Kilada and Tezuka: Survey designs for estimating recreational fishery catch 



233 



unknown. Hence, we slightly modified the procedure for 

 estimating D,. by Dpi., where p^. is the proportion of day 

 permits sold in ^th month to the annual total number of 

 day permits sold (D). 



Day permits issued by the cooperatives are sold mainly 

 in fishing tackle shops. We selected four tackle shops and 

 surveyed the total number of day permits sold at the se- 

 lected jth fishing tackle shop (D^), and the total number of 

 day permits sold at the selected /th fishing tackle shop in 

 /.■th month (D^i.). The proportion of day permits sold in ^th 

 month was estimated by 



Pk = 



" n 



i;.^. 



where h is the number of fishing tackle shops selected 

 from a total of// shops. The evaluation of the variance of 

 P/. was similar to Equation 3: 



Vlftl = 



"'""'tI'"..-".'.''- 



D'hih- 



Some day permits, however, were sold at the fishing sites, 

 and the above variance estimator was not appropriate for 

 this situation. Assuming S'^'^j/), was selected by simple 

 random sampling from D, we evaluated the variance by 

 (Cochran, 1977, p. 52, Eq. 3.8) 



^E>.-i)' 



The modified estimator for the total number of fish 

 caught by day-permit anglers in /;th month is 



k 



DpA 



(26) 



Here p^ and Rf, are independent because these are esti- 

 mated from different survey data. The variance of revised 

 d''' was estimated by using Goodman's (1960) method; 



ViCi"'): 



: d-'[r'^V(p,) + pIv(R, ) + V(ft mR, )}. 



The total fishing days in /jth month was estimated by 

 Equation 15 but in this case /)^ was unknown. The modi- 

 fied estimator was 



Mn = M, + Dp, 



and the variance was slightly revised as 



Vmn) = N''Vm,) + E)'V(p,). 



The annual catch was estimated by Equation 16, sub- 

 stituting Equation 8 by Equation 26. In this case, we 

 estimated C[ and C,- ' from the same sample of season- 



permit anglers. Hence, the fourth term of the covariance in 

 Equation 17 must be considered. The approximate covari- 

 ance is estimated by (see Appendix 4) 



c'o^(c;;",c;/') = D'~p,,p,,c^v{R,^,Rf^.), ai) 



where the covariance between /?^, and /?;,. is 



Cov(R,,Rk)- 



N' 



M,M,, 



^^Cov(C;-'',M^.) 



M,Ml 

 M'kM^. 



Cov( Mi,C;?' 



+ ± Z Cov(M^,M^.) 



Here Cov(Ci'",Ci?') and Cov(M,..Mi,.] are already given by 

 Equation 18 and Equation 24. The other covariance com- 

 ponents are 



c^v(&;\M,. ) = ^-'\ f (C,, - ^, )(M„. - M,.) 



n~{n - 1) ■^ 



C'^(M„C;?') = ^~'\ j^(C„. - 4 "M,, - M„ ). 

 n (n -1)~ 



The annual catch in weight was estimated by Equation 19, 

 substituting Equation 8 with Equation 26. The covariance 

 in the fourth term of V(W) in Equation 17 was estimated 

 with Equation 20 by 



c^( W;!'", vv;.'" ) = (t,(tj..(5rv(c;'",c;?' ) 



where Cov(C/ ,C^' ) is given in Equation 27. 



Results 



In 1993, 21,962 season permits and 9066 day permits were 

 sold (Table 1). The total number of day permits sold at the 

 four fishing tackle shops was 4776, and the number (pro- 

 portion, p^) sold was 2732 (0.572) in June, 1,189 (0.249) in 

 July, 716 (0.150) in August, 124 (0.026) in September, and 

 15 (0.003) in October. 



We received 104 logbooks from the 120 season-permit 

 anglers sampled, a return rate of 86.7%. In addition, two 

 anglers voluntarily submitted logbooks, but we did not in- 

 clude these unsolicited returns because they were not ran- 

 domly selected. The modes of the catch rates by the sam- 

 pled anglers were from five to ten fish per month (Fig. 2). 

 The histograms show a large variation in the catch rate 

 among season-permit anglers. The peak fishing season was 

 from June to July. In September, the number of anglers 

 decreased, and the fishing season ended in October The 



