Miller et al : Relation between otolith size and larval size at hatching for Gadus morhua 



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row. For a lapillus of average area, the preiiicted 

 mean larval SL at hatching was 4.55 mm. The 951 

 CIs around this value were 4.4 mm < SL < 4.66 mm, 

 a range of 0.2 mm. However, in our application we 

 were more interested in the 95^7^ CIs of an individual 

 prediction. The range in these values was much 

 wider, 3.66 mm < SL < 5.41 mm., a range of L75 

 mm. We conducted a similar analysis for the radius 

 of the lapillus at hatching (LR, Fig 4B), which was 

 significantly and positively related to SL at hatch- 

 ing. Overall, longer larvae had wide lapilli at hatch- 

 ing. As with the results for the total area of the lapil- 

 lus, the 95'7f CIs for larval SL predicted for a lapillus 

 of average radius were narrow. For a lapillus of av- 

 erage radius at hatching (14.15 |im), the associated 

 95'7f CIs of the mean were 4.44 < SL < 4.69 mm, a 

 range of 0.25 mm. However, the prediction is less 

 precise for individual back calculations for the asso- 

 ciated 95*7^ CIs of the individual prediction were 3.72 

 < SL < 5.49 mm, a range of 1.77 mm. 



We conducted a similar regression analysis for the 

 area and radius of the sagittae and SL at hatching. 

 There were significant linear relationships for both 

 measures of otolith size and SL at hatching (Fig. 5). 

 For an average sagittal area of 276 |im, the predicted 

 SL at hatching was the same as that for the lapillus. 



The 95% CIs for the population average were 4.38 

 mm < SL < 4.75, a range of 0.37 mm. The wider con- 

 fidence intervals for the population mean for the sag- 

 ittal measurements compared with the lapillar mea- 

 surements reflected the lower coefficient of determi- 

 nation ir") of the regression. Moreover, the 95% CIs 

 of an individual prediction, based upon sagittal area, 

 were also wider than those for lapillus-based predic- 

 tions (3.48 < SL < 5.64, a range of 2.16 mm). Similar 

 patterns were observed for the regressions for sagit- 

 tal radius at hatching (Fig. 5B). 



We examined the potential for egg size and tem- 

 perature to increase the predictive power of the re- 

 lationships. We performed these analyses on data 

 aggregated to the deployment level. Standard length 

 at hatching was positively related to egg size: SL = 

 0.656 (±0.46) -1- 2.55 (±0.31) x egg diameter, n = 128, 

 r~ = 0.345, P = 0.0001. To explore the potential for 

 egg size to explain additional variation in otolith- 

 size and SL-at-hatching models, we regressed the 

 residuals from the relationship of egg diameter to 

 SL on several measures of otolith size. If egg size 

 explains additional variation, independent of SL at 

 hatching, we would expect to see a significant re- 

 gression statistic. The residuals were significantly 

 related to the area and the radius at hatching of the 



