tion of M. This equation is given by 



T, L \n r+l frJ 



i_m \ (cf r+1 +X)(l-e-Wr+x)r,) /J 



where r signifies the width (in weekly units) of 

 experimental time intervals r or r+1, 71 identifies 

 the number of recaptures in the same intervals, 

 and c denotes the average coefficient of propor- 

 tionality relating fishing mortality to fishing 

 effort, j T . 



Equation (3), accounting inherently for varying 

 fishing effort, is linear in j, and a logarithmic ex- 

 pression (left side) corresponding to the ratios in 

 successive time intervals of the numerical abun- 

 dance of marked individuals composing the experi- 

 mental population. Accordingly, simple regres- 

 sion procedures involving at least two iterations 

 lead to fairly good estimates of c and X, the slope 

 and y-intercept, respectively. The latter value 

 may be viewed as a measure of the average total- 

 loss rate that would have prevailed during the 

 experiment in the absence of any fishing activity. 



Use of expression (3) assumes that bias intro- 

 duced by the practical need to treat fishing effort 

 as a discontinuous function of time is negligible. 

 Its application to appropriate recapture data and 

 corresponding values of effective fishing effort 

 gave, after three iterations, estimates of c=0.171, 

 X=0.55, and average F=0.96 for the fully 

 exploited phase of the Tortugas experiment (fig. 

 11). Interestingly, the resulting value for Z= 

 (F-fA') = 1.51 compared quite favorably with the 

 preliminary value calculated earlier, viz, Z= 1.39, 

 differing on the order of but 9 percent. Relevant 

 statistics are presented in table 8. Note here the 

 incorporation of effort data slightly modified from 

 those used earlier to obtain the preliminary esti- 

 mate of Z. The decision to subject to analysis 

 only those measurements of effort expended in- 

 side 20 fathoms was prompted by the observation 

 that none of the 252 marked shrimp retrieved 

 during the period of interest (table 8) was re- 

 captured beyond this range. Such adjustment 

 seemed necessary to minimized the likelihood of 

 violating, in terms of the experimental population 

 and that portion of the fishery's overall activity 



2.0- 



z 

 o 



I- 

 <t 



o 



=cj r +x (3) a 



9 

 en 



LL 



UJ 



FULLY EXPLOITED 

 PHASE 



Slope = c = O.I7l 

 Intercept = X = 0.55 



5 



EFFECTIVE FISHING EFFORT 



~T~~ 

 10 



(f) 



Figure 11. — Estimating the other-loss coefficient A' using 

 equation (3) of text. [Refer to table 8 for description 

 of data and associated statistics.] 



directly associated with it both spatially and 

 temporally, the functional relationship between 

 fishing mortality and fishing effort (or intensity) 

 stated above. 



Transformation of estimated F and X to cor- 

 responding weekly rates of reduction in marks 

 resulted in values of 0.62 for that due to fishing, 

 and 0.42 for that due to all other causes (see 

 Ricker, 1958, p. 25, for discussion of relationships). 

 These results, while indicative of greater mortality 

 pressure on parent shrimp populations than had 



Table S. — Statistics employed to estimate with equation (8) 

 of text the other-loss coefficient X for the fully exploited 

 phase of the Tortugas experiment 



[Resulting F values are given in the last column; c = 0.171] 



1 Treated here as synonymous with fishing intensity which, in broader peo- 

 Eraphieal application than is here neccssiry, is explicitly defined as fishing 

 effort per imii area; data represent only ih it innumi of eiTort expended on 

 the Tort uc. is fishing grounds inside t he l'i) f.tthom contour (re table 2). 



330 



U.S. FISH AND WILDLITE SERVICE 



