conversely, 2) lactating females were under- 

 represented. Ongoing analyses of data for the 

 spotted dolphin, S. attenuata (J. E. Powers pers. 

 commun.), indicate that small calves are probably 

 overrepresented in small single-set samples. In 

 addition, the absence of sharp change in length 

 of calves at weaning as estimated by the 

 cumulative-calves method speaks against the 

 alternative explanation of development between 

 the years of differential bias against calves and 

 lactating females. The balance of evidence favors 

 the first alternative above, that of progressive 

 overrepresentation of both nursing calves and 

 lactating females as the average number of 

 animals encircled has increased and the average 

 number killed per net haul has decreased 1 accen- 

 tuating the factor of differential stamina. 



Gross Annual Reproduction 



Estimates of gross annual reproductive rates 

 can be calculated based on the two methods of 

 estimating pregnancy rate (Table 5). It must be 

 noted that if, as discussed above, small calves are 

 overrepresented in small samples (which make up 

 most of the aggregate sample), then pregnancy 

 rate (and, therefore, gross annual reproductive 

 rate) under Method 1 are underestimated to an 

 unknown, but probably small, degree. This factor, 

 of course, would also cause overestimation of the 

 proportion of the total sample female and the pro- 



'Staff, Porpoise/Tuna Interaction Program, Oceanic Fisheries 

 Resources Division. 1975. Progress of research on porpoise mor- 

 tality incidental to tuna purse-seine fishing for fiscal year 1975. 

 SWFC Admin. Rep., Natl. Mar. Fish. Serv., La Jolla, Calif., 

 LJ-75-68, 98 p. (Unpubl. rep.) 



portion of total females which are reproductive, 

 causing a countering overestimation of gross 

 annual reproduction of unknown, but again prob- 

 ably small, size. 



Standard errors are attached to the various 

 estimates where sample size sslOO, under the 

 assumption that the binomial distribution tends 

 to normality in large samples (Bailey 1959), 

 allowing calculation of the standard error as: 



SE 



V. 



p(l — p)/n 



where p = proportion (estimate of parameter) 

 n — sample size. 



Although gross annual reproductive rate as 

 calculated in Table 5 is a product of three esti- 

 mates, it can be calculated directly from the total 

 sample (number of females pregnant ■*■ total 

 number of males and females), to yield the same 

 estimate and allowing estimation of the variance 

 by the above method. The total sample size was 

 adjusted downward by a factor equal to the propor- 

 tion of mature females in unknown reproductive 

 condition. The effect on the variance by the con- 

 stant used to adjust the pregnancy rate to an 

 annual rate was ignored, because the constant 

 (11.5 mo gestation -^ 12 mo, or 0.958) is close 

 to unity. 



The estimates of pregnancy rate (and gross 

 annual reproductive rate) for 1973 and 1974 based 

 on structure of the samples (Method 1) are sig- 

 nificantly different from each other (using ±2 SE 

 as an approximation of a 959c confidence interval), 

 and the estimate for 1975, although not statis- 

 tically different from that for 1974, continues the 

 trend. The estimates based on independent esti- 



TABLE 5. — Calculation of estimates of gross annual reproductive rate of offshore spotted dolphin, Stenella attenu- 

 ata, for 1973-75, using two alternative estimates of pregnancy rate (see text). Standard error follows estimate 

 (see text). 



632 



