SIZE OF ANIMAL POPULATIONS 

 Table 3. — Data from a lagging experiment on migrating adult sockeye salmon 



201 



2C. = 10,472. 

 2 To = 2,351. 



Taking our estimate of qa as before (23), and as 

 our estimate of N 



a y o 



we have, then, 



„ i m.i rria. 



(31) 



(32) 



which is the same result as obtained in formula 25. 

 Application of this method of population estima- 

 tion may be illustrated by the data from a tagging 

 e.xperiment conducted by me on a migrating popu- 

 lation of adult sockeye salmon in British Columbia. 

 A total of 2,351 fish were tagged in a certain river, 

 on the waj' to their spawning grounds, over an 

 8-week period. Later, tag-ratio samples were 

 drawn regularly over a 9-week period as the fish 

 spawned and died on the spawning gi-ounds 

 farther upstream: 10,472 fish, of wliich 520 had 

 been tagged, wore recovered in these san^ples. In 

 table 3 are tabulated, in the same form as the 

 table on page 200, tag recoveries by week of tagging 

 and week of recovery, with data on total numbers 

 tagged and recovered for each week. From these 

 (lata are computed values of Talma, and dim., 

 tabulated along the margins. From these com- 

 puted values and the tag-recovery data tabulated 

 in the body of the table has been computed the 

 estimate of the population, as shown in table 4, 

 according to formulae 24 and 25 (or 32). Tiie 

 values in the body of tliis table are values of 



Ta d 



n 



mat which sum to the estimate of A^, 



ma. m.i ' 



47,860 fish. 



Table 4. — Compulation of pofidalion estimate by formulae 

 2/f and S5 from the data of table 3 



From formula 25 (or 32) it may be seen that 

 where the tagging or the sampling is uniform, this 

 estimate reverts to the simple case first discussed. 

 For, if the probabiUty of being tagged is constant 



for all i, the expected value of 

 Then, 



N*=j:j:ma>^ 



d 



n 



m-i m' 



■, a constant. 



n 



ma- m - 



T 



m . 



(33) 



wliich is identical with formula 1 since m..=t in 



formida 1. 



Likewise, if the probabiliity of being recovered is 



T T 

 constant, the expected value of — - is , a constant. 



Then, 



m„ 



m..' 



A'*=z;z;wai 



d T 



(34) 



m.i m. . m . . 



The tagging experiment illustrated in table 3 is 



a practical situation of this sort. iVlthough the 



probabihty of a fish being recovered, estimated 



from dlm.t, changed very much during the course 



