Edwards and Pemn Annual dolphin mortality 



639 



one trip responsible for over 500 deaths of common 

 dolphins) will be much greater in smaller fleets. 



The accuracy and precision of mortality estimates 

 are affected less by fleet size per se than by observer 

 coverage level for a given fleet size, and the fleet's 

 variability in kill per day. Kill per day is affected not 

 only by the fishermen's choices of fishing methods and 

 areas, but also by the type of dolphin found associated 

 with a given school of tuna. Because these are not 

 factors that can be controlled, small fleets will gener- 

 ally require higher coverage level than larger fleets to 

 achieve a given level of accuracy and precision in mor- 

 tality estimates. 



Simulation procedures and estimates 



The simulation procedure used in this study was de- 

 signed to reflect the sampling process as it would oc- 

 cur in the real world. More precise and less biased 

 estimates of mortality rates for the population of trips 

 contained in the 1987 data set would have resulted 

 from simple random sampling of the 124 trips in the 

 data set as a whole. But simple random sampling im- 

 plicitly assumes that all vessels are equal in fishing 

 ability. This is not the case, and it is likely that some 

 fleets as a whole may have greater (e.g., those newer 

 to purse-seining and therefore less experienced) or 

 lesser (e.g„ the more experienced fleets) mortality rates 

 than the average for the ETP purse-seine fleet overall. 

 In addition, in the real world, not all trips made by all 

 purse-seine vessels fishing in the ETP would be avail- 

 able for sampling. Only trips made by the vessels in a 

 particular fleet would be available for sampling, and 

 only those vessels actually observed would contribute 

 data. If vessels (or more properly, the crew) differ in 

 their ability to release dolphins unharmed (or not), 

 then fleets with more (or fewer) "low kill" vessels will 

 have lower (or higher) mortality rates than other fleets 

 of comparable size. Although it would have been pos- 

 sible to estimate the number of trips that would have 

 been made, on average, by a fleet of a given size, and 

 to have then randomly sampled that many trips from 

 the 1987 data base, the results would have been unre- 

 alistically precise. The cluster sampling resulting from 

 the selection of trips only after selecting vessels adds 

 variability in the estimates but is more realistic than 

 simple random sampling. The sampling scheme used 

 here is a single stage cluster sampling, for which a 

 ratio estimator is the most appropriate choice of esti- 

 mation procedure (Cochran, 1977). 



Discussion 



Although the kill-per-day estimator used in this simu- 

 lation study is no longer used by NMFS because 100% 



observer coverage has made estimation unnecessary, 

 the results of this study have general implications for 

 current estimation procedures based on kill per set 

 (e.g.. Hall and Boyer, 1986) and for mortality estima- 

 tion procedures in general where data quality may 

 vary between stocks. 



The uneven structure of the data set for common 

 dolphins has unfortunate implications for deriving es- 

 timates of mortality for dolphin groups that are char- 

 acterized by having such infrequent and widely vari- 

 able kill per day. Specifically, estimates of mortality 

 can vary widely depending on which trips happen to 

 be chosen. In our simulation, we could resample the 

 total population of vessels repeatedly, thus generating 

 relatively unbiased, though individually variable, esti- 

 mates of mortality. In the real world, only one sample 

 (one set of mortality data per dolphin group type) will 

 be collected per year. If this sample is collected under 

 low percent coverage, it appears very likely that the 

 data may be affected by undetectable sampling biases. 

 This bias is more likely to underestimate than to over- 

 estimate mortality because sets with large kill are rare 

 and likely to be underestimated, even though the mor- 

 tality during such sets may be responsible for a dis- 

 proportionately large percentage of the total kill. 



The problem with missing the rare large-kill sets is 

 that the kill in these sets can apparently be one or two 

 orders of magnitude greater than the "usual" kill. For 

 very abundant groups, missing a few large kills will 

 miss only a small percentage of the total number of 

 dolphins in the group; underestimating mortality could 

 be relatively harmless. For less abundant groups, the 

 large kills might represent a significant proportion of 

 the existing stock. Underestimating this mortality could 

 lead to seriously underestimating the impact of mor- 

 tality due to fishing operations on these stocks. 



In the case of the 1987 data set for dolphin kill by 

 the U.S. fleet, coverage greater than 96% (the highest 

 observed) would be required for all boats in order to 

 generate mortality estimates for common dolphin with 

 CYs less than 20% . Alternatively, if only the most abun- 

 dant groups are considered (e.g., offshore spotted dol- 

 phin), CV's less than 20% could be achieved with only 

 50% coverage of fleets as small as 5 boats. There ap- 

 pears to be no unique solution that is optimal for all 

 groups. 



In addition, the poor quality of the data presented 

 here for common dolphin in fact underestimates the 

 true extent of the problem for this species. In actual 

 practice, the species is managed as three separate 

 stocks rather than as one combined stock as presented 

 here. The data are thus extremely sparse for the indi- 

 vidual stocks, and the problems with estimating mor- 

 tality, given anything less than full observer coverage, 

 are greatly exacerbated. 



