Hightower et al.: Population dynamics and relative abundance for adult Sci@enops ocellatus 165 
evaluate between-reader precision (Beamish and Fournier, 
1981; Campana, 2001). Two-sample Kolmogorov—Smirnov 
tests were used to examine differences in fractional age dis- 
tributions between sexes. 
Modeling growth 
To estimate growth parameters for red drum in this study, 
the von Bertalanffy growth function (VBGF) was fit to 
female and male red drum and to red drum of unknown 
- sex for the complete data set, the fishery-independent 
Marine Resources Division gill-net data set, and the bot- 
tom longline data set, by using the following equation (von 
Bertalanffy, 1938): 
iy, Sth Cog), (2) 
where L, = the predicted TL in millimeters; 
L,, = the mean asymptotic length in millimeters; 
K = the Brody growth coefficient (years 1); 
t = the time (fractional age) in years; and 
t) = the hypothetical age in years at which length 
equals 0. 
The VBGF was used to model sex-specific growth. Eight can- 
didate versions of the VBGF were fit to the sex-specific frac- 
tional age data: a general version, where all 3 parameters 
(L.., K, and t)) could vary between sexes; 3 versions where 
2 of the 3 parameters could vary between sexes; 3 versions 
where only 1 parameter could vary between sexes; and a 
common version where all 3 parameters were held constant 
between sexes (Ogle, 2016; Nelson et al., 2018; Jefferson 
et al., 2019). Akaike information criterion (AIC) values were 
used to rank these models on the basis of fit and to iden- 
tify the best-fitting version (Akaike, 1998; Katsanevakis 
and Maravelias, 2008; Ogle, 2016). All growth parameters 
were modeled in statistical software R, vers. 4.1.0 (R Core 
Team, 2021), with the add-on packages FSA (vers. 0.9.1; 
Ogle et al., 2021) and nlstools (vers. 1.0-2; Baty et al., 2015). 
Estimating mortality 
By using whole ages of fish sampled in bottom longline 
surveys, an age-based catch curve (Chapman and Robson, 
1960) was created for calculating total mortality; however, 
graphical examination of the catch curve revealed that crit- 
ical assumptions necessary for estimating instantaneous 
total mortality had been violated (Tuckey et al., 2007; 
Smith et al., 2012). Specifically, red drum did not appear 
to fully recruit to the gear until age 20; therefore, any mor- 
tality estimates generated from this catch curve would not 
be representative of the stock. Although total mortality 
estimates were unattainable, M was calculated by using 
3 empirical methods (Then et al., 2015; Ogle, 2016): 
1. Hoenigg.;.,, Hoenig’s (1983) log-transformed linear 
regression for fish species, 
M= ere = TOI¢8 e(tmax)s (3) 
where t¢,,,, = the maximum age of the animal in years; 
2. the Hoenig,), (nonlinear least squares) estimator 
(Then et al., 2015), 
M = 4.899t,°°1°; and (4) 
3. the Pauly,),7 (nonlinear least squares, omitting tem- 
perature) estimator (Pauly, 1980; Then et al., 2015), 
M = 4.118K°? 7°33 | (5) 
where K and L,, are parameters from the combined VBGF. 
All mortality analyses were conducted with FSA in R. 
Relative abundance 
Yearly changes in CPUE for red drum sampled during 
bottom longline surveys were examined by generating a 
nominal index of relative abundance. To standardize the 
index of relative abundance, a negative binomial gener- 
alized linear model (Hardin and Hilbe, 2007) was fit to 
the CPUE data by using the glmmTMB package (vers. 
1.1.2; Brooks et al., 2017) in R. Abiotic variables thought 
to influence CPUE were added to the model by using for- 
ward stepwise model selection. Akaike information crite- 
rion values were used to identify the best-fitting model. 
Model fit was examined by using the DHARMa package 
(vers. 0.4.3; Hartig, 2021) in R to check for uniformity, 
outliers, dispersion, and zero inflation. Multicollinearity 
was tested by using the performance package (vers. 0.7.3; 
Ltidecke et al., 2021) in R, with variance inflation factors 
less than 10 signifying low correlation (Dormann et al., 
2013). To create a standardized yearly index, the abiotic 
variables thought to influence CPUE were set to their 
median values. 
Spatial analysis 
The index of relative abundance generated as described 
above was used to examine trends in relative abundance 
of red drum. First, minimum distance from shore (in kilo- 
meters) was calculated in QGIS, vers. 3.8.1 (QGIS Devel- 
opment Team, 2019). Then, nominal CPUE was calculated 
for 4 discrete areas: <3 nmi from shore (i.e., state waters), 
3-6 nmi from shore, 6—9 nmi from shore, and >9 nmi from 
shore. Finally, a one-way analysis of variance, followed by 
a Tukey’s multiple-pairwise-comparison test, was used 
to test for differences in nominal CPUE between these 
4 areas. Age and length were examined in relation to dis- 
tance from shore to identify the composition of red drum 
vulnerable to recreational fishermen in state waters ver- 
sus that of those protected in federal waters. 
Habitat modeling 
Boosted regression trees (BRTs) were used to describe the 
relationships between the CPUE of red drum from bottom 
longline surveys and environmental variables potentially 
influencing distribution and abundance. Specifically, BRTs 
were fit for 3 seasons (meteorological spring, summer, and 
autumn); winter data were not included in BRT analysis 
