situations, the curve of yield value on recruitment 

 age reaches a maximum. 



VALUE IN RELATION TO SIZE 



For the purposes of this study, particular atten- 

 tion was given the price structure for pink shrimp 

 landed at Key West, Fla., during the Tortugas 

 experiment, September to December 1961 (table 

 9) . A plot of mean price on whole-weight equiva- 

 lents for each of 11 size (headless-count) categories 

 suggested that price could be treated as a logarith- 

 mic function of weight (fig. 14). The empirical 

 relationship proved to be satisfactorily described 

 by an equation of the form 



p = a+b\n [\n w], w< 10 



where p signifies the price per pound, w is the cor- 

 responding weight on an individual-shrimp basis, 

 and a and b denote constants. Note that the ex- 

 pression has been rendered discontinuous at a 

 shrimp weight of slightly more than 10 g., which 

 corresponds to the minimum commercial size of 

 70 headless-count recognized earlier, and which 

 commanded the lowest price then in effect (fig. 14). 

 Dealers accepting them paid the prevailing min- 

 imum rate (30 cents per pound) for all smaller 

 shrimp. 



Having established a reasonably acceptable 

 expression for the basic relationship between 

 market price and individual shrimp weight, it was 

 then possible to develop one relating the latter 

 variable to corresponding shrimp value (fig. 14). 



Data generated in the process served the needs of 

 subsequent analyses. 



VALUE AS A FUNCTION OF TIME 



Since shrimp value increases predictably with 

 weight, a corollary is that it behaves similarly with 

 respect to time. Thus, simple transformation of 

 weight to value units results in a temporal distri- 

 bution of points which may be empirically defined 

 by the growth equation employed in a previous 

 section. By treating the Tortugas experimental 

 data (table 4) accordingly, estimates of the con- 

 stants in the regression of value on time were 

 computed. The counterparts of W a and K, 

 respectively, F«, = 4.8 cents approximated the 

 shrimp's maximum attainable value, and K v =0.0S 

 represented an index of the rate of value decrease; 

 t ; remained fixed at 0.68 week, the value em- 

 ployed above in the description of growth in 

 weight. When fitted to the experimental obser- 

 vations, the resulting expression for shrimp weight 

 in terms of value as a function of time yielded a 

 curve over the range of values 0.5 to 5.0 cents 

 (per shrimp) closely comparable to that given by 

 the corresponding expression for growth in weight. 



DETERMINATION OF YIELD-IN-VALUE 

 MAXIMUMS 



After appropriate substitutions were made for 

 the above growth-in-value constants, solution of 

 equation (4) for various recruitment ages (£„,) at 

 each of four levels of natural mortality {M) per- 

 mitted construction of the desired yield-in-value 



Table 9. — Weekly ex-vessel prices paid for pink shrimp landed at Key West, Fla., 1961 

 [Values are in cents per pound for headless shrimp graded by sample (box) count] J 



1 Source: Market News Service, Bureau of Commercial Fisheries. U.S. Fish and Wildlife Service. 



DYNAMICS OF A PENAEID SHRIMP POPULATION 



335 



