152 



Fishery Bulletin 94| 



1996 



35 



30 



.", 



2 20 



Mode 



1-2 mm 



2 3 mm 



3-4 mm 



as wide as possible 



0.2 0.4 0.6 8 1 12 14 16 1.8 



Age (yr) 



Figure 2 



Growth curves estimated with five scenarios of width se- 

 lection of the central locations by using the proposed 

 method with the data in Table 1. The legend indicates the 

 width of the spread from the mode to each side. 



June and July 1989) in order to avoid the overlap- 

 ping part with other cohorts; therefore, the ranges 

 of the central locations for these length distributions 

 were the same for scenarios 3, 4, and 5. This may 

 reduce the variations in growth parameters esti- 

 mated by the five scenarios and indicates that the 

 spread of 2-3 mm is a reasonable choice. 



Comparison between the ELEFAN I, 

 Bhattacharya, and proposed methods 



Statistical tests with the modified Hotelling's T 2 sta- 

 tistic (Hanumara and Hoenig, 1987) and Equation 2 



indicated no significant difference (P>0. 1 ) in growth 

 parameters estimated by the proposed method and 

 the Bhattacharya method (Table 7) with the same 

 length-frequency data. The Bhattacharya method 

 estimates the population density function of the 

 length-frequency distribution for a cohort on the ba- 

 sis of the normal assumption; therefore, the method 

 requires very complicated calculations and involves 

 a subjective selection of the estimated population 

 density function (Pauly and Caddy, 1985). The pro- 

 posed method, however, avoids the tedious calcula- 

 tions. Therefore, the sophisticated computer pack- 

 ages for length-frequency analysis are not necessary 

 with the proposed method. Moreover, at least for the 

 oldest age class of green tiger prawns, to define the 

 width of the central location is more objective than 

 to define the population density function. The 

 Bhattacharya method has an advantage over the 

 proposed method in that it estimates the mean length 

 at age with standard deviation, which can be used to 

 estimate the degree of overlap among cohorts 

 (McNew and Summerfelt, 1978). 



It is impossible to compare the proposed method 

 with ELEFAN I by an analytical approach because 

 ELEFAN I cannot estimate the variances of the 

 growth parameters. The growth parameters esti- 

 mated by using ELEFAN I (Table 8) with the same 

 length-frequency data were similar to those esti- 

 mated by the proposed method, although the para- 

 meter K estimated by ELEFAN I tends to be lower 

 (six out of eight) and the parameter C tends to be 

 higher (six out of eight). The simulation studies by 

 Rosenberg and Beddington ( 1987) and Isaac ( 1990) 



