heavily to fluctuations in the survival of different 

 year classes. 



Values in Tables 1 and 2 were also analyzed 

 under the multiple linear regression model 



Y = A + B,Xi + 52^:2 + B3X3 + E 



where y = kill at age Syr in thousands, Xj = male 

 pups born in thousands, X2 = survival rate pups on 

 land, and X3 = survival rate during the first 20 mo 

 at sea. £ is a random error term; the intercept A 

 and slopes fi, are parameters to be estimated. 



Table 3 shows that multiple regression is highly 

 significant (F = 26.60, P<0.001). Given that the 

 pup survival rate on land is not significant (dele- 

 tion of A'2 causes no change in R^ here), 100 R'^ 

 = 82% of the annual variation in estimated abun- 

 dance at age 3 yr, as indexed by the kill, is 

 explained by annual changes in pup production 

 and in the survival rates of different year classes 

 during their first 20 mo at sea. The remaining 

 variability, 18%, is due to random sampling errors 

 and possibly to systematic errors. 



Discussion 



This report helps to quantify the importance of 

 early ocean mortality in determining the average 

 number of males available for harvest at age 3 yr 

 and their pronounced annual fluctuations. Ken- 

 yon et al . (1 954 ) speculated that only half the pups 

 survive the attempted transition from a milk diet 



T.\BLE 3. — Statistics and tests for linear regression of male seals 

 killed on St. Paul Island at age 3 yr( thousands) from the 1950-70 

 year classes (V ) on pups born (A', . thousands), estimated survival 

 rate of pups on land i.Vji, and estimated survival rate during the 

 first 20 mo at sea until age 2 yr (Xj ). 



Hem 



Calculated value 



Source of sum of squares, 

 degrees of freedom, and 

 mean square 

 Multiple regression 

 Deviations 

 Total 

 Test of multiple regression 

 Square ot multiple correla- 

 tion 

 Parameter estimates and 

 variances 

 a.s'. 



Tests of individual regresions 

 Pups born 

 Land survival rate 

 Ocean survival rate 



1.53160/3 = 510 53 



326-2617 = 19 19 



1.857 86/20 ^ 92 89 



F -- 510 53/19 19 ^ 26 60" 



R' = 1,53160/1.857.86 = 0.82 



-70 355. 533 294 



21 389, 753 857 



103012, 350 151 



on the Pribilof Islands to the quest for fishes and 

 squids in a stormy environment after the islands 

 are left behind. The authors stated that starvation 

 during prolonged storms is a direct cause of death 

 and noted that unusually large numbers of young 

 seals from the 1949 year class were washed ashore 

 on the Washington coast in emaciated condition 

 during the severe winter of 1949-50. Ichihara 

 ( 1974) postulated that the apparently higher mor- 

 tality of males between birth and age 3 yr (Chap- 

 man 19641 was due to the greater proportion of 

 males wintering in stormy northern areas than in 

 calmer waters to the south where females pre- 

 dominate. 



Literature Cited 



Bartholoiview, G. a., Jr., and p. G. Hoel. 



1953. Reproductive behavior of the Alaska fur seal, Cal- 

 lorhinus ursinus. J. Mammal. 34:417-436. 



CHAPMAN, D. G. 



1961. Population dynamics of the Alaska fur seal 

 herd. Trans. North Am. Wildl Nat. Resour. Conf. 

 26:356-369. 

 1964. A critical study of Pnbilof fur seal population esti- 

 mates. U.S. Fish Wildl. Serv., Fish. Bull. 63:657-669. 



1973, Spawner-recruit models and estimation of the level 

 of maximum sustainable catch. Rapp. P.-V. Reun. Cons. 

 Int. Explor. Mer 164:325-332. 



Ichihara, T. 



1974, Possible effect of surface wind force on the sex- 

 specific mortality of young fur seals in the eastern Pa- 

 cific, Bull, Far Seas Fish, Res, Lab, (Shimizul 11:1-8, 



Kenyon, K. W., V, B. Scheffer, and D. G. Chapman, 



1954, A population study of the Alaska fur-seal herd. 

 US. Fish Wildl. Serv., Spec. Sci. Rep. Wildl. 12, 77 p. 



Lander. R. H. 



1975, Method of determining natural mortality in the 

 northern fur seal \Callorhinus ursinus) from known pups 

 and kill by age and sex. J. Fish. Res. Board Can, 

 32:2447-2452. 



Marine Mammal Biological Laboratory, 



1971, Fur seal investigations, 1969. U.S. Dep. Commer., 

 Natl Mar. Fish. Serv., Spec. Sci. Rep Fish. 628, 90 p. 

 Peterson, R, S, 



1968. Social behavior in pinnipeds with particular refer- 

 ence to the northern fur seal. In R. J. Harrison et al. 

 (editors), The behavior and physiology of the pinnipeds, p. 

 1-53. Appleton-Century-Crofts, N.Y. 



Richer, W, E, 



1973. Linear regressions in fishery research. J. Fish. 

 Res. Board Can. 30:409-434. 

 SCHEFFER. V. B. 



1950, Growth layers on the teeth of Pinnepedia as an indi- 

 cation of age. Science (Wash,, DC) 112:309-311 



ROBERT H. Lander 



t, = 203/v_0 0qi 6 42" 

 , = 21 389/v'753857 =^0 78 

  103 012'v'350,157 = 550" 



Northwest and Alaska Fisheries Center 

 National Marine Fisheries Sennce, NOAA 

 212h Montlake Boulevard East 

 Seattle. WA 98112 



314 



