# 8.9 COHORT DURING ITS LIFE - SIMPLIFICATION OF BEVERTON AND HOLT MODEL

(3.7)

GROUP I

The recruitment to the exploitable phase of horse-mackerel, Trachurus trachurus, in Ibero-Atlantic waters (Div. VIIIc and IXa) occurs at age 1.

The recruitment at the exploitable phase was simplified by adopting the age tc = 2 year.

The parameters of the von Bertalanffy equation estimated for this stock are the following:

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

The weight-length relation: 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 coefficient, F = 0.14 year-1, constant during all the exploited phase.

1. Calculate, using the simplification of Beverton and Holt:

a) The recruitment Rc to the exploited phase.
b) The number of deaths during all the exploited life.
c) The cumulative number of survivors during all the exploited life.
d) The cumulative biomass during all the exploited life.
e) The catch in number during all the exploited life.
f) The catch in weight during all the exploited life.
g) The mean weight of the individuals of the cohort during all the exploited life.
h) The mean weight of the individuals caught during all the exploited life.

GROUP II

The data presented in Section 8.8 - Group I show a great variety in the values of F. However, in Section 8.9, the simplification of an F constant was adopted, F = 0.14 year-1. The purpose, now, is to compare the results from Section 8.8 with those obtained in this exercise, using the simplification of Beverton and Holt.

1.

a) Determinate the cumulative number, the cumulative biomass, the total catch in number, the total catch in weight and the mean weight in the catch.

b) Compare the results with those obtained in Section 8.8 (Group I-2).

2.

a) Using a 30 percent bigger value of F calculate the cumulative number, the cumulative biomass, the total catch in number, the total catch in weight and the mean weight in the catch and compare with the corresponding values obtained in the Group I-1.a).

b) Compare the percentages of variation of the characteristics obtained in 2.a) with those obtained in Section 8.8 (Group III).