Barlow and Berkson: Evaluating methods for estimating rare events with zero-heavy data 
345 
half of the observed catch from the U.S. Atlantic pelagic 
longiine fishery between 1992 and 2002 (Beerkircher et 
al., 2004). The rest of the catch was incidental bycatch. 
Sharks, rays, and finfishes composed the majority of 
bycatch during this period, and the incidental capture 
of sea turtles and marine mammals made up about 1% 
of the observed catch (Beerkircher et ah, 2004). For ex- 
ample, out of the 944 observed sets in 2007, 114 caught 
a sea turtle (Fairfield and Garrison, 2008). A fishing 
set is a single deployment of fishing gear; a vessel on 
average fishes 6 sets per 9-day trip (NMFS, 2006). 
Although the incidental capture of the loggerhead sea 
turtle ( Caretta caretta ) and leatherback sea turtle ( Der - 
mochelys coriacea ) is rare, it is notable because these 
species are protected under the Endangered Species 
Act (ESA) of 1973: the leatherback sea turtle is listed 
as endangered and the loggerhead sea turtle is listed 
as both endangered and threatened. The endangered 
distinct populations of the loggerhead sea turtle include 
one in the northeast Atlantic, and the distinct popula- 
tions listed as threatened include a population in the 
south Atlantic and another in the northwest Atlantic. 
Because the sea turtles that are caught by the U.S. 
Atlantic pelagic longiine fishery are protected under 
the ESA, scientists at the Southeast Fisheries Science 
Center (SEFSC) of the National Marine Fisheries Ser- 
vice estimate the number caught annually. These an- 
nual bycatch estimates are compared with the fishery’s 
incidental take statement (ITS), which stipulates the 
maximum number of sea turtles the fishery may catch 
incidentally before formal consultation under section 
7 of the ESA must be undertaken. If the maximum 
number stipulated in the ITS is exceeded for a turtle 
species, the SEFSC must assess whether the fishery 
is jeopardizing the survival of that turtle species and, 
consequently, how the fishery is allowed to proceed 
(McCracken, 2004). Therefore, accurate and precise 
estimates are necessary for both sea turtle conservation 
and appropriate fishery management. 
The SEFSC bases its estimates of sea turtle bycatch 
on 2 sources of data: logbooks kept by vessel captains 
and records made by independent observers deployed 
on ~8% of vessels (Beerkircher et al., 2004). Vessel 
captains are required to keep logbooks and record in- 
formation about fishing gear, location, effort, target, 
and catch. Observers are charged with collecting un- 
biased data that are representative of the total catch 
composition (Crowder and Murawski, 1998; Fairfield 
and Garrison, 2008). To estimate fleetwide sea turtle 
bycatch, bycatch rates are extrapolated from observer 
data and on the basis of observer logbook data are ap- 
plied to unobserved fishing sets (Fairfield and Garrison, 
2008). Generally, bycatch is estimated by identifying 
a relationship between fishing effort or environmental 
characteristics and the number of turtles caught on 
observed fishing sets and then by assuming that that 
relationship holds for unobserved sets. 
The estimation methods essentially can be categorized 
as sample-based estimators or model-based predictors. 
For sample-based estimators, sampling probabilities 
are assumed but, for the most part, assumptions are 
avoided regarding the structure of the target popula- 
tion and features being estimated. These estimators 
allow the observed bycatch rate to be raised to fleetwide 
estimates on the basis of total reported fishing effort. 
Sample-based estimators are usually less efficient (i.e., 
they require more samples to achieve a specified level 
of performance) than model-based predictors, where a 
statistical model of bycatch is assumed. The statistical 
model used in model-based predictors represents the 
process that is generating the response variable as a 
function of explanatory variables (McCracken, 2004). 
In our example, parameters can be estimated with the 
data from observed sets and used to relate the explana- 
tory variable values recorded in the logbooks to the 
number of sea turtles caught. These relationships can 
be used to estimate the number of turtles caught on 
unobserved sets. 
Current SEFSC estimates of sea turtle bycatch by 
the U.S. Atlantic pelagic longiine fishery have wide 
confidence intervals, and their accuracy is unknown. 
Consequently, it is difficult to determine the level of 
bycatch in a single year and the trend over time, and 
insufficient bycatch information impedes management. 
The ability of the SEFSC to estimate bycatch — and, 
thus, of the NMFS to manage the fishery and conserve 
protected species — may be improved if alternative esti- 
mation methods are systematically compared and the 
most suitable estimation method is identified. Evalua- 
tion of estimation methods with regards to frequently 
encountered data complexities, such as small sample size 
( 8 % observer coverage), overdispersion (greater variance 
than expected), excess zeros (many observed sets with- 
out bycatch), and hierarchical observations (sampling 
fishing sets within trips), is particularly warranted. 
In this study, we evaluated 2 of the most prevalent 
methods for estimating rare events with zero-heavy data: 
the delta-lognormal method, a sample-based estimator 
(Pennington, 1983); and the generalized linear model 
(GLM), a model-based predictor (Lindsey, 1997), in the 
context of sea turtle bycatch in the U.S. Atlantic pe- 
lagic longiine fishery. The SEFSC has used the delta- 
lognormal method to estimate sea turtle bycatch in the 
U.S. Atlantic pelagic longiine fishery since 1997, but, in 
recent years, the SEFSC has considered switching to a 
GLM approach (Fairfield and Garrison, 2008; Garrison 2 ). 
In comparison, the Southwest Fisheries Science Cen- 
ter (SWFSC) and Pacific Islands Fisheries Science Cen- 
ter (PIFSC) have estimated sea turtle bycatch in the 
U.S. Pacific pelagic longiine fishery. The SWFSC used a 
survey sampling theory in 1994 and 1995 and a regres- 
sion tree model in 1996 (Skillman and Kleiber, 1998). 
In 2000, McCracken (2004) of the PIFSC completed 
the first official report that systematically examined 
different methods for estimating sea turtle bycatch in 
the U.S. pelagic longiine fishery, although sea turtle 
2 Garrison, L. P. 2009. Personal commun. National Marine 
Fisheries Service Southeast Fisheries Science Center, Miami, 
FL. 
