and then used to remove the effects of its uneven 

 distribution from subsequent mortality estimates. 

 Results of an earlier mark-recapture experiment 

 performed with the same species but in an adjacent 

 area and for a different purpose corroborated 

 growth-parameter estimates from the Tortugas 

 experiment. 



After the various metric relationships used to 

 convert length to weight units were documented, 

 the von Bertalanffy growth function was fitted to 

 the mean weights (sexes combined) of marked 

 shrimp recaptured during successive, equal-width 

 time intervals characterizing each experiment. 

 The more meticulously executed Tortugas experi- 

 ment yielded for the function's parameters the 

 values: W 7 „ = 42.0 g.; J£=0.071; and ^=0.68 

 week. Weekly growth in weight during the rec- 

 tilinear phase of the observed growth pattern 

 averaged 1.5 g., which corresponded to a length 

 increment of about 3.4 mm. In terms of com- 

 mercial count size, the average experimental 

 shrimp required 12 weeks to increase in size from 

 123 to 37 headless-count. Minimum commercial 

 size (70 headless-count) was reached approxi- 

 mately i% weeks after the experiment began, and 

 at an estimated age of 15 weeks. The life expect- 

 ancy of the pink shrimp was assumed on the basis 

 of other studies to be about 83 weeks. 



The Tortugas experiment had to be subdivided 

 into partially exploited and fully exploited phases 

 before fishing and natural mortality could be 

 calculated. Rates of total mark-loss during both 

 phases were estimated by regression techniques 

 from recapture data grouped by weeks and adjust- 

 ed for nonuniform fishing effort. Separation of the 

 value obtained for the fully exploited phase into 

 its fishing and natural mortality components, F 

 and M respectively, proved impractical, however, 

 when attempts were made to apply mathematical 

 procedures designed specifically to accommodate 

 unadjusted recapture data generated by a constant 

 fishing effort. Difficulty arose from an inability 

 to evaluate satisfactorily the absolute size of the 

 experimental population at the start of its fully 

 exploited phase. Subsequent measurement of F 

 and M by a procedure independent of the initial 

 size of the marked population's second phase, and 

 inherently accounting for varying fishing effort 

 throughout, yielded estimates of 0.96 and 0.55 

 respectively- Their transformation to weekly 



mortality rates gave the corresponding values 

 0.62 and 0.42. Notwithstanding statistical limita- 

 tions, these observations draw attention to the 

 fact that at least in some areas, certain age groups 

 (or broods) of commercial shrimp may be sub- 

 jected to rather rapid deterioration from artificial 

 as well as natural causes. 



After substituting therein observed and hypo- 

 thetical values for the parameters of growth and 

 mortality, a relatively simple yield equation was 

 solved for each in a series of selected age-at-recruit- 

 ment values. With 15 weeks (corresponding to a 

 size of 70 headless-count) established as the 

 absolute commercial minimum age and thereby 

 serving as the point of departure, the resulting 

 curves of yield on age at recruitment clearly 

 showed that unless the expected level of natural 

 mortality falls well below that observed, post- 

 ponement of fishing until shrimp reach a greater 

 initial age (or size) is not justified. Observed 

 growth, although comparatively high, cannot offset 

 concurrent losses due to the substantial natural 

 mortality that seemingly prevails when shrimp 

 availability is at a maximum. Delaying the start 

 of harvesting woidd subsequently result in slightly 

 greater catches of shrimp in the larger size cate- 

 gories, but only at the expense of an appreciably 

 diminished overall catch. 



Even more convincing were the results of a 

 similar analysis in which weight and hence the 

 growth function's parameters were expressed in 

 terms of value. For any level of natural mortality 

 (observing the restriction imposed by the absolute 

 commercial minimum presently in effect), maxi- 

 mum yield in value is attained when fishing com- 

 mences at a shrimp size perceptibly below that at 

 which maximum yield in weight would be expected. 



The questions tentatively answered by this 

 study have far greater implications from an eco- 

 nomic than from a biological standpoint. Still of 

 great concern is the problem of resource mainte- 

 nance. We are unquestionably in a better position 

 to judge when, in the development of any age 

 group, the harvesting of shrimp should begin so as 

 to obtain maximum production therefrom. But 

 it remains for us to evaluate that level of fishing 

 which, for a given set of environmental conditions 

 ami for the shrimp resource as a whole, is most 

 conducive to our ultimate objective: maximum 

 equilibrium yield. 



DYNAMICS OF A PEXAEID SHRIMP POPULATION 



337 



