214 
Fishery Bulletin 109(2) 
science in North America, vol. 31 (R. J. Beamish and 
B. J. Rothschild, eds.), p. 137-165. Fish & Fisheries 
Series, Springer Science, Hoboken, NJ. 
Moustahfid, H., J. S. Link, W. J. Overholtz, and M. C Tyrrell. 
2009. The advantage of explicitly incorporating preda- 
tion mortality into age-structured stock assessment 
models: an application for Atlantic mackerel. ICES 
J. Mar. Sci. 66:445-454. 
Myers, R. A., N. J. Barrowman, J. A. Hutchings, and A. A. 
Rosenberg. 
1995. Population dynamics of exploited fish stocks at 
low population levels. Science 269:1106-1108. 
Myers, R. A., and R. W. Doyle. 
1983. Predicting natural mortality rates and repro- 
duction-mortality trade-offs from fish life history 
data. Can. J. Fish. Aquat. Sci. 40:612-620. 
PFMC (Pacific Fishery Management Council). 
2008. Status of the Pacific coast groundfish fish- 
ery through 2008, stock assessment and fishery evalua- 
tion: stock assessments, STAR panel reports, and rebuild- 
ing analyses, 13 p. [Available from Pacific Fishery 
Management Council, 7700 NE Ambassador Place, Suite 
101, Portland, OR 97220-1384.] 
Punt, A. E. 
2003. Evaluating the efficacy of managing west coast 
groundfish resources through simulation. Fish. Bull. 
101:860-873. 
Punt, A. E. and T. I. Walker. 
1998. Stock assessment and risk analysis for the school 
shark (Galeorhinus galeus) off southern Australia. Mar. 
Freshw. Res. 49:719-731. 
Pauly, D. 
1980. On the interrelationships between natural mor- 
tality, growth parameters, and mean environmental 
temperature in 175 stocks. J. Cons. Int. Explor. Mer 
39:175-192. 
Quinn, T. J., II, and R. B. Deriso. 
1999. Quantitative fish dynamics, 542 p. Oxford Univ. 
Press. New York. 
Roff. D. A. 
1992. The evolution of life histories, 535 p. Chapman 
and Hall, New York. 
Rose, K. A., J. H. Cowan, K. O. Winemiller, R. A. Myers, and R. 
Hilborn. 
2001. Compensatory density dependence in fish popu- 
lations: importance, controversy, understanding and 
prognosis. Fish Fish. 2:293-327. 
Schnute, J. T. and L. J. Richards. 
1995. The influence of error on population estimates 
from catch-age models. Can. J. Fish. Aquat. Sci. 
52:2063-2077. 
Thompson, G. G. 
1994. Confounding of gear selectivity and the natural 
mortality rate in cases where the former is a non- 
monotone function of age. Can. J. Fish. Aquat. Sci. 
51:2654-2664. 
Vetter, E. F. 
1988. Estimation of natural mortality in fish stocks: a 
review. Fish. Bull. 86:25—43. 
Wallace, J. R., and O. S. Hamel. 
2009. Status and future prospects for the darkblotched 
rockfish resources in waters off Washington, Oregon, and 
California as updated in 2009. Status of the Pacific coast 
groundfish through 2009, stock assessment and fishery 
evaluation: stock assessment, STAR panel report, and 
rebuilding analysis, 179 p. [Available from Pacific 
Fishery Management Council, 7700 NE Ambassador 
Place, Suite 101, Portland, OR 97220-1384.] 
Wang, S. P, C. L. Sun, A. E. Punt, and S. Z. Yeh. 
2006. Application of the sex-specific age-structured 
assessment method for swordfish, Xiphias gladius, in 
the North Pacific Ocean. Fish. Res. 84:282-300. 
Worm, B., R. Hilborn, J. K. Baum, T. A. Branch, J. S. Collie, 
C. Costello, M. J. Fogarty, E. A. Fulton, J. A. Hutchings, 
S. Jennings, O. P. Jensen, H. K. Lotze, P. M. Mace, T. R. McCla- 
nahan, C. Minto, S. R. Palumbi, A. M. Parma, D. Ricard, A. A. 
Rosenberg, R. Watson, and D. Zeller. 
2009. Rebuilding global fisheries. Science 325:578-585. 
Yin, Y., and D. B. Sampson. 
2004. Bias and precision of estimates from an age-struc- 
tured stock assessment program in relation to stock 
and data characteristics. N. Am. J. Fish. Manag. 24: 
865-879. 
Appendix: Description of simulation model 
and data errors 
The population is age-structured and is assumed to 
be subject to one fishery with constant selectivity over 
years. There are two survey indices. Recruits vary over 
years and there are sampling errors in surveys, catches, 
and age-composition data. 
where R 0 = initial (virgin) recruitment; 
a min = age of recruitment (minimum age in model); 
a max = maximum age, including age-plus groups; 
and 
M x a = natural mortality for sex x, at age a, which 
is constant across years, and can be con- 
stant or vary by age, depending on the 
model setup. 
Initial condition and cohort growth 
Population dynamics 
Initial conditions of the population are numbers of fish at 
sex x, at age a, and at the first model year (y=0), which 
is given by the equation 
N 
x,0 ,a 
[ 0.5R 0 
|-^x,0,a-l 
-M r „ 
e 
if a — a. 
ifa min <a< 3 *a m ax 
( 1 ) 
The numbers of fish in subsequent years are given by 
the equations 
N = 
0.5 R 
J ’ x,y-\,a-Y~ 
N e~ ( ‘ 
if a = a min 
if a. <a<a , 
“’( 2 ) 
+N xy _ 1 ifa = a n 
