794 



Fishery Bulletin 100(4) 



40 r 



30 



20 



o 10 



5 6 7 



Method 



Figure 3 



Scatterplot of the slopes of the regression of back-calcu- 

 lated length at age 2 versus age at capture for the ten back- 

 calculation methods that used all annuli. The numbers 

 plotted indicate the shape of the OR-TL relation examined 

 1 1=0R-TL/SIG [sigmoid], 2=0R-TL/LIN [linear], 3=0R-TL/ 

 EXP [exponential], 4=0R-TL/ASYM [asymptotic]). 



The sigmoid shape of the OR-TL relation was evident in 

 the shape of the percent error plots for methods 1 through 

 10 (Fig. 4). Wlien the OR-TL relation was sigmoid-shaped 

 and all annuli were used, the least error resulted from em- 

 ploying a ordinary least-squares regression coupled with 

 the log-transformed Fraser-Lee back-calculation equation 

 (method 7, SS=0.4913). The greatest error appeared when 

 using the direct proportion equation (Fig. 4, method 1, 

 SS=1.4016). Using the y-intercept of the OR-TL relation 

 in the back-calculation equation (methods 3/13 and 5/14 



Figure 4 



Error in mean length at age estimates using all annuli and 

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

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



in Table 1 ) had little effect on the total sum of squares 

 when comparing method 2 with method 3; in addition, 

 correcting for different limits of the Weibull function in 

 methods 8 versus 10 had little effect. However, the log 

 transformation of methods 6 and 7 reduced the sum of 

 squares considerably. 



