Ortiz et al : Estimates of bycatch from tfie sfinmp trawl fishery in tfie Gulf of Mexico 



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our study, the delta lognormal model showed a larger year 

 variability of bycatch with prominent peaks in 1980 and 

 1992. The normalized plot of Spanish mackerel bycatch 

 illustrates that estimates from the general linear model 

 and delta lognormal model followed similar trends from 

 1972 to 1981, and from 1988 to 1995 (Fig. 7). The time 

 period from 1984 to 1987, the period of greatest oscilla- 

 tion in bycatch estimates for the delta lognormal model, 

 corresponds with the years of no bycatch observations in 

 the commercial fishery. Although delta lognormal bycatch 

 estimates show a comparable trend to the general linear 

 model estimates in the later years (1987-95), the magni- 

 tude of bycatch is much greater; the peak estimate of 14.4 

 million fish in 1993 is twice as high as the reported esti- 

 mates from the general linear model (Nichols'"). 



The delta lognormal model protocol appears to be an 

 improved alternative procedure for estimating shrimp 

 bycatch in the U,S. Gulf of Mexico compared with the 

 currently used general linear model. In theory, the delta 

 model allows for an explicit probability for zero catches, 

 which are highly common in the bycatch data set, espe- 



cially when dealing within single species cases. Myers and 

 Pepin (1990) stated that lognormal-based estimators are 

 sensitive to violations of model assumptions, in particular 

 if the number of observations is below 40 or if there is no 

 confirmation that the sample came from a true lognormal 

 distribution (or if both situations occur). However, their 

 arguments are restricted to the positive tows (i.e. nonzero 

 observations); they concluded that lognormal estimators 

 should be used only in cases where the assumed lognor- 

 mal distribution can be confirmed. Following their criteria, 

 Myers and Pepin's arguments should then be applied to 

 the delta lognormal model (more specifically to the density 

 estimation component that models the nonzero catches) 

 and to the current general linear model as well (if a log- 

 normal distribution can be assumed for all observations, 

 Nichols et al.-). In the bycatch database, there are a large 

 number of cells with low number of observations (i.e. <40). 

 Restricting the database to cases where the number of 

 observations per stratum (year, area, season, depth, and 

 dataset) were greater than 40, we were able to use cumu- 

 lative CPUE distributions more approximate to lognormal 



