BOEHLERT: AGE DETERMINATION IN FISHES 



termination exists with sections. For this reason, I 

 also constructed a hybrid multiple regression 

 model based upon a combination of otolith section 

 and whole otolith ages. The decision on which age 

 to use was arbitrary in the following way: If the 

 difference (otolith section age minus whole otolith 

 age) was "^ 5 yr, whole otolith age was chosen; if the 

 difference was >5 yr, otolith section age was cho- 

 sen. The resulting models are described in Table 5. 

 Independent variables similar to those in the 

 other two models were chosen, and the multiple 

 correlation coefficients were greater in each case. 



To analyze the precision of the models, subsam- 

 ples of 50 male and 50 female S. diploproa were 

 taken from the remaining samples not used in the 

 calibration subsample. Lengths and ages were 

 representative of the respective ranges in the 

 overall collection. Ranges of whole otolith age, 

 NMFS age (that from the other agency), and 

 otolith section age in these samples were 2-50, 

 3-49, and 2-75 for females and 3-34, 4-25, and 3-84 

 for males, respectively. 



Whole otolith age was predicted based upon the 

 appropriate whole otolith age models. Values of 

 estimated age, whole otolith age, and NMFS age 

 as a function of length are plotted in Figure 4. The 

 deviation of NMFS age from whole otolith age 

 increases with increasing length for both males 

 and females. Deviations from the first whole 

 otolith age are presented in Figure 5. Model- 

 induced variability is the difference between es- 

 timated whole otolith age and whole otolith age; 

 between-agency variability is whole otolith age 

 minus NMFS age; within-agency variability is the 

 difference of two successive age determinations by 



Table 5. — Regression coefficients and associated statis- 

 tics on the multiple regression models of age in Sebastes 

 diploproa . The ages used for the calibration of these mod- 

 els are based upon either whole otoliths or otolith sec- 

 tions as described in the text. 



Variable 



Coefficient 



SE 



Females (A/ = 290) 



Otolith weight 0.2233 



(Otolith width) 2 -0.2983 



(Otolith weight)^ -0.1244 x 10" 



Otohth length -2,495 



Constant (a) 17.7993 

 SD = 4.3967 

 Multiple correlation, R = 0.962 



Males {N = 246) 



Otolith weight 0.2504 



(Otolith width)2 -0.3598 



(Otolith weight) 3 -0.1272 x IQ- 



Otolith length -2.4123 



Constant (a) 16.6069 

 SD = 4.7479 

 Multiple correlation, R = 0.958 



0.0135 

 0.0403 

 0,1685 X 10- 

 0.5084 

 3,7339 



0,0157 

 0,0549 

 0-2800 . 10-' 

 0,6071 

 3,9145 



0001 



0,001 



;0.001 



-0.001 



0,001 



; 0.001 



0,001 



0,001 



;0.001 



tO.001 



the same reader Mean values of these sources of 

 variation are presented in Table 6 for females and 

 Table 7 for males. In both cases, the mean 

 between-agency variability is greater than either 

 model-induced or within-agency variability. 

 One-way ANOVA demonstrates a significant dif- 

 ference among the three sources (Tables 6, 7). Mul- 

 tiple range testing (least significant difference, 

 a = 0.05), moreover, demonstrates that the means 

 are significantly different for both females and 

 males; the range tests suggest that within-agency 

 and model-induced variability are equal and are 

 both significantly less than the between-agency 

 variability. 



Only a single otolith section age was determined 

 for specimens from the 1980 confirmation subsam- 

 ple. Ages were estimated from the multiple re- 

 gression model of section age (Table 4) and com- 

 pared with conventionally determined section age 



35rT 



14 16 18 20 22 24 26 28 30 32 34 36 38 40 

 FORK LENGTH (cm) 



FIGURE 4. — Comparisons of mean whole otolith ages at length 

 for the confirmation subsample of Sebastes diploproa . Trian- 

 gles represent age from reader A, circles the age estimated by the 

 model, and squares the age determined by another laboratory. 



109 



