268 
Fishery Bulletin 107(3) 
Table 2 
Scenarios designed to examine the effects of uncertainty ofF, M, and t c on the estimates of biological reference points of sailfish 
( Istiophorus platypterus) in the waters off eastern Taiwan. Scenarios A-D were used to evaluate the effects of changes in a single 
parameter, scenarios E-H were used to evaluate the results of changes in combinations of two parameters, and scenarios I and 
J were used to evaluate the results when three parameters were subject to uncertainty. (a F =standard deviation from the boot- 
strapped estimation; M = natural mortality per year; t c = age at first catch) 
Parameters 
o F M 
Scenario 
Female 
Male 
Female 
Male 
t c 
Base 
0 
0 
0.26 
0.27 
5 
A 
0.046 
0.045 
0.26 
0.27 
5 
B 
0 
0 
0. 2-0.3 
CO 
O 
1 
03 
o 
5 
C 
0 
0 
0.15-0.35 
0.15-0.35 
5 
D 
0 
0 
0.26 
0.27 
5-7 
E 
0.046 
0.045 
0.2-0. 3 
0.2-0. 3 
5 
F 
0.046 
0.045 
0.15-0.35 
0.15-0.35 
5 
G 
0 
0 
0.2-0. 3 
0.2-0. 3 
5-7 
H 
0 
0 
0.15-0.35 
0.15-0.35 
5-7 
I 
0.046 
0.045 
0.2-0. 3 
CO 
o 
1 
03 
o 
5-7 
J 
0.046 
0.045 
0.15-0.35 
0.15-0.35 
5-7 
Biological reference points 
The following biological reference points were estimated 
in order to determine the current status of the sailfish 
fishery: F ov F SSB25 , and E SSB40 . F SSB2 5 _ and E SSB40 are 
fishing mortality rates corresponding to the 25% and 
40% of the spawning biomass per recruit at unfished 
level. The choice of 25% or 40% was relatively arbi- 
trary for the fishery, but these values have been used 
as different levels of reference points for other relatively 
long-lived marine fishes (e.g., Griffiths, 1997; Kirchner, 
2001; Sun et al., 2002, 2005). The spawning potential 
ratio {SPR) is the SSB/R at a given fishing mortality 
divided by the SSB/R without fishing (Gabriel et al., 
1989; Goodyear, 1993; Katsukawa et al., 1999; Wata- 
nabe et al., 2000; Sun et al., 2002, 2005) and can be 
calculated as 
SPR = 
SSB/R 
SSB/R\ f 
( 11 ) 
Several authors have advocated designating F 0 1 
or F SSB40 as target reference points and F SSB25 as a 
threshold reference point in order to obtain near op- 
timal yields while minimizing the likelihood of stock 
collapse (Gulland and Boerema, 1973; Deriso, 1987; 
Hilden, 1993; Sun et al., 2002, 2005). We adopted these 
target and threshold reference points in this study. 
quantify the uncertainty of F, F was assumed to follow 
a normal distribution with a mean and standard devia- 
tion (o F ) — the latter estimated from the bootstrapped 
estimation of F. However, there was no information on 
the distribution of M and t c . We assumed a uniform 
distribution for M and t c by referring to the estimation 
of Pauly’s empirical equation and the age at full recruit- 
ment from the age composition of sailfish in the waters 
off eastern Taiwan. The values of M and t c were sampled 
randomly from the corresponding uniform distributions 
defined in Table 2. Ten scenarios were designed to exam- 
ine the effects of different combinations of the uncer- 
tain in parameters F, M, and t c on the estimation of 
biological reference points (Table 2). Scenarios A-D 
were used to evaluate the effects of changes in a single 
parameter, scenarios E-H were used to evaluate the 
results of changes in combinations of two parameters, 
and scenarios I and J were used to evaluate the results 
when three parameters were subject to uncertainty. 
For each scenario, 100 replicates of biological reference 
points were estimated by using the parameters of F, M, 
or t c randomly drawn from their assumed distributions. 
The median and the interquartile range were used to 
quantify the central tendency and variation for the dis- 
tributions of estimated biological reference points. 
Results 
Simulation study 
The Monte Carlo simulation approach was applied to 
evaluate the sensitivity of estimating biological reference 
points with respect to parameters F, M, and t c . To 
Age composition 
Length data were obtained for 12,323 sailfish (3532 
females and 8791 males), and age data for 1166 of these 
