Size Selectivity of Passive Fishing Gear (1)
ectivity of Passive Fishing Gear: A Correction for
Encounter Probabi
Lars G. ~udstarn,'John J. Magnuson, and William M. Tonn
Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/04/13
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Center for Limnology and Department of Zoology, University of Wisconsin- fadis is or?, Madison, kVl53706, USA
Rudstam, k. C., I. 8 . Magnuson! and W. M. Tsnn. 1984. Sine selectivity of passive fishing gear: a correction
for encounter probability applied to gill nets. Can. ). Fish. Aquat. Sci. 41: 1252-1255.
The probability s f catching a fish in a gilt net may be separated into two components: (1)the probability of
the fish encountering the net and (2)the probability of the fish being caught and retained in the net. W e
consider the probability of encounter to be directly proportional to the distance travelled by the fish during
the sampling period. This distance will increase with fish sine if different-sized fish swim for the same
amount of time because swimming speed increases with fish sine. Routine swimming speed measured in
the laboratory for three size-classes sf bloater (Coregonus hoyi) increased with length to the 0.8 power.
Corrections fsr encounter probability were incorporated i n gill net selectivity calculations for samples of
cisco (Coregonus artedii), a species closely related to bloater. These corrections can significantly increase
the proportional estimates of smaller relative to larger animals in the estimated population structure. The
approach should also be applicable t o other passive fishing gear, such as longlines and set nets.
La probabilitk de capture d'un poisson dans u n filet maillant peut &re divisee en deuw composantes, soit (1)
la probabilite que le poisson rencontre le filet et (2)la probabilit6 que le poisson soit capture et retenu dans
le Filet. Fes auteurs csnsidi?rent que la probabilite de rencontre est directement proportionnelle i la
distance parcourue par le poisson pendant la periode d'kchantillonnage. Cette distance s'accroit en
fonction de la taiile d u poisson si des individus de differentes longueurs nagent pendant la meme p6riode
car la vitesse de nage augmente par rapport it la taille. Les vitesses de nage mesurees systematiqrsernent en
labsratoire chez le cisco de fumage (Coregonus hoyi) appartenant
trois classes de longueur ont
augment6 en fonction de la longueur 2 la puissance 0,8. Des corrections pour la prsbabilit6 de rencontre
ont 4te incsrporees dans les calculs de la sklectivite des fiiets maillants pour les echantillons de cisco de lac
(Caregonus artedii), espece etroiternent apparerstee au cisco de fumage. Ces csrrections peuvent
nettement accrsitre les estimations proportionnelles des petits animaux par rapport auw gros dans la
structure estimee de la population. Cette approche devrait aussi &re applicable 5 d'autres engins de peche
cornme la palangre et Ie filet mouille.
Received September 7, 14983
Accepted April 25, 198%
ize selectivity of gill nets (the probability sf capturing a
certain size of Ash in one unit of operation sf the gear) is
best considered as a characteristic of the entire fishing
operation (Lagler 1968; Hamley 1 975). Therefore, gear
selectivity will depend both on the probability that a fish
encounters the net and on the probability that the fish is caught
and retained by the net (Regier 1975; Hamley 1975). Factors
that affect either s f these probabilities will affect net selectivity.
In a comprehensive review of gill net selectivity, Hamley
(1975) described methods used to date to construct selectivity
curves (plots of the selectivity of a net as a function of some
measure of fish size) from the size distribution of catches in
different mesh sizes, The shape of these curves, at least for
species that are caught primarily by wedging, e. g . coregonines,
is similar with different mesh sizes when selectivity is plotted
against the ratio of fish girth to mesh perimeter (McCornbie and
Fry 1968; McCombie and Berst 1969). A combined selectivity
curve for a set of nets differing in mesh size can be obtained by
sw resent address: Department of Zoology, University of Stockhulnn,
S-106 91, Stockholm, Sweden.
1252
R e p le 7 septembre 1983
Accept6 8e 25 avail 1984
summing the selectivity curves of each net. This requires that
the relationship between the efficiencies of different nets
towards the fish size that they catch the best is known. This
maximum efficiency is often assumed to be the same for all nets
used, an assumption that has been criticized (Bicker 1949;
Regier and Bobson 1966; Hamley 1975). With walleyes
(Stizostedksn e~kaeum vktreum) , Hamley and Wegier ( 1973)
found that nets with larger mesh were more efficient than those
with smaller mesh.
At least part of this greater efficiency of larger mesh
nets results because larger fish have a higher probability of
encountering a net than do smaller fish (Lagler 1968). In this
paper we describe how an expression for length-dependent
encounter probability can be incorporated into selectivity
calculations, and we illustrate the potential magnitude of bias
our method can correct for, using gill net catch data on cisco
(Coregsnm4s artedii). Encounter probability is considered to be
directly proportional to distance travelled by a fish during the
sampling period. We posit that distance travelled is proportional
to speed s f spontaneous swimming activity (routine speed) (see
hfagnuson 1978).
Can. /. Fish. Aqua?. Sci., Vol. 41, 1984
Selectivity C~erlculatic~ns
The probability of catching an individual of size 1 by a net
of mesh size m may be separated into two independent
probabilities: (1) the probability that the fish will encounter the
net during a sampling period, B(El), and (2) the probability that
the fish will be caught and retained by the net of mesh size nz
after encounter, P(RIm).Therefore:
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where Cl, = the number of fish s f size H caught and retained per
sampling period in a net of mesh size m and Nl = the number of
fish of size k occurring in the lake.
The expression for B(Rl,) was obtained by fitting a function
to Berst's (1961) selectivity curve for cisco from Lake Huron
(Table 1). This curve was derived using the method of
McCsmbie and Fry (1960). In the terminology of Regier and
Robson (1966), Berst combined type B selectivity curves (i.e.
graphs of selectivity versus mesh size for a given fish size)
plotted against fish girth : mesh perimeter ratios into a single
type B master curve by adjusting each curve to a unit area. This
master cuwe also represents a type A curve (i,e. a graph of
selectivity versus fish size for a given mesh size) because the
ratio girth : perimeter is a function of both fish size and mesh size
(Hamley 1975). The assumption that each type B curve has the
same area is equivalent to considering B(El) as a constant.
Therefore, Berst's selectivity curve is proportional to the
probability that the fish is caught and retained after encounter
(P(R1,)). Since girth can be related to fish length, P(RIm)can be
written as a function of fish length and mesh perimeter (Table
1).
W e n B(El) is considered to be a function of fish size, as in
this paper, each type B curve should be scaled according to the
value of B(El) for the fish length in question. From these curves,
new type A curves can be constructed. Our combined function
(P(El).B(RI,)) represents such type A curves, since, for each
fish length I, the value of P(R1,,) is scaled by B(EI).For the sake
of clarity, we keep the two functions separate.
The encounter probability should be directly proportional to
the distance travelled by the fish during the sampling period.
This distance is directly proportional to routine speed if (1)
TABLE1. Equations used for calculating retention probability fcx
cisco. The equations were obtained by fitting a modified logistic
functi~n(Thornton and Lessem 1978) to the increasing and decreasing
parts of the selectivity cuwe presented by Berst (196 1) for Lake Huron
cisco using the method of least squares. The equation for fish girth was
also derived from Berst (1961) by a linear approximation of his two
equations.
P(R1,) = A?.f(1. P P ~ )
f(1, n z ) = z l ( i + :)
where z = 1 . 1 0 ~ l ~ ~ f -o r~x e< ~1.26
~ ~and'
:= 2.$1 . 1 0 ~ . e - ' " ' ' for x > 1.26
x = ((0.399.1) + 12.7)i2m
Sym bobs
f(1, m): retention function dependent on fish length and mesh size
x: girthinlesh perimeter
m: mesh size (strech mesh, mm), half of the perimeter
I: fish length (total length, mm)
Can. J . Fish. Aquas. Sci., k'ol. 41, 1984
different-sized fish swim for the same amount of time during the
sampling period and (2) different-sized fish occupy the same
habitat. The degree to which these conditions rare satisfied will
depend on the fish species studied. Since swimming speed can
be approximated as a power function of fish length (Bainbridge
1958; 'dates 1983), we obtain
where A l is a constant.
The exponent in the expression for routine and/or sustained
swimming has been determined for several fishes and is often
about 0.5 (e.g. see Magnuson 1978; Brett and Glass 1973; Wu
and Yates 1978). Since routine speeds of coregonines have
not been reported, we measured this parameter for bloater,
Coregonus hoyi, a cisco from the Laurentian Great takes. The
fish were kept in large aquaria, 1.5 and 2.5 m in diameter, at the
Center for Great Lakes Studies, University of WisconsinMilwaukee. Bloater and cisco are in the same subgenus (Scott
and Crossman 1973) and behave similarly in captivity (F.
Binkowski, Center for Great Lakes Studies, University of
Wisconsin-Milwaukee, pers. comm.). Both species swim
continuously, day and night, in one direction around the tank.
Woutine swimming speeds were measured for three size-classes
of bloaters held in separate aquaria. The individuals were timed
as they swam around the tank past two points 30 crn apart. All
measurements were made between 8 and 10 a.m. on June 20,
1983. The temperature in all three tanks was between 12.3 and
12.5"C. The value for the length exponent calculated from these
measurements, 0.8, was used for cisco (Table 2).
Inserting expressions for P(RI,) from Table I and P(EI) from
equation 2 into equation 1, we obtain
where A 1 and A2 are constants.
Given our assumptions, the expression (A2.f(H, m)).(A
is the absolute selectivity coefficient of a net with mesh size an
towards fish of size I. To obtain the values for the constants
are needed. In most instances these constants are not known and
only relative values for the numbers of fish in each length group
can be obtained. By scaling this selectivity coefficient to 1 for a
particular size fish (in our example, a 20-cm-long cisco), we
obtain a curve of the relative selectivity coefficient as a function
of fish length. The relative selectivity curves for each mesh size
can be summed to yield a total selectivity curve for a set of nets
(Fig. I). A corrected size distribution is obtained by dividing the
catch for each length group by its relative selectivity coefficient.
Field merho& - Samples were from Big Muskellunge and
Sparkling lakes (Vilas Co., Wisconsin) in August 1981 and
TABLE2. Laboratory measurements of routine swimming s p e d of
three size-classes of bloater in relation to their length. Linear
regression: In (swimming speed) = 0.6 + 0.8 In (length), r2 = 0.650,
standard error of exponent = 0.05.
Total length of fish
Age-class
Mean (cm)
SD
Routine swimming speed
N
Mean (cm:s)
SD
h1
t
TABLE3. Catch per unit effort of cisco of
all ages in three Wisconsin lakes summed
from six vertical gill nets over 48 h. The
catch in the 25-mm net added for Lake
Mendota is not included. Catch per unit
effort was calculated from 6 1) field data, (2)
field data corrected for retention probability, and (3) field data corrected for both
retention and encounter probabilities.
1.2% A. P ( E ) Constant
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/J
SUM
Catch per unit effort
(no. per set)
-
>
B. P ( E ) P r o p o r t i o n a l t o l e n g t h
1.50
6)
Lake
(1)
(2)
(3)
Big Muskellunge
Sparkling
Mendota
186
116
65
308
177
82
498
291
60
SUM
TABLE4. Age structure and mean length of cisco in three FFTisconsin
lakes sampled with vertical gill nets. Relative age structure was
calculated from (1) field data, (2) field data corrected for retention
probability, and (3) field data corrected for both retention and
encounter probabilities.
Age structure (5%)
Lake and year
(no. caught)
8
10
20
38
40
50
TOTAL L E N G T H ( c m j
60
70
FIG. 1. Relative selectivity curves for cisco assuming that thcir
probability B(E) of encountering the net is (A) constant and (B)
proportional to fish length to the 0.8 power. The selectivity curves for
individual nets (mesh sizes 19, 25, 32, 38, 51, 64, and 89 mm stretch
mesh) and for the whole set of nets are presented. The selectivity
coefficients for the whole set of nets are scaled to 1 for 20-cm-long fish.
Uncorrected selectivity curves and girth-length relationships were
derived from Berst (1961) (see Table I).
Age
group
Total
length
(cm)
(1)
(2)
(3)
Big Muskellunge,
1981
(186 fish)
Sparkling,
2981
(I I 6 fish)
Mendota,
1982
(77 fish)
fmrn Lake hfendota (Dane Co., Wisconsin) in September 1982
(Rudstam 1983). In 1981, cisco populations were sampled with
six vertical gill nets, each with a different mesh size (19,32,38,
51, 64, and 89 rnm stretch mesh). In 1982, a 25-mrn mesh net
was added. All nets were 4 m wide and 18 m deep and were
suspended from surface to bottom along the 18-113 depth
contour.
The potential magnitude of bias on age structures is also
illustrated (Table 4). YOY fish made up a larger percentage of
the population after corrections for encounter probability, while
older fish made up a smaller percentage after the correction. In
some cases the changes were large. For example, in Lake
Mendota, YOY fish made up 14% of the population before and
27% after the correction, thus doubling their estimated contribution to the population.
Ca&cu/ceeions- We calculated uncorrected catch per unit
effort (CPUE) and percent age structure and then corrected for
retention probability and retention probability plus encounter
probability for the three populations of cisco (Tables 3 and 4).
Incorporating the correctiora for encounter probability illustrates the possible magnitude of bias associated with uncorrected estimates of abundance. For example, the CPUE in Lake
Mendota is 46% of the CPUE in Sparkling Lake before and 2 1%
after corrections for encounter probabilities were included
(Table 3). This occurs because the fish in Mendota were larger
than those in Sparkling; thus, more fish per unit time would have
encountered the net relative to fish in Sparkling Lake. For
c o m p ~ s o nbetween
s
years within a single lake, the effect could
be of similar magnitude if the size structure of the population
changes with time.
During a sampling period, fish of different sizes should travel
a distance proportional to their swimming speed, if they have
the same daily activity pattern. If fish of different sizes also
occupy the same habitat, the encounter probability should be
directly proportional to the swimming speed of the fish. Pelagic
planktivsres, such as cisco, may fulfill these conditions reasonably well. Cisco and other ccpregonimes swim constantly in
captivity (F. Binkowski, pers. comm.) and the cisso has been
described as one of the most active of fishes in Wiscorasirm (Cahn
1927). Furthermore, all sizes appear to be distributed across the
entire lake at night when almost all cisco are caught in gill nets
(Engel and Magnuson 1976; Rudstarn 1983). Although direct
observations of the routine speed of different sized sisco in the
Can. 9.Fish. Aquaf. Sci., kid. 41, 1984
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field were not available, our laboratory measurements on
bloaters provide the best available approximation for cisco.
Thus, the correction for encounter probability seems reasonable. In general, our approach should be most appropriate for
schooling fishes that spend all or almost all of their time
swimming, such as coregonines , scombrids , and carangids .
The effect of incorporating our size-dependent expression for
encounter probability will increase with the size range of fish
caught and with the size of the exponent z (equation 2). In our
cisco example, the differences in encounter probability estimated by our model appear large enough to significantly bias
estimates of catch per unit effort and age structure. Thus, catch
curve data and mortality estimates would be biased as well. This
could be an important consideration in calculation of population
dynamics for a number of important fisheries that rely on
passive fishing gear. Examples are tuna longline fisheries.
high-sea salmon gillnet fisheries, and drift gill nets for herring.
The magnitude of the correction would be directly proportional
to the swimming speeds of the sizes or species of fish being
compared. The correction thus could be large. For example,
peiawmis) have routine
75-cm-long skipjack tuna (Kat,wwonra~:
speeds twice that of yellowfin (Thunnus estbacarss) (Magnuson
1973) and, thus, at equal densities, they should encounter
passive gear twice as often as yellowfin. For other continuously
swimming species, the exponent relating speed to length may be
different from the 8.8 we observed for bloater. It is 0.5 for
wavyback skipjack ( E u t h y ~ tafllitis)
~s
(Magnuson 1970),0.420.50 for sockeye salmon (Oncsrhynchus nardcw) (Brett and
Glass 1973; Ware 1978), and 0.6 for jack mackerel (Trachurus
syrnsaicus) (Hunter 1971).
To investigate whether corrections for encounter probability
might apply to passive fishing gear other than gill nets and fish
other than cisco, we calculated the exponent in the expression
for P(Es) for perch (Percaflavescens) caught in fyke nets and
central rnudminnows (Umbra kimi) caught in minnow traps
from data obtained as part of a study on density compensation
(Tonn 1983). For these gear, we assume P(Rl,) to be constant
for the sizes of fish normally caught. Single mesh sizes (5 mm
square mesh for fyke nets and 6mm for minnow traps) were
used for each type of gear. Data were available on population
size (determined through mark-recapture), catch per unit
effort, and mean length of fishes for several sampling periods
from June to October 1980-82 in three small bog lakes in
northern Wisconsin. A log-log linear regression of (CPUEI
population size) against mean length of fish resulted in an
exponent of 1.6 (95% C.I. = 0.5-2.6, N = 22) for yellow perch
and 2.7 (95%C.I. = 1.2-4.2, N = 17) for central mudminnows. Although these data are from three different lakes and
from different time periods, they indicate an increase in
efficiency of these gears towards larger fish. We attribute this
increase partly to increased swimming speeds of larger fish.
A correction for encounter probability based on swimming
speed may not completely account for the increased efficiency
observed for larger fish after corrected for mesh size selection in
gill nets. Hamley and Regier (1973) observed larger increases rm
i
selectivity of large mesh nets for walleye than could be
accounted for by our corrections. Other factors may be
involved, such as differences in daily activity patterns and/or
habitat utilization of different size walleyes, or decreased
visibility of larger mesh nets.
We thank the staff, students, a n d hourly employees at the Center for
Can. 9 . Fish. Aquar. Sci., Vol. 41, 1984
Limnology of the University of Wisconsin-Madison for assistance
during the field sampling. Particular thanks go to T. Kratz, J. Lyons, P.
Rasmussen, a n d the Zoology 316 students. W e are grateful to F.
Binkowski for allowing us t o measure swimming speeds on his captive
bloaters a n d for assistance with these measurements. T. Kratz, B.
P m i s h , P. Rasmussen, a n d W. Regier provided valuable comments o n
the manuscript. The research w a s supported by a Wisconsin Alumni
Research Foundation Fellowship and N S F grants DEB 80123 13 a n d
DEB 79 12337.
References
BAINBRIWE,R. 1958. The speed of swiinming fish as related to size and to
frequency and amplitude of the tail beat. J. Exp. Biol. 35: 109-133.
BERST,A. H. 1961. Selectivity and efficiency of experianental gillnets in South
Bay and Georgian Bay of Lake Huron. Trans. Am. Fish. Soc. 90:
413-418.
BRETT,J. R., AND %Pa. R. GLASS.1973. Metabolic rates and critical swimming
speeds of sockeye salmon, Oncorhynchus nerka, in relation to size and
temperature. J. Fish. Res. Board Can. 30: 379-387.
CAHN,A. R. 1927. An ecologicaH study of southern Wisconsin fishes, the brook
silverside and the cisco, and their relation to the region. Ill. Bisl. Monogr.
ll(1): 151 p.
1976. Vertical and horizontal distributions
ENGEL,S. S., AND J. B. MAGNUSON.
of coho salmon (Oncorh~nchuskimbch), yellow perch (Percaflavescens),
and cisco (Coregonus arredii) in Pallette Lake, Wisconsin. J. Fish. Res.
Board Can. 33: 2718-2715.
HAMLEY,
J. M. 1975. Review of gillnet selectivity. J. Fish. Res. Board Can. 32:
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HAMLEY,
J . M . . A N D H.A. REGHER.
1973. Direct estimates of gillnet selectivity
to walleye (Stizostedion virrensm vibreuna). J. Fish. Res. Board Can. 30:
$17-830.
HUNTER.J. R. 197 1. Sustained speed of jack mackerel, Trcmckurus symmetricus. Fish. Bull. 69(2): 267-271.
LAGLER,
K. F. 1968. Capture, sampling and examination of fishes, p. 7-44. Pn
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waters. BBP Handbook No. 3. Blackwell Scientific Wablications, Oxford.
MAGNUSON,
J. J. 1970. Hydrostatic equilibrium of Euthynnus afinis, a pelagic
teleost without gas bladder. Cspeia 1970: 56-85.
1973. Comparative study s f adaptations for continuous swimming
and hydrostatic equilibrium of scombroid and xiphoid fishes. Fish. Bull.
71: 337-356.
1978. Locomotion by scombrid fishes: hydrodynamics, morphology,
and behavior, p. 239-3 13. In W. S. Hoar and D. J. Randall [ed.] Fish
physiology. Vol. VII. Locomotion. Academic Ress, New York, NY.
MCCOMBIE,A. M . , A N D A. H. BERST. 1969. Some effects of shape and
stmcture of fish on selectivity of gillnets. J. Fish. Res. Board Can. 26:
268 1-2689.
MCCBMBIE,A. M . , A N D F. E. FRY. 1960. Selectivity of gill nets for lake
whitefish, Coregonus clupaafoanzis. Trans. Am. Fish. Soc. 89: 176-184.
REGIER,H.A. 1975. To survey, monitor or appraise fishery resources: some
general concepts. EIFAC Tech. Pap. No. 23, Suppl. 1 , Vol. 11: 690-703.
RBG~ER,
H. A., A N D D. S. ROBSON.1966. Selectivity of gill nets, especially to
lake whitefish. J. Fish. Res. Board Can. 23: 423-454.
R~CKER,
W. E. 1949. Mortality rates in some little exploited populations of
fresh-water fishes. Trans. Am. Fish. Soc. 77: 1 14- 128.
RUDSTAM,
L. 6 . 1983. The cisco, Coregonrrs arfadii, in Wisconsin lakes: long
term csmparison of population structure and an analysis of their vertical
distribution. M.S. thesis, University of Wiscsnsin-Madison, Madison,
WI. 131 p.
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K. W., A N D A. S. LESSEM.1978. A temperature algorithm for
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in northern Wisconsin lakes. Ph.9. thesis, University of WisconsinMadison, Madison, WI. 179 p.
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Encounter Probabi
Lars G. ~udstarn,'John J. Magnuson, and William M. Tonn
Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/04/13
For personal use only.
Center for Limnology and Department of Zoology, University of Wisconsin- fadis is or?, Madison, kVl53706, USA
Rudstam, k. C., I. 8 . Magnuson! and W. M. Tsnn. 1984. Sine selectivity of passive fishing gear: a correction
for encounter probability applied to gill nets. Can. ). Fish. Aquat. Sci. 41: 1252-1255.
The probability s f catching a fish in a gilt net may be separated into two components: (1)the probability of
the fish encountering the net and (2)the probability of the fish being caught and retained in the net. W e
consider the probability of encounter to be directly proportional to the distance travelled by the fish during
the sampling period. This distance will increase with fish sine if different-sized fish swim for the same
amount of time because swimming speed increases with fish sine. Routine swimming speed measured in
the laboratory for three size-classes sf bloater (Coregonus hoyi) increased with length to the 0.8 power.
Corrections fsr encounter probability were incorporated i n gill net selectivity calculations for samples of
cisco (Coregonus artedii), a species closely related to bloater. These corrections can significantly increase
the proportional estimates of smaller relative to larger animals in the estimated population structure. The
approach should also be applicable t o other passive fishing gear, such as longlines and set nets.
La probabilitk de capture d'un poisson dans u n filet maillant peut &re divisee en deuw composantes, soit (1)
la probabilite que le poisson rencontre le filet et (2)la probabilit6 que le poisson soit capture et retenu dans
le Filet. Fes auteurs csnsidi?rent que la probabilite de rencontre est directement proportionnelle i la
distance parcourue par le poisson pendant la periode d'kchantillonnage. Cette distance s'accroit en
fonction de la taiile d u poisson si des individus de differentes longueurs nagent pendant la meme p6riode
car la vitesse de nage augmente par rapport it la taille. Les vitesses de nage mesurees systematiqrsernent en
labsratoire chez le cisco de fumage (Coregonus hoyi) appartenant
trois classes de longueur ont
augment6 en fonction de la longueur 2 la puissance 0,8. Des corrections pour la prsbabilit6 de rencontre
ont 4te incsrporees dans les calculs de la sklectivite des fiiets maillants pour les echantillons de cisco de lac
(Caregonus artedii), espece etroiternent apparerstee au cisco de fumage. Ces csrrections peuvent
nettement accrsitre les estimations proportionnelles des petits animaux par rapport auw gros dans la
structure estimee de la population. Cette approche devrait aussi &re applicable 5 d'autres engins de peche
cornme la palangre et Ie filet mouille.
Received September 7, 14983
Accepted April 25, 198%
ize selectivity of gill nets (the probability sf capturing a
certain size of Ash in one unit of operation sf the gear) is
best considered as a characteristic of the entire fishing
operation (Lagler 1968; Hamley 1 975). Therefore, gear
selectivity will depend both on the probability that a fish
encounters the net and on the probability that the fish is caught
and retained by the net (Regier 1975; Hamley 1975). Factors
that affect either s f these probabilities will affect net selectivity.
In a comprehensive review of gill net selectivity, Hamley
(1975) described methods used to date to construct selectivity
curves (plots of the selectivity of a net as a function of some
measure of fish size) from the size distribution of catches in
different mesh sizes, The shape of these curves, at least for
species that are caught primarily by wedging, e. g . coregonines,
is similar with different mesh sizes when selectivity is plotted
against the ratio of fish girth to mesh perimeter (McCornbie and
Fry 1968; McCombie and Berst 1969). A combined selectivity
curve for a set of nets differing in mesh size can be obtained by
sw resent address: Department of Zoology, University of Stockhulnn,
S-106 91, Stockholm, Sweden.
1252
R e p le 7 septembre 1983
Accept6 8e 25 avail 1984
summing the selectivity curves of each net. This requires that
the relationship between the efficiencies of different nets
towards the fish size that they catch the best is known. This
maximum efficiency is often assumed to be the same for all nets
used, an assumption that has been criticized (Bicker 1949;
Regier and Bobson 1966; Hamley 1975). With walleyes
(Stizostedksn e~kaeum vktreum) , Hamley and Wegier ( 1973)
found that nets with larger mesh were more efficient than those
with smaller mesh.
At least part of this greater efficiency of larger mesh
nets results because larger fish have a higher probability of
encountering a net than do smaller fish (Lagler 1968). In this
paper we describe how an expression for length-dependent
encounter probability can be incorporated into selectivity
calculations, and we illustrate the potential magnitude of bias
our method can correct for, using gill net catch data on cisco
(Coregsnm4s artedii). Encounter probability is considered to be
directly proportional to distance travelled by a fish during the
sampling period. We posit that distance travelled is proportional
to speed s f spontaneous swimming activity (routine speed) (see
hfagnuson 1978).
Can. /. Fish. Aqua?. Sci., Vol. 41, 1984
Selectivity C~erlculatic~ns
The probability of catching an individual of size 1 by a net
of mesh size m may be separated into two independent
probabilities: (1) the probability that the fish will encounter the
net during a sampling period, B(El), and (2) the probability that
the fish will be caught and retained by the net of mesh size nz
after encounter, P(RIm).Therefore:
Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Renmin University of China on 06/04/13
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where Cl, = the number of fish s f size H caught and retained per
sampling period in a net of mesh size m and Nl = the number of
fish of size k occurring in the lake.
The expression for B(Rl,) was obtained by fitting a function
to Berst's (1961) selectivity curve for cisco from Lake Huron
(Table 1). This curve was derived using the method of
McCsmbie and Fry (1960). In the terminology of Regier and
Robson (1966), Berst combined type B selectivity curves (i.e.
graphs of selectivity versus mesh size for a given fish size)
plotted against fish girth : mesh perimeter ratios into a single
type B master curve by adjusting each curve to a unit area. This
master cuwe also represents a type A curve (i,e. a graph of
selectivity versus fish size for a given mesh size) because the
ratio girth : perimeter is a function of both fish size and mesh size
(Hamley 1975). The assumption that each type B curve has the
same area is equivalent to considering B(El) as a constant.
Therefore, Berst's selectivity curve is proportional to the
probability that the fish is caught and retained after encounter
(P(R1,)). Since girth can be related to fish length, P(RIm)can be
written as a function of fish length and mesh perimeter (Table
1).
W e n B(El) is considered to be a function of fish size, as in
this paper, each type B curve should be scaled according to the
value of B(El) for the fish length in question. From these curves,
new type A curves can be constructed. Our combined function
(P(El).B(RI,)) represents such type A curves, since, for each
fish length I, the value of P(R1,,) is scaled by B(EI).For the sake
of clarity, we keep the two functions separate.
The encounter probability should be directly proportional to
the distance travelled by the fish during the sampling period.
This distance is directly proportional to routine speed if (1)
TABLE1. Equations used for calculating retention probability fcx
cisco. The equations were obtained by fitting a modified logistic
functi~n(Thornton and Lessem 1978) to the increasing and decreasing
parts of the selectivity cuwe presented by Berst (196 1) for Lake Huron
cisco using the method of least squares. The equation for fish girth was
also derived from Berst (1961) by a linear approximation of his two
equations.
P(R1,) = A?.f(1. P P ~ )
f(1, n z ) = z l ( i + :)
where z = 1 . 1 0 ~ l ~ ~ f -o r~x e< ~1.26
~ ~and'
:= 2.$1 . 1 0 ~ . e - ' " ' ' for x > 1.26
x = ((0.399.1) + 12.7)i2m
Sym bobs
f(1, m): retention function dependent on fish length and mesh size
x: girthinlesh perimeter
m: mesh size (strech mesh, mm), half of the perimeter
I: fish length (total length, mm)
Can. J . Fish. Aquas. Sci., k'ol. 41, 1984
different-sized fish swim for the same amount of time during the
sampling period and (2) different-sized fish occupy the same
habitat. The degree to which these conditions rare satisfied will
depend on the fish species studied. Since swimming speed can
be approximated as a power function of fish length (Bainbridge
1958; 'dates 1983), we obtain
where A l is a constant.
The exponent in the expression for routine and/or sustained
swimming has been determined for several fishes and is often
about 0.5 (e.g. see Magnuson 1978; Brett and Glass 1973; Wu
and Yates 1978). Since routine speeds of coregonines have
not been reported, we measured this parameter for bloater,
Coregonus hoyi, a cisco from the Laurentian Great takes. The
fish were kept in large aquaria, 1.5 and 2.5 m in diameter, at the
Center for Great Lakes Studies, University of WisconsinMilwaukee. Bloater and cisco are in the same subgenus (Scott
and Crossman 1973) and behave similarly in captivity (F.
Binkowski, Center for Great Lakes Studies, University of
Wisconsin-Milwaukee, pers. comm.). Both species swim
continuously, day and night, in one direction around the tank.
Woutine swimming speeds were measured for three size-classes
of bloaters held in separate aquaria. The individuals were timed
as they swam around the tank past two points 30 crn apart. All
measurements were made between 8 and 10 a.m. on June 20,
1983. The temperature in all three tanks was between 12.3 and
12.5"C. The value for the length exponent calculated from these
measurements, 0.8, was used for cisco (Table 2).
Inserting expressions for P(RI,) from Table I and P(EI) from
equation 2 into equation 1, we obtain
where A 1 and A2 are constants.
Given our assumptions, the expression (A2.f(H, m)).(A
is the absolute selectivity coefficient of a net with mesh size an
towards fish of size I. To obtain the values for the constants
are needed. In most instances these constants are not known and
only relative values for the numbers of fish in each length group
can be obtained. By scaling this selectivity coefficient to 1 for a
particular size fish (in our example, a 20-cm-long cisco), we
obtain a curve of the relative selectivity coefficient as a function
of fish length. The relative selectivity curves for each mesh size
can be summed to yield a total selectivity curve for a set of nets
(Fig. I). A corrected size distribution is obtained by dividing the
catch for each length group by its relative selectivity coefficient.
Field merho& - Samples were from Big Muskellunge and
Sparkling lakes (Vilas Co., Wisconsin) in August 1981 and
TABLE2. Laboratory measurements of routine swimming s p e d of
three size-classes of bloater in relation to their length. Linear
regression: In (swimming speed) = 0.6 + 0.8 In (length), r2 = 0.650,
standard error of exponent = 0.05.
Total length of fish
Age-class
Mean (cm)
SD
Routine swimming speed
N
Mean (cm:s)
SD
h1
t
TABLE3. Catch per unit effort of cisco of
all ages in three Wisconsin lakes summed
from six vertical gill nets over 48 h. The
catch in the 25-mm net added for Lake
Mendota is not included. Catch per unit
effort was calculated from 6 1) field data, (2)
field data corrected for retention probability, and (3) field data corrected for both
retention and encounter probabilities.
1.2% A. P ( E ) Constant
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For personal use only.
/J
SUM
Catch per unit effort
(no. per set)
-
>
B. P ( E ) P r o p o r t i o n a l t o l e n g t h
1.50
6)
Lake
(1)
(2)
(3)
Big Muskellunge
Sparkling
Mendota
186
116
65
308
177
82
498
291
60
SUM
TABLE4. Age structure and mean length of cisco in three FFTisconsin
lakes sampled with vertical gill nets. Relative age structure was
calculated from (1) field data, (2) field data corrected for retention
probability, and (3) field data corrected for both retention and
encounter probabilities.
Age structure (5%)
Lake and year
(no. caught)
8
10
20
38
40
50
TOTAL L E N G T H ( c m j
60
70
FIG. 1. Relative selectivity curves for cisco assuming that thcir
probability B(E) of encountering the net is (A) constant and (B)
proportional to fish length to the 0.8 power. The selectivity curves for
individual nets (mesh sizes 19, 25, 32, 38, 51, 64, and 89 mm stretch
mesh) and for the whole set of nets are presented. The selectivity
coefficients for the whole set of nets are scaled to 1 for 20-cm-long fish.
Uncorrected selectivity curves and girth-length relationships were
derived from Berst (1961) (see Table I).
Age
group
Total
length
(cm)
(1)
(2)
(3)
Big Muskellunge,
1981
(186 fish)
Sparkling,
2981
(I I 6 fish)
Mendota,
1982
(77 fish)
fmrn Lake hfendota (Dane Co., Wisconsin) in September 1982
(Rudstam 1983). In 1981, cisco populations were sampled with
six vertical gill nets, each with a different mesh size (19,32,38,
51, 64, and 89 rnm stretch mesh). In 1982, a 25-mrn mesh net
was added. All nets were 4 m wide and 18 m deep and were
suspended from surface to bottom along the 18-113 depth
contour.
The potential magnitude of bias on age structures is also
illustrated (Table 4). YOY fish made up a larger percentage of
the population after corrections for encounter probability, while
older fish made up a smaller percentage after the correction. In
some cases the changes were large. For example, in Lake
Mendota, YOY fish made up 14% of the population before and
27% after the correction, thus doubling their estimated contribution to the population.
Ca&cu/ceeions- We calculated uncorrected catch per unit
effort (CPUE) and percent age structure and then corrected for
retention probability and retention probability plus encounter
probability for the three populations of cisco (Tables 3 and 4).
Incorporating the correctiora for encounter probability illustrates the possible magnitude of bias associated with uncorrected estimates of abundance. For example, the CPUE in Lake
Mendota is 46% of the CPUE in Sparkling Lake before and 2 1%
after corrections for encounter probabilities were included
(Table 3). This occurs because the fish in Mendota were larger
than those in Sparkling; thus, more fish per unit time would have
encountered the net relative to fish in Sparkling Lake. For
c o m p ~ s o nbetween
s
years within a single lake, the effect could
be of similar magnitude if the size structure of the population
changes with time.
During a sampling period, fish of different sizes should travel
a distance proportional to their swimming speed, if they have
the same daily activity pattern. If fish of different sizes also
occupy the same habitat, the encounter probability should be
directly proportional to the swimming speed of the fish. Pelagic
planktivsres, such as cisco, may fulfill these conditions reasonably well. Cisco and other ccpregonimes swim constantly in
captivity (F. Binkowski, pers. comm.) and the cisso has been
described as one of the most active of fishes in Wiscorasirm (Cahn
1927). Furthermore, all sizes appear to be distributed across the
entire lake at night when almost all cisco are caught in gill nets
(Engel and Magnuson 1976; Rudstarn 1983). Although direct
observations of the routine speed of different sized sisco in the
Can. 9.Fish. Aquaf. Sci., kid. 41, 1984
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field were not available, our laboratory measurements on
bloaters provide the best available approximation for cisco.
Thus, the correction for encounter probability seems reasonable. In general, our approach should be most appropriate for
schooling fishes that spend all or almost all of their time
swimming, such as coregonines , scombrids , and carangids .
The effect of incorporating our size-dependent expression for
encounter probability will increase with the size range of fish
caught and with the size of the exponent z (equation 2). In our
cisco example, the differences in encounter probability estimated by our model appear large enough to significantly bias
estimates of catch per unit effort and age structure. Thus, catch
curve data and mortality estimates would be biased as well. This
could be an important consideration in calculation of population
dynamics for a number of important fisheries that rely on
passive fishing gear. Examples are tuna longline fisheries.
high-sea salmon gillnet fisheries, and drift gill nets for herring.
The magnitude of the correction would be directly proportional
to the swimming speeds of the sizes or species of fish being
compared. The correction thus could be large. For example,
peiawmis) have routine
75-cm-long skipjack tuna (Kat,wwonra~:
speeds twice that of yellowfin (Thunnus estbacarss) (Magnuson
1973) and, thus, at equal densities, they should encounter
passive gear twice as often as yellowfin. For other continuously
swimming species, the exponent relating speed to length may be
different from the 8.8 we observed for bloater. It is 0.5 for
wavyback skipjack ( E u t h y ~ tafllitis)
~s
(Magnuson 1970),0.420.50 for sockeye salmon (Oncsrhynchus nardcw) (Brett and
Glass 1973; Ware 1978), and 0.6 for jack mackerel (Trachurus
syrnsaicus) (Hunter 1971).
To investigate whether corrections for encounter probability
might apply to passive fishing gear other than gill nets and fish
other than cisco, we calculated the exponent in the expression
for P(Es) for perch (Percaflavescens) caught in fyke nets and
central rnudminnows (Umbra kimi) caught in minnow traps
from data obtained as part of a study on density compensation
(Tonn 1983). For these gear, we assume P(Rl,) to be constant
for the sizes of fish normally caught. Single mesh sizes (5 mm
square mesh for fyke nets and 6mm for minnow traps) were
used for each type of gear. Data were available on population
size (determined through mark-recapture), catch per unit
effort, and mean length of fishes for several sampling periods
from June to October 1980-82 in three small bog lakes in
northern Wisconsin. A log-log linear regression of (CPUEI
population size) against mean length of fish resulted in an
exponent of 1.6 (95% C.I. = 0.5-2.6, N = 22) for yellow perch
and 2.7 (95%C.I. = 1.2-4.2, N = 17) for central mudminnows. Although these data are from three different lakes and
from different time periods, they indicate an increase in
efficiency of these gears towards larger fish. We attribute this
increase partly to increased swimming speeds of larger fish.
A correction for encounter probability based on swimming
speed may not completely account for the increased efficiency
observed for larger fish after corrected for mesh size selection in
gill nets. Hamley and Regier (1973) observed larger increases rm
i
selectivity of large mesh nets for walleye than could be
accounted for by our corrections. Other factors may be
involved, such as differences in daily activity patterns and/or
habitat utilization of different size walleyes, or decreased
visibility of larger mesh nets.
We thank the staff, students, a n d hourly employees at the Center for
Can. 9 . Fish. Aquar. Sci., Vol. 41, 1984
Limnology of the University of Wisconsin-Madison for assistance
during the field sampling. Particular thanks go to T. Kratz, J. Lyons, P.
Rasmussen, a n d the Zoology 316 students. W e are grateful to F.
Binkowski for allowing us t o measure swimming speeds on his captive
bloaters a n d for assistance with these measurements. T. Kratz, B.
P m i s h , P. Rasmussen, a n d W. Regier provided valuable comments o n
the manuscript. The research w a s supported by a Wisconsin Alumni
Research Foundation Fellowship and N S F grants DEB 80123 13 a n d
DEB 79 12337.
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