Perkins and Edwards: A mixture model for estimating discarded bycatch 



331 



moderate amounts of tuna discard and in a 

 smaller proportion of sets than does log fishing 

 (Joseph, 1994). Dolphin fishing generates small 

 amounts of tuna discard and only infrequently. 

 Thus, tuna discard data from dolphin sets are 

 almost all zero observations, whereas data from 

 log sets are mostly nonzero observations, and 

 school sets are an intermediate case. 



In this paper we develop a method for using 

 a single probability distribution to model dis- 

 card per set for these three disparate types of 

 data and show how to use the model to esti- 

 mate mean discard per set for each set type. 

 The focus of the present study is development 

 and description of the model as a solution to a 

 common problem in discard estimation. In gen- 

 eral, the method presented is applicable to any 

 situation involving analysis of data character- 

 ized by subsets with varying proportions of zero 

 observations. Detailed results of applying the 

 model and its implications for the U.S. tuna 

 purse-seine fishery in the ETP are the subject 

 of a future paper. 



Methods 



Data 



The data consisted of per-set estimates of total tons 

 of tuna discarded by the U.S. fleet only. We did not 

 have access to data on species or size composition of 

 tuna discards nor to data on nontuna discards. 



Data were collected by National Marine Fisheries 

 Service (NMFS) or Inter-American Tropical Tuna 

 Commission (IATTC) observers placed aboard U.S. 

 tuna purse-seiners during routine fishing trips to the 

 eastern tropical Pacific Ocean (Fig. 1) as part of a 

 bycatch study initiated in 1989 by the IATTC. Ob- 

 servers recorded time and position of all sets made 

 by U.S. vessels fishing in the ETP during the 31- 

 month study period (from 1 September 1989 to 30 

 March 1992). Observer coverage was 100% during 

 this period. However, during the first eleven months 

 (from 1 September 1989 to 30 July 1990), discard 

 information was recorded only for approximately half 

 of the sets. Observers recorded discards for all sets 

 during the remaining twenty months. 



Because it was not feasible to weigh tuna discard 

 directly, observers estimated the discard weight by 

 counting the number of brailers (large fish baskets) 

 used to empty the net after each set, multiplying by 

 an estimated tonnage per brailer, and then multi- 

 plying by the estimated fraction of nontarget tuna 

 in the catch. Observers estimated this fraction bv 



Pacific Ocean 



160 W 150 140 130 120 110 100 90 



80 70 W 



Figure 1 



Geographic strata used in developing models to estimate mean 

 discard per set for the U.S. tuna purse-seine fleet fishing in the 

 eastern tropical Pacific Ocean, 1989-92 (Federal Register, 

 1989). Area 3 includes all ETP not explicitly included in areas 

 1 and 2. 



observing the composition of brailers or by observ- 

 ing catch sorting on deck. Occasionally the majority 

 of the catch was discarded before being brailed 

 aboard. In these cases, observers estimated discard 

 weight by first estimating the weight of the total 

 catch and then subtracting an estimate of the ton- 

 nage loaded by brailer. 



Observer estimates of discard tonnage were 

 rounded to integer values, with rounding interval 

 increasing with amount of discard (Fig. 2). There is 

 a systematic tendency toward rounding to the near- 

 est 5 or 10 metric tons (t) for small and medium esti- 

 mates of discard and to the nearest 25 or 50 t for the 

 largest estimates. For sets with moderately small 

 amounts of discard, observer estimates tended to be 

 more precise because the bycatch, as well as the tar- 

 get fish, were brailed aboard the vessel, then sorted 

 on deck. This allowed the discard to be easily com- 

 pared with the total catch. For sets with large 

 amounts of discard, the fish may not have been 

 brought on board, making precise estimates more 

 difficult and rounding tendencies greater. For sets 

 with very small amounts of discard, weights were 

 rounded to the nearest ton so that it was not pos- 

 sible to distinguish observations with no discard from 

 those with very small amounts of discard (less than 

 one-half ton). Thus, "zero observations" may corre- 

 spond to either case. 



We did not attempt to account for the uncertainty 

 introduced by these sources of measurement error 

 and rounding. In the absence of data or studies for 

 determining the ground truth of observer estimates 



