(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 |
|
N95 (109) |
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, 1929-1938 and 1950-1958.
|
Age (years) |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
|
C/f |
1929-38 |
125 |
1355 |
2352 |
1761 |
786 |
339 |
159 |
70 |
28 |
|
C/f |
1950-58 |
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 1929-1938 and 3.1 million hours of trawl in 1950-1958. 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 1988-1994.
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 (Ci) 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 |
|
1960-69 |
Catch (Ci) in million |
256 |
237 |
211 |
187 |
161 |
138 |
113 |
87 |
62 |
36 |
12 |
|
1970-79 |
|
268 |
226 |
180 |
141 |
105 |
76 |
50 |
30 |
15 |
6 |
1 |
|
1980-89 |
|
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.
