FISHERY BULLETIN: VOL. 71, NO. 3 



taneous total mortality rate (Z = 1.47) and ex- 

 ploitation rate ()U = 0.50), the instantaneous 

 fishing mortality rate (F) is calculated to be 

 0.95 and the natural mortality rate (M), 0.52. 

 Each year 50% of the fish in the fishery are being 

 caught and 24% are dying from natural causes. 

 This estimate of rate of fishing is in general 

 agreement with the others based on an analysis 

 of the catch and effort data in earlier years 

 (Schaaf and Huntsman, 1972) at a higher level 

 of fishing effort. We are continuing to analyze 

 and to add additional years of data to reduce 

 the effects of fluctuating availability upon the 

 estimates. 



AVAILABILITY 



Tagging studies suggest that in Chesapeake 

 Bay there are significant fluctuations in avail- 

 ability of Atlantic menhaden within and be- 

 tween years. Since most of the summer catch of 

 Atlantic menhaden is landed in Chesapeake 

 Bay (60% to 75% , 1967 through 1970) and since 

 our movement data suggest that in the summer 

 the stocks in different areas are relatively 

 stable, we made a special study of the fluctua- 

 tions in availability there. Fluctuations in 

 availability may be caused by factors making 

 the fish more or less accessible, such as weather 

 and horizontal or vertical distribution of the 

 fish or by differences in vulnerability brought 

 about by changes in fish behavior, gear selec- 

 tivity, or numbers of fish (Gushing, 1968). 

 Murphy (1966) developed a population model 

 for the Pacific sardine, incorporating the idea 

 of variation in availability. In his model: 



!:[iSl = e -M- {rvf)i = S: 



where 



A^, is the number of fish present in the popu- 

 lation in years; 



e is the base of the natural logrithms; 

 M is the instantaneous natural mortality rate; 

 /is fishing effort; 

 r is an index of availability; 

 V is a residual constant; and 

 Si is the annual survival rate of the popula- 

 tion. 



As Murphy indicated, errors in measuring / 

 also contribute to r but in the menhaden fishery 

 in Cheasapeake Bay we use a vessel week as 

 the unit of effort (Nicholson 1971b), and there 

 is little error in this measurement. 



The factor v includes changes in vessel effi- 

 ciency or fishing power which are separable 

 from effects of availability. Schaaf and Hunts- 

 man (1972) concentrate on changes in the catch- 

 ability coefficient {rv) resulting from changes 

 in vessel efficiency and changes in distribution 

 of effort. Over a number of years and major 

 fishing innovations, efficiency of the vessels 

 has increased markedly. However, for the 

 limited number of years in our analysis (1967- 

 70) and in consideration of only the Chesapeake 

 Bay area, we believe it is reasonable to assume 

 that unit efficiency and consequently v, may 

 be considered constant. The quantity rv is a 

 variable catchability coefficient and, since v is 

 assumed constant, relative estimates of r can be 

 obtained from the percentage of tags recaptured 

 per unit of fishing effort (Gulland, 1963). 



Fluctuations in availability, or percent tag 

 recaptures per unit of fishing effort, in Chesa- 

 peake Bay were observed in 1967 through 1970. 

 Estimates in 1970 were even more striking than 

 those obtained in the earlier years. The data 

 used for this analysis are based upon tags re- 

 leased during the first 2 wk of the purse seine 

 fishery in Chesapeake Bay by our best taggers. 

 The number of tags released varied by year, i.e., 

 1967, 4,290 tags; 1968, 10,387 tags; 1969, 

 2,147 tags; and 1970, 21,189 tags. Table 16 

 shows the actual and relative values, compared 

 with the base year 1967, of catch, effort, catch 

 per unit effort (CPUE), percent recapture, 

 availability index, and population size. The 

 percentage of tagged fish recaptured, shown in 

 Table 16, is not comparable to the exploitation 

 given for Chesapeake Bay in Table 15 because 

 no adjustment was made in Table 16 for tagging 

 mortality and tag shedding which we assume 

 to be constant each year, nor were recoveries 

 considered at plants outside of Chesapeake Bay 

 during the summer or fall. Consequently, the 

 data shown in Table 16 for population size are 

 relative estimates and cannot be considered 

 true estimates of the number of fish. Table 16 

 shows that while the CPUE increased almost 



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