# 8.8 COHORT DURING ALL LIFE - BIOMASS AND CATCH IN WEIGHT

(3.6)

GROUP I

The recruitment to the exploitable phase of horse-mackerel, Trachurus trachurus, distributed in the Ibero-Atlantic waters (Div. VIIIc and IXa) occurs at age 1. In order to make the calculations, let us consider the exploitable phase between the ages 1 and 10 years and the recruitment of a cohort equal to 1 000 individuals.

The parameters of the von Bertalanffy equation were estimated by the Working Group of ICES (ICES, 1998a), using the mean lengths, at age of the catch, as being:

L = 34.46 cm
K = 0.225 year-1
to = -1.66 year

The weight-length relation was also estimated, using the mean weights by age adopted by the WG for the long-term projections (ICES, 1998a), as being:

W(g) = 0.011 L(cm) 2.90

The mortality of this stock is characterized as:

• A constant natural mortality coefficient during all the exploitable phase: M = 0.15 year-1.
• Fishing mortality coefficients in 1996 (ICES, 1998a) are different with age as:
 Age (year) 1 2 3 4 5 6 7 8 9 10 Fi (year-1) 0.24 0.26 0.1 0.08 0.06 0.09 0.12 0.14 0.18 0.24

1. Organize the calculations in a spreadsheet, in order to calculate, for each age of the life of the cohort (from age 1 to 10):

a) The number at the beginning of the age
b) The individual weight at the beginning of the age
c) The biomass at the beginning of the age
d) The number of deaths during the age
e) The mean number of survivors during the age
f) The mean individual weight during the age
g) The mean biomass during the age
h) The Catch in number during the age
i) The Catch in weight during the age

2. Determine:

a) The cumulative number of survivors during all the exploitable phase
b) The cumulative biomass of the cohort during all the exploitable life
c) The total catch, in numbers, from the cohort during all the exploitable life;
d) The total catch, in weight, from the cohort during all the exploitable life;
e) The mean weight of the individuals caught, during all the exploitable life;
f) The mean weight of the individuals of the cohort, during all the exploitable life.

GROUP II

Present the histograms of:

1. Mean numbers of survivors of the cohort in each age, during all the exploitable life.

2. Mean biomasses of the cohort at each age, during all the exploitable life.

3. Catches in number by age of the cohort, during all the exploitable life.

4. Catches in weight by age of the cohort, during all the exploitable life.

GROUP III

Suppose now, that one intends to analyse the case in which all the fishing mortality coefficients were 30 percent bigger than those indicated in the table of Group I.

1. Calculate the characteristics of the Group I-2 that could be obtained from the same cohort during all its life, in this alternative situation.

2. Compare the values of the characteristics obtained under these conditions with those obtained in Group I-2, calculating the percentage of variation of those characteristics in relation to the corresponding values of the previous situation.