He et at: Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models 
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Table 5 
Estimated natural mortalities (M) with 2.5% and 97.5% quantiles in parentheses for runs 13 to 16. A single M for all ages is 
estimated in runs 13 and 15, and four M values (break points) are estimated in runs 14 and 16. See the Methods section for how 
these four M values were assigned to each age group. 
Run no. 
M : 
m 2 
M, 
m 4 
13 
0.150(0.139, 0.161) 
14 
0.448 (0.377, 0.513) 
0.148 (0.108, 0.193) 
0.147 (0.119, 0.169) 
0.359 (0.321, 0.404) 
15 
0.148 (0.138, 0.163) 
16 
0.285 (0.131, 0.450) 
0.169 (0.068, 0.258) 
0.139 (0.080, 0.225) 
0.074 (0.010, 0.389) 
Age 
Figure 5 
Estimated selectivity functions from simulation (Sim) and stock 
synthesis (SS3) assessment models for run 1. Dashed lines 
are 2.5% and 97.5% quantiles from assessment model outputs. 
assessment models (runs 3 and 4). Population 
depletion, as well as other stock assessment pa- 
rameters, was well estimated if M was constant 
in both simulation and assessment models (run 
3, second row in Fig. 6 and Table 3). The esti- 
mated double normal selectivity functions in the 
assessment model also matched well with that in 
the simulation model (run 3 in Fig. 7). Estimated 
population depletions were also matched reason- 
ably well, even with misspecified natural mortali- 
ties, but the estimated OFL statistics were about 
10% negatively biased (run 4, Table 3). However, 
if natural mortality was higher for younger and 
older age classes in the simulation models but was 
constant in the assessment models, the estimated 
population trajectories were different, with the 
estimated jB 0 biased high (run 4 in Fig. 6; Table 
3). Selectivity functions matched fairly well in the 
ascending limb between the simulation and as- 
sessment models but failed to match the descend- 
ing limb of the selectivity curve (run 4, Fig. 7). 
Convergence of the estimation model was poor in 
this setting. In runs 3 and 4, 86.2% and 78.6% of 
500 SS3 runs finished successfully, respectively, 
whereas only 81.3% and 48.2% of 500 SS3 runs 
produced satisfactory MGC values (Table 4). 
If selectivity functions were logistic in the simulation 
models but were double normal in the assessment mod- 
els and M was correctly specified (runs 5 and 6, Table 
2) , most of the estimated parameters from the stock 
assessment models were close to those in the simulation 
models, generally less than 10% of differences (Table 
3) . However, when natural mortality in the simulation 
model varied, but was assumed constant in the assess- 
ment model, the estimated catchability coefficient for 
the juvenile survey (q 2 ) was positively biased (run 6, 
Table 3). Time series of estimated spawning output 
matched reasonably well (runs 5 and 6, Fig. 6), and 
the estimated selectivity function showed a negative 
bias for old fish (runs 5 and 6, Fig. 7). Convergence 
performance was poor (Table 4); less than 83.3% of 
runs finished and only 53.0% of runs satisfied the MGC 
criterion (Table 5). 
If selectivity functions were double normal in the sim- 
ulation model but were misspecified as logistic functions 
in the estimation model (runs 7 and 8, Table 2), the 
curves fits were very poor, as expected (last row in Fig. 
7 and Table 3). Spawning output was poorly estimated; 
all estimated spawning outputs were lower than those 
in the simulation models in the early years (last row in 
Fig. 6). If natural mortality was incorrectly specified in 
the assessment models (run 8), estimated parameters 
from the stock assessment models were strongly biased 
(Table 3). This bias included high correlations between 
the two stock recruitment parameters (B 0 and /?), and 
positive biases in both catchability coefficients (q l and 
q 2 ) (Table 3). Convergence of the assessment models, 
however, was very good. The percentages of runs finish- 
ing successfully and satisfying the MGC criterion were 
100% (Table 4). 
If no prior for h was used in the assessment models 
and natural mortality was assumed to be constant 
(runs 9 tol2), the results in general were very similar 
to those from runs 1 to 4, where a prior on h was used 
(Figs. 8 and 9; Table 3). However, an important ex- 
