old male kill in 1970 is 10.0 thousand. The 

 standard error of this forecast is 7.2 thousand. 

 In our forecast for 1969 (Marine Mammal 

 Biological Laboratory, 1970b), we gave two 

 estimates of the 3- and 4-year-old male kill 

 to be expected from the 1966 year class, one 

 of 46.0 thousand (based on a temperature re- 

 gression) and another of 46.8 thousand (based 

 on a regression in which pup weight and the 

 dead pup count were used) . Like the estimate 

 given earlier, the above estimates imply a 4- 

 year-old male seal kill in 1970 of 28 to 29 

 thousand and a ratio of less than 0.40 between 

 the kill at age 3 and the combined kill at ages 

 3 and 4. Again, this situation seems totally 

 improbable and hence the forecasts by these 

 methods must be discarded. 



Combined estimates of the kill of 4-year- 

 old male seals on St. Paul Island. — The sev- 

 eral estimates and the best weighted combina- 

 tions are: 



Method or basis 



Estimate 



Standard 

 error 



Tho^lsands Thousands 



Regression on kill at age 3, 

 median date of kill at age 

 3, and starting date of 

 kill 12.0 3.8 



Yearling male seal popula- 

 tion estimate 10.0 7.2 



Weighted average 11.6 3.4 



Forecast of the Kill of 3-Year-Old 

 Male Seals 



Variables that have been used to forecast 

 the kill of 3-year-old males are counts of dead 

 pups, weights of pups, mean air temperature, 

 and estimates of the number of yearling males 

 derived from tag returns at age 2. In previous 

 studies the regression in which weights of pups 

 and air temperatures are used as predictor var- 

 iables have been handled separately because 

 the series of available data were of different 

 lengths. The length of the data series on 

 weights of pups, however, is now sufficiently 

 long; moreover, it is likely that the effect of 

 air temperature at present population levels 

 may be different from that obtained in the 



early 1950's. For these reasons, a multiple 

 regression equation has been calculated in 

 which these variables are used for year classes 

 1957-65. Table 21 shows the basic data. 



Table 21. — Weights of seal pups, mean air temperature, 

 and observed kill of 3- and 4-year-old male seals, 

 year classes 1957-65, St. Paul Island 



Year 

 class 



Mean weight 



of unmarked 



pups 



in autumn 



(W) 



Deviation of the mean 



annual air temperature 



from 32° (in tenths of a 



degree above 32°) 



(T) 



Kill of males 

 at ages 

 3 and 4 



(K) 



Regression of the kill of male seals at age 

 3 on weights of pups and on air tempera- 

 ture. — The regression equation derived from 

 these data is 



K = 5.9W + 0.44T— 37.7. 



For the 1967 year class, W = 10.23, T = 48, 

 so that K = 43.8. We use this method to esti- 

 mate the total kill at ages 3 and 4. If the per- 

 centage of this kill taken at age 3 is 66.6 (the 

 average for the past 10 complete age classes) , 

 we predict a kill of 28.9 thousand at age 3. The 

 standard error of this forecast is 18.9 thousand, 

 which is unusually large because weights of 

 pups and air temperatures for the 1967 year 

 class deviate considerably from the mean. In 

 fact, the mean air temperature for the 1967 

 year class is the highest so far observed, which 

 makes its validity as a predictor variable even 

 more doubtful than usual. 



Estimate of the kill of 3-year-old male 

 seals from the yearling male seal popula- 

 lation estimate. — To use the yearling data, it 

 is necessary to work with the estimates based 

 on tag recoveries at age 2. These estimates 

 are biased, but if the bias is of the same order 

 of magnitude they represent a usable predictor 

 variable. The basic data are shown in table 22. 



23 



