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Fishery Bulletin 113(3) 
Tabte 1 
Formulae, estimates of model parameters, and corresponding simulated random 
errors for the length-weight relationship (a and b are coefficients, and ££,w=the 
corresponding multiplicative error), N=the population size in numbers; von Ber- 
talanffy growth function (K=the growth coefficient (/year), L M =the asymptotic 
length (mm), to=th e theoretical age at length of zero (year), and fGR=the mul- 
tiplicative error of the growth curve), M=the natural mortality (/year); CM=the 
standard deviation of M\ F cur =current fishing mortality (/year); fishing process 
under gear selection (ccq and deselection curve coefficients), and maturation 
process of female Japanese eel ( Anguilla japonica) in the lower reach of the 
Kao-Ping River in southern Taiwan ( /Jq and /h=the maturation curve coefficients, 
and spo and £/ 3 i=the standard error for /?q and Pi, respectively). The means and 
standard deviations of the parameters are from previous studies conducted in 
1998-2006 on life history parameters and the fishery of Japanese eel in the Kao- 
Ping River, Taiwan (Lin and Tzeng 2009, Lin et al. 2010a, 2010b). 
Formula 
Parameter 
Weight at age t, Wit ) 
W(t) = aL(t) b e £LW 
Lit) = LJl -e~ K(t ~ to) ]e eGR 
Population size in number at age t, Nit) 
Nit) — e ^ F(t)+iM+e M )](t-t r ) 
Fishing process under logistic gear selection, Fit) 
Fit) 
x 
e[a 0 +a l Lit)\ 
1 + c[(Xq -f- a 1 Li t )] 
Maturation (silvering) proportion at age t, Sit ) 
[( At +£$))+( Pi+ e ft)L{t)] 
qif \ = _1 
1 _|_ g^^o+ e A>)+(A +£pj)Lit)] 
Others 
Maximum observed age, t max 
Length and age at recruitment, L r , t T 
Length and age at first capture, L c , t c 
a, b = 4.56 x lO- 8 , 3.55 
£LW ~ N(0, 3.93 x 10- 4 ) 
L^,K, t 0 = 1024, 0.12, -0.69 
£ G R~N(0, 3.10x 10- 2 ) 
M = 0.18/year 
£M ~ N(0, 1.98 x 10- 5 ) 
F cur ~ Gamma with mean of 
0.12 and variance of 
1.06 x 10- 2 , a 0 , a 1= -4, 0.02 
P 0 , Pi= -13.31,0.02 
£/) 0 ~ N(0, 1.36) and 
Ep l ~ N(0, 4.04 x 10- 6 ) 
16 years 
55 mm, 0.489 year 
200 mm, 1.15 year 
Four Fbrps were calculated to compare with 
F cur ( 0.120/year, Lin et al., 2010b): F max , the fishing 
mortality at which yield per recruit is at its maximum; 
Fo.i, 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 (King, 2007); and 
FpQ% and Fx,o%, the fishing mortality rates at which the 
SPR is 30% and 50% of the SPR when fishing mortality 
is zero (Goodyear, 1993). 
The reference points F max and Fq i can be regarded 
as boundaries in order to constrain harvesting below 
the level within which the fish population can produce 
maximum sustainable yield (United Nations, 1995), 
and they usually are used as limiting and precaution- 
ary indicators of growth overfishing, respectively; fish- 
ing mortality rates above F max indicate that fish are 
caught before they reach optimal size given the rate of 
natural mortality and their growth rate (Gabriel and 
Mace, 1999; Quinn and Deriso, 1999). Fishing mortali- 
ties at 30% and 50% of SPR, compared with SPR at 
F= 0, are considered to be the limiting and precaution- 
ary levels for anguillid eels (ICES 1 ). Therefore, Fpo% 
and F 50 % were considered the limiting and precaution- 
ary reference points for recruitment overfishing, where 
the spawners are insufficient in numbers to produce 
enough offspring to replace themselves (Sissenwine 
and Shepherd, 1987). 
Incorporation of uncertainties in parameters 
We used Monte Carlo simulation, which has been wide- 
ly applied to other species (e.g., Chen and Wilson, 2002; 
Grabowski and Chen, 2004; Chang et al., 2009; Lin et 
al., 2010a) to incorporate the uncertainties of the pa- 
rameters into the models. In each run, random errors 
for natural mortality (£m) and for coefficients in the 
logistic maturation curve (ep Q and fp 1 ), as well as 
1 ICES (International Council for the Exploration of the Sea). 
2002. Report of the ICES/EIFAC Working Group on Eels. 
ICES Council Meeting (C.M.) Documents 2002/ACFM:03, 55 
p. [Available at website.] 
