Wade Population size of Stenella longirostris onentalis 



777 



the quantity of data made the MOPS estimates of abun- 

 dance more precise for this stock, whereas the increased 

 coverage of the stock range reduced the potential bias 

 of geographical variation in abundance. 



Both Holt and Powers (1982) and Wade and 

 Gerrodette (1992b 1 ) used line-transect analysis meth- 

 ods (Burnham et al., 1980) to estimate abundance. 

 However, the relatively low number of sightings that 

 resulted from the 1979 survey required an analysis 

 technique that pooled sightings of different stocks and 

 species of dolphin to estimate the abundance of each 

 stock (Holt and Powers, 1982). Although the same tech- 

 nique was used initially to estimate annual abundance 

 for the first four years of the MOPS data (Holt and 

 Sexton, 1989, 1990, a and b; Gerrodette and Wade, 

 1991), the greater number of sightings in each year 

 made this unnecessary. Therefore, to examine trends 

 in abundance, a revised analysis of all five years of 

 MOPS data was undertaken in which annual estimates 

 of abundance for each stock were made only from 

 sightings of that stock (Wade and Gerrodette, 1992a). 

 These estimates were considered to be less biased esti- 

 mates of abundance than earlier estimates available 

 for eastern tropical Pacific dolphins (IWC, 1992). No 

 significant trend in abundance for eastern spinner dol- 

 phins was observed over this short period, but the 

 power of detecting a trend was low (Gerrodette, 1987; 

 Wade and Gerrodette, 1992a). The five annual esti- 

 mates of abundance for the eastern spinner dolphin 

 ranged from 391,200 to 754,200, with a mean of 

 588,500. 



Wade and Gerrodette ( 1992a) discussed in detail the 

 differences between their analysis technique and the 

 Holt and Powers (1982) technique, but I will briefly 

 summarize the two major differences here. First, Holt 

 and Powers (1982) calculated a single effective strip 

 width (i.e., 2.0/flO), Burnham et al., 1980) for all dol- 

 phin species, whereas Wade and Gerrodette (1992a) 

 estimated a separate value for each stock. These effec- 

 tive strip widths varied substantially between the dif- 

 ferent dolphin stocks, ranging from a low of 2.5 km to 

 a high of 11.9 km (Wade and Gerrodette, 1992a), indi- 

 cating that the Holt and Powers (1982) technique may 

 have introduced considerable bias by pooling across 

 different stocks and species. 



Second, Holt and Powers ( 1982) estimated the abun- 

 dance of each stock by making a pooled estimate for 

 each species, and then divided the species estimate 

 between the stocks of that species according to the 

 relative size of the area occupied by each stock. For 

 example, an estimate of spinner dolphin abundance 

 was made by pooling sightings of eastern spinner dol- 

 phins with sightings of whitebelly spinner dolphins, a 

 different morphological form that is distributed far- 

 ther offshore and partially overlaps the area occupied 



by the eastern spinner dolphin (Perrin et al., 1985, 

 1991). The abundance estimate for the eastern spin- 

 ner dolphin was then made by multiplying this pooled 

 estimate by the ratio of the area occupied by the east- 

 ern spinner dolphin to the sum of that area plus the 

 area also occupied by the whitebelly spinner dolphin. 

 This approach would only be un-biased if the two stocks 

 had exactly the same density (number of animals per 

 unit area) within their respective stock areas. There is 

 no reason to assume this is true; therefore, an analy- 

 sis based solely on sightings of eastern spinner dol- 

 phin, as in Wade and Gerrodette (1992a), is likely to 

 be less biased. 



To obtain a best estimate of absolute abundance, the 

 five years of MOPS data were pooled across years for a 

 second analysis to estimate average abundance for the 

 period for 25 stocks of cetaceans in the ETP, including 

 the eastern spinner dolphin (Wade and Gerrodette, 

 1992b 1 ). The analysis technique of Wade and Gerrodette 

 (1992a) was used, supplemented by a technique for 

 prorating sightings from unidentified categories. Abun- 

 dance estimate from this analysis should represent 

 the (least biased and most precise) abundance esti- 

 mate currently available for eastern spinner dolphin, 

 and was therefore used as the starting point for the 

 back-calculations. A summary of the methods and re- 

 sults from that paper for the eastern spinner dolphin 

 has been presented here. 



Methods 



Pooled (1986-90) abundance estimate 



The methods of Wade and Gerrodette (1992a) were 

 mostly repeated but were applied to all five years of 

 data together rather than separately to each year by 

 itself. Population abundance (N) of eastern spinner 

 dolphins was computed by line-transect methods 

 (Burnham et al., 1980) as: 



where 



and 



N = X N, 



n k f k (0) 



N„ = _ S k A k 



2L, 



(1) 



(2) 



N,, = abundance estimate for eastern spinner dol- 

 phins in stratum /?, 



n k = number of eastern spinner dolphin schools in 

 stratum k, 



f t (0) = detection function in stratum k, evaluated at 

 zero distance, 



S k = mean school size for eastern spinner dolphin 

 schools in stratum k, 



