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Fishery Bulletin 96(2), 1998 
sented by Richards et al. (1994), who proposed the use 
of a modified generalized logit model to carry out a 
categorical form of response surface analysis, allow- 
ing the estimation of transformation parameters on 
the explanatory variables along with other para- 
meters. Perkins and Edwards (1996) have used mix- 
ture models, consisting of the negative binomial dis- 
tribution with added zeros, as a solution to analyz- 
ing bycatch with many zero observations. 
In this paper we use loglinear and logit models to 
examine patchy data with bycatch from the gulf 
menhaden, Brevoortia patronus, fishery. Menhaden 
bycatch can be classified into two groups: 1) bycatch 
that is pumped directly into the hold with the men- 
haden and that is termed “automatically retained 
bycatch”; and 2) all other bycatch that is termed “re- 
leasable bycatch.” In this paper we analyze only re- 
leasable bycatch. With the exception of Christmas et 
al. (1960) and Condrey, 1 previous studies on menha- 
den bycatch have not taken releasable bycatch into 
account. Furthermore, all previous work has been 
qualitative in nature. Our examination of releasable 
bycatch, however, serves both as an analysis of patchy 
data with categoi’ical techniques and as a quantita- 
tive description of a biologically important portion 
of the menhaden bycatch. 
Species taken as bycatch may be caught because 
they are associated with the target species or simply 
because they were encountered on a random basis 
(Hall, 1996). An analysis of the structure of bycatch 
species assemblages associated with a fishery can 
provide valuable information for both management 
and ecological purposes. Hudson (1990), examining 
shrimp and fish bycatch assemblages in the Cana- 
dian Eastern Arctic, observed three associations that 
she proposed were related to the origin of the pre- 
dominant water masses in the region. Harris and 
Poiner (1991 ) documented changes in the species com- 
position of demersal fish fauna over a 20-year period 
in the Gulf of Carpentaria, Australia, and suggested 
that increases in the benthopelagic taxa over this 
period could be partially explained by discard of 
bycatch in the banana prawn fishery. Because little 
information on spatial and temporal associations for 
species assemblages of the menhaden fishery exists, 
we describe areal and temporal associations for these 
species, together with the fate of these species, as a 
first step in accruing such information. We have used 
correspondence analysis, a categorical form of ordi- 
nation, to describe these association patterns. 
1 Condrey, R. E. 1994. Bycatch in the U.S. Gulf of Mexico men- 
haden fishery. Results of onboard sampling conducted in the 
1992 fishing season. Coastal Fisheries Institute, Louisiana 
State Univ., Baton Rouge, LA. Final report for NA27F0007-01, 
42 p. [Available through the NOAA library, Silver Springs, MD.] 
The fishery 
The U.S. Gulf of Mexico menhaden fishery has ex- 
isted since the late 1800’s (Nicholson, 1978) and is 
the largest fishery in tonnage in the northwestern 
Gulf of Mexico. Estimates of menhaden landings for 
the 1994 fishing season were approximately 0.7 mil- 
lion metric tons (t) (Leard et al., 1995). Although gulf 
menhaden is the primary clupeid sought, finescale 
menhaden, B. gunteri, yellowfin menhaden, B. 
smithi, and Atlantic thread herring, Opisthonema 
oglinum, are occasionally taken opportunistically 
(Leard et al., 1995). 
Schools of menhaden are located visually by the 
senior crew aboard the fishing vessel or with the help 
of spotter planes. A purse seine, deployed from a pair 
of small (12.2-m) purse-seine boats, is used to en- 
circle the school. Once the school is encircled, the 
bottom of the net is drawn up to hold the catch. The 
seine is then retrieved mechanically by each purse- 
seine boat until the fish are confined to a small sec- 
tion of the net. The catch is then pumped into the 
refrigerated hold of a larger (43 to 61 m) carrier ves- 
sel. The number of times the purse net is set each 
day depends on the availability and size of schools. 
Schools contain from 3 to 100 t of menhaden (Leard 
et al., 1995). Once the hold of a vessel is full, or a trip 
is otherwise complete, the menhaden are transported 
to one of the processing plants located from Moss 
Point, MS, to Cameron, LA. Although the fishing area 
extends from Apalachicola, FL, to Freeport, TX, more 
than 86% of the menhaden caught from 1990 to 1994 
were taken off Louisiana (Leard et al., 1995). 
Materials and methods 
Loglinear and logit models 
As reviewed in Agresti (1990) and Freeman (1987), 
loglinear and logit models are special cases of the 
generalized linear models introduced by Nelder and 
Wedderburn (1972). Agresti (1990) summarizes a 
generalized linear model as “a linear model for a 
transformed mean of a variable having a distribu- 
tion in the natural exponential family.” 
Loglinear models describe association patterns 
among categorical variables. With this approach, cell 
counts in a contingency table are modeled in terms 
of association among the variables. Loglinear mod- 
els may be viewed as analogous to correlation analy- 
sis where cell counts in a loglinear contingency table 
are treated as independent Poisson variables. 
In a 1 x J table, where N = IJ cells consisting of n 
multinomial samples, let n k denote the count of the 
