Bacheler et al.: Influence of soak time and fish accumulation on the catches of reef fishes 
223 
in a trap. We limited our analysis to soak between 50 
and 150 min and to fishacc less than 200 total fish 
per trap because of low small sample sizes outside of 
these ranges (i.e., <2% of all observations). Year was 
included as a categorical variable (1990-2011), but 
all other variables were included as continuous vari- 
ables. Depth (depth) was measured in meters for each 
trap deployment; depths were recorded in a range of 
13-218 m over the course of the surveys used in our 
study. Because of small sample sizes, samples collected 
at depths >100 m were excluded from our analyses 
and remaining depths were log-transformed to achieve 
normality. Time of day (tod) was measured in Coordi- 
nated Universal Time, and day of the year (doy) was 
the day of the year that the trap sample was collect- 
ed. Water temperature (temp) was bottom water tem- 
perature measured in degrees Celsius for each group 
of 6 simultaneously deployed traps, and latitude (lat) 
was the latitude (degrees north) at which the samples 
were collected. Longitude was not included because of 
its statistically significant correlation (PcO.OOl) with 
depth that occurred because of the north-south orien- 
tation of our study area. 
Before the development of models, multicollinearity 
among predictor variables was examined because its 
presence can cause erratic model behavior and should 
be avoided (Zar, 1999). We assessed the severity of 
multicollinearity among predictor variables through 
calculation of the variance inflation factor (VIF) for 
each variable, which measures the amount of variance 
that is inflated for each variable as a result of its col- 
linearity with other predictor variables. The VIF for 
all predictor variables was less than 4.0 — below the 
level generally acknowledged to be problematic (5-10; 
Neter et al., 1989) — thus indicating no significant 
multicollinearity among predictor variables in our 
data set. 
We also included fishacc as a predictor variable in 
our GAMs. Because trap catch often was composed of a 
mixture of fish species in the multispecies survey, the 
contribution of a single species to the fishacc variable 
was generally small, but there were instances when the 
catch in traps was dominated by a single species. Inclu- 
sion of samples in which the catch was dominated by a 
single species may have positively biased the reported 
deviance of the models for those particular species, 
but the functional relationship between single species 
catch and fishacc was not affected. If catch of a single 
species was influenced entirely by fishacc, the relation- 
ship between the 2 variables would have been perfectly 
linear. By definition, then, any deviation from a linear 
relationship between the 2 variables could not have 
been the result of a potential lack of independence. Be- 
cause we were primarily interested in the shape of the 
relationship between catch and fishacc, we agree with 
Li et al. (2011) that the inclusion of the fishacc variable 
is a useful approach to examine trap saturation due to 
fish accumulation. 
Initially, a full model was fitted on the presence-ab- 
sence data for each species. Following Li et al. (2011), 
we used a binomial GAM submodel to estimate the 
probability of presence for each species being caught 
in individual traps (rj), which was assumed to be an 
independent draw from a binary variable with a prob- 
ability of success p: 
E(p) = v~ 1 (r\); (1) 
N 
r| = a + g 1 (soak) + g 2 (fishacc)+ £ Sj^ x j\ 
j = 3 
where E(p) 
v 
a 
soak 
fishacc 
Sj 
N 
the expectation of p; 
the logit link function; 
the intercept; 
soak time; 
fish accumulation; 
are smoothing functions, 
the number of predictor variables in the 
model; and 
the yth remaining explanatory variable. 
We next coded a positive-catch GAM submodel that 
related the Gaussian fourth-root transformed catch 
of each reef fish species when caught to the 8 predic- 
tor variables. We compared the error structure of log- 
normal, log-gamma, and Gaussian (with a fourth-root 
transformation) distributions using the Akaike infor- 
mation criterion (AIC; Burnham and Anderson, 2002) 
for each full model: 
AIC = -21og(z(0|y)) + 2A, (2) 
where 
= the log-likelihood; and 
= the number of parameters of each 
model . 
The model with the lowest AIC value was considered 
the best model in the model set. For all species, the 
Gaussian distributions with fourth-root transforma- 
tions had the lowest AIC values and were therefore 
considered the most parsimonious distributions for the 
positive-catch submodels. 
For the positive-catch GAM submodel, we used the 
following equation: 
AT 
y 0 ' 25 = a' + h^soak) + h 2 ( fishacc) + £ A. y ( JCy ), (3) 
7=3 
where y = the trap catch of a particular reef fish 
species; 
a' = the intercept; 
hj are smoothing functions; 
N = the number of predictor variables in the 
model; and 
Xj = the yth remaining explanatory variable. 
For each reef fish species, we then compared the 
full GAM submodels containing 8 predictor variables 
to various reduced models that contained fewer predic- 
tor variables. We compared various binomial GAM sub- 
models with the unbiased risk estimator (LIBRE) score. 
