ABUNDANCE OF CONNECTICUT RIVER SHAD 



253 



C, the error in estimating N results from any error 

 in these three quantities. 



A 



When C and T are without error, the error in N 

 results from the sampling error in T c ; the variance 

 of T e takes on the form pqn; in this case, it is 

 (TJT) (l-TJT) (T), or T e (l-TJT). An ap- 



A A A 



proximation to the asymptotic variance of N= V(N) 



A 



is obtained from the expectation of (dN) 2 

 (Deming 1943) which gives 



Table 5. — Number of days fished each week during fishing 

 seasons, 1935-51, by sample of Connecticut River fishermen 



where (dT c ) 2 is equal to V{T t ), or T c (l-T c /T). 

 For r=633, T c =359, and C= 100,967, the esti- 

 mated variance of N is 38 X 10 6 , and the standard 



deviation of N equals 6,175. The reader is referred 

 to papers by Chapman (1948) and Schaefer (1951) 

 for discussions of other formulae for estimating 



A 



the variance of N. 



DETERMINING SIZES OF RUNS AND 

 ESCAPEMENTS, 1935-50 



The fishing power of a standard fishing unit has 

 been defined as the ability of one unit of gear to 

 capture a certain fraction of the fish present in 1 

 day's fishing. For the Connecticut River shad 

 fishery this fraction will be designated by p and 

 can be considered to be constant within a seasoa 

 and between seasons, provided: (1) There is no 

 innovation in design or manipulation of gear to 

 make it more, or less, efficient as a means of taking 

 fish, (2) the fishing effort is uniform throughout 

 the season, and (3) the migration pattern of shad in 

 the river is similar each year. Daily catch and 

 effort records kept since 1930 by a few fishermen 

 and interviews with many fishermen indicate that 

 the Connecticut River shad fishery meets these 

 three requirements. Table 5 gives the number of 

 days fished each week by a few fishermen who kept 

 records of their fishing activities in past years. 

 The sample is small but it does give an indication 

 that the men fish consistently throughout a given 

 season. 



Considering the shad run as a whole and de- 

 noting its size by N, the number of fish removed 

 in the first standard-fishing-unit day is pN. 

 The number remaining after the first standard- 

 fishing-unit day is qN, where 2=1— p. The fish 

 that escape in the first standard-fishing-unit day 



are susceptible to capture in the second standard- 

 fishing-unit day; the number removed during the 

 second standard-fishing-unit day is pqN. The 

 number remaining after the second standard- 

 fishing-unit day, and the numbers removed and 

 remaining after succeeding standard-fishing-unit 

 days are as follows : 



Number Number 



removed remaining 



1st s. f. u. day pN qN 



2d s. f. u. day pqN q 2 N 



3ds. f. u. day pq'N q 3 N 



4th s. f. u. day pq*N q*N 



n — \ s. f. u. day pq"~ 2 N q n ~ l N 



nth s. f. u. day pq"~ l N q n N 



