8.27 LENGTH COHORT ANALYSIS (LCA)

(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 classes (cm)	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 von-Bertalanffy curve, L_∞ and K Natural Mortality Coefficient, M and constants a and b of the weight/length relation

Growth		Natural Mortality		Weight/length relation w_i = a. (L_i)^b
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 1985-94

Age (sliced)	Length classes (cm)	Years
Age (sliced)	Length classes (cm)	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
3	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 1-10 September, 1997.)