would have resulted in diminished reliability of 

 sample length and weight estimates, each growth 

 statistic hereinafter computed and substituted in 

 yield equations reflects a compromise or "sexes- 

 combined" situation. Although such statistics 

 are in a sense artificial, their use is justified in that 

 they define the average growth pattern within the 

 experimental population during that period when 

 the age group represented was enjoying greatest 

 biomass, was most accessible, and its sex ratio had 

 not yet begun to indicate a preponderance of 

 females. Each estimate obtained may be viewed 

 as lying intermediate between some upper value 

 for females and a lower value for males. 



It follows also that experimental length and 

 weight data from a sexually heterogeneous popula- 

 tion yield the most reliable growth-parameter 

 estimates when the sex ratio of marked recaptures 

 remains constant throughout the experiment. In 

 the case of the Tortugas experiment, the sampling 

 distribution of ratios generated over the period t\ — U 

 revealed no significant statistical departure when 

 checked for goodness of fit against the uniform 

 distribution theorized from the sex ratio established 

 at the experiment's beginning [x 2 =12.15 compared 

 with x 2 -05 (6 degrees of freedom) = 12.59]. 



Table 4. — Mean lengths and weights of marked pink shrimp 

 recaptured during successive weeks of the Tortugas experi- 

 ment, September- December 1961 (sexes combined) 



» Total numljer of recaptures used for growth computation (422) does not 

 agree with total number recaptured during experiment (442) because breakage 

 or other damage precluded carapace-length measurement in somi 

 mens. 



2 Data from 47 recaptures combined with sample data (table I) secured 

 during period of n I i 



* Measurements (nun this specimen excluded from growth computation. 



* One other specimen I v) returned 3 months after recapture was tiot in- 

 included in analysis. 



Although comparable growth data contributed 

 by the Sanibel experiment did nut meet the re- 

 quirement of constant sex ratio (table 5), their 

 greater temporal range gave a better indication 



324 



of the probable shape of the pink shrimp growth 

 curve. Subsequent plots of mean weights of 

 marked shrimp recaptured during successive 

 time increments within each experiment suggested 

 that von Bertalanffy's (1938) growth-in-weight 

 equation offered, as it has in a wide variety of 

 species, the most meaningful and at the same 

 time the most practical solution to the problem 

 of mathematically characterizing shrimp growth 

 (fig. 9). In addition to the exponent b, which is 

 obtained from the weight-length relationship, the 

 function itself, 



w. 



^WM-e-KC-'o))", 



contains three parameters that are presumed 

 effectively constant when describing growth over 

 the greater part of the shrimp's life span. W. 

 represents the asymptotic or maximum weight 

 attained by the average shrimp; K is a coefficient 

 proportional to the rate of catabolism; and t' 

 defines a hypothetical age at which the shrimp's 

 weight would have been zero had its growth pat- 

 tern always been the same as that suggested by 

 the experimental data. 5 If growth be assumed 

 isometric, then b takes the value 3; in the present 

 case, the estimated value, 3.14, was employed. 

 For more extensive discussions on the rationale 

 underlying the von Bertalanffy equation and the 

 advantages that render it particularly adaptable 



Table 5. — Mean lengths and weights of marked pink shrimp 

 recaptured during successive 4-week periods of the San,ibel 

 experiment, December 1960- June 1961 (sexes combined) 



1 Indicates number of specimens sampled to determine mean length and 

 weight of marked shrimp at start of experiment. 



2 Data from single recaptures not used in growth computation. One ad- 

 ditional specimen (<?) recaptured in l-'th month was also disregarded. 



s To remind the reader that the estimation of growth parameters from mark- 

 recapture experiments necessarily involves the translocation of size and time 



- the notation t' herein replaces the standard <». The latter represents 

 the true pi. pul. it ion parameter which may be most accurately estimated only 

 when a reasonably complete series of weight-at-age data for agiven species is 

 available For all practical purposes, it is assumed that the difference 

 between (,, and (J,, or bias, is negligible. 



Throughout tins paper, the symbols t and In designate, respectively, the 

 base of, and abbreviation for. the natural or Naperian logarithm. 



U.S. FISH AND WrLDLrFE SERVICE 



