204 
Fishery Bulletin 116(2) 
Assessment year 
Figure 8 
The root mean square error (RMSE) when survey data are available during 
rebuilding of a stock for relative spawning biomass in the assessment year 
for each case, (A) time invariant and (B) time varying, and data scenario 
(full data, reduced data, eliminated data). 
samples from multiple data sources can improve esti¬ 
mates of recruitment, spawning biomass, and relative 
spawning biomass (Yin and Sampson, 2004; Wetzel and 
Punt, 2011). 
The median relative errors for the relative spawn¬ 
ing biomass were negative during the rebuilding period 
for the full data scenario and resulted in the estima¬ 
tion method failing to determine whether the popula¬ 
tion in the operating model was at, or above, the tar¬ 
get biomass (median number of rebuilding years was 
greater than those in the operating model, Table 2). 
Failing to correctly determine that the population has 
rebuilt would lead to unwarranted extended harvest, 
a situation to avoid in fishery management. However, 
the reduced estimation variability (within and among 
simulations) offered by the full data scenario resulted 
in an improvement in the consistency of estimates by 
subsequent assessments, offering a level of stability 
for fisheries managers and stakeholders. In contrast, 
the higher between-assessment variation in estimates 
of spawning biomass for the reduced data scenario re¬ 
sulted in simulated stocks being estimated as rebuilt 
when the true population was still below the target 
biomass, a result that could have undesirable outcomes 
for fisheries management. Overly optimistic estimates 
of relative spawning biomass can result in overfishing 
when catch limits are set too high, leading to further 
reductions in biomass and potentially resulting in an 
overfished declaration based on a future assessment. 
Loss of data during rebuilding resulted in a num¬ 
ber of simulations that failed to estimate rebuilding 
because of poor initial estimates of steepness, a key pa¬ 
rameter that controls how quickly a stock can rebuild 
from low biomass levels. In the absence of new data, 
the first and subsequent assessments were entirely 
dependent on the quality of the historical data to in¬ 
form parameter estimates. The simulations that failed 
to correctly detect rebuilt stocks were driven by erro¬ 
neously low estimates of steepness at the time of the 
first assessment. Therefore, initially Identifying a stock 
as less productive than the true population resulted 
in lower estimates of spawning biomass and relative 
spawning biomass, and the assessment predicating 
harvest levels that were well below the true acceptable 
biological catch. The reduced harvest allowed the popu¬ 
lation in the operating model to rebuild to, or above, 
the target biomass. However, in the absence of new 
(and informative) data, the estimation method did not 
detect the correct simulated stock size. The population 
in the operating model had a 2-way trend of abundance 
(decline and increase in biomass) with the fishery data 
available during the fishing down and recovery periods, 
data that previous studies have found informative in 
estimating steepness (Magmisson and Hilborn, 2007; 
Conn et al., 2010). This work showed that a one-way 
trip scenario in stock size with limited data may not 
be adequate to correctly estimate steepness, but the 
inclusion of even limited data can, with a contrast in 
stock size, improve the estimation of steepness even if 
the initial assessment produced a poor estimate (Figs. 
6C and 7). 
The general trend in results when the operating 
model included time-varying natural mortality and 
fishery selectivity was similar to the trend in results 
for the time-invariant case, although the among-sim- 
ulation estimates were more variable across all data 
scenarios. Natural mortality was fixed at a single value 
in the estimation method across all years equal to the 
mean value that was used to generate the autocorre- 
lated annual deviations in the operating model. This 
setup was a strategic choice that allowed variation in 
the composition data that the estimation method would 
not be able to account for, but it was not anticipated to 
result in strongly biased estimates due to model mis- 
specification. The processes that control natural mor¬ 
tality rates in real systems over the life span of an 
