He et al. : Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models 
201 
Table 2 
Model and parameter specifications in simulation and assessment models used to evaluate interactions between mortality and 
selectivity. Constant natural mortality (M=0.15) is used in all runs except runs 14 and 16. A normal prior is used as h prior. 
Selectivity 
Run no. 
No. of 
simulations 
True 
selectivity 
function 
used in 
assessment 
h prior 
in 
assessment 
True M in 
simulation 
M estimated 
in 
assessment model 
1 
3000 
Logistic 
Logistic 
Yes 
Constant 
No 
2 
500 
Logistic 
Logistic 
Yes 
High M in juvenile and old fish 
No 
3 
500 
Double normal 
Double normal 
Yes 
Constant 
No 
4 
500 
Double normal 
Double normal 
Yes 
High M in juvenile and old fish 
No 
5 
500 
Logistic 
Double normal 
Yes 
Constant 
No 
6 
500 
Logistic 
Double normal 
Yes 
High M in juvenile and old fish 
No 
7 
500 
Double normal 
Logistic 
Yes 
Constant 
No 
8 
500 
Double normal 
Logistic 
Yes 
High M in juvenile and old fish 
No 
9 
500 
Logistic 
Logistic 
No 
Constant 
No 
10 
500 
Logistic 
Logistic 
No 
High M in juvenile and old fish 
No 
11 
500 
Double normal 
Double normal 
No 
Constant 
No 
12 
500 
Double normal 
Double normal 
No 
High M in juvenile and old fish 
No 
13 
500 
Logistic 
Logistic 
No 
Constant 
Yes (1 parameter) 
14 
500 
Logistic 
Logistic 
No 
High M in juvenile and old fish 
Yes (4 parameters) 
15 
500 
Double normal 
Double normal 
No 
Constant 
Yes (1 parameter) 
16 
500 
Double normal 
Double normal 
No 
High M in juvenile and old fish 
Yes (4 parameters) 
estimation except for spawner-recruit steepness 
(h), in which case h = 0.6 and a normal prior with 
standard deviation (SD)=0.1 was either used (runs 
1-8), or not used (runs 9-16) in the assessment 
models. 
Comparisons of simulation and assessment results 
For evaluating each simulation scenario (Table 
2), the simulation was repeated 500 times and 
the simulated data from each run were input- 
ted into the SS3 model. A successful assessment 
model run was then achieved if the value of the 
maximum gradient component was less than 0.05. 
If an assessment model run did not converge, 
that realization was flagged as a failed run and 
a new set of data was generated from the operat- 
ing model. 
Assessment model outputs were compared with 
known quantities from the simulation model for a 
subset of key assessment results. These included 
1) a time series of spawning output; 2) estimated 
stock-recruitment parameters; 3) terminal stock 
depletion; 4) the overfishing limit (OFL); and 5) 
catchability coefficients. The OFL is a recently 
developed reference point used in the United 
States and is defined as the catch available from the 
estimated terminal biomass if fished at F MSY . For each 
comparison between the simulation and assessment 
models, a discrepancy statistic was computed. For four 
Age (year) 
Figure 1 
Patterns of natural mortality by age used in simulation models 
to evaluate interactions between mortality and selectivity. 
Ml has constant M by age, and M2 has higher M values in 
juvenile and old fish. 
quantities, i.e., virgin spawning output (B 0 ), virgin re- 
cruitment iR 0 ), stock depletion, and OFL, the relative 
discrepancy (S % ) was computed as a percent deviation 
from the simulation model: 
