Barlow and Berkson Evaluating methods for estimating rare events with zero heavy data 
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Table 1 
Data from the National Marine Fisheries Service (NMFS) Southeast Fisheries Science Center (SEFSC) and the scientific litera- 
ture that were used in the simulation model built to represent interactions of sea turtles with the U.S. Atlantic pelagic longline 
fishery. 
Model features 
based on existing data 
Values 
Source 
Mean number of 
annual fishing sets 
8000 
SEFSC 
Mean mainline 
length of fishing sets 
50 km 
SEFSC 
Attributes of fishing sets 
Set number within a trip, mainline length, target 
species, presence of light stick, number of hooks, 
sea-surface temperature, fishing area, date, 
latitude, longitude 
SEFSC 
Spatial scenarios 
of fishing sets 
Clumping apparent in location records 
SEFSC 
Observer coverage 
8% 
SEFSC 
Spatial and temporal 
variation in fishing effort 
and bycatch 
Variation across 4 calendar quarters and 10 fishing 
areas in the Atlantic Ocean, Caribbean Sea, 
and Gulf of Mexico 
SEFSC 
Probability of sea 
turtle capture 
Variation across calendar quarters and fishing areas 
SEFSC 
Density of sea turtles 
0.5 turtles/km 2 
Byles (1988); Nelson (1996); Mansfield 
(2006); Goodman et al.( 2007) 
Spatial scenarios 
of sea turtles 
Clumping related to currents, frontal regions, 
bathymetric features, and prey 
Williams et al. (1996); Bigelow et at. 
(1999); Witzell (1999); Polovina et al. 
(2000); Lewison et al. (2004); Gilman 
et al. (2006); Gardner et al. (2008) 
Clumping area 
90x90 km 
Gardner et al. (2008) 
and that there seemed to be increased clumping from 
July to October. Also, clumping was more pronounced 
with loggerheads than with leatherbacks (Gardner et 
al„ 2008). 
Therefore, we modeled clumped and uniformly random 
sea turtle distributions. Although existing data indicate 
that turtles clump, very little information about the spa- 
tial extent or density of clumps is available. A density 
estimate of 0.5 turtles/km 2 was assumed for modeling be- 
cause it is an intermediate value based on the estimates 
available in the scientific literature, bearing in mind 
that an individual turtle may surface and be available 
to aerial surveys 5.3% to 30% of the time (Byles, 1988; 
Nelson, 1996; Mansfield, 2006; Goodman et ah, 2007). 
As for fishing sets, SEFSC maps of longline set loca- 
tions suggest that sets do not have a uniformly ran- 
dom distribution (Fairfield and Garrison, 2008). For 
analysis, the SEFSC has divided the Atlantic Ocean, 
Caribbean Sea, and Gulf of Mexico into 10 geographic 
regions or statistical areas, and the agency estimates 
bycatch in each area for each calendar quarter and 
then sums these estimates to generate a total annual 
estimate. Sets appeared clumped whether their distribu- 
tion was considered across all fishing areas or within 
a single fishing area. However, the mechanism behind 
this clumping is not well understood. We modeled 2 
possible scenarios: 1) fishing sets clump in the same 
areas in which sea turtles clump and 2) sets clump 
independently of turtles. The first scenario could occur 
if both fishermen and turtles target productive areas 
of the ocean. The latter could result from either fisher- 
men or turtles imperfectly targeting productive areas or 
clumping based on another cue. For example, fishermen 
might aggregate from peer influence. 
The spatial scenarios with clumped sets were ex- 
pected to be most realistic, but considering the amount 
of uncertainty in the nature of the interactions of sea 
turtles with the pelagic longline fishery, we thought 
it useful to analyze other distributions as well. For 
example, a scenario with uniformly random turtles 
and sets served as a null model. Further, the results 
from spatial scenarios considered less realistic for the 
interactions of sea turtles with the U.S. Atlantic pelagic 
longline fishery could illuminate general properties 
