490 



Fishery Bulletin 101 (3) 



1 V- F. 



Total bycatch- ^^^ = — > — ^ x total shrimp landed (11) 



Total bycatch 



"-^. 



■■=1 



- X total shrimp landed ( 12) 



where total bycatch^ pgg = the total fleet bycatch of the i"^ 



species estimated by the basic 

 F:S ratio estimator; 

 total bycatch^ pgQ = the total fleet bycatch of the i'^ 

 species estimated by the grand 

 F:S ratio estimator; 

 F, ^, = the expanded weight or number 

 of the /''^ bycatch species ob- 

 served in the e'*' tow, day, or trip; 

 S^ = the expanded weight of market 

 shrimp observed in the e'*^ tow, 

 day, or trip; 

 n = the number of tows, days, or 

 trips observed; and 

 total shrimp landed = the sum of the total weight of 

 shrimp landed by the fleet. 



1 -v-i F 

 Tdtal b\calch^^p^g = —y —'^^x total hours fished (13) 



Total bycatch ^ p^^; = -^ x total hours fished (14 ) 



where total bycatch, cpi^g = the total fleet bycatch of the f* 



species estimated by the basic 

 CPE ratio estimator; 

 total bycatch, (-.p^-Q = the total fleet bycatch of the 

 /"' species estimated by the 

 grand CPE ratio estimator; 

 F, ^ = the expanded weight or 

 number of the i*-^ bycatch 

 species observed in the e"" 

 tow, day, or trip; 

 //^, = the hours fished in the e''' tow, 

 day, or trip; 

 n = the number of observed tows, 

 days, or trips; and 

 total hours fished = the sum of all hours fished by 

 the fleet. 



To avoid confusion, it is important to note how fishing 

 effort is used in the five estimators. All five estimators use 

 a unit measure of fishing effort, such as a tow, day, or trip, 

 as one sample, and the sample size for a fleet is the number 

 of tows, days, or trips observed. In the CPUE mean-per-unit 

 estimator, the estimate of total bycatch is a simple expan- 



sion of the observed bycatch per sample to the whole fleet. 

 In the F:S ratio estimators, the unit effort appears in the 

 calculations because the ratios of fish to shrimp are the 

 amounts caught per tow, day, or trip (i.e. per sample). In 

 the CPE ratio estimators, two measures of effort are used. 

 As before, one measure of effort is the unit effort, such as 

 a tow, day, or trip, that is equivalent to a sample, and the 

 second measure of effort is the variable measure of effort, 

 such as the hours fished, the distance towed, or the area 

 covered, that is used as the auxiliary variable. The CPE 

 ratio estimator is thus based on the amount offish caught 

 per hour fished (for example) in each tow, day, or trip. 



The delta lognormal simulations were very similar to 

 the normal simulations, except that I simulated the catch 

 of fish and shrimp by using probabilities of catching fish 

 or shrimp ranging from 0.05 to 0.95, multiplied by average 

 catches offish or shrimp generated from random lognormal 

 distributions with means ranging from 0.01 to 1000. Log- 

 normal functions have parameters of// and a'^. which are 

 the mean and variance of the normally distributed variable 

 before logarithmic transformation. To obtain values of;/ 

 and a^ from a lognormal distribution with a given mean 

 and variance, I used an iterative procedure (the Solver 

 procedure in Microsoft Excel, vers. 2000, Microsoft Corpo- 

 ration, Redmond, WA) to estimate fj and o^ based on the 

 following equations: 



mean = e 



[-^) 



(15) 



(16) 



where mean = the mean of the lognormal distribution of 

 the catch offish or shrimp; 

 var - the variance of the lognormal distribution 

 of the catch offish or shrimp; 

 H = the mean of the normally distributed catch 

 of fish or shrimp before logarithmic trans- 

 formation; and 

 o^ = the variance of the normally distributed 

 catch of fish or shrimp before logarithmic 

 transformation. 



Levels of observer coverage and CVs for fish catch, 

 shrimp catch, and effort and were the same as in the 

 normally distributed data. In these simulations, sampled 

 shrimp catch could be zero if the probability of catching 

 shrimp was low and the number of observations was small, 

 leading to F:S ratios of infinity. In these cases, for the basic 

 F:S ratio estimator, the fish-to-shrimp ratio was the catch 

 offish divided by the expected catch of shrimp (probability 

 of catching shrimp times the mean catch ). For the grand F: 

 S ratio estimator, if the average bootstrapped sample catch 

 of shrimp was zero, Matlab substituted a value of 65535 

 to avoid division by zero. To avoid biases, these grand F; 

 S simulations were left out of the subsequent analyses. In 

 field saini)liiig, tows that caught no shrimp at all were rare, 

 but tows that caught only small unmarketable shrimp that 

 were discarded as bycatch occurred occasionally early in 

 the season and after big rainstorms. 



