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Linking the dynamics of harvest effort to
recruitment dynamics in a multistock, spatially
structured fishery
Eric A. Parkinson, John R. Post, and Sean P. Cox
Abstract: A freshwater sport fishery that targets hundreds of geographically isolated stocks is simulated by combining
a model of angler behavior with a model of rainbow trout (Oncorhynchus mykiss) population dynamics. Ideal free dis-
tribution (IFD) theory, which suggests that angling quality will be similar on all lakes, is used to drive angler effort
distribution. Model parameters are based on creel survey data from 53 lakes and empirical relationships between
growth, survival, and density derived from whole-lake density manipulations on nine lakes over a period of 10 years.
We compared angling quality, population density, fish size, and yield under unfished conditions, harvest rates that max-
imize sustained yields (MSY), and an IFD equilibrium driven by angler behavior. The IFD equilibrium rarely maxi-
mized yields. Stocks with high MSY angling quality are overexploited at the IFD equilibrium because anglers move to
take advantage of exceptional angling opportunities. These stocks would often be viewed as more resistant to harvest
pressure because they have higher stock productivities and habitat capacities. However, in our model, they are system-
atically overharvested because their high fish density attracts excessive angling pressure. Conversely, stocks with low
MSY angling quality are underexploited because anglers move to take advantage of better angling quality on other
lakes.
Résumé : La combinaison d’un modèle de comportement des pêcheurs à un modèle de dynamique de population de la
truite arc-en-ciel (Oncorhynchus mykiss) nous a permis de simuler une pêche sportive d’eau douce qui cible des centai-
nes de stocks isolés géographiquement. La distribution libre idéale (IFD), qui suppose que la qualité de la pêche sera
la même dans tous les lacs, détermine la répartition des efforts de pêche des pêcheurs. Les variables du modèles sont
tirées de statistiques de pêche sportive dans 53 lacs et les relations empiriques entre la croissance, la densité et la
survie ont été obtenues par des manipulations de la densité dans neuf lacs entiers sur une période de 10 ans. Nous
avons comparé la qualité de la pêche, la densité de la population, la taille des poissons et le rendement de la pêche en
l’absence de pêche sportive, ainsi qu’à des taux de récolte qui maximisent le rendement soutenable (MSY) et à un
équilibre IFD dû au comportement des pêcheurs. Les stocks avec une qualité de pêche de fort MSY sont surexploités à
l’équilibre IFD, car les pêcheurs se déplacent pour jouir des conditions exceptionnelles de pêche. Ces stocks seraient
souvent considérés comme plus résistants à la pression de capture parce qu’ils ont une plus forte productivité et font
une utilisation plus grande de l’habitat. Cependant, dans notre modèle, ces stocks sont systématiquement surexploités,
parce que leurs fortes densités de poissons suscitent une pression de pêche excessive. Inversement, les stocks qui pos-
sèdent une qualité de pêche de faible MSY sont sous-exploités, car les pêcheurs se déplacent vers d’autres lacs pour
profiter des meilleures conditions de pêche.
[Traduit par la Rédaction] Parkinson et al. 1670
Introduction
A fundamental problem in managing multistock fisheries
is that optimal harvest rates often vary substantially among
stocks because of variation in stock–recruitment parameters.
When multiple stocks are harvested at a single place and
time, this variation in optimal harvest rates implies that the
maximum yield of the mixed-stock fishery will be less than
the combined maximum yields of the individual stocks
(Paulik et al. 1967). If fishers can target individual stocks,
the problem of multistock management is substantially re-
duced and, in theory, maximum yields can be achieved for
each stock. In reality, fishery managers rarely have tight
control over either the total effort or the allocation of har-
Can. J. Fish. Aquat. Sci. 61: 1658–1670 (2004) doi: 10.1139/F04-101 © 2004 NRC Canada
1658
Received 3 April 2003. Accepted 19 February 2004. Published on the NRC Research Press Web site at http://cjfas.nrc.ca on
15 November 2003.
J17445
E.A. Parkinson.1British Columbia Ministry of Water, Land and Air Protection, The University of British Columbia, Vancouver,
BC V6T 1Z4, Canada.
J.R. Post. Division of Ecology, Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, AB
T2N 1N4, Canada.
S.P. Cox. Resource Management and Environmental Studies, Simon Fraser University, Burnaby, BC V6T 1Z4, Canada.
1Corresponding author (e-mail: eric.parkinson@gems9.gov.bc.ca).
vesting effort among individually targeted stocks. This raises
the possibility that some stocks will be overharvested, even
if total effort in the fishery is not excessive.
The two main approaches to the problem of overexploitation
have been the biological theory of stock–recruitment rela-
tionships (Ricker 1975) and the economic theory of exploita-
tion of a common property resource (Gordon 1954). In
general terms, the biological theory of population regulation
suggests that there are optimum population levels that will
achieve the desired balance between the conflicting goals of
maximizing yield or economic value while minimizing risk
of collapse (Hilborn and Walters 1992). In sport fisheries,
maximum sustainable biomass yields can be replaced by a
maximum sustainable benefit, which can be defined as an-
gler effort multiplied by a measure of angling quality. Quan-
titative models of recruitment dynamics and yield range
from simple two-parameter analytic models (Barrowman and
Myers 2000) to complex age-structured models (Peterson
and Evans 2003; Post et al. 2003).
Economic theory predicts that exploitation will be driven
by fishers’ expectations of economic returns. The distribu-
tion of effort will be determined by the relative economic re-
turns in alternative fisheries (Holland and Sutinen 1999). For
commercial fisheries with open access (i.e., effort is not re-
stricted), many authors have recognized that economic forces,
poor data, and lack of catch restrictions often result in the
severe overharvest of many common property resources
(Hilborn 1985; Ludwig et al. 1993). In simple terms, an eco-
nomic equilibrium results when boats stop entering a fishery
because exploitation has driven catch per unit effort (CPUE)
down to the point where revenue from sales is equal to the
cost of fishing. In many cases, this equilibrium results in
excessive fishing effort and depressed fished populations,
which, in turn, result in various schemes designed to reduce
effort (DeVoretz and Schwindt 1985). The equivalent of an
economic equilibrium in a sport fishery occurs when harvest
by anglers drives angling quality down to the point where
additional anglers stop entering the fishery.
Freshwater sport fisheries are often based on many small,
independent population units (stocks in hundreds of lakes)
that are tied together into a single fishery by a mobile angling
population (Billings 1989; Shuter et al. 1998). In multilake
systems, angler movement among lakes is an important fac-
tor driving changes in angling quality. The movement behav-
ior of anglers can be modeled using ideal free distribution
(IFD) theory, which has been developed by behavioral ecol-
ogists to predict the distribution of foragers relative to the
distribution of their prey resources (e.g., Gillis et al. 1993;
Levin et al. 2000). IFD theory predicts that angling quality
should be similar on all lakes. This prediction is based on
the belief that differences in angling quality should result in
shifts in effort that, at equilibrium, result in a situation
where individual anglers cannot experience an improvement
in quality by moving to another lake (Cox et al. 2002). As-
sumptions in IFD theory include zero cost to moving, per-
fect information about angling quality on all lakes,
equivalent costs (e.g., travel time, regulation complexity) on
all lakes, and equivalent ancillary benefits (e.g., facilities,
aesthetics) on all lakes. In the simplest case, when fish size
is not included in either the biological and harvest models,
IFD theory suggests that numbers caught per unit of effort
(NPUE) should be the same on all lakes (Cox 2000; Post et
al. 2002). However, size structure is clearly an important
factor in both angling quality and the dynamics of fish popu-
lations. Angling quality can be defined in terms of individ-
ual fish size and the total weight of the catch in addition to
the number of fish caught. However, various combinations
of fish size and NPUE can be defined as equivalent if it can
be shown that anglers do not prefer one combination over
another (e.g., many small fish versus fewer large fish). Ex-
ternal factors, such as aesthetics and facilities, also influence
angling quality but are usually assumed to be independent of
fish population structure.
In contrast with the homogeneity in angling quality pre-
dicted by IFD theory, observations of fish habitat and popu-
lations suggest that optimal densities will vary among lakes.
For example, the rainbow trout (Oncorhynchus mykiss) fish-
ery on the interior plateau of British Columbia, Canada, is
supported by many small, independent stocks that vary sub-
stantially in both density and size structure. This variation
among lakes can be linked to variation in the quality and
quantity of stream spawning areas (Larkin 1954) and lake
habitat (Northcote and Larkin 1956), which suggests that op-
timal densities and harvest rates should also differ among
lakes. The contrast between variation in optimal densities
and the homogeneity predicted by IFD theory implies that
the dynamics of the angler effort response will rarely result
in optimal harvest rates in fisheries where effort is free to
move among biologically independent populations. This con-
trast reflects the situation for many single-stock fisheries
where the economic equilibrium typically does not match
the optimum derived from stock–recruitment theory.
In this paper, we explore the dynamic interactions be-
tween angler effort and fish populations that vary in biologi-
cal productivity and examine the implications in terms of
harvest. Our goal is to identify conditions that are likely lead
to overexploitation in open access fisheries and quantify the
gains that might be expected under alternative management
policies. We explore these interactions in two stages. First, we
develop a simple analytical model to illustrate the general
problem. Second, we develop a more complex size-structured
simulation model that directly links angling quality (catch
rates and fish size) data to angler behavior, biological pro-
ductivity, and harvest outcomes. We develop and paramete-
rize this simulation model with biological and fishery
processes and data from Walters and Post (1993), Post et al.
(1999), Cox (2000), and Post et al. (2002).
Methods
Model development and parameterization
Our simulations model a fishery that consists of multiple
stocks that are biologically independent but are exploited by
a common pool of harvesting effort. Two population models
drive the dynamics of fish growth, survival, and reproduc-
tion. A simple numerical model is used to illustrate the gen-
eral behavior of this type of system. A size-structured model
provides a more accurate depiction of the demographic and
harvest processes that are both strongly size dependent.
Model parameters are derived from monoculture, lacustrine
rainbow trout populations in British Columbia Management
Region 3. In both models, biological differences among pop-
© 2004 NRC Canada
Parkinson et al. 1659
ulations are simulated by varying the maximum rate of in-
crease at low population density (stock productivity) and the
maximum population density over a plausible range for
monoculture rainbow trout in British Columbia lakes. An-
gling quality is linked to the fish population model using
empirical catchability data. To simulate the effects of mobile
effort, we used the IFD prediction that angling quality will
be similar on all stocks. The IFD equilibrium is driven by
effort that moves among lakes when angling quality is either
better (more anglers go to a lake) or worse (some anglers
leave) than the average in Region 3. The IFD equilibrium is
found by searching for an effort level that produces both the
target angling quality and a stable fish population. The same
models were used to evaluate the status of the fishery under
both minimal and optimal harvest rates. Optimal conditions
for each fish population are those that maximize yield.
A simple numerical model
Recruitment was modeled with a Beverton–Holt stock–
recruitment relationship between the lake density (fish per
hectare) of spawners (N) and recruits (N1).
(1) NN
N
11
=+
α
αβ(/)
The demographic parameters of the fish population are stock
productivity (αis the maximum recruits per spawner) and
habitat capacity (βis the asymptotic density of progeny pro-
duced with very large spawner densities). Parameters were
varied over an eightfold range in the case of β(50, 100, 200,
and 400 fish·ha–1; Stringer et al. 1980) and a fourfold range
for α(2, 4, 8, and recruits·spawner–1; Myers et al. 1999).
With the addition of catchability (q), harvest mortality can
be incorporated into eq. 1. If angling effort (E, angler-days
per hectare) is constant, harvest rate (HR) is a density-
independent function of qand E.
(2) HR=1–exp(–qE)
Catchability was set at 0.09 ha·angler-day–1 (Cox 2000).
Since HR is, in effect, a density-independent mortality
factor, analytical solutions can be derived for angling quality
and yield as functions of effort at the fished equilibrium.
Equilibrium spawner numbers at the fished equilibrium (Ne)
can be obtained by replacing αand βin eq. 1 with α′ =α(1 –
HR) and β′ =β(1 – HR) and setting N1=N.
(3) Ne=′−′′ββα/
For particular values of α,β, and HR, substituting eq. 3 into
eq. 1 gives recruits at the fished equilibrium (N1e). Yield in
the fishery (Y) is the difference between recruits and spawn-
ers at the fished equilibrium
(4) Y=N1e –Ne
and angling quality (NPUE, fish·angler-day–1) is the ratio of
Yto effort
(5) NPUE = Y/E
Since Yis a function of E,α,β, and q, then equilibrium
NPUE can plotted as a function of E, the demographic param-
eters αand β, and the constant q. The IFD equilibrium for a
given set of demographic parameters occurs where Eis such
that NPUE equals the regional average (2.07 fish·angler-day–1;
Stone 1988). Given E, then Neand Ycan be calculated for
each combination of αand βusing eqs. 1–4.
Spawner densities, yields, and harvest rates under maxi-
mum sustained yield (MSY) conditions can be derived ana-
lytically as functions of αand β(Ricker 1975). Effort at
MSY is derived by substituting the MSY harvest rate into
eq. 3 and MSY angling quality can then be calculated using
eq. 5.
Size-structured demography
The age-structured simulation model runs on an annual
time step that mimics the annual sequence of events for rain-
bow trout in lakes. Rainbow trout spawn in streams where
they rear as juveniles for 0–2 years before migrating to the
lake and growing to adult size (Northcote 1969). Spawning
takes place in May and most of the harvest is taken in May,
June, and July. In the simulation model, all newly emerged
fry enter the lake in July at a size of 2.6 cm at the start of
the annual cycle. Effective density is calculated at this point
from the numbers and lengths of fish in each age-class.
Growth and survival for the coming year are calculated for
each age-class. In May, all fish greater than age 2 mature,
and spawning mortality is applied. Egg production is calcu-
lated using the lengths after growth and the numbers of ma-
ture fish are calculated after size-dependent mortality but
prior to spawning mortality and harvest. Harvest is applied
to the population in each age-class that remains after the ap-
plication of spawning and size-dependent mortality. After
harvest, the remaining fish graduate into the next age-class
and the annual cycle is repeated. Maximum age is 7, which
is implemented as 100% spawning mortality at the end of
the seventh year of life. The number of newly emerged fry is
the product of egg production and egg–fry survival. Egg–fry
survival is assumed to be density independent and covers the
period from just prior to egg deposition to just after the age-
0 fish enter the lake. Stock productivity is varied by assign-
ing a density-independent egg–fry survival that covers an
eightfold range (1%, 2%, 4%, and 8%). Using the model, we
evaluate the status of populations at equilibrium over a range
of stock productivities (analogous to α), habitat capacities
(analogous to β), and effort densities. We compare the status
in terms of fish densities, growth rates, yields to the fishery,
and angling quality for three equilibriums. At the unfished
equilibrium, a minimal effort (0.001 angler-days·ha–1) is used
to establish angling quality. The MSY state is evaluated by
searching for the effort that maximizes biomass yield. The
IFD state is evaluated by searching for the effort that results
in an angling quality equal to that experienced by anglers on
Region 3 lakes.
Density-dependant growth is modeled as a function of ef-
fective density (ΣL2) of the fish in the lake rather than more
conventional measures such as numerical density (ΣL0)or
biomass density (ΣL3). Walters and Post (1993) showed that
the effective density can be used to represent the total de-
mand for food resources by individuals that vary in size.
Using empirical data from lakes that varied in both density
and size structure, Post et al. (1999) demonstrated that effec-
tive density explains a higher proportion of among-lake vari-
ance in growth than either numerical density, which weights
small fish heavily, or biomass density, which weights large
fish heavily.
© 2004 NRC Canada
1660 Can. J. Fish. Aquat. Sci. Vol. 61, 2004
Effective density is used to model density-dependant growth
using Walford plots that represent annual growth with the
equation
(6) Li+1 =a+bLi
where Liis the length at age i,ais the Walford intercept, and
bis the Walford slope. Assuming that competition among
size-classes is symmetrical (i.e., based simply on their ca-
pacity to consume food resources), Walters and Post (1993)
demonstrated that avaries as a linear function of effective
density but bdoes not. The result is that growth can be de-
scribed by a series of parallel lines that correspond to varia-
tions in density (Fig. 1). As density approaches zero, both
growth rate and aapproach a maximum. At very high densi-
ties, aapproaches zero, growth rates are negative, mortality
increases, and density falls. An estimate of b(mean 0.71, SE
036) was obtained from Walford plots of multimesh gillnet
samples of rainbow trout from 34 lakes in southern British
Columbia (B.C. Ministry of Sustainable Resource Manage-
ment, unpublished data, available at http://srmapps.gov.bc.
ca/apps/fidq/). Only a few (three to six) age-classes were
present in each lake and estimates of bfrom individual lakes
were homogeneous (analysis of covariance (ANCOVA), p=
0.087).
If the Walford bis constant, density-dependent growth can
be modeled by expressing the Walford aas a function of ef-
fective density. The relationship between effective density
and the Walford ain eq. 6 was parameterized using a linear
regression (r2= 0.82) fitted through data (Fig. 2) collected
by Post et al. (1999).
(7) a=18.8–2.8×10
–5 ×D
where Dis the effective density (square centimetres per hect-
are) at the start of the year and 18.8 (cm) is the maximum
value of athat is observed at very low densities. The maxi-
mum growth rate (a= 18.8 cm when D= 0) is presumably
controlled by factors such as the genetic characteristics of
the stock and the physical characteristics of the environment
(e.g., temperature) rather than food density. The minimum
observed growth rate (a= 5 cm when density = Dmax)ispre
-
sumably controlled by factors such as the minimum length at
maturity and the minimum length needed to survive the first
winter.
To simulate a range of habitat capacities (analogous to β
in eq. 1), we varied the slope of this relationship (eq. 7). The
rate at which the Walford intercept adeclined with density
(i.e., the slope in eq. 7) was set at four multiples (0.25, 0.5,
1, and 2 times) of the slope (–2.8 × 10–5) estimated from the
data in Fig. 2. The minimum value for a(i.e., the intercept
in eq. 7) is assumed to be constant, which implies that Dmax
is set at 4, 2, 1, and 0.5 times that observed by Post et al.
(1999). The biological interpretation is that, at low habitat
capacity, growth will decline rapidly with density (i.e., Dmax
is small) and at the highest habitat capacity, growth declines
slowly with density (i.e., Dmax is large). When combined
with the stock productivity range described above, this range
of habitat capacity produces densities and size structures that
are within the range observed in natural lake populations of
rainbow trout in southern British Columbia.
Survival is a function of initial length of cohorts of rain-
bow trout and the density of fish in the lake (Fig. 3). Rain-
bow trout from five size groups were stocked in nine experi-
mental lakes that varied in density among lakes and among
years (see Post et al. (1999) for details). The initial size of
cohorts was manipulated through a combination of incuba-
tion temperate and size selection. Mean lengths of the five
groups were 2.6, 3.6, 8.8, 10.4, and 11.9 cm. The range of
lengths within each group was <0.5 cm. In the model, as in
the empirical data, the observed annual survival for fish of
age-class i(Si) declined exponentially with total density of
all age-classes (D) and an exponent (mi) that is related to size.
(8) SS mD
ii i
=−
max exp( )
This relationship was parameterized using annual survival
data for the five size-classes of age-0 and age-1 trout. Maxi-
mum annual survival rates were empirically estimated as a
saturating function of length at the start of the year (Fig. 4a).
(9) SL
Lr
ii
i
max 2
0.49 1.81
1 0.49 1.81) 0.95=−
+−
⎡
⎣
⎢⎤
⎦
⎥=
(,
where Liis the length (centimetres) for fish of age iat the
start of the year fitted to the intercepts of the empirical rela-
tionships between annual survival and initial total density
(Fig. 3) for five size-classes of juvenile trout. The empirical
relationship between the exponent miand Liwas
© 2004 NRC Canada
Parkinson et al. 1661
Fig. 1. Density-dependent growth of lacustrine rainbow trout in
southern British Columbia as represented by Walford plots when
competition among size-classes is symmetric (Walters and Post
1993). The slope (b) of all three lines is 0.71, which represents
the average slope from gillnet samples from 34 local lakes and is
assumed to not vary with effective density (cm2·ha–1). Maximum
growth (thick solid line) represents an extrapolation of the inter-
cept (a) to zero density using the data of Post et al. (1999). At
high densities, the minimum growth (dotted line) is limited by the
minimum size at maturity and the size needed to survive the first
winter. Growth at an effective density of 200 000 cm2·ha–1 (dashed
line) lies between these two extremes. The thin solid line repre-
sents the one-to-one relationship. The asymptotic sizes are 64, 17,
and 45 cm. If all fish are 30 cm long, 200 000 cm2·ha–1 is equiva-
lent to about 220 fish·ha–1 or 68 kg·ha–1.
(10) mi= –3.27 × 10–6 ln(Li)+1.21×10
–5,
r2= 0.94
where the observed mi(Fig. 4b) are again derived from sur-
vival versus density relationships for five size-classes (Fig. 3).
To simulate the effect of different habitat capacities on sur-
vival, the miderived from the empirical data was multiplied
by 0.25, 0.5, 1, or 2. The effect of this is that the density
necessary to depress survival to a given value is 4, 2, 1, or
0.5 times the empirical estimate from eq. 10. The biological
interpretation is that, at low habitat capacity, survival will
decline rapidly with density (i.e., miis large) and at the high-
est habitat capacity, survival declines slowly with density
(i.e., miis small).
A postspawning survival of 30%, with a maximum age of
7, was chosen to match the age distribution in naturally
spawning populations of lightly exploited rainbow trout in
British Columbia. Age at first maturity was assumed to be
constant at 3 years (Cox 2000). Egg production per mature
adult of age i(Fi) was derived data collected by local hatch-
eries.
(11) FLr
ii
=−=exp[ ln( ) ],2.9 10.6 0.92
2
where Liis the length (millimetres).
The harvest process is modeled in a manner similar to that
of Cox and Walters (2002) who analyzed fishing effort, ex-
ploitation, and size-selectivity data from eight rainbow trout
fisheries in lakes in southern British Columbia. Annual an-
gler effort (E, angler-days per hectare) is a driving variable
that is assumed to be constant in a given run. Cox and
Walters (2002) derived a two-parameter fishing mortality
rate (f) function of the form
(12) f=qvE/(2v+qE)
where qis a catchability coefficient and vis the instanta-
neous turnover rate between pools of available and unavail-
able fish. This model attempts to account for the fact that
catch rates in sport fisheries are somewhat dependent on fish
reactivity (i.e., to lures of various types) and the relative dis-
tributions of fish and anglers, both of which change (at rate
v) over short time scales. Equation 12 is thus an instanta-
neous fishing mortality rate, which can be used to compute
the annual exploitation rate for fully vulnerable fish (Umax).
(13) Umax = 1 – exp(f)
Tagging data collected by Cox (2000) indicates that exploi-
tation rate of an age-class (Ui) is a sigmoid function of its
length.
(14) UU L
LL
ii
w
i
ww
=+
⎛
⎝
⎜⎞
⎠
⎟
max
half
where Lhalf is the length at which 50% of age-class ifish are
vulnerable to harvest and wis the steepness of the curve at
© 2004 NRC Canada
1662 Can. J. Fish. Aquat. Sci. Vol. 61, 2004
Fig. 2. Walford intercepts (ain eq. 2) as a function of effective
density calculated from the data of Post et al. (1999). Each data
point represents the growth of a group of age-0 fish. Lengths at
the end of the growing season were estimated directly from field
data. Length at age 1 was calculated by adding an increment that
represented growth between the end of the growing season and
the anniversary of lake entry in early July. This increment was
estimated using a relationship between age-1 growth rate
(mm·month–1) and effective density. The Walford intercept for
each group is calculated assuming a slope (bin eq. 6) of 0.71
and a length at lake entry of 2.6 cm.
Fig. 3. Annual survival of five size-classes of fish as a function
of effective density derived from data collected by Post et al.
(1999). Each data point represents the survival of a group of
age-0 or age-1 fish. Initial lengths of each size-class are 11.9 cm
(solid squares, solid line), 10.4 cm (shaded squares, dark shaded
line), 8.8 cm (open squares, light shaded line), 3.6 cm (solid dia-
monds, dashed line), and 2.6 cm (open diamonds, dotted line).
Lines fitted through each set of points are of the form ln(Si)=
ln(Simax)–miDand have r2values that range from 0.31 to 0.92.
Lhalf. Except for effort, harvest parameter values are those
used by Cox (2000). They are q= 0.09 ha·angler-day–1,v=
1.61·year–1,Lhalf = 20 cm, and w= 8. With these parameters,
the maximum exploitation rate at very high effort levels
(Umax) is 80% (rather than 100%) of the fully vulnerable fish
per year. Over the range capacities and egg–fry survivals
used in the model, maximum yields in the model are less
than the maximum yields (~120 kg·ha–1; B.C. Ministry of
Sustainable Resource Management, unpublished data, avail-
able at http://srmapps.gov.bc.ca/apps/fidq/) observed for lakes
in this region.
In the size-structured simulations, the anglers’ perception
of identical angling quality is defined using an isopleth on a
plot of catch rate versus fish size. To empirically describe
the trade-off that anglers make between average length and
NPUE, we parameterized an isopleth for southern British
Columbia interior rainbow trout lakes using mean length and
NPUE data collected in a variety of creel surveys over the
last 15 years on lakes in Region 3. We excluded three lakes
where the number of interviewed anglers was low (<100 an-
gler-hours) and two lakes that were not directly accessible
by road. Data from winter ice fisheries were also excluded.
The reduced data set from 38 lakes reflects the angling qual-
ity conditions experienced by the population of anglers that
fish lakes in this general area during the ice-free season. If
anglers can move freely among these lakes, IFD theory sug-
gests that a curve fitted through these points can be assumed
to represent an isopleth of equivalent angling quality for
lakes that differ in fish density and size structure. For com-
parison, we have also included data from 15 lakes in British
Columbia Management Region 5.
Results
A simple numerical model
The implications of an effort-driven IFD equilibrium can
be seen in the relationships of angling quality and yield ver-
sus effort (calculated using eqs. 1–5) for three fish popula-
tions that vary in habitat capacity (β) but share a common
stock productivity (α) and catchability (q) (Fig. 5). At a
given level of effort, both angling quality and yield increase
with β. In each case, angling quality declines linearly with
effort and the IFD equilibrium occurs where this line of de-
clining angling quality intersects the regional average an-
gling quality (Fig. 5). It is important to note that there is no
reason to expect that the IFD-driven equilibrium should cor-
respond to the peak of the yield curve (i.e., MSY). The IFD
equilibrium is driven by the angling quality experienced by
individual anglers rather than the total number of fish cap-
tured by all anglers. For high values of β, IFD yields are less
than MSY because high densities of fish attract high levels
of effort, which result in higher than optimal harvest rates
(Fig. 5). For low values of β, IFD yields are also less than
MSY because angling quality is not high enough to attract
the effort necessary to produce MSY. At very low values of
β, effort is expected to be zero, since angling quality at zero
effort is less than the regional average.
Similar results are predicted when both αand βvary.
MSY increases with both αand β, but yield under the IFD
assumption is relatively insensitive to increases in β
(Fig. 6a). Since MSY is by definition a maximum, the IFD
yields are almost always less than MSY (Fig. 6b). However,
this simple model also illustrates that, in many cases, yields
are only a fraction of those possible under optimal manage-
ment control. At low values of αand β, angling quality
(Fig. 6b) is not high enough to attract the amount of effort
necessary to produce maximum yields. Alternatively, when α
and βare high, then angling quality (NPUE) at MSY is
much greater than the regional average, which attracts exces-
© 2004 NRC Canada
Parkinson et al. 1663
Fig. 4. Relationships between (a) maximum annual survival
(Simax) and (b) the rate of change of mortality with density (mi)
and mean initial length as derived from the intercepts and slopes
of relationships in Fig. 3. Each point represents a size group
where annual survival was repeatedly measured across a range of
densities to develop a relationship between initial length and an-
nual survival across a range of densities. In Fig. 4b, the number
of survival estimates for each point is given as n.
sive effort that drives the spawner populations at the IFD
equilibrium below MSY levels. These populations are capa-
ble of sustaining higher yields but do no do so because of
systematic recruitment overfishing.
Angling quality and harvest rates in size-structured
populations
Empirical data on angling quality and effort are consistent
with the prediction, based on IFD theory, that angling qual-
ity should be similar among lakes within a region but higher
on lakes that are farther from population centers. The rela-
tionship between catch rate and fish size is significant but
differs among regions (ANCOVA, p< 0.001) (Fig. 7). Lakes
in Region 5, which are farther from British Columbia’s ma-
jor population center (Greater Vancouver), have a numbers–
size trade-off that is similar in form to Region 3, but with
higher angling quality. The higher angling quality in Region
5 is associated with a lower density of anglers (8 versus 45
angler-days·ha–1·year–1), higher mean depths (9.9 versus
8.5 m), and lower total dissolved solids (167 versus 191 ppm).
Angling quality in Region 3 can be described as a power
function:
(15) NPUE 1 0.70
4.17 2
=× =
−
320 000 Lr
c,
where Lcis the average length of fish in the creel. These pa-
rameters are used to define the IFD equilibrium in the size-
structured model. This relationship suggests that anglers in
Region 3 place a premium on size. When fish are small the
observed NPUE is on average higher and when fish are large
the observed NPUE is on average lower than that predicted
if the numbers–size trade-off was simply proportional to
weight (Fig. 7).
The size-structured population dynamics model produced
stable equilibriums in the unfished (pristine) state over the
full range of habitat capacity and stock productivity. Density
increases with both productivity (egg–fry survival) and ca-
pacity (Dmax) (Fig. 8a). Growth declines with stock produc-
tivity because higher density populations grow slower at a
given lake capacity (Fig. 8b). Growth does not depend on
capacity because the effect of higher densities, at higher
habitat capacity, is exactly balanced by the increases in habi-
© 2004 NRC Canada
1664 Can. J. Fish. Aquat. Sci. Vol. 61, 2004
Fig. 5. Yield (solid lines) and angling quality (broken lines) pre-
dicted from the simple analytical model for three populations
that share a common stock productivity (α= 4 recruits·spawner–1)
and catchability (q= 0.08 ha·angler-day–1) but vary in habitat ca-
pacity (β= 300, 75, and 40 fish·ha–1). For each curve, the IFD
equilibrium yield (open diamonds) and angling quality (solid dia-
monds) have been calculated by assuming that the IFD equilib-
rium point is where angling quality equals the regional average
in British Columbia rainbow trout lakes (2.07 fish·angler-day–1).
Fig. 6. (a) Yield achieved at MSY (solid lines) and at an IFD
equilibrium with a target angling quality of 2.07 fish·angler-day–1
(broken lines) and (b) yield at the IFD equilibrium as a percentage
of MSY (solid lines) and angling quality at MSY (broken lines) as
function of habitat capacity (β). In each case, results for three val-
ues of stock productivity (α= 2, 4, and 8 recruits·spawner–1) are
given with darker lines representing higher values of α.
tat capacity. This outcome results from the direct proportion-
ality between mortality and growth as a function of capacity
in eq. 10.
When linked to the population model, the harvest model
produces stable equilibriums (with constant effort) and an
asymmetrical, dome-shaped yield curve over a range of an-
gler effort (Fig. 9a). The MSY equilibrium (kilograms per
hectare) can be estimated from this curve after using the
relationship in eq. 15 to express yields in standard units to
account for angler preferences for larger fish. Effort levels
that result in an angling quality that lies somewhere on the
equal quality isopleth (Fig. 7; eq. 15) can be used to define
the position of IFD equilibrium (Fig. 9b). The IFD equilib-
rium conditions involve both a biological equilibrium (i.e.,
spawners = recruits) and an angler effort equilibrium be-
cause a lake is assumed to attract effort if angling quality
lies above the angling quality isopleth and lose effort if an-
gling quality is below the isopleth.
The trajectory followed by a hypothetical lake (Dmax =
452 000 cm2·ha–1, egg–fry survival = 2%) under increasing
amounts of effort, expressed in terms of the angling quality
at equilibrium, can be used to illustrate the equilibrium pro-
cess (Fig. 9b). In this case, pristine angling quality consists
of an NPUE of just under 4 fish·angler-day–1 for fish that are
28.6 cm long. With increasing effort, density of fish in the
lake declines and growth rates improve but the average size
of fish is relatively stable because harvest rate is assumed to
be a steep, sigmoid function of fish size (eq. 14). NPUE de-
clines rapidly and sustained effort levels that are greater than
15 angler-days·ha–1 drive angling quality below the equal
quality isopleth. Harvest pressure alone cannot drive the
population to extinction because mortality has been assumed
to be smoothly compensatory and anglers leave the lake if
angling quality falls below the isopleth.
A comparison of equilibrium conditions for three system
states (pristine, MSY, and IFD) over a range of stock pro-
ductivity and habitat capacity suggests that large differences
can be expected for many combinations. As in the simple
numerical model, angling quality under MSY conditions is
most strongly depressed (relative to pristine values) for higher
productivity stocks but is independent of lake capacity
(Fig. 10a). By definition, IFD angling quality is the same on
all lakes but, when expressed as a fraction of pristine quality,
IFD angling quality is depressed at both higher productivity
and higher capacity. High capacity and stock productivity re-
sult in high densities of large fish under pristine conditions.
As a result, pristine angling quality is very high and the dif-
ference between these and the IFD quality (eq. 15) is very
large. IFD quality is often less than MSY quality and, in ex-
treme cases, IFD angling quality is a small fraction of MSY
angling quality.
For many combinations of stock productivity and habitat
capacity, yields under the IFD equilibriums are substantially
less than MSY (Fig. 10b). On low-capacity lakes, yields are
low relative to MSY because angling quality at MSY is less
than IFD angling quality. As a result, harvest pressure on
these lakes at the IFD equilibrium is not high enough to
maximize yield. Furthermore, if pristine angling quality is
below the equal quality isopleth, angler effort should be
close to zero. On lakes with high capacities, angling quality
at MSY is well above the equal quality isopleth. Under IFD
conditions, this higher quality attracts more angler effort,
which depresses spawning populations to below the opti-
mum and results in lower yields because the stock is over-
fished. IFD yields approximate the MSY only when angling
quality at MSY lies close to the equal quality isopleth.
The biological characteristics of the population are also
strongly impacted by the high harvest rates that are needed
to drive the system to the IFD equilibrium. For the highest
lake capacities, growth rates are close to the maximum over
the full range of stock productivities (Fig. 10c). These high
growth rates are the result of severe depressions in spawner
densities to as little as 2% of pristine conditions (Fig. 10d).
In general, overfishing at the IFD equilibrium results in much
larger changes in biological characteristics and angling qual-
ity than those observed in yield.
Discussion
IFD theory predicts patterns in angling quality among lakes
and regions that are similar to those that we observed. Within
a region, most of the variance in catch rate is explained by
differences in fish size and, as a result, angling quality can
be described by an isopleth of NPUE versus fish size. The
position of individual lakes along this numbers–size isopleth
is determined by factors, such as the quality of juvenile hab-
itat, that affect recruitment of trout but are unrelated to an-
gler behavior. In contrast, factors that can be linked to angler
behavior, such as travel time to the lake, are expected to af-
fect angling quality. In our study area, angling quality was
higher in Region 5, which was farther from the major popu-
lation center; even though total dissolved solids and mean
depth suggested that lake productivity of the lakes in this
© 2004 NRC Canada
Parkinson et al. 1665
Fig. 7. Angling quality for 38 lakes in British Columbia Man-
agement Region 3 (triangles) and 15 lakes in British Columbia
Management Region 5 (diamonds). The solid line is the best-fit
power function (NPUE 4.17
=×
−
1 320 000 Lc,r2= 0.70) for the
Region 3 data points. The broken line is a similar power func-
tion fitted to the Region 5 points (r2= 0.58). The shaded line is
the best-fit line though the Region 3 data points that assumes a
constant weight of fish per day on all lakes.
region are about the same as in Region 3. Cox (2000) pre-
sented data on this fishery that are consistent with IFD the-
ory; effort densities were linearly related to stocking density
in both regions but the effort response per fish stocked was
lower in Region 5. The distribution of harvesting effort in
other fisheries is also consistent with the predictions of IFD
theory (Gillis et al. 1993; Swain and Wade 2003). This dy-
namic view of angler behavior contrasts with the static por-
trayal of site selection where angling quality is simply one
of many fixed factors that affect fishing site selection by an-
glers (Hunt and Ditton 1997).
The results of the simple numerical model clearly demon-
strate the implications of IFD angler behavior for spatially
structured fisheries where stock–recruitment parameters vary
among stocks. Variable stock–recruitment parameters imply
that optimum densities, and therefore catch rates, should
vary among stocks. IFD harvesting behavior implies that ac-
tual catch rates, and therefore densities, should be similar,
even among stocks that vary dramatically in optimal densi-
ties. The net result is that stocks are either underfished,
when optimal densities are low, or overfished, when optimal
densities are high. This in turn implies that, even if overall
effort is not excessive, optimum harvest rates on individual
stocks are unlikely to be achieved when anglers are free to
move their harvesting effort among stocks.
The simple model assumes that catchability is constant
with catch rates that are directly proportional to fish density.
Empirical data suggest that catchability depends on both fish
size and density (Cox 2000; Post et al. 2002). Since catch
rate is the key link between recruitment dynamics and harvest
dynamics, the implications of relaxing the constant
catchability assumption need to be tested. The size-
structured model incorporates size- and density-dependent
growth, survival, and catchability with outcomes that are
similar to those of the simple numerical model. This consis-
tency suggests that our conclusions are relatively robust with
respect to model structure.
The process of population regulation in harvested species
has typically been considered in isolation from the dynamics
of the harvesting effort. Biological management models pre-
dict densities and surplus production over a range of harvest
rates, but the role of catch rates in determining the level of
harvesting effort is rarely incorporated into the dynamics of
population regulation. Our model of size-structured trout
populations illustrates the effects of angler effort dynamics
in a system where the biological mechanisms of population
regulation are well documented. An empirical model of the
biology, combined with an assumption of simple IFD angler
behavior, predicts that open access management will rarely
result in optimal populations of rainbow trout in lakes and,
in some cases, densities will be depressed to a small fraction
of pristine values. Lakes that are naturally capable of sup-
porting high densities of large fish are the most likely to ex-
perience severe overfishing but stocks will rarely be driven
to extinction if mortality is assumed to be smoothly compen-
satory. Post et al. (2002) suggested that this may often not be
true and discussed a variety of depensatory mechanisms that
may make it very difficult for fish stocks to recover after be-
ing depressed to very low levels. The focus on high-density,
high-productivity populations contrasts with other threats
that are generally seen to be more severe for small popula-
tions with low productivity (Lande 1993; Caughley and
Gunn 1996).
Another clear prediction is that angler effort densities will
be variable among lakes that vary in either habitat capacity
or stock productivity but that angling quality will be much
more uniform (Cox 2000; Post et al. 2002). Moreover, the
observed variation in angling quality should be predictable
from ancillary variables, such as remoteness, accessibility, or
facilities that reflect attractiveness to anglers, rather than
© 2004 NRC Canada
1666 Can. J. Fish. Aquat. Sci. Vol. 61, 2004
Fig. 8. Variation in (a) numerical density and (b) growth among modeled populations of rainbow trout modeled over a range of stock
productivity (egg–fry survival) and habitat capacities. Lake capacities are 0.5 times (open triangles), 1 times (open diamonds), 2 times
(solid triangles), and 4 times (solid diamonds) the standard capacity derived from the lakes used by Post et al. (1999). These values
represent stable equilibriums under unfished (pristine) conditions.
from characteristics of the lakes that affect the biology of
the population. An exception will be lakes with little or no
effort where angling quality will be lower than for other
lakes. In these cases, angling quality will vary with pristine
fish density and size structure, which are in turn a function
of stock productivity and habitat capacity.
Both of these results can be generalized to a wide variety
of fisheries. The theory behind the dynamics of harvesting
effort has been empirically tested in some fisheries (Holland
and Sutinen 1999) and it is clear that the effort dynamics
play a critical role in determining current densities in many
species. The fact that commercial fisheries with inadequate
regulation have depleted many species to a fraction of their
former abundance is generally recognized (Pauly et al. 2002)
and the role of recreational harvest is now being documented
(Post et al. 2002).
Although the process is general, the quantitative outcomes
should not be. The position of the equal quality isopleth
should vary with the costs of accessing the fishery. In more
remote areas, such as Region 5 versus Region 3, we expect
that the quality isopleth will be displaced away from the ori-
gin. Depletion will be less severe and there will be a greater
likelihood that harvest rates will be close to zero because
pristine angling quality lies below the isopleth. However, in
locations near major population centers, we would predict
severe depletion or even extinction of fish stocks when de-
pensatory mechanisms are present (Post et al. 2002). In gen-
eral terms, we expect that the position of the quality isopleth
will be a function of a variety of factors such as remoteness,
regulations, facilities, and aesthetics as well as preferences
for individual fish species.
The biology of the system will also affect the outcome. In
some species, biomass accumulates in older age-classes un-
der pristine conditions and optimal populations consist of
relatively high densities of large, old fish. If these high-
density populations result in unusually high angling quality,
harvesting effort will increase and deplete the stock. In
Kananaskis Lake, for example, bull trout (Salvelinus con-
fluentus) spawning populations expanded rapidly following
the implementation of catch and release regulations that dra-
matically reduced both the effort and the mortality of cap-
tured fish (Mushens et al. 2001). Kananaskis Lake is less
than a 2-h drive from the large city of Calgary, Alberta, and
bull trout are long-lived salmonids that grow to almost a
metre in length. In general, depletion should be expected to
be more severe in long-lived, slow-growing species, such as
lake trout (Salvelinus namaycush) or walleye (Stizostedion
vitreum), than in short-lived species, such as the rainbow
trout in this study.
We recognize the problems associated with focusing on
the equilibrium when assessing the outcome of a dynamic
process such as angler movements and fish population dy-
namics. Neither of these processes is expected to be particu-
larly stable. Angler effort and distribution will be perturbed
by factors such as the state of the economy, shifting social
values, and changes in access to fishing opportunities. Fish
populations will be affected by annual fluctuations in weather
as well as longer term changes in climate and habitat. As a
result, there is no particular reason to expect a system such
as the one we have modeled to exist in a state of equilib-
rium. However, at least some of the processes involved
strongly favor equilibrium. Anglers clearly use cues such as
new access points, regulation changes, and the experiences
of others to quickly focus in on exceptional angling quality
that results from perturbations (Johnson and Carpenter 1994).
Knowledge of angling quality is not perfect and varies
among individuals. Differences in NPUE can be difficult to
detect but differences in fish size should be more obvious
(Parkinson et al. 1988). However, studious anglers with many
connections in the angling community may be adept at de-
© 2004 NRC Canada
Parkinson et al. 1667
Fig. 9. (a) Yield as a function of effort for a model rainbow trout
population. MSY is the peak of this curve. The arrow indicates
the approximate position of the IFD equilibrium derived in
Fig. 9b.(b) Angling quality (open circles) in a single lake under
increasing amounts of effort. The equal quality isopleth (shaded
line) is from the relationship described by eq. 15. The point where
the two cross is a stable equilibrium driven by angler behavior un-
der an IFD assumption. In both panels, the position of the open
circles indicates effort increments of 10 angler-days·ha–1·year–1.In
both cases, egg–fry survival is 2%, and capacity is the standard
derived from the data of Post et al. (1999).
tecting transient opportunities with better angling. If these
are regular seasonal occurrences, or are predictable from
factors such as weather, we expect rapid response to excep-
tional opportunities.
The implications of IFD angler movement have parallels
with the more familiar mixed-stock fishery problem (Paulik
et al. 1967). In the conventional mixed-stock fisheries, sev-
eral stocks are exploited in a single fishery with a single ex-
ploitation rate. If they differ in stock productivity, optimal
harvest rates will differ among stocks and the combined
yield from all stocks is below MSY. In mixed-stock fisheries
involving IFD angler distribution, a mobile angler popula-
tion holds all stocks at similar population densities. If stock
productivities or maximum densities vary among stocks, then
optimum population densities will differ among stocks and
MSY cannot be achieved without restricting angler move-
ment.
A key reason for the disconnection between sport fish
management and angler dynamics may be the perception
that management can effectively regulate fisheries without
directly controlling angling effort. Biological models are of-
ten designed to provide reference points for the regulatory
process rather than to explore the consequences of ineffec-
tive regulation. A variety of models (e.g., Luecke et al.
1994) have considered the effectiveness of alternative regu-
latory regimes but have not incorporated the dynamics of
angler effort. Catch and release regulation is an effective
conservation measure but pressure to permit harvesting and
nonharvest mortality can both be serious problems when
catch rates are high (Nelson 1998; Post et al. 2003). In some
cases, the simple observation that anglers are less inclined to
fish when catch rates are low has led to the idea that sport
fisheries are “self-regulating”, that is, anglers will leave a
fishery that has been overharvested and thus allow it to re-
© 2004 NRC Canada
1668 Can. J. Fish. Aquat. Sci. Vol. 61, 2004
Fig. 10. (a) Angling quality (fish·h–1) as a fraction of pristine conditions for the MSY (broken line) and the angler-driven IFD states.
(b) Yield (kg·ha–1) under the IFD state as a fraction of MSY. (c) Growth in the pristine (dotted line) and IFD states. (d) Spawner den-
sity relative to pristine under the IFD and MSY (broken line) modeled over a range of stock productivity (egg–fry survival) and habitat
capacities. In all cases, solid lines represent IFD equilibriums. Lake capacities are 0.5 times (open triangles), 1 times (open diamonds),
2 times (solid triangles), and 4 times (solid diamonds) the standard capacity derived from the lakes used by Post et al. (1999). Angling
quality is expressed in terms of catch rates of standard-sized fish (~30 cm). Both IFD and MSY yields are expressed in terms of kg
30-cm fish·ha–1. MSY yields, pristine growth rates, and MSY spawner densities do not vary with lake capacity.
cover (Hansen et al. 2000). Our results suggest that sport
fishery management should be refocused onto strategies that
deal with the negative consequences of unrestricted growth
and movement of effort.
Acknowledgements
Thanks to the staff at the Fraser Valley Trout Hatchery for
assistance in the field and for accommodating our unusual fish-
rearing and stocking requirements. Thanks to Tom Johnston for
his helpful comments. We especially thank Carl Walters whose
ideas formed the foundation of this work and who is still “The
Old Man” that we all look to for inspiration. We sincerely ap-
preciate the efforts of an anonymous reviewer who made many
suggestions that improved the organization of the paper. This
research was supported by the Government of British Colum-
bia and by Natural Sciences and Engineering Research Council
of Canada strategic and operating grants to J.R.P.
References
Barrowman, N.J., and Myers, R.A. 2000. Still more spawner–
recruitment curves: the hockey stick and its generalizations.
Can. J. Fish. Aquat. Sci. 57: 665–676.
Billings, S.J. 1989. Steelhead harvest analysis, 1987–88. Prov. BC
Fish. Tech. Circ. 85.
Caughley, G., and Gunn, A. 1996. Conservation biology in theory
and practice. Blackwell Science, Cambridge, Mass.
Cox, S.P. 2000. Angling quality, effort response, and exploitation in
recreational fisheries: field and modeling studies on British Co-
lumbia rainbow trout (Oncorhynchus mykiss) lakes. Ph.D. thesis,
The University of British Columbia, Vancouver, B.C.
Cox, S.P., and Walters, C.J. 2002. Modeling exploitation in recre-
ational fisheries and implications for effort management on Brit-
ish Columbia rainbow trout lakes. N. Am. J. Fish. Manag. 22:
21–34.
Cox, S.P., Beard, T.D., and Walters, C.J. 2002. Harvest control in
open-access sport fisheries: hot rod or asleep at the reel? Bull.
Mar. Sci. 70: 749–761.
DeVoretz, D., and Schwindt, R. 1985. Harvesting Canadian fish and
rents: a partial review of the report of the Commission on Cana-
dian Pacific Fisheries Policy. Mar. Resour. Econ. 1: 347–367.
Gillis, D.M., Peterman, R.M., and Tyler, A.V. 1993. Movement dy-
namics in a fishery: application of the ideal free distribution to
spatial allocation of effort. Can. J. Fish. Aquat. Sci. 50: 323–333.
Gordon, H.S. 1954. The economic theory of a common property
resource: the fishery. J. Pol. Econ. 62: 124–142.
Hansen, M.J., Beard, T.D., Jr., and Hewett, S.W. 2000. Catch rates
and catchability of walleyes in angling and spearing fisheries in
northern Wisconsin lakes. N. Am. J. Fish. Manag. 20: 109–118.
Hilborn, R. 1985. Fleet dynamics and individual variation: why
some people catch more fish than others. Can. J. Fish. Aquat.
Sci. 42: 2–13.
Hilborn, R., and Walters, C.J. 1992 Quantitative fisheries stock as-
sessment. Chapman and Hall, New York.
Holland, D.S., and Sutinen, J.G. 1999. An empirical model of fleet
dynamics in New England trawl fisheries. Can. J. Fish. Aquat.
Sci. 56: 253–264.
Hunt, K.M., and Ditton, R.B. 1997. The social context of site selec-
tion for freshwater fishing. N. Am. J. Fish. Manag. 17: 331–338.
Johnson, B.M., and Carpenter, S.R. 1994. Functional and numeri-
cal responses: a framework for fish–angler interactions? Ecol.
Appl. 4: 808–821.
Lande, R. 1993. Risks of population extinction from demographic
and environmental stochasticity and random catastrophes. Am.
Nat. 142: 911–927.
Larkin, P.A. 1954. Introductions of the Kamloops trout in British
Columbia lakes. Can. Fish Cult. 16: 1–10.
Levin, P.S., Tolimieri, N., Nicklin, M., and Sale, P.F. 2000. Inte-
grating individual behavior and population ecology: the poten-
tial for habitat-dependent population regulation in a reef fish.
Behav. Ecol. 11: 565–571.
Ludwig, D., Hilborn, R., and Walters, C. 1993. Uncertainty, re-
source exploitation, and conservation: lessons from history. Sci-
ence (Wash., DC), 260: 17.
Luecke, C., Edwards, T.C., Jr., Wengert, M.W., Jr., Brayton, S., and
Schneidervin, R. 1994. Simulated changes in lake trout yield,
trophies, and forage consumption under various slot limits. N.
Am. J. Fish. Manag. 14: 14–21.
Mushens, C.J., Post, J.R., Stelfox, J.D., and Paul, A.J. 2001. Dy-
namics of an adfluvial bull trout population following the imple-
mentation of catch-and-release only regulations. In Bull Trout II
Conference Proceedings, 17–20 November 1999, Canmore, Al-
berta. Edited by M.K. Brewin, A.J. Paul, and M. Monita. Trout
Unlimited, Calgary, Alta. pp. 77–78.
Myers, R.A., Bowen, K.G., and Barrowman, N.J. 1999. Maximum
reproductive rate of fish at low population sizes. Can. J. Fish.
Aquat. Sci. 56: 2404–2419.
Nelson, K.L. 1998. Catch-and-release mortality of striped bass in
the Roanoke River, North Carolina. N. Am. J. Fish. Manag. 18:
25–30.
Northcote, T.G. 1969. Patterns and mechanisms in the lakeward
migratory behaviour of juvenile trout. In Symposium on Salmon
and Trout in Streams. Edited by T.G. Northcote. Institute of
Fisheries, The University of British Columbia, Vancouver, B.C.
pp. 183–204.
Northcote, T.G., and Larkin, P.A. 1956. Indices of productivity in
British Columbia Lakes. J. Fish. Res. Board Can. 13: 515–540.
Parkinson, E.A., Berkowitz, J., and Bull, C.J. 1988. Sample size re-
quirements for detecting changes in some fisheries statistics from
small trout lakes. N. Am. J. Fish. Manag. 8: 181–190.
Paulik, G.J., Hourston, A.S., and Larkin, P.A. 1967. Exploitation of
multiple stocks by a common fishery. J. Fish. Res. Board Can.
24: 2527–2537.
Pauly, D., Christensen, V., Guenette, S., Pitcher, T.J., Sumaila,
U.R., Walters, C.J., Watson, R., and Zeller, D. 2002. Towards
sustainability in world fisheries. Nature (Lond.), 418: 689–695.
Peterson, J.T., and Evans, J.W. 2003. Quantitative decision analysis
for sport fisheries management. Fisheries, 28: 10–21.
Post, J.R., Parkinson, E.A., and Johnston, N.T. 1999. Density-
dependent processes in structured fish populations: interaction
strengths in whole-lake experiments. Ecol. Monogr. 69: 155–175.
Post, J.R., Sullivan, M., Cox, S., Lester, N.P., Walters, C.J., Parkin-
son, E.A., Paul, A.J., Jackson, L., and Shuter, B.J. 2002. Can-
ada’s recreational fisheries: the invisible collapse. Fisheries, 27:
6–17.
Post, J.R., Mushens, C.J., Paul, A.J., and Sullivan, M. 2003. Assess-
ment of alternative management strategies for sustaining recre-
ational fisheries: model development and application to bull trout,
Salvelinus confluentus. N. Am. J. Fish. Manag. 23: 22–34.
Ricker, W.E. 1975. Computation and interpretation of biological sta-
tistics of fish populations. Bull. Fish. Res. Board Can. No. 191.
Shuter, B.J., Jones, M.L., Korver, R.M., and Lester, N.P. 1998. A
general, life history based model for regional management of
fish stocks: the inland lake trout (Salvelinus namaycush) fisher-
ies of Ontario. Can. J. Fish. Aquat. Sci. 55: 2161–2177.
© 2004 NRC Canada
Parkinson et al. 1669
Stone, M. 1988. British Columbia freshwater results of the 1985
National Survey of Sport Fishing. Prov. BC Fish. Tech. Circ. 79.
Stringer, G.E., Tautz, A.F., Halsey, T.G., and Houston, C. 1980. Fur-
ther development and testing of a lake stocking formula for rain-
bow trout in British Columbia. Prov. BC Fish. Manag. Rep. 75.
Swain, D.P., and Wade, E.J. 2003. Spatial distribution of catch and
effort in a fishery for snow crab (Chionoecetes opilio): tests of
predictions of the ideal free distribution. Can. J. Fish. Aquat.
Sci. 60: 897–909.
Walters, C.J., and Post, J.R. 1993. Density-dependent growth and
competitive asymmetries in size-structured fish populations: a
theoretical model and recommendations for field experiments.
Trans. Am. Fish. Soc. 122: 34–45.
© 2004 NRC Canada
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