FISHERY BULLETIN: VOL. 81, NO. 3 



assumption implies that similar processes occur in 

 regions of the otolith that appear somewhat different 

 superficially. We feel it is not an unreasonable 

 assumption, however, because one can usually en- 

 hance the quality of a preparation by increasing the 

 amount of time and care devoted to it, bringing out 

 distinct increments in regions which otherwise would 

 remain uninterpretable. For example, Radtke (foot- 

 note 3) has shown that the core area of opakapaka 

 otoliths requires substantially more etching time 

 than does the marginal zone. He improved the quality 

 of his samples by employing differential etching 

 times, a tedious but effective technique. Wild and 

 Foreman (1980) used similar methods in their study. 

 Presumably, the visual quality of a preparation is 

 largely limited by the ability of the investigator to un- 

 veil its contents. 



A second and more important assumption is that it 

 is reasonable to extrapolate the growth of a sexually 

 mature fish based on its individual pattern of growth 

 prior to gonad maturation. Because all data gathered 

 at otolith lengths > 6,000 /xm were deleted, age es- 

 timates obtained from Equation (3) are bound by this 

 constraint. We have argued that otolith increments 

 become equivocal chronometers past maturity, due 

 to interrupted growth. Both Pannella (1971) and 

 Wild and Foreman (1980) reached similar con- 

 clusions in their studies of red hake, Urophycis chuss, 

 and skipjack tuna, Katsuwonus pelamis , respectively. 

 Significantly, in the latter study growth interruptions 

 were not evident in yellowfin tuna, Thunnus alba- 

 cares, and almost all specimens were of immature 

 size (Schaefer et al. 1963). Not only has maturation 

 been implicated in interrupting otolith growth, but 

 also reduced food (Irie 1960; Methot and Kramer 

 1979; Uchiyama and Struhsaker 1981) and low tem- 

 perature (Irie 1960; Taubert and Coble 1977). It is 

 apparent from these studies that any factor which 

 arrests the growth of the whole fish, temporarily or 

 otherwise, can lead to errors in the time chronicle of 

 daily increments (Pannella 1980). Clearly, if the ad- 

 ditional energy burden incurred at sexual maturity is 

 substantial (sensu Gadgil and Bossert 1970), ex- 

 trapolation beyond 6,000 /xm may be an unrealistic 

 exercise and growth rates of large fish may in fact be 

 overestimated. However, it is pertinent to note that 

 the proportions in opakapaka of both ovarian and 

 testicular tissues relative to total body weight are not 

 great, ranging from 1 to 4% among Stage III females 

 and slightly less among males (Ralston 1981). 

 Furthermore, most models offish growth currently in 

 use (e.g., von Bertalanffy and Gompertz models) do 

 not treat maturity as a growth singularity, i.e., a time 

 when the pattern of growth changes. In spite of their 



relative simplicity, these models have adequately 

 described fish growth dynamics in a surprisingly 

 large number of situations (Ricker 1979). Undoubt- 

 edly this is because fine scale departures from model 

 growth (e.g., seasonal trends) are averaged out when 

 treating a lifespan measured in years. Finally, the 

 procedure we have used involves extrapolating, at 

 most, 68% beyond the range of the data (6,000- 

 10,000 /xm). In most cases, the amount we ex- 

 trapolated was far less. Nonetheless, this particular 

 assumption is critical and yet remains unresolved. 

 Additional research on this topic is essential. 



At the other extreme, by applying a linear model to 

 the data (Equation (2)), we have assumed that otolith 

 growth rate is greatest as otolith length approaches 

 zero. This is unrealistic (see, for example, Pannella 

 1974; Brothers and McFarland 1981). The average 

 width of increments actually decreases very near the 

 focus (Fig. 2). We evaluated the extent of bias in- 

 troduced by this computational simplification, 

 however, by comparing age estimates derived from 

 both analytical (Equation (3)) and complete numeri- 

 cal integration of all the otolith growth- rate data, 

 broken down by 100 /xm size classes. The largest ab- 

 solute difference between the two types of age es- 

 timates was 18 d. This was for the youngest of fish, as 

 might be expected, and indicates that the analytical 

 method provides a poor approximation for fish < 1 

 mo old. However, because our results are intended to 

 describe growth over the entire size range of 

 opakapaka, measured on a time scale of years, and 

 because the difference between the two estimates 

 becomes progressively smaller among the larger fish, 

 we consider this a negligible error. 



A final assumption is that one increment forms each 

 day in preproductive individuals. We have presented 

 evidence that validates this assumption, at least for 

 fish 30-34 cm FL, in the form of in vivo marking of 

 otoliths with tetracycline. Furthermore, evidence 

 from the field (Fig. 10) also strongly supports this 

 conclusion, again for immatures (27-35 cm FL). A 

 final assessment of this assumption can be made by 

 comparing the growth of opakapaka, as developed 

 here, with studies available in the literature on lut- 

 janid growth. 



Researchers have long recognized the interdepen- 

 dence of growth parameters. Beverton and Holt 

 (1959) presented values of K and L„ computed from 

 the von Bertalanffy growth model and noted an in- 

 verse relationship between these parameters. Simi- 

 larly, Cushing(1968) presented graphs relating growth 

 parameters for several large taxonomic categories 

 (e.g., Clupeoidei, Gadiformes, Salmonoidei, etc.). 

 Pauly (1979) has attempted to quantify the relation- 



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