have diminished predictably as the experimental 

 population declined. It is noteworthy that ad- 

 justment of each value in the recapture time- 

 series under discussion here was itself independent 

 of time, and hence did not superimpose additional 

 bias whose presence might further curtail the use- 

 fulness of mortality coefficients to be estimated 

 by regression techniques from data already serially 

 correlated. 



Since it was derived specifically to cover the 

 general case where fishing effort varies throughout 

 an experiment, the second method, which yielded 

 estimates of X as well as Z, did not necessitate 

 any preliminary adjustment of raw data. In 

 large degree, measurements of Z by both tech- 

 nicpues proved mutually confirmatory. 



Table 7. — Unadjusted and adjusted numbers of marked pink 

 shrimp recaptured during successive weeks of the Tortugas 

 experiment, September-December 1961 



TRANSITION 



1 0.80 confidence intervals. 



Subdivision of the Experiment 



* Preparatory to mortality estimation, plots of the 

 adjusted Tortugas recapture data revealed a 

 distinct but not unexpected discontinuity in the 

 pattern of exploitation during the experiment 

 (fig. 10). Prior to its fifth week, in which most 

 members reached a size acknowledged to be the 

 commercial minim um, the experimental popula- 

 tion experienced a measurable amount of pur- 

 posively selective fishing. Not until the beginning 

 of the experiment's sixth week can it be presumed 

 that recruitment to the "commercial" population 

 was effectively complete. Most interest attaches 

 to the experiment's second phase since estimates 

 of fishing mortality between the points of com- 

 plete recruitment to and virtual disappearance of 



328 



w 60- 



s I 



jf so 

 a. '■> 



1 §30- 



• < 



»- SELECTIVITY 



5 S 



a 



3 4 I 5 6 7 8 



Figure 10. — Mortality of pink shrimp. Curves are fitted 

 to numbers of marked shrimp recaptured during suc- 

 cessive weeks of the Tortugas experiment (September- 

 December 1961) and adjusted for nonuniform fishing 

 effort. [Number liberated (N„) = 2,090.] 



the marked population from the fishery (i.e., from 

 h to t i0 ), and natural mortality just prior to and 

 over the same period (i.e., from t t to t l0 ), are 

 included among the major objectives of this 

 study. 



The experiment may therefore be conveniently 

 subdivided into two phases arbitrarily separated 

 by a brief (1-week) interval of transition. They 

 are: (1) A period in population development when 

 the fishery exercised moderate selectivity — the 

 partially exploited phase, which was characterized 

 by varying degrees of purposive as well as gear 

 selectivity ; and (2) a period of nonselectivity — the 

 fully exploited phase, during which every popula- 

 tion member was vulnerable to all operating causes 

 of mortality. 



Total Mortality During Partially Exploited Phase 



Proceeding from theorem (1), which, upon trans- 

 formation to logarithmic form, becomes linear in 

 In iV,and t, Beverton and Holt (1957, pp. 185-191) 

 give in terms of the recaptures themselves a com- 

 parable expression intended for use with marked 

 populations subjected to a uniform fishing (re- 

 capture) effort. Thus, making appropriate 

 substitutions, 



dn 

 di 



=FN,=FN e- iF+x " 



and. ultimately, 



In n 2 =ln ni — (F+X)r 



(2) 



U.S. FISH AND WILDLIFE SERVICE 



