PARRACK: ASPECTS OF BROWN SHRIMP GROWTH 



not in general fall close to the modeled line, the 

 scatter is not severe. 



Growth in Weight 



The Marquardt algorithm (Marquardt 1963) 

 was employed to estimate parameters of weight- 

 length relations used to transform individual re- 

 lease and recapture lengths into weights so that 

 growth in weight could be modeled. Plots of the 

 estimated relations (Figure 2) indicate them to be 

 sex specific. Support plane confidence intervals 

 (Conway et al. 1970) on equation parameters (90% 

 probability) for males did not overlap those for 

 females further indicating that the functions dif- 

 fer between sexes. In addition the data were log- 

 ged to linearize the relation and covariance 

 analysis techniques applied to test for differences 

 between sexes. The probability that the linearized 

 functions are the same is small (P,. <0.00 1 ) further 

 indicating the sex specificity of these relations. 

 Further inspection of the plots shows the scatter of 

 observations to be restricted and that the models 

 effectively fit. These sex specific models were 

 therefore employed to transform the data. 



The magnitude of residual sums of squares (Ta- 

 ble 3) indicates the monomolecular model is the 

 best predictor of weight at age and the linear 

 model the poorest. The residual term for the linear 

 fit is about twice as large as that for the 

 monomolecular model and about 1.8 times that of 

 the Gompertz for both sexes. The reduction in re- 

 siduals of the monomolecular model as compared 

 with the Gompertz was much smaller, 25*^ in the 

 case of males and 14% in the case of females. 



As in the case of growth in length, estimated 

 growth parameters indicate that growth in weight 

 is sex dependent. Both the Gompertz and the 

 monomolecular model estimate females to be 

 much larger than males of the same age. Asymp- 

 totic weight (monomolecular model) is estimated 

 to be 75 g for females and 46 g for males; support 

 plane confidence intervals (90% probability) on 

 these estimates do not overlap. Estimates of the 

 parameter k in the monomolecular model appear 

 to be about the same for both sexes and in fact the 

 support plane confidence interval for males com- 

 pletely includes that interval for females. 



The differences in growth between sexes and the 

 degree of fit of the monomolecular model is shown 

 in Figure 1. Although appreciable scatter is ap- 



o 



(NlT 



o. 



o 



MALES 

 WEIGHT = 3.931587 x IQ-^ LENGTH 3. 152658 



24 48 72 96 120 144 168 192 

 LENGTH (MM) 



24 48 72 96 120 144 168 192 216 240 

 LENGTH (MM) 



Figure 2. — Weight-length relationships for brown shrimp. 



831 



