22 
Fishery Bulletin 106(1) 
small loss in potential MSY (negative relative error 
was slight). 
Results of this study are insensitive to the assump- 
tion that fecundity is linearly related to body weight, 
most likely because there are few females remaining 
at ages where curves of fecundity at age and weight 
at age would diverge if £ 2 *3. This finding provides 
support for using spawning biomass as a proxy for 
total egg production, which is reassuring given that 
this assumption is commonplace in assessments. How- 
ever, it does not support the conventional proxy (SO 
unless fertilization rates are nearly constant over a 
wide range of sex ratios. Furthermore, this finding 
does not address whether total egg production itself 
represents reproductive potential adequately. As dis- 
cussed by Murawski et al. (2001), total egg production 
does not include potentially important influences such 
as spawning experience or effects of maternal age and 
size on offspring quality. 
For simplicity, the simulations considered only knife- 
edge selectivity. In some fisheries, selectivity is dome 
shaped, as a result of regulations (e.g., slot limits), gear 
type (e.g., traps), or migration patterns (e.g., if larger 
fish leave the fishing grounds). In protogynous fish, 
dome-shaped selectivity would reduce fishing pressure 
mainly on males. If enough fish can survive the ages 
of full exploitation, dome-shaped selectivity could allow 
the proportion of males to remain sufficiently high to 
avoid severe decline in fertilization success. This effect 
should maintain sex ratio in the range where Sf and S b 
would perform comparatively well. Indeed, this expecta- 
tion was confirmed by additional simulations where we 
repeated our primary analysis but with dome-shaped 
rather than knife-edge selectivity. 
Although this simulation study focuses on protogy- 
nous fish, we expect the results to hold for any stock 
that experiences preferential fishing on males. This may 
occur in gonochoristic stocks, for example, if sexually 
dimorphic growth or spatial segregation renders males 
more vulnerable to fishing gear. 
This investigation was deterministic by design, so that 
error from model misspecification could be isolated. A 
useful extension would be to include other sources of er- 
ror — observation, process, or both. Data sets that incor- 
porate these additional sources could be generated with 
the simulation model, and then fitted with the assess- 
ment model. This type of approach would make it pos- 
sible to evaluate the effect of additional error sources on 
estimates of key population parameters (for example, un- 
fished recruitment [f? 0 ] or steepness [, h ] in the spawner- 
recruit relationship) and on management advice. 
Although S b performs best in general, no measure of 
spawning biomass is best in all cases. One consistent 
finding is that the relative errors of Sf and S b tend to 
have opposite signs over the range of k that we consider 
probable; therefore, the use of St and S b in assessments 
should bound uncertainty in estimates of BRPs. This 
pattern of relative errors tending to have opposite signs 
occurred because Sf never accounts for reduction in 
fertilization success and S b always does. As a result, St 
tends to overestimate the ability of a stock to support 
exploitation, and S b tends to provide more conservative 
reference points. 
This consistent pattern in the relative errors of Sf and 
S b indicates that error in reference points could be re- 
duced by creating a measure of spawning biomass that 
counts both sexes, but with a heavier weight on females 
(the measure S b counted both sexes equally). Alterna- 
tively, error could be reduced by combining estimates 
through model averaging (e.g., Brodziak and Legault, 
2005). Either way, estimates from Sf and S b could be 
used to bound uncertainty in biological reference points 
for managing protogynous fish. 
Acknowledgments 
This work was supported by Marine Fisheries Initia- 
tive Program (MARFIN) grant 04MFIH10. The authors 
are grateful for comments from G. Fitzhugh, C. Porch, 
J. Powers, M. Prager, G. Scott, A. Stephens, and E. 
Williams. 
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