# 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, CI (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 wi = a. (Li)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 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 La = 20 cm and ta = 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.)