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Fishery Bulletin 96(2), 1 998 
is denoted as [SARD] were S stands for season, A for 
area, B for bycatch, and D for dolphins, and the model 
includes all possible interactions up to and includ- 
ing the four-way interaction. Because the saturated 
model would naturally provide the best fit, we were 
interested in determining if a simpler model could 
be found that would also satisfy the criteria of a logit 
model with bycatch as the response variable. The stan- 
dardized residuals of the resulting model were then 
examined to ensure that lack of fit was not a problem. 
Contrasts We anticipated that we would have sig- 
nificant interaction terms in our analyses that would 
require detailed examination of interactions. For the 
logit form of the selected model, we constructed a 
series of contrasts that might help to explain the 
nature of these potential interactions. The contrasts 
of interest had two general forms: 
1 Given a specific area, are the odds of observing a 
set with high bycatch the same between any two 
different seasons. This results in three unique con- 
trasts for each area (spring vs. summer, spring vs. 
fall, summer vs. fall) and a total of 12 contrasts. 
Let F t j be the logit of high bycatch for season i 
and area j and let F h/ be the logit of high by catch 
for season h and area j. 
The hypotheses being tested were 
H o '■ Fy - F h j = 0 , 
where F y = a + (3 ; s + (3 A + (3 (/ SA ; 
F J hj = a + (3/ + (3';' + p'/ A ; and 
h and i = spring, summer, and fall, such 
that h * i for each j, and j = area 
11-12, area 13-14, area 15-16, 
and area 17-18. 
2 Given a specific season, are the odds of observing 
a set with high bycatch the same between any two 
different areas. This results in six unique contrasts 
for a given season and a total of 18 contrasts (11— 
12 vs. 13-14, 11-12 vs. 15-16, 11-12 vs. 17-18, 
,15-16 vs. 17-18). 
Let F (/ be the logit of high bycatch for season i 
and area j and let F jk be the logit of high bycatch 
for season i and area k. 
The hypotheses being tested were 
Ho'Fij ~ Fik ~ 0’ 
where F-- = a + (3 s + (3 A + [3 SA ; 
Fik= a + (3 ; s + (3/ + (3 ; / A ;and 
j and k = area 11-12, area 13-14, area 15-16, 
and area 17-18, such that j * k for 
each i, where i = spring, summer, 
and fall. 
Because 30 contrasts were performed, the type-I 
error level of 0.10 was adjusted by using the 
Bonferroni technique, and only P-values less than 
0.0033 were considered significant. The estimated 
odds ratios for the conditions associated with the 
hypotheses were calculated from the parameter es- 
timates given by the analysis. 
Bycatch species associations To examine the as- 
sociation between species and fates of the releasable 
bycatch, we used correspondence analysis on a spe- 
cies-by-fate table for all seasons and areas combined. 
Area and species associations of the releasable by- 
catch were also examined for each of the three seasons 
with correspondence analysis on species-by-area tables. 
For all correspondence analyses we defined two 
groups of species. The first group, consisting of those 
species that were common in terms of number and oc- 
currence, was used in the main table. Releasable 
bycatch species falling into this group had a minimum 
of 230 individuals and were found in at least 30% of 
the sets. The second group of species consisted of re- 
leasable bycatch that were less common; these were 
species for which a minimum of 30 individuals were 
observed, which occurred in at least 4% of the sets, and 
which did not meet our criteria for well represented 
species. These species were included as supplementary 
variables in our analysis (Greenacre, 1984). Supplemen- 
tary variables are represented as points in the joint 
row and column space but are not used in determining 
the locations of the active rows and columns of the table. 
Species included in the main and supplementary table 
accounted for 97% of the total number of organisms 
observed during the study period. Species that did not 
meet these criteria were not used in the analyses. 
Results 
Preliminary analysis 
A total of 15,579 bycatch organisms representing 62 
species or species groups were observed as releas- 
able bycatch in 257 sets. The estimated catch of stan- 
dard menhaden per set ranged from 5,000 to 500,000 
with a median, mean, and standard deviation of 
50,000, 67,000, and 61,000 respectively. Skewness 
and kurtosis values of 2.5 and 10.7 indicated that 
the distribution of the estimated menhaden catch was 
positively skewed (Fig. 2). 
