Ortiz et al.: Estimates of bycatch from the sfirimp trawl fishery in the Gulf of Mexico 



587 



Finfish 



c = l 



__4_ c = 0.5 

 ....... c = 10 



....... minpos CPUE 



72 74 76 78 80 82 84 86 88 90 92 94 



1.4E+6 



1.2E+6 



i= 1.0E+6 , 



•5 8.0E+5 J 



I 6.0E+5 



1 4.0E+5 . 



2 0E+5 



OOE+0 



Atlantic croaker 



Red snapper 



72 74 76 78 80 82 84 86 88 90 92 94 



Spanish mackerel 



Figure 2 



Estimated total with the general linear model with different c-values used in the logarithmic transformation of bycatch CPUE. 

 Base scenario (f=l). 



cies. For Spanish mackerel and red snapper, using c = 10 

 increased the estimates of bycatch ( 1009^ and 15%. respec- 

 tively). In contrast, bycatch estimates decreased for Atlan- 

 tic croaker and finfish (75% and 6%, respectively). Wlien 

 the c was the smallest positive value of the data, annual 

 estimates increased on average 47% for red snapper. 43% 

 for finfish. and 1694% for Atlantic croaker, whereas bycatch 

 estimates decreased on average 70% for Spanish mackerel. 

 These results show that the general linear model is 

 highly sensitive to the logarithmic c value added to the 

 observed CPUE values. Although it is known that loga- 

 rithm transformations are affected by the selection of a c 

 value, the large variations in magnitude of estimates for 

 bycatch species should at least merit a review and analy- 

 sis of the criteria for choosing an appropriate c value. In 

 a review of logarithmic transformations. Berry ( 1987) sug- 

 gested choosing a c that normalizes the log-transformed 

 data. He specified an additive function of the skewness 

 and the kurtosis of the data, where skewness and kurtosis 

 are defined as 



^1*'"' = V^'.v-y*' /^no') and 



gjc): 



iv-v)' Hna')-3 



respectively. 



where y = the predicted means; 

 y = the observations; and 



(T = the estimated standard deviation within the 

 defined strata. 



When the observations are normally distributed, then the 

 gj function has a mean of zero, and the function g., has a 

 mean equal to -6/(d-t-2), where d is the number of degrees 

 of freedom of the error. The additive function of skewness 

 and kurtosis is then defined as 



gJc) = \gj^, \ + \gJc) + 6 / {d + 2)\. 



Thus, the c value that minimizes gn'c) will make the 

 residuals closer to a sample that follows a normal distribu- 

 tion. Using CPUE values for Spanish mackerel, we evalu- 

 ated several c values ranging from l.OE - 8 up to l.OE + 3. 

 We did not find a minimum solution for g^ic), but rather an 

 asymptotic behavior with c values less than 0.05, indicat- 

 ing that it is not possible to normalize the Spanish mack- 

 erel bycatch data by using a logarithm transformation. 

 Therefore, there is not an objective criterion for selecting 

 a particular c value, and as shown before, even relatively 

 small changes of the c value could cause significant varia- 

 tion of the annual bycatch estimates. Furthermore, inde- 

 pendent of the method used to select the c constant in 



