(7.7)
GROUP I
A swept area cruise allowed the scientists of the Marine Research Institute in Bergen, Norway, to estimate the abundance of the different age classes of the stock of cod fish, Gadus morhua, in January of 1995 (following table).
Age (years) 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
N_{95} (10^{9}) 
1984 
440 
160 
103 
82 
65 
54 
43 
33 
27 
26 
21 
17 
13 
10 
1. Represent on a graph, the logarithms of the numbers of survivors against the age.
2. Select the age interval from which the total mortality coefficient, Z, can be taken as constant.
3. Estimate the total mortality coefficient, Z, of the stock in January 1995.
GROUP II
The following table presents the mean catches by age, in number, of plaice, Pleuronectes platessa, per 100 trawl hours in two periods, 19291938 and 19501958.
Age (years) 
2 
3 
4 
5 
6 
7 
8 
9 
10 

C/f 
192938 
125 
1355 
2352 
1761 
786 
339 
159 
70 
28 
C/f 
195058 
98 
959 
1919 
1670 
951 
548 
316 
180 
105 
1. Estimate the total mortality coefficient, Z, of the stock in each of the periods.
2. Consider that the mean fishing effort on the North Sea plaice during the two periods was 5 million hours of trawl in 19291938 and 3.1 million hours of trawl in 19501958. Estimate for each period:
a) the natural mortality coefficient, M;
b) the catchability coefficient, q;
c) and the fishing mortality coefficient, F.
GROUP III
The following table presents the annual composition of the catches by age from 1988 to 1994, in millions of individuals, for a certain resource:
CATCHES (million individuals)
Age 
1988 
1989 
1990 
1991 
1992 
1993 
1994 
0 
599 
239 
424 
664 
685 
478 
330 
1 
678 
860 
431 
1004 
418 
607 
288 
2 
1097 
390 
1071 
532 
335 
464 
323 
3 
275 
298 
159 
269 
203 
211 
243 
4 
40 
54 
75 
32 
69 
86 
80 
5 
6 
9 
13 
18 
8 
25 
31 
6 
1 
8 
3 
5 
5 
3 
8 
7 
6 
0 
1 
0 
1 
1 
1 
1. Calculate the mean annual composition during 19881994.
2. Estimate Z, based on that mean composition.
3. Estimate Z, based on the mean age of the mean composition of the catch.
4. Estimate Z for each year of the given period.
5. Compare the annual Zs with the values of Z obtained in questions 2 and 3.
GROUP IV
The following table shows the length composition, in equilibrium, of a certain resource, with L_{∞} = 100 cm and K = 0.2 year^{1}.
Length class (cm) 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
85 
90 
95 
Catch (C_{i}) in million 
7 
10 
20 
51 
46 
44 
41 
36 
33 
28 
23 
17 
8 
1. Calculate the relative ages corresponding to the lower limit of each length class.
2. Determine the age interval corresponding to each length class.
3. From which class can one consider Z constant?
4. Determine Z using:
a) The catches in each class.
b) The cumulative catches.
c) The mean length in the catch.
5. Compare the values of Z obtained by the different methods of question 4.
GROUP V
The length compositions of the catches for three different periods of time are known for a certain fishing resource.
Period 
Length classes (cm) 
45 
50 
55 
60 
65 
70 
75 
80 
85 
90 
≥95 
196069 
Catch (C_{i}) in million 
256 
237 
211 
187 
161 
138 
113 
87 
62 
36 
12 
197079 

268 
226 
180 
141 
105 
76 
50 
30 
15 
6 
1 
198089 

212 
161 
116 
79 
52 
31 
17 
8 
3 
1 
0 
Consider the 45 cm length class as the first class completely recruited.
Adopt K = 0.3 year^{1} and L_{∞} = 100 cm as the von Bertalanffy growth parameters for this resource.
1. Estimate the values of the total mortality coefficient, Z, for each period and comment on the results.