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Fishery Bulletin 105(1) 



radius were regressed on age and otolith radius and 

 age on standard length. Second, Pearson correlation 

 coefficients of the otolith radius and standard length- 

 on-age residuals were quantified to estimate the amount 

 of age-independent variability. If no age-independent 

 variability existed in the OS-FS relationship, the re- 

 siduals of otolith radius-on-age and standard length- 

 on-age should be perfectly correlated. The unexplained 

 variability in the correlation between the residuals of 

 the two models can be considered the degree to which 

 age-independent variability can influence the OS-FS 

 relationship. To account for growth rate effects, Pearson 

 correlation coefficients were quantified for the residuals 

 of age-on-length and otolith radius-on-length. Moreover, 

 significant growth effects were detected with a positive 

 correlation. Lastly, the slopes of the OS-FS relationship 

 for each life stage were compared to account for ontoge- 

 netic effects. If otolith growth and fish somatic growth 

 are in constant proportion throughout the life stages 

 in question, the slopes between otolith-fish size should 

 not be significantly different (Cock, 1966). The slope of 

 otolith size to fish size was calculated with an allome- 

 tric model of the form y = ax'', where log transformation 

 results in the formula log(y) = log(a) -i- 6xlog(x) and the 

 parameter b is equal to the slope (Gould, 1966). 



Back-calculations 



Size-at-age was back-calculated by using three models 

 (Table 2). First, we examined the TVG model. This model 

 accounts for variability in the underlying assumption 

 of constant proportionality of otolith size to fish size 

 by adjusting the contribution of increment widths by a 

 growth factor. Second, we applied the MF model, which 

 accounts for a nonlinear relationship between otolith size 

 and fish size by directly estimating the shape param- 

 eters with a simple allometric model. Finally, a modified 

 stage-specific form of the BI model was applied. Although 

 this model depends on a constant proportion between 

 otolith and fish size, we mediated this effect by applying 

 the model to each specific life stage. To account for our 

 stage-specific differences in the OS-FS relationship, we 

 back-calculated size-at-age for the larval stage (5.4 mm 

 SL to 12 mm SL) and juvenile stage (>12 mm SL) with 

 12 mm SL as the biological intercept. The mean back-cal- 

 culated size-at-age trajectory was compared to measured 

 standard lengths at time of sampling. We evaluated the 

 fit of each model to the standard length-at-sampling data 

 by comparing the r~ values, as well as the minimum and 

 maximum percent deviation of the mean back-calculated 

 size-at-age value from the mean length-at-sampling. 



