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that we believed would help determine relative ef- 
fectiveness of each hook type at catching fish and on 
mechanisms during the fish-hook interaction (strike, 
hook-up, and retention). We inspected data plots to 
determine factors other than hook that contributed 
to variability in catch rates. Base models for each 
level of fish interaction were then constructed without 
hook main effects and hook interactions. For each of 
these potential base models we calculated a quasi- 
Akaike’s information criterion (QAIC; Burnham and 
Anderson, 2002). QAIC was computed instead of AIC 
because of potential over-dispersion of the data used 
as the response variable in each model (Burnham and 
Anderson, 2002). At each level of fish interaction, we 
selected the base model with the lowest QAIC value. 
The most parsimonious base models had 1) main ef- 
fects (excluding hook) plus a leader-species interaction 
at the catch level; 2) main effects (excluding hook) 
plus leader-species and species-user interactions at 
the strike level; 3) main effects (excluding hook) plus 
a leader-user interaction at the hook-up level; and 4) 
main effects (excluding hook) plus a species-user in- 
teraction at the retention level. After the base model 
was selected, we developed incrementally more com- 
plex models that then included a hook effect and in- 
teraction terms between hook and other factors. This 
sequential model building allowed us to determine if 
the main factor of interest — hook type — covaried with 
other factors potentially influencing interactions with 
fishes. Any models with three-way interactions also 
included two-way subinteractions. QAIC ( values were 
then used to compare fits among all i models (includ- 
ing the base model) at each level of fishing interac- 
tion to help determine the combination of predictors 
that best explained variation in the data. The AQAIC 
value for each model was calculated as the differ- 
ence between any particular model (QAIC,) and the 
minimum QAIC for the best fitting model in the set 
(QAIC min ). The model with the QAIC min value was, for 
each model set, considered to be the one representing 
the data adequately with the fewest parameters; how- 
ever, we regarded models that differed by <~ 4 AQAIC 
as all having reasonable support (Burnham and An- 
derson, 2002). We also computed Akaike weights (w t ) 
for each model to help gauge the relative support for 
each model in the model set; the value of w t varies 
between 0 and 1, with a greater value indicating that 
a particular model better fits the data. See Burnham 
and Anderson (2002) for equations used to compute 
QAIC and w t . 
Highly parameterized models often resulted in sin- 
gular Hessian matrices, indicating that one or more 
parameters were nonidentifiable. However, we retained 
these models in each model set because our primary 
goal was to obtain parsimonious predictions of how 
hook type affected catch rates. In an information-the- 
oretic context, over-parameterized models would simply 
be penalized for requiring additional parameters to 
explain the same amount of variation in the data and 
therefore would be unlikely to be selected with QAIC. 
The selection of base models and development of more 
complex models incorporating a hook main effect and 
hook interactions by using data on taxa (e.g., dolphin- 
fish, “tunas,” and “mackerels”) followed the process used 
for the three species. Base models at each level of fish 
interaction were the same as in the species analyses 
described above with the exception of the retention 
level, where a model consisting of main effects (except 
hook) plus a leader-species interaction best fitted the 
taxa data. 
We computed the relative effectiveness of circle and 
J hooks (effect size) by comparing predicted circle 
and J hook catch rates of dolphinfish, yellowfin tuna, 
and wahoo on their respective directed leader types. 
Effect size was calculated for each catch model with 
a positive Akaike weight ( w i ) (see Results section). 
Effect size (ES) for each of these models was com- 
puted as 
ES = ^-, ( 1 ) 
where fi x and - the predicted mean catch-per-trip 
values on circle and J hooks, respectively. 
Effect size theoretically ranges from zero to greater 
than one. An effect size less than, equal to, or greater 
than one indicates that circle hooks are less, equally, 
or more effective than J hooks, respectively. The 
variance (a 2 ) about each effect size was calculated 
as 
where o x 2 and o 2 are the variances about the mean 
predicted mean catch-per-trip values of circle and J 
hooks. The values for user and wave were held constant 
(at 0.48 and 0.79 m, respectively) when computing effect 
size for the three species-leader combinations from each 
aforementioned catch model. The effect size from each 
model was weighted by the relative w ( value. Weighted 
effect size values from each model were summed to 
determine an overall effect size for each of the three 
species caught on its directed leader type. This model- 
averaging procedure was repeated to compute overall 
variance about each average effect size; model averag- 
ing for variance was conducted by multiplying each 
model’s variance by the squared value of the Akaike 
weight (w 2 ). Computations of predicted effect sizes 
and associated variances were repeated with the data 
on taxa. 
For each species, we compared median lengths be- 
tween hook types with a median ranks test (a=0.05). 
Data were combined across leader types and user 
groups for each of these size-based analyses. For each 
species, we compared rates of jaw (mouth) and deep 
hooking (gut, gills, or eyes) among hook types using 
a chi-square square test of independence. 
