SIZE OF ANIMAL POPULATIONS 



193 



visibility of cows and rabbits, even in a narrow 

 strip. 



Jackson (19:^3) developed a method of comput- 

 ing the population of tsetse flies in a closed area 

 by marking flies with colored paint and taking a 

 sample to determine the ratio of marked to un- 

 marked. In a later paper (1936) Jackson states 

 that he discovered this method independently in 

 1930, but meanwhile became cognizant of Lin- 

 coln's work and hastens to credit Lincoln with the 

 method. 



Jackson mentioned, also, that a representative 

 sample of the population as regards mark ratios 

 would be obtained if either the marking or the 

 subsequent sampling were carried out in a non- 

 selective fashion. This is of considerable prac- 

 tical importance. It is not necessary that both 

 be nonselective. If the marks are randomly, or 

 evenly, distributed in the population, any sample of 

 n members will yield a consistent estimate of the 

 mark ratio in the population. (The term "mark 

 ratio" or "tag ratio" will be used in this paper to 

 mean the quotient of the number of marked mem- 

 bers in a group divided by the total members in 

 the group.) Similarly, a representative sample of 

 the population will yield a consistent estimate of 

 the mark ratio regardless of the distribution of 

 marked members in the population. 



Sato (1938) estimated the stock of red salmon 

 in the western North Pacific. He stated: 



2. The stock (S) of red salmon may be estimated by the 

 formula: 



Y:X = S:Z, 



where Y is the number of tagged fishes, X, the number of 

 recaptured fishes, and Z, the total catch of the fish. 



His estimate of 94.7X10^ individuals in 1936 

 was made from 1,358 marked fish and 177 re- 

 captures among a sample of 12,339X10^ He 

 made no attempt to estiniate the reliability of the 

 result. It may be seen from formula 7, however, 

 that the sampling error is actually quite large. 



Green and Evans (1940) employed this method 

 for computing populations of snowshoe hares. 

 Hares were trapped and banded during a long 

 "prccensus period" lasting all winter and up to 

 mid -April. The banded hares at Uberty from 

 these operations were taken as the kno\vn niunber 

 of marked members, and the ratio of marked to 

 unmarked was determined during a short "census 

 period" in April. The formula employed by 



these authors is essentially formula 1, since they 



take 



Hares banded in precensvis period 

 Other hares present in precensus period 



_ New-banded hares trapp>ed in census period ,„. 

 Other hares trapped in census period ^ ' 



and compute the number of "other (unmarked) 

 hares present in precensus period," and add it to 

 the number of marked hares to get the total 

 population. This may be illustrated by the 

 suuple example we have employed before, where 

 we have a population containing 100 marked 

 members and draw a sample of 500 containing 

 50 marked members. Green and Evans would 

 compute "other hares present in precensus period," 

 as follows: 



100_ 50 

 X ~450 



X=900 



and add the 100 marked hares to get the population 

 estimate of 1,000. 



These authors consider the effects of several 

 possible sources of error. They show that migra- 

 tion in and out of the area of study is unimportant. 

 The "evenness" of the sampling Ls also considered. 

 They state that "It is essential that trapping 

 throughout the area be uniform during the census 

 retrap in the spring. . . . LTniformity need not 

 be so rigidly maintained during the precensus 

 period." This, of course, is a special case of the 

 rule that either the sampling for tagging must be 

 uniform or the subsequent sanapling for tag ratio 

 must be such as to \aeld a representative sample 

 of the whole population. 



Green and Evans also consider the "error of 

 random sanapling." Using their notation, wc 

 find that they take: 



p= proportion of hares trapped in census period that were 

 not banded (trapped) in precensus period. 



P = number of the hares trapped in census period that were 

 not trapped (banded) in precensus period. 



.V= total number of hares trapped in the census period. 

 P 



They then take ffp for the standard deviation 

 of p and state that 



■V 



pq 



N 



(9) 



where q=l—p- Taking P±2<jpN, and emplojnng 

 these values in place of the second quotient 



