Table 18. --Fraction of the seal pup population in August of 



their birth year that is represented by the harvest 

 (survival) of male seals on the Pribilof Islands at 

 ages 2 to 5 from the same year class, and the mean 

 annual air temperature and count of dead pups on 

 St. Paul Island 



1_/ (Mean annual air temperature for 12 -month period 

 ending 30 June of the birth year-32° F. ) X 10. 



where S = percent survival 

 D = dead pup count 



For the 1966 year class, D = 22.5, so that § 

 = 33.4. According to our estimate of its size 

 (277.5 thousand) on St. Paul Island in August 

 of the year of birth, the 1966 year class should 

 yield a total kill of 46.3 thousand males, i.e., 

 (0.5) (277.5) (0.334). Because the St. Paul 

 Island kill from this year class to date is 19.5 

 thousand (17,826 were taken at age 3), the 

 balance to be taken at age 4 is 26.8 thousand 

 minus a few hundred seals that will be killed 

 in 1971 at age 5. The kill from a year class 

 at age 4 has exceeded the number taken at age 

 3 only once since 1947, when we began de- 

 termining the ages of seals — 30.7 and 31.4 

 thousand, respectively, were taken at ages 3 

 and 4 from the 1952 year class. Even so, ex- 

 cessive numbers of 4-year-old males from the 

 1952 year class were taken only because the 

 kill in 1956 was extended to 15 August, where- 

 as the kill at age 3 in 1955 ended 31 July. For 

 the past 10 year classes for which complete 

 data are available (1956-65), the ratio on St. 

 Paul Island of the kill from a year class at age 

 3 to the kill at ages 3 and 4 has averaged 0.666. 

 During the same period, the ratio reached a 

 low of 0.576. The standard deviation of these 

 10 ratios is 0.07. If the estimate (46.3 thou- 

 sand) given above for the harvest from the 

 1966 year class is correct, an age 3 to age-3- 



plus-4 ratio of about 0.41 is implied, which is 

 about 3.6 standard deviations from the mean. 

 Although the mean and standard deviation are 

 estimates, a ratio of 0.41 is improbable and the 

 estimate must therefore be discarded. Conse- 

 quently, we will not use this method to forecast 

 the 4-year-old kill but will use two methods that 

 for 1968 were demonstrated to be the best (Ma- 

 rine Mammal Biological Laboratory, 1970b) . 



Forecast of the Kill of 4-Year-Old 

 Male Seals 



Three- and four-year-old seals dominate the 

 harvest of males, and the ratio between these 

 two age groups is about 2:1. This ratio could 

 be used to provide a forecast of the kill of 4- 

 year-old males that would be relatively satis- 

 factory. We can, however, try to improve the 

 forecast by considering the timing of the 3- 

 year-old returns. If the 3-year-olds have 

 peaked early, we can expect a small remaining 

 balance of the year class for killing the follow- 

 ing year at age 4 because fewer seals will have 

 returned after the end of the kill. In earlier 

 years, we have measured timing by the mean 

 "round" of killing, but because the round sys- 

 tem has since been modified, we now use a 

 median date of return. We have also adjusted 

 the data to account for different starting dates 

 but in this forecast we have entered the start- 

 ing date as a third predictor variable. This 

 variable contributes little to the total variation 

 explained but has been retained nevertheless. 

 We still must adjust the kill of males because 

 of variations in ending dates of the kill. 



Regression of the kill of male seals at age 

 4 on the kill at age 3, median date of the 

 kill at age 3, and the starting date of the 

 kill. — The regression equation derived from 

 adjusted data given in table 19 is 



Y = —8.57 + 0.64Xj + 3.16X 2 — 0.31X 3 . 



For the 1966 year class, Xi = 17, X 2 = 3.5, 

 X 3 = 3, hence, Y = 12.4 thousand. 



The standard error of this forecast is 3.8 

 thousand. If we adjust this prediction for the 

 kill in August 1969 and a potential kill in Aug- 

 ust 1970, it yields a final estimate of about 12.0 



21 



