Kitada and Tezuka: Survey designs for estimating recreational fishery catch 



235 



w 8- 



o 4- 



n 

 E 



8- 



June 



September 



£2. 



5 10 15 20 25 



July 



8- 



4- 



II 



5 10 15 20 25 



October 



5 10 15 20 25 5 10 15 20 25 



4n 



August 



2- 



Total 



n^r. 



5 10 15 20 25 10 30 50 70 90 



Number of fistiing days 



Figure 3 



Distributions of the ayu fistiing days per angler by niontii for 104 sampled 

 season-permit anglers in the Nakagawa River 



Cov{C'if\Cl-[) in V(C'")and Cov(M;,,,M,. ) in Equation 22. 

 The CVs of C and W were also evaluated at about 21% and 

 were strongly affected by the covariances between months 

 in Equation 17. The variance of the total number estimate 

 V[C) was 1.2604 x 10'-. and variance by neglecting the 

 covariance term in Equation 17 was 1.2230 x 10". The 

 CV of C without the covariance term was 6.53%. If we ne- 

 glect the covariance, the variance is substantially under- 

 estimated. The variance was 10.31 times larger when the 

 covariance term was included. 



We obtained similar point estimates of anijual catch by 

 method 2 iTotal'"'^'^. 2 ;„ -pable 2 ). The CVs of M , Mj, C, and 

 W for day-permit anglers were about 7%, but that of i?'" 

 was reduced from 19.7% to 6.6% by not considering the co- 

 variance terms. The CVs of C and W dropped about 10% 

 from 21% without the covariance. Similar point estimates 

 and smaller variance estimates were obtained. The vari- 

 ance estimate of the annual catch obtained by method 1 

 with covariances ( 1.2604 xlO'-'l was 4.11 times larger than 

 that by method 2 13.0667 xlO"). 



The relationship between the sample size and the pre- 

 cision of the annual catch estimate for season-permit an- 



glers was examined. We calculated the values ViC) for var- 

 ious values of n by using Equation 7. To obtain precision 

 over the season for CVs of C''"( = Vviti/r) below 10%, a sam- 

 ple size of 120 or more is required (Table 3). 



A high positive correlation in catches between adjacent 

 months was detected (Table 4). We mapped anglers (ob- 

 jects) and fishing days (categories) into a two-dimension- 

 al graph by correspondence analysis (Hayashi, 1950; Ben- 

 zecri, 1992) using the function "pqS.prcomp" in S version 

 4 (Chambers and Hastie, 1992). Correspondence analysis 

 showed the relations between rows and columns in a fre- 

 quency table gi'aphically as points in a common low-di- 

 mensional space (Clausen, 1998). Both objects (rows) and 

 categories (columns) of variables are represented as points 

 in such a way that an object is relatively close to its catego- 

 ry and relatively far from other categories (Leeuw and van 

 Rijckevorsel 1988). For example, the 72nd angler fished 10 

 days in June, five days in July, seven days in August, three 

 days in September, one day in October, and this angler was 

 mapped closed to June, reflecting the month of his high- 

 est fishing effort (Fig. 7). The results suggest several fish- 

 ing patterns with high catch seasons in June-July, July- 



