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Fishery Bulletin 91(4), 1993 



L h = total effort in stratum k in kilometers, 



A/. = total area in stratum k in square kilometers. 



This represents a stratified analysis, where only 

 sightings from a stratum were used to calculate the 

 density and, therefore, abundance within the stratum. 

 Abundance estimates for each stratum were summed 

 across the four strata to get a total estimate for the 

 stock. The only change in methodology from Wade and 

 Gerrodette (1992a) involved the calculation of f(0). In 

 that analysis, f(0) was estimated by pooling across 

 strata because of inadequate sample sizes in each stra- 

 tum in each year. With the larger sample sizes avail- 

 able from pooling the five years of data, there were 

 enough sightings in the inshore and middle strata 

 (Wade and Gerrodette, 1992a; fig. 1) to estimate f(0) 

 independently in each stratum. A third stratum (west) 

 on the edge of the stock area had only four sightings, 

 so a single pooled estimate of f(0) was estimated for 

 the middle and west strata. As expected, because it 

 was outside of the range of eastern spinner dolphin 

 (Perrin et al., 1985), there were no sightings in the 

 fourth stratum (south). A hazard rate model (Buckland, 

 1985) was fit to the data to estimate f(0). The perpen- 

 dicular distances were truncated at 5.5 km, because 

 not all dolphin schools further than 5.5 km perpen- 

 dicular distance were pursued for species identifica- 

 tion and school size estimation. 



Eastern and whitebelly spinner dolphins partially 

 overlap in range, but can be distinguished from each 

 other by their color pattern and morphology (Perrin, 

 1990; Perrin et al., 1991). Out of 134 sightings of spin- 

 ner dolphins in the area of overlap between the two 

 stocks, 16 were, for various reasons, unidentified to 

 stock. Those sightings were prorated to the eastern 

 stock of spinner dolphin by using the estimated pro- 

 portion of spinner dolphin in the overlap area from the 

 eastern stock (Wade and Gerrodette, 1992b 1 ). Simi- 

 larly, sightings of unidentified dolphins were prorated 

 to the eastern stock, based on the estimated propor- 

 tion of dolphins from the eastern stock in each stra- 

 tum (Wade and Gerrodette, 1992b 1 ). The prorated por- 

 tions of unidentified spinner dolphin and unidentified 

 dolphin were added to the original estimate to give a 

 final estimate of abundance. The standard error of the 

 abundance estimate was calculated by bootstrap meth- 

 ods (Efron, 1982), by using legs of effort as the re- 

 sampling unit, with 1,000 iterations. 



Fisheries kill estimates 



Estimates of dolphin kill from the tuna fishery in the 

 ETP have been revised since Smith (1983). Lo and 

 Smith ( 1986) presented revised kill estimates for 1959- 



1972, and Wahlen (1986) presented revised kill esti- 

 mates for 1973-1978, in each case with associated stan- 

 dard errors. Additionally, kill estimates for 1979-87, 

 with associated standard errors, have been published 

 (IATTC, 1989). However, Lo and Smith ( 1986) reported 

 total dolphin kill and did not divide it into stock cat- 

 egories, while Wahlen (1986) reported kill estimates 

 by stock, but only for the U. S. tuna vessel fleet. There- 

 fore, I divided the estimates of Lo and Smith ( 1986) to 

 stock by the same stock proportions used in Smith 

 (1983). I adjusted the estimates of Wahlen (1986) us- 

 ing the estimated total number of sets, as reported in 

 Punsly (1983). Wahlen (1986) reported the estimated 

 number of sets by the U.S. fleet. I multiplied the kill 

 estimate in each year from Wahlen ( 1986) by the ratio 

 of the sets made by the entire fleet to the sets made by 

 the U.S. fleet to produce an estimate of the total num- 

 ber of eastern spinner dolphins killed in each year. 

 This assumes that the kill rates of the unobserved 

 international fleet were the same as the U.S. fleet. 



Population model 



The methods of Smith (1983) were duplicated, by us- 

 ing the simple recursive relationship 



N M = N t -K t + R t {N t -\K t \ (3) 



where 

 N, = population abundance in year t 

 K, = fisheries kill in year t 

 R, = net recruitment rate in year t. 



Density-dependence is incorporated into the equa- 

 tion through the net recruitment rate, which is de- 

 fined as 



R, = R, 



im 



(4) 



where 

 R m = maximum net recruitment rate 

 z = shape parameter that sets the maximum net 



productivity level (MNPL) 

 N t , = historical population size (assumed to be the 



equilibrium population size). 



For any value of R,„ and MNPL, z can be calculated 

 as in Polachek (1982). Equation 1 can be solved for N, 

 as a function of iV, +1 , R„ and K r Therefore, by specify- 

 ing an initial population size, the number of animals 

 killed in each year, the maximum net recruitment rate, 

 and the maximum net productivity level, these two 

 equations can be iteratively solved for N b . 



