PARRACK: ASPECTS OF BROWN SHRIMP GROWTH 



Sx= an equation parameter, the asymptotic 

 size, 



b = an equation constant related to the size 

 at birth, 



Aa = a^ - o„, = time at large, 



Gr - age of an individual on the date recap- 

 tured, 



a,„ = age on the date marked and released, 



and G, g, and k are equation parameters. 



Equation parameters S^, k, G, and g were esti- 

 mated by utilizing the Marquardt algorithm to 

 minimize the residual sum of squares: 



y:iS'-s f 



\ f J./ 



where n = the number of individuals marked 

 and recaptured, 

 S'r = the observed size at recapture, and 

 Sr = the size at recapture as estimated by 

 the growth equation. 



The remaining equation constants, b in Equa- 

 tions (la) and (2a) and a, in Equation (3a), are 

 respectively computed: 



6 = (sjs^)-i 

 b = is^-s^)is 



a. 



In 



1- 



In (S^ IS.) 



g 



(5a) 

 (5b) 



(5c) 



where S^ is the size at birth and other symbols are 

 as before. The parameter b in Equation (4a) is 

 simply the size at birth. 



Studies of the early development of brown 

 shrimp indicate that newly hatched larvae are 

 0.35 mm total length (Cook and Murphy 1971). 

 Estimates of the equation constant b in the logistic 

 and von Bertalanffy models were based on that 

 length at birth. 



Shrimp eggs are 0.26 mm in diameter (Cook and 

 Murphy 1971) and about the density of water 

 (Cook and Lindner 1970) so that the weight at 

 hatching is about 0.000009 g. Brown shrimp un- 

 dergo metamorphosis 11 to 15 days after hatching 

 (Cook and Lindner 1970) and are 0.0008 g at that 

 time (Wheeler 1969). The weight at birth was cal- 

 culated as the midpoint between that weight and 

 the egg weight. Calculations of b and a, in the 

 various models were based on that weight at birth. 



RESULTS 



Growth in Length 



In anticipation that differences in growth be- 

 tween sexes may exist, equations were fit for 

 males and females separately. Estimated equa- 

 tion parameters (Table 2) are quite different be- 

 tween sexes. The fitted models indicate that 

 females are much larger than males of the same 

 age. The estimates of the growth coefficient k do 

 not differ greatly between sexes for both the lo- 

 gistic and the von Bertalanffy models; the 90% 

 probability support plane confidence intervals 

 (Conway et al. 1970) extensively overlap for both 

 models. The estimates of asymptotic length are, 

 however, greatly different and such confidence in- 

 tervals on those estimates are very disjoint. Pool- 

 ing all data together to estimate overall growth 

 functions for both sexes combined was therefore 

 judged unrealistic. 



The relative abilities of the von Bertalanffy, 

 logistic, and linear models to correctly reflect 

 growth was judged by comparing residual sums of 

 squares (Table 3). The von Bertalanffy function 

 produced the smallest residual and the linear 

 model the largest. The residual sum of squares for 

 the linear model was well over three times that of 

 the von Bertalanffy and logistic models for both 

 males and females. The difference between the 

 two nonlinear models was much smaller; the re- 

 sidual of the logistic was but 8% larger than that of 



Table 2. — Growth models for brown shrimp. Lengths (L) in millimeters, weights {W) in grams, and ages (a) in months. 



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