Wade Population size of Stenella longirostris orients/is 



779 



Estimates of R and MNPL 



m 



Values used by Smith (1983) for R,„ were 0.0, 0.03, and 

 0.06, which he thought to encompass the range of pos- 

 sible values of R m for spinner dolphins. No direct esti- 

 mate of net reproductive rate (R) exists for eastern 

 spinner dolphins because of the difficulty in estimat- 

 ing survival rates. The calving interval is approximately 

 three years (Perrin and Reilly, 1984). The age of sexual 

 maturity (ASM) has been reported as five years (Perrin 

 and Henderson, 1984). However, a new study using a 

 much larger data set estimated ASM for the eastern 

 spinner dolphin to be approximately 10 years, by us- 

 ing data collected from 1974 to 1990-. This is similar 

 to the estimate of approximately 11 years for the con- 

 gener northern spotted dolphin, Stenella attenuata 

 (Chivers and Myrick, 199P; Myrick et al., 1986), which 

 is found in the same region of the eastern tropical 

 Pacific. 



There are no estimates of survival rates for eastern 

 spinner dolphin. Therefore, estimating the net repro- 

 ductive rate for eastern spinner dolphin required us- 

 ing estimates of survival rates from another species. 

 Among the best estimates of survival rates for a 

 delphinid come from a long-term study of known indi- 

 viduals of a coastal population of Tursiops truncatus, 

 with estimates of adult and calf survival of 0.96 and 

 0.80, respectively (Wells and Scott, 1992). From Reilly 

 and Barlow (1986), those survival rates in combina- 

 tion with a calving interval of three years and an ASM 

 of nine years resulted in an R of 0.03, which could be 

 considered the best estimate of R for the eastern spin- 

 ner dolphin. Those survival rates may be low, how- 

 ever, because the Wells and Scott (1992) study was of 

 a population that was thought to be at equilibrium, as 

 it had been relatively constant in abundance for many 

 years. Using the maximum survival rates considered 

 by Reilly and Barlow (1986) with the same calving 

 interval (3 yr) and ASM (9 yr) results in an R of 0.05. 

 If the eastern spinner dolphin was well below half its 

 equilibrium population size in 1979 (Smith, 1983), then 

 its net reproductive rate should have been very close 

 to its maximum, /?,„. For this paper I therefore consid- 

 ered 0.04 as the best estimate of R,„ currently avail- 

 able for the eastern spinner dolphin, with 0.06 the 

 greatest value of R m possible. Therefore, the same range 

 of values as in Smith (1983) was used fori?,,,, ranging 



-'Susan Chivers, Southwest Fish. Sci. Cent., La Jolla, CA. Pers. 

 commun. 



'Chivers, S. J., and A. C. Jr. Myrick. 1991. Comparison of age at 

 sexual maturity for two stocks of offshore spotted dolphins sub- 

 jected to different rates of exploitation. Dep. Commer.. NOAA. Natl. 

 Mar. Fish. Serv., Southwest Fish. Sci. Cent., P.O. Box 271 La Jolla 

 CA 92038. Admin. Rep. LJ-91-31. 19 p. 



from 0.00 to 0.06 by increments of 0.002, for a total of 

 31 values. 



Values used by Smith (1983) for MNPL were 0.50, 

 0.65, and 0.80 (MNPL is expressed as a fraction of 

 equilibrium population size in this paper), correspond- 

 ing to z values (see Eq. 4) of 1.0, 3.482, and 11.216, 

 respectively. These encompassed the range of actual 

 values of MNPL for long-lived marine mammals, such 

 as dolphins, based on work by Fowler (1981). No di- 

 rect estimate of MNPL exists for the eastern spinner 

 dolphin. Fowler (1984) gave evidence that MNPL was 

 greater than 0.50 for cetaceans. A value of 0.60 is cur- 

 rently being used for management of cetaceans under 

 the U.S. MMPA (Federal Register, 31 October, 1980, 

 45FR64548), and for this paper, will be considered the 

 best working value of MNPL currently available for 

 the eastern spinner dolphin. Values of z were used so 

 that MNPL ranged from 0.50 to 0.80 (the same range 

 as in Smith, 1983), by using increments of 0.01, for a 

 total of 31 values. The exact value of z necessary to 

 give the specified MNPL for any value of R m was cal- 

 culated as in Polachek (1982). 



The 31 values used for both R„, and MNPL produced 

 a total of 961 parameter combinations for which rela- 

 tive population size was estimated. This large number 

 of parameter combinations allowed the calculation of 

 contours for the estimate of relative population size as 

 a function of the 2 parameters of the model. 



Confidence limits for N 



n 



For every combination of the parameters R„, and 

 MNPL, confidence limits for relative population size 

 were calculated by a Monte Carlo simulation (Buckland, 

 1984) which incorporated the sampling error of the 

 current abundance and kill estimates. On each of 1,000 

 iterations, an artificial data set was randomly gener- 

 ated by sampling values for the current abundance 

 and for the fisheries kill in each year. These values 

 were each drawn from Gaussian distributions with 

 means and variances equal to the appropriate point 

 estimates. Relative population size was then estimated 

 for each of these artificial data sets, and 95% confi- 

 dence limits for relative population size were calcu- 

 lated using the percentile method (Efron, 1982). 



The kill estimates for 1959-1972 were not indepen- 

 dent from each other, as Lo and Smith (1986) esti- 

 mated the kill in each year by multiplying an average 

 mortality-per-set for 1959-1972 by the number of 

 fishing sets in each year. Therefore, on each simula- 

 tion iteration the kill values for 1959-1972 were ran- 

 domly generated with the same random deviate. This 

 resulted in the kill values for those years being per- 

 fectly correlated amongst themselves from simulation 



