Since the kill of 3-year-old males in 1965 was 

 19,000, a balance of 19,700 for the kill of 

 4-year-old males in 1966 is innplied. 



By this nnethod, the standard error of the 

 predicted Y {kill of 3- and 4-year-old males) 

 is 9,600. This is also the standard error of the 

 forecast of the kill of 4-year-olds in 1966. 



Estimated return based on estimates of year- 

 ling population . - -As shown elsewhere in this 

 report, the estimated mumber of yearling 

 males in 1962 (from the 1961 year class), 

 based on 352 recoveries to date, is 77,827, 

 whereas the estimated number of yearling 

 males in 1963 (from the 1962 year class) is 

 73,320 (180 recoveries). If possible bias in the 

 latter estimate based on recoveries through 

 age 3 is disregarded, cind if mortality varies 

 most during the first year of life, the returns 

 from the 1962 year class should be 

 73,320-^77,827, or 94 percent of those from the 



1961 year class. At the end of the kill in 1965, 

 the St. Paul Island returns fronn the 196l and 



1962 year classes to date were: 



Kill at 

 age 



2 

 3 



4 

 Total 



Ninety-four percent of 35,600 is 33,500, and, of 

 this return, the number remaining is 12,000. 

 The standard error of this estimate, which is 

 difficult to measure, depends on the variability 

 in survival after age 1, on which we have no 

 information, together with the variability in the 

 estimates of the yearling groups. The minimum 

 error in the difference between the two groups 

 is given by the formula: 



S. E. (Difference 



n; 



when Nj, N2 are the respective population 

 estimates and sj, S2 are the tag recoveries on 

 which they are based. Hence, S.E.= 6,800. 



The effect of this S.E. on the forecast of the 

 kill of 4-year-old males in 1966 can be 

 evaluated in the following way. The S.E. of 

 6,800 represents about 9 percent of the esti- 

 mate of the yearling populations. A 9 percent 

 error in the returns of the 1961 year class is 

 3,200 and this, then, is the lower limit of the 

 S.E. of the forecast of the kill of 4-year-old 

 males in 1966. In addition to ignoring varia- 

 tions in mortality after age 1, this standard 

 error ignores any variability incurred because 

 of errors in determining the ages of seals 

 selected for tagging as yearlings or any 



possible clustering effects. To allow very 

 roughly for these effects, a standard error of 

 4,000 is estimated. 



Weighted Estimate on the Kill of 4- year-old 

 Males .- -From the foregoing methods, the three 

 estimates regarded as valid and their standard 

 errors are: 



(1) Fronn regression of percentage of kill at 

 age 3 on termination date and median 

 date: 



Estimate 10,200 S.E. 4,500 



(2) From temperature-return equation: 

 Estimate 19,700 S.E. 9,600 



(3) From estimates of yearlings: 



Estimate 12,400 S.E. 4,000 



The weighted mean estimate is 12,300. The 

 unweighted mean estimate is 14,100. In view 

 of the uncertainty of the S.E. of the third 

 estimate, and the fact that the estimate of 

 yearlings of the 1962 year class maybe some- 

 what low, it is perhaps best to use the un- 

 weighted mean estimate, 14,100. 



Prediction of Kill of 3-Year-Old Males 



Correlation of kill of 3-year-old males with 

 return of 2-year-olds . --The prediction of this 

 component of the kill is more difficult. As 

 shown in appendix table 2, the kill from a year 

 class at age 3 represents 67 percent of the 

 kill at ages 3 and 4 and is by far the largest 

 component. The number of 2-year-old males 

 killed is extremely variable because most of 

 them are below the acceptable length limits 

 and because the timing of their return ap- 

 parently varies. If substantial numbers of 

 2-year-olds return in early August, they will 

 appear in the kill, but if their return is de- 

 layed by a few days the number of 2-year-olds 

 killed is much smaller. For these and perhaps 

 other reasons, as noted by Chapman (Roppel, 

 Johnson, Anas, and Chapmam, 1965), the corre- 

 lation of the kill of 3-year-old males with the 

 best present index of 2-year-old returns (kill 

 in a late round) is extremely small (r^=0.20). 

 Such a regression essentially yields the long- 

 term mean as the predicted value and, hence, 

 particularly fails as a forecasting tool. A 

 prediction is of value primarily if it can 

 identify those years when deviations much 

 above or much below the mean will occur. 



The suggestion has been made that the pro- 

 portions of tagged males in the kill have been 

 directly related to the survival of the year 

 class; this idea in turn has given rise to the 

 thought that the proportion of tags among 



28 



