Richard D. Clark, Jr.
Institute for Fisheries Research
Ann Arbor, Michigan
Abstract.-I simulated fluctuating
year-class strength in a brown trout (Salmo trutta) fishery
to estimate how the annual variability in population size and
harvest was affected by exploitation under different minimum size
limits and fishing mortality rates. My model included realistic
details common to many fish populations in temperate regions;
discrete annual reproduction and age-specific natural mortality,
maturity, and fecundity. I hypothesized the primary mechanism
regulating population size was density-dependent mortality in early
life, but also that early mortality had a density-independent component
which varied due to random environmental factors. I proposed a
new method of representing this hypothesis quantitatively and
of interpreting it ecologically. I conducted two series of stochastic
simulations in which random variation was introduced at different
stages of year-class formation. In the first, a range of instantaneous
fishing mortality rates from 0.0 to 2.0 was simulated for 60 years
each while the minimum size limit was held constant at 229 mm.
In the second, a range of minimum size limits from 120 mm to 305
mm was simulated for 60 years each while the instantaneous fishing
mortality rate was held constant at 0.7. Coefficients of variation
(100 s/
) for mean population sizes and harvests were used to compare
relative variability between simulations. I found that the number
of fish in the simulated populations had minimum variability when
exploited near maximum sustainable yield (MSY) in weight, fishing
rates of 0.6 to 1.6 at the 229-mm size limit and size limits of
150 mm to 250 mm at the 0.7 fishing rate. Simulated populations
were highly variable when lightly exploited because the compensatory-density-dependent
response was strong enough to overshoot the population's equilibrium
level after a random disturbance. As exploitation increased, it
reduced the strength of the density-dependent response. Near MSY,
the strength of density dependence was about equal to the strength
of random disturbances, and this minimized variation in population
size. Higher exploitation reduced the strength of density dependence
to where it could not fully compensate for random disturbances,
so variability increased. Variability of harvests did not match
variability of populations because they had different age structures,
a normal consequence of minimum size limit regulations or gear
selectivity. Changing the fishing rate had little effect on variability
of harvest, but changing the size limit from 120 mm to 305 mm
increased the coefficient of variation of harvest from 13% to
44% when the standard deviations of random year-class fluctuations
were 50% of their means. I concluded that for fisheries with fluctuating
year-class strength, variability in annual catch is minimized
by maintaining the lowest practical size limit and managing the
fishery by controlling fishing effort.