326 
Fishery Bulletin 11 7(4) 
Estimates of aging precision were compared with previ¬ 
ously determined levels of acceptance of <5.5% for IAPE 
(Campana, 2001; Matta and Kimura, 2012), which are 
applicable to deepwater snappers (Wakefield et al., 2017). 
Age-bias plots were examined to assess aging bias or the 
systematic variation in enumerated annuli counts. 
The ages of all goldeneye jobfish and goldflagjobfish were 
estimated from the counts of opaque zones from a single 
age reader following the established aging criteria, with all 
samples read twice and at least 2 weeks between readings. 
Opaque zone counts for each fish were accepted if they were 
the same between the 2 readings, otherwise a third or, in 
rare cases, a fourth reading was required until a match was 
made with a previous count and considered the final age. 
Comparison of size and age distributions 
Kolmogorov-Smirnov tests were used to compare species- 
specific differences in the size and age frequency distribu¬ 
tions between the sexes and between fished and unfished 
areas. 
Akaike information criterion corrected for small sample 
sizes (AIC c ) (Burnham and Anderson, 2002). Statistical 
analyses were conducted in the statistical software envi¬ 
ronment R, vers. 3.5.1 (R Core Team, 2018), with the nls 
function in the stats package. 
Mortality 
Estimates of natural mortality of goldeneye jobfish and 
goldflag jobfish were produced by applying a multinomial 
catch curve with logistic selectivity to the age composition 
of the unfished populations. This approach assumes that 
total mortality is equal or close to that of natural mor¬ 
tality. The mortality and selectivity parameters of age at 
50% selectivity for the unfished population (A 5 u 0 nf ) and of 
the difference between the ages at 95% and 50% selectiv¬ 
ity for the unfished population (A unf ) were estimated from 
the age composition by using a multinomial negative log- 
likelihood ( nLL un{ ) function: 
nLL anf = -X__, Cr ( log ( P'f ), (4) 
Growth trajectories 
Species-specific growth of goldeneye jobfish and goldflag 
jobfish was described with the von Bertalanffy growth 
function (VBGF; von Bertalanffy, 1938) fitted to the FL 
at age by using nonlinear least squares regression with 
constant residual variance: 
L t =L,( l-e“ K[t ' to1 ), (2) 
where L t = the predicted mean FL at age t (in years); 
= the asymptotic length (in millimeters); 
K = the growth coefficient (per year); 
t = estimated age (in years); and 
t 0 = the theoretical age (in years) at which fish 
would have zero length. 
Allowing the VBGF to estimate t 0 resulted in large nega¬ 
tive values in some of the data sets because of the lack of 
smaller fish (<200 mm FL). Constrained growth models 
(t 0 = 0) provided a more realistic representation of growth 
for the younger age classes. 
To examine the effects of sex and fishing pressure on 
growth, these factors were added as covariates to a con¬ 
strained (t 0 =0) Kimura’s (2008) extended VBGF (EVB). In 
this general fixed-effects nonlinear model, L x and K are 
modeled as functions of the covariates ((3): 
( \ 
C, 
' > 
Pol + X ilPlL + X i2$2L 
if, 
V 1 7 
PoK + X ilPlK + X i 2 p 2 K J 
where x n = the sex (female or male) dummy variable 
(either 0 or 1); and 
x i2 = the fishing pressure (fished versus not fished) 
dummy variable for the ith fish. 
Models with no effects, just sex, just fishing pressure, and 
with sex and fishing pressure were compared by using the 
where C a unf = the observed catch in numbers of age-a indi¬ 
viduals; and 
P u .f = the expected proportion of age-a individuals 
in the age composition, calculated as follows: 
^ unf 
^ unf 
Relative catch (C a ) of age-a individuals is the product 
of survivorship at age a (S a unf ) and gear selectivity at age 
a (V a nf ). Expected per-recruit survivorship at age in the 
unfished population (S™ f ) was calculated as a negative 
exponential function with natural mortality as the only 
source of mortality: 
c a - sr f V'f, 
gunf = g-M(«-l) > and 
yunf _ 4 
-log(19)[a-Aff) 
A un ^ 
1 + e 
( 6 ) 
(7) 
( 8 ) 
The multinomial catch curve results were compared with 
results from 2 natural mortality (M) estimators. The first 
was Hoenig’s (1983) updated method, which is based on 
maximum age (Then et al., 2015): 
M = 4.899t m ° a f 16 , (9) 
where t max - maximum observed age. 
The second indirect method was the updated Pauly estima¬ 
tor, which is based on VBGF parameters (Then et al., 2015): 
M = 4.118 k 073 L^- 33 , 
( 10 ) 
where K = the growth coefficient (per year); and 
L„ = the asymptotic length (in millimeters) estimated 
by using species-specific final growth estimates. 
