Lin et al.: Sensitivity of models to bias and imprecision in life history parameters 
309 
in significant changes only in the SDs of the 4 
Fbrps examined. Therefore, as indicated in the 
Appendix Figure, the risks of both growth and 
recruitment overfishing were affected more by 
the changes in the mean of Mthan by changes 
in the SD. The bias in M seems to be more im- 
portant than the imprecision in M in influencing 
the risks of overfishing. 
Effects of uncertainty in growth parameters 
The shape of the YPR curve also was altered 
by K (fig. 17.22 in Beverton and Holt, 1957). 
The flattening of the YPR curve with decreas- 
ing K accounts for the accelerating increase in 
the mean and SD of F max . On the other hand, 
Beverton and Holt (1957) found that the changes 
in Woof equivalent to under the same length- 
weight relationship) did not affect the shape of 
the YPR curve. This insensitivity of the YPR 
shape on L«, explains our finding that changes 
in Loo did not affect the mean and SD of F max 
and Fq i or the corresponding risk of growth 
overfishing. 
The peaks in the values of RC in the means 
and SDs of F^q% and F§q% when K and L^were 
around 40-60% possibly resulted from the use 
of a length-dependent maturation curve for an- 
guillids (Davey and Jellyman, 2003) in the cal- 
culation of SPR. In the cases with extremely 
small values of K or the proportion of ma- 
ture eels was close to zero even at the maxi- 
mum age (16 years). A very small part of the 
spawning biomass was lost because of fishing, 
consequently resulting in higher Fqq% and Fqq% 
values. 
Effects of current fishing mortality 
The bias and imprecision in F cur played an im- 
portant role in determining risks of overfishing. 
Greater effects due to changes in the mean of 
F cur on the risks of both growth and recruit- 
ment overfishing were expected because differ- 
ences in the mean played an important part 
in influencing the composite risk, as in the ex- 
ample of 2 standard normal random variables 
(Appdx Fig.). Given the same difference in the 
means, a larger SD leads to lower composite 
risks (Appendix. Figure, panels B and D), ac- 
counting for the observed decreasing risks of 
overfishing with increasing £p cur . Given that 
F C ur is from the gamma distribution, decreas- 
ing composite risks with increasing £p cur also 
resulted in the convergence of 4 risks of over- 
fishing. This finding indicates that a high £p cur 
value may mask the distinction between target 
(usually Fq i or Fqq%) and threshold (F max or 
Fqq%) ^BRPs because the risks of target and 
threshold Fq rp are similar. 
Parameter magnifier (%) 
Figure 3 
The composite risks of overfishing in scenarios 2-6, 8, and 9, 
where the mean and standard deviation (SD) of the natural 
mortality (M and Cm), the von Bertalanffy growth coefficient 
( K ), the asymptotic length (L„), the multiplicative error in the 
growth curve (cgr)- and the mean and SD of current fishing 
mortality (F car and £f ciu ) were under-specified from 5% to 95% 
and over-specified from 150% to 1000% (except forvalues of 
that went from 50% to 200%). The black solid line indicates 
the composite risk of F cur exceeding the fishing mortality at 
which yield per recruit is at its maximum, the black dashed 
line indicates the composite risk of F cur exceeding the fishing 
mortality at which the increase of yield per recruit is only 10% 
of the increase of yield per recruit F=0,and the gray solid and 
dashed lines indicate the composite risk of F cur exceeding the 
fishing mortality rates at which the spawning biomass per re- 
cruit (SPR) is 30% and 50% of the SPR when F= 0. 
