352 
Fishery Bulletin 1 10(3) 
nonlinear effects of predictor variables have not been 
extensively studied in the Atlantic and estimation of 
these effects typically requires data sets larger than 
the ones available to the SEFSC for annual estima- 
tion of bycatch. For example, Kobayashi and Polovina 
(2005) fit GAMs with 55,785 unobserved sets and 2812 
observed sets fished over 5 years in the Pacific fishery. 
Therefore, in our study, we focused on evaluating the 
delta-lognormal method and GLMs. 
Delta-lognormal estimates are essentially the product 
of the proportion of fishing sets with bycatch and the 
average rate of bycatch for those sets (Yeung, 2001). The 
delta-lognormal method accommodates a predominant 
group of observations with a value of zero by including 
a probability of zero catch, and observations with non- 
zero values are assumed to be lognormally distributed 
(Pennington, 1983; Ortiz et ah, 2000; NMFS, 2001; 
Fairfield and Garrison, 2008). A lognormal distribu- 
tion is a continuous probability distribution where the 
logarithm of the random variable has a normal distribu- 
tion. Minimum-variance unbiased estimators of means 
and variances are provided under the delta-lognormal 
method when data contain many zeros and the non-zero 
values are lognormally distributed (Pennington, 1983; 
NMFS, 2001; Garrison, 2003). 
The GLM extends the classical linear model by sup- 
porting the use of distributions other than the nor- 
mal distribution. The GLM most commonly applied to 
count data, the log-linear model, uses a Poisson error 
distribution (McCullagh and Nelder, 1989). In a Pois- 
son model, counts are assumed to be independent and 
randomly distributed in space, and the mean and vari- 
ance of the random variable are assumed to be equal 
(McCracken, 2004; Sileshi, 2006). However, bycatch 
data do not always show this relationship. The variance 
is often larger than the mean — a case known as over- 
dispersion (McCracken, 2004; Potts and Elith, 2006). 
Patchy distributions, hierarchical data, the observation 
of a rare event, or lack of independence can lead to the 
presence of excess zeros, variance heterogeneity, and in 
turn, overdispersion (McCracken, 2004; Lindsey, 2004; 
Fahrmeir and Echavarria, 2006). Poisson models are 
the most commonly used and most straightforward 
models for count data, but the Poisson distribution ac- 
counts for neither zero-inflation nor overdispersion. If 
overdispersion is not addressed, standard errors can 
be seriously underestimated and the form of the linear 
predictor can be misinterpreted (Rideout et al., 2001; 
Potts and Elith, 2006). 
Modeling responses as a negative binomial random 
variable may be more appropriate if data are over- 
dispersed (Welsh et al., 1996; Thurston et al., 2000; 
Lindsey, 2004; Venables and Dichmont, 2004). Unlike 
the Poisson distribution, which has 1 parameter, the 
negative binomial distribution has 2 parameters: a 
mean and a dispersion parameter (White and Bennetts, 
1996). The dispersion parameter can be understood as 
a measure of the degree of clumping in a population. 
The negative binomial distribution with a dispersion 
parameter that approaches infinity is consistent with 
the Poisson distribution where spatial independence 
is assumed. The spatial independence assumption is 
relaxed in the negative binomial distribution (White 
and Bennetts, 1996). 
Estimation methods applied 
Generalized linear model In the past, the SEFSC and 
PIFSC have used fishing area, data source (observer or 
logbook), light stick use, gear depth, month, latitude, 
sea-surface temperature, day of the year, and number 
of hooks as explanatory variables in GLMs (Witzell and 
Cramer, 1995; McCracken, 2004). Our set of potential 
explanatory variables consisted of all variables recorded 
both by SEFSC observers and in SEFSC logbooks. It is 
important that data are recorded in both sources because 
the model must be fitted with data from observed sets, 
and data from logbooks must be used to predict bycatch 
on unobserved sets. The common variables are set 
number (the sequence of sets within the trip), mainline 
length, target species, presence of light stick, number of 
hooks, date, latitude, longitude, sea-surface temperature, 
and fishing area. 
We included mainline length and number of hooks 
as potential covariates because they are measures of 
fishing effort and we suspected a positive relationship 
between amount of effort and number of sea turtles 
caught. SEFSC data indicate that bycatch rates vary 
seasonally and spatially. Therefore, we included date as 
a seasonal covariate and latitude, longitude, and fish- 
ing area as spatial covariates. Sea-surface temperature 
was expected to influence the distribution of sea turtles 
because they are ectotherms, and research has shown a 
relationship between temperature gradients and aggre- 
gation of sea turtles and swordfish (Bigelow et al., 1999; 
Polovina et al., 2000; Lewison et al., 2004). Set number, 
target species, and light stick presence were included in 
the GLMs as covariates describing fishing methods that 
may have different levels of interactions with turtles. 
Gear configuration and fishing method vary depending 
on the target species and location of fishing (Beerkirch- 
er et al., 2004). When targeting swordfish, longlines are 
set overnight at shallow depths (10-100 m), and a light 
stick is often attached several meters above the hook 
on every second or third branchline. In contrast, when 
tuna are targeted, longlines are set at dawn and hauled 
in at late afternoon or evening. Further, sea turtles are 
attracted to light sticks (Wang et al., 2007). 
In the simulation model, variable values were selected 
from real fishing sets observed by the SEFSC from 2005 
to 2007 and assigned to simulated sets. When a simu- 
lated set had bycatch, we assigned variable values from 
an SEFSC-observed set with bycatch. Likewise, when a 
simulated set did not have bycatch, variable values from 
an SEFSC-observed set without bycatch were assigned. 
Variable assignment was also designed to reflect the 
spatial distribution of simulated fishing sets. In scenari- 
os with uniformly random sets, if the first simulated set 
in a stratum did not have bycatch, one SEFSC-observed 
set that did not have bycatch was selected at random 
