8.11 STOCK - LONG TERM PROJECTION

(4.4)

The mortality parameters of the Iberic Stock (Div. VIIIc e IXa) of Sardine, Sardina pilchardus, were estimated by the Assessment Working Group of ICES (ICES, 1997b) as:

Natural Mortality Coefficient = 0.33 year^-1
Fishing Mortality Level in 1996 = 0.56 year^-1

Assume that the exploitable phase occurs from the beginning of age zero until the end of age six.

Relative pattern of exploitation, s_i, during 1996

s_o	s₁	s₂	s₃	s₄	s₅	s₆
0.21	0.41	0.79	1.18	1.34	1.43	1.68

The parameters of the individual growth and the weight length relation of this stock were estimated (Pestana, 1989) as:

Von Bertalanffy growth parameters	Weight length relation W = a.L^bwith L in cm and W in g
L_∞ = 22.3 cm K = 0.40 year^-1t₀ = -1.6 year	a = 0.0044 b = 3.185

GROUP I

1. Calculate the evolution in number and the biomass of a cohort during its life at the beginning of each age, supposing that growth, natural and fishing mortality parameters are the given values.

2. The recruitment at age 0 in 1996 was estimated as being 4300 million individuals. Calculate the cumulative number, the cumulative biomass, the catch in number and in weight, during all the life of the cohort.

GROUP II

It was estimated that, at the beginning of 1996, the considered stock had the following age structure, in number, representing i the age and N_i the number of survivors at the beginning of age i, expressed in millions of individuals:

I	0	1	2	3	4	5	6
N_I	4300	279	591	233	561	384	180

To make a long-term projection of the stock, all the mortality and growth parameters will be considered stable during the following years. Consider, also, that the recruitment in those future years will be equal to the recruitment of 1996.

1. Based on these assumptions, project the numbers of survivors at the beginning of each year and age, until 2006.

2. Compare the structures of the stock in the years 2003 and 2006.

3. Compare the evolution of the 1996 cohort with the structure of the stock at the beginning of 2003.