FISHERY BULLETIN: VOL. 76, NO. 4 



proximately 80% of the recaptured individuals 

 utilized in this analysis were large juveniles when 

 marked. These shrimp were marked and released 

 in estuarine waters before migrating to offshore 

 waters (Table 1). The remaining 20% were large 

 adults marked and released in offshore gulf wa- 

 ters along the Texas coast. These marking experi- 

 ments were carried out during 1967, 1968, and 

 1969. A full explanation of the data is given by 

 Clark et al. ( 1974). These data include total length 

 (i.e., the distance from the anterior end of the 

 rostrum to the posterior end of the telson) when 

 released and when recaptured, the dates of release 

 and recapture, and the sex of each individual. 

 Data entries with the same release and recapture 

 dates do not reflect growth and therefore were not 

 used to estimate growth rates. 



In order to analyze growth in weight, release 

 and recapture length were converted to weights 

 according to weight-length relations. These rela- 

 tions were estimated from data collected from the 

 commercial landings at Galveston, Tex., during 

 June, September, and December of 1965 and 

 March of 1966 (Fontaine and Neal 1971). 

 Parameters of the model weight = a (length)^ were 

 estimated for males and for females separately by 

 minimizing the expression S (W — Wg) where W 

 is weight defined by the model, W„ is observed 

 weight, and n is the number of observations. The 

 Marquardt algorithm (Marquardt 1963) was 

 employed to find the minimum. Plots of the esti- 

 mated relations through the scatter of the obser- 

 vations were observed to discern male/female 

 differences and the predictive usefulness of the 

 models. 



Since mark-recapture data were employed, 

 growth functions of interest were expressed in 

 terms of the change in age rather than absolute 

 age (see Appendix for derivation of equations). 

 Each recaptured individual was of some unknown 

 age on the date marked and on the date recaptured 

 so that the change in age is equivalent to the time 



at large. Expressed in these terms the logistic 

 function changes from 



S = S /(I + 6e -"") 



a «= 



(la) 



to 



S = SJH^lie-'^^''^^) {S-S)IS]) (lb) 



o° mm 



by substitution and rearrangement of terms. 

 Likewise, the von Bertalanffy equation 



S^ = SJl-be-''-) (2a) 



is expressed as 



S = S -(S -S )e-''<^''>. (2b) 



The Gompertz function 



S^ = S.exp[G(l-exp[-^(a-c.)])] (3a) 

 becomes 



S^. = S.[expG][S,J(S.expG)]^''P[-^<^°>l (3b) 

 A linear function of size upon age 



S = b + ka (4a) 



a 



is written 



S = S +k{Aa) . (4b) 



r rn 



Definitions of symbols employed above are: 



Sa = size at age a, 



Sr = size at recapture, 



S,„ = size when marked. 



Si = size of the smallest animal in the data, 



a, = age of the smallest animal in the data, 



Table l. — Brown shrimp mark- recapture experiments, northern Gulf of Mexico. 



828 



