Diamond: Estimation of shnmp trawl bycatch 



489 



F, J = the sum of the expanded 

 weight or number of the ;'"' 

 species observed in all tows 

 made on the d^^ day; 

 Sj = the sum of the expanded weight 

 of market shrimp observed in 

 all tows made on the c/* day; and 

 n = the number of days observed. 



Because of the small number of days observed in each 

 area, I also used the basic F:S ratio estimator with the 

 Hartley-Ross correction for biases caused by small sample 

 size (Cochran, 1977): 



Toliil hvccilcli^ f^if = total hxcatch, ^ j„ H (\\-rx), (8) 



)i - 1 



where total bycatch^ ^jf^ = the total fleet bycatch of the ;'"' 



species estimated by the bias- 

 corrected F:S ratio estimator; 

 total bycatch^ p,.g = the total fleet bycatch of the ("^ 

 species estimated by the basic 

 F:S ratio using Equation 6; 



n = the number of days observed; 



N = the total number of days fished 

 from the trip ticket database; 



y, = the mean bycatch of of the ;"^ 

 species observed per day in 

 weight or numbers from Equa- 

 tion 4; 



F = the mean of the F:S ratios from 

 Equation 6; and 



.V = the mean catch of market 

 shrimp observed per day in 

 weight or numbers. 



Total shrimp landings used in Equations 6 and 7 were 

 obtained from the NCDMF trip ticket database for the 

 northern region from July to October and for the southern 

 region from August to October. In the trip ticket database, 

 some shrimp weights were reported as "heads-on" and 

 others as "heads-ofT'; therefore I converted heads-off weight 

 to heads-on weight with a conversion factor of 1.583, taken 

 from the average of pink, brown, and white shrimp conver- 

 sion information used by the National Marine Fisheries 

 Service (Fisheries Statistics of the United States, 1977). 



Bycatch simulations 



For the bycatch simulations, I created different fishing 

 fleets of 1000 "boats" in Matlab 5.0 (The Mathworks, 

 Natick, MA). For the normally distributed catch data, the 

 catch of fish, the catch of shrimp, and the hours fished for 

 each boat in a fleet were generated by using multivariate 

 random normal distributions with a mean and variance 

 that was specific to that fleet. I simulated observer data 

 for each fleet by taking a random sample of boats from 

 the fleet, resampling the sample 1000 times, then using 

 the mean of the bootstrapped observer data in the equa- 

 tions described below to estimate fleet bycatch. In the dif- 

 ferent fleets, the mean catches of fish and shrimp ranged 



from 0.01 to 1000, giving fish to shrimp ratios of 0.001 to 

 100,000. In some fleets, the catches offish and shrimp were 

 correlated, with correlation coefficients ranging from 0.5 to 

 -0.5 (Table 1). Coefficients of variation (CVs) for fish catch 

 and hours fished ranged from 20% to 80%, CVs for shrimp 

 catch ranged from 20% to 120%, and the number of obser- 

 vations ranged from 20 to 500, giving observer coverages of 

 2% to 50%. of the fleet. Although the range of mean catches 

 I used in the simulations may seem fairly broad, they are 

 within the range of the field data, depending on whether 

 these were the mean catches per tow, per day, or per trip. 

 The ranges of CVs for fish and shrimp catches were fairly 

 narrow compared to those from the field data because CVs 

 vary up to several hundred percent, particularly for patchy 

 species. Observer coverage in the field is usually much less 

 than 50%>, but I picked 50% as the upper limit of the range 

 to see if greater observer coverage (i.e., a greater sample 

 size of observations per fleet) increased the accuracy of the 

 bycatch estimates. 



Bycatch estimates were calculated by using a mean per 

 unit estimator and four forms of the ratio estimator, as 

 described below. The CPUE mean per unit estimator was 

 calculated by using the following equations, which are 

 more general versions of Equations 4 and 5: 



Total bycatch, , 



Mean obsen'ed bycatch, I 

 UE 



Mean hvcatch 



(9) 



UE 



-xtntal fleet effort. (10) 



where mean observed the observed average bycatch of 

 bycatch^ per UE = the i"" species per unit of effort 

 (tow, day, or trip); 

 n = the number of observed tows, 

 days, or trips; 

 F, ug = the expanded weight or number 

 of the i'*' bycatch species observed 

 on the [/£"' tow, day, or trip; 

 total bycatch-,(,piji' = the total fleet bycatch estimated 

 by the CPUE method; and 

 total fleet effort = the total number of tows, days, 

 or trips fished by the fleet. 



The four ratio estimators were as follows: 1) the mean 

 of the individual F:S ratios, called the "basic F:S'' ratio 

 estimator (Eq. 11), 2) the ratio of the F:S means, called 

 the "grand F:S" ratio estimator (Eq. 12), 3) the mean of the 

 individual catch per effort ratios using a variable measure 

 of effort such as hours fished as the auxiliary variable, 

 called the "basic CPE" ratio estimator (Eq. 13), and 4) the 

 ratio of the mean catch per mean effort using a variable 

 measure of effort such as hours fished as the auxiliary 

 variable, called the "grand CPE" ratio estimator (Eq. 14). 

 Both F:S ratio estimators (Eqs. 11 and 12) are similar to 

 the ones used in the field study (Eqs. 6 and 7), except that 

 the observations could be from a tow, day, trip, or other 

 measure of unit effort, rather than one day, as used in the 

 field study. 



