APPENDIX A 



PREDICTIONS OF 1966 KILL OF MALES 



Douglas G. Chapman 



18 November 1965 



Prediction of 4-Year-Old Male Kill 



Regression of kill of 4-year males on kill of 

 3-year males and the mean date of the kill at 

 age 3. --Predictions of the kill at age 4 have 

 been relatively easy and more accurate than 

 predictions of the kill at age 3. This differ ence 

 is to be expected, because the return at age 3 

 gives much information on the strength of the 

 year class. Initially an estimate was made of 

 the escapement of 3-year-old males fronn the 

 kill which, in turn, provided an estimate of the 

 return at age 4. Subsequently, 1 found that this 

 estimate of the escapement was in fact a 

 considerable underestimate. It seemed more 

 reasonable, therefore, to estimate the returns 

 at age 4 directly rather than through a fictitious 

 escapement estimate. This approach was based 

 on a regression where the independent (i.e., 

 predictive) variab-les were (a) the number of 

 3-year-old males killed in July, and (b) the 

 timing of the return as measured by the mean 

 date of the kill of 3-year-olds in July. A suf- 

 ficiently long series of comparable data is 

 available only for the month of July, although 

 substantial numbers of male seals were also 

 killed in August in recent years. Adjustments 

 have been made for extensions of the kill into 

 August. 



The regression for the returns of year 

 classes 1952-61 is: 



Y =-15.0+0.62Xi +5.07X2 

 where 



Y = kill of 4-year-old males to 31 July 



plus 80 percent of the 



kill of 3-year-old males after 31 July 



of the previous year 

 Xi =kill of 3-year-old males to 31 July 

 X, = mean date of the kill of 3-year-old 



males in July, as measured from 



15 July 



The coefficient of multiple correlation is 0.90 

 (r2=0.81). 



In recent years, not only has the kill been 

 extended into August but the first day of the 

 kill has also been advanced. Comparable data 

 have been obtained only by adjusting to the 

 basis of a 27 June starting date (the starting 

 date during the middle 1950's). When the 

 starting date was 2 July, it was necessary to 

 prorate a portion of the 2-6 July kill that might 

 have been taken 27 June to 1 July, if the kill 

 had started at the earlier date. 



In 1965, the kill began on 7 July, so that 

 a further backward extrapolation became nec- 

 essary to estimate X^. It is not surprising, 

 therefore, that the resulting estimate is not 

 reasonable. For 1965, Xl= 12, X2 =6, and Y is 

 30,000. The X2 value of 6 is higher than any 

 that occurred in the period from which the 

 regression is computed. 



Regression of percentage of the kill from a 

 year class at ages 3 and 4 taken at age 3 on 

 (a) date of termination, and (b) median date of 

 the kill at age 3 .-- The data for this regression 

 are given in appendix table 1. 



An average of 67.4 percent (standard devia- 

 tion 10.17) of the kill of males from a year 

 class at ages 3 and 4 occurs at age 3. The 

 95-percent confidence interval for any 

 individual observed percentage is: 



67.4 + 2.16(1 + -—) ^/^(10.17) 



i.e., (44.7, 90.1). 



At the lower confidence lin-iit, the percentage 

 of 44.7 nneans that the upper bound of the kill 

 at ages 3 and 4 from the 1962 year class is 

 19,000^0.447, or 43,000. This figure leaves 

 26,000 for the kill of 4-year-olds in 1966, 

 which, although below the estimate from the 

 regression based on the mean date, is still a 

 high estimate. 



The above estimate of 26,000 can be im- 

 proved by calculating the regression of P3 

 (percentage of kill at ages 3 and 4 taken at 

 age 3) on the termination date (t) and either 

 the mediandate (m) or the last round percentage 

 (I), Either of the variables, median date or 

 percentage in the last 5 days of July, measures 

 to some degree the lateness of the returns. 

 Perhaps the median date yields a better esti- 

 mator than does the percentage in the last 5 

 days. The respective equations are: 



P3= 74.7+0.391-0.40/ 

 and 



P3=62.4 +1.95t-2.21m 

 where 



R = 0.50 



R=0.64 



p T = percentage of the kill at ages 3 and 



4 from a year class taken at age 3 

 t = termination date (in days after 31 



July) 

 / = percentage of the 3-year-old males 



killed in last 5 days in July 

 m = median date of the kill of 3-year-old 



males 



26 



