(5.2.3) and (5.2.4)
During the meeting of the Assessment Working Group (ICES, 1998b) on the Iberic stock (Div. VIIIc and IXa) of hake, Merluccius merluccius, the following population parameters were estimated:
Natural mortality coefficient: 
M = 0.2 year^{1}; 


Fishing mortality in 1996: 
F_{96} = 0.24 year^{1} 
Mean weight in the catch (g):
Age (year) 
0 
1 
2 
3 
4 
5 
6 
7 
8+ 
4 
37 
106 
205 
358 
517 
706 
935 
1508 
Maturity ogive (percent):
Age (year) 
0 
1 
2 
3 
4 
5 
6 
7 
8+ 
% mature_{i} 
0 
0 
1 
6 
20 
49 
76 
91 
100 
For the longterm projections, the Working Group adopted the mean exploitation pattern for the period 19941996, as shown in the next table:
Age (year) 
0 
1 
2 
3 
4 
5 
6 
7 
8+ 
s_{i} 
0.001 
0.11 
0.398 
1.3 
1.261 
1.019 
1.473 
1.874 
1.874 
1. Calculate the longterm annual mean biomass, the spawning biomass, the annual catch in weight and the mean weight in the catch.
2. Draw the curve of the annual catch in weight and the mean biomass against F, for values of F_{factor} between 0 and 2.5 year^{1}, with intervals of 0.1 year^{1}. Calculate the TRPs F_{max} and F_{0.1}.
3. Calculate the biological reference point F_{med}, knowing the recruitments (million individuals at age 0) and the spawning biomasses (thousand tons) between 1982 and 1996, estimated by the Working Group, presented in the following table:
Year 
N (age 0) 
Spawning biomass 
1982 
125 
59.8 
1983 
107 
61.4 
1984 
136 
58.8 
1985 
97 
44.1 
1986 
104 
26.4 
1987 
97 
24.2 
1988 
84 
22.8 
1989 
56 
18.9 
1990 
59 
19.4 
1991 
69 
20.5 
1992 
86 
21.5 
1993 
70 
21.0 
1994 
63 
16.5 
1995 
32 
15.2 
1996 
83 
18.0 
4. Calculate the longterm mean biomass, the spawning biomass, the catch in weight and the mean weight in the catch for F_{med}. Compare with the values obtained in question 1 and make your comments.
5. Adopting the Ricker stockrecruitment relation, estimated by the Working Group (a = 4.43 R/kg and K = 78.13 thousand tons), calculate F_{MSY}, B_{MSY }and Y_{ MSY}. and compare the different Ftarget estimated.