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BIOLOGICAL REFERENCE POINTS FOR MANAGEMENT OF WALLEYE (Sander vitreus) FISHERIES
Nigel P. Lester, Harkness Laboratory of Fisheries Research, Ontario Ministry
of Natural Resources, 300 Water St.,
Peterborough, Ontario K9J 8M5, Canada, nigel.lester@mnr.gov.on.ca, and George
Morgan, Cooperative Freshwater
Ecology Unit, Department of Biology, Laurentian University, 1222 Ramsey Lake
Rd., Sudbury, Ontario P3E 2C6,
Canada.
Introduction. Walleye (Sander vitreus), the rmost
popular sport fish in Ontario, are known to inhabit
approximately  4000  lakes  in  the   province.
Management of this dispersed fishery is difficult
because it is not economically feasible to monitor
each lake.  A practical alternative is a sampling
approach in which data from a statistical sample of
lakes are used to evaluate the state of the resource
and decide whether a change in fishing regulations is
needed to protect walleye from over-exploitation
(Lester et al. 2003). This judgement requires that
indicators from each lake be compared to reference
values that specify the maximum (or minimum) level
that must be sustained to safeguard the long-term
productivity of a stock. These reference values,
known as Biological Reference Points (BRP), are
expected to vary among lakes depending on
environmental characteristics that affect walleye
carrying capacity and maximum intrinsic rate of
increase.   This paper describes a method of
establishing MSY-based reference levels of total
mortality rate and stock biomass for walleye. These
reference points are interpreted as upper (mortality)
and lower (biomass) limits.
Methods. We used the classical Graham-Schaefer
model of surplus production (Quinn and Deriso 1999)
as a basis for calculating reference points. This
model implies that as fishing mortality rate. (F)
increases from zero, the equilibrium biomass (B) of a
stock decreases linearly, starting at B.. (i.e., carrying
capacity) and reaching zero when F = Fes, (i.e.,
maximum intrinsic rate of increase). Because yield
equals F * B, this relationship produces a dome
shaped yield curve with a maximum sustainable yield
(MSY) described as
MSY = Fmsy Bm,,
where Fmjy = Fexi/2 and B,,sy = B.12.
To estimate Fea we used a life history based
model (Lester and Shuter in prep.) that assumes
density-dependent  growth  and   an   optimum
reproductive schedule (i.e., the age of maturation and
the investment in egg production maximizes net
reproductive  rate).  That model predicts the
relationship between Fox,, M (natural mortality rate)
and the degree of growth compensation (h,/ho) is:
M                   -h
where ho is growth rate (cm/yr) of the unexploited
population (F = 0) , hi is growth rate of heavily
exploited population (i.e., F = Fex,), L, is the size of a
fish when it is recruited into the fishery. This model
also implied, for walleye, M = hd(20 + 0.4ho).
Observed variation in growth rate, combined with
results from bioenergetics models, implied that ho is
higher in warmer climates: ho = 5.63 (G - 0.7)0.67,
where G is growing degree days above 5"C x 10-3,
and that maximum growth rate (h,) is approximately
2.5 times the unexploited rate. Assuming hho = 2.5
and L4=30 cm, we calculated M and Fex,, for climatic
conditions that span the province of Ontario.  A
reference point for total mortality rate was then
calculated as: Z4., = M + FI,/2.
We calculated the expected walleye biomass
at MSY as Bmy =  MSY/FmS3 , in which MSY was
calculated from an empirical formula (Lester et al.
2002):
MSY = 1.70 H093 TDS042 G' 86
Area
where TDS is total dissolved solids (mg/l) and and H
is average daily thermal-optical habitat area available
for walleye during the summer (ha). H is calculated
as
H = Area PT zele
where PT is area of the lake shallower than the
thermocline,  Zrel is  relative  Secchi  depth:
Zrei =              z- _  Za.. is effective maximum
depth (i.e., maximum depth of the lake or depth of
the thermocline if the lake is thermally stratified) and
s is a basin shape parameter typically having a value
near 1.
Results. Our model indicates that Fa,, is
approximately 1.6 times M when the growth
compensation ratio is 2.5, implying that Zmsy is
approximately 2.6 times M (Figure 1). Across a
climatic gradient of 1000 to 2400 GDD, M ranges
from 0.12 to 0.34 and Z,,,y, ranges from 0.34 to 0.85.
The implied exploitation rate at MSY ranges from
20% to 40%.
Biomass at MSY depends on water clarity
relative to lake depth, as well as nutrient levels.
Examples in Figure 2 illustrate that B,.,), is very
sensitive to water clarity, reaching maximum values
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