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Fishery Bulletin 93(2), 1995 



ern/southern stocks of offshore spotted dolphins for 

 1959-72, by using the methods of Lo and Smith 

 (1986). My second objective was to revise estimates 

 of annual kill for the eastern and whitebelly stocks 

 of spinner dolphin by correcting minor problems in 

 previous data and analyses. My final objective was 

 to estimate variances for these stock-specific mor- 

 tality estimates, which has not previously been done. 



Background 



The number of purse-seine sets capturing dolphins 

 ("dolphin sets" or "sets") is known from fishing ves- 

 sel logbooks for every year since 1959 (Punsley, 1983). 

 Data on mortality per set (MPS) of dolphins have 

 been collected by scientists on tuna purse seiners 

 since 1964 (Smith and Lo, 1983). A formal observer 

 program to collect MPS data was started by NMFS 

 in 1971 (Edwards, 1989). Estimates of incidental 

 dolphin mortality were first presented during work- 

 shops 2,3 to assess the status of impacted dolphin 

 stocks and were first published by Smith ( 1983). The 

 most recent estimates of dolphin mortality for 1959- 

 72 are from Lo and Smith (1986). 



Since 1979, the Inter-American Tropical Tuna 

 Commission (IATTC) has been responsible for esti- 

 mating the number of dolphins killed from each stock 

 (IATTC, 1989). At the request of NMFS, IATTC pro- 

 vided revised estimates of kill for the northeastern 

 stock of spotted dolphin for the years 1979 to 1992. 4 

 Additionally, they revised the estimates for 1973 to 

 1978, last calculated by Wahlen ( 1986). 



IATTC chose not to revise estimates for 1959 to 

 1972, citing the scarcity of observer data on MPS, 

 the lack of a formal observer program prior to 1971, 

 and potential biases in the data. 5 However, the num- 

 bers of sets made during that period are known with 

 high precision (Punsley, 1983). Lo and Smith (1986) 

 presented a method of analysis that should provide 

 accurate estimates of kill for 1959-72, given certain 

 important but reasonable assumptions. Therefore, I 

 used that method to estimate the number of dolphins 

 killed in each stock annually for the years 1959 to 

 1972. 



2 Anonymous, 1976. Report of the Workshop on stock assessment 

 of porpoises involved in the eastern Pacific yellowfin tuna fish- 

 ery. NOAA, Natl. Mar. Fish. Serv., SWFC Admin. Rep. LJ-76-29. 



3 Smith, T. (ed.). 1979. Report of the status of porpoise stocks 

 workshop (August 27-3 1, 1979, La Jolla, Ca. ). NOAA, Natl. Mar. 

 Fish. Serv., SWFC Admin. Rep. LJ-79-41, 120 p. 



4 Estimates provided to National Marine Fisheries Service by J. 

 Joseph, Director, IATTC, La Jolla, CA, 18 May 1993. 



5 Joseph, J., director, IATTC, La Jolla, CA, 17 February 1993, in 

 a letter addressed to Michael Payne at the NMFS Office of Pro- 

 tected Resources, Silver Spring, MD. 



Lo and Smith ( 1986) estimated the variance of the 

 total kill of dolphins in each year, but uncertainty in 

 prorating that total to individual stocks has not pre- 

 viously been accounted for. In this study, I include 

 uncertainty of the species and stock proportions by 

 bootstrapping the variance estimates (Efron, 1982) 

 instead of using the analytical estimates of Lo and 

 Smith (1986). This procedure allows this source of 

 variance to be correctly included for the first time in 

 assessments of the status of these dolphin stocks. 



Methods 



Lo and Smith ( 1986) formulated a model of total dol- 

 phin kill, 7), as: 



2 2 2 



T t-ZuzSlj R "jk x tuk , 

 i=\j=\k=\ 



(i) 



where 



Rtijk = estimated mortality-per-set of dolphins in 



year t and stratum ijk; 

 X ti  , = the number of dolphin sets in year t and 

 stratum ijk, 



and where strata were defined as 



i = 1 for large vessels (capacity >600 tons), 2 



for small (capacity <600 tons); 

 j = 1 for successful yellowfin tuna catch (>l/4 



ton); 2 for unsuccessful catch (<l/4 ton); 

 k = 1 if the backdown procedure was used to 



release dolphins; 2 if the backdown was 



not used. 



Lo and Smith ( 1986) chose these strata because they 

 accounted for significant differences in dolphin kill: 

 MPS was higher for small vessels with successful 

 tuna catches and with sets without backdown (Lo et 

 al., 1982). Lo and Smith ( 1986) modified Equation 1 

 to estimate total dolphin kill as: 



f t =j^R mill X til .\ 

 (=i 



P f )\ + R., 2 .X i 



ir.l. 



(2) 



where 



• = data were pooled across that stratum; 

 p = the proportion of successful sets using the 



backdown procedure to release dolphins, 

 C = R..12/ R..n, the ratio during successful sets 

 of MPS without backdown to MPS with back- 

 down, pooled across large and small vessels. 



