454 



Fishery Bulletin 105(4) 



outcomes, previous findings indicate that possible eco- 

 logical changes may have occurred at a particular 

 size range, as evidenced by otolith characters such as 

 the check-mark. Nishimura (1993) reported that 32% 

 of age-1 walleye pollock caught in the Bering Sea re- 

 vealed check-marks inside the first annual ring of the 

 otolith and he concluded that the check-mark would 

 have been formed at 40-80 mm FL (mode: 70 mm) at 

 an age of 4 months. This check-mark was frequently 

 detected in our samples (Fig. 3B). Similarly, in Funka 

 Bay, Japan, 58% of age-1 walleye pollock had check- 

 marks inside the first annual ring (Katakura et al., 

 2003). The settlement of juvenile walleye pollock from 

 pelagic to benthic habitat began from 70 mm TL and 

 was completed when the fish reached >85 mm TL in 

 Funka Bay (Nakatani and Maeda, 1987). Our calcu- 

 lated FL at the first inflection point was 68.7 mm, 

 which is approximately the same size as that when 

 settlement begins. The check-mark on the otoliths of 

 walleye pollock appears to occur, irrespective of dif- 

 ferences in geographic features of inhabited waters. 

 Victor (1982) suggested that the check-mark occurs 

 as a settlement mark and indicates the occurrence of 

 physiological changes or biological processes associ- 

 ated with settlement. Thus, we conclude that the first 

 inflection point at a particular size in our allometric 

 growth curve shows the adaptive response of walleye 

 pollock to physiological and environmental changes at 

 the time of settlement. 



The state of fe<0 but a<0 in the third function (Eq. 

 19.3) also implies that somatic growth is slower than 

 otolith growth. The allometric coefficient between OL 

 and somatic length drastically changes in association 

 with sexual maturity (Bervian et al., 2006). The Bo- 

 goslof area in the Aleutian Basin is known as one of 

 the main spawning grounds of walleye pollock in win- 

 ter. In this area, fish length at maturity was 360-570 

 mm FL (mean 464 mm) in males and 370-610 mm FL 

 (482 mm) in females (Traynor et al., 1990). The second 

 inflection point that appeared at 433.0 mm FL in our 

 study is situated within the size range of maturing 

 fish. We assume that the fish length around the second 

 inflection point corresponds to the timing of an energy 

 shift from somatic growth to gonad development, and 

 to corresponding changes that occur in the shifts of the 

 allometric growth curve. 



Both the third inflection point at 525.0 mm FL and 

 the fourth function (Eq. 19.4) indicate faster somatic 

 growth than otolith growth. Otolith growth persists 

 despite the cessation of body growth (Mugiya, 1990; 

 Secor and Dean, 1992); therefore, the otolith is also 

 assumed to grow throughout the lifetime of walleye 

 pollock (McFarlane and Beamish, 1990). Older annual 

 rings appear on the ventral proximal surface region, 

 as evidenced in the transverse section (McFarlane 

 and Beamish, 1990), similar to those seen in the 

 proximal surface region of the frontal section (Fig. 

 3A). The shape of the large otolith is an arched curve 

 connecting the tip of the rostrum, core, and tip of the 

 postrostrum. Thus, the third inflection point is con- 



sidered to be closely related to the slow growth phase 

 of otoliths, accompanying the change in the direction 

 of growth in otoliths from length (between the tips of 

 rostrum and postrostrum) to width (proximal surface 

 region increasing), and an increase in the slope of 

 the curve. 



The best equations that describe the relation of 

 SOR to FL, and LOR to FL were also represented by 

 the four-phase allometric smoothing function with 

 three inflection points (Eqs. 21.1-21.4 and 23.1-23.4). 

 The characteristics of the allometric otolith and so- 

 matic growth patterns are similar, as found in the 

 OL and FL relation. These relationships can be useful 

 for the analysis of growth of juvenile walleye pol- 

 lock from the back-calculation of adult otoliths. The 

 measurements of the SOR or LOR of fish at young 

 ages allow one to convert these measurements to FL 

 values. Similarly, our equations allow the conversion 

 of FL from any otolith measurement (OL, SOR, and 

 LOR) into BW. 



The resultant coordinates of the two inflection points 

 at FL of 70.0 mm and 431.2 mm derived from our FL 

 and BW relationship (Eqs. 25.1-25.3) were very close to 

 the first (68.7 mm FL) and second (433.0 mm FL) inflec- 

 tion points that emerged in the OL and FL relationship 

 (Eqs. 19.1-19.4). Because settlement and sexual ma- 

 turity are distinct biological events in the life history 

 of this fish, the timing of these events will be clearly 

 demonstrated in allometric growth. 



The condition factor (CF) offish is generally calcu- 

 lated by a formula (CF=10-^xBW/FLM. However, our 

 results indicate that the relation between FL and BW 

 is not constant over the lifetime of walleye pollock, and 

 probably for other fish species. In our equations, b in- 

 creased as fish grew in association with life stages from 

 6, = 2.77 to b2 = ^.02 and 6^ = 3.09, and this inflation 

 has potential implications for studies of fish growth. 



The present equations can be applied to the recon- 

 struction of size composition of fish from the remnant 

 otoliths found in the digestive organs of predators. We 

 expect that these reliable equations, with transforma- 

 tion of otolith measurement data into FL or BW values, 

 are useful not only for fish growth analysis, but also for 

 food habit and energetic studies (e.g., food conversion ef- 

 ficiency studies) because these studies rely substantially 

 on the back-calculation method. 



The samples of walleye pollock used in this study 

 provided a range offish lengths from 4.56 mm FL (=TL 

 in larvae) to 803 mm FL. Newly hatched walleye pollock 

 measure about 4.6 mm TL (Nishimura and Yamada, 

 1988), and the oldest fish reported from the Bering Sea 

 was 28 years old and measured 530 mm FL (McFarlane 

 and Beamish, 1990). Thus, the present data set can be 

 regarded as including almost the entire size range of 

 walleye pollock over the whole life span. Because the 

 proposed allometric smoothing functions can be exten- 

 sively applicable to all life stages of walleye pollock, 

 we term these equations "allometric smoothing func- 

 tions for otolith and somatic growth over the lifespan 

 of walleye pollock." 



