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Fishery Bulletin 98(3) 



estimate a formation time of less than 3 months for opaque 

 zones on otoliths from L. erythropterus marked twice in 

 1993. Those individuals clearly showed springtime formation 

 of the opaque zones in that year, but we also concluded 

 that completion occurred earlier in the following year, 

 about 1-2 months after the minimum water temperature in 

 August, indicating that commencement and formation could 

 have occurred during winter 1994. This difference was not 

 explained by interannual variation in the occurrence of 

 minimum water temperatures and may have been due to 

 changes in metabolism and physiology induced by capture, 

 transport, handling, and captivity. These are plausible 

 artifacts, given that opaque zone formation is under control 

 of a poorly understood combination of environmental 

 and endogenous factors that influence endolymph fluid 

 chemistry (Beckman and Wilson, 1995; Romanek and 

 Gauldie. 1996). The location of the cages may have 

 contributed to mortality or lack of growth of the otoliths of 

 L. bohar,L. fulviflarnma, L.gibbus.L. kasmira, andL. vitta 

 transported inshore from their reef habitats, whereas the 

 other inshore species were expected to be more tolerant of 

 the cage environment. 



The models produced similar, but more informative, 

 conclusions to the application of the informal approaches. 

 Analyses following MacLellan and Fargo ( 1995) indicated 

 an annual periodicity of opaque zone formation for 10 

 study species with few exceptions. The "method of best 

 fit" estimated mean calendar completion dates that were 

 inside the confidence intervals of the direct method, with 

 the exception of L. erythropterus, for which the method 

 was sensitive to the interannual variability in timing of 

 annulus completion. 



Sources of bias 



Assumptions concerning otolith growth rate in the direct 

 method were the best available approximations, given both 

 our observations and the current understanding of otolith 

 growth, and we were confident that their main effects were 

 accounted for by excluding outliers and by measures of 

 variation reported about the mean results. 



Earliest models of otolith growth presumed that no net 

 accretion occurred when fish stopped growing, and these "no- 

 growth" horizons provided the foundation for the recognition 

 of annual winter marks in otoliths (Romanek and Gauldie, 

 1996). However, otolith growth is not directly coupled to 

 somatic growth (e.g. Mosegaard et al., 1988) and has been 

 observed to show complexities correlated by various authors 

 with factors such as food intake, life-history stage, tem- 

 perature, and metabolic rate (Romanek and Gauldie, 1996; 

 Schimpa and Goodyear, 1997 ). Most recently, Romanek and 

 Gauldie ( 1996) proposed that otolith growth along the main 

 growth axis is continuous, with the rate of deposition (that 

 is, the microincrement width) being modulated by tempera- 

 ture and pH of the endolymph. This model was based on the 

 known physiology of the endolymph and the physical chem- 

 istry of aragonite, and was tested by Payan et al. ( 1997 ) and 

 Gauldie and Romanek ( 1998). 



We therefore assumed a constant rate of otolith growth. 

 while recognizing that a number of factors might be 



expected to vary regularly during continuous growth of 

 the otolith, including the widths of daily micro-increments, 

 trace element concentrations, matrix proteins, and arago- 

 nite crystal structure (Gauldie and Nelson, 1990; Gauldie 

 et al., 1990). It remains unknown which combination of 

 such variable characteristics integrate into the optical 

 macrostructure of otolith sections viewed as opaque and 

 translucent zones (Fowler, 1995). 



If alternating periods of slow and fast otolith growth 

 occurred regularly throughout each increment cycle, in 

 violation of our working approximation, errors would 

 tend to cancel one another during calculation of peri- 

 odicity. In Equations 1-3, the initial fraction of otolith 

 growth (7F) was estimated by using a numerator from 

 the last part of a cycle, but the final fraction (FF) was 

 estimated from the first part of a cycle by using the mar- 

 ginal increment as a numerator. If IF was underesti- 

 mated because the otolith grew slowly at the end of a 

 cycle, it would be countered by an overestimation of FF 

 caused by faster otolith growth at the start of a cycle. Our 

 method was most vulnerable to interannual differences 

 in otolith growth rate, which were evident for some fish 

 as anomalous otolith growth, possibly as a physiological 

 response to captivity or tagging. 



The widths of outer increment cycles were assumed to 

 be the same in our second working approximation because 

 an exponential decrease in growth along otolith reading 

 axes and equidistant outer zones are a feature of several 

 families from the central GBR, including lutjanids (Fowler 

 and Doherty, 1992; Choat and Axe, 1996; Newman et al., 

 1996). The exponential curves presented in our study sup- 

 ported the approximation for the 50 marked fish that had 

 completed their fourth increment cycle but did not support 

 so well for the younger fish sacrificed during their fourth 

 (^=28) and third cycles in=4}. Finally, the model assump- 

 tion that the increment cycles had the same time period 

 of formation in an individual otolith was supported for our 

 estimation of closing dates by the determination of the 

 annual periodicity of opaque zone formation. 



There was bias in interpretation of the position of the 

 first annulus, causing significantly higher estimates of total 

 age by the unfamiliar reader, but not of the number of 

 annuli past the OTC marks. The structural check rings at 

 the outer edges of opaque zones were the best feature of 

 the large lutjanid otoliths, and the potential for errors in 

 interpreting the annuli on outer margins (Francis et al., 

 1992) was reduced by sacrificing most fish in late summer 

 and autumn. The longer ventral axis was the most useful 

 because of the variability in growth, measurement errors, 

 and significant differences in estimates of closing dates 

 from measurements along the shorter sulcal axis. However, 

 growth in older otoliths with complex prismatic structure 

 becomes restricted by the otic cleft (Gauldie and Nelson, 

 1990), and the sulcal axis may provide the only straight 

 axis for measurement in future applications of the models. 



Related studies 



In contrast to our results for the "red snappers" L. erythro- 

 pterus. L. malaharicus. and L. sebae, Milton et al. (1995) 



