784 



Fishery Bulletin 91(4), 1993 



(1992a) discuss a number of sources of potential bias 

 when applying line-transect theory to the MOPS sur- 

 vey data. Several potential sources of bias do not ap- 

 pear to have a major effect. Independent observer ex- 

 periments indicate that few schools (and no large 

 schools) were missed on the trackline (Wade and 

 Gerrodette, 1992a). Aerial photographs have confirmed 

 that little bias has been introduced by the observer's 

 estimate of school size (Gerrodette and Perrin, 1991 4 ). 

 One partially unresolved issue is that of vessel avoid- 

 ance by dolphin schools, which would bias the esti- 

 mate downwards, although this may not have been a 

 major problem (Au and Perryman, 1982; Hewitt, 1985). 

 Additionally, mean school size is likely over-estimated 

 owing to the decreased probability of detection of small 

 schools at larger perpendicular distances (Drummer 

 and McDonald, 1987). Although some stocks in the 

 MOPS surveys appeared to be biased by as much as 

 20% by this problem, the eastern spinner and other 

 stocks were not (Wade and Gerrodette, 1992a). Finally, 

 the distribution of the eastern spinner dolphin is well 

 known (Perrin et al., 1985) and is well within the MOPS 

 study area (Fig. 1), so it can be concluded that the 

 abundance estimate applies to the entire population. 

 Therefore, the estimate of abundance did not contrib- 

 ute any major bias to the estimate of relative popula- 

 tion size. 



Bias may also have been introduced by assuming 

 that the simple model specified in Equation 3 correctly 

 models eastern spinner population dynamics, although 

 a simulation study has shown that a simple model can 

 perform as well as a more complex model for this type 

 of analysis (Lankester and Cooke, 1987). The most 

 important feature of eastern spinner population dy- 

 namics for this analysis is their inability to undergo 

 large increases in population size from one year to the 

 next. Their relatively low maximum population growth 

 rate, which is due to the biological constraints of their 

 life history discussed above, was incorporated into 

 Equation 3 by using only biologically plausible values 

 of R m . The only way in which the actual population 

 could have substantially differed from the model would 

 be if the population had a much lower growth rate 

 than expected in some years. For example, large inter- 

 annual variations in oceanographic conditions related 

 to El Nino events in the eastern tropical Pacific (Fiedler 

 et al., 1992) may lead to large changes in the quantity 

 of prey available for the dolphins. This could lead to 

 lower growth rates in some years, which would cause 



the specified model to over-estimate relative popula- 

 tion size. 



Of more concern is the lack of age-structure in the 

 model (Goodman, 1984 5 ). The age-distribution of the 

 northern spotted dolphin (S. attenuate/,) kill of 1974 to 

 1983 was heavily biased towards mature animals 

 (Barlow and Hohn, 1984). If the kill of eastern spinner 

 dolphin was similar for all years, then the simple model 

 used would have over-estimated relative population 

 size. Removing proportionally more mature animals, 

 whose reproductive value was highest, would have tem- 

 porarily reduced the growth rate of the population and 

 caused the population to decline for a longer period 

 than predicted by the simple model. 



In fact, an independent abundance index derived 

 from data on sightings of dolphin schools from tuna 

 vessels estimated that the population experienced a 

 statistically significant decline from 1975, the first year 

 the index was available, until 1982 (Buckland et al., 

 1992). This is different from the population trajectory 

 I estimated here, which declined only until about 1977 

 (Fig. 5). Additionally, Buckland et al.'s (1992) trajec- 

 tory indicated that the population level in 1988 was 

 not substantially different from that of 1979, which 

 conflicts with the model trajectories presented here 

 with higher growth rates (Fig. 6), in which substantial 

 growth occurs over 1979-1988. If Buckland et al.'s 

 (1992) estimated population trajectory was an accu- 

 rate assessment of the true population trend, then the 

 results presented here suggest either 1 ) that the popu- 

 lation growth rate was less than R„,=0.04; or 2) that 

 kill was under-estimated during the 1980s for reasons 

 discussed above; or 3) that a skewed age-structure led 

 to a lagged response to the large decrease in kill dur- 

 ing the 1970s; or 4) some combination of these possi- 

 bilities. 



Current status 



Estimated kill from the fishery in recent years has 

 been as high as 19,526, with an average kill of 13,900 

 from 1986 to 1990 (DeMaster et al., 1992), which rep- 

 resented a kill rate of 2.1% of the population estimate 

 of 632,700. As indicated by Equation 3, the estimates 

 of historical population size presented here, which are 

 back-calculated from 1988, were based only on kill data 

 through 1987. Estimated kill was 18,793 in 1988 

 (IATTC, 1989) and 15,245 in 1989 (Hall and Boyer, 

 1991), representing 3.0% and 2.4% of the abundance 



'Gerrodette, T., and C. Perrin. 1991. Calibration of shipboard esti- 

 mates of dolphin school size from aerial photographs. Dep. Commer., 

 NOAA, Natl. Mar. Fish. Serv., Southwest Fish. Sci. Cent., P.O. Box 

 271, La Jolla, CA 92038. Admin. Rep. U-91-36, 24 p. 



''Goodman, D. 1984. Consideration of age structure in back projec- 

 tion calculations for the northern offshore spotted dolphin popula- 

 tion. Dep. Commer., NOAA, Natl. Mar. Fish. Serv., Southwest Fish. 

 Sci. Cent., P.O. Box 271, La Jolla, CA 92038. Admin. Rep. LJ-84- 

 26C, 25 p. 



