Barlow and Berkson Evaluating methods for estimating rare events with zero-heavy data 
359 
in each stratum and an observer distribution that is 
independent of the presence of sea turtles. 
Conclusions 
Recommendations for management 
Bycatch in commercial fisheries is believed to be the 
main anthropogenic threat to sea turtles, and the 
pelagic longline fishery is considered one of the 3 fisher- 
ies most affecting sea turtles ( Witherington et ah, 2009). 
Therefore, improving bycatch estimates is important for 
sea turtle conservation and effective fishery manage- 
ment. Results from this study indicate that estimating 
bycatch with the stratum-level delta-lognormal method 
is appropriate and support the current procedure used 
by the SEFSC. 
General application to zero-heavy data analysis 
Not accounting for excess zeros and using models with 
inappropriate assumptions can result in biased esti- 
mates and incorrect conclusions (Martin et ah, 2005), 
as was seen in the performance of the GLMs in our 
simulation. This study further supports the notion that 
no one model is clearly most appropriate for analyzing 
zero-heavy data (Sileshi, 2006). Rather, models must be 
compared to select a model that is most suitable for the 
data and the required output (Sileshi, 2006). We cannot 
recommend one method for addressing all zero-heavy 
data, but our study shows the importance of recogniz- 
ing variance across time and space, demonstrates the 
necessity of representative samples and sample size, 
and indicates that the delta-lognormal method gener- 
ates estimates that are less biased and more precise 
than the GLMs in the case of sea turtle bycatch by 
the U.S. Atlantic pelagic longline fishery. Many other 
fields with zero-heavy data also would benefit from an 
increased understanding of the delta-lognormal method 
and GLM. 
Acknowledgments 
We wish to thank M. Kelly, P. Richards, and E. Smith 
for helpful suggestions regarding this project. We also 
would like to thank C. Beasley, J. Hatt, J. Hepinstall- 
Cymerman, T. Prebyl, and C. Ricketts for their com- 
ments on this manuscript. Funding was provided by the 
National Marine Fisheries Service Southeast Fisheries 
Science Center. 
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