FISHERY BULLETIN: VOL. 85, NO. 3 



Estimates of Initial Annual Rate 



of Instantaneous Fishing 



Mortality 



Although a single method of estimation for the 

 starting instantaneous annual fishing mortality 

 rate (F ) for backward calculations in VPA is de- 

 sirable, a few year classes required alternate ap- 

 proaches. Year class-specific catch curves were 

 examined visually. All years of age from the old- 

 est to youngest that lie within a reasonably 

 straight portion of a semilogarithmic catch plot 

 were logg transformed and regressed against age. 

 The slope was taken as an estimate of -Z (total 

 instantaneous mortality) and by subtracting M a 

 "general trend" F was obtained. Starting F's were 

 obtained by this method for all year classes except 

 1947, 1948, 1949, 1954, 1966, 1971, 1974, and 

 1978. Since only 2 years of landings after full 

 recruitment were available for the 1978 year 

 class, an estimate of Z was made: logg (catch in 

 numbers of age 3/catch in numbers of age 2). The 

 estimate for 1949 was obtained similarly using 

 ages 7 and 8. The 1954, 1966, 1971, and 1974 year 

 classes experienced an apparently higher fishing 

 rate during their last year in the fishery com- 

 pared with that experienced 1 year earlier. Thus, 

 starting F's were obtained from average VPA 

 results from several other age classes caught in 

 the same year. Starting F for age 8 of the 1954 

 year class was estimated as the mean F for ages 

 5-7 (year classes 1955-57) caught in the same 

 1962 season. Initial F for age 5 of the 1966 year 

 class was the annual VPA estimate of age 4 

 from the 1967 year class. Similarly, starting 

 values of F for the 1971 and 1974 year classes 

 were the means of the same fishing season age-4 

 and age-5 values for the 1972 and 1973, and 

 1975 and 1976 year classes. Starting F's on 

 age 8 for the 1947 (one age class represented) 

 and 1948 (two age classes represented) year 

 classes were means of similar fishing season 

 VPA F's for ages 5-7. The initial annual F values 

 and their sources for VPA are summarized in 

 Table 5. 



Conducting the VPA computations for the an- 

 nual series was straight forward, as the trial F's 

 were annual. The quarterly series and mixed 

 time interval series required trial and error runs. 

 Trial starting F's for these VPA's were adjusted 

 downward until the sum of the F's within the last 

 year (oldest fish of the year classes) were ±0.5% 

 of the initial annual F estimate for each year class 

 (Table 5). 



Except for the sensitivity computations, the 

 general results of the VPA's are presented and 

 discussed where they are subsequently used. 

 Using a relatively wide range of starting values 

 for the 1955 year class, estimates of age-specific F 

 and numbers at age present at the beginning of a 

 season (Fig. 7) converged quite rapidly to similar 

 values for the (younger) ages which dominate the 

 fishery in both numbers and biomass (Figs. 8, 9). 

 This is expected because of the relatively high 

 rates of fishing mortality exerted on the stock 

 (Ulltang 1977). The lower the exploitation rate, 

 the slower the values will converge. The 1955 

 year class had the lowest starting F of any year 

 class (Table 5) (other than 1947 which had only 

 one age class represented) and relatively low to 

 moderate rates of exploitation on all age classes. 

 Thus the estimates for the other year classes 

 should converge more rapidly than the one 

 shown. Since it is highly unlikely that the initial 

 estimates of F differ from true values to the ex- 

 treme degrees tested, the VPA estimates used 



Table 5. — Estimates of initial Ffor annual virtual population analy- 

 ses (VPA's) of Atlantic menfiaden, source of estimate, and ages 

 involved, by year class. 



'See text 



580 



