FISHERY BULLETIN: VOL. 79, NO. 1 



TABLE 1.— Ages, lengths, parameter estimates, and predicted lengths, under models M, and M2, for 15 



Population I fish. 



matter which population it belongs to. On the 

 other hand, we take M2 to specify that the aver- 

 age length of a fish whose age is x is Equation (4) 

 with a, b, and c replaced, respectively, by a/, bi, 

 and a, if the fish belongs to population i, for i = 

 1, 2. Note that in the notation of the previous 

 section d is the vector whose elements are a, b, 

 and c, while 6i is the vector whose elements are 

 at , bi , and a , for i = 1, 2. Also n -15 and m = 14, 

 for this example. 



The ith row, or threesome, for i = 1,...,15, of 

 the third column of Table 1 is the set of least 

 squares estimates of ai , 61 , and Ci obtained by 

 assuming M2 to be correct and using all of the 

 age-length data pairs in Table 1, except for the 

 ith pair, to estimate oi , 61 , and Ci . For example, 

 when the data point (8, 31.9) is ignored, the least 

 squares estimates of ai , 61 , and ci are, respec- 

 tively, 55.43, 0.36, and -2.73. The fourth column 

 of Table 1 gives the predicted lengths for each of 

 the first population fish, assuming M2 is correct. 

 That is, the ith element in this column is 



am) 



I -I- g-^bi(i)Xi + Ci(i)) 



(5) 



where xi is the ith element of the first column 

 and ai(i), biH), and cm) represent the ith three- 

 some of the third column. 



The ith row, or threesome, for i = 1,...,15, of 

 the fifth column of Table 1 is the set of least 

 squares estimates of a, 6, and c obtained by 

 assuming Mi to be correct and using all of the 

 age-length data pairs in Tables 1 and 2, except for 

 the ith pair in Table 1, to estimate a,b, and c. The 

 last column of Table 1 gives the predicted lengths 

 for each of the first population fish, assuming Mi 

 is correct. The ith element of this column is (5) 

 after dm), hm), and cm) have been replaced by 

 dii), b{i), and cn), where the latter threesome is 

 the ith row of column five. 



The discussion of columns three, four, five, and 

 six of Table 2 is completely analagous to that 

 given in the preceding two paragraphs for these 



98 



