488 



Fishery Bulletin 101(3) 



species sample weight 



species sample number 



the weight of the t"^ species 

 in the bycatch sample from 

 the/*^ net; and 

 the number of whole indi- 

 viduals of the /''' species in 

 the bycatch sample from 

 the./"^ net. 



To expand the observed bycatch from selected net to the 

 entire tow, I multiplied either the species net weight or the 

 species net number from each net by the number of nets 

 towed concurrently. 



Bycatch estimation To compare the methods of bycatch 

 estimation used in past studies, I estimated the bycatch 

 of Atlantic croaker, spot, and weakfish (three of the most 

 commonly caught bycatch species) using two categories 

 of statistical estimators: a mean-per-unit estimator using 

 the mean observed bycatch per day expanded by the total 

 number of days fished (the CPUE-mean-per-unit method) 

 and a ratio estimator using the observed ratio of fish to 

 shrimp expanded by the total shrimp landings (the F:S ratio 

 method). Because my purpose was to compare bycatch esti- 

 mation methods and not to generate bycatch estimates that 

 could be used for management purposes, I estimated total 

 bycatch of these three species only for certain months and 

 geographic regions within North Carolina corresponding to 

 the times and areas that I observed shrimp trawling. The 

 term "shrimp fleet" in the following paragraphs therefore 

 refers only to shrimpers operating in those times and areas. 

 In the calculations, I used bycatch per day instead of the 

 bycatch per tow or bycatch per trip. I could not use tow as 

 the unit of effort because there was no information on the 

 number of tows made by the fleet to use as an expansion 

 factor Although information on the number of trips made 

 by the fleet was available, I could not use trip as the unit of 

 effort because, although trips can last several days, all of the 

 trips that I sampled were one-day trips. If my observations 

 had also included a random sample of multiday trips, the 

 unit of effort would have been trips instead of days. 



The CPUE mean per unit method was based on the fol- 

 lowing equations: 



Mean ohsened hyaiich^ 

 day 



X"^- 



(4) 



where mean observed _ the observed average bycatch in 

 bycatch per day weight or number of the i^^ spe- 

 cies on the d^^ day; 

 n = the number of days observed; and 

 F^ J = the sum of the expanded weight 

 or number of the (''' bycatch spe- 

 cies observed in all tows made 

 on the d"' day; and 



mean obser\'ed bycatch' 



Total bycalcli, .-/.yf =  x 



clay 



tiiiiil trips X 



mean days 

 trip 



(5) 



where total bycatch ^(.p^,^. = the total fleet bycatch 



of the (''^ species esti- 

 mated by the CPUE 

 method; 



mean observed bycatch ^ per day = the observed average 



bycatch of the i^^ spe- 

 cies per day from Equa- 

 tion 4; 

 total trips = the total number of trips 

 taken by the shrimp 

 fleet; and 

 mean days per trip = the average number of 

 days that each fishing 

 trip lasted based on the 

 fleet. 



The total trips and mean days per trip were calculated from 

 the North Carolina Division of Marine Fisheries (NCDMF) 

 trip ticket database, as follows. To obtain the total number 

 of trips, I first collapsed the trip ticket database so that each 

 fisherman could have only one ticket for shrimp on a single 

 day. In the database, each trip ticket does not represent one 

 trip, but the sale to one dealer Fishermen could obtain more 

 than one trip ticket per day by selling different size catego- 

 ries of shrimp (each size category commands a different price, 

 and generates a separate trip ticket ), or by selling their catch 

 to more than one dealer I then calculated the time (in days) 

 between the first and last trips for each fisherman whose 

 trips occun-ed between 1 July and 31 October in Pamlico 

 Sound and its tributaries (called the northern region) and 

 between 1 August and 31 October in the Cape Fear River 

 and nearby waters (the southern region). Because inshore 

 waters were closed to shrimping on weekends, I multiplied 

 all time spans greater than 7 days by 5/7 (0.714) to obtain 

 the number of days fished. The number of days fished was 

 summed and then divided by the number of trips for each 

 region to obtain the mean days per trip. 



The F:S ratio estimator method was initially undertaken 

 in two ways: by using the mean of the fish to shrimp ratios, 

 called the mean of the ratios or the "basic" F:S ratio esti- 

 mator method (Equation 6), and by using the ratio of the 

 average catch offish to the average catch of shrimp, called 

 the ratio of the means or the "grand" F:S ratio estimator 

 method (Equation 7). The two methods are shown math- 

 ematically as follows: 



Total h\catch, , ^„ = — > -^ x total shrimp landed. 



(6) 



Total hvcatcli ,v,. =-^ x total slniinp landed, (7) 



rf=l 



where total bycatch, y,,i, = the total fleet bycatch of the ;"' 



species estimated by the basic 

 F:S method; 

 total bycatch, ^^g = the total fleet bycatch of the /"' 

 species estimated by the grand 

 F:S method; 



