Barlow and Berkson: Evaluating methods for estimating rare events with zero heavy data 
351 
with a uniform probability distribution. The distribu- 
tions of sea turtles were constructed as described above. 
Simulating bycatch After sea turtles and fishing sets 
were distributed, we modeled bycatch. To quantify the 
number of takes, we first tallied the number of turtles 
that occurred in fished cells. Then, we applied a prob- 
ability of capture, given co-occurrence of a turtle and 
set in a cell, to each encountered turtle to determine 
whether the set caught the turtle (Table 2). The capture 
probabilities varied across quarter-area strata and were 
based on observed bycatch rates from the SEFSC for the 
period from 2005 to 2007 (Walsh and Garrison, 2006; 
Fairfield-Walsh and Garrison, 2007; Fairfield and Gar- 
rison, 2008). 
We calculated observed bycatch rates by stratum 
for leatherback and loggerhead sea turtles for each 
year from 2005 to 2007 and averaged the stratum by- 
catch rates across years. We decided to use the rates for 
leatherback sea turtles in the simulation model because 
leatherbacks are more of a conservation concern than 
are loggerheads and the average number of observed 
sets per year without take was smaller for leatherbacks 
(100 sets) than for loggerheads (179 sets), and therefore 
the data for leatherback sea turtles gave us a larger 
sample size for calculating capture probabilities. 
Some of the 40 SEFSC quarter-area strata had no 
fishing effort, observer coverage, or observed bycatch 
from 2005 to 2007. The strata without effort or observer 
coverage were eliminated from the simulation model. 
Eight strata had either no fishing effort or no observer 
coverage from 2005 to 2007, and therefore we simulated 
32 strata. For observed strata with a bycatch rate of 
0 turtles/set, we calculated probabilities of capture 
from bycatch rates in those strata at different quarters, 
when possible, or used a median bycatch rate across all 
quarter-area strata. This algorithm was consistent with 
the SEFSC’s pooling method in which there was pool- 
ing across quarters before pooling across fishing areas 
(Garrison, 2003). 
The simulated bycatch probabilities also varied de- 
pending on the spatial scenario because of the different 
turtle densities. The bycatch rates for strata ranged 
from 0.263 to 0.011 turtles/set. We divided these rates 
by the average number of sea turtles to be encoun- 
tered in 5 cells. Then, this probability was applied to 
each turtles that occurred in fished cells to determine 
whether it was caught. A set fishing among uniformly 
random turtles on average encountered 10.125 turtles, 
and a set fishing among clumped turtles on average 
encountered 250 turtles. 
Observer distribution We attempted to simulate 
observed fishing sets in a design consistent with the 
SEFSC’s procedure, in terms of both the number of 
observers and their spatial distribution. The SEFSC’s 
goal for observer coverage has been 8% since 2002 (Beer- 
kircher et al., 2004). In our model, 8% observer coverage 
equated to 2 observed sets per computational group of 
25 fishing sets. 
The SEFSC distributes observers according to a sim- 
ple random sampling design based on reported effort 
(Witzell and Cramer, 1995). Vessels are selected for 
observation in proportion to the amount of fishing re- 
ported in a quarter-area stratum in the previous year, 
and vessels are sampled without replacement within a 
quarter. Our simulation model was for one year; there- 
fore, we had no effort from a previous year upon which 
to base the observer distribution. Rather, for each com- 
putational group of 25 sets, a single cell from the grid 
of 100x100 cells was chosen at random to represent an 
area of high fishing effort. Observers were placed on 
the 2 sets closest to this cell. Although this method in- 
cluded assumptions differentiating it from the SEFSC’s 
procedure, the most important feature in both practices 
was the same: observers were distributed independent 
of bycatch rates. 
In summary, the simulation model included the fol- 
lowing main assumptions: 
• Computational groups of 25 fishing sets distributed 
across a grid of 100x100 cells where each cell rep- 
resented 10x10 km 
• Clumps of sea turtles and fishing sets represented 
in grids of 9x9 cells 
• Scenarios with clumped turtles in 5 clumps per 
computational group 
• Scenarios with clumped sets in 5 clumps of 5 sets 
each per computational group 
• Overlap of set and turtle clumps 
• Methods for placing turtles in the grid 
• Methods for placing sets in the grid 
• Methods for determining the direction of fishing 
• 2 sets selected for observation in each computational 
group 
Properties of estimation methods 
We applied 3 estimation methods to the simulated data: 
1) the delta-lognormal method, 2) GLM-P, and 3) GLM- 
NB. Each method was used to estimate bycatch at 2 
spatiotemporal scales: 1) for each of the quarter-area 
strata individually and 2) for all quarter-area strata 
combined. At the stratum scale, we estimated bycatch 
for individual quarter-area strata and summed stratum- 
specific estimates to obtain a total annual bycatch esti- 
mate. For the second spatiotemporal scale, we pooled 
sets across all quarter-area strata and estimated total 
annual bycatch. Hence, 6 estimates of total annual 
bycatch (all combinations of the 3 methods and 2 scales) 
were made for each of the 5 spatial scenarios. 
We focused on evaluating the delta-lognormal method 
because it has long-standing use by the SEFSC. We also 
chose the GLM-P and GLM-NB because they are simple 
model-based predictors for count data and, thus, a logi- 
cal place to begin evaluation of this class of models for 
estimating bycatch with zero-heavy data. Although the 
GAM performed well in work reported in McCracken 
(2004), we did not include it in this analysis because 
