endeavors. Variation in trip costs for a particular
angler depends on the distance an angler travels; consequently, a
horizontal angling supply curve is defined for every possible angling
distance (Figure 2). For a particular travel distance, numerous angling
trips may be taken at a relatively constant cost per angler day (Talhelm,
1972, 1973b, 1976).

The above interpretation of supply provides the foundation for
statistically estimating demand equations for a variety of angling
experiences. A point on a per-capita-demand curve is formed by each
of the respective price and quantity/1000 capita observations. There-
fore, given supply prices and observed use of angling for anglers residing
at hypothetical locations (A and B), a demand function can be formed
by points a and b (Figure 3).

Given a demand schedule the social value (all—or—none value or
consumer surplus) of fishing at the plant site was estimated. The
"all-or-none value" is the maximum willingness of anglers to pay or
accept monetary compensation to have the use of an angling site, as

opposed to not having it at all.

5. Description and Operation of the J. R. Whiting Plant

 

The J. R. Whiting plant (Figure 4), owned and operated by Consumers
Power Company, is a fossil fueled facility located on the western shore
of Lake Erie, in Erie Township, Monroe County. The plant has three
coal-fired units; Units 1 and 2 each have a gross capacity of 105 mega-
watts (MWe) of electricity, and Unit 3 has a gross capacity of 133 MWe.

The plant started electrical production in 1952, and it has a life

34

 

 

 

 

3:
q
o
E
..I '3'? SUPPLY (a)
(9’ ".
Z I
4 | 0
I5 I “"694

I '-
0. : "4'0
1’3 l . a: SUPPLY (A)
LIJ | I .'
9 I I
E I I

I I

l 41

FROM 8 FROM A

QUANTITY (ANGLER DAYS PER CAPITAI

Figure 3. An angling demand curve traced out by supply curves
(prices) and quantities of angling for anglers
residing at hypothetical locations A and B.

35

 

Figure 4. J. R. Whiting plant site. 1=North Maumee
Bay, 2=intake, 3=discharge channel, 4=Lake
Erie.

36

expectancy of 50 years. Condenser cooling water for the plant is drawn
from the north end of North Maumee Bay. Three vertical traveling
screens (3/8-inch wire mesh) prevent fish and smaller debris from en-
tering the plant. Each generating unit has two circulating water pumps.
Pumps for Units 1 and 2 each discharge water at a maximum rate of
30,000 gpm, and for Unit 3 at 47,000 gpm. The discharge from the

plant flows east via a 900 ft. long discharge duct into Lake Erie.
Angling activity occurred in the discharge duct and in the power plant

plume of Lake Erie.

III. METHODS

l. Roving Creel Survey

 

Stratified random sampling employing a roving creel survey was

conducted along the Monroe County shoreline to sample catch and effort.

The shoreline was stratified into the following segments:

A.

Five areas (Figure 5)

1.

2.

Area 1 (between 1 and 2)
Area 2 (between 2 and 3)
Area 3 (between 3 and 4)
Area 4 (between 4 and 5)

Whiting plant site.

Three seasonal periods

1.

2.

3.

Winter—Spring (Period 1, January through May: January
1979, February 1978 through May 1978)

this period was further segmented:

3. ice fishing

b. non-ice fishing

Summer (Period II, June 1978 through August 1978)

Fall (Period III, September 1978 through December 1978).

Sample dates

1.

2.

Weekdays

Weekends/Holidays

37

38

 

I'
I
I

 

 

Greg-Se I la
~ ‘ - v ’

WASHTENAW CO.
WAYNE CO

Flat Rock

.I. ....... _/— ——————— 7‘ /

TAONROE co

 

Q
~
\-

75/

033

P\o 5

§————— — ——J

Km
0b 9’ SMI
be, - ‘ ‘
931's,” _ .- ‘ @ Stony Pom!
’ \

he,
(0/

CD .

MONROE

    

 

    

<3
AV
O‘g/
953’
\
I
I
/
mm“ /
gs, L A K E
(II/Q
E’s»

QB

  

‘

Woodhck Penmsula

L" "" 5/. MAE-6
OLED ~
I" o If.

f / AMA

 

Figure 5. Map of western Lake Erie.

I
' '0“!
I DETROIT

WEI. II
I / v “\ /
I \«o ’

o" I
YPSI LANTI
”A FIgrmng
Bland

 

WINDSOR \

 

39

D. Type of fishermen
1. Boat

2. Shore

The sizes of the four geographic areas, and consequently the sampling
effort of the interviewers within these strata, was determined by the
angling pressure and coastal mileage within each area so that each
area could be sampled intensively in one sampling day. Each area was
sampled between 36 and 55 days during the year. Since fishing pressure
was expected to vary seasonally and different angler behavioral patterns
were expected on weekends versus weekdays, it was decided that the
seasons and days of the week should be segmented. The weekends and
weekdays were divided into two groups and sampled independently. Three
weekdays and every weekend day were sampled per week. Holidays were
considered weekend days. Every holiday was sampled except Christmas
day. The areas and days of the week were selected randomly. Inter-
viewers had two consecutive days off per week, and three holiday sub-
stitute days vacation. It was deemed important to stratify the data
into boat and shore fishermen, since both groups are not equally accessible
for interview, and each may catch different fish species. Although
the survey sampling methods utilized for shore and boat fishermen differed,
interviewers sampled both types of fishermen during a sampling day.
The sampling of boat fishermen is discussed later in this chapter.

One full-time and one part-time interviewer were employed simul-
taneously during Period I 1978 only (part-time interviewer hired only
for the ice fishing season). During Period II there were two full-time

interviewers. The rest of the time only one full-time interviewer

40

was necessary. In each period during any given sampling day one inter—
viewer was solely responsible for the intensive sampling of a partic—
ular area. Each interviewer recorded on a questionnaire (Appendix A)
the number of hours fished, species caught, and other pertinent infor—
mation concerning the anglers encountered.

Talhelm (1972) provided calculations for estimating catch (numbers

and pounds) of shore anglers:

Vik (ch)ijk xi nik (ch)ijk
(TFC). = z . —— (C.F.) + 2 —— - h . (C.F) (13)
1k j=1 (hr)ijk mi j=1 (hr)ijk ijk
where
(TFC)1k = total fish caught (number or pounds) on day i for
species k,
(ch)ijk = catch so far on day i by angler j for species k,
(hr)ijk = hours fished so far on day i by angler j for species

k.

x1 and mi defined in equation (1),

vik’ nik’ and hijk are equ1valent to v and hij in
equation (1) except for subscript k indicating species,

1’ n1,

C.F. = correction factor.

Talhelm (1972) indicated that equations (1) and (2) (Open-ended)
could possibly underestimate angling hours and angler days when anglers
fish beyond the "normal" angling day length. Therefore, I estimated
a correction factor (equation 3) for each period by randomly selecting
two weekend and two weekdays per month for interviewing anglers. On

these days, I initiated interviewing much earlier (two and one-half hours

41

before sunrise) and much later (two and one-half hours after sunset)
than the other interviewers. I traversed an area once every hour,
counted the total number of anglers, and then interviewed all of them
compiling the total number of hours they fished during the day. Anglers
were not re-interviewed if encountered more than once in the area.

Since most anglers stayed at least one hour in an area, I assumed the
angling population did not change from one traverse to the next.

Then I summed the total number of angler days and angling hours for

each randomly selected weekday and weekend sampling day (four per month).
I compared total angler day and angling hour estimates of my randomly
selected weekdays and weekends with the total angler days and total
angling hours which I estimated from the other interviewers' data for
identical sample days. The estimates of angler days and angling hours
from the interviewers' data appeared to be slightly low. To rectify
this apparent error a correction factor for each period was estimated
from the calculations above and subjectively introduced into equations

(1) and (2). The correction factors were:

 

Correction
Period Factor
I (ice fishery) 1.08
I (non-ice fishery) 1.02
II 1.05
III 1.03

Fishing beyond the "normal" angling day length was minimal throughout
the year for shore fishermen except during ice fishing when vast numbers
of yellow perch can be caught. The remaining fishing effort throughout

the year was concentrated on walleye, white bass, catfish, and other

42

species. I suggest that future creel survey forms incorporate more
detailed questions regarding angling beyond what the investigator con—
siders to be the "normal" angling day length.

The procedure for estimating catch and effort for boating anglers
was somewhat different. Usually interviewers traversed an area three
times on a sampling day; consequently with the aid of binoculars each
interviewer recorded on a special form (Appendix C) three instantaneous
counts (one per traverse) of the number of boat fishermen in the ap—
prOpriate sector of the lake. Each count was taken at the beginning
of the traverse. From June through the middle of November a sixteen-
foot aluminum boat with a six-horsepower engine was rented one weekday
and one weekend day per week. This enabled the interviewer to sight
shore and boat fishermen easily. By dividing the three instantaneous
counts by three the average instantaneous number of boat fishermen,

R, could be estimated. The total angling hours (tik) of all boat
fishermen in the particular area sampled was estimated by multiplying
R times the length of the angling day.

Based on actual interviews of returning boat fishermen at lake
boat access points, the total catch, effort, and catch rate for each
speciescxiaisampkaday in a particular area were calculated. Total angler
days (visits/per day or number of fishermen) for the entire sampling
day were estimated by first determining the average hours fished per

fisherman:

ijk ik (14)

43

where
fiijk = average hours/fisherman on day i for species k,
hijk = total fishing hours on day i by angler j for species
k.
vik = number of different interviews on day i for species k.

Angler days were then calculated for a particular sample day:

aik = tik/hijk (15)
where

aik = total angler days on day i for species k,

tik = total angling hours on day i for species k.
Total catch rate (rik) equals

Vik vik
r. = Z c . / 2 e . (16)
1k j=1 ijk j=1 ijk

where

rik = total catch rate on day i for species k,

cijk = catch (actual number or pounds) on day i by angler

j for species k,
eijk = effort (actual hours fished) on day i by angler j

for species k.

Total catch (tc)ik was estimated by multiplying rik by t During

ik'
Periods I and III virtually all the angling effort (tik) by boat fisher—
men was directed toward yellow perch. From June to the middle of

August (most of Period II) 60 to 80 percent of their angling effort was

expended on walleye with the remaining effort going to yellow perch.

44

Simple statistical analyses were performed to test the validity of
the boat fishermen estimates (Appendix D).

Once the angling hours, angler days, and catch were computed for
both shore and boat fishermen for each sampling day and area, then
seasonal estimates (for Periods I, II and III) of the different vari-
ables were calculated. Cochran (1977) provided formulae for determining
seasonal population totals and variances, standard errors, and degrees
of freedom. The creel survey was initiated during the fourth week of
February 1978 and terminated the last week in January 1979. The sample
information gathered from the fourth weekcfiEFebruary 1978 was extra-
polated back to the third week of February 1978, and the samples taken
in the last two weeks of January 1979 were extrapolated forward to the
second week of February 1979. These extrapolations were necessary
in order to attain population estimates for the month of February.

The results of the survey are in Table 2, Chapter II.

2. Surplus Production and Leslie Matrix Models

 

The general block diagram (Figure 6) illustrates the interrelation—
ships of the different mathematical equations and life history data
utilized by the surplus production and Leslie matrix models.

The commercial catch and effort data from the National Marine
Fisheries Services, Ann Arbor, Michigan, and the sport catch and effort
data from the Michigan Department of Natural Resources, Lansing,
Michigan, provided the necessary input data for estimating the param-
eters of the surplus production model. Catch in commercial fisheries

was reported in pounds. The harvestable biomass (in pounds) of the

45

.523... .60... E23... .2280 .o 2.5...

 

.... .... 8......
.m .... ......32
......m

......o
8......)

.6... 5.2.8.... I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

......3...» 8.3.2.8.
3.2.503 u..- ‘
_. I cud-o> :0:- nun-.0
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. 82.6... 5...... ...... « ...... II®
. > 30.0 00¢ I. 83.5....
. ... .364“: I 03-325...
_ . ...... IO
_
_ _..III.IIII..I.II..IITI.IIIII1 IIIII
58> 5.5.00 I o
. .8 5...... :3 mm. moo... mm. .3... wow «.3 «I: «84 if) 25¢ w. I coo...
_ 3.3.. 22cm .. I .. c l .. I F .. ® I .. i ..
. 3:0 oo< .3 fl
. :2... Bo...»
. ...oiEEoo
_ ....- toaw .o , Sam .56 8.5 .56 E5 .55 .....m
. 6.. .. 8.2.3....
_ 3...... o ... .... .3 .3 a... a
0. < m < I v0 0 n V N i w. I1 00 <
_ .. mm. «m» .. nmé .. @«m» .. .mfi .. and ..
" FIIIIII. IIIII PILTIILIIIL IIIII .I IIIIII Iy
_ m ,
on. ,
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. 2.2208560 @
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r IIIIII 8:... o... ..2 .u 2... ......3 ..m I I I I

 

 

 

 

 

a

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

I.

-—-——-——--—--_———-——-——————--d

46

commercial fishery for a particular year can be converted to numbers
of fish by knowing:

1. The harvestable biomass in pounds during a particular

year.
2. The percent of catch by weight of age classes.
3. The age specific average weight of different age class
fish.
Only the number of age class 3 yellow perch (n3 in Figure 6) was es-
timated since age class 3 includes the youngest yellow perch that are
highly vulnerable to the commercial fishing gear. By either dividing
or multiplying by the survival rate, the numbers of fish in the other
age classes may be calculated (Figure 6).

Sport fishing catch data were reported in numbers of fish. Yellow
perch in the sport fishery become highly vulnerable to the gear at age
2. Given the number of age 2 fish the remaining calculations for
estimating the number of sport fish in other age classes are similar
to those of the commercial fishery (n2 in Figure 6).

The initial population, N represented in the Leslie matrix model

0,
as a column vector (Figure 6), was estimated by adding together the
number estimates of fish of identical age classes from both the sport

and commercial models. The Leslie matrix model can simulate the effects
of power plant mortality on the various age classes and total population
through time. The model includes estimates of the initial population,
N0, fecundity, and survivorship values (from the life table and specified
in the A matrix). Since the survivorship figures include males and

females together, the fecundity figures were multipled by the proportion

47

of females within each age class (Table 1, Chapter II). This represents
fecundity per adult in equation (12).

To apply the surplus production model, the yellow perch commercial
catch and effort data for the years 1960 to 1969 were converted to a
standard gear. Only current commercial catch and effort data were
used. Commercial fishermen used several gear types, but the gear
most utilized was the shallow trapnet. The total yield per unit of

effort (YPE) as described by Jensen (1976) is calculated as:

YPE = total yield/total effort (17)
where

Total Effort = x ° y/z (18)
where

x = effort with standard gear

y = total yield

2 = yield with standard gear

Angling effort is reported only in angler days, so angling effort was
not standardized. To apply the surplus production model sport fishery
data for the years 1970 to 1977 were used. Yellow perch Sport catch
and effort have been available only since 1970.

Schaefer (1957) develOped a method for linearizing equation (6).

Jensen (1976) described the equations developed by Schaefer as follows:

Bt = <1/q) (Yt/Et) = <1/q) (Ut) (19)
where

Bt = average biomass during year t,

Yt = yield for year t,

U = yield per unit of effort for year t,

48

Et = effort for year t.

The derivative of equation (6) can be approximated with the two point

formula (Hamming, 1962):

 

 

dB _
(II—E) ' Bt+1 ' Bt-l '- (l/q) (wt) (20)
t
2
where
AUt = (Ut-I-l ' Ut-l)
2

Substituting equations (19) and (20) into equation (6) gives the linear

equation:

Zt = ale + aZX2 + a3X3 (21)
where

Zt = AUt’

X1 = Ut’

x2 = If,

x3 = Yt,

a1 = k,

a2 = -k/Kq,

a3 = -q

The constants and a were estimated by least squares regression.

al 32 3
The parameters were estimated separately for the commercial and
Sport fisheries surplus production models employing Schaefer's method.

These parameter values were then varied separately (for commercial

and sport fisheries) and substituted into a computer systematic search

49

routine to find parameter values which minimize the residual sum of
squares (Jensen, 1976). Further details are in Appendix B. Once the
parameters were estimated an equilibrium stock production curve was
plotted for each fishery utilizing equation (7).

The most recent estimates of harvestable biomass (B69) and
numbers (N77) of the commercial and sport fisheries respectively were
employed to estimate the initial population, NO, in the Leslie matrix
model.

Sport fishermen harvested yellow perch throughout the period of
commercial fishing, but no catch and effort data are available. The

harvestable biomass (in pounds) of the commercial fishery in 1969 was

converted to numbers of fish by the formula:

 

D3 = b69 (F3) (454) (22)
G3
where
n3 = number of harvestable yellow perch at age 3 (age of high
vulnerability to commercial fishing gear),
b69 = harvestable biomass in pounds in 1969,
p3 = percent of catch by weight of an age 3 fish (Muth, 1978),

1 pound = 454 gm,

w3 = age specific average weight of an age 3 fish in grams.

The effect on the yellow perch stock of entrainment and impingement

was simulated over the 50-year life expectancy of the plant with the
Leslie matrix. The analysis was carried out in four ways assuming:

1. No plant mortality

50

2. Entrainment only
3. Impingement only

4. Both entrainment and impingement.

It was assumed that entrained larvae had survived from some greater
number of spawned eggs. In order to assess the estimates of entrained
eggs it was necessary to backcalculate to the number of potentially
spawned eggs (age 0) required to produce the entrained larvae (Stone and
Webster, 1978). It was shown that yellow perch larvae reach the juvenile
stage 52 days after spawning (Mansueti, 1964), so the assumption was made
that larvae older than 52 days could not fit through the 3/8 inch mesh
screen of the power plant. All juveniles entrained throughout the year
are assumed to be 52 days old (t in equation (23)). Stone and Webster

(1979) provided a negative exponential function with a daily loss rate,

d, equal to .02 to estimate the potential number of spawned eggs (N0):
N0 = Ntedt (23)
where
Nt = total annual number of larvae (age 52 days) that managers
of the power plant reported entrained,
N0 = total annual number of eggs (age 0) from which the
entrained larvae came,
d = daily entrainment loss rate,
t = time in days.

The entrainment and impingement mortality figures were supplied by
Consumers Power of Michigan (Wapora, Inc., 1979).
Lastly, the effects of changes in the growth rate, A, were estimated

by a sensitivity analysis, given the following assumed changes in

51

survivorship values of the Leslie model A_matrix:
1. Age 0 survival was increased ten times its normal
value, while the survivorship of age classes 1 to 6
remained at their original values.
2. The survival rates of age classes 1 to 6 were increased
to 100 percent survival separately while age class

0 remained at its original survivorship value.

This analysis indicates which age classes are most sensitive to changes
in survivorship. All changes hisurvivorship were arbitrarily chosen to

test the system's response.

3. Price and Demand Equations for the
J. R. Whiting Plant Site

 

Data Collection

 

Interviewers sampled angling at the J. R. Whiting plant site in con-
junction with sampling in area 4. They collected and recorded data
on a special questionnaire (Appendix E) concerning origin-destination
patterns, angling catch and effort, and travel and other costs to anglers
who visited the plant site. A more detailed discussion of how the data

is employed can be found in Appendix H.

Price and Demand Equations

 

The price and demand equations used in this study are similar in
functional form to those estimated for an inland lake study of boating
and angling in Michigan (Talhelm, 1976), and similar to those developed
from a general theory of supply and demand for outdoor recreation (Talhelm,

1978).

52

Price equations were developed to express angler travel costs as
a function of travel time and distance (mileage) to the site.1 Costs
attributable to fishing include: 1) the estimated value of time and,
2) expenditures on travel, equipment, fees and lodging. The functional

form for the price equation is:

P = c+b1T+b21n(T+l) (24)

where
P = price in dollars per angler day

Clble = constants

T = one-way travel time

1n = natural logarithm

Separate price equations were derived for Periods I, II, and III re—
spectively.

The Whiting Plant site was considered a separate area, so catch and
effort (angler days) were estimated separately from areas 1, 2, 3, and
4. Angler days and catch were calculated using the same statistical
procedure described previously (Cochran, 1977).

The information required for estimating demand functions is: 1) the
number of angler days use at the plant site from each origin and, 2) the
corresponding minimum (supply) prices of angling at the plant site from
every origin. The demand analysis in this study consisted of a single—
site model for estimating the all—or-none value of this particular

plant site. I assume that only one "product" or kind of angling was

 

1All of the individuals who were interviewed had traveled to the

Whiting Plant site solely for the purpose of fishing.

available at the

53

plant site: moderate catch rate of non-salmonid fish

(some of the species include white bass, catfish, and carp) at the plant

discharge channel and plume. Given the information from every origin

concerning the prices and quantities of use of the plant site product,

demand equations were estimated. Each demand function can be described

by the following

where

general functional form:

bO + blP + bZ/P (25)

number of visits per 1000 capita at the plant site
for non-salmonid fishing,
minimum available price of non-salmonid fishing,

b1, b2= constants.

The demand equation was estimated using ordinary least squares regression.

Separate demand equations were derived for Periods I, II, and III respec-

tively.

IV. RESULTS AND DISCUSSION

1. Roving Creel Survey

 

It was imperative that reliable catch and effort estimates be
derived from this creel survey. These estimates, the Michigan Depart-
ment of Natural Resources (MDNR) catch and effort estimates, and the
commercial catch and effort data were utilized to estimate the parameters
of two surplus production models (commercial and sport).2 The commercial
and sport surplus production models were used to estimate the yellow
perch population size (numbers)in the Michigan waters of Lake Erie.

Based on a mail survey of anglers, the 1976 "Michigan Great Lake
Yellow Perch Survey," the MDNR estimated yellow perch sport catch and
effort for the Michigan waters of Lake Erie.3 Slightly less than 95
percent of the Lake Erie yellow perch catch and 85 percent of the effort
was in Monroe County (the remaining was in Wayne County). Comparing
the results of the MDNR's Monroe County catch and effort estimates
with those of this roving creel survey it appears that either the
MDNR is overestimating both catch and effort by a factor of about 4,

or my creel survey is underestimating catch and effort by the same amount.

 

2See Appendix F for catch and effort of other species caught in
Monroe County.

3Michigan Department of Natural Resources, Office of Surveys and
Statistics, "Michigan Great Lake Yellow Perch Survey," 1976. (unpublished).

54

55

The estimated yellow perch annual sport catch (numbers) and effort
(angler days) from my survey were 509,001 and 29,411 respectively
(Table 2).4 The estimated annual yellow perch catch and effort from the
1976 MDNR survey were 1,865,990 and 129,960 respectively. I compared
the catch and effort estimates of my survey to the 1976 MDNR survey
because the MDNR 1976 survey estimates of yellow perch sport catch and
effort are the only estimates pertaining solely to Lake Erie yellow
perch. The regular MDNR "Michigan Sport Fishing Survey" estimates of
Lake Erie yellow perch sport catch and effort (Table 3) also include
the effort of salmonid, non-salmonid, and stream anglers. The number of
salmonid and stream anglers is minimal. The catch and effort data in
Table 3 also include Wayne and Monroe counties together. However, I
will assume that all catch and effort in this table are from Monroe
County, since the MDNR 1976 survey indicated approximately 95 percent
of the catch was in this county. Jamsen (1979) indicated that the MDNR
1976 survey can be effectively compared with my creel survey catch and
effort data.5

The MDNR catch and effort totals for Monroe County (Table 3) were
applied in this study to estimate sport harvestable yellow perch numbers

(N77) for the year 1977 (Equation 19).6 Rybicki and Keller (1978)

 

4Yellow perch comprised over 95 percent of the total catch in Monroe
County. This percentage excludes fish caught at power plant sites.

5Jamsen (1979) recently reported that 1978 yellow perch catch and
effort data are slightly higher than previous years. However, he stated
there has been little variation in catch and effort since 1970.

6Bt and Nt may be substituted for one another.

56

Table 2. Yellow Perch Sport Catch and Effort Estimates from the Roving
Creel Survey in Monroe County from February 1978 to January

 

 

 

1979.
1
Period Catch or Effort Y i_t975,deE
I: Angling Hours 57,358 i;l4,568
Angling Days 14,906 :_4,192
Pounds 27,253 :_13,197
Numbers 154,027 :_81,824
II: Angling Hours 21,807 :_3,524
Angling Days 5,273 i 862
Pounds 8,800 i_2,387
Numbers 39,302 : 11,748
III: Angling Hours 41,064 1 9,452
Angling Days 9,232 i_2,060
Pounds 63,009 :_19,995
Numbers 315,672 :_102,349

 

1The degrees of freedom. (df)for Periods I, II, and III were 3, 56,

and 27 respectively. In Period I, the majority of the yellow perch
were caught during the short ice fishing season; consequently, the

degrees of freedom are low.

57

Table 3. Yellow Perch Sport Fisheries Data Reportedfbr Michigan
Waters of Western Lake Erie.

 

 

 

 

Estimates
Total Catch Effective Effort
Year (numbers) (angler days)
1970 2,013,520 136,650
1971 2,542,060 295,140
1972 1,563,150 .214,540
1973 1,780,560 203,220
1974 2,719,980 401,940
1975 2,243,490 416,840
1976 1,874,240 372,800
1977 2,342,067 443,555

 

1Catch and effort for 1974 are projected figures (G. Jamsen, MDNR per-

sonal communication).

Remaining catch and effort reported by the

Department of Natural Resources, Lansing, Michigan.

58

showed that the MDNR overestimated lake trout catch by a factor of 5,

so my creel survey results apparently indicated that the MDNR is over-
estimating the catch and effort of yellow perch in Monroe County by a
factor of 4. Consequently, I compensated for the apparent overestimation
when I calculated the harvestable p0pulation numbers, N77. After cal-
culating N77 (Equation 19) using the catch and effort in Table 3, I

multiplied N times .273 giving n since the roving creel survey

77 77’
catch estimate was .273 of the MDNR 1976 survey figure. Only one year
of data from the roving creel survey is available for comparison with
the MDNR catch and effort data. Consequently, an adjusted harvestable
population number was assumed to lie halfway between the upper and
lower limits of N77 and n77 respectively. The adjusted harvestable

population number was calculated as:

N77 = N77 + H77 (26)
2
where
N77 = adjusted sport yellow perch harvestable population

number. This number is reported in the next

section.

The adjusted sport yellow perch harvestable population number will be
used to estimate the sport yellow perch population size by age class
(next section). The effects of impingement and entrainment on the popu—

lation would be less if N were substituted since a larger population

77

size estimate would result. Substituting n would decrease the p0pu-

77

lation size estimate somewhat but the effects from impingement and entrain-

ment on this population would still be minimal.

59

2. Surplus Production and Leslie Matrix
Models and Sensitivity Analysis

 

Surplus Production

 

To calculate the estimates of yellow perch commercially harvestable
biomass, commercial catch and effort data fortimzyears 1960 to 1969
were utilized (Table 4). Sport catch and effort estimates for the
years 1970 to 1977 provided the necessary input for estimating recrea-
tionally harvestable numbers (Table 3).

Table 5 contains a list of parameter estimates of equation (7) for
the yellow perch commercial and sport fisheries. The most recent
harvestable commercial biomass estimate (B69) and harvestable sport
numbers estimate (N77) are 354,968 pounds (Equation 19) and 1,680,430
fish (Equations 19 and 26) respectively.

By substituting into equation (22) the commercially harvestable
biomass of 354,968 pounds, 61.3 percent of the catch by weight of age
class 3 fish (Muth, 1978), and the age specific average weight of 117 gm
(life table), the numbers of age class 3 fish were estimated to be ap-

proximately 844,345 (equivalent to n in Figure 6). This is the first

3

age class to become highly susceptible to commercial fishing.
Yellow perch become highly vulnerable to sport fishing at age class 2.

Age class 2 yellow perch constitute about 50 percent of the sport catch.

Multiplying the harvestable sport numbers estimate (N77) by .5 gives

an estimate of age class 2 fish of 840,215 (n2 in Figure 6).

As mentioned in Chapter III, page 50, once n of the sport model

2

and n3 of the commercial model are calculated, these estimates are then

multiplied or divided by the survivorship values of the respective models.

60

Table 4. Yellow Perch Commercial Fisheries Data Reported for Michigan
Waters of Western Lake Erie.

 

 

Total Catch

 

Year (pounds) Trapnet Effort2
1960 117,858 3,274
1961 103,600 4,000
1962 96,875 2,735
1963 89,701 2,516
1964 36,751 2,248
1965 68,997 2,271
1966 136,748 2,664
1967 112,177 2,020
1968 172,929 2,012
1969 111,815 1,750

 

1Catch and effort data provided by the National Marine Fisheries
Service, Ann Arbor, Michigan.

2One lift of a trapnet is 1 unit of effort.

61

Table 5. Estimates of the Parameters k, K, and q for the Commercial
and Sport Surplus Production Models.

 

 

Fishery k K q

 

Commercial .55 1,400,000(pounds) .18 x 10'

Sport 2.10 4,406,625(numbers) .20 x 10'

 

62

The initial population, N0 (Table 6), was determined by adding together
the number of fish of identical age classes from both the sport and
commercial models.

The stock production equations for the commercial and sport fisheries

are:

252.0E - .082E2 (27)

Commercial fishery: Y

8.81E - .00000839E2 (28)

Sport fishery: Y

The commercial and sport stock production curves in Figures 7 and 8
respectively have yield plotted as a function of effort. The mean short
run yield curve of the commercial fishery intersects the equilibrium
curve (parabola) to the right of the maximum sustained yield level

(apex of the parabola) which indicates the stock is overexploited. The
sport fishery seems slightly underexploited since the mean short run
yield curve interests the equilibrium curve to the left of MSY. The
parameter values of the commercial and sport surplus production models
(Table 5) were used to calculate predicted yields. See Appendix B for

a graph showing a plot of observed yields and predicted yields.

Leslie Matrix

 

The effects of impingement and entrainment on the yellow perch
population were simulated for a 50-year period with the Leslie matrix.
This was accomplished by assuming respectively:

1. no impingement and entrainment mortality from the
plant (Table 7),
2. only entrainment (Tables 8 and 9),

3. only impingement (Tables 8 and 9),

63

Table 6. Yellow Perch Population Estimate in the Michigan Waters of

the Western Basin of Lake Erie by Age.

 

 

 

Age Survival Population1
0 .01175 10,600,000,000
1 .08572 125,000,000
2 .08572 11,000,000
3 .17499 916,000
4 .25872 160,000
5 .33132 41,000
6 0 14,000

 

1Numbers quoted were rounded to three significant figures.

24,

YIELD IN POUNDS X IO4

 

64

v: 252.05 - .082E2

Y= 37.7IE
(r2= .82)

 

Figure 7.

 

EFFORT X 103

Estimated equilibrium yield and effort relation
(parabola), and regression of yield on effort
(solid line). The points are observed yield
and effort values from 1960 to 1969 for the
commercial fishery.

65

3'20 rwas: E - 00000839 :2

Y= 6.44E

2.30 (r 2 =36)

2.40

2.00

LSD

l.20

YIELD IN NUMBERS x 10‘5

.80

.40

 

 

 

l J. 1 J 1
0 2 4 e a no
EFFORT x I05

Figure 8. Estimated equilibrium yield and effort relation (para—
bola), and regression of yield on effort (solid line).
The points are the observed yield and effort values
from 1970 to 1977 for the sport fishery.

66

Table 7. The A_Matrix with Survivorship and Fecundity Estimates of
the Existing Natural POpulation and Initial POpulation by

 

 

 

 

 

Age Class.
0 0 0 8629 11743 14129 16096
.01175 0 0 0 0 0 0
0 .08572 0 0 0 0 O
A = 0 0 .08572 0 O 0 0
- 0 0 0 .17499 0 0 0
0 0 0 0 .25872 0 0
0 0 0 0 0 .33132 0

 

 

 

 

Initial population as a column vector NO

1 —_—

10.600.000.000
125,000,000
11,000,000
916,000
160,000

41,000

14,000

 

 

 

 

67

Table 8. Number of Yellow Perch Impinged and Entrained by Age at the
J. R. Whiting Plant from March, 1978 to February, 1979.

 

 

 

Type Of 1 Annual
Mortality Age Total Mortality
Entrainment 0 4,840,000 .00046
Impingement 1 52,489 .00042
Impingement 2 59,189 .00538

 

1Wapora, Inc., 1979.

2Annual mortality is calculated by dividing the number of fish en-
trained or impinged in a particular age class by the estimated
number of fish in that age class (Table 6). For example, the
calculation of entrained fish at age 0 is:

4,840,000

10.600.000.000 = '00046

Annual mortality =

68

Table 9. Fifty-Year Simulated Loss to the Yellow Perch POpulation
in the Michigan Waters of Lake Erie.

 

 

Estimates of
Percentage Loss

 

Type of Mortality per Year
Impingement 1.6
Entrainment .4

Impingement and
Entrainment 1.7

 

69

4. both entrainment and impingement (Table 9).
Impingement and entrainment reduce the yellow perch population by a
small percentage annually. This can be represented by what is known
as a "harvest matrix" (Appendix J). Age classes 0, 1, and 2 are harvested
(from impingement and entrainment) each year, t. The number of fish
in each age class at the start of the next year, t + I, will therefore
h

be reduced accordingly. If pj represents the percentage of the jt

age class that is harvested during year, t, where ij :1, then (l-p )

J 3
will be the percentage of the jth age class that is left. The effect of
impingement and entrainment was simulated by multiplying the harvest
matrix by the Leslie A_projection matrix where pj = the annual impingement
and entrainment mortality rates for age class j (Table 8). The population
was at equilibrium (A,= 1.0) before harvesting began. After harvesting,
the combined effects of impingement and entrainment reduced the whole
yellow perch population (all age classes combined) by 1.7 percent per
year (Table 9; Appendix J). The assumption was made that the population
was in a steady state before harvesting was initiated. Therefore each
age class separately was assumed to be reduced by 1.7 percent per year.
Stone and Webster (1978, 1979) stated that the fisheries yield will be
reduced by the same proportion (1.7 percent per year) as the whole p0pu-
lation, assuming a steady state population and no change in fishing
strategy.

The economic loss from the J. R. Whiting plant was computed under
these assumptions:

1. The maximum mortality loss from impingement and entrainment

will probably result in an annual 1.7 percent reduction

70

in the yellow perch catch during the 50 years of plant
operation.

2. The dockside value of yellow perch (in the round) is
$1.50/pound although selling it without a license is
illegal (N. Fogle, 1979, and the Bay Port Fish Company,
personal communication). Since 1970 yellow perch
commercial fishing has been prohibited in Lake Erie;
therefore, only the economic loss to the yellow perch
sport catch from impingement and entrainment is
estimated. It appears that the sport fishery will
continue to predominate in Lake Erie in the future.

A more detailed economic analysis, outside the scope
of this dissertation, will estimate a more accurate
change in economic value of the yellow perch sport
fishery resulting from impingement and entrainment.
Therefore, $1.50/pound, a gross value, should be

considered a provisional figure at this time.

The average sport catch of yellow perch from 1970 to 1977 was approxi-
mately 2.1 million fish/year. The average weight/fish of yellow perch
caught by anglers was .2 pounds (creel survey estimate) resulting in

an average weight of yellow perch caught/year of 420,000 pounds. The
impingement and entrainment mortality loss from the plant was 1.7 percent/
year. A 1.7 percent loss/year in catch would be 7,140 pounds/year

and an economic loss of $10,710/year or $535,500 at the end of 50 years

of plant operation assuming $1.50/pound for yellow perch.

71

The Leslie matrix, a population simulation model, is density-
independent and suitable for this study because insufficient information
was available to incorporate density-dependent or compensatory mechanisms.
Compensatory mechanisms could increase egg and larval survival. If
compensatory mechanisms are Operating in this population then these
population reduction estimates should be considered an upper limit of

power plant impact (Stone and Webster, Inc., 1978).

Sensitivity Analysis

 

A sensitivity analysis utilizing the Leslie matrix model tested
the effect of changes in the elements of the A_matrix (survival rates)
upon the population growth rate. Table 7 lists the survivorship values
of the original yellow perch population along the subdiagonal of the A
matrix by age class. During the sensitivity analysis each age specific
survivorship value was increased by a certain value while the remaining
age class survivorship values remained at their original values. As
a particular age class had its survivorship value incremented by a
certain amount (others remained at their original values) the eigenvalue
,(A) was estimated and then plotted on the graph (Figure 9). The eigen-
value (A) for each of the six age classes was estimated and plotted:h1this
manner. Age C) survivorship was multipled by 10 times its original
value, while the remaining age classes were increased to 100 percent
survival. These incremental values were arbitrarily chosen to test
the response of the system. The original population, without any in-
cremental changes, had an eigenvalue (A) or growth rate of 1.0. When

S was increased 10 times its original value and the other age classes

0

72

 

2.5
A 20*
A
E
4
a:

I c
,_ 1.5
3
O
O:
(D
6
_ IOb
’2:
.J
D
“- I
0
CL
05-
O 1 l 1 l l

 

 

 

 

I 2 3 4 5 6
AGE

Figure 9. New growth rate of Lake Erie yellow perch
for each respective change in survivorship
within each age class.

73

remained constant the eigenvalue (A) jumped to 1.7. This represents an
increase of 70 percent. SO, 81’ and $2 (pre-reproductive years) showed

the greatest sensitivity to changes in growth rate in response to survivor-
ship changes (70 percent increase from 1.0 to 1.7). Fishery biologists
consider the critical period for success of a year class to be early

in the fishes' life; it appears that the sensitivity analysis agrees

with this assumption. F

3. Price Equations, Demand Analysis,
and Consumer Surplus

 

".4.

Price Equations

 

A price equation for angling at the plant was derived for each
period.7 These equations are graphically represented in Figures 10, 11,
and 12. The specific price equation coefficients (Table 10) were derived
from the ordinary least squares regression analyses of equation (24).

The price of angling from every population origin will be incorporated
into equation (25) to estimate the demand equation for the plant product

for each period (see next section).

Demand Analysis

 

The demand for angling at the J. R. Whiting plant site for each

period is shown in Figure 13. The demand equations are:

Period 1: Q = -11.59 + .11? + 304.53/P
(4.88) (.05) (104.99)

 

7All species caught at the plant site were considered non-salmonid
fish. See Appendix G.

74

R_ DAY)
0
O

 

PRICE ($ PER ANGLE

 

l l l l I 4

I 2 3 4 5 6
TRAVEL TIME IN HOURS (ONE-WAY)

Figure 10. Price curve, Period 1, showing the user cost of angling
as related to travel time to the J. R. Whiting plant
site.

75

 

5

O
3500 -
.J

o

<21

m 75
LIJ

G.

g 50
LIJ

2

g 25

 

1 1 l l l l

I 2 3 4 5 6
TRAVEL TIME IN HOURS (ONE-WAY)

Figure 11. Price curve, Period II, showing the user cost of

angling as related to travel time to the J. R. Whiting
plant site.

E5
0

8

PRICE ($ PER ANGLER DAY)
N N
0| 0|

Figure

76

 

 

4 l l l # J

I 2 3 4 5 6
TRAVEL TIME IN HOURS (ONE-WAY)

12. Price curve, Period III, showing the user cost of
angling as related to travel time to the J. R. Whiting
plant site.

77

Table 10. Price Equation Coefficients for Fishing at the J. R.
' Whiting Plant Site from February, 1978 to January, 1979.

 

 

 

 

Statisticsl’2

Period C T ln(T+1) R2 DW
I 24.79 1.80 19.39 .18 1.7
II 24.12 -.57 26.66 .04 1.9
III 18.67 6.85 26.52 .26 2.0

 

1The t and F tests for the price equation coefficients were signifi-
cant at the 95 percent confidence level, except that the t-test

for the T coefficients was not significant. C is a constant and
T is one-way travel time.

2Maddala (1977) describes the Durbin-Watson statistic.

78

 

;8

g OI’

m

LIJ

6'60

Z

4

a:

If
40

1’3

DJ

2

E20

 

 

2 4 6 8 ID I2 I4 I6
ANGLER DAYS PER I000 CAPITA

Figure 13. Demand curves for non-salmonid fishing at the J. R. Whiting
plant site during Periods I, II, and III.

79

DW 2.8

R = .71

Period II: Q = -4.84 + .04P + 156.08/P
(2.70) (.03) (56.21)

DW = 3.3

R = .77

Period III: Q = -3.10 + .02P + 103.24/P
(1.66) (.01) (36.99)

DW = 2.7

R2 = .76

The t—test was significant at the 90% confidence level for all demand
equation coefficients except for Period II; the second coefficient was
significant at the 70% confidence level. The F-test for all demand
equations was significant at the 95% confidence level. Secondly, in
Periods I, II, and III the Durbin-Watson statistic was slightly high,
indicating autocorrelation. It is possible that several variables could
have been included or omitted in the demand analysis. In the future a
slightly different structural form of demand equation (25) may be needed

for demand analyses at power plant sites.

Consumer Surplus

Given the demand schedule for each period the consumer surplus
(all-or-none value or total social value) of the non-salmonid fishery
at the plant site was calculated. Consumer surplus is the maximum amount
of money all the anglers together would pay to keep the plant site in
existence for angling, rather than give it up entirely. Geometrically the

consumer surplus is equivalent to the entire area under the demand curve

80

and above the price at which the supply curve intersects the demand
curve. Each population origin has a different supply curve. Total
consumer surplus can be derived by summing all the individual areas

left from the intersection of the supply curves from each origin. The
total value of the plant site was estimated to be approximately $30,900
per year or $1,545,000 after 50 years of plant operation. This value,
however, is never found in a real market situation since only a monopo-
list could acquire this amount by collecting every increment of payment
as prices increased to their maximum. In the final analysis the most
revenue a real owner of this non-salmonid fishery could recover from
anglers is probably one-quarter of the consumer surplus; this value
minus administrative costs would be the market value of this fishery
(Talhelm, 1973b). It appears that the economic loss to the yellow perch
fishery could possibly range from $357,000 to $1,428,000 (one to four
dollars per pound) as compared to the non-salmonid marketable value of
$386,000 (one-quarter total social value) after 50 years of plant Operation.
Given the present dockside value of $1.50/pound the economic loss is
assessed to be $535,500. However, the all-or-none-value or total social
valuecfi $1,545,000 indicates that all the anglers together would be willing
to pay this maximum amount of money rather than not havetfiuaplant site

as a sport fishery resource. The public's interest (anglers) apparently
would be best served by the existence of the plant since the total social
value of $1,545,000 is more than the economic loss of $535,500 from
impingement and entrainment. However, in the marketplace, and as far as
Consumers Power is concerned, the economic loss of the fishery from the

plant outweighs its economic benefits.

V. CONCLUDING OBSERVATIONS

This study attempted to analyze the positive and negative effects
of impingement and entrainment at the J. R. Whiting power plant on
the commercial and sport fisheries in the Monroe County, Michigan area
of Lake Erie. During the projected 50-year life of the plant, the
economic losses (negative effect of impingement and entrainment) would
seem to outweigh the positive economic benefits of the plant site for
angling in the marketplace, but not in total social value.

The most significant findings were that impingement of adult yellow
perch had a greater effect on future adult populations than did entrain-
ment of eggs or larvae, and that anglers were willing to pay a maximum
of $1.5 million (during the life expectancy of the plant) to keep the
plant site in existence for angling. The major obstacle was that no
compensatory mechanisms were simulated. These mechanisms may involve
increases in egg and larval production which could in turn increase
the yellow perch population size. Therefore, the power plant population
mortality estimates should be considered an upper limit of power plant
impact.

Most fish populations exhibit some variation in their natural sur—
vivorship rates. In order to strengthen the results of the Leslie
matrix model, I recommend that future impingement and entrainment studies
incorporate stochastic variation of age-specific survivorship rates into

the A projection matrix. Age 0, 1, and 2 yellow perch are most affected

81

82

by impingement and entrainment in the Michigan waters of Lake Erie. The
mean yellow perch survivorship of age classes 1 and 2 can be estimated
from at lga§£_2 or 3 years of mark-and-recapture field data in the
Monroe County area. Age 0 fish can be subdivided into several different
life stages beginning with eggs and then proceeding through the various
juvenile stages. Larval density in a column of water is monitored

in the field by high-speed samplers. Subsequently, the mean survivor-
ship is estimated for each juvenile life stage covering at'l£§§£_a 2-

or 3-year period. The variance in age-specific mean survivorship for
age 0, 1, and 2 yellow perch is estimated and introduced into the Leslie
matrix model utilizing a table of random numbers which contains boundary
conditions for the variance. Numerous simulations of the stochastic
version of the Leslie matrix provide a range of p0pulation sizes, and
consequently a range in the annual percentage reduction of the yellow
perch population size from impingement and entrainment.

Harvestable biomass or numbers was estimated in this study utilizing
the surplus production model. A single yellow perch stock was assumed
to inhabit the Michigan waters of Lake Erie. A more complete assessment
of harvestable biomass or numbers would test the validity of this as-
sumption. If a number of different stocks are prevalent the surplus
production model could be applied separately to these stocks, and a
more realistic estimate of harvestable biomass or numbers might result.
Tagging studies could provide insight into the migratory patterns of the
yellow perch, and therefore the number of stocks in an area. In con-
junction with tagging studies electrophoretic techniques could be em-

ployed to analyze the blood groups of the different stocks and to help

83

verify the existence Of different stocks. Populations within a species
often differ from one another in the gene concentration of these blood
groups. Differentiation of populations by the frequencies Of indi-
vidual genes enable investigators to analyze the species structure

and to detect intraspecific groups. HOpefully, a more concise estimate
of the harvestable biomass of all the yellow perch stocks would become
available.

In previous studies Talhelm (1973b, 1976) found considerable
variation about price equation (24) which was employed in my economic
analysis. Sources of variation include differences in wage rates,
supplies and equipment, lodging choices, length of stay, and errors
in measuring travel distance or time. Talhelm found that only about
20 percent of the variation was attributable to travel time. Similar
results were obtained in my study. The greatest cost item in producing
recreation trips is the Opportunity cost of time for travel and parti—
cipation.

Although the J. R. Whiting plant in isolation from other plants
seems to provide some economic benefit to the Monroe County area, a
few perplexing questions remain unanswered:

1. Are there any additive mortality effects from impingement
and entrainment induced by other power plants in the
area on the yellow perch stock studied in this report?

2. What effect does impingement and entrainment have on
the prey and predators of yellow perch?

3. Are impingement and entrainment the only adverse effects
of the plant on yellow perch?

It is hoped that future researchers will answer these vital questions.

APPENDICES

APPENDIX A

GENERAL CREEL SURVEY QUESTIONNAIRE

APPENDIX A

 

 

 

 

 

 

 

 

 

 

 

 

 

GENERAL SURVEY
interviewer: Area inner Date /
1 2 3 4
l - Yellow Perch 5 - Large-00th has 11 - Pike 15 - Suckers
2 - Hhite bass 7 - Seelleouth boss 12 - Trout l7 - Panfish
3 . Freshwater Drum 8 - Chinook salIIon 13 - Bullheads 18 - Other
Sheepshead) _ . . _
4 _ Halleye 9 Coho salmon 14 Catfish 0 non-boat type of
5 _ Rock bass 10 - Salmon 15 - Carp 1 - boat - fishemn
P211501 41 42 l3 I4 95 95
me 578957895789578957895789
Traverse lunar _ __ _ _ _ _
10 10 10 10 10 10
Type of Fishemn _ _ _ __ _ _
11 ll 11 11 11 11
110. Licensed Fishemn __ _ _ _ _ _ _ _ _ _ _ _
12 13 12 13 12 13 12 13 12 13 12 13
No. Unlicensed Fisher-en _ _ _ __ _ _ __ _ _ _ __ _
14 15 14 15 14 15 14 15 14 15 14 15
No. Fishermen Shipped _ __ _ _ _ _ _ _ _ _ _ _
15 17 15 17 l5 17 15 17 15 17 15 17
Tot. 140. Mrs. Fishing so
far on this site — -—- — — — — — — -— — — —
18 19 18 19 18 19 18 19 18 19 18 19
Tot. Io. Hrs. you plan to
fish on this site — — -- - -- - -— — - — — _-
20 21 20 21 20 21 20‘ 21 20 21 20 21
lot. 110. end Tot. wt. of SP — — — — — — — — — — -- -—
each species caught on 22 23 22 23 22 23 22 23 22 23 22 23
thissite ___ ___ ___ ___ ___ ___
24 25 25 24 25 25 24 25 25 24 25 25 24 25 25 24 25 25
27 28 29 27 28 29 27 28 29 2728 29 2728 29 2728 29
Tot. 110. endTot.1it. of SP — — — — — — — — -- — — -
each species caught on 30 31 30 31 I) 31 3) 31 30 31 I) 31
thissite __ __ _ ___ ___. ___ ___ ___.
323334 323334 323334 323334 323334 323334
"0 .... .... _. __ _— —— — —— — —— — ___ .—
35337 353 37 355 37 355 37 353 37 353537
lot. No. and lot. Ht. of _ _ _ __ __ __ _ _ _ _ _ _
each species caught on SP 38 39 38 39 38 39 33 39 38 39 38 39
this site
"T 404142 404142 404142 404142 404142 404142
110 ——-————-—— ——-———— ——— ———
43 44 45 43 44 45 43 44 45 43 44 45 43 44 45 43 44 45

84

APPENDIX B

PARAMETER ESTIMATION OF THE
SURPLUS PRODUCTION MODEL, AND
A PLOT 0F OBSERVED YIELDS VERSUS

PREDICTED YIELDS

APPENDIX B

Jensen (1976) estimated the parameters of the surplus production

model by nonlinear least squares using the approximation:

t+1

 

y(t+1) = qE I B dt = qE (B(tFD + B(t)) (29)
t 2
where
-(k-qE)t -1
B(t)= k + _1. -1<______ e (30)
Bm(k-qE) B0 Bm(k-qE)

 

 

 

 

All variables were defined in equations (5) and (6) except Bco which equals
K, and B0 which is the initial biomass.

In my analysis initial guesses of the parameters k, Ba, and q were
derived from the Schaefer (1957) method discussed in Chapter III. These
initial guesses were substituted into equation (30) to calculate B(t)
for all values Of t from 1960 to 1969 for the commercial fishery and 1970
to 1977 for the sport fishery. B(t) is calculated and then substituted
into equation (29) to estimate yield. The residual sum of squares
(RSS) is then calculated: £(Y-Y)2. Y is observed yield and Y is pre-
dicted yield. The RSS is calculated several times with different
parameter values of Bm, q, and k until an approximate minimum RSS is
found.

A simple linear regression involving Observed yield and predicted
yield was then run:

85

86

Y = a + bY (31)

Ideally it is hoped that the observed and predicted yields are identical
(R2=1). In my studythe commercial and sport R-squared values equaled
.31 and .74 respectively. A plot of Observed yields versus predicted
yields over time for the commercial and sport fisheries is shown in

Figures Bland BZ respectively.

87

.wm: mfi mafia HOOOONHHOS vwaow use .huonmww
HmwoquEoo mnu you AOOHH ponmmpv Homoa :OHOOSpoum msaauam osu
ha wouowpmua mpaow» can Aocaa pwaomv mpaow» vu>pomno .Hm muswwm

mmm. wwm. www. Nwfl 0mm.

 

a . a a _ J _ q _ O

 

 

I
(D
(U
,01 x $011008 NI 013M

 

YIELD IN NUMBERS x 10‘

Figure B2.

1320*

24{)

88

 

L60

O)
O
1

 

0

 

 

EWO

J 1 1
I972 I974 I976

Observed yields (solid line) and yields predicted by

the surplus production model (dashed line) for the
sport fishery. The solid horizontal line is MSY.

 

APPENDIX C

DATA SHEET FOR RECORDING BOAT

COUNT INFORMATION

APPENDIX (2

 

BOAT COUNT DATA AND NOTES

 

 

 

 

 

 

 

89

Interviewer Area Mulber
__/__
2 3 4 5 ll
Count Nuaber
ll 32 43 #4 95 95
Tile 5 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9 E"
Tot. no.
Boat -------- ---—--—--—- -—----—--—- -------- -------- --------
Fish-n. 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13 10 11 12 13
at site
Start End Tot. I IHIOS
lileege
. Approxieete Tine

transects. Begin End

1 — —

2 —— —

3 ——- _—

4 _ —

5 —— _—
Notes:

 

APPENDIX D

STATISTICAL ANALYSIS OF BOAT FISHERMEN

TOTAL ANGLER DAYS

 

E!

APPENDIX D

To test the validity of the procedure used for estimating the
number of boat fishermen angler days, samples were drawn from a hypO-
thetical boat fishermen population. Actual field data (frequency of
angling hours fished, etc.) were employed to assist in the establishment
of this hypothetical population of angling activity. Two tests were
performed to show that consistent estimates of the average angling hours/
fisherman can be Obtained by subsampling this hypothetical population.
The average angling hours/fisherman was used for estimating the total
angler days during a sample day. For both tests assumptions were made
that 1) anglers arrive and depart randomly and 2) anglers are concluding
their angling day when they return to their access entry points
(typical Of Monroe anglers).

In test one each fisherman in the hypothetical population was
numbered. From a table of random numbers a twenty-five percent sample
of the numbered boat fishermen was taken from the hypothetical p0pulation,
and their angling hours recorded. A t—test was performed to determine
whether there was a significant difference between the population and
sample mean angling hours of the fishermen. The result showed no signif-
icant difference between the population and sample means (p (.05).
Numerous populations were employed in this procedure. In conclusion,
accurate estimates of the average angling hours/fisherman can be

obtained from field data.

90

91

Test two was based upon the probability of encountering each in-
dividual fisherman within the hypothetical population. For example,
there is a 2/5 probability of encountering fishermen who stay for 2
hours throughout the day with an angling day length of 15 hours and 3
traverses (%fi%'= %%-= g). Based upon the frequency distribution Of
angling hours fished by fishermen in Monroe County (from actual data)
each member of the population was assigned a particular number of angling N
hours and consequently a probability of encounter. Based upon these

probabilities a table of random numbers was used to determine which

fishermen were included in the sample taken from the population. A

 

t-test was again performed to determine if there was a difference be—
tween the population and sample means (p <.05). Numerous populations
were employed in the procedure. The results showed no significant
difference between the population and sample means. Therefore, accurate
estimates of the mean angling hours/fisherman are attainable in the
field.

The sample means of these tests represent'h‘ijk in equation (14).
Although there was no significant difference between the population
and sample means, the sample mean values that were calculated did vary.
Consequently, after substituting these different sample means into
equation (15) a range of values resulted for the total angler day
estimates. This range was up to fifteen percent above or below the
actual population number of angler days.

During most of the year at Monroe County the angling day length

for boat fishermen was assumed to be one-half hour before sunrise and

one-half hour after sunset (same as shore fishermen). There usually

92

was no correction factor involved since very little boat fishing occurred
before or after these hours. However, during the major holidays of
Memorial, Independence, and Labor Day weekends some fishing occurred
beyond the normal angling day length. This augmentation of angling
activity during these holidays and several other days of the year was

accommodated by increasing the assumed day length used in the calculations.

 

 

APPENDIX E

WRITING PLANT SITE QUESTIONNAIRE

 

 

APPENDIX I
“11"“ PLANT SITE

 

 

 

 

 

 

 

 

 

 

 

 

 

INTERVIEW“ Area Under Date _I
1 2 3 4 5
l - Yellow perch 5 - Large-outh bass 12 - Trout l5 - Suckers
2 - 101m bass 7 - Sullmth bass 13 - Bullheads 17 - Panfish
3 - Fresheter Dru 8 - Chinook salon 14 - Catfish l8 - Other
(sheepshead) 9 - Coho salnn 15 - Carp 0 - non-boat T f " he
4 - Walleye ype o s men
10 - Salmon 1 - boat
5 - lock bass ll _ N“
2511501 51 92 I3 44 45 05
Tina 6 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9 5 7 8 9
"mm "°' 10 10 10 10 10 10'
Type of Fish- _ — — — _ _
erun ll 11 11 11 11 11
lo. Licensed — _ _ — — — _ _ - _ _ —
Fishermen 12 13 12 13 12 13 12 13 12 13 12 13
lo. Unlicensed — -— — — — — — — -— —- — —-
Fisher-en 14 15 14 15 14 15 14 15 14 15 14 15
110. Fisherun — -— -- — — — — — - — — —
Skipped 15 17 15 17 l5 17 15 17 15 l7 l5 l7
Tot. 110. Hrs. _ _ _ _ _ _ _ _ _ __ _ __
Fishing so far 0
on this site 18 19 l8 19 18 19 l8 l9 18 19 18 1.
Tot. 110. hrs.
you plan to — — — — — — - — -- — — '—
fish on this 20 21 20 21 20 21 20 21 20 21 20 21
site
Tot. 110. hrs. you
plan to spend on _ _ _ __ _ _ _ __ _ __ _ _
other activities
on this site 22 23 22 23 22 23 22 23 22 23 22 23
What 3 of your F __ __3 _ __3 __ _3 _ _3 _ _3 __ _3
trip was for
11511199: what 24 25 24 25 24 25 24 25 24 25 24 25
3 for other pur- 0 _ _1 _ __S _ __3 _ _3 _ _3 __ _3
9““ 26 27 27 25 27 25 27 25 27 25 27
Tot. No. 5 Tot. 6
wt. of each p - — -- - -' — — — -" "' — '-
species caught 28 29 28 29 28 29 28 29 28 29 28 29
on this site no
30 31 32 30 31 32 30 31 32 30 31 32 30 31 32 30 31 32
wt _ _ _ _ _ _ _ ______
33 34 35 33 34 35 33 34 35 33 34 35 33 34 35 33 34 35

 

93

94

 

 

 

 

 

 

 

 

 

 

9611601 41 42 43 44 46 46
Tot.110.5T0t. 3P __ __ __ __ __ _—
36:1;th 9M 36 37 66 37 36 37 36 37 36 37 36 :17
6621116616. "°'——— ——— ——-- -——— ——— ———

383940 383940 383940 363940363940 966940
«___ ___ ___ ___ ___ ___
41 42 43 41 42 4:1 41 42 43 41 42 43 41 42 43 .41 42 4:1
16:. Io.|Tot. ,
wt.ofeech p —— —— —— —— —— ——
species cau¢1t 44 45 44 45 44 45 45 44 45 44 45
onthissite no._____ ___ ___ ___ ___ ___
464746 4746 464746 4748 4746 464746
wt___ ___ ___ ___ ___ ___
496061 496061 496061 496061 496061 496061
Tripcostfra
ha: I
4006-64-26:»: 52535455 52535455 52535455 52535455 52535455 52535455
1.Trensport.Pd.
(664m- 0 -—-" -"'" _—'-" —--"' "T’ —_"'-
“mm“; 55575859 66676669 66676669 66676669 66676669 66676669
2.Food58evg. ___ ___ ___ ___ ___ ___
m'w'” 606162 606162 606162 606162606162 606162
3.Lodging(rent- ___ ___ ___ ___ ___ ___
61 basis)
53 64 55 53 64 66 53 64 66 53 64 66 53 64 66 53 64 66
4.861t.Lures ___ ___ ___ ___ ___ ___
666766 666766 666766 666766666766 666766
5.566.0i111406t ___ ___ ___ ___ ___ ___
69 70 71 69 70 71 69 70 71 59 70 71 69 70 71 69 70 71
5.FeeslIother ___ ___ ___ ___ ___ ___
72 7:1 74 72 73 74 72 73 74 72 73 74 72 73 74 72 73 74
I.FixedCosts
(PresentValue)
ers. othfl' eqp. 76 76 77 76 76 77 7s 76 77 76 76 77 76 76 77 76 76 77
used today
J. J. _I J. J J.
60 60 60 60 60 60
Arealo. _ _ __ _ _ _
1 1 1 1 1 1
041: ____ ____ ____ ____ ___- ____
2345 2345 2345 23452345 2345
711: ____ _____ ____ ____ ___- ___-
5789 6769 5789 67696769 6769
80at.e0tor
water skis.etc. ____ ____ ____ ____ -___ ___—
m‘ m” 1011 1213 1011 1213 1011 1213 10111213 1011 1213 1011 1213

 

E95

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11611601 41 42 43 44 46 46
Type of fishing __ _ _ _ _ _
"m“ 14 14 14 14 14 14
Tot. Io. days
youvilluse __ __ __ __ __ __
"""""‘°""‘ 16 16 16 16 1s 16 16 16 16 16 16 16
Boat license
if yes enter 1 _ _ _ _ _ _
"”"W'"? 17 17 17 17 17 I7
I“. he m
you will use __, ___ ___ ‘__ .__ .__ ___ __, __ .__ ___ ___ .__ .__ ... ... ... ...
““"m 16 19 20 16 19 20 16 19 20 16 19 20 16 19 20 16 19 20
Enloynnt end
incole -' '— —’ "’ "’ "‘
21 21 21 21 21 21
22 22 22 22 22 22
23 23 23 23 23 23
Am of rest» 24
dence ’
city or It
tomship g
0" 2L
out-of-stete
county Q
g
30
31
32
33
34
36
36
37
36
39
40
4L
42
_l .1! .1 .3. .1
60 60 60 60 so

 

Fishing Licenses:

.2

m

l - Resident Sportun's license

2 - Resident Senior sportlen's license
3 - Resident ennuel
4-R.A.lTroutstq

5 - Sen or Resident Annual
5 - S. R. A. I Trout st“
3 - -Resident ennuel

9 n

R. A. I Trout stn

E

I.
Dei

 

96

WHITING PLANT — EMPLOYMENT AND INCOME

Are you presently employed? 1 = yes

If not, are you: 2 student, college 3 = student, other

4

housewife 5 = retired 6 = unemployed (21)

Will you tell me in which of these categories is your current

annual wage rate? If you have more than one occupation, please

answer for the lowest paying one. (22)
Annually Hourly

1. under $3,000 under $1.50

2. $3,000-4,999 $1.50—2.50

3. $5,000-6,999 $2.50-3.50

4. $7,000-9,999 $3.50-5.00

5. $10,000—14,999 $5.00-7.00

6. $15,000-25,000 $7.00-12.00

7. over $25,000 over $12.00

APPENDIX F

ESTIMATED CATCH AND EFFORT

BY SPORTS FISHERMEN
IN LAKE ERIE WATERS OF MONROE COUNTY
FROM FEBRUARY, 1978 TO JANUARY, 1979

WITH PERIODS I, II, AND III COMBINED

APPENDIX F

Table F1. Estimated Sport Fishing Catch and Effort for Monroe County

Waters of

Lake Erie from February, 1978 to January, 1979.

 

 

Species

Catch (Numbers)

Effort (Angler Days)

 

Yellow Perch
White Bass
Freshwater Drum
Walleye

Rock Bass
Pike

Trout
Bullheads
Catfish

Carp

Suckers
Panfish

Other

509,001
2,408
2,080

14,381
272

54

3

680
5,265
593

28

574

96

29,411
636
1,262
7,851
131

42

383
1,878
288
11
260

36

 

97

APPENDIX C

ESTIMATED CATCH AND EFFORT
BY ANGLERS
AT THE J. R. WHITING PLANT SITE
FROM FEBRUARY, 1978 TO JANUARY, 1979

WITH PERIODS I, II, AND III COMBINED

APPENDIX C

Table Cl. Estimated Catch and Effort at the J. R. Whiting Plant Site
from February, 1978 to January, 1979.

 

 

 

Species Catch (Numbers) Effort (Angler Days)
White Bass 25,906 2,305
Freshwater Drum 789 300
Bullheads 534 166
Catfish 4,028 2,058
Carp 1,597 1,076
Other 1,744 259

 

1Yellow perch were not caught at the plant site. Neill and Magnuson
(1974) indicated that yellow perch avoided thermal discharges at
power plants.

98

APPENDIX H

DESCRIPTION AND APPLICATION
OF THE DATA FROM THE CREEL
SURVEY, BOAT COUNT, AND
J. R. WHITING PLANT SITE

QUESTIONNAIRES

APPENDIX H

This is a description of the questionnaires used for the roving
creel survey, the boat count data and notes, and the J. R. Whiting plant
site (Appendices A, C, and E respectively). It includes an explanation
of how the information, derived from the questions on the forms, was
employed in the procedures and calculations integral to this entire
study. A few of the questions are extraneous, since these questionnaires
were utilized in other studies which required more detailed information
than was needed in my analysis. I will not describe what questions
were omitted. If they are not mentioned in this section, then they
were ignored.

All the questions in Appendix A are identically described on page
one of Appendix E (numbering of questions not identical to Appendix
A). Appendix A will be discussed in detail. However, the same infor-
mation also applies to Appendix E. Numbers 1 through 11 (Appendix A)
were qualitative questions used to segregate the information into dif-
ferent categories such as area or type of fishermen. It was assumed
all anglers were licensed.

Usually all shore anglers encountered in an area during a sample

day were interviewed. During Period I (ice fishery) occasionally

 

shore fishermen were skipped. The number of these anglers was recorded.
It was assumed that the catch and effort data of each angler skipped

was identical to that of the previous angler who was actually interviewed.

99

100

Each horizontal number (labeled person), 1 through 6, represents the
information from one interviewed angler. To facilitate my calculations
each skipped angler was recOrded as one interview.

The information pertaining to catch and effort (numbers 13 to
45) is substituted into equations (1), (2), (3), or (13) to obtain
total catch and effort in an area for a particular sample day. For
boat anglers the above information is substituted into equations (14),
(15), or (16) for total catch and effort. Appendix C contains the
instantaneous counts of boat anglers in an area during a sample day.
This information is incorporated into equation (15) so total angler
days can be estimated.

In addition to the questions contained in Appendix A, the J. R.
Whiting plant site questionnaire (Appendix E) has questions pertaining
to the supply and demand analysis of the plant site. The information
collected included the: (1) purposes of the trip, (2) record of costs
incurred by the respondent, and miles driven at his expense, (3) number
of days he expects to use his license, (4) employment status, (5)
current lowest wage rate, and (6) city in which the respondent lives.
Given this information the price (supply) of fishing for an individual
angler at the plant site can be estimated. Talhelm (1972, 1978)

provided these equations for estimating an angler's costs:

 

Pf = Tth + Twa + COSTS (32)
AD
where
Pf = price of angling in dollars/angling day,
T = travel time in hours,

where:

FOOD
EQUIP
LIC

LDU

101

angler days (usually==1),
wage rate ($/hr),
angling time in hours,

.1 MT + .25 FOOD + (1 + .OI-EQUIP) + LIC/LDU

miles of automobile travel paid by the respondent,
cost of food purchased as part of the trip,
current market value of equipment,

license cost,

number of days the license is used.

Traveling time from one geographical area to another in Michigan and

surrounding states was provided by the Michigan Department of State

Highways and Transportation.

APPENDIX I

COMMON AND SCIENTIFIC

NAMES OF FISH SPECIES

CAUGHT IN MONROE COUNTY

 

APPENDIX I

Table 11. Common and Scientific Names of Fish Species Caught in
Monroe County from February, 1978 to January, 1979.

 

 

Common

Scientific

 

Yellow perch
White bass

Freshwater drum
(Sheepshead)

Walleye

Rock bass
Northern pike
Lake trout
Yellow bullhead
Channel catfish
Carp

Suckers

Panfish

Perca flavescens

 

Roccus Chrysops

 

Aplodinotusggrunniens

 

Stizostedion vitreum vitreum

 

Amb10plites rupestris

 

Esox lucius

 

Salvelinus namaycush

 

Ictalurus natalis

 

Ictalurus punctatus

 

Cyprinus carpio

 

Catostomus and Moxostoma spp.

 

Lepomis spp.

 

102

APPENDIX J

ANNUAL REDUCTION IN THE

YELLOW PERCH POPULATION

FROM THE COMBINED EFFECTS

OF IMPINGEMENT AND ENTRAINMENT

APPENDIX J

Table Jl. Annual Simulated Percentage Loss in the Yellow Perch
Population Prior to Stabilization from the Combined Effects
of Impingement and Entrainment.1

 

 

 

Percent Reduction Percent Reduction
Year (ri,t> Year (ri,t)
0 0 13 1 9
1 0 14 1 9
2 .0 15 1.9
3 .0 16 1.9
4 .9 17 2.8
5 .9 18 2.8
6 .O 19 2.8
7 .0 20 2.8
8 9 21 3 8
9 1 9 22 2 8
10 .9 23 2.8
11 .9 24 3.8
17 l 9 25 3 8

 

1Beyond 25 years the population reaches stabilization. Saila and

Lorda (1977) state that power plant impact should be considered

during the perturbation period (impact of impingement and entrainment)
prior to stabilization. Stabilization is defined as the period or
time it takes for the perturbed population to converge to a new stable
age distribution.

103

104

The reductions in the population from impingement and entrainment

are represented by the harvest matrix:

 

 

 

l-p0 0 0 . 0
H = 0 l-p1 0 0
0 0 0 . l-pn
___ ___l,

where

Pj = fractional or percentage reduction from impingement and

entrainment of the jth age class.

Carrying out the matrix multiplication of the harvest matrix (H) and

the Leslie projection matrix (A) will give:

(l-p )s O ... O 0
HA = 1 O
0 (1-p2)81 ... 0 0

 

 

105

The equation for calculating the annual percentage loss from the

combined effects of impingement and entrainment:

r1,t = ((pw’o - pi,t)/Pw,o) x 100 (33)
where
ri,t = percent reduction in p0pulation size from
impingement and entrainment (1) during year , t,
Pw,o = population size without plant mortality (w)
during year, 0,
pi,t = population size from the combined effects Of

impingement and entrainment during year, t.

The equation for estimating the average annual percentage loss

after 25 iterations or years:

25
ri,25 = 2 ri,t/25 = 1.7 (34)
t=1
where
£1.25 = average percentage loss from impingement and
’

entrainment after 25 iterations and just

prior to stabilization.

It is assumed that after stabilization the plant will reduce the yellow
perch population by 1.7 percent per year for 50 years (life of the
plant).

Patterson (1979), utilizing a materials balance model, estimated
a .8 to 4.7 percent annual entrainment loss of larval yellow perch
by the Monroe power plant (Monroe, Michigan) in the Michigan waters of

Lake Erie. My estimated annual entrainment loss of larval yellow perch

106

by the J. R. Whiting plant was .4 percent (Table 9). However, the
Monroe plant has nearly nine times the total generating capacity of the
Whiting plant, so my lower estimate is probably somewhat comparable to

Patterson's results.

LIST OF REFERENCES

LIST OF REFERENCES

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Fogle, N. 1979. Michigan Department of Natural Resources. (Personal
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107

108

Hayne, D. W. 1966. Notes on creel survey for Tennessee Cooperative
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109

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110

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I'IICHIGRN TATE UNIV. L ARIES

| 11 111111111161 1

312930099

 

‘2

9