Zischke and Griffiths: Stock assessment of Acanthocybium solcndn in the Pacific Ocean 
411 
where At = the change in age; and 
F t = the fishing mortality at age, which is a 
product of fishing mortality and selectiv- 
ity at age for each fishery: 
= = ( 6 ) 
j j 
where S t ,j = the selectivity at age; and 
F j = the fishing mortality of the yth fishery 
(Quinn and Deriso, 1999). 
A recent reproductive study for wahoo off eastern 
Australia reported the FL at which 50% of females are 
mature (L 50 ) as 1046 mm, which corresponds to an 
age at 50% maturity (A 50 ) of approximately 7 months 
(Zischke et ah, 2013a). No estimate of L 50 was report- 
ed for male wahoo; however, as growth parameters do 
not differ significantly between sexes (Zischke et ah, 
2013a), it is assumed to be similar to that of females. 
The maturity-at-length (mp) logistic function reported 
in this study was used to calculate SSB/R (Table 1). 
Wahoo are exploited by multiple fisheries, including 
recreational sport fisheries that often practice catch 
and release; therefore, it is important to account for 
the effect of discard mortality on stock biomass. Dis- 
card mortality is the product of the probability that a 
fish is discarded and the probability that, if released, 
the fish still dies because of the physiological stress 
of capture. Discard mortality at age (H t ) is likely to 
be fishery specific, where the fishing mortality for the 
jth fishery ( F- ) can be expressed with the following 
equation: 
F- = — ln(l — iT t j(l — e~ Ft ’i )), (7) 
where F t j = a product of the fishing mortality at age 
and the selectivity at age (Quinn and De- 
riso, 1999; see Eq. 6 ). 
Postrelease mortality is expensive to evaluate, par- 
ticularly for large oceanic fishes, and there is currently 
no species-specific estimate for wahoo. Two electronic 
tagging studies of wahoo have reported relatively low 
levels of postrelease mortality. Theisen (2007) deployed 
pop-up satellite archival tags on 3 wahoo in the At- 
lantic Ocean, and all fish survived more than 5 days 
after release, a time period that is often used to assess 
postrelease mortality (Domeier et al., 2003; Kerstetter 
and Graves, 2006). In the eastern Pacific Ocean, Sepul- 
veda et al. ( 2011 ) deployed 108 archival tags on wahoo 
caught by using recreational fishing techniques and 
had up to 62% tag recovery in areas with high fishing 
effort. These results indicate that postrelease mortal- 
ity may be relatively low. Similarly, for juvenile bluefin 
tuna (T. thynnus), another scombrid, in the Atlantic 
Ocean, Skomal et al. (2002) reported postrelease mor- 
tality of 28% when recreational fishing techniques were 
used. As such, we assumed the postrelease mortality of 
wahoo from the EC Rec was also 28%. Approximately 
6-38% of wahoo were reported as released by the EC 
Rec (Zischke et al., 2012). Assuming a mean release 
percentage of 20 %, combined with a postrelease mor- 
tality of 28%, the percentage of fish at age t incurring 
mortality in the EC Rec fishery is 86 %, or Hi=0.86. 
Discard mortality may be higher for pelagic long- 
line fisheries because a large proportion of fish are al- 
ready dead once they are hauled onto a vessel (Kerstet- 
ter and Graves, 2008). Observer data from the ETBF 
were investigated to identify the life status of wahoo 
upon hauling — ranging from dead and in rigor mortis 
to alive and vigorous. Less than 10% of wahoo were 
alive (sluggish or vigorous) upon hauling, and only 3% 
of all wahoo were released. As such, it was assumed 
that 100% of longline-caught fish died (H t = 1.0). 
Per-recruit analysis was undertaken by using an 
age-structured virtual population model with 1 -month 
time intervals to capture the variability in the biologi- 
cal dynamics of wahoo (e.g., growth and maturity) that 
occurs primarily within the first year of life (Zischke 
et al., 2013a; Zischke et al., 2013b). To assess the sta- 
tus of the wahoo stock in the study area, F current was 
compared with 2 limit and 2 target reference points. 
From the Y/R analysis, the limit reference point was 
the fishing mortality at which maximum Y/R is pro- 
duced (F max ), and the target reference point was Fo i- 
For the SBB/R analysis, the limit and target reference 
points were defined as the fishing mortality at which 
the SSB/R is 25% of the SSB/R at F= 0 (Fssb 25 ) and as 
F SSB40’ respectively. 
Sensitivity and management simulations 
A sensitivity analysis was conducted to examine the 
effect of variability in growth and maturity estimates 
on Y/R and SSB/R. Rather than use mean biological 
parameters, new parameters were randomly selected 
from a normal distribution defined by the mean and 
standard error for each parameter (Table 1). Randomly 
selected parameters were used in all subsequent calcu- 
lations, including M (Eq.l only), catch-curve analysis, 
selectivity, and the per-recruit analysis. To investigate 
uncertainty in stock assessment outputs under this sce- 
nario (SI), 100 model iterations were conducted. With 
this scenario, M is assumed to be constant throughout 
the life of a fish; however, M has been shown to vary 
ontogenetically in pelagic tunas and may be an order 
of magnitude higher for small fishes (Hampton, 2000). 
To examine variable mortality for wahoo, we also ran a 
scenario (S2) in which natural mortality at age was set 
at an order of magnitude higher for fish 0-2 months old 
and mortality for all other age classes (i.e., >2 months 
old) remained unchanged. 
To assess the efficacy of potential fishery manage- 
ment measures, a number of model scenarios were 
explored with the same iterative approach outlined 
previously. Currently, the only size restriction for wa- 
hoo in any Australian recreational fishery is a mini- 
mum legal length of 75 cm TL in Queensland. Be- 
cause L 50 is considered to be 104.6 cm TL (Zischke et 
al., 2013a), for the first fishery management scenario 
