18 

 20 



35 



- 40 



50 

 60 

 68 

 75 



- 100 



200 

 300 



20 30 40 

 CARAPACE LENGTH 



Figure 7. — Total weight-carapace length relationship in 

 pink shrimp. 



sions of the types treated here become necessary. 



All length-to-weight conversions required in 

 subsequent analyses are made with the informa- 

 tion shown in figures 7 and 8. 



Of particular interest in the present study is 

 whether or not shrimp growth is isometric or, more 

 specifically, whether or not the total weight-total 

 length relationships derived above conform to the 

 well-known cube law, viz, w=aP > , where 6 = 3. 

 Conformation (or lack thereof) should be acknowl- 

 edged when growth and mortality parameters are 

 integrated to solve the yield equation referred to 

 earlier and described in a later section. The fact 

 that the parameters of the mathematical expres- 

 sions relating total weight to total length proved 

 almost identical for both sexes (fig. 8) simplified 

 somewhat their statistical assessment. Upon 

 being tested with sexes separate or combined, the 

 hypothesis of no exponents differing significantly 

 from 6 = 3 had to be rejected. [For sexes com- 

 bined— H : 6 = 3. 00 when in fact 6 = 3.14 — 1= 



11.16, compared with <. os (33 degrees of freedom) = 

 2.04.] 



ESTIMATING GROWTH PARAMETERS AND 

 FITTING CURVES 



Recaptures from the Tortugas experimental 

 population provided some of the best data yet 

 obtained for describing growth in North American 

 Penaeidae (table 4). Tn synthesizing these data 

 for practical application later, a growth differential 

 between sexes materialized as the only real impedi- 

 ment, there being no evidence of growth inhibition 

 by the mark employed. Ideally, growth constants 

 for both sexes should be treated separately (via 

 summation methods) in all yield predictions, 

 particularly since the maximum size attained by 

 male shrimp appears to fall far short of that 

 attained by females (re table 3). Whether or not 

 both sexes have equivalent life expectancies poses 

 still another argument that would have to be 

 reconciled. But, to obviate undue complexity 

 and because breakdown of recapture data by sex 



4 



TOTAL LENGTH 



Figure 8. — Total weight-total length relationship in pink 

 shrimp. 



DYNAMICS OF A PENAEID SHRIMP POPULATION 



323 



