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Fishery Bulletin 11 6(2) 
ment period (Fig. 6, D and E). The medians of the esti¬ 
mates of relative spawning biomass for the eliminated 
data scenario were larger than operating model val¬ 
ues at the start of the management period but became 
smaller than the values as simulated stocks rebuilt to 
target biomass levels and data collection resumed (Fig. 
6F). 
Inclusion of time-varying selectivity resulted in 
the median estimates of the size at maximum selec¬ 
tivity (the earliest size at which selectivity reaches a 
maximum value) across all data scenarios exceeding 
the mean of the operating model values (Fig. 6, J-L), 
although the full data scenario resulted in the low¬ 
est among-simulation variation. The full and reduced 
data scenarios, which were allowed to estimate dome¬ 
shaped selectivity (width at maximum selectivity) 
during the recovery period, resulted in highly variable 
among-simulation estimates at the start of the man¬ 
agement period and the variability for the estimates 
decreased earlier for the full data scenario (Fig. 6, M 
and N). 
Compared with the case with time-invariant pa¬ 
rameters, the RMSE was higher for all data scenarios 
when time-varying parameters were present within the 
operating model (Fig. 4). The RMSE for the estimated 
spawning biomass for the full data scenario was lower 
than that of the other scenarios for the entire man¬ 
agement period (Fig. 4B). Similar to the time-invariant 
results, the RMSE of spawning biomass for the elimi¬ 
nated data scenario was the highest between the sce¬ 
narios across the entire management period, peaking 
in assessment year 68 at 221% (a single simulation for 
the eliminated data scenario, with extreme outliers for 
2 assessment years, was removed for a more informa¬ 
tive summary of the RMSE). 
The time-varying results for the eliminated data sce¬ 
nario were qualitatively similar to those for the time- 
invariant case, in which stocks were not projected by 
the estimation method to be rebuilt for a large number 
of simulations (32 simulations). As was observed in the 
time-invariant case, the simulations with time-varying 
parameters and stocks projected to fail to rebuild bio¬ 
mass had median estimates of spawning biomass and 
relative spawning biomass below the operating model 
values at the time of the first assessment, which were 
driven by estimates of steepness that were consider¬ 
ably lower than the true value (not shown). 
The inclusion of time-varying parameters in the op¬ 
erating model resulted in shorter median estimated re¬ 
covery times in relation to the time-invariant case for 
the full and reduced data scenarios (Table 2). However, 
the median number of years to rebuild for stocks in the 
operating model were similar between the time-varying 
and time-invariant cases. The estimation method pro¬ 
duced earlier recovery times for the time-varying case 
because of the increased variability in the estimates of 
relative spawning biomass and resulted in the estima¬ 
tion method having an increased frequency of errone¬ 
ous estimation of the biomass to be above the target 
stock size (Fig. 3, D-F, versus Fig. 6, D-F). 
The eliminated data scenario had the highest me¬ 
dian average catch during the recovery period because 
of the subset of simulated stocks that were estimated 
to be less depleted than the population in the operating 
model, resulting in more aggressive catch estimates 
from the estimation method (Table 3; Fig. 6, D-F). Ad¬ 
ditionally, the eliminated data scenario had the low¬ 
est median AAV during the rebuilding period (Table 3). 
The eliminated data scenario also resulted in the high¬ 
est number of simulated stocks that never reached the 
target biomass (Table 2) as a result of incorrect param¬ 
eter estimates at the start of the management period 
that resulted in catch estimates exceeding the harvest 
that would allow rebuilding within the population in 
the operating model (Table 3). 
Estimation performance when survey data are also 
available 
The estimates of spawning biomass (Fig. 7, A-C ) and 
relative spawning biomass (Fig. 7, D and E) for the 
time-invariant case were median unbiased at the time 
of the first assessment in year 50. The addition of a 
survey index and composition data for all data scenari¬ 
os led to less among-simulation variability and reduced 
median bias over the management period in relation to 
the simulations without survey data (Fig. 3, A-F). The 
presence of survey data when fishery data were elimi¬ 
nated (eliminated data scenario) allowed the majority 
of the simulated stocks to be estimated as rebuilt by 
the end of the management period (Fig. 7) compared 
with the large fraction of simulations in which the 
stocks failed to be estimated as rebuilt when only his¬ 
torical data were available from the fishery (Fig. 3). 
Similar to what was observed in the time-invariant 
case, reduced among-simulation variability in the es¬ 
timates of spawning biomass and relative spawning 
biomass (not shown) were observed when the inclusion 
of survey data, in addition to fishery data when time- 
varying parameters were present. 
The full data scenario had the lowest RMSE for rel¬ 
ative spawning biomass during the early portion of the 
management period for both cases (time-invariant and 
time-varying), when the majority of simulations were 
estimated to be rebuilding for both cases (Fig. 8 ). How¬ 
ever, midway through the management period, after a 
majority of the simulated stocks had rebuilt and data 
restrictions were removed, the data scenarios resulted 
in similar RMSEs (Fig. 8). The inclusion of survey data 
for all data scenarios resulted in similar estimates of 
the median number of years required to recover to the 
target biomass, and these estimates were similar to the 
median rebuilding time from the operating model. 
Discussion 
Maintaining fishery data at historical levels during re¬ 
building reduced the variation in estimates for spawn¬ 
ing biomass, relative spawning biomass, and steepness 
