310 
Fishery Bulletin 113(3) 
The assumption of a gamma distribution of F cur may 
be the reason for increasing risks of exceeding F m ax 
when fpcur lies between 5% and 200%. When £R cur was 
50% or less, the gamma distribution of F cur resembled 
the normal distribution with density highly concentrat- 
ed around its mean. Because F max (0.151) was much 
larger than F cur (0.120), the area of the distribution of 
F cur that exceeded F max became smaller and smaller as 
fpcur decreased, resulting in lower risks. 
Asymmetry in the sensitivities of reference points 
The responses of the means and SDs of 4 Fbrp s to the 
changes in the means of M or K showed disproportion- 
ate increases, indicating that the means and SDs of 
FrrPs were more sensitive to over-specification. This 
accelerating trend, arising from the nonlinear relation- 
ship between these parameters and Frrp s (Schnute 
and Richards, 1998), indicates that under the same 
degree of misspecification (e.g., 50%) an over-specified 
mean of M or K could result in seriously overestimated 
values of Frrp s . Consequently, the risks of overfish- 
ing would be underestimated, potentially leading to 
overexploitation. 
In summary, bias in life history parameters, such 
as M, F cur , K, and L <*,, resulted in considerable changes 
in the means and SDs of 4 selected Frrp s : F max , Fq i, 
F%q%, and F 50 %. Different degrees of the imprecision 
in the life history parameters did not affect the means 
of Fbrp s but substantially influenced their SDs. Over- 
specification of the mean of M and K led to larger val- 
ues of RC in the means and SDs of Frrp s than did 
under-specification of the means of M and K. 
The composite risks of F cur exceeding these 4 Frrp s 
were affected mainly by bias in the life history pa- 
rameters rather than by their imprecision. Both bias 
and imprecision in F cur played crucial roles in deter- 
mining the risks of F cur exceeding these 4 Frrp s . The 
variation in growth curves and length-weight rela- 
tionships did not affect results of the per-recruit mod- 
els. Our results agreed with those of previous studies 
without consideration of parameter uncertainty, indi- 
cating that they can apply to YPR and SPR models 
for other species. We recommend 1 ) minimizing the 
bias in the life history parameters, especially bias in 
M, K , and F cur , and 2) maximizing the precision in 
F cur as the most relevant approaches for development 
of correct estimates of Fbrp s and determining risks of 
overfishing. 
Acknowledgments 
This study is financially supported by the Aims to Top 
University Project, National Taiwan University. We 
are thankful to A. Punt, School of Aquatic and Fish- 
ery Sciences, University of Washington, for providing 
comments on the early draft, B. Jessop, Department of 
Fisheries and Oceans, Bedford Institute of Oceanogra- 
phy, for providing both scientific and grammatical com- 
ments on the manuscript, and to anonymous reviewers 
for their suggestions. 
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