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HHITE SUCKER POPULATION DYNAMICS IN THE
BIG THO-HEARTED RIVER

By

Terence James Miller

A THESIS

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

MASTER OF SCIENCE

Department of Fisheries and Wildlife

I986

ABSTRACT

HHITE SUCKER POPULATION DYNAMICS IN THE
BIG THO-HEARTEO RIVER

3!

Terence James Miller

The white suckers of the Big Two-Hearted River were studied
during their spawning migration using an existing electric
weir. Life history information was obtained at intervals
within the spawning season. Tagged fish were returned to the

river and subsequent recaptures were noted.

During 1979, the white suckers of the Big Two-Hearted River
had an annual mortality rate of 40 percent and appeared to
grow at approximately 6 percent per year after reaching
maturity. The female white suckers grew faster after

reaching maturity than the males.

Analyzing the potential yield from this white sucker
population using the Dynamic Pool Model indicated that there
is no optimum level of exploitation. The maximum yield
identified occurs when harvest begins with four-year-old fish
at an instantaneous fishing mortality of 1.1. This equates
to approximately 2,800 pounds per year.

ACKNOHLEDGHENTS

This project was possible through the efforts of numerous
individuals. Niles Kevern suggested this project and I took
it hook, line and sinker. I thank Dr. Kevern for his
patience. I thank those who helped me collect the field
data, John Sefcick, James Bohan, Richard Hoppe and my wife,
Bernie, they had quite an experience. I thank the personnel
of Sea Lamprey Control at Marquette, Michigan, especially Leo
Hilkewitz. Additional thanks go to the members of my

committee: Drs. William H. Taylor and Ivan Mao.

ii

TABLE OF CONTENTS
Page
L1St Of TaDIESOOOOOO0.0.0.0...0.0...OOOOOOOOOOOOOOOOOOO 1v

L1St Of F1gurESeooooooooooeo.coco.0.0000000000000000... v

0-0

IntrOdUCt1onoooeeoooooooeeo00000000000000.0000.ooooeeeo
BaCkgroundOOOOOOOOCOOOOCOOOOOOCOOOOOOOO0.0.0.0....

Purpose of This Investigation.....................

MEthOdSe0000000000eeoeeoooooe0.0000000000000000...

‘0‘”th

Site Description..................................
Fishery........................ .......... ......... 10
Population Dynamics - Spring 1979...................... 12
Length Description................................ 12
Length-Height Relationships.. ..................... 17
Survival.......................................... l9
Growth-Adult Nhite Suckers........................ 24
Recruitment....................................... 30
Yield Estimation....................................... 31
Model Description................................. 31
Model Application................................. 33
Ancilliary Dbservations................................ 37
Summary and Conclusions................................ 38
Summary........................................... 38
Conclusions........................................ 41
Appendix - General References.......................... 43

List Of ReferenceSQo000000000000000000000000000.0000... 46

Table

 

LIST OF TABLES
Page
Length (standard deviation), desired half-widths
of 95% confidence interval (D) at each age for

female white suckers and estimated sample size.. 8

Length (standard deviation), desired half-widths

of 95% confidence interval (D) at each age for

male white suckers and estimated sample size.... 9

Summary statistics for males - Spring 1979........ 16

Summary statistics for females - Spring 1979...... 16

LIST OF FIGURES

Figure Page
1 Big Two-Hearted River and electric weir location. 11
2 Length-frequency of white suckers - Spring 1979.. 13
3 Distribution of males throughout spawning........ 14
4 Distribution of females throughout spawning..... 15
5 Catch curve for Spring 1979..................... 22
6 Ford-Nalford plot for maximum length............ 27
7 Ford-Halford plot for maximum weight............ 29
8 Yield-per-recruit at various fishing mortalities

(F)........................................... 34

9 Yield-per-recruit for various ages at first catch 35
lo YIEId contour d‘agraMOOOOOOOOOOOOOOOOOOOOOOOOOO. 36
11 Average recaptures over the spawning period..... 39

INTRODUCTION

Background

Changes in fish community structure over the last 50 years
have been dramatic for the Great Lakes. But.even before
that, man destroyed some fish stocks in streams tributary to
the Great Lakes through logging and dam building. The later
invasion of the sea lamprey (Petromyzon marinus) severely
diminished or drove to extinction the most valued commercial
fish (Hile 1946, Eschmeyer 1955). The ensuing exploitation
of under-used habitats by the invading smelt (Dsmerus mgrggx)

and alewife (Alosa psuedoharengus) applied increased pressure

 

on already struggling species such as the midwater chubs
(Christie 1974). The result was a partially collapsed and

totally changed commercial fishery.

There remains few high-value fish stocks in a healthy state.
The survival of the commercial fishery depends, partly, on
the economic development of abundant stocks of fish

here-to-fore largely unused.

The biology of these under-used species is not well known,

especially age 0 to age at recruitment. There has been some

2
estimation of yield potential for some stocks, but Lake
Superior stocks have been widely ignored for numerous
reasons. Lack of a large inplace commercial fishery,
infertility of Lake Superior compared to the other Great
Lakes and lack of accessibility are three reasons. One
compelling reason for now investigating the Lake Superior
fish, is the widespread contamination of fish with pesticides

and industrial contaminants.

Scott (1974) reported a decrease in Michigan commercial
fishery licenses from 900 in 1963 to approximately 660 in
1967. Now commercial licenses number approximately 70. In
recent years efforts to develop the Great Lakes fishery by
the State of Michigan have been directed toward establishment
of a recreational salmonid fishery. Included in the species
of choice are the chinook salmon (Oncorhynchus tshawytscha),

coho salmon (Oncorhynchus kisutch), and steelhead (Salmo

 

ggirdneri). The federal role, carried out by the 0.5. Fish
and Nildlife Service, is the attempt to develop
self-sustaining populations of lake trout (Salvelinus
namaycush) through stocking, behavioral and contaminant
research, and sea lamprey control. Although Native American
fishermen are taking lake trout and other salmonids in their
catch, the salmonids as a whole are protected from other
commercial exploitation. Efficient and equitable allocation

of the Great Lakes fishery resources is a difficult problem.

3
Traditionally there have been two methods of allocating
resources, either on a first come first served basis or on a
monetary basis with the highest value taking precedence.
Nith the commercial fishery but a shadow of its former self
and the recreational fishery for Michigan waters described as
a 550 million dollar industry annually (Douglas Jester,
personal communication), it leaves little doubt how the
highly valued salmonids are likely to be allocated.
Therefore, commercial interests must work with what is
available and one of the available fish is the white sucker
(Catostomus commersoni). Neither the commercial harvest nor
the markets have been fully developed for this species;

leaving the white sucker underutilized.

Nhite suckers in the Great Lakes spawn in streams tributary
to the lakes. They are also suspected of spawning in the
shallow shoal areas of the lakes (Scott and Crossman 1973).
Nhite suckers are thought to have a strong tendency to home
to a spawning stream (Olson and Scidmore 1963). Spawning
occurs from April to July. Green, et. al. (1966) observed
the beginning of spring spawning migrations when stream
temperatures reached 10° C. Barton (1980) observed that in
addition to stream temperature, stream discharge was an
important contributing factor in initiation and run strength

for spring spawning migrations.

The fish scatter their demersal eggs along gravelly stream

4
substrate. The usual number of eggs per female is probably
20,000 to 50,000 (Scott and Crossman 1973). Survival from
egg to migrant fry may be as little as 0.3 percent (Green,
et. al. 1966).

According to Scott and Crossman (1973), sexual maturity is
normally attained by the third or fourth year in Ontario,
Canada. Growth of males and females is similar up to age of
maturity. After sexual maturity, females grow faster than

males.

Mortality is thought to be low during spawning, usually less
than 20 percent. Annual survival of adult white suckers is
quite high. An annual survival rate of 0.87 is reported by
Olson (1963) for a lake in Minnesota. Coble (1967) reported
an annual survival estimate of 0.75 for South Bay, Lake
Huron. The maximum age for the species reported by Scott and
Crossman (1973) is 17 years which coincides with the age of
the oldest fish in this study.

Purpose of This Investigation

This thesis reports the result of two years of research,
having as its purpose, a description of the population
dynamics of the white sucker in the Big Two-Hearted River and
an estimation of the potential for exploitation of this

resource. Electrical weir information collected by the 0.5.

5
Fish and Nildlife Service revealed that two sucker species
utilize the Big Two-Hearted River for spawning purposes, the
white sucker and the longnose sucker (Catostomus catostomus).
Neir information is available for over 20 years on the
abundance of suckers running the river, however, no life

history information was taken until this study.

To evaluate the potential for harvest and the impact of
various harvest strategies on the recruited population, data
were needed regarding (1) the age and sex composition and (2)

general growth and mortality rates.

The objectives of this investigation were: (1) to determine
the approximate size of the white sucker population, and (2)

to estimate the potential level of harvest.

So that fishery managers and commercial fishermen might be
able to estimate output from this fishery, an accurate
production estimate is necessary. Even though an accurate
estimate of potential harvest ensues, to greatly expand the
market for suckers, impediments need to be removed, such as

the poor reputation of suckers held by consumers.

Methods

Samples of white suckers caught in the electrical weir oh the

Big Two-Hearted River were obtained during the spring of 1978

6
and 1979. Data collected from the 1979 fish were used to
determine the size, age, sex composition and general growth
and mortality rates. Estimates of relative yield per recruit
were calculated using the Dynamic Pool Model described by

Beverton and Molt (1957).

All calculations assume a population of white suckers in
equilibrium, that is, the population size, general growth and

mortality rates are constant.

An attempt was made to estimate the recruited population of
white suckers using mark and recapture. Due to the long
periods between samplings, the assumption of equal
probability of capture was violated and an attempt to
estimate the population using traditional techniques was
unsuccessful. An estimate of the approximate size of the
population was calculated using the average recapture rate

during the spawning season.

Electrical weir records show that white suckers comprised
most of the weir catch since 1975 and their yearly spawning
run strength is less variable than that of the longnose
sucker. Therefore, the white suckers were chosen for study.
Because of the distances involved in travel, a holding pen
was provided so that a week's catch could be held for
sampling. Fish were handled at stream-side and returned to

the water. Each fish was sexed by external determination

7

(Spoor 1935), measured to the nearest 0.1 cm (total length),
and weighed to the nearest 10 grams on a spring-loaded
hanging scale. A pectoral fin was taken for aging purposes,
and the fish was tagged with a spaghetti tag near the base of
the dorsal fin. Obvious morphological anomalies were noted,
e.g., broken back and fin parasites. The state of maturity
was also noted. Sampling for life history data took place in
the spring of 1979 between the months of May and July.

Aging was accomplished using pectoral fin rays because of
information developed by Beamish and Harvey (1969) and
Beamish (1973) indicating that after age 5, scales provide an
inaccurate estimate of age. Green et. al. (1966) suspected
inaccuracy in the scale aging method based on recaptured
tagged fish that they knew were older than indicated by the

scale aging method.

The first three rays of the pectoral fin were sectioned to
0.5 mm using a microtome provided by the Michigan Department
of Natural Resources as described by Beamish (1973). The
sections were mounted in mineral oil on microscope slides and
the annuli counted with the assistance of a variable power
dissecting scope. Only fin ray sections capable of being
clearly read were used for aging purposes. The fin ray
method of aging was verified using both scales and fin rays
from young fish to ascertain whether all the annuli were

being observed.

8
Nhen attempting to calculate the sample size necessary to be
certain that confidence intervals did not overlap for ages,
data from Vondracek (1977) were used as an estimate of
variance for each age and sex. Estimates of variation in
length were available for ages 2 through 10 for white suckers
from the Ahnapee River, Hisconsin, for females. Estimates of
variation in length were available for ages 2 through 6 for

males from the same location.

For female white suckers from the Ahnapee River, the desired
half-width of the 95% confidence interval and subsequent
ageable number of fish needed based on the Hisconsin data are

shown in Table 1.

Table 1. Length (standard deviation), desired
half-widths of 95% confidence interval (0) at each age
for female white suckers, and estimated sample size

 

Age Groug Length (mm) 0 (mm) Sample Needed
II 296 (43.1) 20 41
III 375 (46.2) 20 48
IV 415 (25.7) 10 27
V 440 (22.4) 10 20
VI 433 (19.6) 10 30
VII 436 (23.0) 10 42
VIII 459 (2.7) 5 3
1x 475 (21.5) 5 167
x 462 (25.5) 10 59

For male white suckers from the Ahnapee River, the desired
half-width of the 95% confidence interval and ageable number

of fish for each age class needed is shown in Table 2.

Table 2. Length (standard deviation), desired
half-width of 95% confidence interval (0) at each age-
for male white suckers, and estimated sample size

 

Age Group Length (mm) 0 (mm) Sample Needed
11 291 (9.6) 25 2
III 344 (14.2) 24 3
IV 392 (21.0) 9 22
V 410 (17.1) 2 293
VI 415 (23.2) 3 469

It was decided that as many fish as possible would be
collected because, (1) one is never certain that fin sections
from any individual fish will be readable, (2) there is no
way to know if you are within your desired half-width of the
confidence interval unless aging is done concurrently with
collecting, and (3) weight estimates are generally more
variable than length estimates. Additionally, based on past
catch records at the weir site, the number of fish needed for
aging to achieve the above specified precision just about

equals the annual catch.

Site Description

The Big Two-Hearted River is a large stream for the Upper
Peninsula. The discharge averages 34.3 cubic meters per
second from April through June. Its water is colored brown
with a total alkalinity of 35 mail as CaC03. The bottom is
sand and gravel. 1t drains an area of 521 square kilometers.
The mouth of the river is located approximately 29 kilOmeters

northwest of Paradise, Michigan.

10

The sampling point was approximately 1/2 kilometer upstream
from where the stream empties into Lake Superior (Figure 1).
The location of the mouth of the Big Two-Hearted River varies
from year to year depending on the volume and velocity of
water. At times, the stream bed scours to more than a meter
below its normal elevation. The stream bottom from the weir
site to the mouth consists largely of sand to cobble-sized

stones.

Fishery

The river supports numerous spring spawning runs of fish in
addition to its resident brown trout (Sglmg_t;gttg) and brook
trout (Salvelinus fontinalis) (unpublished U.S. Fish and
Nildlife Service records). The Big Two-Hearted River
supports viable runs of steelhead, smelt, brown trout, white

sucker, and longnose sucker.

The steelhead run gets much attention and receives a sizable
amount of recreational fishing pressure. The suckers receive
light fishing pressure, especially for the longnose sucker
since it is easier to take by hook and line than the white

sucker.

11

 

Lake Superior

 

Ii. two-Neon“
liver
sale im hm
as:—
O 1 2

 

 

acne in ate"

___n
I;
rf—f

 

 

 

Figure 1. Big Two-Hearted River and electric weir location.

POPULATION DYNAMICS - SPRING 1979

Length Description

The spawning white suckers in the Big Two-Hearted River were
sampled for life history information three times from May 12
through June 13, 1979. There were 457 fish sampled for age
determination (five immature, 246 males and 206 females).
Figure 2 shows the length frequency distribution of immature
and mature male and female white suckers. Fish were grouped
into 19 mm length groups (i.e., 200-219 mm, 220-239 mm,
etc.). The figure illustrates the size distribution
difference between the male and female spawners in 1979.
Figures 3 and 4 illustrate the length frequency distributions
for male and female by time period in the spawning season.
Figure 3 shows that proportionately there is a higher
occurrence of males less than 400 mm toward the end of the
spawning period. There is no clear indication of any size
differences among these three time periods for females

(Figure 4).

12

501

40"

”a:

20‘

IO'

13

Females

 

 

 

 

 

 

Mer

Males

 

 

 

 

 

 

mgr—I _1—.

 

 

Ilmmtures

 

 

220 260 300 340 380 420 460 500
Length Class (I)

Figure 2. Length-frequency of white suckers - Spring 1979.

14

d
D
a

 

6/13

5/21

 

 

 

IO -

 

 

 

5/12

10m

 

 

 

or_.__a=3———S=~fi - - - - -
a“) an mm» am an 4“) an
zoo zzo zoo :00 no no 420 460

Length Class (I)

Figure 3. Distribution of males throughout spawning. -

15

 

 

 

 

 

 

 

 

 

 

 

 

 

Laue
6/13
30 o
20 -
O I
5121
a. n -
5 2.-
IO -
0
5/12
m -
m .
10 -
O I====a - e m - - - - a J=
220 260 aoo 340 380 420 460 soo S40
240 280 320 360 400 440 400 520

Length Class I-)

Figure h. Distribution of females thoughout spawning.‘

16
Table 3 shows the summary statistics for the male white

suckers during the spring of 1979.

 

Table 3. Summary statistics for males
Spring 1979
Number Agg’ Avg Length (mm) CV 1 Avg Neightjggl' CV 1
2 3 374.5 600

27 4 379.6 4.66 588.5 14.6
59 5 381.5 4.98 606.1 18.0
61 6 393.2 5.51 674.5 16.6
36 7 406.5 5.37 738.0 13.8
26 8 406.4 5.95 _732.7 14.7
18 9 416.5 4.25 ' 807.1 13.7
10 10 428.8 5.75 881.7 12.8
4 11 448.0 3.70 1026.7 10.6
2 13 437.0 3.20 840.0 11.9

1 17 452.0 1040.0

Table 4 shows the summary statistics for the female white

suckers during the spring 1979 spawning run.

Table 4. Summary statistics for females
Spring 1979

Number Agg_ Avg Length (mm) CV 1 Avg Height (gm) CV 3
12 4 369.7 17.1 635.4 45.8
50 5 406.1 5.7 800.5 14.1
48 6 414.4 6.1 815.6 18.1
41 7 429.8 5.5 893.9 19.9
15 8 459.4 5.5 1088.0 18.5
18 9 454.8 5.8 1095.6 15.4
14 10 476.1 6.2 1265.0 15.7
4 11 457.5 1.1 1150.0 8.2

1 12 515.0 1520.0

1 13 520.0 1730.0

1 15 472.0 1110.0

Numerous fish captured at the weir had broken backs

(presumably from impact by the electric field) and these

17
individuals were not used in calculation of the statistics for

length and weight.

Length-Height Relationships

Growth of the white sucker population for the spring of 1979
was analyzed separately for males and females. The
relationship of body weight as a function of length was
investigated. The von Bertalanffy theoretical growth equation
describes the growth in weight as an exponential function of

length (Gulland 1969). The generalized formula is:

H " a Lb(e)
where: N 8 weight,
a - a constant,
L - length,
b - growth exponent, and

e - random error term.

The linearized form of the growth equation for use in linear

regression analysis is:

ln N . In a + b ln L + ln s.

The spring 1979 length-weight relationship for males, ages 3
through 11, is given by:

18
ln v - 0.000005 + 3.1 In L + ln s.
n2 - 0.99.

The measure of fit (R2) of the regression indicates that the
natural logarithm of length explains 99 percent of the
variability in the natural logarithm of weight for the male

white suckers.

The spring 1979 length-weight relationship for females, ages 4
through 10, is given by:

ln w - 0.000070 + 2.7 ln L + ln s.
R2 . 0.99.

The measure of goodness of fit (R2) indicates that the natural
logarithm of length again explains 99 percent of the
variability in the natural logarithm of weight for female

white suckers.

The spring 1979 length-weight regression for males and females

taken as one population, ages 3 through 11, is given by:

ln v . 0.0000053 + 3.1 ln L + Inez,
n2 - 0.99.

Again the natural logarithm of length accounts for 99 percent
of the variability in natural logarithm of weight for the

white sucker population.

19
The growth constant (b), for the population as a whole is very
close to 3, therefore, the assumption of isometric growth
(growth in weight as the cube of the length) appears justified
for use in growth estimation within the Dynamic Pool Model.
Analysis of covariance, however, shows that the slopes in the
separate regressions for the males and females differ
significantly (p - .01). The analysis indicated that after
maturity the female white suckers grow at a faster rate than
the males. The author has no site specific information on the

growth rates for the two sexes prior to maturity.

Survival

There are numerous methods to calculate the survival of fish.
The method used here is survival based on the assumption of a
geometric distribution of numbers of fish with age (Chapman
and Robson 1960).

Adult white sucker mortality based on the assumption of a
geometric distribution assumes that there are few older fish
relative to young fish. The basic formula of population

survival is:

"(xi-1) g 5 ° Nx,‘

where: N(x+1) - number of fish at the next older age

Nx - number of fish of age x, and

20
s - the annual survival rate between age x
and age (x+1)
This translates to

Nx ' (1-8)x No,

where: Nx - number of fish at age x,

(l-a)x - the annual survival rate at the specific age x,
No - the initial number of fish at recruitment, and
a - the annual mortality rate.

The assumption is that the population is in equilibrium and
the number of fish in each age group diminishes geometrically
with age, implying that the annual survival rate is constant
over age and time. If this assumption is correct then there
is some age x0, such that for all ages x 3.xo, the probability
of selection is the same and the annual survival rate is the
same. The ages can be relabeled for convenience so the first

fully vulnerable age x0 t O.

For the white sucker population the annual survival rate 5,
was based on the ages observed in the random sample of 318

individuals from the population.

The formula provided by Chapman and Robson (1960) for ‘

calculation of mortality using coded ages is:

21

2xi
a n + ZXi-l

M)

where: n . sum of all coded age groups 0, I, 2...
3 - annual survival rate, and

2x1 . weighted sum of the coded age groups 1. 2, 3....
The variance for survivorship is:
Var (é) = g (E -

For the female white suckers the survival is calculated
starting from age 6, which is the age at which the female fish
are fully represented in the catch as indicated by the catch

curve (Figure 5).

An estimate of the survivorship of the female white sucker is:

2"1 ‘ 243

S 3m 3m = 0.5045.

The mortality is therefore:
8 : 0.3955.

An estimate of the variance of the survivorship is:
Var (§)4- 0.0061 and
the error bound 8 - 2'N/Var s - 0.0494.

22

 

 

 

Catch Curve
5.0 -
4.0 4
3.0 3
.fl
3
8
O
8
.J
2.0 .
1.0 .
a s 6 7 8 9 10
Age

Figure 5. Catch curve for Spring 1979.

23
Therefore, the survivorship with an approximate 95%
confidence interval is:

0.5045 1 0.0494.

For the male white suckers the age at which the fish are

fully vulnerable to the weir is also age 6.

Proceeding as before:

§= 2x1 =321=05912
———Tn+2xi- 334 ' -:

a - 0.4059,
Var (§) . 0.000663. and
the error bound 6 - 2VVar (£) - 0.0515.

Therefore the survivorship with an approximate 95% confidence
interval is:

0.5912 1 0.0515.

According to the above calculations the annual survivorship
for the males and females is so close that they can be

treated as the same.

The annual survival for further calculations will be 0.60 and
the annual mortality is then 0.40. The instantaneous total
mortality rate, 2, defined as the negative natural logarithm

of survival, is 0.51.

24
Since there is essentially no sport fishery for white suckers
in the Big Two-Hearted River, the instantaneous natural
mortality rate M will be assumed to be equal to the

instantaneous total mortality rate.

Growth - Adult Nhite Suckers

 

For population analysis it is desirable to express the growth
of fish in a mathematical expression. The basic requirement
is an expression giving the size (in terms of weight or
length) at any given age which agrees with the observed data
(Gulland 1969). It also is desirable to be able to easily
incorporate this expression in a model for yield. The von

Bertalanffy growth equation is often used (Gulland 1969).

There are arguments for the retirement of the von Bertalanffy
equation (Roff 1980), but it appears to work well when
applied to the Big Two-Hearted River white sucker population.
The assumption of isometric growth inherent with the use of

this equation seems to be warranted.

The von Bertalanffy growth equation can be used both for
determining the 'rate' of growth (increase in weight or
length per unit time) and the size of a fish at various ages.
The instantaneous rate of growth will not be known, only
lengths at certain times, however, for use in the yield model
for the spawning population of white suckers in the Big
Two-Hearted River that is sufficient.

25

The general equation used is:

'(x) " 1* Lox)"

where: H(x) weight at a given age x,

a a constant,

L(x) length at a given age x,

b - growth constant, and

e the random error term. -
Usually b is assumed to approximate 3. According to previous
growth regressions this assumption appears to be valid.
According to Gulland (1969) the growth in length equation
derived by von Bertalanffy is of the form:

LIX) ' L(max) (I’B'K(x'*o)) e

where: L(max) . maximum length attained by the species,
K - annual growth constant,
x0 - theoretical age of fish at length 0,
x - age of fish, and

e s the random error term.

The linearized form of the above equation for investigating
the relationship of the length at age x to the length at age

x + 1 can take the form:

25
L (Xil) ' L(max) (l'e'K) + e 'K L(x) + e

Regressing length at age x on length at age x + 1 results in:
L(‘+1) - 34.54 + 0.9397 L(x) + e.

The theoretical maximum length of the white suckers in this

population can be calculated by rearranging:
L(nax) ' l ' 572.8 ”M.

Ford (1933) and later Nalford (1946) independently developed
an equation describing each year's growth increment as less
than the previous year's. Nalford noted that if length at
one age was plotted against the length at the next younger
age the result was a straight line and that the point of
intersection of the growth line and a 45° line drawn from the

origin is an estimate of L(max)-

Figure 6 shows a Ford-Halford plot of the length at age x+1
against length at age x.

The annual growth constant (K) can be derived from the

regression and is defined as:

- ln e'K
or

-ln 0.9397 = 0.063.

27

572.8 -

Length at age :01 (n)
5
\
\\

.‘... /

M ‘

 

 

fl V
a

an 'mb two on in in in in an no so
Length at age a (a)

Figure 6. Ford-Waltord plot for maximum length.

28
Therefore K - 0.063 or the annual rate of growth of the white
suckers is approximately 6 percent per year after maturity.
The weight of these white suckers has been shown to vary as a

power of the length (see Length-Height Relationships).

The regression describing the data for the weight of these
fish as a function of length is:

ln H(x) = 0.000006 + 3.1 ln L(x) +nln e and
"(max) - a L(max) 5, therefore,

Figure 7 shows a Ford-Halford plot of weight at age (x + 1)
against weight at age x.

One of the remaining parameters to be calculated before the
von Bertalanffy growth equation can be incorporated into the

Dynamic Pool Model is the theoretical age at length 0, (x0).
L(x) ‘ L(max) [l-e'K(X'Xo)] X E
rearranging this equation gives

e'KIX'X I - L(max)'L(§) x c
v1(max)

taking the natural logarithm yields

x0 . x + 1 ln L(max)’L(§) + ln s
-K—' ( L(nax) )

29

23!)-

2M!)

uxn
1AM).

A A A A

1509‘

Height at age x+l (9)

 

 

 

100T300T 5001700 910 11003300 1500717001900‘21'00 23008910
Height at age x (9)

Figure 7. Ford-Walford plot for maximum weight.

30

which can be solved using linear regression techniques

x0 = a + b ln (away-Lu), + lne .
(max)

 

The value for x0 is -8.72 years. This value is simply a
theoretical value and has no biological meaning but is needed

to compute the growth form from time 0.

Recruitment

 

The age of recuitment is defined as the age at which the
fish are fully vulnerable to the particular gear. In this
situation, recruitment will be defined as the age when all of

the fish have matured and joined the spawning population.

To determine this age a simple catch curve can be
constructed. A catch curve is the natural logarithm of the
number of fish caught, at a particular age, plotted against
the ages of the fish in the population. This plot forms a
type of parabola and the maximum height of this parabola
represents the point at which all succeeding ages are fully
represented in the catch. In this instance, the age of
recruitment for the male and female white suckers combined is

5.5 years (Figure 5).

YIELD ESTIMATION

Model Description

The Dynamic Pool Model as it is normally used is a single

stock yield model. The model incorporates data obtained on
size and age composition of the fish stock. In essence the
model considers the population as the sum of the individual

fish.

The model can be used to analyze various fishing mortalities
and ages of recruitment to a particular fishery. Assuming
that recruitment is independent of stock size and that the
stock is in equilibrium, the average yield from the stock
during any period is proportional to the average recruitment.
This leads to the conclusion that the yield from an average
cohort during its life is equal to the average yield from all
cohorts during any year. In addition, the yield from a
cohort is proportional to the number recruited to it. Yield

per recruit is, then, an expression of yield.

The Dynamic Pool Model in its simplest form is merely:

yield - fishing mortality x number of fish x weight of the fish

for any specific age group of fish. Nhen incorporating the

functions estimating the mortality, weight, and numbers over

all the age groups the model can be used to estimate the

31

32
yield from the entire population subject to exploitation.
Two areas where the fishery can be affected are (1) the rate
of fishing mortality and (2) the age at which the fish are

first harvested.

Investigation of the consequences of exploitation is
accomplished using the following general formula of the
Beverton and Holt Dynamic Pool Model.

3 e'K(xc'xo)

1 .
Y/R = F e'M(xc-xr) w(max) (_7— ' Z + K +

 

3 e-ZKngrxo) - e-3K(xc-xo) )
Z +'2K Z + 3K

 

where: Y I yield in grams,
R I number of individuals recruited,

F I instantaneous fishing mortality,

M I instantaneous natural mortality,
xc I age of the fish at catch,
x, I age of fish at recruitment,
"(max) I maximum weight of fish in population,
I I instantaneous total mortality (Iln survival),

K I von Bertalanffy growth constant, and

x0 I the theoretical age when a fish's length is 0.

33
Model Application

There is presently no significant fishery for white suckers
on the Big Two-Hearted River, sport or commercial.

Therefore, the age of fish at catch and the fishing mortality
will be adjusted to inspect the reaction of yield to these

variable changes.

In an effort to visually display the yield for catch at ages
3 and 6 and various fishing mortalities a plot of yield per
recruit versus instantaneous fishing mortality was
constructed (Figure 8). Figure 9 shows the yield per recruit
for an instantaneous fishing mortality of 0.80 and the range

of ages for the white suckers in the stream.

A yield contour diagram was prepared to visually display the
various ages at catch and instantaneous fishing mortalities
(Figure 10). There appears to be no optimum harvest rate.
In other words the harder the white suckers are fished the
more production can be obtained. The assumption is that as
the fishing mortality increases the natural mortality will

decrease allowing the population to sustain itself.

For the most part, the fish are not available in the river
until they are mature so given the high fecundity of the
white sucker (Kononen 1981) a relatively small number of

spawners should be able to sustain the stock.

34’

1700 .

1400 . First age at catch I 3

Yield oer recruit (YIN) 0

§§§§§§§§§

 

First_gge at catch . 6

 

 

0:1 0:2 0:: 0.4 0.5 0.5 027 0.9 0:9 1.0 111 {.2
Instantaneous fishing mortality (F)

Figure 8. Yield-per-recruit at various fishing mortalities(F).

35

1300 l
1200 .
1100 3
1000 . Instantaneous fishing mortality (F) 0.80
9°01
”0‘
70° .
500 .

sma

Yield per recruit (Y/R) 9

ago .

Md

 

 

3 4 5 5 7 8 9 10 II 12
Age at first catch (xc)

Figure 9. Yield-per-recruit for various ages at first catch.

36

100 g
9.
8'4
200 g
7..
‘5
'3 300 g
u .
‘5
E: 6 ' 400 g
.3 500 g
8% .
.g 5 j 600 g
700 g
800 g
44 9009
. 1000 g
34

 

 

I ‘T 1 ‘ V V

0.1 0.2 0.3 0.4> 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Instantaneous fishing mortality (F)

J

Figure 10. Yield contour diagram.

37
Ancillagy Observations

Numerous fish were afflicted with parasites between the rays
in the paired fins. No attempt was made to identify the type
of worm between the fin rays. Kononen (1981) made a similar

observation for suckers in Saginaw Bay.

Lamprey parasitism was not apparent in the fish handled.

The electric weir was located approximately 1/2 kilometer
upstream from the mouth of the stream. The stream bottom in
this section of the stream is comprised of cobble, gravel and
sand. From the mid 19505 to 1979, the white suckers have
been limited to this section for spawning (weir to mouth).
Despite the confinement, this papulation has not had a
noticeable decline in numbers during this period. Apparently

the white sucker is a very adaptable species.

Nhen examining the tagging data it became apparent that these
white suckers have quite an extended spawning period.
Numerous fish that were first captured in late April were

recaptured throughout the spawning season even into July.

Because of the distance to the river, daily tagging and
releasing was not possible. Therefore, a population estimate
could not be made using any of the commonly used methods.

However, as I examined the recapture of tagged fish for the

38
various periods of study it became apparent that the time
within the spawning season that a fish was first captured and
tagged strongly influenced the number of times an individual
was captured. A plot of the average recapture rate as a
function of the date of first capture within the spawning
season should indicate how large the spawning population is
relative to the total weir capture. Examination of Figure 11
shows that the average recapture rate over the season is 1.4
recaptures per individual. Therefore, if the total number of
fish captured in the 1979 field season is divided by 1.4 a
rough estimate of the spawning population can be had. The
index number at the weir was 2,384 so the probable adult

population is approximately 1,600.

SUMMARY AND CONCLUSIONS

Summary

The objective of this investigation was to determine the
approximate size of the white sucker population and to
estimate the potential level of exploitation in this river.
The population dynamics (e.g., age and growth information)
are only considered representative of the stock spawning in
the Big Two-Hearted River. There is evidence, however, from
tag returns that some of the adult suckers caught in the Big
Two-Hearted River will ascend other nearby rivers, presumably

to spawn.

39

1.5‘

 

0.5.

 

#

Periodj Periodj Period Period Period Period Period Period Period
1 2 3 h 5 6 7 8 9

 

Figure 11. Average recaptures over the spawning period.

40
The method of capture used in this study (electric weir) is
assumed to capture all the white suckers attempting to pass
the point of the weir in the stream. It is further assumed
that those fish captured represent the true spawning
population of the river. The first assumption is subject to
equivocation as it is the opinion of some workers operating
these electric weirs that the suckers 'stack-up' downstream
of the barrier. This investigator observed that some of the
fish entering the stream and first captured in April were
recaptured numerous times spanning the duration of the
spawning season indicating a strong urge by these fish to
ascend the stream to spawn, thus supporting the assumption
that all the fish would attempt to pass the point of the weir
and be captured. The fact that immature white suckers (less
than 225 mm in length) as well as large numbers of other
small fish (i.e., smelt) were captured tends to support the
assumption of total susceptability to the gear, thus a

representative catch.

The length-weight relationship developed for the males and
females show that the females grow faster than the males
after they reach maturity. No data were available prior to
maturity for these fish. The growth constant (b) within the
function describing the relationship of length to weight for
the whole population is very close to 3 indicating that the

assumption of isometric growth is justified.

41
These white suckers appear to have a mortality rate similar
to populations studied elsewhere. Operating under the
assumption of an equilibrium population and constant
survival, the annual survival rate is 0.60. The survival
rate reported by Kononen (1981) for Saginaw Bay white suckers
ranged from 0.59 to 0.72 and that reported by Coble (1967)
for South Bay, Lake Huron, ranged from 0.70 to 0.75.

The age at which all fish are mature and recruited to the
spawning population appears to be age 6. Males start
maturing at age 3 and females at age 4. Use of a catch curve
(natural log of catch vs. natural log of age) demonstrated
that the maximum height of this parabola, representing the
point at which all succeeding ages are fully represented in

the catch, is age 5.5.

Conclusions

Calculation of yield per recruit as a function of fishing
mortality showed that there is no optimum rate of
exploitation (e.g., the higher the fishing mortality the
greater the yield). In an effort to visually display the
result of various ages at first capture and fishing
mortalities, a yield contour diagram was prepared (Figure
10). According to the model, the greatest yield is 800 grams
per recruit while fishing four-year old fish with an
instantaneous fishing mortality of 1.1. This information

42
combined with the estimate of the adult population ascending
the Big Two-Hearted River indicates the yield from this
stream would be approximately 2,800 pounds per year. This

estimate is for whole fish, in-the-round.

If the exploitation of this stock is undertaken, it is
recommended that similar calculations be completed as part of
an ongoing monitoring program because of probable changes in
age at maturity and rate of growth adjustments induced by

exploitation.

Future studies should focus on obtaining an adequate
population estimate for the spawning run and investigating

the life history of the immature fish.

APPENDIX

General References

APPENDIX

General References

Borgeson, D.P. (ed.) 1972. Status of Michigan's fisheries
management, 1971. Mich. Dept. Mat. Res. Fish. Div.
Fish. Manage. Rep. No. 4: 31 p.

Derisco, R.B. 1980. Harvesting strategies and parameter
estimation for an age-structured model. Can. J. Fish.
Aquat. Sci. 37: 268-282. '

Eddy, S. and J.C. Underhill. 1974. Northern fishes.
University of Minnesota Press, Minneapolis: 414 p.

Fox, N.R., Jr. 1971. Random variability of parameter
estimation for the generalized production model. Fish.
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Fox H.H., Jr. 1975. Fitting the generalized stock
production model by least squares and equilibrium
approximation. Fish. Bull. 73(1): 23-27.

Galloway, J.E. and N.R. Kevern. 1976. Michigan suckers,
their life histories, abundance and potential for
harvest. Michigan Sea Grant Program Tech. Rep. No. 53:
46 p.

Gatto, M. and S. Rinaldi. 1980. On the determination of a
commercial fishery production model. Ecol. Modelling.
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Great Lakes Environmental Contaminant Survey. 1974.
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Hall, A.E.. Jr., and O.R. Elliott. 1954. Relationship of
length of fish to incidence of sea lamprey scars on
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Hilborn, R. 1979. Comparison of fisheries control systems
that utilize catch and effort data. J. Fish. Res. Board
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Nile, R. 1962. Collection and analysis of commercial

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43

44

Jensen, A.L. 1974. Leslie Matrix models for fisheries
studies. Biometrics. 30(3): 547-551.

Jensen, A.L. 1976. Assessment of the United States lake
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Kevern, N.R. 1975. Increasing the economic use of Upper
Michigan's commercial fishery. First Year Report to the
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Kevern, N.R. 1978. Increasing the economic value of Upper
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Latta, H.C. 1959. Significance of trap-net selectivity in
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McGaw, R.L. 1980. Confidence invervals for optimal effort
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Ricker, U.E. 1975. Computation and interpretation of
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Rybicki, R.U. 1979. Assessment of underutilized anadromous
fishes in the Great Lakes. MDNR - Proj. - AFC - 12.
Compl. Rep. Mich. Dept. Mat. Res. Fish. Div.: 82 p.

Schaefer, M.B. 1968. Methods of estimating effects of
fishing on fish populations. Trans. Am. Fish. Soc. 97:
231-241.

Seber, G.A.F. 1973. The estimation of anim. abundance and
related parameters. Charles Griffen and Co.. Ltd..
London. 506 p.

Smith, S.H., et. al. 1961. Fishery statistical districts of
the Great Lakes. Great Lakes Fish. Comm. Tech. Rep. No.
2: 24 p.

Snedecor, G.U. and N.G. Cochran. 1967. Statistical methods.
The Iowa State University Press, Ames. 593 p.

Uhler, R.S. 1980. Least squares regression estimates of the
Schaefer production model: Some Monte Carlo simulation
results. Can. J. Fish. Aquat. Sci. 37: 1284-1294.

45

Vaughan, 0.5. and 5.8. Saila. 1976. A method for
determining mortality rates using the Leslie Matrix.
Trans. Am. Fish. Soc. 105(3): 380-383.

LIST OF REFERENCES

LIST OF REFERENCES

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Beamish, R.J. and H.H. Harvey. 1969. Age determination in
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Beamish, R.J. 1973. Determination of age and growth of
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Beverton, R.J.H. and 5.0. Holt. 1957. On the dynamics of
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Chapman, 0.6. and 0.5. Robson. 1960. The analysis of a
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Christie, H.J. 1974. Changes in the fish species
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Coble, D.H. 1967. The white sucker population of South Bay,
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Eschmeyer, P.H. 1955. The near extinction of lake trout in
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Hile, R. 1946. Trends in the lake trout fishery of Lake
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"mmmmES