Xu and Mohammed An alternative approach to estimating growth parameters 



149 



quency on the growth estimates by the proposed 

 method. The monthly length-frequency data in Table 

 1 were resampled 100 times with replacement and 

 thus 100 length-frequency data sets were generated 

 which were used to estimate the growth parameters 

 with the proposed method in this study. The bias 

 caused by the variations in length-frequency distri- 

 butions was estimated from 100 bootstrap estimates 

 compared to the true value, i.e. bias - estimate - true 

 for K, t n , C, and t , and bias = (estimate - true)/l0 for 



' 0' ' s' 



L^ . The boxplot (Fig. 1 ) showed that the bias distri- 



butions were fairly symmetrical, and the medians of 

 the biases in bootstrap estimates for growth param- 

 eters, shown as a bar in the box of the boxplot, were 

 located very close to the center of the box and to the 

 horizontal zero line. The means of L x , K, t , C, and t s 

 from 100 bootstrap estimates were 35.88 mm, 1.98 

 yr -1 , -0.06 yr, 0.73, and -0.41 yr which were very 

 close to the true values (Table 4 ). The bootstrap simu- 

 lations indicated no trend of over- or under-estima- 

 tion of the growth parameters by the proposed 

 method. The proposed method works well for green 



