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surveys. In this case there is no logical way within the 
estimation model to identify these poorly estimated pa- 
rameters. In cases where survey indices are derived to 
measure absolute population abundances, catchability 
coefficients for these survey indices could be estimated 
to be greater than unity because of misspecified natural 
mortality. 
The best to model selectivity in stock assessment 
models poses great challenges. This is especially true 
in modeling the selectivity of old fish. That is, one must 
decide if asymptotic (i.e., logistic) or dome-shaped (i.e., 
double normal) selectivity should be used. In most cas- 
es, no field or experimental data exist to support the 
choice of which form of selectivity is appropriate. As 
shown in this study, decreased selectivity in old fish 
can erroneously be attributed to increased natural mor- 
tality in old fish, and stock assessment models cannot 
resolve this error. In addition, the available sampling 
data for old fish in either age or length compositions 
are typically rare and render the estimation of the 
descending portions of selectivity curves imprecise and 
uncertain. Moreover, misspecifications of selectivity for 
old fish can still lead to moderately incorrect estimates 
of population status and management parameters (runs 
7, 8, 11, and 12). Such incorrect estimates can have 
a greater effect on population status if old fish have 
higher weight-specific fecundity than young spawners, 
as is the case in many rockfish species along the U.S. 
west coast (Dick, 2009). 
Double normal selectivity has been widely used in 
recent stock assessments where the SS3 program was 
used. It has six parameters and is a very flexible selec- 
tivity function that can model a wide range of shapes 
for fishery selectivity (Methot, 2009a). Our study shows 
that double normal selectivity can sometimes lead to 
“unstable” estimations in stock assessment models. That 
is, the model may fail to converge properly, even in the 
absence of model specification error (runs 3 to 6, and 
runs 11 and 12). In the case of run 3, in which double 
normal selectivity is used in both the simulation and 
the assessment model, and natural mortality is also cor- 
rectly specified, model runs succeeded only 86% of the 
time and the MGC criterion was satisfied only 81% of 
the time. This finding further highlights the difficulty 
in estimating the descending portion of a dome-shaped 
selectivity curve and the uncertainty in estimating se- 
lectivity parameters. Unstable descending curves have 
also been observed in some recent west coast groundfish 
assessments, where selectivities for the last age (length) 
group drops to a very small value (He et ah, 2009). Fur- 
ther study on the stability of double normal selectivity 
may be needed to address this issue. 
We also conducted additional runs, in which high 
natural mortalities were simulated only for juvenile 
fish, and only for old fish, but were assumed to be con- 
stant in assessment models. The results showed that 
if high natural mortalities in juvenile fish existed but 
were misspecified in the assessment model, catchability 
coefficients for surveys of juveniles would be estimated 
to be much higher in assessment models (from 2.5 to 3.6 
as compared to the true value of 1.0). Other assessment 
results for runs with high natural mortalities in juve- 
nile fish, however, were very similar to runs presented 
in this paper. If only high natural mortalities for old 
fish existed but were misspecified in the assessment 
model, assessment results would also be very similar 
to those of runs presented in this study with no biases 
in estimates for catchability coefficients for surveys of 
juveniles. This conclusion would indicate that effects of 
misspecifications of natural mortalities for juvenile and 
old fish on assessment results are mostly independent 
of each other. 
Natural mortality has rarely been treated as an esti- 
mable parameter and has often been set as a constant 
in stock assessment models. Our study shows that, 
given informative age composition data, natural mor- 
tality can be estimated if M is constant across ages or 
selectivity is asymptotic. However, if M is high in both 
juvenile and old fish, and selectivity is dome-shaped, 
estimates of M for old fish are very unreliable because 
that parameter strongly interacts with selectivity. Be- 
cause we examined only limited scenarios of data and 
model configurations, further and more detailed studies 
are needed to fully explore the feasibility and benefits 
of estimating natural mortality for fishery stock as- 
sessments. 
Stock assessment models in this study were fitted 
to data from simulation models with known model 
structure and error variance. In all simulation runs, 
the stock-recruitment function variability parameter 
was fixed (S^O. 5) and is relatively small compared to 
that of some stock assessments of the U.S. westcoast 
groundfish (Field et al., 2009; He et al., 2009; Wallace 
and Hamel, 2009). Given that the simulation data were 
much “better” than those available for most stock as- 
sessments, we found that it is still difficult to estimate 
the stock-recruitment relationship. As shown in runs 9 
to 12, in which no priors for steepness (h) were given 
to the model, steepness was often estimated to be near 
or at the upper bound of 1.0 (Fig. 10), as has been 
found in other studies (Magnusson and Hilborn, 2007; 
Haltuch et al., 2008). This finding indicates that it is 
very difficult, if not impossible, to accurately estimate 
stock productivity in practice, where other uncertain- 
ties, such as model structures or lack of recruitment 
surveys, may further confound this issue (Haltuch et 
ah, 2009). Test runs on the simulation and assessment 
models with much longer time periods (300-year runs 
with 200 years of fishing down and data outputs to as- 
sessment models) show that estimates of stock recruit- 
ment relationships were reasonably close to true values. 
But this long period of data collection is generally not 
available for stock assessments. In many previous stud- 
ies, the difficulty in estimating stock recruitment rela- 
tionships has been emphasized, and sufficient biologi- 
cal information and fisheries data, which are lacking 
in many fisheries, are required to achieve reasonable 
estimation for stock recruitment relationships (Myers 
et ah, 1995; Rose et al., 2001; Magnusson and Hilborn, 
2007; Conn et ah, 2010). Further studies on how or if 
