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DYNAMICS OF LIGHTLY EXPLOITED POPULATIONS OF THE
LAKE WHITEFISH, ISLE ROYALE VICINITY,
LAKE SUPERIOR
by
Ann M. Koziol
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science
in Fisheries
School of Natural Resources
The University of Michigan
1982
Committee members:
Dr. Karl F. Lagler Chairman
Dr. W. Carl Latta
ACKNOWLEDGMENTS
This research was supported by the Institute for Fisheries
Research of the Michigan Department of Natural Resources. All data
were graciously procured from the Michigan Department of Natural
Resources by Gerald P. Rakoczy and Richard R. Schorfhaar who
also provided useful information of Lake Superior whitefish.
I am indebted to Richard D. Clark, Jr., who gave invaluable
advice and assistance during this endeavor. I would like to thank
Drs. Karl F. Lagler and W. Carl Latta for their advice throughout
the project and review of the manuscript. My appreciation is extended
to Grace M. Zurek for typing the final draft and Alan D. Sutton for
drafting the figures.
Special thanks go to my family, especially Dorothy and
Walter Koziol, whose encouragement and support helped me through
this study.
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iV
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
LIST OF APPENDIX TABLES ....................................... Vi
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vii.
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
MATERIALS AND METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
GROWTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Age-Length Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Length-Weight Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
MORTALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
YIELD PER RECRUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
iii
LIST OF TABLES
Table
1. Estimated mean lengths (mm) at age (years) for
the whitefish stock in northern area . . . . . . . . . . . . . . . . . . . .
2. Estimated mean lengths (mm) at age (years) for
the whitefish stock in Southern area . . . . . . . . . . . . . . . . . . . .
3. Mean ages in years of the annual whitefish catches
of the northern and southern Isle Royale, Keweenaw,
and Whitefish Point stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Mean weights (kg) at age (years) for the north and
South areas calculated with the length-weight
regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tº
5. Number of fish remaining at age (years), potential
egg number (millions) and yield per 1,000 age- 4.42
recruits (Y /R) with varying instantaneous fishing
mortality (F) and size limit (x,) in millimeters for
whitefish of northern Isle Royāle © tº º e º 'º e º 'º e o 'º e º e o e º e º e º &
6. Number of fish remaining at age (years), potential
egg number (millions) and yield per 1,000 age- 3.88
recruits (Y/R) with varying instantaneous fishing
mortality (F) and size limit (xe) in millimeters for
Whitefish of Southern Isle Royāle . . . . . . . . . . . . . . . . . . . . . . .
iV
Figure
LIST OF FIGURES
Isle Royale, Lake Superior, showing the north
and South study regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fitted von Bertalanffy curve and empirical mean
length-age relationship with 95% confidence limits
for northern and southern Isle Royale whitefish
from 1978 through 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Catch curve for northern Isle Royale whitefish
collected With gill nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Catch curve for southern Isle Royale whitefish
Collected with gill nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Yield in grams per 1,000 age-4.42 recruits as a
function of age at entry (xc) and instantaneous
fishing mortality (F) for whitefish of the northern
area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Yield in grams per 1,000 age- 3.88 recruits as a
function of age at entry (Xe) and instantaneous
fishing mortality (F) for whitefish of the southern
area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page
15
16
19
20
Appendix
A.
LIST OF APPENDIX TABLES
Back calculated lengths (mm) at age (years)
for lake whitefish of southern Isle Royale
for the Spring of 1978 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of southern Isle Royale
for the Spring of 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of southern Isle Royale
for the Spring of 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of southern Isle Royale
for the Spring of 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of northern Isle Royale
for the Spring of 1978 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of northern Isle Royale
for the Spring of 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of northern Isle Royale
for the Spring of 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Back calculated lengths (mm) at age (years)
for lake whitefish of northern Isle Royale
for the Spring of 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page
27
28
29
30
31
32
33
34
ABSTRACT
Two lightly exploited Stocks of lake whitefish (Coregonus
clupeaformis) near Isle Royale, Lake Superior, were compared in terms
of growth, mortality rates, and yield per recruit. The stocks are
Separated geographically to the north and south of the island.
The ages of 501 lake whitefish from both stocks were deter-
mined. Length at age was estimated by conventional back calculation
methods. The whitefish from the northern and southern areas were
judged to be of different stocks. The southern stock averaged 50 mm
longer at a given age than the northern stock. Total mortality rates
were calculated for both stocks but they appeared to be high due to
gear selectivity.
The Beverton and Holt dynamic pool model was applied to the
stocks. Maximum yield per recruit for both stocks was attained at a
fishing rate of 2.0 and a size limit of 482 mm (19 inches). The impli-
cations of this increase in fishing pressure were viewed in terms of
remaining reproductive potential. Potential egg numbers were compared
for the stocks at the fishing rate of 2.0 and a fishing rate of 0.7,
which approximates that found in northern Lake Michigan. At the
0.7 fishing rate, there were 108% more potential eggs for the southern
stock and 46% more for the northern stock than at the higher fishing
rate of 2.0. The increase in yield per recruit at the 2.0 fishing rate,
however, was only 9% and 7% for the northern and southern stocks,
respectively.
The present size limit (432 mm or 17 inches) of the Isle Royale
whitefish was hypothetically increased to 482 mm (19 inches) along with
the instantaneous fishing mortality to 0.7. With a raised size limit of
482 mm, the decrease in yield per recruit was only 0.001% for the
southern stock and 0.04% for the northern stock. The increase in
residual egg potential was substantial, however, with 58% more potential
eggs for the northern region and 59% for the southern region.
viii
INTRODUCTION
Lake whitefish (Coregonus clupeaformis), a schooling fish of
the subfamily Coregoninae are classified with salmon and trout, in the
family Salmonidae. According to the Michigan Department of Natural
Resources, lake whitefish are the most sought after of all Lake Superior
commercial species, and their production in recent years has increased
(Rakoczy 1982). Their growth is rapid in all of the Great Lakes except
Lake Superior (Carlander 1950). However, the largest individual of
record was caught in Lake Superior off Isle Royale (Van Oosten 1946).
- The purpose of this study was to assess two lightly exploited stocks of
lake whitefish in the vicinity of Isle Royale, Lake Superior, in terms of
growth, mortality, and potential yield per recruit. Growth and mortality
data for these stocks were used to predict yields. Hopefully with these
figures in hand, a fishery biologist can regulate the exploitation of a
fishery to achieve the goal of sustaining the population while maximizing
the yield.
Isle Royale parallels the northwestern shores of Lake Superior
(Fig. 1) in the MS-1 statistical district of the State of Michigan waters
of the upper Great Lakes (Hile 1962). Approximately 45 miles long and
9 miles wide at maximum, the island is a National Park and provides
various fish habitats such as open and sheltered shores with variously
steep or gently sloping bottoms (Lagler 1982). The commercial fishery
of the surrounding waters depends primarily on several members of
the whitefish subfamily and on the lake trout (Salvelinus namaycush).
ONTARIO
Fort
William
___NORTH AREA
f-
|
|
|
|
|
.
LAKE
| SUPERIOR
|
"south AREA
N
Copper YHarbor
Keweenqv
Penninsula
Ontonagon
0 10 20 'L'Anse
|-H
STATUTE MILES M|CHIGAN
Figure 1. -- Isle Royale, Lake Superior, showing the north and
South study areas.


The populations of these fishes are monitored by the Michigan Department
of Natural Resources to record the natural dynamics of fish stocks. This
is accomplished through the issuing of research fishing permits only to
the three remaining traditional commercial fishermen. Each permit assigns
the areas to be fished, and limits of the catch, and requires the taking
of annual assessment data on various species of fishes. In this study,
two areas were considered. A northern area with many small islands
and protected irregular shoreline but, primarily, neighboring Lake
Superior; and a Southern area with mainly the large Siskiwit Bay and
adjacent waters.
Both stocks are considered very lightly exploited, yielding on
the average 2,067 kilograms per year from the northern area and 1,159
kilograms from the southern area (Andrew Nuhfer, Michigan Department
of Natural Resources, personal communication). These yields are ex-
tremely small compared to other Lake Superior stocks such as Keweenaw
with 6,925 kilograms per year and Whitefish Point with 65,176 kilograms
per year averaged Over the same years and approximately the same size
area. The Keweenaw Stock is regarded as lightly exploited and Whitefish
Point stock as heavily exploited (Rakoczy 1982).
MATERIALS AND METHODS
All data reviewed were collected for the Michigan Department
of Natural Resources by commercial fishermen as a requirement of the
research fishing permit. For the two sample regions, gill nets with
mesh sizes ranging from 114 mm to 140 mm (stretched) were used to
catch fish. The biological data and scale samples were taken from
100 whitefish from each fisherman's total catch each spring from 1978
through 1981. Data included catch per effort, total length, and
occasionally, the weights of the fish. A total of 205 scales (about 52
per year) were aged from the northern site and a total of 284 scales
(about 71 per year) were aged from the southern site. Of each avail-
able inch group (fish 15.0-15.9 inches, 16. 0-16.9 inches, etc.), 10 scale
samples were subsampled for age assessment. Scales were mounted in
water between two microscope slides and examined on a microprojector
with 48 mm magnification. Growth fields were measured to the nearest
millimeter from the focus through the anterior portion of the scale.
Aging was often difficult due to the condition of the scales, the
closeness of circuli of the older fish caused by slow growth, small
number of scales taken from each fish, and the possibility of the fisher-
men not taking the scales from the correct anatomical place on the side
of the fish.
- The criteria for annulus dermination, as set by Van Oosten (1923)
and ranked by Bell et al. (1977) were rigorously applied as follows:
(1) cutting over of circuli into the lateral fields; (2) a break in the
pattern of circuli indicated by discontinuity; and (3) spacing of the annuli.
Because the samples were taken in the Spring, the margin of the
scale was taken to represent the most recently laid down annulus.
GROWTH
Age-Length Relationship
Average length at age and annual growth increments were
calculated with a FORTRAN program which follows the standard back
calculation formula (Lagler 1956).
L_ = S_ (L_- a) + a
Il Il C
S
C
Where : Pn = length of fish when annulus n was formed
Po = length of fish at capture
Sn = radius of annulus n
a = intercept from regression of body length on radius
So = total scale radius
It was decided not to use the calculated intercept of the body:
scale regression (2.0 mm for both the north and south sampling regions).
As stressed by Carlander (1981), a calculated intercept can be a misrepre-
sentation due to the gear selectivity of gill nets and subsequent insufficient
sample size of the smaller and larger fish. Although the difference from
the calculated value was small and probably insignificant a recorded Lake
Superior intercept value of 1.0 mm (Carlander 1950) was used.
The lengths at age were estimated for each year (Appendix A-H)
and the mean lengths at age for the four years were used in further
calculations (Tables 1 and 2). Scale samples from both study sites came
from fish ranging from 5 to 14 years of age. The lengths of the southern
fish averaged 50 mm longer than the northern fish in the same age class.
Taking into account the 95% confidence limits, the mean lengths overlapped
through age 3 but proved to be significantly different for fish older than
age 3 (Fig. 2).
Table 1. --Estimated mean lengths (mm) at age (years) for the whitefish
stock in northern area.
The 95% confidence limits are in parenthesis.
Year Age in years
1 2 3 4 5 6 7 8 9 10 11 12 13
1978 104 198 279 351 421 478 525 563 594 613 621 644 668
(4) (8) (10) (11) (11) (11) (10) (11) (16) (32) (54) (84) (74)
1979 102 198 278 354 420 473 520 555 584 614 608 623 635
(6) (11) (14) (19) (19) (20) (21) (23) (35) (56) (24) (23) (38)
1980 103 189 270 345 416 470 512 541 573 597 627 649 695
(6) (8) (10) (10) (12) (11) (11) (11) (13) (16) (21) (25) (12)
1981 111 190 263 332 397 457 507 543 564 602 252
(9) (10) (12) (13) (14) (14) (15) (16) (16) (17) (26)
Mean 105 194 272 345 413 471 516 550 579 607 627 638 666
(6) (9) (12) (13) (12) (12) (13) (15) (21) (31) (31) (44) (38)
Table 2. --Estimated mean lengths (mm) at age (years) for the whitefish
stock in Southern area.
The 95% confidence limits are in parenthesis.
Year Age in years
1 2 3 4 5 6. 7 8 9 10 11 12 13
1978 100 198 2.91 381 467 530 577 616 645 666 691 718
(3) (7) (11) (13) (13) (12) (11) (12) (12) (12) (18) (27)
1979 96 202 298 388 469 537 586 622 647 671 704 727 756
(4) (7) (11) (13) (13) (12) (11) (13) (13) (14) (16) (19) (24)
1980 97 192 2.76 352 4.24 492 549 590 621 642 664 690 706
(5) (8) (13) (13) (14) (12) (12) (11) (11) (14) (17) (22) (27)
1981 102 214 312 404 483 549 593 628 651 679 696 717
(5) (8) (12) (14) (14) (13) (14) (15) (18) (33) (9) (34)
Mean 99 201 294 381 460 527 576 614 641 664 689 713 731
(5) (8) (12) (13) (14) (12) (12) (13) (14) (18) (22) (26) (26)

7OOr
6OOH
500-
4OOH o = North Area
/ L=8061-EXPſ-O15(x-OO6)]
3OOH
- / • = SOUth Area
200H / L=820ſ-EXPſ-O17(x-O3O]]
I | | | | 1 1 |
| |
1 2 3 4 5 6 7 8 9 10 11 12 13
Age in Years (x)
Figure 2. --Fitted von Bertalanffy curve and empirical mean length-age
relationship with 95% confidence limits for northern and southern Isle Royale
whitefish from 1978 through 1981.
Different size gill nets were used when collecting data, possibly
causing the difference in the northern and southern whitefish mean
lengths. The southern whitefish were obtained with 114-mm mesh gill
nets in 1978 and 140-mm mesh from 1979 through 1981, while gill nets
of 133-mm mesh size were used all 4 years in the northern area.
Although the greatest dissimilarity in mesh size occurred between the
1978 and remaining southern whitefish data, no difference in their
mean lengths was observed (Table 2). Therefore, it was assumed
the variation in the mean lengths of the north and South study areas
was not due to mesh size difference.
In the back calculated lengths for both the north and South
areas, positive Lee's phenomenon was present. The younger the age
group of fish used for the back calculations, the greater the mean
length for the earlier years of life. Lee's phenomenon is often caused
by the size selective mortality of the faster-growing fish which become
vulnerable to the fishing gear first and are removed from the year
class. In these lightly exploited stocks, however, this selective
mortality should not be a major problem. Bias in the sampling of gill
nets, which resulted in little representation of the smaller individuals
of the younger age groups and the larger individuals of the older age
groups, is more likely the major basis for the Lee's phenomenon in this
case. The catch curve considered in the mortality estimates below re-
flected the same selectivity. Using mean lengths at age undoubtedly
offsets any effects of Lee's phenomenon on growth.
Rakoczy (1982) suggested that for satisfactory population
maintenance, the mean age of a Lake Superior Whitefish catch should
be at least 6.5 years. This allows the fish to spawn 1.5 times before
10
death, which has been reported to be necessary for a stable whitefish
population (Christie and Regier 1973). Both the north and south stocks
had mean ages of catch over 8 years as might be expected from very
lightly exploited stocks. The mean ages were slightly higher than the
lightly exploited Keweenaw stock but almost double the heavily exploited
Whitefish Point stock (Table 3).
The mean back calculated lengths were utilized in a FORTRAN
program of the following von Bertalanffy growth equation (Rafail 1973) :
1, = L. (1 - exp [-k (x - xo)] }
where: *x length at age
L. = theoretical asymtotic length in millimeters
k = growth coefficient
xo = theoretical time when length is zero
The result for the two stocks of whitefish were as follows, with
the 95% confidence limits in parenthesis:
L k X
OO sº O
North 806 0.15 0.06
(0.63) - (0.07) (0.05)
South 820 0.17 0.30
(0.10) (0.01) (0.30)
The 95% confidence limits of k and *o overlapped, while those for
L. did not. The difference in the L. parameters means the von Bertalanffy
growth curves are statistically different. This provides further support
that the northern and southern whitefish are indeed separate stocks.
The predicted growth curves and the observed mean lengths are
very close with the northern fish showing more variation in the higher
ages (Fig. 2).
11
Table 3. --Mean ages in years of the annual whitefish catches for the
northern and southern Isle Royale, Keweenaw, and Whitefish Point
Stocks.
Area Years
1978 1979 1980 1981
North 8. 6 9. 0 8.2 8.8
South 8.4 8. 3 9.4 8. 8
Keweenaw 8.4 6.2 7. 3 not
(Rakoczy 1982) available
Whitefish Point 4.5 5.2 5. 1 not
(Rakoczy 1982) available
12
Length-Weight Relationship
Individual weights were only available for the southern
whitefish population. Least squares regression was used to describe
the length-weight relationship as expressed in the conventional
equation:
W = al.”
where: W = weight
L = length
a and b = constants
For the southern Isle Royale whitefish, this relationship was :
1n W = -18. 7020 + 3.0497 1n D. The southern Whitefish were heavier at
a given length than the northern whitefish (Table 4. ).
13
Table 4. --Mean weights at age for the north and south areas calculated
with the length-weight regression.
South - NOrth
Mean . Mean
Age length Weight length Weight
(mm) (kg) (mm) (kg)
1 99 0.01 105 0.01
2 201 0.08 192 0. 07
3 2.94 0.30 272 0.20
4 381 0. 60 345 0.40
5 460 0.99 413 0. 70
6 527 1.50 471 1. 10
7 576 2. 00 - 516 1. 40
8 614 2. 40 550 1. 70
9 641 2. 71 579 2.00
10 664 3.05 607 2. 32
11 689 3.41 627 2. 60
12 713 *3. 79. 638 2. 70
13 731 4. 19 666 3. 10
MORTALITY
Total mortality rate (Z) is the sum of the instantaneous natural
(M) and fishing (F) mortality rates. The total mortality rate of a very
lightly exploited stock should approximate the natural rate. Relatively
high mortalities Were calculated, however, in both the northern (Z = 0.81)
and the Southern (Z = 0.71) stocks. These estimates were derived through
the regression of the natural logarithm of the catch per effort (catch per
1,000 feet of gill net per day) on age (Figs. 3 and 4). Total mortality
(Z) is depicted by the slope of this regression line, but the line can be
misleading if the young and old fish are not represented in the catch
according to their abundance.
It seems probable that my estimates for total mortality are high
due to selectivity of gill nets (Healey 1975). Gill nets of a constant mesh
size catch the larger fish in the younger age groups and the smaller fish
in the older age groups. The former problem was eliminated by considering
in the regression only fish over age 7 for the southern area and age 8 for
the northern area; but the latter problem probably exaggerated the steep-
ness of the slope and, thus, overestimated total mortality (Z). Using trap
nets to catch whitefish gives a more realistic view of age classes. The
more exploited stocks of Keweenaw and Whitefish Point were found to have
total mortality rates of 0.43 and 0.59, respectively (Rakoczy 1982). Therefore,
an instantaneous natural mortality (M = 0.3) recorded for an unexploited
whitefish stock of Grand Traverse Bay (Patriarche 1977) was used in the
yield calculations.
A covariance test was conducted for the north and south regressions.
No significant difference was found between the regression lines at the 95%
level suggesting mortality is probably the same in both areas.
14
6T-
3S
5 5H.
I
§ 4H O
-C
S
§ 3F O
Ln(y) = a-0.8x
O 2
R* = O.97
e 2h
O
—l
E 1H
Inj
º
2 1 | | | -l
6 7 8 9 1O 11
Age in Years (x)
Figure 3.--Catch curve for northern Isle Royale whitefish collected
with gill nets.


Ln(y) = a-O.7x
2H- R* = O.94
3
f
|- 1. | | | - | | 1
5 6 7 8 9 1O 11 12
Age in Years (x)
Figure 4.--Catch curve for southern Isle Royale whitefish collected
with gill nets.

YIELD PER RECRUIT
The Model
The dynamic pool model weighs the parameters of growth against
the instantaneous natural and fishing mortality rates for the purpose of
predicting the best level of exploitation for fish stocks. Although there
is often difficulty in estimating these parameters confidently with avail-
able data, this management model is intuitively more appealing to biologists
than others such as the surplus production model. The parameters and
structure of the dynamic pool model can also be more meaningful in a
biological sense.
A FORTRAN program of the Beverton and Holt (1957) model
available at the Institute for Fisheries Research, Michigan Department
Of Natural Resources, was used to make yield computations. This
program is slightly changed from the standard Beverton and Holt model
in at least three ways. First, it uses the von Bertalanffy parameters
of growth in length rather than growth in weight, and it converts
length to weight for yield computations by using the length-weight
regression coefficients. Second, it uses the Baranov catch function
to compute catch in numbers by age. And third, it calculates the
number of fish by age remaining in the population. All these changes
were suggested by Tyler and Gallucci (1980) and are described in more
detail in their paper.
The standard procedure of computing the isopleths of yield, as
they vary with age of entry (size limit) and fishing mortality rate, was
followed. The additional information provided by the program on number
of fish at age in the population was used to compare relative egg pro-
duction potential for selected size limits and fishing rates.
17
18
The smallest fish vulnerable to the gill nets of both sample areas was
381 mm (15 inches). Therefore, computations were based on 1,000
recruits of age 3.88 years (381 mm) for the southern stock and age
4.42 years (381 mm) for the northern stock.
Results and Discussion
The results of repetitive model applications with varying
instantaneous fishing mortality (F) and age at entry (size limit) are
presented in isopleth diagrams (Figs. 5 and 6). The isopleths show
yield increasing assymptotically with fishing mortality rate (F) and a
maximum yield per recruit is attained at the fishing rate of 2.0 and a
size limit of about 482 mm (19 inches) for both stocks. The natural
mortality rate used was 0.3. The actual fishing pressure of the Isle
Royale populations is unknown, but if similar to the rates recorded for
the lightly exploited Keweenaw area (0.14) or even the heavily exploited
Whitefish Point (0. 30), a substantial increase in exploitation could be
sustained by these populations. It seems unlikely, however, that they
could sustain a fishing rate of 2.0 with no ill effects on recruitment.
The isopleth diagrams were useful in establishing the maximum
yield per recruit and the variations caused by changing size limit or
fishing pressure. More information is needed, however, for proper
yield predictions as the isopleths ignore the possible impact of fishing
on recruitment. Constant recruitment was assumed by the model.
Using for comparison a fishing rate of 0.7, which approximates that
reported for northern Lake Michigan whitefish (Patriarche 1977), the
effects of raising the fishing rate to 2.0 were viewed in terms of
residual reproductive potential. Assuming a 1:1 sex ratio, that 56%
of Lake Superior whitefish females are mature by age 5 (Rakoczy 1982),
19
14 r.
– 200 –686
Tº 12H
><
92 H 309
E – 635
§ 10|-
O
º pme +584
LL
8}-
ºf -1533
g, ſ --|482
<ſ 6H-
Wºme –432
|
4. | | l ! | ! | | |
OOO O4O O.80 1.2O 1.60 2.00
Instantaneous Fishing Mortality (F)
Figure 5. --Yield in kilograms per 1,000 age-4.42 recruits as function
of age at entry (xe) and instantaneous fishing mortality (F) for whitefish
of northern area.

ZU
15 T-
H.
OO
13H 2
3 F 309
# 11 H. 686
G. L AOQ -168
CU
O
º, 9 H. 635
iT L
& 584
g’ſ
<C L 533
482
5 H- -
4.32
-]] 381
3 l | l l l | | | |
O.OO O4O O.80 1.2O 1.6O 2.OO
Instantaneous Fishing Mortality (F)
Figure 6. --Yield in kilograms per 1,000 age- 3.88 recruits as a function
of age at entry Gºe) and instantaneous fishing mortality (F) for whitefish of
the southern area.

21
and an average whitefish fecundity of 18, 200 eggs per kilogram per
female (Cucin and Regier 1966), potential egg productions Of the re-
maining females were calculated at various size limits and fishing rates
(Tables 5 and 6). At the 0.7 fishing rate, there are 108% more
potential eggs for the southern stock and 46% more for the northern
stock than at the higher fishing rate of 2.0. The increase in yield per
recruit at a 2.0 fishing rate is only 9% and 7% for the northern and
southern stocks, respectively. This suggests the small increase in
yield per recruit in going from 0.7 to 2.0 carries with it a substantial
risk in reducing overall recruitment and therefore overall yield.
Patriarche (1977) suggested an elevation of the minimum size
limit for the whitefish in northern Lake Michigan from 432 mm (17 inches)
to 482 mm (19 inches). He reasoned this would provide greater survival
of the spawning stock and, hence, more stable recruitment. My results
agree with his recommendation. For the Isle Royale fishery, I calculated
the age of a 432-mm southern whitefish to be 4.6 years and a northern
whitefish 5.3 years. If fishing pressure became high enough, many
immature fish would be harvested at a 432-mm size limit. This may
debilitate recruitment and not provide the necessary 1.5 spawnings for
stable whitefish population maintenance (Christie and Regier 1973).
Because the Isle Royale fishing pressure is so light, however, very few
fish under 6 years were noted in the catches and mean ages were over
8 years (Table 3).
Based on the mean fishing mortality rate for the whitefish of
northern Lake Michigan of 0.72 (Patriarche 1977), the hypothetical
fishing rate 0.70 was considered for the 432-mm and 482-mm size limits.
Table 5. --Number of fish remaining at age, potential egg number (millions),
and yield per 1,000 age- 4.42 recruits (Y/R) with varying instantaneous
fishing mortality (F) and size limit (xe) in millimeters for whitefish of
northern Isle Royale.
Size
Fishing limit
mortality Xc
Number of fish remaining at age
Yield
per
1,000 Potential
recruits number
Y/R of eggs
F (mm) 4. 42 5 6 7 8 9 10 11 12 13 (kg) (millions)
Unexploited 1,000 839 622 460 341 253 187 139 102 76 . . . 36. 8
0.7 432 1,000 839 377 139 51 19 7 2 0.9 0.3 637 9. 9
0.7 482 1,000 839 622 275 101 37 14 5 2 0. 7 613 15. 7
2.0 482 1,000 839 622 105 11 1. 1 0.1 670 10. 7
Table 6. --Number of fish remaining at age, potential egg number (millions), and
yield per 1,000 age- 3.88 recruits (Y/R) with varying instantaneous fishing
mortality (F) and size limits (xe) in millimeters for whitefish of southern
Isle Royale.
Size
Fishing limit
mortality Xc
Number of fish remaining at age
Yield
per
1,000 Potential
recruits number
Y/R of eggs
F (mm) 3. 88 4 5 6 7 8 9 10 11 12 13 (kg) (millions)
Unexploited 1,000 964 714 529 392 290 215 159 118 87 65 © & c 43. 1
0.7 432 1,000 964 535 197 72 26 10 4 1 0. 5 0.2 721 7. 9
0. 7 482 1,000 964 714 342 126 46 17 6 2 0.8 0.3 720 12. 3
2.0 482 1,000 964 714 151 15 1.5 0.2 . . . . . . . . . . . . 766 5. 9
24
For both stocks, the difference in size limit produced little change in
the yield per recruit (Tables 5 and 6). In fact, the raising of the size
limit from 432 mm to 482 mm resulted in only a 0.001% decrease in the yield
per recruit for the southern stock and 0.04% for the northern stock. The
major change was in the number of remaining fish available for spawning and
consequent egg production (Tables 5 and 6). With a higher size limit for
the southern fishery, the increase in reproducing females and potential egg
production was 59% from 7.9 to 12.3 million eggs. The increase for the
northern stock was 58% from 9.9 to 15.7 million eggs. This large residual
egg potential would probably lead to increased stability in year-class strength
while not affecting the yield of the fishermen.
The survival rate of the eggs is difficult to ascertain as density
dependent mortality must be considered. Heretofore, the spawner-recruit-
ment relationship of whitefish has not been adequately researched to be
able to predict the level of egg production needed for a sound recruitment.
I recommend such studies be conducted as an additional useful tool for the
setting of size limits and fishing pressures for maximum sustainable yield.
SUMMARY
Northern and southern populations of lightly exploited white-
fish of Isle Royale, Lake Superior, were assessed in terms of growth
and found to be different stocks. The difference in the mean lengths
at age of the stocks was obvious with the southern fish averaging 50 mm
longer at a given age than the northern whitefish. The difference in
the mean lengths was judged not to be caused by the sampling with
different sized gill nets by comparison of the mean lengths among the
southern stock which was fished with the most variable mesh sizes.
Lee's phenomenon was observed but it was not believed to bias the
calculations of average growth in length of the two stocks.
The von Bertalanffy growth coefficients (k) and theoretical
time of length zero Gºo) were found to be similar in the stocks but
the theoretical asymptotic lengths (L.) were statistically different,
supporting the assumption that northern and southern whitefish were
of different stocks. -
Evidence of stable population maintenance for both stocks was
found in the mean age of the catches. The recommended age of catch
for Lake Superior whitefish is 6.5 years Both stocks had mean ages
over 8 years.
The total mortality rates of 0.71 for the southern fish and 0.81
for the northern fish were determined to be overestimates. The lack
of representation of the larger, older and smaller younger fish of the
populations, due to the gear selectivity, was most likely the cause.
Yield per recruit from the application of the Beverton and Holt
dynamic pool model was depicted in isopleth diagrams for which a fishing
25
26
rate of 2.0 and size limit to 482 mm were demonstrated to produce
maximum yield per recruit for both stocks.
Number of fish remaining at various levels of fishing pressure
and different size limits was used to establish the potential increase or
decrease in egg number. For the northern stock it was found that if
the size limit was 482 mm and the instantaneous fishing mortality was
2.0, a decrease to the approximate mean fishing rate of the Lake Michigan
whitefish (0.7) would result in 108% more residual reproducing females
with only a 6% decrease in yield per recruit. Under identical conditions
the northern Stock had 48% remaining females and a 9% decrease in
yield. Although survival rate of the eggs is unknown, a conservative
fishing rate of 0.7 with little change in the fishermen's yield but a
probable increase in stability of year-class strength would be prudent
management.
The size limit at the fishing pressure of 0.7 was reviewed.
Presently the size limit for whitefish is 432 mm (17 inches). Again,
the change in yield per recruit with a raise in size limit to 482 mm
(19 inches) for both stocks was small and again there was • Sub-
stantial preservation of potential egg numbers implying a raise in
size limit would be beneficial for recruitment and overall yield.
27
Appendix A. --Back calculated lengths (mm) at age (years) for lake whitefish of
Southern Isle Royale for the spring of 1978. -
Mean
total Age in vears
Number length g y
Age of at
group fish capture 1. 2 3 4 5 6 7 8 9 10 11 12
V 3 563 107 243 365 467 563
VI 10 565 97 204 304 405 490 565
VII 20 581 96 202 297 382 466 529 581
VIII 11 624 106 200 289 379 461 537 585 624
IX 11 663 99 202 294 388 474 534 589 632 662
X 8 666 95 187 277 362 446 510 557 600 631 666
XI 10 688 107 183 266 354 440 509 564 602 635 662 688
XII 5 718 100 185 269 357 454 517 576 617 649 676 697 718
Weighted means 100 198 2.91 381 467 530 577 616 645 666 691 718
28
Appendix B. --Back calculated lengths (mm) at age (years) for lake whitefish of
Southern Isle Royale for the spring of 1979.
Mean
total A in I*S
Number length ge 1n yea
Age of at
group fish capture 1 2 3 4 5 6 7 8 9 10 11 12 13
V 1 521 73 2 16 342 431 521
VI 9 581 95 216 331 423 505 581
VII 22 598 92 203 300 395 479 545 598
VIII 6 635 96 205 307 394 461 524 589 635
IX 12 650 102 209 304 400 473 540 588 626 650
X 9 658 104 185 250 323 397 475 540 592 627 658
XI 2 686 109 197 286 357 480 527 586 626 645 669 686
XII 5 725 95 189 282 380 478 550 606 642 666 686 707 725
XIII 2 756 84 197 303 387 472 524 599 639 666 692 717 732 7.56
Weighted means 96 202 298 388 469 537 586 622 647 671 704 727 7.56
Appendix C. --Back calculated lengths (mm) at age (years) for lake whitefish of
southern Isle Royale for the spring of 1980.
Mean
total Age in Vears
Number length g y
Age Of at
group fish capture 1 2 3 4 5 6 7 8 9 10 11 12 13
V 1 582 180 313 433 519 582
VI 3 537 88 197 293 366 460 537
VII 9 582 92 203 308 389 459 526 582
VIII 16 601 96 187 264 341 424 497 556 601
IX 16 636 98 188 273 357 424 499 558 601 636
X 9 644 95 191 275 343 399 466 520 580 613 644
XI 11 662 98 194 274 340 408 472 538 580 613 637 662
XII 4 701 106 181 233 328 407 476 543 597 625 654 677 701
XIII 4 731 95 182 278 363 437 512 552 595 631 664 685 710 731
XIV 4 708 89 181 257 309 387 451 506 549 588 615 638 660 681
Weighted means 97 192 276 352 424 492 549 590 621 642 664 690 706
30
Appendix D. --Back calculated lengths (mm) at age (years) for lake whitefish Of
southern Isle Royale for the spring of 1981.
Mean
total Age in vears
Number length g y
Age Of at
group fish capture 1 2 3 4 5 6 7 8 9 10 11 12
VI 12 582 107 223 336 436 516 582
VII 13 619 104 220 315 413 492 563 620
VIII 16 648 103 216 322 411. 487 552 601 648
IX 11 671 96 202 284 376 465 530 578 618 659
X 3 686 109 219 319 415 480 542 586 619 646 686
XI 3 708 91 210 2.95 368 444 494 558 612 651 686 703
XII 3 717 94 189 261 337 401 473 532 582 627 664 689 717
Weighted means 102 214 312 404 483 549 593 628 651 679 696 717
Appendix E. --Back calculated lengths (mm) at age (years) for lake whitefish of
northern Isle Royale for the spring of 1978.
Mean
total Age in Vears
Number length g y
Age of at - -
group fish capture 1 2 3 4 5 6 7 8 9 10 11 12 13
VI 1 513 129 239 348 403 458 513
VII 14 529 103 194 279 352 426 481 529
VIII 20 567 107 203 280 353 420 470 522 567
IX 16 600 101 200 284 363 433 491 537 568 600
X 7 635 101 196 273 337 412 480 526 566 604 635
XI 2 633 118 191 261 344 409 472 518 555 587 609 633
XIII 2 617 87 173 225 259 311 362 414 466 490 517 558 586 617
XIV 2 739 98 194 283 354 429 515 558 593 619 640 671 702 718
Weighted means 104 198 279 351 421 478 525 563 594 613 621 644 668
32
Appendix F. --Back calculated lengths (mm) at age (years) for lake whitefish of
northern Isle Royale for the spring of 1979.
Mean
total Age in vears
Number length g y
Age Of at
group fish capture 1. 2 3 4 5 6 7 8 9 10 11 12
VI 1 531 132 238 325 491 511 531
VII 7 528 101. 205 290 378 440 489 528
VIII. 17 554 102 195 278 344 415 464 514 554
IX 8 57.1 109 208 283 361 420 468 513 546 575
X 9 594 107 205 280 353 430 496 555 593 617 643
XI 3 633 82 154 244 315 375 447 510 542 578 605 633 . . .
XII 3 641 94 181 253 326 402 456 492 531 557 583 610 641
XIII 3 635 91 188 269 329 393 439 474 505 535 555 580 604
Weighted means 102 198 278 352 419 472 519 555 583 612 608 623
33
Appendix G. --Back calculated lengths (mm) at age (years) for lake whitefish of
northern Isle Royale for the spring of 1980.
Mean
total A in alſº
Number length ge 1n years
Age Of at
group fish capture 1 2 3 4 5 6 7 8 9 10 11 12
V 2 498 75 170 257 344 480
VI 3 535 135 236 308 382 469 535
VII 11 549 113 207 301 375 452 501 549
VIII 12 560 97 187 268 344 410 471 514 556
IX 12 575 100 185 270 339 406 457 502 535 575
X 7 592 97 163 232 321 393 461 511 541 569 592
XI 4 638 105 193 264 339 401 446 487 533 577 604 638 . . .
XII 5 640 98 181 253 310 371 429 481 527 563 588 611 640
XIII 1 696 137 204 279 371 442 489 510 543 591 628 652 672
XIV 1 732 90 152 221 296 344 403 447 530 584 619 636 670
Weighted means 103 189 270 345 416 470 512 541 573 597 627 649
34
Appendix H. --Back calculated lengths (mm) at age (years) for lake whitefish of
northern Isle Royale for the spring of 1981.
Mean
total Age in years
Number length
Age Of at
group fish capture 1. 2 3 4 5 6 7–8 9 49–H–
VII 7 552 134 215 300 362 430 494 552
VIII 11 580 114 185 261 335 410 470 527 580
IX 12 560 102 183 250 322 380 437 483 525 560
X 11 601 102 186 259 325 386 446 492 530 567 601
XI 3 652 110 198 252 313 373 434 483 525 569 608 652
Weighted means 111 190 263 332 397 457 507 543 564 602 652
LITERATURE CITED
Bell, G., P. Hardford, and C. Dietz. 1977. Dynamics of an exploited
population of lake whitefish (Coregonus clupeaformis). Journal of
the Fisheries Research Board of Canada 34:942–953.
Beverton, R. J. H., and S. J. Holt. 1957. On the dynamics of ex-
ploited fish populations. United Kingdom Ministry Agriculture
Fisheries, Fisheries Investigations (ser. 2) 19:533 pp.
Carlander, K. D. 1950. Handbook of freshwater fishery biology.
Wm. C. Brown Company, Dubuque, Iowa. 281 pp.
Carlander, K. D. 1981. Caution on the use of the regression method
of back-calculating length from scale measurements. Fisheries
6:2-4.
Cristie, W. M., and H. A. Regier. 1973. Temperature as a major
factor influencing reproductive success of fish--two examples.
Rapports et Proces-Verbaux des Reunions, Conseil International
pour l'Exploration de la Mer 164:208–218.
Cucin, D., and H. A. Regier. 1965. Dynamics and exploitation of
lake whitefish in southern Georgian Bay. Journal of the Fisheries
Research Board of Canada 23(2): 221–274.
Healey, M. C. 1975. Dynamics of exploited whitefish population and
their management with special reference to the northwest territories.
Journal of the Fisheries Research Board of Canada 32:427–448.
Hile, R. 1962. Collection and analysis of commerical fishery statistics
in the Great Lakes. Great Lakes Fishery Commission Technical
Report 5. 31 pp.
Lagler, K. 1956. Freshwater Fishery Biology. Wm. C. Brown Company,
Dubuque, Iowa. 421 pp.
Lagler, K. F. 1982. Fishes of Isle Royale. Michigan Sea Grant.
Isle Royale National History Association. 58 pp.
Patriarche, M. H. 1977. Biological basis for management of lake white-
fish in the Michigan waters of northern Lake Michigan. Transactions
of the American Fisheries Society 106:295-308.
Rafail, S. Z. 1973. A simple and precise method for fitting a
von Bertalanffy growth curve. Marine Biology 19:354-358.
Rakoczy, G. P. 1982. Recommended harvest levels for commerically
exploited stocks of lake whitefish in Michigan waters of Lake
Superior. Michigan Department of Natural Resources, Fisheries
Research Report (In press).
36
Tyler, A. V., and V. F. Gallucci. 1980. Dynamics of fished stocks.
Pages 111-147 in R. T. Lackey and L. A. Neilsen, editors.
Fisheries Management. John Wiley and Sons, New York. 422 pp.
Van Oosten J. 1923. The whitefishes (Coregonus clupeaformis). A
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Fisherman, 14(8): 17-18.
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