Wade Population size of Stenella longirostris orientate 



781 



here. The different results must be due 

 to either the use of revised estimates of 

 abundance and kill or the use of 1988 as 

 a starting point rather than 1979; these 

 were the only differences between the 

 analyses. As will be shown, most of the 

 difference resulted from the higher esti- 

 mate of current population size, although 

 the lower revised kill estimates also con- 

 tributed to a higher estimate of relative 

 population size. Repeating the back-cal- 

 culation of Smith (1983) from 1979, but 

 using revised population and kill esti- 

 mates, resulted in nearly the same esti- 

 mate of relative population size as re- 

 ported here. For example, for R„=0.03 

 and MNPL=0.65, back-calculating from 

 1979 as opposed to 1988 resulted in an 



estimate of relative population size of 0.41 versus 0.42, whereas 

 Smith (1983) reported a value of 0.20. An inspection of the popula- 

 tion trajectories (Fig. 5) confirms that the difference was not due to 

 the different starting year, as the model trajectories, except at the 

 highest growth rates, indicated little change in the population size 

 between 1979 and 1988. This also agrees with the independent re- 

 sults of Buckland et al. (1992), which indicated little difference in 

 relative population size between those two years. Therefore, the 

 difference in the results reported here and those of Smith (1983) 

 should not be interpreted as a recovery in the population between 

 1979 and 1988. These new, higher estimates of status should in- 

 stead be interpreted as a revision of the estimate of relative popula- 

 tion size, due mostly to the improved abundance estimate available 

 from the MOPS surveys. 



The new estimates of relative population size, although higher 

 than Smith (1983), are still below MNPL for all parameter combina- 

 tions. Because the parameter values used encompassed those values 

 possible for a spinner dolphin (Reilly and Barlow, 1986), this result 

 indicated that, as of 1988, the eastern spinner dolphin was still well 

 below its 1959 population size. With R n =0.04 and MNPL=0.60, the 

 population was estimated to be at 44% of its historical size. Even 

 with the maximum value of R m of 0.06, the population in 1988 was 

 estimated to be 43% (MNPL=0.50) to 58% (MNPL=0.80) of its size in 

 1959. However, careful consideration must be given to several issues 

 before accepting these results as valid. These issues include the 

 precision (reflecting the precision of the abundance and kill esti- 

 mates) and potential biases (reflecting either biased abundance and 

 kill estimates or mis-specification of the model) of the result, and 

 the quality of pre- 1972 fisheries kill data. 



Precision 



The precision of the estimates of relative population size was inves- 

 tigated by simulation to explore the uncertainty of the results due to 

 sampling error, under the assumptions that the population model 

 and parameter values were true. This addresses the question of how 

 likely the estimates of relative population size were below MNPL if 

 the true relative population size was above MNPL, solely because of 

 variability associated with sampling the current abundance and 

 fisheries kill estimates. The upper 95% confidence limit of relative 

 population size was below MNPL for the majority of the parameter 

 combinations, moving above MNPL only for values of R,„ greater 

 than 0.018 (Fig. 3). If MNPL was assumed to be 0.60, then the 

 upper 95% confidence limit of relative population size was only above 

 MNPL for values of R m greater than 0.034 (Fig. 3). The upper confi- 

 dence limit was always above MNPL if/?,,, was at least 0.046. Viewed 

 in a hypothesis testing context, this result indicated that the null 

 hypothesis that relative population size was greater than MNPL in 

 1988 could be rejected for most of the parameter combinations. Only 

 at higher growth rates could this hypothesis not be rejected. From 

 sampling error alone, it was equally possible that the population 

 was actually worse off than estimated, as the lower 95% confidence 

 limits go as low as 0.22, and were as low as 0.28 even at the highest 

 growth rate of i?„=0.06. 



