FISHERY BULLETIN: VOL. 76, NO. 4 



parent, systematic departure of the observed 

 points from the model is not evident so that the 

 model does reflect the data. 



CONCLUSIONS 



The relative abilities of prediction of the differ- 

 ent models can be judged by comparison of their 

 residual sum of squares. The comparison strongly 

 suggests that the linear function was by far the 

 poorest model of brown shrimp growth both in 

 length and weight. Although the size-age relation 

 does appear linear for small young individuals, 

 the rate of increase in size decreases with age, a 

 phenomenon documented for many organisms 

 both terrestrial and aquatic. A nonlinear function 

 is therefore required to model brown shrimp 

 growth throughout their entire life span. 



The residual sum of squares for the von Ber- 

 talanffy equation was smaller than the logistic 

 equation when modeling weight; however, these 

 differences were not large. It is therefore not com- 

 pletely evident that the von Bertalanffy equation 

 is vastly superior to the logistic and Gompertz in 

 the modeling of brown shrimp growth. The von 

 Bertalanffy equation did, however, constantly fit 

 these data best for both sexes in the modeling of 

 both length and weight. This study does therefore 

 show the von Bertalanffy model to be slightly 

 superior to the logistic and the monomolecular 

 model superior to the Gompertz for both sexes. 



The difference in the size-age function between 

 sexes was found to be large. This phenomenon was 

 previously reported for brown shrimp in the 

 southern Gulf of Mexico (Chavez 1973) and 

 northwest Atlantic (McCoy 1972) and for many 

 other marine organisms. This study indicates that 

 male brown shrimp apparently grow to approxi- 

 mately only three-fifths the weight and five-sixths 

 the length of females; however, the coefficients of 

 growth, as indexed by /j in the monomolecular and 

 von Bertalanffy models, are roughly equivalent. It 

 is interesting to note that the rate of increase in 

 size tends to fall off at an earlier age for males than 

 for females (see Figure 1). Since, in general, a 

 decrease in that rate roughly conforms to the age 

 of maturity and sexual activity, it is not unreason- 

 able to assume that males mature at a younger age 

 than do females. 



Comparison of growth functions derived herein 

 with those generated by other workers indicate 

 that brown shrimp growth in the northern Gulf of 

 Mexico is very different than that in the southern 



gulf and in U.S. Atlantic coastal waters. Growth 

 functions derived from populations off Mexico 

 (Chavez 1973) demonstrated a faster and pro- 

 longed growth compared with growth observed in 

 this study. That trend was consistent for both 

 males and females. Studies off North Carolina 

 (McCoy 1972) showed growth in Atlantic waters 

 to be very rapid although a smaller asymptotic 

 size was realized. As before, that trend was the 

 same for both sexes. The kinds of data used and the 

 methods employed to fit the growrth models dif- 

 fered in all three studies; therefore, some dis- 

 agreement in results may be expected. The 

 magnitude of the differences observed, however, 

 indicated truly different rates of growth may well 

 exist in the three geographical locations. The 

 growth of wild populations of white shrimp, 

 Penaeus setiferus, a similar species, is correlated 

 with water temperature (Gaidry and White 1973) 

 in the shallow estuarine and nearshore areas they 

 inhabit throughout their entire life span. Since 

 the temperature of seasonally homothermic deep 

 offshore waters where brown shrimp spend their 

 adult life may be assumed to increase with de- 

 creasing latitude, the differences in growth be- 

 tween northwest Atlantic, northern gulf, and 

 southern gulf brown shrimp populations are likely 

 positively correlated with gross water tempera- 

 ture. 



ACKNOWLEDGMENTS 



The staff at the Southeast Fisheries Center Gal- 

 veston Laboratory, National Marine Fisheries 

 Service, NOAA, provided assistance in this study. 

 Susan Brunenmeister and Edward Klima con- 

 tributed helpful advice in the reviewing of this 

 manuscript. Patricia Phares and Scott Nichols 

 provided valuable advice as to applicable statisti- 

 cal procedures. 



LITERATURE CITED 



BERTALANFFY, L. VON. 



1938. A quantitative theory of organic growth (Inquiries 

 on growth laws. II). Hum. Biol. 10:181-213. 

 ChAVEZ, E. a. 



1973. A study on the growth rate of brown shrimp 

 (Penaeus aztecus aztecus Ives, 1891) from the coasts of 

 Veracruz and Tamaulipas, Mexico. Gulf Res. Rep. 

 4:278-299. 



CLARK, S. H., D. A. EMILIANI, AND R. A. NEAL. 



1974. Release and recovery data from brown and white 

 shrimp mark-recapture studies in the northern Gulf of 



832 



