Schirripa: An evaluation of back calculation methodology using simulated otolith data 



795 



Figure 5 



Error in mean length at age estimates using the last annu- 

 lus only and the ten back-calculation methods outlined in 

 Table 1 for the sigmoid-shaped OR-TL relation. SS = sum 

 of squares. 



75  



- 

 -0 r> - 

 7S  



0- f--*-^ 



<I75- 

 9 75' 



C  



u 



I -0 75 J 

 75 



-0 75 



75 







-0 75 



-• —  — • — » • > 



SS = 0047 



SS = 0001 



SS = 0063 



<» i ii - t . « ■<■ >. I 



SS = 0540 



9 10 11 12 13 1 



-0 75 

 75 





 -0 75 

 75 

 0- 



-0 75 

 75 



 



-0 75 



75 







-0 75 



Age 



• > — • — »  



Method 6 

 SS = 1296 



SS = 0873 



Method 10 



12 3 4 5 6 7 



9 10 11 12 13 14 



Figure 6 



Error in mean length at age estimates using all annuli and 

 the ten back-calculation methods outlined in Table 1 for the 

 linear-shaped OR-TL relation. SS = sum of squares. 



The sigmoid shape of the OR-TL relation was not as 

 evident in the shape of the percent error plots for methods 

 11 through 20 (Fig. 5). When only the last annulus was 

 used, the least error resulted from employing a direct pro- 

 portionality back-calculation equation (Fig. 5, method 11, 

 SS=0.0951), and the greatest error from using direct sub- 

 stitution into the OLS regression equation (Fig. 5, method 

 12, SS=1.3938). When only the last annulus was used with 

 comparable back-calculation equations, as in methods 12 

 versus 13 and 18 versus 20, both the sum of squares and 

 bias were reduced considerably. 



Linear-shaped OR-TL relation 



Of the four functions fitted to OR-TL/LIN, the ordinary 

 least squares and functional linear regressions resulted in 

 the highest coefficient of determination value (r'=0.916). 

 The curvature of the Weibull and quadratic fits showed 

 that the relation deviated slightly from a straight line. 



There was a high degree of similarity between the percent 

 error plots for all twenty methods (Figs. 6 and 7), suggest- 

 ing that the estimation of length-at-age is not as sensitive 

 to the method of back-calculation when the OR-TL relation 

 is linear as when it is curved. When the OR-TL relation was 

 linear, the least error resulted from employing a functional 

 regression coupled with the Fraser-Lee back-calculation 

 equation when all annuli were used (Fig. 6, method 5, 

 SS=0.0001) and when only the last annulus was used (Fig. 7, 

 method 15, SS=0.0013). The greatest error resulted from 

 direct substitution into the OLS regression following a 

 natural log transformation of all parameters, both when all 



-0 75 

 75 



-0 75 

 75 



-0 75 

 75 



-0 75 

 75 



Method 11 

 SS = 0031 



Method 13 



■0.75 ' 

 75 



-0 75 

 75 T 



-0 75 

 75 



-0 75 



75 



SS = 0564 



SS = 0398 



Method 18 

 -« — • — •— * — ^— •  



SS = 0054 



Age 



Figure 7 



Error in mean length at age estimates using the last annu- 

 lus only and the ten back-calculation methods outlined in 

 Table 1 for the linear-shaped OR-TL relation. SS = sum of 

 squares. 



annuli were used (Fig. 6, method 6, SS=0.1296) and when 

 only the last annulus (Fig. 7, method 16. SS=0.1245). 



