120 



Fishery Bulletin 89(1), 1991 



Total consumption of mackerel by each 

 predator was calculated as 



B, • %BW • %Rmj • Tr (1) 



where 



Ci = 



Bi 



%BW 

 %Rm 



Tr = 



i = 



consumption of mackerel by 

 predator i, 



biomass of predator i, 

 daily ration estimate, 

 percent of total ration com- 

 posed of mackerel for pred- 

 ator i, 



residence time of predator 

 and prey (days), and 

 1,3. 



The estimated consumption in weight 

 was then converted to numbers eaten on 

 the basis of information on the abundance 

 of age-1 and -2 mackerel in the sea and 

 the mean weights of each age group. Con- 

 sumption estimates were combined with 

 landings-at-age for 1973-80 and a new 

 VPA was completed for these years 

 (Overholtz et al. 1988). A residual natural 

 mortality rate (Ml) of 0.20 was used in 

 this analysis to account for other sources 

 of mortality at ages 1 and 2 and for all 

 the other age groups (3-14) in the anal- 

 ysis. A similar assumption has been used 

 by ICES in the multispecies VPA model 

 of the North Sea (ICES 1987). The mortality rates from 

 the VPA were a proxy for F and M2 and were appor- 

 tioned by using the ratios of consumption and landings 

 to total deaths (numbers). This gave an estimate of F 

 and M2 mortalities for 1973-80 (Table 3). Consump- 

 tion (numbers) of age-1 mackerel exceeded landings of 

 that age group in all years from 1973 to 1980 and was 

 generally smaller than landings at age 2 (Table 2). Sizes 

 of incoming year-classes increased up to a factor of two 

 in the revised VPA over the 1973-80 period (Overholtz 

 et al. 1988). When mortality rates from the VPA were 

 apportioned by consumption estimates and landings, 

 natural mortality rates (M = Ml + M2) were generally 

 higher in the 1973-76 period, when mackerel were 

 abundant, than in 1977-80 (Table 3). 



These values and the new VPA stock size-at-age 

 estimates were used in regressions to study the rela- 

 tionship between M2 and year-class strength. The 

 results of this analysis suggest a positive relationship 

 between M2 for ages 1 and 2 and year-class size (R = 

 0.37, 0.78, P = 0.363, 0.0234), respectively (Fig. 3A, B). 

 An examination of the scatter plots from these two 

 regressions revealed that the M2 value from 1976 was 



high relative to the number of age-1 and -2 fish in the 

 stock. There were fewer age-1 fish in the stock in 1976 

 (Fig. 2C); furthermore, food habits data indicated that 

 mackerel was not present in the diet of the three pred- 

 ators in 1976. The 1976 data point was dropped and 

 a new regression was fitted for age 1 (R = 0.60, 

 P = 0.157, Fig. 3A). 



We were cognizant of the fact that results of this 

 analysis may have been influenced by the assumption 

 of proportional feeding. However, the suggestion that 

 natural mortality rates may change with year-class size 

 is an interesting research question. A positive relation- 

 ship between year-class size and predation mortality 

 rate has obvious implications for assessment and man- 

 agement, and thus the potential impacts of density- 

 dependent predation mortality were a major focus of 

 our modeling studies. 



Model structure 



A simulation model addressing changes in growth, per- 

 cent maturity-at-age, and predation mortality rates 



