145 



AbStTeJCt. - An alternative ap- 

 proach. Central Location Measure, to 

 estimating the growth parameters from 

 length-frequency data was proposed 

 and applied to green tiger prawns, 

 Penaeus semisulcatus, from Kuwait 

 waters. The proposed method estimates 

 mean length at age by defining a cen- 

 tral location around the mode of the 

 length-frequency distribution for a co- 

 hort and then estimates the growth pa- 

 rameters by using the method of the 

 nonlinear least squares. The variances 

 and covariances for the growth param- 

 eters derived from the nonlinear-fitting 

 technique enable statistical compari- 

 sons of growth performance between 

 sexes, cohorts, or populations. Boot- 

 strap simulations indicated that the 

 proposed method was satisfactory in 

 estimating the growth parameters for 

 green tiger prawns, and that, therefore, 

 it may be applied to other short-lived 

 crustacean species with discontinuous 

 recruitment. Significant differences in 

 growth between male and female green 

 tiger prawns in Kuwait waters were 

 detected by using a multivariate test 

 (P<0.005), and annual variations in 

 growth were more obvious in males 

 than in females, indicating that growth 

 of males may be more vulnerable to 

 environmental changes. 



An alternative approach to 

 estimating growth parameters from 

 length-frequency data, with 

 application to green tiger prawns 



Xucai Xu* 



Hussain M. A. Mohammed 



Manculture and Fisheries Department, Kuwait Institute for Scientific Research 

 P O. Box 1638, 22017 Salmiya, Kuwait 



'Present address: Department of Mathematics and Statistics. Simon Fraser University 

 Burnaby, B.C. V5A 1S6, Canada 



Manuscript accepted 12 September 1995. 

 Fishery Bulletin 94:145-155 ( 1996). 



Growth parameters for crustacean 

 populations are usually estimated 

 from length-frequency data because 

 of the lack of reliable methods for 

 ageing decapods. Pauly and David 

 ( 1980) integrated Petersen's method 

 (Petersen, 1891) and Modal Class 

 Progression Analysis (George and 

 Banerji, 1964) into a single ap- 

 proach named ELEFAN I, which 

 has been implemented in the com- 

 puter software of Compleat ELEFAN 

 (Pauly, 1987; Gayanilo et al„ 1989). 

 It has been widely applied in growth 

 studies, especially in the tropical 

 and subtropical areas. Shepherd 

 (1987) proposed th( SLCA method 

 which performs a similar analysis 

 to ELEFAN I in that both methods 

 estimate the growth parameters by 

 detecting the peaks and troughs in 

 the length-frequency data; SLCA, 

 however, applies a different good- 

 ness-of-fit function in model estima- 

 tion (Holden and Bravinton, 1992). 

 Harding (1949), Cassie (1954), 

 Tanaka (1956), Hasselblad (1966), 

 Bhattacharya (1967), MacDonald 

 and Pitcher (1979), and Sparre 

 (1987a) developed methods for 

 analysis of length-frequency distri- 

 butions based on the normal distri- 

 bution assumption of the length-fre- 

 quency for each cohort. McNew and 

 Summerfelt (1978) discussed the 

 case when the length distribution 

 at each age was not normal. Some 



computer programs (Abramson, 

 1971; Young and Skillman, 1975; 

 Sparre, 1987b; Sparre et al., 1989) 

 were developed for implementing 

 these parametric methods. A diffi- 

 culty in applying probability distri- 

 butions to separate each age group 

 is that the breaking points between 

 age groups can be quite ambiguous 

 owing to the problems of overlapping 

 distributions. Schnute and Fournier 

 (1980) proposed an approach using 

 biological structure as constraints to 

 eliminate the ambiguity. 



All the above methods are based 

 on information on the central loca- 

 tion of the length-frequency data. 

 There are many ways to measure 

 the central location of a distribu- 

 tion, such as the mode if the distri- 

 bution is symmetric, the median, 

 the mean, and the trimmed mean. 

 The mean is sensitive to outlying 

 values in a sample, whereas the 

 mode and median are insensitive to 

 these outliers. The trimmed mean 

 is a compromise between the mean 

 and median in the sensitivity to 

 outliers (Devore, 1987) and might 

 be preferred in order to obtain a rep- 

 resentative location of the length 

 distribution of an animal by a 

 sample. For a species with multiple 

 overlapping cohorts in length dis- 

 tribution, however, it is impossible 

 to estimate the mean, median, and 

 trimmed mean without an assump- 



