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Fishery Bulletin 91 (4|. 1993 



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MONTHS AT SEA 



Figure 2 



Months spent at sea per trip by U.S. -registered tuna purse-seine 

 vessels carrying observers during 1987. 



trips killed no spotted dolphins, and trips with higher 

 kills occurred with decreasing frequency. Data for 

 whitebelly spinner dolphins were intermediate in qual- 

 ity. They were fewer but still relatively smoothly dis- 

 tributed. About half the trips killed no whitebelly spin- 

 ner dolphins, but of those incurring mortality, most 

 trips were responsible for about 0.1 dolphins per day. 

 Higher kills again occurred with decreasing frequency, 

 with little evidence of extreme outliers. Data for com- 

 mon dolphins exhibited the worst quality, being both 

 sparse and very unevenly distributed. Of the 12 trips 

 incurring mortality of common dolphins, 9 killed about 

 0.5 dolphins per day, 2 trips killed 1-1.5 dolphins per 

 day, while the remaining trip was responsible for about 

 9 deaths per day. That one trip was responsible for 

 67% (594/882) of U.S.-caused common dolphin deaths 

 during 1987. 



Simulations 



We first selected randomly and without replacement 

 5, 10, or 20 vessels from the total of 33 observed ves- 

 sels (Fig. 4). We then sampled randomly and without 

 replacement, 25% , 50%, or 75% of the trips made by 

 each of these selected vessels, without regard to actual 

 timing of those trips throughout the year. We did not 

 force temporal stratification on these small fleet simu- 

 lations because fleet sizes of 5 or 10 vessels generated 

 so few data. 



Vessel selections were replicated 10 times at each 

 combination of fleet size and percent coverage. Trip 

 selections were replicated 50 times from each of the 10 

 sets of selected vessels. Thus, selected vessels were 

 the same within each set of 50 replicate samples of 



trips but differed between sets of 50 replicates. 

 Trips conducted by selected vessels in each sample 

 fleet represent the "population" of trips for that 

 fleet replicate. 



Each set of 50 replicate selections of trips from 

 a given set of selected vessels generated 50 esti- 

 mates of cumulative annual mortality (cumula- 

 tive mortality through December 31). For each 

 set of 50 estimates, we calculated the mean esti- 

 mate, the coefficient of variation for the mean 

 estimate, and the relative bias of the mean esti- 

 mate. Thus for each combination of fleet size and 

 percent coverage we generated 10 averaged esti- 

 mates of annual mortality, 10 coefficients of varia- 

 tion, and 10 estimates of relative bias. 



Because the "true" kill varied between fleet rep- 

 licates depending on the particular vessels and 

 trips selected, the average of these 10 averaged 

 estimates (from the 50 replicates I of annual mor- 

 tality is not a particularly useful measure in this 

 study. This average represents only the average 

 of the 10 sets of vessels that happened to be chosen for 

 the 10 replicates of fleet size. However, the coefficients 

 of variation and estimates of relative bias for each of 

 the 10 averaged estimates are relevant indicators of 

 the ability of the estimation process to precisely or 

 accurately, or both, reflect the true kill, whatever it 

 happens to be for a particular sample of vessels. Ac- 

 cordingly, we present results only for the averages of 

 the 10 estimates of CV and RB generated for each 

 combination of percent coverage, fleet size, and dol- 

 phin mortality type. We do not discuss directly the 

 individual mortality estimates. 



Estimates 



The estimates in this simulation study were derived 

 by using the ratio estimator kill per day, rather than 

 the more precise estimator kill per set (Lo et al., 1982; 

 Hall and Boyer, 1986) because at the time this study 

 was designed and executed, kill per day was still the 

 estimator of choice for NMFS 1 . 



'Kill/day was used by NMFS up until 1987 when IOC* observer 

 coverage began, because the quota system required that dolphin 

 kills be monitored continuously throughout the year rather than 

 simply summed at the end of the year. Estimates based on kill/day 

 can be made on a reasonably real-time basis because the day that a 

 vessel leaves port is a readily available datum, and observers report 

 kills by radio on a biweekly basis throughout each observed trip. 

 Number of days fished by the entire fleet (observed plus unobservedl 

 can then be determined relatively simply by summing the number 

 of days at sea since leaving port, and total kill estimated as the 

 product of total fleet days times the estimator kill/day. Biweekly 

 estimates based on kill/set are not possible because observers are 

 not permitted to report set data over the radio. Set data do not 

 become available until after vessels have returned to port. 



