Ortiz et a\ . Estimates of bycatch from thie sfirimp trawl fishery in the Gulf of Mexico 



585 



Table 1 



Distribution of number of cells and observations per cell for the general linear model and the modified models. The 3-area model 

 refers to a reduced number of levels in the area factor of the general linear model (from 4 to 3) by combining areas 2 and 3 into a 

 single area (see text for description of each area). The 2-season model refers also to a reduced number of levels in the season factor 

 of the general linear model where season 1 is from September to April and season 2 is from May to August. The no-depth-zone 

 model refers to the general linear model without the depth zone factor. The combined model refers to a model of 3 areas, 2 seasons, 

 and no depth zone. The year and dset (data set) refers to a general linear model with only these two factors (i.e. excluding season, 

 area, and depth-zone factors). Percent coverage refers to the proportion of cells in the matrix that have tow observations, both by 

 type of data (commercial, research, and combined) as well as the number of positive bycatch tows with Spanish mackerel. 



Matrix structure of general linear model 



Research 



Commercial 



Total 



Scenario 



No. cells 

 of matrix 



Cells with 

 tows 



Cells with 

 Spanish 



No. cells Cells with Cells with 

 of matrix tows Spanish 



General linear model .576 274 175 576 181 77 



3 areas 432 176 129 432 148 68 



2 seasons 384 236 153 384 152 69 



No depth zone 288 143 110 288 112 61 



Combined 144 80 66 144 71 41 



Year dset only 24 24 24 24 15 10 



Percentage coverage 



General linear model 

 3 areas 

 2 seasons 

 No depth zone 

 Combined 

 Year dset only 



erel, an(i reci snapper) were use(i to compare results of 

 the sensitivity analysis. Atlantic croaker is a species com- 

 monly caught as bycatch, found in about 6V7r of tows. Red 

 snapper and Spanish mackerel are important commercial 

 and recreational fisheries in the U.S. Gulf of Mexico; the 

 directed fishery management actions for these fisheries 

 are influenced by the level of bycatch in the shrimp trawl 

 fishery. Red snapper is caught as bycatch in the shrimp 

 fishery in about 28% of tows, whereas Spanish mackerel is 

 less commonly caught in only 5% of tows. 



To evaluate the general linear model, we first describe 

 some characteristics of the database that are important 

 regarding assumptions entailed with the use of the model 

 and analysis of the model , then we present a sensitivity 

 analysis on the model structure and parameters. Three 

 main analyses were performed: 1) analysis of the general 

 linear model matrix structure, 2) analysis of the logarith- 

 mic scaling of the observed CPUE values, and 3) analysis 

 of the standard tow time unit used to calculate observed 

 CPUE values. 



Evaluation of the general linear model 



The present general linear model configuration for esti- 

 mating bycatch created a matrix of 1152 cells, comprising 



data for 24 years, 2 datasets, 4 areas, 3 seasons, and 

 2 depth zones. Although there were a relatively large 

 number of observations in the database (26,380), the per- 

 centage of cells in the matrix that had observations was 

 only 39'>, only 4160 tows (16'7f) were from commercial 

 vessels during normal shrimp fishing operations, and the 

 remaining 22,220 (84%) tows were from research vessels. 

 In addition, the number of observations per cell varied 

 largely, from 1 to 466 within research tows, and from 1 to 

 181 within the commercial tows. 



Given the unbalanced distribution of observations per 

 cell, we investigated the effects of the matrix structure 

 on the general linear model. Our approach was to fit the 

 model to scenarios with a reduced number of levels within 

 factors or a reduced number of factors in the model (or to 

 scenarios with both). For example, we combined seasons 1 

 and 3 to reduce the season factor to two levels or we elimi- 

 nated the season factor from the model. Table 1 describes 

 all the scenarios' evaluated. Correspondingly, shrimping 

 effort was adjusted to the new general linear model matrix 

 by adding the annual shrimping effort within the modified 

 strata, and annual bycatch was estimated as the product 

 of the predicted CPUEs and the shrimping effort for each 

 cell. Defining the percentage of coverage as the number of 

 cells with observations divided by the total number of cells 



