306 
Fishery Bulletin 113(3) 
Table 3 
Mean and standard deviation (SD) per year of 4 fishery-mortality-based 
reference points(FBRPs( — the fishing mortality at which yield per recruit 
is at its maximum (F max ),the fishing mortality at which the increase of 
yield per recruit is only 10 % of the increase of yield per recruit when 
fishing mortality is zero(Fo.i), and the fishing mortality rates at which 
the spawning biomass per recruit (SPR) is 30% and 50% of the SPR 
when fishing mortality is zero(F 30 %and ^ 50 %) — and the composite risks, 
PlFcur^BRPk calculated as percentages, of current fishing mortality, 
F cur ( 0 . 120 /year), exceeding FbrPs after repeating the standard scenario 
1000 times. Numbers in the parentheses provide the ranges of relative 
changes in means and SDs from random Monte Carlo simulation with 
data for female Japanese eel ( Anguilla japonica ) in the Kao-Ping River 
in southern Taiwan. 
Fbrp 
Mean 
SD 
1 max 
Fo.i 
F 3 0% 
F50% 
0.156 (99.95-100.04%) 
0.111 (99.96-100.03%) 
0.129 (99.97-100.03%) 
0.073 (99.97-100.03%) 
1.6xl0- 3 (97.23-103.89%) 
9.2xl0- 4 (97.24-103.90%) 
8.7xl0- 4 (97.32-104.44%) 
4.6xl0- 4 (97.31-104.43%) 
P(F CUT >F max ) 
P(F cut >Fqi) 
P(F cur >F; 30 %) 
P(F cur >F 50 %) 
13.44 
56.44 
35.48 
94.31 
0.47 
0.70 
0.65 
0.32 
Tp = the same statistic of the same Fbrp from 
the standard scenario. 
The sensitivity of an Frrp also has to be distinguished 
from the random variation that results from Monte 
Carlo simulation, namely the variation that results 
from the incorporation of random errors in M, length- 
weight relationship, and maturation process. To under- 
stand the scale of this random variation, the standard 
scenario (scenario 1 , without any biasesor impreci- 
sion in parameters) was repeated 1000 times, produc- 
inglOOO corresponding RC values for the means and 
SDs of Fbrps- The minimum and maximum values of 
RC from these 1000 repetitions of scenario 1 were used 
as the lower and upper limits of random variation from 
the Monte Carlo simulation. The effect of changes in 
the mean or SD of a parameter was considered sig- 
nificant only when its RC is lower than the minimum 
or larger than the maximum RC. All the computations 
and simulations were completed in R, vers. 3.1.0 (R 
Core Team, 2014). 
Results 
Magnitude of the random variation from Monte Carlo 
simulation 
Running the Monte Carlo simulation of the stan- 
dard scenario 1000 times produced RC values for 
the means of F max , Fo.i, F 3 o%,and F^q% that ranged 
from 99.95% to 100.04%, from 99.96% 
to 100.03, from 99.97% to 100.03, and 
from 99.99% to 100.03%, respectively 
(Table 3). The SD values of the Frrp s 
had larger RC values that ranged 
from 97.23% to 103.89% for F max , 
from 97.24% to 103.90% for Fq.i, from 
97.32% to 104.44% for F 3 o%, and from 
97.31% to 104.43% for F 50 %(Table 
3). Therefore, variation of RC within 
0.05% for the mean and within 4.50% 
for the SD of the Fbrp was applied 
as the criterion for significance of ef- 
fects; that is, we considered the effect 
of changing one parameter on the Fbrp 
to be significant when the resultant RC 
was wider than this criterion. 
Sensitivity of reference points from the 
YPR model 
The means of Frrp s from the YPR model, 
namely F max and Fo.i, were sensitive to 
both the means of M and K, which had 
similar trends but different magnitudes 
(Fig. 1, left panels). The RC values for the 
means of F max and Fo.i decreased slowly 
to 75-80% when M and K decreased to 
5%. As M and K increased to 1000%, their 
RC values rose with an accelerating trend, especially for 
F max , to more than 12,000% and 1100%, respectively. 
However, the means of F max and Fq.i were not sensi- 
tive to changes in L „ and £gr because their RC varied 
less than 0.05%. The had marginal effects on the 
mean of F max and Fo.i, given that the RC was around 
100.6% when became 1000% (Fig.l, left panels). The 
SD values of F max and F 0.1 were also sensitive to the 
means of M and K with similar accelerating trends. The 
SD of F max was more sensitive to changes in M and K 
than was the SD of Fq.i (Fig. 1 , right panels). In addi- 
tion, the SD values of F max and Fq.i were nearly related 
linearly to Em- Similar to the means, the SD values of 
F ma x and F 0.1 did not show significant sensitivity to 
and £gr, and their RC values did not exceed the 
significance level of 4.50%. 
Sensitivity of reference points from the SPR model 
The means of Frrp s from the SPR model, F 3 o%, and 
F§o%, were sensitive to the mean of M, but their RC 
values (from 90% to 170%; Fig. 2, left panels) were 
smaller than those of F max and Fo.i- When K decreased 
to 40%, the RC for the mean of F 3 q% and F 5 0 % reached 
a minimum of around 80%. As K increased to 1000%, 
the RC of the means of F 3 o% and F 5 q% increased to 
300% and 400%. They also were affected by L 0 0 such 
that the RC was around 85-125% as L M increased from 
50% to 200%. Neither cm nor £qr affected the means 
of F 30 % and F 5 0 %. The SD values of F 30 % and F 50 % 
showed the highest sensitivity to the mean of M, with 
