Katakura et al.: The relation between otolith and somatic growth over the lifespan of walleye pollock (Theragra chalcogramma) 



451 



Figure 3 



The frontal sections of an otolith from an adult 

 walleye pollock {Theragra chalcogramma) (567 

 mm FL) viewed under transmitted light (A) and 

 from a juvenile (138.8 mm FL) under reflected 

 light (B). (A) The short otolith radius (SOR) was 

 measured from the core (middle black arrow) to 

 the tip of rostrum (right white arrow), and the 

 long otolith radius (LOR) was measured from the 

 core to the tip of postrostrum (left white arrow). 

 The older annual rings are seen in the proximal 

 surface region (the upper left side of the otolith, 

 the clear white region). (B) The check-mark (left 

 arrow) was observed inside of the first annual ring 

 (right arrow). Scale bars = 1 mm 



section. The section was finally polished by han(i with 

 wet sandpaper (no. 1200). The thickness of the polished 

 frontal section (including the thickness of the wax) was 

 0.28 ±0.07 mm (mean ±SD, w = 50). The OL in the frontal 

 section shrank (98.7 ±2.5%, n=1775) after the polishing; 

 however the decrease was not analyzed in this study. 



Results 



Relation between otolith length (OL) and fork length (FL) 



The most suitable equation to describe the OL (mm) and 

 FL (mm) relationship chosen with the minimum AIC was 



900 



600- 



c 



10 20 



Otolith length (mm) 



Figure 4 



The equation that best describes the relation between 

 otolith length (2.27xl0---25.98 mm) and fork length 

 (4.56-803 mm) of walleye pollock (Theragra chalco- 

 gramma) in the Bering Sea (n=2354). Open circles 

 (O) indicate individual samples of walleye pollock. 

 The grey line represents a four-phase allometric 

 smoothing function, and the dashed lines above and 

 below are the 95% confidence intervals. 



the four-phase allometric smoothing function (Fig. 4). The 

 minimum AIC in the general equations was an allome- 

 tric equation with a constant term {Eq. 4). In the AIC, 

 all allometric smoothing functions produced lower esti- 

 mates than all of the general equations. In the allometric 

 smoothing functions, the AIC decreased with the number 

 of allometric smoothing functions, which increased from 

 two to four. However, the AIC in the five-allometric 

 smoothing function was higher than that in the four- 

 phase allometric smoothing function (Table 2). The rela- 

 tion between OL (mm) and 6^,^ (mm) is given as follows: 



FL = 31.55 OLO 87 + 4.05 (0.00<OL<2.92) (19.1) 



FL = 5.64 OLi 51 -H 40.11 (2.92<OL<16.48) (19.2) 



FL = -26083.56 OL-^ 49 + 831.85 



(16.48<OL<19.65) (19.3) 



FL = 1.28x10-" OL*^'^ + 424.57 (19.65<OL) (19.4) 



CT,, = 0.41 OL^^'^ + 1.80. (20) 



The coordinates (OL, FL) of the three inflection points were 

 found at (2.92, 68.7), (16.48, 433.0), and (19.65, 525.0). 



Relation between short otolith radius (SOR) and 

 fork length (FL) 



For the relation between SOR (mm) and FL (mm), we 

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



