Bacheler et al.: Influence of soak time and fish accumulation on the catches of reef fishes 
221 
Figure 2 
Schematic of the design of the chevron trap used to 
sample reef fish species in 1990-2011 by the Marine 
Resources Monitoring, Assessment, and Prediction Pro- 
gram and the Southeast Fishery-independent Survey. 
The gray oval is the mouth opening of the trap (-18 
cm wide and 45 cm high), and the total trap volume 
is 0.91 m 3 . 
than 15%, but individuals of all species were included 
in analyses of fish accumulation. 
Data analyses 
We used a generalized additive modeling approach to 
test the hypothesis that trap catch of reef fishes was 
influenced by soak time and fish accumulation. GAMs 
use nonparametric smoothing functions to account for 
nonlinearities between predictor and response vari- 
ables (Hastie and Tibshirani, 1990; Bacheler et ah, 
2009). GAMs extend traditional additive models by al- 
lowing for alternative distributions of underlying ran- 
dom variation, just as generalized linear models allow 
for alternative distributions in linear models. 
We developed delta-GAMs because there was a high 
proportion of zero observations (>50%) for the catch of 
each species that could not be modeled appropriately 
with standard statistical distributions. We considered 
zero-inflated models, but they were challenging to work 
with because they rarely converged, and when they did, 
model solutions were often unreasonable. Therefore, we 
developed a delta-GAM for each of the 8 species. Each 
delta-GAM contained 2 submodels that estimated the 
influence of soak time and fish accumulation on catch: 
90 110 130 150 
soak 
50 
100 
fishacc 
150 
doy 
i i i i i i i r 
27 28 29 30 31 32 33 34 35 
I at 
temp tod 
Figure 3 
Histograms of predictor variables used in the delta-generalized-additive models of reef fish catch from trap surveys con- 
ducted by the Marine Resources Monitoring, Assessment, and Prediction Program and the Southeast Fishery-independent 
Survey in the Atlantic Ocean from North Carolina to Florida during 1990-2011. Variables were soak time (soak; min), fish 
accumulation (fishacc; total fish per trap), year of sampling (year), day of the year (doy), latitude (lat; °N), depth of sampling 
(depth; m), bottom water temperature (temp; °C), and time of day (tod; Coordinated Universal Time). 
