Chiang et al.: Analysis of sex-specific spawning biomass per recruit of Istiophorus platypterus in off eastern Taiwan 
267 
where p = the age at the mode of the dome-shaped 
selectivity; and 
ct = the standard deviation of the dome-shaped 
selectivity. 
The expected catch (C t ) of fish at age t can be estimated 
based on the catch equation (Ricker, 1975): 
= ^-NAl-e- (M+FS ‘\ 
M + FS t 1 
(3) 
The parameters of N 0 , F, p, and o can be estimated 
simultaneously by minimizing the following composite 
objective function: 
^ (C t -C t ) 2 + (max(S f )-l) 2 , (4) 
t 
where C t = the observed numbers of catch at age t. 
The F estimated above was considered as the current 
fishing mortality ( F CUR ) in this study. The approach 
outlined above for the catch-curve analysis is similar to 
the one described in Rudershausen et al. (2008). 
A total of 1000 independent bootstrap samples of F 
were derived from 1000 sets of length-frequency data 
drawn randomly with replacement from the individuals 
of original length-frequency data. 
Pauly’s (1980) empirical equation was used to esti- 
mate M for each sex, and the mean sea surface tem- 
perature around eastern Taiwan waters fitted to the 
equation was about 26°C. 
Per-recruit analyses 
Yield per recruit (Y/R) of sailfish in the waters off east- 
ern Taiwan was estimated from the following model: 
Table 1 
Biological parameters used in the per-recruit analysis 
for the sailfish ( Istiophorus platypterus ) in the waters off 
eastern Taiwan during the period from July 1998 to July 
2005. VBGF is the von Bertalanffy growth function, L „ = 
the asymptotic length, K = the growth coefficient, t 0 = 
the hypothetical age at length zero; Length-weight, rela- 
tionship is W = AxL B , where W = rought weight (in kg) 
and L = lower jaw fork length (in cm); Maturity fraction 
parameters r m = the slope of logistic equation fitted to the 
maturity data collected, and t rn = the age at 50% sexual 
maturity. 
Parameter Female Male 
VBGF 
L a 250.29 cm 240.539 cm 
K 0.138/yr 0.145/yr 
t 0 -2.99 -2.781 
Length-weight relationship 
A 2.3234xl0- 6 1. 1933xl0- 5 
B 3.1013 2.7828 
Maturity fraction 
r m 1.525 
The maximum lifespan ( t max ) of sailfish in the waters 
off eastern Taiwan was unknown but was estimated by 
using the empirical relationship of Taylor (1958): 
2.996 
K ' 
( 8 ) 
The equation for spawning stock biomass per recruit 
(SSB/R) is 
Y/ 
/r 
( 
W. x^x[\-e^ M) 
xe 1=0 
, (5) 
where W t - the mean weight of fish at age t\ and 
t c = the age at first capture. 
Mean weight at age was computed as a power function 
of midyear lower jaw fork length (. L t ): 
W t =axL b t , ( 6 ) 
^max 
X 
' t - 1 \ 
fr t xW t xe i=tr 
t=t 
m 
V 
(9) 
where W t = the mean weight at age t that was calcu- 
lated from the von Bertalanffy function 
and length-weight relationship for female 
sailfish; and 
fr = the fraction of female sailfish that are 
mature. 
and midyear lower jaw fork length was estimated from 
the von Bertalanffy growth function 
L t = L„[l-e- K{t+0 - 5 - to) Y (7) 
In this case fr is represented by a logistic equation fitted 
to maturity data collected from sailfish caught in the 
eastern waters off Taiwan (Chiang et al., 2004, 2006). 
The logistic equation can be written as 
where K = the growth parameter; 
= the average asymptotic length; and 
Co = hypothetic age at length of 0 (Ricker, 1975; 
see Table 1). 
where r m 
= the slope of the logistic curve; and 
= age at which 50% of fish are mature. 
(10) 
