Figure 9. — Growth in weight of pink shrimp. Curves 

 are fitted to mean weights of marked shrimp re- 

 captured during successive time intervals of the 

 Tortugas and Sanibel experiments (sexes combined). 

 [Open circles indicate weights of single recaptures not 

 used to fit curves.] 



to incorporation in theoretical population models, 

 the reader is referred to the works of von Berta- 

 lanffy (1957), Beverton and Holt (1957), Ricker 

 (1958), and Tomlinson and Abramson (1961). 



Approximations to W a were obtained by first 

 transforming the von Bertalanffy equation to a 

 form linear in w)' b and then fitting the linear re- 

 gression of w)'^ on w]" 1 . The intersection of the 

 resulting line with that of proportionality yielded, 

 upon retransformation, the desired estimates 

 (Beverton and Holt, 1957, p. 283). In effect, the 

 intersect signifies the approximate weight at which 

 the ratio of successive growth increments reaches 

 unity, i.e., growth is arrested and maximum weight 

 is attained. The slope of the regression line pro- 

 vides an estimate of e~ K . 



A distinct disadvantage of this method when 

 working with data from mark-recapture experi- 

 ments is the requirement that weights be obtained 

 for every one of a reasonably wide range of suc- 

 cessive, equal-width time intervals. Unfortu- 

 nately, W m is quite sensitive to changes in the 

 slope of the fitted line and therefore has real 

 meaning only when the marked population that 

 yielded the data was at all times completely 

 vulnerable to the sampling (fishing) gear, the sex 



ratio of recaptures remained static, and the re- 

 sulting mean sample weights display consistent 

 as well as good reliability. Thus, its estimation 

 from the somewhat inadequate Sanibel data had 

 to rely on but four pairs of values (from U_ — 1 6 ), 

 whereas*that from the superior Tortugas data was 

 substantiated by seven pairs (from U — U). Be- 

 cause of considerably less variation about the 

 fitted line, the estimate derived from the Tortugas 

 data is regarded the more stable, and hence the 

 more meaningful of the two (table 6). When 

 estimating W a) there was no suggestion in the 

 case of the Tortugas data, and only faint evidence 

 in the Sanibel data, that the fishing gear in gen- 

 eral use was selective for faster-growing individuals 

 during the early stages of either experiment. 



Table 6. — Pink shrimp growth statistics computed from 

 mean weights of marked shrimp recaptured during succes- 

 sive time intervals of the Tortugas and Sanibel experiments 

 (sexes combined) 



1 Equivalent to a size of 17 headless-count. 



After adjusting w t and W a to unity at the be- 

 ginning (t n ) of each series of data, the slope of 

 the linear relationship 



In (W^-wV») = {hx (W'J")+Kt' }-Kt 



provided estimates of K, and the ordinate at which 

 the regression line intersects In FT„ gave estimates 

 of t (table 6). Substituting these in the von 

 Bertalanffy equation, theoretical values for w t 

 were calculated and ultimately defined the curves 

 depicted in figure 9. It is assumed that the values 

 for the constant t' , although based on data of 

 weight at undetermined age, would have compared 

 reasonably well with those obtained had the actual 

 (rather than the relative) age at each t t been 

 known. 



From table 6 and figure 9, it may be concluded 

 that the results of both experiments are in large 

 degree mutually corroborative. With the Tor- 

 tugas results arbitrarily established (on statistical 

 grounds) as the standard for comparison, W a is 

 of the same relative order of magnitude while the 



DYNAMICS OF A PENAEID SHRIMP POPULATION 



325 



