(5.2.1)
Consider the stock of cod fish, Gadus morhua, in the Irish sea (Div. VIIa). The following mortality and biological parameters were estimated by the Working Group of ICES (ICES, 1998c):
Natural Mortality Coefficient: 
M = 0.20 year^{1} 


Fishing Level in 1996: 
F_{96} = 0.58 year^{1} 
Mean weight (kg) in the catch and in the stock:
Age 
0 
1 
2 
3 
4 
5 
6 
7 
0.001 
0.883 
1.778 
3.597 
5.695 
7.904 
8.502 
9.200 
GROUP I
Assume that the stock was constituted by the age groups 0 to 7 years and that it was exploited with the following exploitation pattern:
Age 
0 
1 
2 
3 
4 
5 
6 
7 
s_{i} 
0.80 
0.90 
0.96 
1.00 
1.00 
1.00 
1.00 
1.00 
1. Calculate, for 1000 recruits, the longterm annual catch in weight and the annual mean biomass, corresponding to the fishing level of 1996.
2. Adopting the factor F_{factor} between 0 and 2.5 year^{1} with intervals of 0.1 year^{1} draw the curve of the annual catch in weight against F_{factor}. Represent, in the same graph, the curve of the mean biomass against F_{factor}.
3. Calculate the biological reference point F_{max}.
GROUP II
1. Answer the previous questions, but considering the following exploitation pattern.
Relative pattern of exploitation adopted by the Working Group:
Age 
0 
1 
2 
3 
4 
5 
6 
7 
s_{i} 
0.00 
0.20 
0.96 
1.30 
1.12 
0.67 
0.58 
0.58 
a) Compare the value of F_{max} of this exercise with the one obtained in the exercise in Group I.
b) Calculate the biological reference point F_{max} knowing that the Working Group considers the group of age 7 as a group of cumulative ages (7+). The mean weights in the catch and in the stock presented at the beginning of the text are maintained, except for the last group of ages which will now be the age group 7+ with the mean weight equal to 10.873 kg. The exploitation pattern is also maintained with the value 0.58 for the group 7+.
c) Compare the two calculated values of F_{max}, considering the last age group as 7 or as 7+.