Wetzel et al.: The effect of reduced data on monitoring overfished fish stocks 
193 
Full data 
CV=0.30 
Brauamoin^^ 
OdiU 1 
Fishery CPUE 
n = 50 
Fishery lengths 
n =25 
Fishery ages 
Reduced data 
CV=0.30 
CV-0.30 
Fishery CPUE 
Fishery lengths 
Fishery ages 
n = 50 
n=10 
n =50 
n =25 
n =5 
n =25 
Eliminated data 
CV=0.30 
CV=0.30 
Fishery CPUE 
Fishery lengths 
n=50 
n-50 
n =25 
n =25 
Fishery ages 
1 1 
Historical 
1 
Overfished 
1 
Rebuilt 
Time period 
Figure 2 
Summary of the data available for each of the 3 data scenarios (full data, reduced data, 
and eliminated data) created to explore the impact of data availability on the ability to 
monitor rebuilding of an overfished stock of rockfish species: coefficient of variation (CV) 
and number of samples (n) for catch per unit of effort (CPUE), lengths, and ages from the 
fishery. Historical length and age data from the fishery begin in year 35, 15 years before 
the first assessment, and the fishery CPUE data start in year 45. The management period 
begins in year 50 when data quantity and quality change by data scenario. Data quantity 
and quality return to historical levels when the simulated stock has been estimated to be 
rebuilt to the target biomass. Thickness of the horizontal lines reflects the different sample 
sizes; all fishery data are shown in dark gray and catches are shown in black. Catches were 
known without error and were available for all data scenarios. 
cending limb of selectivity curve reached maximum 
selectivity (termed size at maximum selectivity , Fig. 
1C, Fig. 2) the width of the plateau for the maximum 
selectivity (defined as a logistic function between the 
peak and the maximum length bin) that results in a 
dome-shaped selectivity curve (termed width at maxi¬ 
mum selectivity , Fig. ID) during the years the simu¬ 
lated stock was overfished. A standard error of 0.05 
was applied annually for the size at maximum selec¬ 
tivity parameter for all years, and a standard error 
of 0.20 was applied for the width at maximum selec¬ 
tivity parameter during the years the simulated stock 
was estimated to be overfished. The level of variation 
for each parameter was selected to ensure that the 
ascending limb of the selectivity curve was greater 
than the length at 50% maturity (37 cm) within the 
operating model and that the width of maximum se¬ 
lectivity (the parameter that creates the dome-shaped 
curve) was small enough to allow potential detection 
by the estimation method (a portion of the population 
with reduced selectivity that is detected because of a 
dome-shaped curve). Additionally, autocorrelated an¬ 
nual deviations in natural mortality were applied to 
the population within the operating model. 
The operating model was a single-sex, age-struc¬ 
tured model in which an annual index of fishery catch 
per unit of effort (CPUE) was observed with error and 
in which length- and age-composition data were col¬ 
lected for select years. These data were used by the 
estimation method to estimate population size and a 
catch level. The catches were removed without error 
from the simulated stock. Data generation, catch es¬ 
timation, and simulated stock updating were conduct¬ 
ed in an iterative fashion for 100 years (termed the 
management period), a length of time that would allow 
the simulated stock to recover to at least the target 
biomass. 
The operating model 
The numbers-at-age at the start of the year are com¬ 
puted with the following equation: 
