scribed by an equation of the linear form, y- 

 bL+a: 



lo 



g 



B (-L \B-L'm A^'mt'-L' 



a Or. 



S 2 



+ 



T2 7"2 



l'- 1 m B 1 - n 



2S 2 



-lOj 



B p 



(2) 



in which B C L is the catch of length L taken in 



mesh B, B L m is the mean selection length of mesh B, 



B p m is the fishing power of mesh B, etc. The log 



B p 



-jjP term will cancel; i.e., log 1=0, by assuming 



A m 



that the two nets have equal fishing power for 

 their respective mean lengths. If the terms from 



,  /rt \ 11 bLz, B^m A^m , 



equation (2) are used, log -77=2/, ™ — =0 



A*-L 



(the slope), and 



aL< n 



T 2 



2S 2 



s 



'=a (the y intercept). 



When equation (2) holds true, a plot of log ^-^ 



A^L 



against various values of L gives a straight line, 

 and the assumption is justified that the mesh 

 selection curve is normal. 



The selection curve parameters, A L m , B L m , and 

 S, are obtained as follows: 



0/6= 



aL„ 



- 7" 2 



m iB^-'rn A L ^m 



2S 2 

 -2a/b= B L m + A L„ 



L m aL>v 



s 2 



Assume that L m is proportional to mesh size (0). 

 Assign a proportionality constant (K). Then, 

 A L m + B L m =—2alb = K{ A QA B Q), from which A L m 

 and B L m can be derived. S can be found from 

 either a or 6. With these values and a table of 

 ordinates for normal distribution (Snedecor, 1956), 

 mesh selection curves can be constructed. 



APPLICATION OF METHOD TO SALMON 

 GILL NET CATCHES 



I have applied the above analytical procedure to 

 length frequencies of three salmon species: pink, 

 sockeye, and chum. To illustrate the method, I 

 have used catch data for 1957 and 1959. In 

 these years the three species were well represented 

 in the gill net catches of the research vessels. 

 ( latch data on sockeye and chum salmon for 1956, 

 1958, and 1960 were used in part of the analysis. 

 Table 1 shows the number of the three species 

 caught and measured during 1956 to 1960. The 

 cat dies were made during May to September on 



the high seas of the North Pacific Ocean (north of 

 lat. 45° N.) and the Bering Sea. 



PINK SALMON 



Table 2 gives the length-frequency distributions 

 of pink salmon taken by the 3K-, 4&-, and 5%- 

 inch mesh gill nets in 1957. Table 3 gives similar 

 data for 1959. Catches were confined to three 

 mesh sizes; the 2%-inch mesh did not catch pink 

 salmon. Since more of the 4K-inch mesh than 

 of the 3%- and 5%-inch meshes was used in a 

 fishing set, catches of the 4%-inch mesh were re- 

 duced to equalize fishing effort. A 1:3 reduction 

 was necessary in 1957; a 1:6 reduction in 1959. 

 Length frequencies were grouped by 3-cm. length 

 classes. Fork length is related to mesh size. 1 



Tables 2 and 3 also give catch ratios of adjacent 

 mesh sizes, 4%/3}4-inch and 5K/4K-inch. The 

 catch ratio at each length class is limited to a 

 combined sample size of 50 or more fish for the 

 paired mesh sizes. By establishing a minimum 

 sample size of 50, I was able to omit smaller 

 samples that may not have been representative 



Table 1. — Gill net catches of pink, sockeye, and chum salmon 

 by U.S. research vessels in the North Pacific Ocean and 

 the Bering Sea, 1956-60 



1 Coho and chinook salmon are excluded because of small catches. 



Table 2. — Catch by mesh size and catch ratio of adjacent 

 mesh sizes, pink salmon, 1957 



1 Original catches of the 4'i-inch mesh were 3 times as large as shown: they 

 were divided by 3 to equalize lishing effort between mesh sizes. 



i Mesh size as shown is factory-labeled size. During the 1060 fishing opera- 

 tions about 400 meshes (miii the fmir mesh sizes were measured. The average 

 measured size was either identical to the factory-labeled size or slightly 

 oversize. 



::si' 



U.S. FISH AND WILDLIFE SERVICE 



