where n u n 2 , . . . n t refer to the number of marked 

 individuals recaptured during the first, second, 

 . . . r th time interval t, respectively; T=t i+i — t t 

 ( = 1 week) ; F and X are the instantaneous co- 

 efficients of reduction of marks due, respectively, 

 to fishing and to all causes other than fishing; and 

 (F+X)=Z. It follows from expression (2) that 

 a linear regression of the natural logarithms of 

 successive numbers of recaptures on time gives 

 estimates of In «; and Z. 



Fitting a regression to the logarithms of Tor- 

 tugas recaptures grouped by weeks and adjusted 

 for nonuniform fishing effort (viz., In n\ through 

 In n' 3 , where the prime indicates an adjusted 

 value) yielded an estimate of 0.76 for Z, the only 

 parameter of interest during the experiment's 

 initial phase. Figure 10 shows that the regression 

 enjoyed a good fit. 



Obviously, a measurable amount of (selective) 

 fishing effort contributed to the total mortality 

 value so obtained, though by far the greater share 

 of this value is presumed attributable to natural 

 causes. Only a very minor part is believed due to 

 the "other-loss" factors defined earlier. There is 

 moreover, no statistical evidence of any differential 

 vulnerability of sexes during the partially exploited 

 phase. Despite the slower growth noted for males, 

 the sex ratio of recaptures never departed signifi- 

 cantly from that observed at the start of the experi- 

 ment (table 7). In summary, a small amount of 

 fishing activity during the experiment's first phase 

 was sufficient to demonstrate an apparently high 

 corresponding rate of natural mortality, which, as 

 will be shown later, continued well into the second 

 or fully exploited phase. Here it became associ- 

 ated with the relatively high rate of fishing 

 mortality established at the moment recruitment- 

 was completed. 



Mortality During Fully Exploited Phase 



After plotting the logarithms of the adjusted 

 numbers of shrimp recaptured during the first 5 

 weeks of the Tortugas experiment's fully exploited 

 phase, and observing that they, too, all fell nearly 

 in a straight line (fig. 10), computation of their 

 linear regression on time [equation (2)] gave a first 

 estimate of Z=1.39 for the instantaneous co- 

 efficient of mark reduction due to all causes. 



Attempts to subdivide the resulting Z into its 

 fishing mortality and "other-loss" components 



proved impractical, however, when recapture data 

 adjusted for varying fishing effort were substi- 

 tuted in techniques implicitly designed for un- 

 adjusted data generated by a uniform effort. 

 Inspection of the basic equations involved (Bever- 

 ton and Holt, 1957, p. 190, equations 14.15 and 

 14.16) reveals that the soundness of F and X (or 

 M) estimated therewith may be influenced not only 

 by the size of N n (or any specified equivalent), but 

 also by variation in the relative magnitude of the 

 antilog of In ni (or its counterpart), where the 

 latter value is derived by means analogous to 

 equation (2). It will be recalled that initial 

 treatment of the recapture data entailed their 

 being grouped on a weekly basis, and then adjusted 

 within each time unit for nonuniformity of fishing 

 effort between units by a factor equal to the re- 

 ciprocal of the quantity (/ f X10~ 3 ), with/, repre- 

 senting the overall effort in hours expended on the 

 fishing grounds during the i th weekly interval 

 (table 7). Subsequent difficulty stems from the 

 arbitrary nature of the attenuation index, 10 -3 , 

 which must be selected so as to yield adjusted 

 recapture values having an average order of mag- 

 nitude moderately close to that of the unadjusted 

 values. 



Whereas analysis of recapture data so adjusted 

 provides [through expression (2)] a good estimate 

 of the total-loss coefficient Z=(F-\-X), such sub- 

 jective treatment imparts bias of unknown degree 

 to the values for F&nd A' when these are delineated 

 by the equations mentioned above. This bias will 

 be proportional to the value of 7? t as estimated by 

 expression (2), and, accordingly, to the relative 

 size of the adjustment index employed. The real 

 problem, however, lies in not being able to specify 

 satisfactorily the relationship between N and 

 the estimated initial value of the recapture time- 

 series based upon adjusted data, as contrasted to 

 that between A^ and the corresponding value of 

 the time-series involving unadjusted data. 



Drawing support from the fundamental theorem 

 stating that over a given time interval r, fishing 

 mortality is proportional to fishing effort (or 

 intensity), i.e., F r = cj T , Beverton and Holt (1957, 

 p. 192) derive solely in terms of recapture and 

 related effort values a useful equation which 

 furnishes — independent of A^ — an estimate of 

 the other-loss coefficient X, regarded herein for 

 the reasons outlined earlier as a close appro xima- 



DYNAMICS OF A PENAEID SHRIMP POPULATION 

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