410 
Fishery Bulletin 113(4) 
Table 1 
Means and 95% confidence intervals (Cl) for biological parameters used in the stock assessment of 
wahoo ( Acanthocybium solandri) in the southwest Pacific Ocean during 2008-2010. TL=total length, 
FL=fork length, WB=body weight, VBGF=von Bertalanffy growth function, L t =length at time t, and 
/??L=maturity at length. Length, weight, and VBGF parameters (t M , K, and to) were obtained from 
Zischke et al. (2013b), and maturity parameters were obtained from Zischke et al. (2013a). 
Model 
Equation 
Parameter 
Mean 
95% Cl 
TL (mm) and FL (mm) 
TL = aFL + b 
a 
1.01 
1.00- 
-1.02 
b 
34.97 
26.23- 
-43.71 
Wg (g) and FL(mm) 
LogW# = aLogFL + b 
a 
3.28 
3.20- 
-3.36 
b 
-13.95 
-14.01- 
-13.89 
VBGF 
L t = ZU 1 - e - K <t-t 0 >] 
Leo 
1498.65 
1465.80-1531.50 
K 
1.58 
1.23- 
-1.93 
g -a+bL F 
to 
-0.17 
-0.35- 
-0.01 
Maturity 
a 
-16.98 
-22.25- 
—11.71 
b 
0.02 
0.01- 
-0.02 
where t m - a maximum age of 7 years (Zischke et 
al., 2013b). In the absence of exploitation, it was as- 
sumed that 1% of fish in the population would reach 
t m (Quinn and Deriso, 1999). An estimate of 7 years for 
t m was based on the maximum observed age in a bio- 
logical study in the southwest Pacific Ocean (Zischke et 
al., 2013b). However, because wahoo may reach an age 
greater than that observed in the study by Zischke et 
al. (2013b), and have undergone exploitation by com- 
mercial and recreational fisheries for at least 15 years, 
this estimate should be viewed with caution. 
Age-based catch curves are often used to estimate 
the annual instantaneous mortality rate (Z) according 
to the description of Beverton and Holt (1957). How- 
ever, for tropical species that have fast growth and a 
short lifespan, length-converted catch curves may be 
more useful (Sparre et al., 1989). Therefore, length-fre- 
quency data from the 3 fisheries (i.e., the 2 commercial 
fisheries, ETBF and New Caledonia, and the EC Rec) 
were used to construct length-converted catch curves 
according to the methods of Pauly (1983, 1984a, 1984b). 
Size-frequency data were converted to age-frequency 
data with the von Bertalanffy growth parameters (Ta- 
ble 1; Zischke et al., 2013b). 
Selectivity may differ with fish size or age, as well 
as with different fisheries, especially for those fisheries 
that use different gear types. Total mortality at age 
(ZQ can be expressed in an equilibrium state in this 
way: 
g _|_ g ETBF p ETBF gEC ^ ec ^ ec 
-bS^ ew 
^iNew Cal 
(3) 
where M t = the natural mortality at age t\ and 
S t and F t = the selectivity and fishing mortal- 
ity at age for the ETBF, EC Rec, and New 
Caledonia (New Cal) fisheries, respectively. 
Selectivity at age in each fishery was estimated with 
standard linear length-converted catch curves by us- 
ing backward extrapolation of the descending regres- 
sion line to include younger fish that were likely to 
be under-represented in catches (Sparre et al., 1989). 
All fisheries in this study were hook-and-line fisheries, 
which tend to have selectivity probabilities that follow 
a logistic function because the fishing gear is capable 
of catching any fish larger than the size at which all 
fish are recruited to the fishery (Hovgard and Lassen, 
2000). Therefore, the selectivity (S t ) at age ( t ) in each 
fishery was determined with the following equation: 
9 1 
t l_|_ e a+ bt’ (4) 
where a = the intercept; and 
b = the slope of a linear regression line fitted to 
the observed selection at age (Sparre et al., 
1989). 
Numbers of fish in each age class for each fishery were 
adjusted according to their respective selectivity prob- 
ability before the catch-curve analysis. Given the simi- 
lar selectivity of the 3 fisheries (see Results section), an 
estimate of Z was obtained from the slope of a linear 
regression line fitted to a length-converted catch curve 
for all fisheries combined, and instantaneous F was cal- 
culated as F=Z-M. 
Per-recruit analysis 
The Y/R and SSB/R of wahoo in the southwest Pacific 
Ocean were assessed by using the model of Quinn and 
Deriso (1999). This model defines the age-specific ex- 
ploitation fraction (p*) in this manner: 
At = 
F t (1 c -At(F t +Afn 
F t + M 
(5) 
