330 



Abstract.— Fisheries discard data 

 are often characterized by a smooth dis- 

 tribution of positive amounts of per-set 

 discard but with an extremely large 

 number of zero observations. This dis- 

 continuity is difficult to fit with a stan- 

 dard distribution. One approach is to 

 model per-set discard with a mixture 

 of two distributions, with one compo- 

 nent representing the zero observations 

 and the other representing the obser- 

 vations of positive discard. In this pa- 

 per, we describe such a mixture model 

 that is suitable when the discard ob- 

 servations have been rounded to inte- 

 ger amounts. In particular, when 

 "rounded" zeros (representing small 

 amounts of discard) and "true" zeros 

 (representing no discard) are indistin- 

 guishable in the data, the mixture 

 model can be used to estimate the pro- 

 portion of either. We fit this model to 

 tuna discard data collected by observ- 

 ers aboard the U.S. tuna purse-seine 

 fleet in the eastern tropical Pacific 

 Ocean during the years 1989-92. We 

 use the model to estimate discard per 

 set, allowing the model parameters to 

 depend upon fishing strategy and geo- 

 graphic location, and we estimate mean 

 discard per set fisherywide. 



A mixture model for estimating 

 discarded bycatch from data with 

 many zero observations: 

 tuna discards m the eastern tropical 

 Pacific Ocean 



Peter C. Perkins 

 Elizabeth F. Edwards 



Southwest Fisheries Science Center 

 National Marine Fisheries Service, NOAA 

 PO Box 271. La Jolla. California 92038 



Manuscript accepted 26 October 1995. 

 Fishery Bulletin 94:330-340 1 1996). 



Many fisheries catch unwanted in- 

 dividuals of nontarget species in 

 addition to target species. This 

 bycatch is generally discarded and 

 in many fisheries few, if any, indi- 

 viduals survive capture and discard 

 (e.g. Joseph, 1994). Estimating the 

 extent of such discard is increas- 

 ingly important as fisheries manag- 

 ers contend with situations where 

 unwanted catch in a fishery is de- 

 sirable in other contexts. For ex- 

 ample, bycatch in one fishery may 

 include juvenile members of the tar- 

 get species in the same or another 

 fishery, or individuals from threat- 

 ened, endangered, or protected spe- 

 cies (e.g. Collins and Wenner, 1988; 

 Caillouet et al., 1991). 



Despite their increasing impor- 

 tance, bycatch and discard remain 

 relatively unstudied. Few fisheries 

 routinely measure discards so that 

 the amount of discard usually must 

 be estimated rather than reported 

 directly (e.g. Berger et al., 1989). 

 The U.S. tuna purse-seine fishery 

 in the eastern tropical Pacific Ocean 

 (ETP) provides an opportunity to 

 examine this problem because 

 quantitative information on discard 

 of tuna (including both nontarget 

 tuna species and juveniles of target 

 species ) has been collected from the 

 fishery since 1988. 



A flexible approach is required to 

 model tuna discard from this fish- 

 ery because the purse-seine vessels 

 capture fish using three distinct 

 fishing strategies. These strategies 

 are defined by the different types 

 of sets involved: "log fishing," 

 "school fishing," and "dolphin fish- 

 ing." Log fishing catches tuna by 

 setting purse seines around fish 

 associated with floating objects. Log 

 sets usually capture schools of small 

 ( 30-50 cm (yellowfin tuna, Thunnus 

 ctlbacares, or mixed schools of small 

 yellowfin and like-size skipjack 

 tuna, Katsuwonus pelamis. School 

 fishing catches tuna by setting 

 purse seines around schools com- 

 posed purely of tuna (again, usually 

 small fish and either pure schools 

 of yellowfin or mixed schools of yel- 

 lowfin and skipjack tuna), located 

 by surface disturbances created by 

 the schools. Dolphin fishing catches 

 tuna by first locating surface distur- 

 bances created by closely associated 

 dolphins (NRC, 1992) and by setting 

 purse seines around both tuna and 

 dolphins. Tuna associated with dol- 

 phins almost always consist of pure 

 schools of large (80-120 cm ) yellow- 

 fin tunadATTC, 1989). 



Log fishing generates large amounts 

 of tuna discard in almost every set, 

 whereas school fishing generates 



