Dippold et al.: Growth, mortality, and movement of Rachycentron canadum 
463 
time between tagging and recapture, and L, the length 
at tagging (millimeters in FL). 
The final model used to describe the length-at-age 
relationship of cobia was the VBGF formulation GRO- 
TAG, which is based on the methods discussed in Fran¬ 
cis (1988). The Francis (1988) equation is 
(3) 
where AL = the expected change in length (millimeters 
in FL); 
A t= the time-at-large (years); 
L 1 = the length of an individual at tagging (mil¬ 
limeters in FL); and 
g a and gp = the mean annual growth rates (millimeters 
per year) of fish at user-selected lengths a 
and P (millimeters in FL). 
The lengths a and P are chosen based on the range of 
lengths included in the tag-recapture records so that 
g a and gp are descriptive of the individual growth rates 
encompassed by the tagging data (Francis, 1988). In 
this study a was 500 mm FL and p was 1100 mm FL. 
After fitting the model, L (millimters in FL) can be 
estimated from g a and gp with the following equation: 
= (/?£«-a£p)(£ a -£p)- (4) 
Similarly, k (per year) can be calculated from the GRO- 
TAG VBGF model parameters by using the following 
equation: 
da Keys, and the U.S. South Atlantic Ocean (Fig. 1). 
We focused on the Gulf of Mexico and South Atlantic 
Ocean because those were the areas in which the co¬ 
operative tagging program occurred. Movement among 
zones was described by calculating the proportion of 
recaptured individuals in each zone that were tagged 
in a specific zone. We included only individuals whose 
time at liberty was greater than or equal to 30 days. 
Our analysis was used to investigate large-scale move¬ 
ment between geographic areas and to identify wheth¬ 
er individual cobia traveled between the Gulf of Mexico 
and South Atlantic Ocean. 
The relationship between recapture zone and month 
of recapture was evaluated by using a loglinear model 
to infer trends in seasonal distribution of recaptured 
cobia in the Gulf of Mexico. Recaptures from the South 
Atlantic Ocean were not included in the analysis to 
meet assumptions in the model regarding nonzero ex¬ 
pected frequencies within each month-zone combina¬ 
tion and because of the limited number of reported 
recaptures in the South Atlantic Ocean. We set a mini¬ 
mum time-at-liberty of 30 days to allow for tagged fish 
to return to normal mixing behavior. Loglinear models 
are an extension of the chi-square test and are used 
to determine associations between categorical variables 
(Knoke and Burke, 1980). A saturated loglinear model 
(with recapture zone and recapture month as the main 
effects) and a 2-way interaction term were constructed 
to evaluate the association between month of recapture 
and recapture zone. The saturated model is 
& = -ln(l + (g a - g$)/(a-f3) (5) 
log(Uij) 
_ ftzone _j_ ^month _j_ ^zone x month 
( 6 ) 
The 95% confidence intervals (CIs) of L r „ and k were de¬ 
termined by using bootstrap methods similar to those 
described in Simpfendorfer (2000). 
After each model was fitted, the performance of the 
3 candidate models was compared by using Akaike’s 
information criterion (AIC) (Burnham and Ander¬ 
son, 2002) and model support was evaluated by using 
Akaike weights ( w ;). The mean growth-parameter es¬ 
timates of the best supported model(s) were compared 
with those reported in other studies of cobia growth 
published in the literature. All analyses were conduct¬ 
ed in R, vers. 3.3.0 (R Core Team, 2016). 
Movement and seasonal distribution 
Broad-scale seasonal and general movements were de¬ 
scribed in this study by defining 7 spatial zones and 
quantifying the spatial and temporal patterns of fish 
tagged and recaptured among the zones. The criteria 
we used to define the 7 spatial zones were based on ar¬ 
eas where recreational fishermen are known to target 
cobia and where boundaries exist that could be use¬ 
ful to managers when setting harvest regulations (e.g., 
state boundaries). Zones were also identified because 
exact locations of capture or recapture are general¬ 
ly not reported. In this study, the 7 geographic zones 
defined were Texas, Louisiana, northcentral Gulf of 
Mexico, Florida panhandle, Florida Gulf Coast, Flori- 
where log(iqj) = the expected counts in each zone-month 
combination; and 
X = the main effect of each predictor variable. 
If no significant interaction is observed in the saturated 
model (indicating a good model fit), the interaction term 
is dropped and a second model with only the main effects 
is constructed. If this model is significant, i.e., the model 
does not fit the data well after removing the interaction 
term, the association between the main effects is con¬ 
sidered significant (i.e., the model fits better when there 
is an association between the main effects). Finally, a 
mosaic plot was constructed that was based on the lo¬ 
glinear model to identify specific recapture zone and 
recapture month combinations that were statistically 
significant. Mosaic plots are useful visual representa¬ 
tions that allow determination of statistically significant 
month-zone groups. Typically, the shading of mosaic 
plots represents the residuals (deviations) from the lo¬ 
glinear model for each cell. In this study, the shading 
of the mosaic plot represents the values of the Pearson 
(standardized) residuals and a value greater than 2 or 
less than -2 is considered significant. 
Mortality 
Estimates of Z were determined by using a suite of 
tag-recovery models fitted to the cobia tagging data in 
