450 



Fishery Bulletin 105(4) 



In the composite of two or more functions, a, and c, of 

 i >2 are calculated by Equations 10 and 11. Therefore, 

 these parameters are not included in the number of 

 parameters needed to calculate the AIC (see Appendix 

 Table). 



The upper and lower 95% confidence intervals (ClA of 

 FLj were determined as follows: 



70 N 



CI=FL+l.96d, 



(18) 



The equations for describing the relation between SOR 

 and FL, LOR and FL, and FL and BW were calculated 

 in the same way. 



Application of equations to walleye pollock 



Walleye pollock were collected and used as a model for 

 long-lived species. The relevant biological data were 

 collected, processed, and compiled from various cruise 

 data conducted by Japanese and U.S. agencies at a total 

 of 97 sampling stations in the Bering Sea (95 stations) 

 and Chukchi Sea (northeastward extension of the Bering 

 Sea; 2 stations) during 1983-2002 (Fig. 2). 



In the central Bering Sea (Aleutian Basin), adult 

 walleye pollock vary in age from 5 to >20 years (McFar- 

 lane and Beamish, 1990; Traynor et al., 1990). Young 

 fish (0 to 4) are distributed on the continental shelf and 

 slope and then migrate into the basin area beginning 

 at age 5 (Traynor et al., 1990). In the present study, 

 the samples of walleye pollock in the Bering Sea are 

 presumed to have been collected from the same popula- 

 tion offish. Samples of juvenile walleye pollock at two 

 discrete positions in the Chukchi Sea were also treated 

 as originating from the Bering Sea. Larvae were sam- 

 pled with a MOCNESS net, and juveniles and adults 

 were captured with mid-water or bottom trawl nets. 

 We measured the somatic length and BW of each fish 

 and removed its otoliths (sagittae). For walleye pollock 

 larger than 15 mm in somatic length, we measured FL, 

 and for those smaller than 15 mm (with undeveloped fin 

 rays), we measured TL. Difference in FL and TL was 

 negligible in fish <15 mm; therefore TL is referred to 

 as FL in the present analysis. 



Specimens examined in the present study ranged 

 from 4.56 mm to 803 mm FL. The number of samples 

 used in the analysis of OL-FL equations is given in 

 Table 1, as well as the size range of otolith measures 

 and fish sizes. The approximate length of newly hatched 

 larvae is 4.6 mm FL (=TL), 0.02 mm OL, and 0.01 mm 

 SOR and LOR. 



The relation between OL and FL was fitted to the 

 general equations (Eqs. 1-4) and the allometric smooth- 

 ing function (Eq. 12). The equations for describing the 

 relation between SOR and FL, LOR and FL, and FL 

 and BW were calculated in the same way. 



Otolith processing 



For measurement of SOR and LOR, the left or right 

 otolith was selected and processed as a frontal section 



65 N 



60 N 



55 N 



50 N 



Siberia 



• • • 



Bering Sea ■w^-'f" ^ • 



M 



?>.•■ 



L 



• • •- V!.«-' 



•• • • 



4 



170 E 



18(1 170 W 160 W 



Figure 2 



Map showing the sampling locations for walleye 

 pollock (Theragra chalcogramma) in the present 

 study. There were 97 total sampling stations: Bering 

 Sea (•: 95 stations) and Chukchi Sea (o: 2 stations) 

 in 1983-2002. 



to reveal the perpendicular structure of the proximal 

 surface, including the tips of rostrum and postrostrum, 

 and core (Fig. 3A). The procedure for otolith processing 

 followed that of Secor et al. (1992). 



Larval and juvenile otoliths were embedded in epoxy 

 resin adhesive (Epoxy bond quick 5; Konishi Co., Ltd., 

 Osaka, Japan) on a glass slide, and OL was measured 

 under a microscope (SMZ-U or Labophot-2A; Nikon 

 Co., Tokyo, Japan) by using an image analysis system 

 (ARGUS-10; Hamamatsu Photonics K. K. Co., Shizuoka, 

 Japan). The otolith was then carefully polished with wet 

 sandpaper (no. 1200) and lapping paper (12-0.3 f-i) as 

 preparation for making the frontal section (Fig. 3B). 



For the frontal section of large otoliths of postjuvenile 

 and adult fish, the otolith proximal surface was placed 

 facing up, and OL was measured. Then, the otolith prox- 

 imal surface was marked at three points: the tip of the 

 rostrum, the tip of the postrostrum, and the core region 

 on the central concave area. The otolith was embedded 

 in epoxy resin (Epoxicure; Buehler Ltd., Lake Bluff, IL) 

 on a hardened epoxy bed about 3 mm deep in a plastic 

 mold. The hardened epoxy block containing the otolith 

 was cut and trimmed by a micro cutter (MC-201; Maruto 

 Instrument Co., Ltd., Tokyo, Japan) to a 3-mm-wide 

 section that included the three marks. The trimmed 

 sample was fixed on a slide glass with hot wax (Stick 

 wax; Maruto Instrument Co., Ltd., Tokyo, Japan) and 

 polished with wet sandpaper (no. 400-800) on a polish- 

 ing machine (ML-101; Maruto Instrument Co., Ltd., 

 Tokyo, Japan and SBT900; South Bay Technology Inc., 

 San Clemente, CA). Polishing was continued until the 

 core and tips of the rostrum and postrostrum appeared. 

 The polishing was also made on the opposite side of the 



