Edwards and Perkins: Estimated tuna discard from dolphin, school, and log sets 
213 
Figure II 
Geographic strata used in estimating average annual discard per set by the U.S. 
tuna purse-seine fleet fishing in the eastern tropical Pacific Ocean, 1989-92. 
March 1992, observers from both agencies collected 
discard data for all observed sets. Because complete 
records of discard were missing for the early part of 
the study period, it was necessary to estimate dis- 
card during the study period rather than to measure 
it directly. 
Complete details of data collection and statistical 
modeling methods and rationale appear in Perkins 
and Edwards (1996). In summary, we chose to model 
the data using a modified negative binomial (NB) 
distribution (the negative binomial with added ze- 
ros, Johnson and Kotz, 1969) because this distribu- 
tion was sufficiently flexible to describe with a single 
form the disparate catch per set distributions for the 
three set types. The modified NB was able to accom- 
modate the preponderance of zeros and the long tails 
(extreme skewness) in the dolphin-set and school- 
set discard data as well as the more strictly negative 
binomial distribution of the discard data from log sets. 
Readily apparent differences in tuna discard per 
set type in different areas contributed to our strati- 
fication of the data into three geographic areas (Fig. 
1), the same areas used currently to determine com- 
parability of U.S. and non-U. S. dolphin mortality 
rates (Federal Register, 1989). For the purposes of 
estimating overall discard rates, we ignored school 
and log fishing in area 2 because no school sets and 
only ten log sets occurred there (Table 1). 
Table 1 
Effort data (number of sets on logs, schools, and dolphins) 
for the U.S. tuna purse-seine fishery in the eastern tropi- 
cal Pacific Ocean 1989-92. Geographic areas as defined in 
Federal Register ( 1989). N = number of sets in a given area, 
n = number of sets examined for discard, and n + = number of 
sets examined for discard in which discard actually occurred. 
Set type 
Area 
N 
n 
n+ 
Dolphin 
1 
2,496 
1,445 
10 
2 
498 
272 
5 
3 
596 
393 
4 
Total 
3,590 
2,110 
19 
School 
1 
399 
279 
32 
2 
0 
0 
0 
3 
867 
681 
48 
Total 
1,266 
960 
80 
Log 
1 
537 
326 
257 
2 
10 
4 
4 
3 
791 
672 
393 
Total 
1,338 
1,002 
654 
There was no distinct difference in discard rates 
among months for any of the three set types, and we 
did not include a monthly or seasonal effect in our 
analyses. Although the sample of sets was unbal- 
anced with respect to months (i.e. the period Sep- 
