Burton et al . : Age, growth, and mortality of Batistes capr/scus from the southeastern United States 
29 
Growth 
Von Bertalanffy (1938) growth parameters were es- 
timated from the observed length-at-age data. The 
chronological age of the fish was adjusted for the time 
of year caught ( Mo c ), therefore, creating a fractional 
age (Age f) from the chronological age ( Age c ) on the ba- 
sis of a July 1 birth date ( Mo b ): 
Age f = Age c + (( Mo c - Mo b)/ 12). ( 1) 
This birth date was selected on the basis of repro- 
ductive studies that show that peak spawning of gray 
triggerfish occurs during June-July in waters off the 
SEUS (Moore, 2001) and in the GOM (Simmons and 
Szedlmayer, 2012). Parameters were derived with the 
PROC NLIN procedure and the Marquardt option in 
SAS 5 statistical software, vers. 9.3 (SAS Institute, Inc., 
1987). A Student’s t-test (P< 0.05) was used to detect 
if there were significant differences in mean sizes be- 
tween sectors for the purpose of determining whether 
pooling of data across sectors was appropriate. We 
also performed an analysis of covariance (ANCOVA) 
of length-at-age data by sector (recreational versus 
commercial), using age as the covariate, to determine 
whether pooling of data was appropriate (i.e., there 
were no significant differences in length at age by 
sector). 
Weight-length relationships 
We regressed fish whole weight (W, in grams) on fish 
FL (in millimeters, n=20,431) and TL (in millimeters, 
«=7618), using data for all gray triggerfish measured 
by the SRHS from 1972 to 2010 and not just those 
fish sampled for aging structures. Total length was 
not measured for many of the fish, and some fish were 
not weighed. The fish used for age analysis (n=6419) 
were a subset of the total number of gray triggerfish 
measured by the SRHS (rc=20,431). We regressed FL 
on TL (n=8065), also with the SRHS data set. For all 
relationships, we evaluated both a nonlinear fit, using 
nonlinear least squares estimation in SAS software 
(SAS Institute, Inc., 1987), and a linearized fit of the 
log-transformed data, examining the residuals to deter- 
mine which regression was appropriate. 
Total mortality 
Age-length keys (Ricker, 1975) were developed for 25- 
mm intervals by using all aged specimens and the cal- 
culation of the age distribution (measured as a percent- 
age) for each interval. Age frequencies for unagecl fish 
by sector were developed with age-length keys (for aged 
fish) weighted by annual landings from the respective 
sector and length frequencies (for unaged fish); data 
5 Mention of trade names or commercial companies is for iden- 
tification purposes only and does not imply endorsement by 
the National Marine Fisheries Service, NOAA. 
for both the landings and length frequencies were ac- 
quired from the SRHS, the NMFS Marine Recreational 
Information Program (MRIP) for samples from recre- 
ational fishermen other than those on headboats, and 
the SEFSC TIP. To optimize the accuracy and precision 
of our estimates, we ensured that we met the criteria 
of Coggins et ah (2013) with respect to total sample 
size (500-1000) and number of aged fish per length bin 
(at least 10 fish per bin). 
Total instantaneous mortality rates (Z) were es- 
timated by using catch curve analysis (Beverton and 
Holt, 1957). Only fully recruited ages (modal age+1) 
were used to estimate Z because the age group at the 
top of the catch curve may not be fully vulnerable to 
the fishing gear (Everhart et ah, 1975). 
Natural mortality 
We estimated the instantaneous rate of natural mortal- 
ity ( M ) using 2 methods. 
1) Hewitt and Hoenig’s (2005) longevity mortality 
relationship: 
M = 4.22 A max , (2) 
where t m ax is the maximum age of the fish in the 
sample; 
2) Charnov et ah’s (2013) method, where von Berta- 
lanffy growth parameters are used: 
M = (L/LcJ -1 - 5 x K, (3) 
where L„ and K are the von Bertalanffy growth equa- 
tion parameters (asymptotic length and growth coef- 
ficient); and 
L = fish length at age. 
With the Hewitt and Hoenig method, life span or lon- 
gevity is used to generate a single point estimate, and 
it is an improvement to the original equation of Hoenig 
(1983). The newer Charnov method, which incorporates 
growth parameters, is an improvement to the empiri- 
cal equation of Gislason et al. (2010) and is based on 
evidence that indicates that M decreases as a power 
function of body size. The Charnov method generates 
age-specific rates of M and is currently in use in South- 
east Data Assessment and Review (SEDAR) stock as- 
sessments (Williams 6 ). 
Results 
Age determination 
A total of 6419 first dorsal spines of gray triggerfish 
were sectioned. The distribution of samples by area and 
fishery sector is shown in Table 1. The majority of sam- 
ples came from the commercial sector in North Caro- 
6 Williams, E. 2013. Personal commun. Southeast Fisher- 
ies Science Center, National Marine Fisheries Service, Beau- 
fort, NC 28516-9722. 
