(7.9.2)
GROUP I
The following table presents the annual catch length composition, of a cohort of a resource with L_{∞} = 130 cm and K = 0.1 year^{1}.
Length 
Catch, C_{I }(million) 
6 
1823 
12 
14463 
18 
25227 
24 
8134 
30 
3889 
36 
2959 
42 
1871 
48 
653 
54 
322 
60 
228 
66 
181 
72 
96 
78 
16 
84 
0 
The natural mortality coefficient was estimated as being M = 0.3 year^{1}.
1. Using the Pope method, and adopting E = 0.5 as being the exploitation rate in the (78) length class of the catch, estimate the number of survivors at the beginning of each length class, the fishing mortality coefficient F and the exploitation rate E in each class.
2. Calculate the mean number of survivors of the cohort.
GROUP II
The following tables 1 and 2 present the basic information on a hypothetical stock during the years 1985 to 1994.
1. Apply the slicing technique to the Catch matrix and comment on the validity of applying cohort analyses by ages.
2. Estimate the matrices [F] and [N] by length classes and years.
3. Calculate the matrix [Fsep] and comment on the hypothesis that the exploitation pattern can be considered to be constant during those years.
Table 1. Growth parameters of the vonBertalanffy curve, L_{∞} and K Natural Mortality Coefficient, M and constants a and b of the weight/length relation
Growth 
Natural Mortality 
Weight/length relation 

L_{∞} (cm) 
42 
M (year^{1}) 
0.8 
a 
0.0023 
K (year^{1}) 
0.5 


b 
3 
Table 2. Catch matrix in thousands of individuals, by length classes and years in the period 198594
Age 
Length classes 
Years 

1985 
1986 
1987 
1988 
1989 
1990 
1991 
1992 
1993 
1994 

0 
20 
35 
41 
30 
17 
49 
69 
34 
61 
46 
29 
21 
338 
400 
292 
167 
472 
662 
327 
593 
442 
276 

22 
805 
952 
699 
400 
1127 
1575 
777 
1404 
1053 
657 

23 
1500 
1766 
1317 
757 
2108 
2923 
1436 
2574 
1962 
1220 

24 
1901 
2222 
1702 
985 
2688 
3678 
1795 
3175 
2485 
1535 

25 
2034 
2357 
1872 
1093 
2902 
3900 
1886 
3276 
2659 
1627 

26 
1898 
2175 
1806 
1067 
2739 
3600 
1722 
2925 
2482 
1502 

1 
27 
1951 
1817 
1228 
1416 
1445 
2932 
3376 
1695 
1785 
2376 
28 
1664 
1529 
1091 
1276 
1250 
2467 
2801 
1369 
1523 
1999 

29 
1382 
1251 
948 
1125 
1053 
2018 
2258 
1071 
1265 
1636 

30 
1127 
1003 
812 
980 
873 
1619 
1782 
818 
1031 
1312 

31 
900 
787 
684 
841 
710 
1269 
1372 
607 
823 
1029 

32 
694 
595 
560 
702 
558 
959 
1017 
432 
635 
778 

2 
33 
809 
565 
290 
389 
834 
511 
759 
832 
221 
518 
34 
584 
399 
226 
310 
618 
361 
522 
544 
160 
365 

35 
403 
267 
170 
240 
439 
242 
340 
335 
110 
245 

36 
262 
168 
122 
178 
294 
152 
207 
191 
72 
154 

3 
37 
165 
168 
66 
71 
175 
214 
93 
128 
75 
46 
38 
86 
84 
40 
45 
96 
107 
44 
55 
39 
23 
Consider L_{a} = 20 cm and t_{a} = 0
(Extracted from: Cadima, E. & Palma, C.,1997. Cohort Analysis from annual length catch compositions. Working document presented to the Working Group of the Demersal Stocks Assessment of the South Shelf, held in Copenhagen from 110 September, 1997.)