Overholtz et al.: Assessment advice for Northwest Atlantic mackerel stock 



121 



04 • 



age 1 



~~ I I I l~~ 



age 2 



1000 2000 3000 



YEAR CLASS SIZE (millions) 



Figure 3 



Relationship between predation mortality (M2) and year-class 

 size for age-1 and -2 Atlantic mackerel from calculations of 

 mackerel consumption by Atlantic cod, silver hake, and spiny 

 dogfish for 1973-80. 



(M2) was constructed to evaluate the potential impact 

 of these population regulatory mechanisms in the con- 

 text of single-species assessment advice. The model 

 was a basic fishery simulator much in the same style 

 as many other common fishery models (Walters 1969, 

 Sissenwine 1977). An age-structured Baranov catch 

 equation was used to compute annual fishery yields, 

 and the negative exponential relationship was used to 

 update stock size for 14 age groups. 



A stochastic recruitment function was used to model 

 recruitment for the mackerel stock. A three-parameter 

 model (Shephard 1982; Table 4) with a lognormal white- 

 noise multiplier was used to generate an annual esti- 

 mate of recruitment as: 



R = (a*SSB)/[l + (SSB/K) b ] * lnm 



where R = recruitment at age 1, 

 SSB = spawning-stock biomass, 



(2) 



a,b,K = parameters, 

 lnm = lognormal multiplier with u and s from 

 the SR data. 



Recruitment estimates were scaled upward by a fac- 

 tor of 1.5 to account for the fact that the original VPA 

 age-1 stock size estimates do not reflect higher natural 

 mortality rates due to predation (Overholtz et al 1988). 



Growth-at-age was based on a two-stage model that 

 related life-history characteristics and year-class size 

 to growth increment for a year-class (Overholtz 1989). 

 Since age-1 fish maintain a separate distribution from 

 the adult stock (Sette 1950) a relationship between 

 age-1 growth and corresponding age-1 year-class size 

 was used to predict weight at age 1. The relationship 

 was parameterized (Table 4) with available empirical 

 data, such that size at age 1 varied from 48 g for slow- 

 growing fish to 122 g for fast-growing fish (Overholtz 

 1989). Weight of age-1 mackerel was calculated as 



Wtj = a - bN, (3) 



where Wt = average weight (g) at age, 



Nj = year-class size at age 1 (numbers), 

 a,b = parameters. 



Age 2-5 growth was determined by relationships 

 between adult stock size (numbers) and growth-at-age 

 (Table 4) calculated as 



Wt, = Wtj_! + Gi 



(4) 



where Wt; = average weight at age i, i = 2,5, 



G; = annual age-specific growth increment 

 (g), 



and 



